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Mathematics identity and sense of belonging in mathematics of successful African-American students in community college developmental mathematics courses

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Mathematics identity and sense of belonging in mathematics of successful African-American students in community college developmental mathematics courses

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Content Running Head: Mathematics Identity in Developmental Mathematics

Mathematics Identity and Sense of Belonging in Mathematics
of Successful African-American Students in
Community College Developmental Mathematics Courses
by
Maxine Tracey Roberts
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
Dr. Estela Bensimon, Dr. Patricia Burch, and Dr. John Slaughter
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(EDUCATION)
May 2018

Mathematics Identity in Developmental Mathematics
2

Abstract
Research on community college students tends to focus on their deficits and failures
rather than assets and achievements. This narrative study focuses on African-American
community college students and their remedial math achievements. Research questions
addressed participants’ descriptions of their mathematics identity (Anderson, 2007; Bishop,
2012; Grant, Crompton, Ford, 2015; Grootenboer & Zevenbergen, 2007; Martin, 2000, 2007,
2009; Nasir & Saxe, 2003), factors that contributed to their success in mathematics, and their
perceptions of instructors’ and peers’ roles in their achievement. Mathematics identity is paired
with sense of belonging in mathematics (Good, Rattan, Dweck, 2000) to create a New
Mathematics Identity framework. Mathematics identity focuses on students’ perceptions of
themselves as math doers and learners and sense of belonging in mathematics addresses feelings
of membership and acceptance in math contexts. Using semi-structured interviews, responses to
vignettes, college transcripts, and math educational history mapping, I explored students’
identities as math learners and the factors that shape their success in math. Findings show that
the components of the New Mathematics Identity framework, instructor support, and
participants’ academic and personal practices shape their success in remedial mathematics. Key
supports include participants’ decisions to link math with financial success, respect for
mathematics, study practices, prayer and religious faith, and their faculty’s social behaviors and
instructional practices. Participants also discussed several obstacles, including the two
languages spoken in the math classroom, racialized math experiences, and institutional
inefficiencies.

Mathematics Identity in Developmental Mathematics
3

Table of Contents
ACKNOWLEGEMENTS ...................................................................................................................6
PROLOGUE ......................................................................................................................................8
CHAPTER ONE: INTRODUCTION ...................................................................................................9
What to Explore? A Gap in Studies on Remedial Education............................................................ 11
Dissertation Study and Rationale ................................................................................................... 12
The Value of Studying Students Who are Successful ....................................................................... 13
Using an Anti-Deficit Perspective to Study African-American Students ........................................... 16
Overview of the Dissertation ......................................................................................................... 17
CHAPTER TWO: LITERATURE REVIEW ...................................................................................... 19
Community Colleges and Developmental Education ....................................................................... 19
Students’ Characteristics and Concerns .......................................................................................... 22
The Need for Effective Instructional Practices ................................................................................ 26
Mathematics Identity and Student Success...................................................................................... 34
Students of Color in Community Colleges and Remedial Courses .................................................... 37
CHAPTER THREE: CONCEPTUAL FRAMEWORK ....................................................................... 43
Defining Identity........................................................................................................................... 43
Mathematics Identity: Gaining an Understanding of Math Success ................................................... 48
Mathematics Identity Defined .................................................................................................... 48
How Mathematics Identity Develops .......................................................................................... 51
Individual Beliefs, Skills, and Agency ............................................................................................ 52
Sense of Belonging in Mathematics. ........................................................................................... 52
Out-of-School Math-Related Interactions. ................................................................................... 56
In-School Math-Related Interactions........................................................................................... 57
Race-Related Math Beliefs......................................................................................................... 60
Combining Martin’s (2000) Framework with Other Math Identity Constructs to Create a New
Mathematics Identity Framework ............................................................................................... 63
How Mathematics Identity Has Been Studied in Developmental Math .......................................... 70
CHAPTER FOUR: METHODOLOGY.............................................................................................. 73
Narrative: The Methodology of Choice .......................................................................................... 73
Why Use Narrative? .................................................................................................................. 74
Mathematics Identity in Developmental Mathematics
4

Addressing Tensions in Narrative ............................................................................................... 78
Neighborhood Demographics and Developmental Education at LA North..................................... 81
Participants ............................................................................................................................... 89
Ethical Considerations ............................................................................................................... 92
Data Collection ......................................................................................................................... 93
Data Analysis and Presentation .................................................................................................. 97
Trustworthiness....................................................................................................................... 102
Study Limitations .................................................................................................................... 104
CHAPTER FIVE: NARRATIVES................................................................................................... 106
Ophelia Jackson.......................................................................................................................... 109
Wesley Simon ............................................................................................................................ 135
Maurice Knight........................................................................................................................... 163
Abdul-Malik............................................................................................................................... 189
Kendon Joseph ........................................................................................................................... 231
Data from All Study Participants.................................................................................................. 253
The Final Meeting: Suggestions from the Resident Experts............................................................ 259
Relational Practices: The Importance of Care and Encouragement ........................................... 259
Pedagogical Practices: Making Math Make Sense and Expecting the Most from Learners ............ 261
CHAPTER SIX: THEORETICAL IMPLICATIONS ........................................................................ 263
Ability ....................................................................................................................................... 264
Obstacles.................................................................................................................................... 273
Instrumental Value and Motivation .............................................................................................. 279
Success and Approach................................................................................................................. 283
Instructors and Supports .............................................................................................................. 290
Sense of Belonging in Mathematics.............................................................................................. 298
Suggestions from the Resident Experts ......................................................................................... 300
CHAPTER SEVEN: CONCLUSION............................................................................................... 303
Mathematics Identity Construction............................................................................................... 304
Contributions to Literature........................................................................................................... 306
Strength and Limitation of the New Mathematics Identity Conceptual Framework .......................... 312
Implications for Practice and Research ......................................................................................... 314
Mathematics Identity in Developmental Mathematics
5

EPILOGUE.................................................................................................................................... 319
REFERENCES............................................................................................................................... 326
APPENDICES ............................................................................................................................... 340
APPENDIX A: Table 3: Alternative Math Identity Definitions and Relevant Constructs.................. 340
APPENDIX B: Recruitment Email Messages ............................................................................... 343
APPENDIX C: Literature Matrix ................................................................................................. 345
APPENDIX D: Interview Protocol ............................................................................................... 347
APPENDIX E: Vignettes............................................................................................................. 350
APPENDIX F: Math Education History Map................................................................................ 353
APPENDIX G: Codebook (Sample) ............................................................................................. 354
APPENDIX H: Analysis (Sample) ............................................................................................... 362

Mathematics Identity in Developmental Mathematics
6

ACKNOWLEGEMENTS
Completing this PhD was truly a community effort, and so I express gratitude for all who
traveled on this journey with me. Thank you, God, for planting this seed of pursuing a PhD in
my mind and giving me the tenacity to bring it to fruition.
To my committee members, Drs. Patricia Burch and John Slaughter, thank you for your
input on my dissertation and support with fine-tuning my study. A special thank you to my
advisor, Dr. Estela Bensimon, for our work together. Your combination of rigor and compassion
during this journey certainly helped to solidify my identity as a scholar.
Thank you to my parents, Maylene Williams and Jeremiah Roberts who entertained my
seemingly crazy idea to leave my life on the east coast to pursue a PhD in Los Angeles. You are
my biggest champions; thanks for reminding me not to take myself so seriously.
Next, I offer a heart-filled thank you to Drs. Jerlando Jackson, Catherine Millett, and
Chera Reid for your guidance during my PhD program selection and during the completio n of
this dissertation.
To my partners in our 2012 cohort, Cheryl, Daniel, Michelle, Federick, Drew, Jahni,
Ayesha, Ananya, Joyce, Vanessa, and Bobby—thank you for joining me on this ride. To my
fellow doctoral students and the staff and consultants at the Center for Urban Education, I
appreciate your words of encouragement throughout this process.
My study participants, Abdul-Malik Baker, Valerie Baylor, Ophelia Jackson, Jackson
Jacobsen, Kendon Joseph, Maurice Knight, Barry Powell, Wesley Simon, Persia Smith, and
Nicole Vincent: Because of your willingness to share your stories, I have this dissertation. I
hope you embrace your success in mathematics and wish you much continued academic success.
Mathematics Identity in Developmental Mathematics
7

To my friends and colleagues: Kevin Austin, Linda Gallo, Diana Porras, and Drs. Robin
Bishop, Fiona Conway, Becky Cox, Alan Green, and Daemon Jones. Thank you for your check-
in phone calls, willingness to read and edit my work, and loving support during this process.
Finally, thank you to the AERA Minority Dissertation Fellowship committee for
recognizing the value of this study and for funding the final year of my PhD program.

Mathematics Identity in Developmental Mathematics
8

PROLOGUE
Maxine: Why did you say ‘yes’ to this study?
Wesley: Well, higher math and higher sciences have a low frequency of Black students.
It's something I’ve noticed, you know, I can't even be absent because it's very
noticeable. Because I’m the only dark face most of the time. Maybe one or two
others, you know, most of the time they're from foreign countries and you know,
they always seem to do pretty well, but as far as what you would consider
African-American, they are not. I always thought there was something wrong
with that.
So, if there's some information that I can provide to help, maybe one or two
more will be there next semester, two more the next and it can grow from there
because from what I know, African-Americans have a strong past history of
science and mathematics and along the way somewhere it got lost and I don't
know why.
This statement from Wesley Simon, a participant in this study, reflects the sentiment of
many who are familiar with African-American’s history as researchers and innovators in
mathematical and scientific fields. With this dissertation study, I explore the experiences of
African-American students who are successful in community college remedial math classes to
learn a few things that can be used to fulfill Wesley’s intention.

Mathematics Identity in Developmental Mathematics
9

CHAPTER ONE: INTRODUCTION
In mathematics- focused educational research, policy reports, and media outlets, African-
American
1
students, regardless of grade level, are often labeled as underachieving, low-
performing learners who do not persist in mathematics-related contexts (Berry, Ellis, & Hughes,
2013; Ladson-Billings, 1994; Martin, 2000; 2009). This ongoing focus on low success rates
minimizes these students’ achievements, overshadows their accomplishments, and focuses on
learners’ challenges by labeling them as unsuccessful students (Ladson-Billings, 1994; Margolis,
Estrella, Good, Holme, & Nao, 2010; Martin, 2000; 2007; Moses & Cobb, 2001; Tate, 1995).
Moreover, when perusing data on enrollment in upper-level mathematics courses, student
populations in mathematics- and science-related majors in post-secondary institutions, and racial
demographics in mathematics-related industries, it is difficult to ignore the underrepresentation
of African-Americans in an essential area of the school curriculum and in fields that are in high
demand (Margolis et al., 2010; Martin, 2000; McGee & Pearman, 2014; Moses et al., 2001).
When reviewing demographics on postsecondary mathematics remediation
2
enrollment, the data
are reversed; a large percentage of Black students are placed into remedial courses, particularly
those who attend community college (Adelman, 2004a; Bailey, Jeong, & Cho, 2010; Bahr, 2010;
Boatman, 2012; Hagedorn, Siadat, Fogel, Nora, & Pascarella, 1999).
For decades, community colleges have served as Black students’ primary access to higher
education (Lewis & Middleton, 2003; Zatynski, Witham, & Wyner, 2016) when they could not
gain entry to nor afford the high cost of four-year colleges and universities. In California,
approximately two-thirds of African-American, first-time students enroll in one of California’s

1
In this dissertation, I use the terms ‘African-American’ and ‘Black’ interchangeably.
2
I use the terms ‘remediation’ and ‘developmental math’ or ‘developmental mathematics’ interchangeably.
Mathematics Identity in Developmental Mathematics
10

community colleges; close to 90% of these students enter remediation (Campaign for College
Opportunity, 2015). Enrollment in these non-credit courses can be challenging because these
students often complete the classes at a slower pace than their peers in college-level courses and
their degree attainment is low (Bahr, 2010; Bailey & Cho, 2010; Bailey et al., 2008; Fong &
Melguizo, 2016; Scott-Clayton & Rodriguez, 2012). Progression is particularly disconcerting
when reviewing the disparities in advancement between different racial and ethnic groups. For
example, although a greater proportion of Black students enter remedial mathematics as
compared to other racial and ethnic groups (e.g., Bahr, 2010; Bailey et al., 2008), a review of
remediation outcomes data between Black students and their peers from other groups show that
Black students have the lowest remediation success rates—18.6% as compared to Latinos
(31.2%), Whites (36.8%) and Asians (45.1%) (California Community College Student Success
Scorecard, 2015). These outcomes draw attention to African-Americans’ progress in
developmental math and inform studies about their performance in these courses.
Attention to Black students’ failures ignores learners who are successful in mathematics
and reinforces deficit-focused perspectives (Martin, 2000, 2009; Tate, 1994, 1995; Varelas,
Martin, & Kane, 2012). When researchers primarily focus on Black students’ failures and the
reasons for their lack of success in mathematics-related contexts, they miss the opportunity to
learn about those who are achieving in mathematics (Martin, 2000). Viewed from a different
perspective, data showing gaps in remedial mathematics success rates between African-
American students’ and their Latino, White, and Asian peers also highlight that several Black
students are successful in these courses. Considering data from this perspective sheds light on a
group of students whose mathematics experiences have not been fully examined: African-
American students who are successful in community college remedial mathematics courses.
Mathematics Identity in Developmental Mathematics
11

What to Explore? A Gap in Studies on Remedial Education
Successful Black students in community college developmental math courses receive
little attention in research literature; instead, many scholars tend to report on the
underachievement of students in these courses (e.g., Bahr, 2010; Bailey et al., 2008; Bailey,
2009; Boatman, 2012; Prince, 2005). When authors continue to highlight students’ low
performance, they perpetuate notions about these learners’ cognitive and academic ineptitude
(Nasir & de Royston, 2013) and encourage beliefs that poor outcomes are the only type of results
that Black students are capable of producing (Harper, 2015). In addition to understanding stories
about students who have not been successful in remediation, it is important to study those who
have achieved in these courses. A new framing offers opportunities to learn about these students
from a new lens, one that leads with their strengths, laying a pathway to understand who they are
and how they achieve success.
Developmental mathematics scholars report about the challenges that learners have in
remediation such as, lack of preparation for college-level courses (Cox, 2009a; Deil-Amen &
Rosenbaum, 2002; Perin & Charron, 2003), financial challenges (Crisp, Reyes, & Doran, 2015;
Perin et al., 2003), and their negative responses to remedial course placement (Deil-Amen, et al.,
2002). Researchers rarely discuss students’ experiences in these mathematics courses, how
instructors’ relational and pedagogical practices influence their achievement, or even how they
perceive their abilities to do and learn mathematics. Knowing these students’ perceptions of
themselves as mathematics doers and learners, or their mathematics identities (Anderson, 2007;
Bishop, 2012; Grant, Crompton, Ford, 2015; Grootenboer & Zevenbergen, 2007; Martin, 2000,
2007, 2009; Nasir & Saxe, 2003), helps scholars begin to explore reasons for learners’ academic
outcomes, success, and failure. Understanding learners’ mathematics identity and the factors
Mathematics Identity in Developmental Mathematics
12

that foster Black students’ success in developmental mathematics contributes to the remedial
education scholarship by providing a counter-narrative to the stories typically told about the
reasons for African-American student outcomes in remediation.
Dissertation Study and Rationale
To shift the conversation about African-American students in remediation, this
dissertation study explores the mathematics identities (Anderson, 2007; Bishop, 2012; Grant et
al, 2015; Grootenboer et al., 2007; Martin, 2000; Nasir et al., 2003) and experiences of African-
Americans who are successful in community college developmental math courses; these
students, their identities, and their successes are rarely considered. I have analyzed data
collected during this study using the following research questions:
• How do Black students who are successful in developmental math courses describe their
mathematics identities?
• How do these learners describe how they achieved success?
• How do these learners perceive the role of instructors and classroom practices in their
success?
I was inspired to study this topic after reviewing Preparing the Underprepared: An Analysis of
Racial Disparities in Postsecondary Mathematics Remediation, an article by developmental
education scholar, Peter Bahr (2010). Bahr sought to determine mathematics remediation
success by ethnic groups and defined success as students who passed a college-level
mathematics course (e.g., courses students take after completing the remedial mathematics
sequence); he found that one-third of Asians, one-quarter of Whites, one-fifth of Latinos, and
one-ninth of Blacks succeeded. While it is likely that Bahr’s readers will notice the gap in
student performance, a percentage of Black students were successful in these classes. Using
Mathematics Identity in Developmental Mathematics
13

Bahr’s (2010) definition of success as a foundation for this study, I define success for this study
as students who (a) were placed in community college remedial math courses, (b) have
successfully completed the developmental math sequence, and (c) are enrolled in their first
college-level mathematics course or have passed a college-level math course
3
. Typically, studies
that focus on successful African-Americans in higher education take place in four-year
institutions, not in community college nor with learners in developmental math courses (e.g.
Fries-Britt, 1997, 1998; Fries-Britt & Turner, 2001; Griffin, 2006; Harper, 2004, 2005, 2010;
Stinson, 2008). Attention to students who are achieving in community college remediation
brings attention to a group of successful students who are rarely addressed in the literature.
The Value of Studying Students Who are Successful
In studies on Black students’ academic strengths in K-12 settings and four-year colleges
and universities, researchers focus on the positive aspects of these learners’ academics and
highlight the factors that contribute to their successes (e.g., Berry, Thunder, & McCain, 2011;
Stinson, 2008; Zavala, 2014). One key benefit of this approach is the learning gained from
studying students who are successful in school. Having knowledge about the factors that
contribute to their success can shape the kind of work that is done with students who struggle
academically. Similarly, understanding the experiences of community college students who are
successful in remediation can inform the ways we support other community college students who
are in remediation.
One construct that researchers can consider when exploring community college students
who are successful in mathematics is these learners’ mathematics identity. Existing studies about

3
Although Bahr (2010) did not focus on students who were in their first college-level math course, I included this
criterion to broaden the number of participants who were eligible to participate in the study.
Mathematics Identity in Developmental Mathematics
14

successful students’ mathematics identity focus on students in K-12 and four-year college
settings. They have documented factors that contribute to learners’ mathematics identity
development including: personal attributes (Martin, 2000; Nasir, 2002a; Hebert & Reis, 1999;
Smith, Estudillo, & Kang, 2011), school-based supports (Ellington & Frederick, 2010; Fullilove
& Treisman, 1990; Jett, 2013; Stinson, 2008; Walker, 2006), and out-of-school factors (Berry, et
al., 2011; Ellington et al., 2010; Stinson, 2008). These identified factors—related to the
individual and to home and school environments—suggest that there are multiple aspects to
consider when exploring community college students’ mathematics identity development,
particularly those who are successful in remediation.
Though scholars explore and discuss mathematics identity and success for African-
Americans in K-16 settings, limited consideration is given to students’ experiences in
community college remedial mathematics courses. Learning about factors that contribute to the
mathematics identities of Black community college students who are successful in remedial
mathematics provides critical data that can be used to support the learning that happens in
classrooms, particularly for those who have not been successful in remediation. Findings from
this study contrast familiar stories of African-Americans’ academic underachievement and
provide a new lens for learning about Black students.
Shifting the focus of research about African-Americans to one that looks at their
achievements rather than their deficits is not a new endeavor; in higher education, these types of
studies have primarily taken place in four-year settings. For decades, scholars reported findings
about African-Americans’ low academic performance in college (e.g., Bonner & Bailey, 2006;
Harvey-Smith, 2002; Loury, 2004; Lundy-Wagner & Gasman, 2011; Palmer, Davis, & Hilton,
2009; Stringfield, 1997). Then, a small group of scholars, focused on Blacks who were
Mathematics Identity in Developmental Mathematics
15

achieving in these settings, began to study the factors that contribute to their success (e.g., Fries-
Britt, 1998, 2002; Fries-Britt & Turner, 2001; Griffin, 2006; Harper, 2004, 2005, 2010; Martin,
2000; Palmer, et al., 2011; Stinson, 2008). They found that peer interactions, enrichment
programs, family and community support, individual agency, campus environments, and
mentoring were among the factors that positively contribute to academic excellence.
Researchers who focus on Black students’ mathematics achievements, sought to understand
these learners’ success (e.g., Martin, 2000; Moses et al., 2001) and attributed outcomes to
numerous factors, including positive mathematics identity development, effective instructional
and relational practices, and teachers’ high expectations. With this dissertation study, I build on
these scholars’ work by exploring the mathematics identities of African-American students who
are successful in community college remedial mathematics courses.
Next, examining the influence that pedagogical and relational practices might have on
Black students in remediation can help developmental math instructors consider the role they
play in student success in developmental education. Bensimon (2005) posits that gaps in
equitable outcomes for students of color will persist until practitioners create educational
environments that foster these learners’ success. In the classroom, faculty can begin to shift
student outcomes by considering and altering the ways they interact with and teach students. By
exploring learners’ perceptions of practices and pedagogy that contribute to their math identity
development (whether positive or negative) and success, this study can offer findings that help
practitioners gain a better understanding of the behaviors that are useful and harmful for learners’
math progress and success.
While many factors are important for student success in mathematics (including learners’
families and community members) this study explores instructors’ roles and classroom practices
Mathematics Identity in Developmental Mathematics
16

in student success. Other factors that contribute to learners’ progress emerged in the study (e.g.,
primary and extended family, community, individual agency); as needed, I engage with
additional bodies of research to learn about other factors that contribute to these students’
progress.
Using an Anti-Deficit Perspective to Study African-American Students
Recognizing a need to shift the deficit-minded perspective about Black males in college
prompted Harper (2010) to create the Anti-Deficit Achievement Framework to study Black
undergraduate males who were successful in post-secondary settings. With this framework,
Harper changed the typical structure of research questions that are used to gain insight into the
achievements of Black males in college settings. For example, rather than asking questions such
as, “Why do so few Black male students enroll in college?” (Harper, 2010, p. 69), his questions
focused on Black college students’ supports and the factors that help them matriculate at, persist
in, and graduate from four-year institutions. Similarly, by using the mathematics identity
framework (Martin, 2000), I shift from the outcomes-based focus on African-American student
performance in developmental mathematics and focus on the experiences of those who are
successful in community college remediation.
My interest in this topic goes beyond the need to address a gap in the literature. Rather,
this topic is important because the ways that math is perceived, how it is taught, and the ways
that the successes of Black students are overshadowed by stories of low performance have
dominated the math success narrative for far too long. These stories affect how scholars and
practitioners view, treat, and teach Black students and subsequently, how these learners perceive
themselves. By studying Black students who are successful in community college remedial
mathematics courses, their mathematics identity, the ways they describe their success, and their
Mathematics Identity in Developmental Mathematics
17

beliefs about the roles that faculty and classroom practices play in their success, scholars and
practitioners can shift the deficit-focused narrative and subsequently support other Black
students who are placed in these courses.
Overview of the Dissertation
In this section, I share my plan, or roadmap, for this dissertation study about the
influences that shape the success and mathematics identities of African-American students in
community college remedial math courses. In Chapter Two, I discuss developmental education
in community college and the racial/ethnic breakdown of students in these courses and highlight
African-American students’ over-enrollment in these courses. I also address the characteristics of
students in remediation, highlight the factors that influence these learners’ outcomes in general,
and then, focus on African-American students more specifically. I then discuss a gap in the
literature regarding the experiences of African-American students who are successful in
developmental math courses. In Chapter Three, I discuss mathematics identity and sense of
belonging in mathematics as conceptual frameworks that can be used to explain the outcomes
and experiences of African-Americans who are successful in remedial mathematics courses.
From my review of the literature, a majority of the mathematics-identity related studies have
been conducted in K-12 settings; a smaller number focus on college students’ mathematics
identity. Therefore, a bulk of the literature in Chapter Three focuses on K-12 studies. In Chapter
Four, I present narrative, the method used in this dissertation study along with the study design,
ethical considerations, practices used to ensure trustworthiness, and limitations of the study. In
Chapter Five, I present the findings of this study by sharing the narratives of five participants
Mathematics Identity in Developmental Mathematics
18

from the sample
4
, data from other participants in the study, and all participants’ suggestions for
improving the success of students who take developmental mathematics courses. Chapter Six
presents an analysis of the stories featured in Chapter Five. In Chapter Seven, the final chapter, I
present the conclusion and offer the study’s larger relevance for policy and practice.

4
I provide rationale for presenting the findings for a smaller group of participants in Chapter Four: Methods
Mathematics Identity in Developmental Mathematics
19

CHAPTER TWO: LITERATURE REVIEW
Previous research on success in developmental education has focused on community
colleges and remediation, students’ characteristics, skills, and concerns, and the need for
effective instructional practices. To describe a new way to focus on learners in community
colleges, I introduce a discussion about mathematics identity and student success. I base my
literature review on scholarship from several fields and disciplines, including economics,
mathematics education, sociology, higher education, and education policy. I begin with studies
that focus on developmental education in community colleges by discussing these topics as they
relate to all racial and ethnic groups; later in the section, I turn my attention toward Blacks in
community colleges. First though, I begin with a description of community college and
developmental education, statistics about developmental mathematics, a discussion about the
student racial ethnic breakdown in developmental mathematics, and a review of studies on
student success in remediation.
Community Colleges and Developmental Education
Nationally, of all students who enter community college and take placement tests,
approximately three-quarters enter remediation (National Center for Public Policy and Higher
Education (NCPPHE) & Southern Regional Education Board (SREB), 2010; Bailey, 2009a,
2009b). In the California community college system, more than three-quarters of students are
placed in developmental math, with the largest proportion referred to courses that are three levels
below college-level (California Community Colleges Chancellor’s Office, 2011). Although
remediation was designed to help students attain the skills to enter college-level courses and
transfer, scholars who study developmental education show that students who place into these
lower levels often struggle to complete remedial courses successfully (Bahr, 2010; Bailey,
Mathematics Identity in Developmental Mathematics
20

2009a, 2009b; Bailey et al., 2010; Grubb & Associates., 1999; Grubb & Gabriner., 2013;
Lazarick, 1997; Merisotis & Phipps, 2000).
Developmental education defined. Some scholars define developmental education as a
system that supports students who are unprepared for college-level coursework by offering
counseling, tutoring, and remedial classes (Attewell et al., 2006; Boatman, 2012; Moss &
Yeaton, 2006). I base my definition of developmental education on its academic aspects (e.g.,
Deil-Amen, 2011; Perin & Charron, 2003) and identify developmental education as non-credit
classes that are designed to improve students’ basic skills and prepare them for college-level
math and English courses. Learners who take these courses struggle to complete them, others
drop out from the classes and never enter college-level courses. Nationally, of the learners in
remediation, fewer than half complete the sequence and 20% of students referred for remedial
math and 37% of learners referred for remedial English complete a college-level math or reading
course within three years of their initial enrollment (Bailey et al., 2010). Setting aside the
challenge of these lower completion rates, it is important to note that overall, 28% of students
who enter community college remediation graduate in 8 1/2 years as compared to 43% of
students who begin in college-level courses (Attewell et al., 2006). These statistics reinforce the
unfortunate reality that developmental education courses, which are designed to help students be
college-ready, can become gatekeeper courses that hinder their success and impede their
progress in community college.
Progress based on racial and ethnic differences. While remediation courses serve as
roadblocks for many students who are placed into developmental education, data show that the
challenges associated with remediation can become obstacles for learners from different racial
ethnic groups, particularly Black students. Remediation data in Table 1 from the Community
Mathematics Identity in Developmental Mathematics
21

College Student Success Scorecard (2017) highlight differential outcomes between Black
students and their peers in remediation. In 2005-2006, Whites and Asians completed community
college developmental math sequences and entered college-level mathematics courses at almost
twice the rate of Blacks (CCCSSS, 2017); ten years later, although all students’ outcomes were
comparable to earlier completion rates, Black students showed the smallest gains of all other
groups; these students’ results were still significantly lower than their peers’ achievements.
Table 1: Remedial Math Sequence Completion Rates (CCCSSS, 2016)
E thnicity 2005-2006 2015-2016
Asian 42.1% 48%
Black 16.3% 19.5%
Latino 26.2% 33.1%
White 33.5% 38.7%
While these data highlight performance gaps between Black, Asian, Latino, and White students,
they also encourage “gap gazing”
5
(Gutiérrez, 2008, p. 357) between groups, and foster negative
stereotypes about Black students’ mathematics abilities. For others they reflect the need to gain
a better understanding of Black community college students, their achievements, and their
identities, particularly those who are successful in remedial mathematics.
Student Progress in Remediation
Multiple developmental education scholars focus on negative student outcomes and the
reasons for failure in these courses (e.g., Bailey et al., 2009; Boatman, 2012). However, a closer
look at some of the remediation scholarship shows that literature is not completely devoid of

5
Gutierrez (2008) defines “gap gazing” as the act of focusing research on the achievement gap between groups .
This behavior leads to blaming students who underperform, and sets White students’ achievement as the norm.
Mathematics Identity in Developmental Mathematics
22

studies on student success. For example, in a quantitative study to determine the effect of
developmental English in a first college-level English classroom (Moss, Kelcey, & Showers,
2014), authors studied classroom, instructor, and student characteristics in 223 community
college composition English courses. Authors reported that two key factors positively affected
student success: (1) the proportion of developmental students who were enrolled in the class and
(2) instructors’ full-time employment status. Other scholars report that redesign of
developmental math courses positively impacts student success (Okimoto & Heck, 2015) and
learners’ self-perceptions about their skills and level of math enjoyment improved after taking a
remedial course (Benken, Ramirez, Li, & Wetendorf, 2015). These studies provide insight about
factors that contribute to student success in remediation, but these are ‘race-less’ studies and as
such, do not broaden knowledge about Black students who are successful in math remediation.
Before focusing on Black students in remediation, it is valuable to understand what scholars have
learned about all students who are placed into these classes.
Students’ Characteristics and Concerns
Scholars who write about success and failure in remediation often explain course
outcomes by focusing on student deficits (e.g., Bahr, 2010; Bailey et al., 2009; Boatman, 2012;
Grubb et al., 1999; Grubb et al., 2013; Perin et al., 2013). By ignoring the other factors that may
contribute to their performance, such as institutional policies and practices, researchers offer a
narrow set of factors to help audiences explain or even understand these learners’ success. In
this section, I discuss multiple reasons that have been used to explain student outcomes when
they are unsuccessful in remediation to highlight the need for a new focus that considers student
successes, not deficits.
Students’ Backgrounds, Beliefs, and Attitudes
Mathematics Identity in Developmental Mathematics
23

Learners’ backgrounds. Researchers who study student outcomes in remediation
attribute learners’ course failure to their personal and financial burdens (Crisp et al., 2015; Perin
et al., 2003), negative perceptions and concerns about their placement into remediation (Deil-
Amen, et al., 2002), barriers associated with minority race and ethnicity (Attewell et al., 2006),
and lack of prior academic success and preparation (Bahr, 2010; Deil-Amen et al., 2002; Perin et
al., 2013). For example, in a study on the racial gap in successful math remediation, Bahr (2010)
shows that of four racial-ethnic groups, (African-American, Asian, Latino, and White), Asians
and Whites have higher successful remediation rates when compared with their Black and Latino
peers. In addition to pointing out the “sizable racial gaps” (p. 227) between Asians and Whites
and their Black and Latino peers, Bahr goes beyond where other scholars who offer similar
outcomes (e.g., Bailey, 2010; Boatman, 2012) stop and posits that differences between racial
groups’ math skills upon entry to college may help explain these gaps in student performance.
Although Bahr (2010) may be attempting to explain that students’ level of preparation, not their
ability, is one culprit in disparities between student performances, he perpetuates the use of a
student deficit perspective to frame learners’ outcomes.
A closer look at the findings in literature on student academic outcomes in remediation
link learners’ performance with unequal educational opportunities and student-related factors. In
a study of Black and White students in remedial and college-level mathematics, Hagedorn and
colleagues (1999) noted that students in developmental math often graduated from high schools
with higher percentages of minority students. In these schools, they also note that students who
lack guidance and encouragement from counselors to complete advanced math courses can
graduate from high school unaware of what to expect in college. With a lack of information
about college expectations and the coursework necessary for success in college, these students
Mathematics Identity in Developmental Mathematics
24

are behind in college even after they graduate from high school and start college at a
disadvantage (Deil-Amen et al., 2002; Margolis, 2010). For some learners, this absence of
information can stem from inadequate support from counselors; for others, their challenges begin
earlier and are the result of poor access to academic resources and preparation before students
attend grade school.
Researchers (e.g., Bahr, 2010; Boatman, 2012; Grubb, 2007; Hagedorn et al., 1999) argue
that poor preparation in K-12 years can result in lower levels of academic success when students
take remedial courses in community college. Grubb (2007) attributes poor student performance
to ‘dynamic inequality,’ which highlights the influence that schooling, family background,
parental aspirations, and family income have on student success. Dynamic inequality causes
children to begin school with different cognitive and non-cognitive skills; although some
students have basic academic skills and others have social skills, all may not have the same skill
set. Depending on resources in neighborhood schools and the skills of teachers who work in
these environments, differences in students’ skills may increase, decrease, or remain the same
over time. As students progress through school, these disparities increase and by 12
th
grade,
some learners excel academically; others may have dropped out or may be somewhere in the
middle. In this collection of studies, scholars link students’ outcomes with their lack of
preparation in their K-12 years and to home and school contexts.
Learners’ beliefs about classroom instruction. Other researchers explore how students’
perceptions of classroom teaching influence the ways that students engage in class (Bickerstaff,
Barragan, Rucks-Ahidianam 2012; Cox, 2009) and, in turn, their course outcomes. Students who
value faculty that engage in lecture-style instruction over those who teach using classroom
discussion techniques, assign collaborative projects, or use peer evaluation activities often
Mathematics Identity in Developmental Mathematics
25

mistrust instructors who teach using collaborative or student-centered practices (Cox, 2009a).
Learners who oppose these types of techniques become suspicious of these faculty and fear that
it is less likely they will be successful without explicit instruction (Cox, 2009a). In other words,
because of these learners’ prior experiences, they question their own capability to succeed when
instructors provide less, rather than more direction; their concerns can result in self-fulfilling
prophesies.
Students’ attitudes about remedial course placement. While some authors have
shown ways that students’ backgrounds contribute to their academic outcomes (e.g., Crisp,
Taggart, & Nora, 2014; Hagedorn et al., 1999), others, maintaining a student-deficit focus, turn
attention to the ways that students’ perceptions, beliefs about themselves, and their attitudes
influence their outcomes in remediation. For some learners, placement into remediation can
result in surprise, anger, disappointment, or fear of stigma (Deil-Amen et al., 2002; Steele,
1997); these emotions shape how students approach these classes and their experiences in these
courses. Even when students do not feel stigmatized by course placement, some develop
concerns about the amount of time that remediation adds to their years in college and whether or
not it will affect their ability to complete their degree on time (Deil-Amen et al., 2002). With a
range of emotions linked to remedial course placement, students may not view themselves as
mathematics learners and with thoughts like, ‘I don’t have what it takes to be good in school,’
become pessimistic about their chances for succeeding in these classes (Merseth, 2011). In fact,
Williams and Clark (2004) found that when learners are uncomfortable with their self-perceived
academic abilities and teacher feedback, they experience anxiety about how instructors and peers
view their class contributions; this concern influences their class participation. Students who
have known themselves to be academically successful in high school also deal with challenges
Mathematics Identity in Developmental Mathematics
26

when they are placed into remediation (Attewell et al., 2006; Larnell, 2016; Ngo, 2017; Scott-
Clayton, Crosta, Belfield, 2014). In those cases, some students experience frustration and
wonder, “Why am I in this class after passing my high school courses?”
These ideas that students’ skills, experiences, backgrounds, and attitudes influence their
performance in remediation are not new. However, having this information informs our
understanding about why a percentage of students who are in remediation do not achieve
success; unfortunately, these discussions do not explain the experiences of those who are
successful in remedial mathematics.
Now that I have addressed how researchers link students’ backgrounds and their attitudes
with their academic outcomes, next I highlight another important aspect of remediation that
shapes student outcomes: instructional practices. Specifically, I discuss literature regarding the
need for effective instructional practices and how this need contributes to learner outcomes in
developmental courses.
The Need for Effective Instructional Practices
Mathematics pedagogy
Faculty’s instructional practices and classroom behaviors can affect how students perceive
their abilities, shape the ways and their willingness to work, and influence their developmental
education outcomes (e.g., Howard & Whitaker., 2012; Mesa, Wladis, & Watkins, 2014). In fact,
scholars who conduct classroom-level observations in developmental mathematics note that less-
engaging, instructor-centered styles of teaching are not only prevalent in these environments,
they also limit learners’ aptitude (Cox, 2015). These instructional practices often stem from a
gap between faculty’s conceptual understanding of what they expect students to be able to do
and what students are prepared to do (McGrath & Spear, 1991). When students do not meet
Mathematics Identity in Developmental Mathematics
27

instructors’ expectations, faculty may resort to basic teaching practices that do not build
students’ skills or prepare them for the next course in the developmental sequence. This style of
instruction further contributes to the ways students perceive themselves as learners in
remediation.
Mesa and colleagues (as cited in Cox, 2015) report that community college mathematics
instructors spent much of their instruction time asking students routine questions that do not
encourage learners to engage in meaningful class activities. These rote practices begin in
grammar school where a focus on rule-following—not conceptual understanding—shapes
classroom instruction (Stigler & Hiebert, 1999). This approach is found at all levels of math, and
an expansive study of community college math faculty found that rule-following was pervasive
in remedial courses (Grubb et al., 1999). Despite the prevalence of these ineffective practices,
Cox (2015) did find variation in community college remedial math instruction, and this has been
found to make a difference in learners’ outcomes. In a study of six developmental mathematics
classrooms, Cox (2015) reported that learners’ success was linked with instructional practices—
students were more likely to advance to the next developmental math course if they took classes
with faculty who used conceptual teaching approaches rather than rote strategies. There was a
link between conceptual teaching approaches and learner beliefs; as learners developed their
math skills, they expanded their beliefs about what they could achieve and their perceptions of
themselves. Thus, instructional practices can make a difference for student learning experiences
and how they view themselves in mathematics classrooms.
Given that many students in developmental mathematics were not successful in high
Mathematics Identity in Developmental Mathematics
28

school math courses and non-traditional students
6
may have not engaged with mathematics for
several years, instructors need to practice new teaching approaches instead of using repeated or
modified versions of teaching practices that mirror these students’ experiences in high school
(Cross, 1971). These new learning experiences require pedagogical training that developmental
education instructors do not always receive; at times, the lack of preparation arises because
instructors do not anticipate they will teach remedial courses (Kozeracki, 2005). The lack of
training to teach these courses influences how instructors teach, what instructors teach, and
ultimately students’ classroom experiences and performance in developmental education courses.
Instructors’ Training
Instructors who teach using contextual learning practices help students achieve success
by connecting course material with students’ lives. By making these connections, instructors
help learners recognize the instrumental value of classroom material (Brickman, Alfaro, Weimer,
& Watt, 2013; Cox, 2009b; Epper & Baker, 2009; Grubb, 2001; Grubb et al., 2013; Perin, 2011;
Wiseley, 2011). Unfortunately, a multitude of challenges are involved with math instructors’
preparation for classroom instruction. Many faculty who teach developmental courses earned
master’s degrees but either have not been trained as educators (Grubb et al., 1999; Hagedorn et
al., 1999) or were in graduate school programs geared toward secondary or middle school
students (Kozeracki, 2005). In preservice teacher education programs, students often take
courses that do not “substantially alter the knowledge and assumptions” (Ball, Lubienski, &
Mewborn, 2001, p. 437) that prospective teachers hold about mathematics, classroom teaching,

6
Non-traditional college students have several characteristics that distinguish them from traditional college -age
students. Non-traditional students, who are often students of color who are the first in the family to attend college.
These learners are often older that traditional college students, come from working –class, low-income backgrounds,
have not attended school for a number of years. As a result, some are unfamiliar with course material and may
question their ability to achieve success in college (Rendon, 1994).
Mathematics Identity in Developmental Mathematics
29

or learning (Ball et al., 2011; Ball & Hill, 2005). Once in community colleges, instructors often
receive little or no pedagogical guidance, engage in minimal peer evaluation, and attend
professional development sessions have been criticized for their lack of intellectual stimulation,
disconnection from teaching and learning, and fragmented content (Ball et al., 2001). So, relying
on their own memories about how they were taught or how they were taught to teach, instructors
resort to didactic approaches and ‘trial and error’ practices and are at a loss when these
techniques fail (Grubb et al., 1999; Kozeracki, 2005). Students in all classrooms benefit from
instructors who are affirming and proficient; unfortunately, instructors who teach in remediation
do not always have the skills nor backing to provide this type of support.
Recognizing the Importance of Culture in Pedagogy
Culturally-Relevant Pedagogy. The need for training goes beyond instruction about
content and extends into the cultural aspects of classroom learning experiences; incorporating
student culture into classroom lessons is an important, yet forgotten aspect of the learning
experience, especially for students of color in developmental education courses. Ladson-Billings
(1995) coined a term to describe this style of instruction: culturally-relevant pedagogy (CRP)
She defines CRP as teaching that incorporates three domains: (a) academic success: students’
intellectual growth as a result of instruction and learning experiences in the classroom; (b)
cultural competence: helping students to embrace and celebrate their culture, while learning and
becoming fluent in another; and (c) sociopolitical consciousness: using knowledge and skills
learned in the classroom to solve real-world problems.
Ladson-Billings (1995; 1997) and Tate (1995) have shown that when instructors focus on
academic achievement, incorporate students’ cultures in classroom instruction, and help learners
use their knowledge to address challenges that exist in the real-world, they help students make
Mathematics Identity in Developmental Mathematics
30

meaningful connections with classroom material and with their academics; this idea is true with
several subjects, especially those seemingly-hard-to-connect areas, like mathematics.
Within the discipline of mathematics and mathematics education, Tate (1994) argued for
connecting mathematics to Black students’ lived experiences. He asserts that mathematics
“pedagogy should try to provide students with opportunities to solve problems using their
experiences,” (Tate, 1994, p. 482) including their culture, experiences and traditions. Taking the
same position, other researchers have reported that when instructors incorporate students’
cultures into mathematics instruction via multicultural education (Russell, 2012), social justice,
and cultural experiences (Gutstein, 2003; Ladson-Billings, 1997; Leonard, 2008), they help to
make the subject relevant to students’ lives.
Tate (1995) reported that instructors who helped learners connect mathematics with their
everyday lives were successful with Black middle school students. Effective instructors found
ways to engage students in a variety of activities, including, incorporating journal writing about
topics in students’ lives into the math classroom (Ensign, 2003) and combining students’ and
their families’ knowledge of gardening in the math classroom (Civil & Khan, 2001). Using these
types of practices that go beyond the subject matter encourage students to engage in “math talk”
about topics that are “personal and meaningful” in their everyday lives (p. 401). In addition to
boosting students’ interest in math, researchers have found that including culturally-relevant
topics such as health issues, sports, and saving money into math classrooms improves students’
scores and their confidence on assessment tests (Hubert, 2013).
By incorporating CRP’s practices, instructors can bring social justice-related topics into
the mathematics classroom and highlight issues that are both relevant and important in students’
everyday experiences. In a practitioner-research study with majority Latino students, Gutstein
Mathematics Identity in Developmental Mathematics
31

(2003) combined math instruction with students’ life experiences; learners noticed how traffic-
stop-data was connected with racial profiling. Similarly, Nasir and de Royston (2013) showed
how using basketball as the context for solving math problems helped African-American
students calculate percentages and averages; subsequently, students in this study displayed a new
level of confidence in their skills. These types of assignments help students learn about familiar
and unfamiliar aspects of their communities in ways that help them to retain math concepts. In a
related report about developmental education reform efforts, Preston (2016) showed that some
institutions (e.g., HBCUs), aware of the increasing numbers of students of color in remediation,
improved student outcomes when they prepared instructors to implement popular reforms (e.g.,
co-requisite models) using CRP practices. It is interesting to note that even with this knowledge
about the value of CRP, Costner and colleagues (2010) showed that although community college
instructors agreed that culture was an important aspect of teaching their Black students, they did
not see the benefit of incorporating culture in their classrooms. Although scholars have shown
that pedagogical practices are important in mathematics education classrooms, instructors often
focus on course content, do not always learn about effective teaching practices, nor consider that
effective instruction is necessary for improving student outcomes.
Culturally-Sustaining Pedagogy: Culturally-Relevant Pedagogy 2.0. Following
Ladson-Billings’s work and researchers’ use of CRP to study classroom instructional practices,
Paris (2012) developed Culturally-Sustaining Pedagogy (CSP), building on Ladson-Billings’s
(1995) original ideas. In Ladson-Billings’s (2014) article entitled, “Culturally-Relevant
Pedagogy 2.0: a.k.a. the Remix” she highlights that CSP extends CRP by recognizing the need to
consider and include the “global identities” (p. 82) that exist in our culture. Said another way,
with CSP, Paris (2012) points out that the construct focuses on the student’s ability to “sustain
Mathematics Identity in Developmental Mathematics
32

the cultural and linguistic competence of their communities while simultaneously offering access
to dominant cultural competence” (p. 95). While Paris acknowledges that White, middle-class
norms are often considered dominant, he highlights the increasing growth and importance of
other cultures. As such, CSP differs from CRP because CSP focuses on more than one racial or
ethnic group and identifies cultural learning as practices that focus on the diversity present in a
multi-ethnic and multi-lingual society. Said another way, by using CSP, instructors help students
appreciate their own cultures, while learning to maneuver, succeed, and even thrive within a
dominant culture. When CSP is enacted in the classroom, value is placed on preparing students
to live in a pluralistic society. The importance of student connections with academics,
understanding of their own and others’ cultures, and awareness of social issues point to the need
for attention to culture, and more specifically, culturally-relevant and culturally-sustaining
pedagogical practices in remediation classrooms.
The Value of Interacting with Black Faculty in the Classroom
Although all instructors can support students in important ways, the quality of the
connections that faculty of color make with students of color benefits learners’ academic and
social development. Initially framed as student-faculty interactions, scholars began studying
these connections between faculty and students in the 1970s (e.g., Snow, 1973), focused
primarily on undergraduates in four-year institutions (e.g., Astin, 1993; Kuh & Hu, 2001;
Terenzini, Pascarella, & Blinding, 1999), and did not disaggregate by race or ethnicity. Decades
later, researchers reported that in some cases, the comfort that students of color have with faculty
or mentors can be linked with race (Banks, 1984; Patton & Harper, 2003; Tan, 1995). Setting
aside the comfort that students experience with similar-race faculty or mentors for a moment,
scholars have also shown that the classroom and authority figure(s)’ demographics can influence
Mathematics Identity in Developmental Mathematics
33

students’ experiences (Steele, 1997, 2011; Steele & Aronsen, 1995). This idea becomes even
more nuanced when considering that Black students benefit when they are exposed to and linked
with Blacks who have succeeded in higher education (Sedlacek, 1987; Willie & McCord, 1972)
and shed light on the value of connecting Black students with Black faculty.
Focusing on the connections between Black students and their instructors, researchers
have explored how students benefit from interacting with faculty at different types of institutions.
Those who have studied Black students’ experiences at historically Black colleges and
universities, report that these learners have greater positive engagement with faculty than at other
types of institutions (Fries-Britt & Turner, 2002; Hurtado, Eagan, Tran, Newman, Chang, &
Velasco, 2011) and as a result, they feel supported, have strong academic and social integration
(Allen, 1992), and greater opportunities for success. At predominately white institutions, Black
students appreciate when African-American instructors’ go “above and beyond” (Guiffrida,
2005, p. 709) in ways that include supporting and advocating for students, advising them
holistically, and having high expectations for learners’ success. These studies mirror reports that
Black faculty, more than other instructors, tend to show interest in students by counseling
learners on their academic and career choices (Allen, Epps, Guillory, Suh, & Bonus-Hammath,
2000) and spending more time working with them (Williams & Williams, 2006). At community
colleges, Black students tend to experience positive faculty-student interactions (e.g., Chang,
2005; Wood & Ireland, 2014) when faculty engage in validating practices (Acevedo-Gill, Santos,
Alonso, & Solorzano, 2015; Rendon, 1994). Despite extensive research on this topic,
researchers have not fully explored engagement between Black faculty and Black students at
community colleges who are successful in remediation.
Mathematics Identity in Developmental Mathematics
34

This overview of the factors that affect students’ success in remediation highlights how
student beliefs and backgrounds, instructors’ teaching practices, and learners’ interactions with
faculty influence student academic performance. Even though these findings offer valuable
insight into reasons for low remediation rates, they do not help scholars and practitioners
understand learners who are successful in remediation nor do they help us understand the factors
that contribute to their success. By studying students who are successful in these classrooms we
can learn more about these learners’ skills, effective and ineffective instructional practices in
developmental education classrooms, and ways to help other students achieve academic success
in remediation. Certainly, instructional and relational practices contribute to student success in
school; so do the ways that learners view themselves as math doers and learners. In the next
section, I discuss mathematics identity and highlight how this construct influences student
success in remedial math.
Mathematics Identity and Student Success
Traditionally, scholars who studied Black students’ mathematics performance in K-16
classrooms addressed these students’ outcomes (e.g., Anick et al., 1981; Cokley, et al., 2011;
Grandgenett, 2011; Jones et al., 1984; Pennington, 2000; Waller, 2006) with a focus on their
underachievement (Gutiérrez, 2008; Ladson-Billings, 1997; Martin, 2009; Stinson, 2008).
Martin (2000) suggests that mathematics identity building is a missing component in
understanding “the mechanisms responsible for producing problematic achievement and
persistence outcomes as well as in accounting for mathematics success among African-
Americans” (p.34). Recognizing the value of mathematics identity in discussions about student
performance in math, a small group of scholars studied the experiences and factors that
contribute to Black learners’ positive mathematics identity development (e.g., Berry et al., 2011;
Mathematics Identity in Developmental Mathematics
35

Grant, et al., 2015; Martin, 2000; Nasir, 2002a; Nasir & Shah, 2011; Stinson, 2008; Terry &
McGee, 2012; Walker, 2006). Identity formation and development are important for student
performance and success (Grootenboer et al.,2006; Sfard & Prusak, 2005; Nasir, 2002a) because
each helps shape learners’ perceptions about themselves, their beliefs about their ability to take
effective actions when they face difficulty with mathematics, and as a result, the likelihood that
they will succeed.
Characteristics of students who positively identify with math
Studies of K-12 African-American students who are successful in mathematics suggest
that these learners’ home and school lives help to frame their identities as mathematicians.
Characteristics that demonstrate positive mathematics identity include recognizing the value that
math has for their future success, having internal and external motivation to take advanced math
courses, and demonstrating a willingness to persist in math even when difficulties arise (Berry, et
al., 2011; Martin, 2000; Stinson, 2008; Terry et al., 2012). These learners are also confident in
their math abilities (Berry et al., 2011; Boaler et al., 2000; Martin, 2000, 2007; McGee et al.,
2011a, 2011b), can rely on their own math understanding and their peers’ knowledge to solve
problems (Boaler & Greeno, 2000; Grant et al., 2015), have people in their lives who support
their math success (e.g., family, instructors, community members) (Berry et al., 2011; Stinson,
2008; Terry et al., 2012), and believe mathematics plays a role in their future aspirations (Martin,
2000; 2007; Stinson, 2008). They may participate in academic learning communities (e.g., study
groups) to seek help for math difficulty (Fullilove et al., 1990; Walker, 2006) and either
positively associate their race or ethnicity with math ability or do not connect race and math at
all (Berry et al., 2011; Boaler et al., 2000; Martin, 2000; McGee et al., 2011a, 2011b; Stinson,
Mathematics Identity in Developmental Mathematics
36

2008). Each of these characteristics reflect components of mathematics identity, which are
discussed in Chapter Three of this dissertation.
Characteristics of students who negatively identify with mathematics
Students can develop negative perceptions of their math abilities when they have had
poor or discouraging math experiences; these may stem from ineffective classroom instruction,
racially-biased or prejudiced experiences, and negative interactions with math peers or
instructors that discourage them from pursuing math-related opportunities (Grant et al., 2015;
Larnell, 2016; Martin, 2000, 2007, 2009; McGee et al., 2011a, 2011b; Moses et al., 2001).
Learners who are not positively math-identified then question their ability to achieve in math-
related contexts (Martin, 2000, 2009), solely use math rules to solve problems, and primarily
depend on an instructor, not themselves to solve math problems (Grant et al., 2015). These
students do not envision math’s value beyond the ways they use it currently (Martin, 2000; 2007)
(e.g., to pass test or complete homework), take the minimum number of required math courses
for completion (e.g. certification or graduation) (Martin, 2000, 2009), receive minimal math
support from instructors, family, or friends (Martin, 2000, 2007, 2009), and often negatively
associate math performance with one’s race or ethnicity (Martin, 2000, 2007, 2009; McGee et
al., 2011a, 2011b; Stinson, 2008). As expected, when some students who do not positively
identify with mathematics have challenges with course material, they may believe they cannot be
successful, question their abilities, and ultimately, give up on learning math skills (Howard et al.,
2011).
Positive mathematics identity development contributes to strong student performance in
math-learning contexts (Jackson & Wilson, 2012) and therefore is key in a study about
academically successful Black students in community college remedial mathematics. Given the
Mathematics Identity in Developmental Mathematics
37

ways that scholars have written about students’ outcomes in developmental mathematics, it is
valuable to use a construct that would help researchers and practitioners ‘makes sense’ of
learners’ mathematics experiences and influence students’ math outcomes positively. If we hope
to have a positive impact on the outcomes of Black students who are enrolled in remedial
mathematics, it is pertinent to learn about these learners’ backgrounds, so in the next section, I
review the characteristics of Black students who attend community college. I begin with a short
discussion about students of color as they are discussed in the remedial mathematics literature.
Students of Color in Community Colleges and Remedial Courses
Studying the ways that students of color experience developmental education (e.g.,
Acevedo Gill et al., Crisp et al., 2010; Crisp, et al., 2015; Solorzano et al., 2013) is a relatively
new exploration in educational research. Most often, these learners’ performance outcomes are
compared with other racial groups to determine how remediation impacts different student
groups (Bahr, 2010), thus treating race as a variable that ‘predicts’ or ‘explains’ students’ lower
success outcomes (e.g., Bahr, 2010; Boatman, 2012). For example, in Boatman’s (2012) study
of the effect of redesigned mathematics courses on students’ academic performance, she notes
this about the sample:
On average, more female and Black students were recommended for
developmental math than for college-level math…Not surprisingly, students
recommended for college-level math had higher high school grade point
averages (GPAs) on average than did students recommended for Developmental
Algebra II, as well as higher average ACT Composite and Math exam scores (p.
17).
Noting that these students’ placement in developmental education can be correlated with their
high school GPAs connects gender and race differences with lower academic performance and
leaves interpretations to the reader. Focusing on racial groups’ outcomes without considering
Mathematics Identity in Developmental Mathematics
38

these students’ experiences may perpetuate beliefs that Black students are to blame for their
remedial course placement and primarily keeps literature’s ‘eye’ on outcomes rather than
underlying issues. While some scholars primarily use race and ethnicity as a categorization
without unpacking it or seeking explanations for observed racial or ethnic differences in student
outcomes, a small group of researchers have focused on Latino students in developmental math.
(e.g., Acevedo-Gil et al., 2013; Acevedo-Gil et al., 2015; Crisp et al., 2010; Crisp et al., 2014;
Nora et al., 2012; Solorzano, et al., 2013). Although these studies offer insight on the academic
success of a group of students in remediation, they do not improve our knowledge about Black
students who are in developmental education courses, these learners’ experiences in these
classes, or even those who are successful in these courses.
Black Students in Community College
Enrollment data on community colleges in California, show that more than half of Black,
first-time students enroll in these institutions (The Campaign for College Opportunity, 2015).
Although these schools provide African-Americans greater access to higher education, the
remediation courses that many students must take before enrolling in college-level courses or
obtaining a college degree can impede their progress. Data on success rates show that
completing this sequence of courses has been challenging for some students and for others, it is
nearly impossible.
The current body of research on Black students in community colleges (e.g., Hagedorn,
Maxwell, & Hampton, 2001; Harper, 2009; Harris et al., 2008; Strayhorn, 2011, 2012; Weis,
1985a; 1985b; Wood, 2014) does not distinguish between learners in remedial education from
those who are not. Rather, researchers describe these students’ experiences uniformly regardless
of their course placement; this lack of focus on Black students in remediation presents a gap in
Mathematics Identity in Developmental Mathematics
39

the literature regarding this subgroup of students that is important to explore. To begin to
understand this subgroup of community college students, I review the characteristics of African-
Americans in community college, and then address the challenges that scholars highlight about
these students. Finally, I highlight a major focus of current studies in this body of literature:
Black males.
A majority of Black students in community college are between the ages of 19 and 22
(Strayhorn, 2011) and either attend these institutions to ‘get off the streets’ or to improve life for
them and their children (Weis, 1985a; 1985b). Many benefit from positive, student-faculty
interactions (Chang, 2005; Mayo, Murguia, & Padilla, 1995; Strayhorn, 2012; Wood & Turner,
2010) and those who have positive experiences with instructors also earn higher GPAs (Chang,
2005; Mayo et al., 1995). For these learners, building strong academic skills in high school (e.g.,
writing, critical thinking, and computation) and frequent, effective college advisement help them
to do well in college (Adelman, 1999; Fehrmann, Keith, & Reimers, 1987; Strayhorn & Johnson,
2014). Once in college, older Black students and those with fewer family obligations are more
satisfied than their younger peers who are responsible for family members (Strayhorn, 2011).
These stories about the factors that contribute to their success and satisfaction tell one story
about Blacks in community college. There are also studies that highlight the reasons for these
students’ lack of success in these institutions.
While many Blacks who enter community college intend to earn a degree or transfer to a
four-year institution (Campaign for College Opportunity, 2015; The Century Foundation, 2013),
in California, approximately one-third accomplish this goal within six years (Campaign for
College Opportunity, 2015). When these students repeat non-credit developmental education
courses (Bahr, 2010; Bailey et al., 2010), they lose both money and time (Melguizo et al., 2008)
Mathematics Identity in Developmental Mathematics
40

that they cannot recover. They often believe they must dispel negative stereotypes that exist
about their group (Weissman, Bulakowski, & Jumiko, 1998) and perhaps because of these
concerns, a large percentage of Blacks leave college before they complete a degree (Campaign
for College Opportunity, 2015; Chenoweth, 1998; Mortenson, 2001). Learning about the
successes and challenges that Black students face in community college helps us to understand
what some of these students may be experiencing in developmental education; however, a recent
focus on Black males in community college provides a more nuanced perspective of a subgroup
of Black community college learners.
Black males in community college. In response to concerns about Black males’
underperformance in community college (e.g., Bush & Bush, 2010; U.S. Department of
Education, 2008; Wood & Williams, 2013), a group of scholars sought to understand these
learners’ academic and personal experiences (e.g., Harper, 2009; Harris et al., 2008; Wood et al.,
2013, Wood, 2014). They discovered that Black males in community college are often older,
married, and have different degree expectations as compared to their Black peers in four-year
colleges (Wood, 2014). These older men are often less satisfied with their community college
experience as compared to younger peers. Their experiences, outcomes, and academic and social
engagement are influenced by several personal and environmental factors, including the ways
they have been socialized to think about school (Harris et al., 2008), concerns about racism and
stereotypes (Bush et al., 2010; Steele & Aronson, 1995), and their institutions’ failure to create
positive, collegiate environments where they can thrive (Harper, 2009). In addition to these
challenges, factors that contribute to their successes include positive student-faculty relationships
(Bush et al., 2010; Wood et al., 2010), clarity about a college major, (Hagedorn et al., 2001) and
clear, high-achievement goals (Hagedorn et al., 2001; Mason, 1998).
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41

All that scholars know about Black students in community colleges provides valuable
knowledge about why these students have challenges as well as the factors that contribute to
their success; this knowledge does not explain the experiences of Blacks in remedial math nor
those who are successful in these courses. This gap in the literature creates an area of study
about a population of learners who have not been studied extensively: Blacks who are successful
in community college developmental mathematics courses. Exploring these students’ math
experiences, learning about their mathematics identities, and the factors that contribute to their
success broadens our understanding about their experiences, informs practitioners’ educational
practices, such as classroom instruction, and can support the success of students who are not
successful in remedial math learning contexts.
Conclusion
Statistics about Black students’ placement in community college remedial mathematics
and studies about these students’ unsuccessful outcomes in these courses are well-documented.
While these types of studies are important, they do not explain the experiences of all Black
students in remediation, particularly those who are successful in developmental math. The lack
of research about these learners’ experiences prompts questions such as, why do these learners
succeed? Which factors influence their success? and What are their beliefs about themselves as
math learners? The last question, in particular, points to the need to understand these learners’
mathematics identities, which can inform how instructors engage with learners, what researchers
study, and how students who are placed in developmental education view themselves and their
abilities. Several scholars have studied the mathematics identities of Black students who have
achieved academic success in K-16 settings; fewer focus on those who achieve success in
Mathematics Identity in Developmental Mathematics
42

community college remedial math. As such, my dissertation study contributes to our
understanding about this important, yet often forgotten subgroup of learners.

Mathematics Identity in Developmental Mathematics
43

CHAPTER THREE: CONCEPTUAL FRAMEWORK
Previous conceptual approaches to studying successful students include a focus on student
self-perception/identities/beliefs, teachers, and curricula; all of which engage within a social
environment. In this dissertation study, the student is the unit of analysis. Although scholars
highlight multiple factors to explain student outcomes in remedial mathematics courses, these
considerations fail to capture the full experience of Black students who perform well in these
courses. In the following sections, I consider how a conceptual framework that incorporates
students’ perceptions of themselves and their abilities can be used to understand Black students’
performance outcomes in math remediation. I begin with a general discussion about identity
(e.g., Wenger, 1998) and then turn to mathematics identity (Anderson, 2007; Bishop, 2012;
Grant et al., 2015; Grootenboer et al., 2007; Martin, 2000; Nasir et al., 2003), the framework that
I use to understand the experiences of Black students who are successful in community college
remedial math courses.
Defining Identity
Perceptions that individuals have about who they are and what they are capable of
achieving shape their behaviors and their identity development (Gee, 2000; Nasir, 2002a). So,
the identity construct is useful for understanding students’ actions and involvement in school and
society (Nasir, 2002a; Sfard et al., 2005) and for making sense of their learning process. From a
general perspective, the term identity refers to one’s political views, vocational choices, sexual
affiliation, and personality (Santrock, 2013); students bring these beliefs, emotions, attitudes, and
life histories to the classroom (Grootenboer et al.,2006) and their beliefs shape their views and
behaviors.
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Scholars interested in the identity of Black students in math-related contexts define
identity from a slightly different perspective (e.g., Martin, 2000, 2006, 2009; Nasir & Saxe,
2003; Stinson, 2008). Identity, from this alternative perspective, involves one’s culture; it is
informed, shaped, and negotiated by community and environmental contexts (Martin, 2000;
Nasir & Saxe, 2003). For the purposes of this study, I refer to learners’ personal and academic
identities because these relate to the views that learners have of themselves in the classroom and
subsequently, influence their math learning experiences. The identities of student groups in
community college have been explored in limited ways (Harris & Wood, 2013), therefore, this
construct offers an opportunity to learn about this student population in a nuanced fashion.
Whether considering identity from a general perspective or with a focus on specific
student populations, moments in students’ lives influence their perceptions of their capabilities
and inform their interests, persistence, and academic motivations (Cobb & Hodge, 2002; Dweck,
2006; Martin, 2000; 2006). Therefore, understanding the construct of identity, or the ways that
“individuals know and name themselves” (Grootenboer, et al., 2006, p. 612), provides a frame to
consider the experiences of learners who are academically successful in community college
remedial math. Before I describe the identity framing that I used in this study, I discuss multiple
ways that identity has been studied.
Identity from multiple theoretical perspectives. Defined within several disciplines,
including psychology, post-structuralism, anthropology, and sociology, identity has been
conceptualized and studied somewhat differently across epistemologies. In Table 2, I have
outlined four frameworks from which identity has been studied (post-structuralism, psychology,
anthropology, and sociocultural). In the table, I provide the source (or locus) of identity, a
description of how identity is formed, and the authors who have written about the construct.
Mathematics Identity in Developmental Mathematics
45

Table 2: Identity defined from four theoretical perspectives (Adapted from Grootenboer, Smith, & Lowrie, 2006)
Poststructuralist Psychological Anthropological Sociocultural
Source of
identity
non-agent related
focused on
‘becoming’

self
self-concept,
self-efficacy
agency,
autonomy
cultural values and
processes

self as related to the external world
social context
human as agent
Identity
formation
a constant state of
evolution
comprised of
political and
institutional
processes
executive
functions of
self—guided
by monitoring
and choice-
making
influenced by
cultural, social
practices, and power
structures
focus is on the
cultural identity
constructed within environment
created as people live their everyday lives
individual also shapes the environment
Authors Derrida,
Foucault (1982)
Moya (1997a;
1997b)
Dweck (2006)
Erikson (1959)
Marcia (1966)
Markus &
Nurius (1986)
Oyserman &
Markus (1990)
Holland, Lachicotte,
Skinner & Cain
(1998)
Nasir (2002)
Nasir & Saxe (2003)
Wenger (1998)
Anderson (2007)
Benken , Ramirez, Li, & Wetendorf (2015)
Berry et al., (2011)
Boaler (2000)
Cobb, Gresfaldi, & Hodge (2009)
Gee (2000)
Grant, Crompton, & Ford (2015)
Grootenboer, Smith, & Lowrie, 2006;
Grootenboer & Zevenbergen (2007)
Martin (2000)
McGee & Martin (2011a, 2011b)
Nasir (2002)
Nasir & deRoyston (2013)
Stinson (2008)

Traditional psychologists have conceptualized identity as an individual phenomenon that
occurs over time, within stages or phases (e.g., Erikson, 1959; Marcia, 1966), and within a
person; identity from this perspective is stable, it does not change across social situations. In
other words, the individual, unaffected by the environment, is responsible for who she is and
ultimately becomes (e.g., Bandura, 1986; Erikson, 1959). Post-structuralists define identity
differently; they frame it as a process of ‘becoming’ which involves ongoing discussions
between people (Foucault, 1982) rather than an individual phenomenon. This ‘process of
becoming’ is what Moya (2001) refers to as “the correlation between one’s lived experience and
Mathematics Identity in Developmental Mathematics
46

social location” (p. 4), where experiences are subjective and entail “personally observing,
encountering or undergoing a particular event or situation” (Moya, 2001, p. 81) and social
location refers to the connection of one’s gender, race, class, and sexuality. In short, according
to post-structuralists, identity is shaped by life experiences and by an individual’s characteristics
(social location) in society (Moya, 1997a; 1997b). Identity, from the anthropological
perspective, focuses on the cultural group as the unit of analysis (Holland, Lachicotte, Skinner, &
Cain, 1998; Sökefeld, 1999). As such, identities are linked to the ways that groups of individuals
make meaning in activities from a collective perspective. These perspectives are created socially
and culturally in what Holland and colleagues (1998) call “figured worlds” (p. 192) or the
activities or traditions in which people figure out, or determine, who they are.
Each of these perspectives is valuable, however insufficient for this study as they either
view the individual as unaffected by the environment (psychology-based), affected by his or her
position in the world (post-structuralism-based), or part of a group that has collective experiences
(anthropology-based). Thus, they view students’ success or failure as contained to them as an
entity, the result of their position in society, or intertwined within the community. In this study
on the mathematics identity of Black students who are successful in community college
developmental math courses, their descriptions of their success, and their perceptions about the
contributions that instructors and their classroom practices have on their success, I use a
sociocultural approach to explore how these learners’ math identities are linked to their social
and cultural experiences. The sociocultural perspective helps to explain how these students,
influenced by social and cultural interactions in their lives and in the classroom, achieve
academic success in mathematics.
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The sociocultural perspective. According to Bandura (1977; 1986), the stories or
perceptions that people create about themselves (their identities) during participation in their
everyday activities, shape their learning process, inform identity, and ultimately, help them to be
academically successful or hinder their progress. This study, about Blacks who are successful in
community college developmental math courses, focuses on learners’ academic experiences and
how these experiences shape students’ mathematics identities. Studying Black students who are
successful in math-related contexts is rare; researchers have not fully explored the mathematics
identity of these students nor their success in community college developmental math courses.
Community college students spend a majority of their time on campus engaging with
instructors and peers in classrooms (Bickerstaff et al., 2012; Chang, 2005; Grubb et al., 1999);
according to sociocultural scholars, these interactions have the potential to influence what
learners believe about themselves, and ultimately, how their identities develop. These
discussions and interactions with peers and faculty can influence their success, contribute to their
anxiety and uncertainty about whether or not they belong in the environment, and shape their
beliefs about the nature of learning (Martin, 2009; Nasir, 2002b; 2009; Tate, 1995). As Blacks
have been successful in the developmental math sequence (Bahr, 2010), it is apparent that these
learners have found ways to use discussions and interactions with peers and faculty to their
benefit; the math environment and classroom culture positively influence their identity
development. Knowing that Black students achieve success in the remedial math environment
when many of their peers do not complete the developmental sequence or enter college-level
math courses, highlights the importance of exploring these successful students’ math experiences
and identity development from a sociocultural perspective. As authors of recent studies on the
progress of Black males in community colleges have reported on the environmental factors (e.g.,
Mathematics Identity in Developmental Mathematics
48

in and out of classroom interactions with faculty and social integration on campus) that influence
these learners’ outcomes (e.g., Bush et al., 2010; Harris &Wood, 2013; Wood, 2014b; Wood &
Ireland, 2014), continuing to explore learners’ math outcomes without considering the role of
environments excludes an important aspect of student identity development. In the next section
of this conceptual framework, I explore mathematics identity (Martin, 2000), a sociocultural
construct, to understand the environmental factors that shape students’ perceptions of themselves
as math doers and learners.
Mathematics Identity: Gaining an Understanding of Math Success
Mathematics Identity Defined
While the term, identity, refers to general aspects of a student’s life, mathematics
identity, a term created by Martin (2000), refers to an individuals’ deeply held beliefs about their
ability to succeed in math-related contexts. He defines mathematics identity as follows:
Mathematics identity encompasses the dispositions and deeply held beliefs that
individuals develop about their ability to participate and perform effectively in
mathematical contexts and to use mathematics to change the conditions of their lives. A
mathematics identity encompasses a person's self understandings as well as how they are
constructed by others in the context of doing mathematics. Therefore, a mathematics
identity is expressed…as a negotiated self, a negotiation between our own assertions and
the external ascriptions of others (p. 206)
Martin learned about individuals’ mathematics identity by exploring four areas of students’
beliefs: (a) ability: the learner’s ability to achieve in math; (b) instrumental value: the utility of
math knowledge in their lives; (c) obstacles and supports: limitations and opportunities in math-
related situations; and (d) incentives and approach: the motivations and strategies they use to
learn math. He used this framework to study Black students’ who were successful in junior high
school math.
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49

Martin’s (2000) study. Martin (2000) combined the concepts of mathematics identity
with mathematics socialization (students’ ability to engage with math in meaningful ways) to
create a multilevel framework to understand the achievements of Black students who were
successful in math. The first level, sociohistorical forces, refers to the differential treatment that
African-Americans have experienced in math-related contexts; this treatment negatively affects
their ability to participate in math. Community forces, the second level, assumes that African-
Americans have common experiences that they associate with being Black, such as unfair
treatment in mathematics-related situations. The third level, school forces, refers to school-based
factors that influence math learning for Black students. Individual Agency, the fourth and final
level, shows how students who are in poor and seemingly unstructured classrooms create the
internal fortitude to succeed in math despite facing a number of challenges, including differential
treatment from teachers and peers.
To understand the ways that these forces and individual agency influence learners, Martin
conducted an ethnographic study to learn how these factors contribute to Black students’ math
performance in a junior high school in Oakland, CA. He selected a predominately African-
American school that was implementing the Algebra Project Transition Curriculum, a program
designed to help African-American students learn math using contextualized methods. In
addition to classroom and school observations, Martin interviewed ten African-American
community members and parents, 35- seventh, eighth, and ninth graders, and three math
teachers. He found that students’ academic experiences were shaped by parental influences,
teachers’ and peers’ behaviors’, learners’ intrinsic desire to succeed, and their agency to do the
work necessary to excel.
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In this dissertation study about the mathematics identity of Black community college
students who are successful in remediation, I use Martin’s (2000) mathematics identity
framework as a foundation for my research for several reasons. First, given that participants in
this study are successful in mathematics at a time when researchers report that many Blacks have
not been prepared for math in community college (e.g. Bahr, 2010; Boatman, 2012; Hagedorn et
al., 1999; Wood, 2014b), studying the mathematics identity of learners who are successful in
remediation is both timely and appropriate. Next, Martin’s (2000) sample (successful African-
American students in junior high school) is similar to the group that I have chosen to study:
Black students who are successful in community college remedial math courses. Finally,
Martin’s (2000) study was innovative and novel at a time when few scholars considered that
Black students in math-related contexts could be successful at any grade level. Since then,
others have used Martin’s (2000) framework or expanded the definition to explore African-
Americans and other student groups that have been successful in K-12 and college math-related
contexts (e.g. Grant, et al., 2015; Larnell, 2016; Nasir et al., 2003; Stinson, 2008; Zavala, 2014),
but in my review of empirical studies, I did not find any that have done so in the community
college developmental math setting. To shed light on how Martin’s (2000) mathematics identity
framework has been expanded and defined in different ways to help scholars understand the
experiences of students who are successful in mathematics, next I introduce some of the topics
authors have studied using the framework and how Martin’s (2000) framework has been
developed.
Other Definitions of Mathematics Identity. Using mathematics identity frameworks,
scholars have explored a broad range of topics including, factors that contribute to students’
math success (Berry et al., 2011; Stinson, 2008), the influence of pedagogical practices on
Mathematics Identity in Developmental Mathematics
51

identity (Boaler et al, 2000), and peer influence on mathematics identity development (Solomon,
2007; Walker, 2006). Some have used Martin’s (2000) framework to understand these topics
(e.g., Borum, Hilton, & Walker, 2016; Stinson, 2008, Walker, 2011), at the same time, others
have built upon the framework or used other concepts in mathematics identity-related studies to
broaden understanding of the concept (e.g. Bishop, 2012; Grootenboer et al., 2007; Lesko &
Corpus, 2006; Nasir et al., 2003; Solomon, 2007). Table 3 (in Appendix A) shows a list of the
mathematics identity-related studies and distinguishes between scholars who use Martin’s
framework and those who use other frameworks to explore students in math-related contexts.
Of the group of 19 mathematics identity-related studies in Table 3, five researchers used
Martin’s (2000) framework, 12 expanded on the framework to create new mathematics identity
definitions, and two used other relevant constructs in mathematics identity related studies.
Scholars who expanded Martin’s (2000) framework or paired it with relevant constructs show
that combining his version of mathematics identity with other constructs enables researchers to
expand their scope of analyses and consider factors that shape student participation and success
in math. One benefit of exploring learners’ mathematics identity is that the construct helps
researchers understand what is happening at any point in a learners’ math development. To
expand on this idea, it is important to explore the ways that students’ mathematics identity
develops.
How Mathematics Identity Develops
Mathematics identity is developed during the social interactions that students have with
people in their lives, including peers, instructors, family members, and with themselves
(Anderson, 2007; Berry et al., 2011; Boaler, 1999; Boaler et al., 2000; Grootenboer &
Zevenbergen, 2008; Keck-Staley, 2010; Stinson, 2008; Terry et al., 2012; Varelas, et al., 2012;
Mathematics Identity in Developmental Mathematics
52

Walker, 2006). As students engage with others inside and outside of the classroom, they develop
perceptions about themselves as math learners, the role of mathematics in their lives, and their
mathematics identity. Researchers have categorized the factors that contribute to mathematics
identity development into four areas: (a) individual beliefs, skills, and agency, (b) out-of-school
experiences, (c) in-school experiences, and (d) race-related math beliefs (Anderson, 2007; Berry
et al., 2011; Boaler, 1999; Boaler et al., 2000; Grootenboer et al., 2008; Keck-Staley, 2010;
Martin, 2000; McGee & Martin, 2011a, 2011b; Martin, 2000; Nasir, 2009; Stinson, 2008; Terry
et al., 2012; Varelas et al., 2012; Walker, 2006). The beliefs that students hold are primarily
influenced by the people in their lives; these influences are described in the remaining sections.
As this dissertation study focuses on students’ perspectives, views of themselves, and their
mathematics identity, it is appropriate to begin this discussion on factors that influence
mathematics identity with a focus on the beliefs that students have about their connection with
mathematics.
Individual Beliefs, Skills, and Agency
Sense of Belonging in Mathematics. Beliefs that students hold about their “feelings of
membership and acceptance in the math domain,” or their sense of belonging (Good, Rattan, &
Dweck, 2012, p. 1) in math environments, influences their mathematics identity development.
This connection, or sense of belonging with math, fosters learners’ ability to score well on math
exams and exercise math-related agency (Perez-Felkner, McDonald, & Schneider, 2014; Sax,
2009; Solomon, 2007); this is especially true for Black students who are often depicted as
unlikely to achieve math success (Ladson-Billings, 2006; Martin, 2012). Researchers in higher
education have shown that sense of belonging (Hurtado & Carter, 1997; Strayhorn, 2012)— or
the feeling of ‘fitting in’ on college campuses—helps students’ know that they matter, are cared
Mathematics Identity in Developmental Mathematics
53

for, valued, accepted, and respected by others on campus (Hurtado et al., 1996; Strayhorn, 2012).
While this construct differs from the math-related sense of belonging construct with regards to
the object of the belonging, it illuminates the importance of feeling connected with one’s larger
environment, whether it is the campus or the mathematics classroom. Sense of belonging is
influenced by a number of factors (e.g. students’ age and faculty-student engagement) and plays
a role in Black men’s progress in community college (Perrakis, 2008). As such, exploring sense
of belonging from a math-focused perspective could shed light on the factors that contribute to
Black students’ feeling of ‘belonging’ in the math classroom and with mathematics, more
generally. Learning about students’ connection with mathematics is particularly important in
studies about developmental math, an area where Blacks are often marginalized in educational
research.
Grant and her colleagues (2015) and Solomon (2007) weave a sense of belonging
framework with Martin’s (2000) construct to illuminate how students’ feelings of acceptance in
the math classroom influence their willingness to participate in math activities with peers. This
relationship with math happens when learners experience being important and contributing
members of the math classroom, believe their peers and instructors support their math learning,
and integrate their own learning into the math environment (Boaler et al., 2000; Good et al.,
2012; Grant et al, 2015). For example, when students connect positively with math, know their
connection matters in class, and believe they are valued members of their math environments,
they make “intentional choice[s] to engage mathematically” (Grant et al., 2015, p. 112), develop
increased confidence in their skills, and experience the development of positive identity over
time (Boaler et al., 2000; Grant et al., 2015). Also, the belief that one can learn math has a
Mathematics Identity in Developmental Mathematics
54

positive influence on students’ sense of belonging even when negative messages exist in the
environment.
Using the sense of belonging in mathematics framework, Good and her colleagues (2012)
studied college students’ gender-based responses to mathematics-related contexts. The authors
reported that participants with a strong sense of belonging in mathematics were less anxious
about math, believed the subject had purpose in their lives, were confident in their math abilities,
and were inclined to continue to take math courses even if they had challenges. Sense of
belonging in mathematics is also important for learners who excel in mathematics. Boaler and
her colleagues (2000) found that although students were successful in Advanced Placement math
courses, some learners opted not to pursue math majors and careers because they did not connect
or feel a sense of belonging with the subject. Without a sense of belonging in mathematics,
students in math-related environments (e.g., classrooms, tutoring groups, etc.) may perceive that
math does not connect with “the type of person they believe themselves to be” (Boaler et al.,
2000, p. 9). This feeling of connection is particularly relevant for African-American students
who have heard stories about Black people’s lack of success in mathematics. As sense of
belonging in mathematics, or one’s connection with math, helps learners cultivate connections
with mathematics that encourage them to persist in math-related contexts, so does their ability to
do the math work that is assigned.
Learners’ Math-Related Skills. Mathematics identity development requires that students
have knowledge of math fundamentals and can demonstrate understanding in math-related
settings. In particular, when students exhibit strong computational skills by third grade, use
basic math functions to compute large numbers, and develop fluency with mental math
strategies, they build speed and accuracy as they develop a strong math foundation (Berry et al,
Mathematics Identity in Developmental Mathematics
55

2011). Learners can continue to develop their skills by taking upper-level math courses and
engaging in more complex material. Students who develop an appreciation for the challenge and
complexity that accompany math learning have a higher likelihood of developing strong
mathematics identity (Berry et al., 2011). Perhaps this is because their appreciation encourages
them to engage with math to understand material and not just complete homework or pass a test.
In turn, learners likely score well on school tests and standardized exams, build confidence in
their abilities and develop a positive mathematics identity (Berry et al., 2011; Boaler et al., 2000;
Martin, 2000; Stinson, 2008). Studies focused on college students show that grade improvement
contributes to learners’ mathematics identity development particularly when they have a history
of math difficulty or have failed prior math courses (Howard et al., 2011). While the
aforementioned factors contribute to students’ identity development, ultimately, agency in math
is needed for learners to take the initiative to solve math problems.
Agency in Mathematics Identity Development. Learners’ beliefs about what they can and
cannot accomplish influence the initiative they take to achieve a goal; ideas about one’s ability to
achieve influences the goals one pursues and are important for student success at any grade level.
In a study of Black men in community college, Hagedorn and her colleagues (2001) reported that
these students benefitted from their belief that they were capable of success. Regardless of
where students are in their academic development, belief in their abilities influences their
initiative to engage with a task (known as one’s agency), shapes their attempts to influence
circumstances in their lives, helps them to be “self-organizing, proactive, self-regulating, and self-
reflective” (Bandura, 2005, p. 9), and is linked with how intentional they are about the choices
they make and the goals they set (Bandura, 2005). Mathematics identity scholars (e.g., Boaler,
2000; Grant et al., 2015; Howard et al 2011; Martin, 2000; Stinson, 2008) have shown that agency
Mathematics Identity in Developmental Mathematics
56

is linked with math engagement and experiences and report that whether students are skilled in math
or struggling with the subject, interactions with family, friends, and community members can
positively influence students’ confidence, contribute to the agency they exercise in math, and
influence their mathematics identity development. This finding highlights the importance of math
experiences that take place outside of the school setting.
Out-of-School Math-Related Interactions. As discussed earlier, researchers who study
identity from the sociocultural perspective posit that learners’ interactions during their everyday
lives contribute to their identity development. While some might believe these interactions
primarily take place in math classrooms, scholars have shown that interactions students have
with family members, community members, and close friends can influence their mathematics
identity development (Berry et al, 2015; Stinson, 2008; Walker, 2012). Black males who earned
high grades in math were encouraged by family and friends who had careers in math, told them
they were skilled in math (Berry et al, 2015), and expected them to achieve academic excellence
(Stinson, 2008; Terry et al., 2012). These family members and friends helped to create what
Walker (2012) calls ‘math spaces,’ or places where “mathematics knowledge is developed,
where induction into a particular community of mathematics doers occurs, and where
relationships or interactions contribute to the development of a mathematics identity” (p. 67). In
other words, during these out-of-school math interactions and in these ‘math spaces,’ students
learn math, develop perceptions of themselves in math-related situations, and gain a sense of
what they can achieve in real-world situations.
These out-of-school experiences shape how students envision math’s connection with
their real lives, and as such, can influence the instrumental value that they believe math has for
their life. Mason (1998) reported similar findings with regards to Black community college
Mathematics Identity in Developmental Mathematics
57

male’s out-of-school interactions with alumni and mentors. These connections helped learners
envision their college program’s utility in their lives and as such, was a positive influence. Out-
of-school interactions can certainly help to shape learners’ math identity development; as
expected, similar outcomes also occur when students engage with math learning in school.
In-School Math-Related Interactions. Similar to the conversations during out-of-
school math-related interactions, in-school discussions shape students’ views of their abilities
and contribute to their identity development (Berry et al, 2015; Boaler et al., 2000; Grootenboer
& Zevenbergen, 2007; Martin, 2000; Stinson, 2008; Walker 2012). Given that learners in
community college settings spend a majority of their time in the classroom, three key
components of the math classroom are important to highlight when considering what contributes
to mathematics identity development: (a) instructors’ behaviors, (b) pedagogical practices, and
(c) learners’ interactions with peers (e.g., Anderson, 2007; Ball et al., 2001; Boaler et al., 2000;
Grant et al., 2015; Grootenboer et al., 2008; Lampert & colleagues, 2013; Martin, 2000;
Solomon, 2007; Terry et al., 2012; Walker, 2012). In this section, I discuss each of these factors
and address their relevance to students’ math identity development.
Instructors’ Behaviors. Instructors do more than teach subject matter to students; their
interactions with learners, expectations of student abilities, and demeanor in the classroom
influence whether students’ have positive or negative math experiences (Berry et al., 2011;
Boaler et al., 2000; Howard, et al., 2011; Martin, 2000; McGee & Martin, 2011a, 2011b; Stinson,
2008). Studies have shown that because of negative perceptions of faculty behaviors, some
students of color in community college often do not seek informal interactions with instructors
(Acevedo-Gill et al., 2015; Bush et al., 2010; Wood et al, 2010). Choosing not to engage with
instructors as a response to faculty behaviors can influence learners’ progress, particularly if they
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58

choose not to seek assistance when academic difficulties arise. Instructors who are perceived as
caring, supportive, engaging, and interested in learners’ personal development foster positive
student learning and mathematics identity development (Berry & McClain, 2009; Stinson, 2008;
Walker, 2012). Also, faculty who check on students’ progress, listen to their concerns,
encourage them to take higher-level courses, and demonstrate expectations for student success
by challenging them with activities that require high-level, cognitive demand and encourage
interaction and engagement with men of color in community college (Wood et al., 2010). With
these practices, faculty help students know that they believe in students and, in turn, strengthen
learners’ beliefs in their own abilities (Ladson-Billings, 1994; Stinson, 2008; Walker, 2012;
Wood et al., 2010). Beyond students’ perceptions of their instructors, how faculty members
teach course material can also influence students’ mathematics identity development.
Pedagogical Practices. Faculty’s instructional practices can strongly influence learners’
mathematics identity development. Instructors who teach in ways that are “uninspiring at best,
an intellectually and emotionally crushing at worst” (Ball et al., 2001, p. 434) can taint learners’
math experiences and hinder their interest in the subject. Those who teach to ensure
understanding, challenge and engage students, ignite their imagination, help them learn to apply
knowledge to real-life situations, encourage them to envision math’s role in their lives
(Anderson, 2007; Lampert & colleagues, 2013), and affect students in positive ways. Students in
classrooms where this type of instruction happens often develop confidence in their capabilities
and more often view difficulties as obstacles to overcome, not setbacks that discourage them
from persevering (Anderson, 2007; Grant et al., 2015). These students are also willing to take on
challenging math tasks as compared to peers in classrooms lacking challenging instruction
(Boaler et al., 2000; Borum et al., 2016; Larnell, 2016; Martin, 2000; Stinson, 2008).
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How instructors teach is equally important as what they know about the students in their
classrooms. This is because faculty’s knowledge of student culture and their approach to
learning influence their math teaching practices and ultimately, shape student mathematics
identity development (Ladson-Billings, 1997; Martin, 2007; Tate, 1995). According to critical
math scholars, collaborative and student-centered pedagogical approaches are more effective for
Black students when practiced by teachers who are culturally aware versus those who believe
that classroom learning and teaching are race neutral (Ladson-Billings, 1997; Martin, 2012;
Matthews, Jones, & Parker, 2013; McGee et al., 2011b; Stinson, Jett, & Williams, 2013; Tate,
1995). Instructors who are culturally-aware consider ways to include aspects of students’
backgrounds and home environments into classroom instruction and help learners create
connections between home and school (e.g., Civil et al., 2001; Costner, Daniels, & Clark, 2010;
Gutstein, 2003; Ladson-Billing, 1994; Tate, 1995). In math classes, these connections increase
student engagement in math learning (Aronson & Laughter, 2016) and provide a sense of the role
that math can have in their lives (Gutstein, 2003; Ladson-Billings, 1997).
Learners’ interactions with peers. While affirming student relationships with math
instructors and faculty teaching practices foster positive mathematics identity development, the
relationships that students create with peers help them to become independent thinkers and
support their mathematics identity development. Along these lines, studies show that interactions
with peers influence the progress of students of color in community college (Bush et al., 2010;
Strayhorn, 2012; Wood, 2012), however these studies considered social interactions primarily,
not students’ academic interactions with peers. During peer connections in the classroom and in
other math environments (e.g., peer tutoring), learners meet individuals who have similar
aspirations (Martin, 2000; Seymour & Hewitt, 1997; Solomon, 2007; Treisman, 1992), share
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their knowledge of subject matter (Webb & Mastergeorge, 2003), engage in group problem-
solving activities (Boaler et al., 2000; Grant et al., 2015), and reduce the chance of losing
knowledge that is shared with a partner or in a group (Hemmasi & Csanda, 2009). Some of these
peer engagement practices include examining a partner’s work, listening and responding to their
explanations, and collaborating to figure out how to solve a problem (Grant et al., 2015;
Henningsen & Stein, 1997). This type of collaborative engagement is particularly effective
when the tasks are high-level and cognitively-demanding (e.g., Henningsen et al., 1997). As
students collaborate with peers to solve challenging tasks, they develop confidence in their skills
and their peers’ skills, learn to rely more on themselves and less on classroom authority figures,
and further develop their own math skill set (Grant et al., 2015). Although peer engagement is
valuable for students and their math learning (Fullilove et al., 1990; Franke, Kazemi, & Battey,
2007; Hiebert et al., 1997), not all students have access to classrooms where teachers encourage
collaborative practices to solve challenging and cognitively-demanding math problems,
particularly Black students (Ladson-Billings, 2006). The issue of the accessibility of ideal
pedagogical practices and learning environments for Black students highlights another factor that
influences Black students’ mathematics identity development: perceptions about African-
American students’ ability to be successful in math.
Race-Related Math Beliefs. As noted earlier, stories about Black students’ failure in
mathematics is prevalent in math education literature; these stories are not new and often paint a
picture of these students’ lack of math ability, document their underachievement in math, and
make causal links between race or ethnicity and underachievement (Secada, 1992). These stories
are often used to justify the lack of accelerated math programs for African-Americans, serve as
rationale for assigning students to lower-level math courses, and become reasons to treat students
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unfairly in math-related contexts (Margolis et al., 2008; Martin, 2000). Scholars have shown that
Black students are aware of these narratives and for some, the stories influence their identity
development and school progress in negative and positive ways (Bush et al., 2010; Larnell, 2016;
Martin, 2000, 2003, 2006, 2007, 2009; McGee et al, 2011a, 2011b; Steele, 1995). Those who
are negatively affected by these stories have been deterred from pursuing higher levels of math
by instructors and counselors, thus they primarily focus on completing required math courses;
others, lacking strong math backgrounds, are often unprepared for upper-level courses and thus
are relegated to lower levels of math (Margolis et al., 2008; Martin, 2000; 2009).
Some Black students, aware of this narrative from their personal experiences, have found
ways to negotiate these negative stories about their math potential, and as a result achieve math
success. A small group of scholars have explored the ways that Black students who excel in
math make sense of these narratives, how learners view themselves in light of these stories, and
the influence these narratives have on their mathematics identity development (e.g., Berry et al.,
2011; Martin, 2000; McGee & Martin, 2011a, 2011b; Nasir 2009; Stinson, 2008). They found
that learners deal with the disparity between the narratives and their performance in different
ways; their refusal to adopt these negative narratives as their own positively influences their
mathematics identity development and contributes to their math success.
Students who frame their connection between race and mathematics positively choose to
engage with these narratives differently. Some Black students believe these stories do not reflect
their abilities, so they reframe the negative discourse and empower themselves with their stories
of success (e.g., Berry et al., 2011; McGee et al., 2011a; Stinson, 2008). Others, frustrated by
these stories, yet determined to prove their worth, engage in stereotype management to help them
achieve success (McGee et al., 2011b; Stinson, 2008). Still others opt to view math as a
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“culturally-free” (Stinson, 2008, p. 990) discipline in which students of any race or ethnicity can
succeed. With each practice, learners use what they know about their abilities and skills to
achieve math success and do not allow the negative narratives to interfere with their
achievement. Despite the positive perspectives and practices that successful Black math students
have adopted, for some, negative narratives about Blacks and math success can be taxing
because they serve as reminders that their blackness may be linked with the perception of
inferiority in mathematics and overall achievement (Bush et al., 2010; McGee et al., 2011a,
2011b; Stinson, 2008).
Even though Black students are able to reframe these discourses, and use their math
knowledge to be successful, their counter-storytelling requires that they constantly negotiate
these negative conversations (McGee et al., 2011a, 2011b; Stinson, 2008). McGee and Martin
(2011b) found that Black math and Engineering students, though academically successful, often
felt undervalued, assaulted, and out of place in their math classes. Their belief in their abilities,
support they received from others in their lives (e.g., parents, community members, and some
instructors), success in non-school-related environments where they learned math, and overall
knowledge that they could be successful, fueled their achievements. Other learners, believing
that Blacks can be successful in math, negotiate the negative narrative by viewing themselves as
“smart” and adopting “postures of confidence and challenge when [they solve] mathematics
problems” (Berry et al., 2011, p. 19). Despite this positive perspective, students reported that
they felt discomfort when they were the ‘only ones’ in the higher-level courses or the only Black
students in the general math classes who were doing well (Margolis et al., 2008). Over time,
although these students develop strong mathematics identities and have academic achievements,
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63

their success comes at a cost as they are forced to negotiate negative racial narratives about
Black students’ success in mathematics (Stinson, 2008).
Newer definitions of mathematics identity and the factors that influence mathematics
identity development reflect the value in expanding Martin’s (2000) framework when studying
Blacks who are successful in developmental math courses. In the next section, I combine
Martin’s (2000) mathematics identity with other frameworks to create one structure to explore
mathematics identity development.
Combining Martin’s (2000) Framework with Other Math Identity Constructs to Create a
New Mathematics Identity Framework
Although Martin’s (2000) mathematics identity framework provides a foundation for
exploring and understanding students’ identity, other scholars’ mathematics learning and identity
frameworks address student practices that demonstrate positive mathematics identity (e.g.,
Anderson, 2007; Grootenboer et al., 2008; Pickering, 1995) and are relevant in this study. For
example, Anderson’s (2007) Faces of Identity, Grootenboer and Zevenbergen’s (2007) Three
Dimensions of the Learning Classroom, Pickering’s (1995) and Boaler’s (2003) Dance of
Agency, and Good and colleagues’ (2012) sense of belonging in mathematics are frameworks
that can be used to explore identity-related practices and provide a deeper understanding of how
students demonstrate their mathematics identity. In the following sections, I combine Martin’s
(2000) framework with these constructs to create a single framework that I use to engage in a
comprehensive study of mathematics identity. I describe aspects of each construct and discuss
how they connect with components of Martin’s (2000) framework.
Ability and instrumental value. During math-related conversations and interactions,
students make decisions about their ability to learn and do math as well as understand the value
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64

that math will have in their lives. Anderson (2007) believes when these discussions occur during
classroom interactions and activities, learners practice the ‘faces of identity’. Derived from
social learning theories (e.g., Nasir, 2002a; Wenger, 1998), these ‘faces’ are practices that help
students develop their mathematics identity. Anderson’s (2007) first face, engagement, connects
with Martin’s (2000) first component of mathematics identity, ability, and highlights that
students gain a sense of their ability to ‘do’ and learn math when they are engaged in math class.
When instructors engage students in math activities that are collaborative and require high-level
cognitive demand, they cultivate learners who create strategies for understanding and solving
math problems, imagine being successful in math, and ultimately, identify with mathematics.
Faculty who do not engage students in collaborative and challenging activities (e.g., primarily
focusing on skill and drill
7
and lecture-based teaching) discourage creativity, deter students from
viewing themselves as math learners, and ultimately impede students’ math-identity
development.
With Anderson’s (2007) second and third faces—imagination and alignment—students
conceptualize math’s value beyond the classroom setting and take steps to improve their math
skills. Imagination, similar to Martin’s (2000) instrumental value, demonstrates how students
understand math’s role in their life. Combined with the third face, alignment, learners take steps
to build their math skills because they understand the value that math has for their lives.
Students who envision math as an important part of their life likely take required and even upper-
level math courses to gain the skills necessary for advancement. Learners who do not see math’s

7
Skill and drill pedagogy focuses on math and English subskills that students learned in grammar school, involves
heavy recitation, fails to evaluate students’ critical thinking or literacy skills, neglects teaching students to create
conceptual connections, and on its own, does not help students develop math or English proficiency (Grubb et al.,
2013)
Mathematics Identity in Developmental Mathematics
65

relevance in their lives are less likely to believe that math has utility for them (Anderson, 2007;
Martin, 2000). These learners may enroll in courses to fulfill basic math requirements for
certificate completion, but might not view themselves as math learners. While Anderson’s
(2007) faces of mathematics identity framework shows how students demonstrate mathematics
identity development, it does not provide constructs that link with Martin’s (2000) last two math
identity components (obstacles and supports and incentives and approach). Other constructs are
needed to understand how students might demonstrate mathematics identity development in
these areas.
Obstacles and supports. Students who identify obstacles to math participation and learn
how to use supports to deal with difficulties in school can overcome barriers that interfere with
their learning; with these practices, students have tangible ways to improve math learning
(Martin, 2000). Grootenboer and Zevenbergen (2007) offer three dimensions of the math
classroom that influence students’ learning experiences and foster or hinder positive identity
development. The first, the discipline of math, refers to how math is taught, how the methods
compare and contrast with the behaviors and practices of mathematicians in the field, and how
pedagogical practices support or hinder positive mathematics identity development. Next,
classroom community, includes the instructor, students, and the physical classroom, the
interactions between these components (as directed by the instructor), and the ways they
influence students’ mathematics identity development. These authors posit that if math
education’s goal is to build “a strong mathematical identity” (p. 245), then the classroom
community—and in particular, the role of the instructor—is key. Students, the final component,
enter math classes with prior math-related histories and experiences that shape their mathematics
identity. Depending on students’ experiences with each dimension, these components can appear
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as obstacles to learning math or supports that help them learn and identify with the subject
(Grootenboer et al., 2007).
Incentives and approach. Students benefit when they are motivated to learn math and
understand how to solve math problems. In studies of mathematicians and research scientists,
Pickering (1995) found that those who were skilled in the discipline solved problems by
combining their knowledge of the subject with their ability to extend and build on concepts;
when necessary, they defer to the subject’s process (e.g., checking answers to determine
accuracy); he calls this the ‘dance of agency.’ Boaler (2003) adapted Pickering’s (1995) concept
for the math classroom and notes that students who engage in this dance go beyond using rules to
solve problems; these learners also demonstrate a level of confidence in their abilities which
helps motivate them to persevere when math becomes difficult (Boaler, 2002). By combining
confidence, math knowledge, and conceptual understanding, these students develop innovative
approaches to solve math problems; they seek ways to expand their knowledge and do not
depend solely on math-based rules to solve math problems. In this study, I sought to understand
how participants approach problem-solving and whether or not any used what they learned in
current and prior math classes. Students who engage in the dance of agency also combine their
skills with confidence in their ability, an understanding of the fundamentals of math, and a
conceptual grasp of material. Learners demonstrate agency by working independently, relying
less on authority figures, using creative methods to solve problems, and expanding their
knowledge of math beyond the fundamentals (Grant et al., 2015).
An Additional Component: Sense of Belonging. While Martin’s (2000) framework is
important for students’ math identity and can influence their math performance, these factors are
only part of what is needed to build positive math identity. Development of a positive identity in
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the math classroom also requires attention to the learner’s sense of belonging with math. As
noted earlier, sense of belonging in mathematics refers to students’ “feelings of membership and
acceptance in the math domain” (Good et al., 2012, p. 1); the construct has been applied to
gender (e.g., Davies, Spencer, Quinn, Gerhardstein, 2002; Good et al., 2012; Perez-Felkner,
McDonald, & Schneider, 2014; Sax, 2009; Schmader, 2002) and less with regards to race. Given
the sociohistorical injustices that Black students have experienced in education and subsequent
exclusion from math-learning environments because of their race (Ladson-Billings, 1997;
Martin, 2000, 2006, 2009; Secada, 1992; Tate, 1994, 1995), Martin (2000; 2006; 2009)
highlights that race is an important part of math learning that must be included in discussions
about mathematics identity. Recognition of the importance of race in math education calls for
looking beyond whether or not students ‘know’ material; it requires that they have a high level of
self-esteem in math-related contexts, believe that they belong with math, and know that they can
connect with the subject in meaningful ways (Boaler, William, & Zevenbergen, 2000). As such,
sense of belonging in mathematics identity is key for students who are marginalized in math-
related conversations, in this case, African-American students.
When students have a positive sense of belonging with math (Boaler et al., 2000; Good et
al., 2012), they interact with groups of math learners in specific ways. They (a) perceive
themselves as part of the group of math learners (b) believe they can be successful in math-
related settings; (c) enjoy and are happy and comfortable in the math-related setting; (d) believe
their peers and professors support their success; (e) engage in the learning community rather than
being ‘invisible’ in learning settings; (f) engage in practices to achieve math success (e.g. attend
study groups and office hours) and (g) intend to take higher level math courses. Sense of
belonging with math is important to explore for African-Americans who achieve in
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developmental math courses as it can be used to explain these students’ math success; therefore,
it is incorporated in the comprehensive framework (in Table 4) to analyze mathematics identity.
In my review of the math identity literature, I did not find scholarship where authors
paired any of the aforementioned constructs with Martin’s (2000) components of mathematics
identity. After a review of each construct, it is apparent that they relate to aspects of Martin’s
framework, offer a sense of how mathematics identity is developed, and provide an
understanding about how students might demonstrate positive mathematics identity
development. In Table 4, I pair these constructs with Martin’s (2000) framework and describe
student behaviors that I used to guide my data analysis.
Table 4: Matching Martin’s (2000) Components of Math Identity with Relevant Frameworks and Constructs to
Highlight Behaviors that E xemplify Positive Math Identity Development
Martin’s (2000) Components
of Mathematics Identity
Anderson’s (2007) Faces of
Identity Development
Student Practices that Indicate Math Identity
Development (Anderson, 2007)
Ability: learner’s capacity to
perform in math situations
Engagement: students imagine
themselves as successful in math
Students understand mathematics context, not
just content.
They develop strategies for solving mathematics
problems and view themselves as capable in
their mathematics community
They also engage with peers in mathematics-
related discussions in the classroom (contingent
on structure of classroom activities)
Instrumental Value: the utility of
math knowledge for one’s life
Imagination: students connect
math with life experiences beyond
the classroom
Alignment: students engage in
math practices that help fulfill the
ways they imagine engagement
with math in their life.
Students view mathematics as important and
necessary for their life (e.g., career, college, and
everyday life)
Students have a positive perspective of
themselves in relation to mathematics
Students consider advanced mathematics as
necessary for postsecondary education or
employment
Students take mathematics classes beyond the
minimal requirements
Martin’s (2000) Component of
Mathematics Identity
Grootenboer & Zevenbergen’s
(2007) Three Dimensions of the
Learning Classroom
Student Practices that May Indicate Math
Identity Development
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69

Obstacles and Supports:
perceived limitations and
opportunities in math-related
contexts
Discipline of math: math pedagogy
Classroom community: instructors,
peers, and the learners and how
they interact with each other
Student: the learner who enters the
math class with a prior history that
shape their mathematics identity
Students (a) can identify the obstacles and
supports that exist in each dimension of the
classroom and (b) identify ways to use supports
to overcome difficulties.
Martin’s (2000) Component of
Mathematics Identity
Dance of Agency: Boaler (2003);
Pickering (1995)
Student Practices that May Indicate Math
Identity Development (Pickering, 1995)
Incentives and Approach:
motivations and strategies used
to learn math
Students engage in a ‘dance of
agency’ by pairing their math-
based knowledge with innovative
ways to solve problems. However,
when necessary, they ‘submit’ to
the discipline of math
Students use creative, math-based knowledge to
solve math problems. They tend to rely on
themselves and peers rather than an authority
and when necessary, are willing to defer to the
‘way that math is done’ when solving problems
(e.g. using a verification process)
An Additional Component: Sense of Belonging
(Boaler, William, & Zevenbergen, 2000; Good, Rattan, & Dweck, 2012)
Sense of Belonging
(Not part of Martin’s (2000)
framework)
Sense of belonging in the math
classroom is comprised of seven
components. Students: (a)
perceive themselves as part of a
group of math learners (b) believe
they can be successful in math-
related settings; (c) are
comfortable and happy in math
settings; (d) believe peers and
instructors support their success;
(e) actively participate in the
group; (f) engage in practices to
achieve math success (e.g. attend
study groups and office hours);
and (g) intend to take higher level
math courses
Students demonstrate a sense of belonging in the
math classroom by: (a) perceiving themselves as
part of a group of math learners (b) believing the
can be successful in math-related settings; (c)
enjoy and feel comfortable happy in math
settings; (d) believing peers and instructors
support their success; (e) participating actively
in the group; (f) engage in practices to achieve
math success (e.g. attend study groups and
office hours) and (g) intend to take higher level
math courses

Adding constructs to the math identity framework is particularly useful when studying aspects of
students’ lives that have not been explored previously or researching student populations that
have not been studied extensively; this practice provides a broader view to study mathematics
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identity development. Next, I share math identity-related studies about a group that is rarely
discussed in this literature, students in remedial math.
How Mathematics Identity Has Been Studied in Developmental Math
Although scholars have used the mathematics identity framework to study students in K-
12 settings, fewer have explored the mathematics identity of students in developmental math
courses (Benken et al., 2015; Howard et al., 2011; Larnell, 2016). Of these studies, only Larnell
(2016) explicitly use the mathematics identity construct to analyze data; the others used two
constructs: affective components (Benken et al., 2015) and Dweck’s (2006) fixed and growth
mindset (Howard et al., 2011). In each authors’ findings, they report results that were similar to
those from studies about students who have experienced positive mathematics identity
development and link to components of Martin’s (2000) framework. Benken and her colleagues
and Howard and her colleague found that as a result of engaging in developmental math courses,
participants reported improved skills and increased confidence (beliefs about ability), recognized
the importance of math outside of school (beliefs about math’s instrumental value), highlighted
the resources and personal barriers to math success (beliefs about supports and obstacles), and
increased their class participation and minimized in-class distractions (beliefs about incentives
and approach). These experiences shifted their views of math from negative to positive,
expanded their impressions of what math could provide for them in their lives, and encouraged
their participation in the subject. This shift reflected a ‘turning point’ (Howard et al., 2011) in
students’ math experiences, which encouraged them to redirect their math efforts, which helped
them achieve math success.
Larnell (2016) reported different results in his narrative study about Black students in
remedial math in a four-year university setting. According to Larnell, students who initially
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identified as high-achieving students in high school, eventually “questioned their mathematics
identities” (p. 246) during the math placement exam; this shift in their beliefs about their abilities
impacted their behavior. According to Larnell, they engaged in what Simon (1955, 1957) calls
‘satisficing,’ or behavior in which an individual pursues a ‘good enough’ rather than best option
(even when they know the best option) to achieve a goal. In the case of Larnell’s (2016)
participants, they ‘clicked through’ questions on the assessment test and ultimately were placed
into remedial math classes. These participants’ identities continued to be challenged when they
were placed into remediation and contended with negative perceptions of Black students in
remediation. This group of studies highlight that while some students who are placed into
remediation improve their mathematics identity, others have to address issues that may be the
cause of their placement into these courses, influence their classroom experiences, and
negatively affect their mathematics identity development.
Summary
Identity development, from the sociocultural perspective, is useful when exploring
student learning in math courses because it encourages researchers to observe the role that social
interactions play in student success. Mathematics identity, or the ways that students think of
themselves as math learners and doers, elevates researchers’ understanding of math students by
offering opportunities to explore how factors, such as instructor practices and behaviors, support
the identity development of learners who are successful in community college developmental
math courses. This construct also encourages researchers to consider factors—beyond student
characteristics—that contribute to math success or failure and prompts researchers to explore
what students believe about their math abilities, the subject’s instrumental value, the barriers and
opportunities that help or hinder their math progress, the incentives and behaviors that result in
Mathematics Identity in Developmental Mathematics
72

their success, and their sense of belonging with math. Said another way, mathematics identity
development encourages researchers to consider the ways that students’ math experiences help or
hinder their success.
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CHAPTER FOUR: METHODOLOGY
Narrative: The Methodology of Choice
Exploring how individuals identify as math learners and doers, the factors that contribute
to their success, and the faculty and classroom interactions that influence their progress, call for
understanding how these participants’ experiences shape their views of themselves. Narrative, a
methodology that allows for learning about another’s experiences (Clandinin & Connelly, 2000),
their emotions, thoughts, and how they interpret events (Chase, 2005) over a period of time
(Polkinghorne, 1991), is appropriate for studying these learners’ identity. Described as a
paradigm (Fisher, 1985) that informs how the researcher conducts the study, narratives are
woven from pieces of interviews, documents, and observations (Riesman, 2008), thus the
researcher can access multiple types of resources to build these stories of participants’ lives.
Within this methodology, the narrator
8
, researcher, and reader play important roles in
bringing narratives to life, while conveying the stories to others and interacting with aspects of
the narrator’s life that are relevant for the story that is being told. The narrator—who is the actor
and observer of others’ actions (Chase, 2005)—uses storytelling to make sense of experiences in
her life (Riessman, 2008). By recalling partial and somewhat disjointed memories (Riessman,
2008), she tells about the events that have informed her views and shaped who she is. While
these experiences may appear random and disconnected (Riessman, 2008), they highlight her
“uniqueness” (Chase, 2005, p. 657) among study participants. The researcher plays a
multifaceted role in this ‘narrative dance.’ In addition to becoming familiar with aspects of the
narrator’s life and part of the environment and milieus in which the narrator is situated

8
In this study, I refer to participants as the “narrator” because I view the participants as “narrators with stories to tell
and voices of their own” (Chase, 2005, p. 660).
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(Clandinin et al., 2000; Daiute, 2013; Frank, 2012), researchers are responsible for constructing
the narrative. So, after listening to the narrator’s experiences, the researcher translates these
experiences into a story, which is then presented to the reader as ‘how it is’ for the narrator
(Fisher, 1985; Riessman, 2008).
Why Use Narrative?
It seems that a simple enough answer to this question is, ‘One should use narrative
because both narrative and identity focus on a similar central components—an individual’s
stories.’ While this answer seems reasonable, it does not touch upon the nuances that
narrative—as a methodology—brings to this research study, the value that storytelling has in
everyday life and conversations, and probably most important, the link between narrative and
identity, a focus of the conceptual framework.
Narrative’s alignment with identity: meaning, construction, and temporality. A
fundamental aspect of both mathematics identity and narrative is their attention to identity; in this
study, narrators’ identity focuses on the ways that they “know and name themselves”
(Grootenboer, et al., 2006, p. 612) as math learners and doers. However, the connections
between the methodology and the conceptual framework do not stop with this link. To highlight
the relationship between the two, next I discuss three key bridges between identity and narrative:
(a) the role of meaning; (b) construction of stories; and (c) temporality in the framing.
The role of meaning. According to Daiute (2013), narrative’s power “is not so much
that it is about life, but that it interacts in life” (p. 2) [author’s emphasis]. In her conversations
about this interaction, Daiute introduces the idea of meaning and notes that it is expressed via
words, style, organization, and actions. But one might ask, “What is meaning within narrative?”
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For clarification, we can turn to Polkinghorne (1988) who defines meaning as an active and
cognitive process in which the narrator—influenced by “history, culture, and character as well as
linguistic convention” (Fisher, 1985, p. 351)—engages; it is not an object or “substance”
(Polkinghorne, 1988, p. 4) that one simply observes. Moreover, he notes that the process of
constructing meaning happens when a narrator identifies “connections or relationships among
events” (p. 6). As such, narrators make multiple connections between events throughout the
narrative meaning-making process. A similar process is used when constructing meaning in
identity—and in the case of this study, mathematics identity.
In mathematics identity, the narrator gives specific meaning to what she sees, is told, and
overhears about herself as related to mathematics (Berry et al., 2011; Grant, et al., 2015; Martin,
2000; Nasir, 2002a; Nasir et al., 2011; Stinson, 2008). However, while the making of meaning is
important, it is not the end of the identity process (the next step in the process will be discussed
in the following subsection). Although we know that both narrative and identity are influenced
by meaning, the next question becomes: how does the meaning that is made become a narrative
or shape one’s identity. For answers to this question, we can turn to the second point of
connection between narrative and identity that I highlight: the construction of stories.
Construction of stories. Construction, or the putting together of multiple parts, is an
important facet of both narrative and identity. Narrative methodologists posit that who we
become is informed by the stories that we assemble from our past experiences, our current
events, and the futures that we anticipate (Bruner, 1987; Polkinghorne, 1991; Riessman, 2008).
As noted in the previous section, narrators assign meaning to these experiences and events and
convey the meaning-filled events to the researcher. Then, the researcher organizes the events
into relevant episodes, noting the contribution that episodes (or compiled events) make “towards
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a particular outcome” (Polkinghorne, 1985, p. 6) in an individual’s life. When the episodes are
all compiled into an organized story format that is designed to convey meaningfulness (Bruner,
1991; Polkinghorne, 1988; Riesman, 2008), a full narrative is constructed.
Similarly, identity—from a sociocultural perspective— is influenced by the events that
take place in the environment, the stories that individuals hear and tell themselves about these
events, and ultimately, what they believe (Bandura, 1977; 1986). Said another way, identity is
composed of selected experiences from an individual’s life and become—for that person—‘the
way that I am’ and even, ‘the way it is.’ So ultimately, narrative and identity are comprised of
similar components: episodes or events; these become the stories that are told. Ultimately,
although identity and the narrative are often created by different individuals—identity by the
narrator and narrative by “the joint production of narrator and listener” (Chase, 2005, p. 657)—
both result in constructed stories.
As related to this study, participants’ experiences in math classrooms and their
interactions with instructors throughout their schooling influence what they believe about
themselves and subsequently, the mathematics identities that they construct. The researcher
organizes these life occurrences into a meaningful string of stories (Bruner, 1991; Chase, 2005;
Polkinghorne, 1988; Riesman, 2008), which becomes the narrative. In the case of this
dissertation study, the narrative inquiry methodology afforded this researcher the opportunity to
explore Black students’ math-related life events and stories in an effort to understand how these
experiences influence narrators’ identities as math doers and learners. Then, the researcher
constructed these narrators’ stories into a format, also known as the narrative.
Temporality in the framing. Temporality, or the passage of time, is a “major element”
(Daiute, p. 210, 2014) or “central feature” (Clandinin et al., 2000, p. 29) of narrative. While
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some narrative methodologists use the construct of time to explain how researchers can write
about the past, present, and future in narrative form (e.g., Daiute, 2013), others highlight how the
passage of time influences the narrator’s experiences beyond the present moment (Clandinin et
al., 2000; Polkinghorne, 1998). Said in another way, narrative inquiry addresses “life as it is
experienced on a continuum” (Clandinin et al., p. 19, 2000). This idea of life ‘on a continuum’ is
reminiscent of Fisher’s (1985) comments about the function of the stories that humans construct.
He notes that these stories (1) justify an individual’s prior actions or decisions and then (2) direct
the actions and decisions that they take. These behaviors also serve as a reminder that with
narrative inquiry, researchers can use data that highlight the ways narrators look to their past,
think of themselves in the present, and look toward the future creating a continuum, or sense of
progression, in their decision-making processes. These types of incidents—and the continuum
that they represent—can be represented in the narrative.
As the passage of time influences narrative construction, so it is with identity
construction. For instance, a participant who heard her grammar school math teacher utter the
words, “You’re not very good at math,” may associate negatively with this statement and believe
the comment; this influences her identity as a math student. The teacher’s words, left
unchallenged and the student’s identity, left uninterrupted, continue to shape her identity beyond
the moment in which the words were uttered; in this case, the sting of those words do not ‘stay in
the past’. In the present, those words can continue to affect the mathematics identities of learners
who have not improved and even the identities of those who are have had success in
mathematics. As related to this study, this continuum offers a sense of the ways that
participants’ mathematics identities have been (and continue to be) constructed by events from
their past, how they see themselves presently, and the way(s) they envision their futures.
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A final note on the use of narrative: Giving voice to the silenced. Narrative’s
connection with identity, makes it appropriate for use in this study not only because of the
similarities in construction, but also because the greater purpose that narrative can serve. As a
methodology that uses storytelling to convey messages about individuals and their lives,
narrative can have multiple roles. Narrative can be used to “indicate who belongs and who does
not” (Daiute, 2013, p 7), “contest historical and cultural narratives” (p. 20), and place attention
on those “who have been silenced or excluded from some public hearings of personal
experience” (Harding, 1988 as cited in Daiute, 2013, p. 10). Because narrative can serve each of
these roles, it is an appropriate methodology to study African-Americans in community colleges
who have been successful in mathematics-related contexts, yet have not been studied broadly in
literature about student success in mathematics.
Addressing Tensions in Narrative
Interpretivism and Narrative. An interpretivist paradigm, the overarching frame for
narrative methodology, foregrounds an ongoing meaning-making process. Interpretivists value
the meaning that participants assign to their own actions and other’s actions and give credence to
the researcher’s role in making choices about how to collect, analyze, and make sense of data.
Essentially, the narrator makes these decisions throughout her life (let alone during the study)
and the researcher makes interpretative decisions throughout the study (Bruner, 1991; Clandinin
et al., 2000; Riessman, 2008). Said another way, narrators, “lead storied lives and tell stories of
those lives, whereas narrative researchers describe narrators’ lives, collect and tell stories, and
write narratives of experience” (Conelly et al., 1990, p. 2). The resulting ‘narratives of
experience’ are not intended to be ‘true’ nor do they reflect the “truth of experience, [instead]
they are reflections on—not of—the world as it is known” (Denzin, 2000, p. xii-xiii). Keeping
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this interplay between interpretivism, the narrator, and researcher in mind reminds us of the
value of a narrative study. Its value lies in the work’s ability to illuminate the meaning that the
narrator has made of events and the implications that arise from these meanings that influence
the development of other work.
Keeping in mind the role that meaning-making has on the researcher’s decisions, in this
study, it was important to consider which aspects of participants’ lives I would highlight as
influential for their identity development. In part, applying mathematics identity as the
conceptual framework addressed this consideration because I focused my attention on events in
math-related contexts. However, because this study focuses on mathematics identity as it is
constructed in the classroom and with instructors, my ongoing challenge throughout the study
was to foreground discussions about math events that took place in the classroom and with
instructors, rather than math-related events that took place in other non-classroom related
settings. As some out-of-classroom experiences influenced participants’ in-classroom
experiences and their identities, at times, I chose to include out-of-classroom experiences in the
construction and the telling of the participants’ narrative. While the location of different
experiences posed one set of challenges, another tension emerged when constructing the stories.
Creating the author’s narrative versus the narrator’s narrative. Clandinin and
Connelly (2000) posit that narrative is a valuable methodology because it allows researchers to
present life experiences “in relevant and meaningful ways,” (p. 10); they also acknowledge that
authors can present inaccurate representations of narrators’ lives as reality. These fictional
depictions of participants’ lives can be constructed in multiple ways, such as altering aspects of
the data or using the data to tell the story that the author wants to tell rather than the narrator’s
story. They note that often this presentation of misinformation can occur when authors become
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wedded to the plot or the story that they are formulating and lose sight of their role as the author
who treads a ‘fine line’ as the writer of the narrative.
To address this issue in the study, I adopted Conolley’s and colleague’s (1990)
suggestion to remain engaged with participants beyond the initial data collection period. To
maintain communication with these narrators, I called, emailed, or texted them periodically to
ask about their progress in school or follow up on an issue that we discussed (e.g., one
participant and I met to create her resume after she sought a new job). These ongoing
conversations made it easy for me to reach out to them when I needed to clarify aspects of their
stories or when questions arose. As this topic extends into a discussion about trustworthiness in
this study, I address this discussion in greater detail in a later section of this chapter.
Sorting themes versus creating a narrative. Narrative’s focus on individuals’
experiences, stories, and perceptions of lived events calls for researchers who use this
methodology to consider how they will address a central tension: theory’s proper place within
the boundaries of narrative writing (Clandinin et al., 2000). Those who employ formalistic
theoretical boundaries privilege the “social structure, ideology, theory, or framework…at work in
the inquiry” (p. 39); they “include and emphasize only some features of the originals [story] and
exclude others as irrelevant to their interests” (Mishler, 1990, p. 425). As a result, they reduce
“[a] rich whole…memory” (Clandinin et al., 2000, p. 36); this process and the outcome are the
antithesis of narrative methodology’s purpose.
This tension presented a conflict for me during different aspects of the inquiry process.
From the development of initial inquiry questions to data analysis, I contended with the decision
to view data through a theoretical framework or from the perspective of the individual’s lived
experiences. Attention to either practice can minimize focus on the other. As noted earlier in
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this section, this tension continues into the writing of the narrative as the author must determine
what one can claim based on the research or what can be derived from the study’s findings.
Because narrative’s contribution is more closely aligned with creating a new understanding of
the topic being researched than producing knowledge claims that can be added to the field, there
is a way to address this dilemma while maintaining fidelity to narrative methodology.
Clandinin and Connelly (2000) suggest that researchers consider the ways events in an
individual’s life contribute to the larger narrative and recommend that the researcher review a
participant’s narrative—without a theoretical lens—to gain a holistic understanding of the
narrator’s experience before analyzing the stories as a whole. Only after gaining an
understanding of each narrator’s experiences, should the author apply theory to each story.
Then, in an effort to bring about a theoretical understanding, these authors suggest that writers
share as much of the narrator’s story as possible to explicate how conclusions are made and to
“offer readers a place to imagine their own uses and applications” (p. 42). I followed these
authors’ suggestions and explain my process later, in the data analysis section.
Neighborhood Demographics and Developmental Education at LA North
One key criticism of narrative is its excessive focus on the individual and lack of focus on
context (Connelly & Clandinin, 1990). So, to help readers gain a deeper perspective of the
neighborhood where the study takes place, I offer a description of the area where the college is
located, compare its demographics to a nearby community in the Los Angeles area, and highlight
developmental mathematics statistics at the institution. With this context, I hope to help the
reader gain a sense of the community in which some of the study participants live and attend
school, not provide ‘labels’ for these participants or pigeonhole them into ‘stereotypical boxes’.
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Sample Site. Los Angeles North City College (LA North)
9
, the research site for this
dissertation research, is located in Tonnely
10
, a fictional area in Los Angeles. This two-year
community college offers courses towards certificates as well as the Associate’s degree. The
table below (Table 5) shows the college’s ethnic, gender, and age group divisions (LA North’s
college website).
Table 5: Demographic divisions at LA North City College
Race/Ethnicity African-American 19%
Asian 6%
Latino 67%
White 7%
Other 1%

Gender Female 48%
Male 53%

Age 20-24 32%
25-34 29%
over 34 22%
under 20 17%
A recent report from LA North highlights demographics that show residents in its
neighborhood have educational and socioeconomic challenges that impact learning
opportunities; these challenges are key for understanding this study’s participants and their
stories. To develop a more in depth understanding of the campus community and surrounding
neighborhood, I draw on public census data, information from the college’s institutional research
office, and the school’s 2015 Student Equity Plan to advance the argument that residents in LA
North’s catchment area live in communities that are greatly affected by socioeconomic
challenges. While these challenges are often illuminated as factors that shape students’ lives and
inform their educational opportunities long before they arrive at LA North, it is also important to

9
LA North is a pseudonym
10
Tonnely is a pseudonym
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remember that these descriptors are based on census data and do not reflect the assets that exist
in the community (e.g., collectivistic practices, perseverance despite struggle, etc.). Therefore,
as stated earlier in this section, these are not the sole indicators that should be associated with the
community of people in LA North’s catchment area, nor the participants in this study.
Population Demographics. The 15 zip-code region which LA North serves spans 882
square miles within the Los Angeles Community College District (LA North’s website).
According to the college’s 2015 College Equity Plan, residents in these areas live in a part of Los
Angeles that is economically-disadvantaged, has challenges such as low high school and college
graduation rates, high unemployment and underemployment, and the lowest median income of
all Community College district service areas in Los Angeles. As an example of one portion of
LA North’s catchment area that reflects these challenges, the zip code which houses the college
has close to 21,000 residents in an area that spans two square miles and nearly 11,000 people per
square mile (Los Angeles Census Reporter). In a nearby wealthier community, Amberly
11
,
which is only eight miles away, a fraction of this number of residents occupy the same space
(See Table 6). As such, the area from which LA North draws its student population is densely
populated and its residents face economic challenges that are often ascribed to urban areas.
More than 90% of elementary and secondary school students within this zip code receive free or
reduced lunch and approximately 70% of the schools in the area receive Title 1 funding (LAUSD
website). According to the U.S. Department of Education, Title 1 funding is designated for
schools with high percentages of children from low socioeconomic backgrounds to ensure that
learners meet the state’s academic requirements. With such a high percentage of Title 1

11
A pseudonym
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84

designated schools in the college’s zip code, it is apparent that students in this area are not only
economically-poor, but they typically attend schools that fail them academically.
Unfortunately, the additional school funding that Title 1 provides for these schools does
not appear to have a significant impact on educational outcomes in the area (See Table 6). After
completing grade school, students’ high school, and college graduation rates are drastically lower
than rates in Amberly. A comparison of demographics, population per square mile, and
educational outcomes between adults who are 25 years and older in LA North’s area and same-
age adults in Amberly shows that those who live in LA North’s immediate vicinity graduate
from high school, attain college and graduate degrees, and earn salaries at rates that are
significantly lower than those who live in Amberly (City Data, 2015).
Table 6. Comparison between High School, College, and Post-Secondary
Graduation Rates for Adults 25 years and older in LA North’s zip code and
Amberly, a nearby wealthier community (www.opendatanetwork.com)
LA North’s zip code outcomes Amberly’s outcomes
Total population 20,000 22,000
Square miles 2 10
People per square mile 11,000 2,200
% with high school
degree or higher
55% 96%
% with four-year degree 23% 58%
% with graduate degree <10% 27%
Adjusted gross income Less than $60,000 More than $500,000
Tonnely’s high poverty rate combined with its low rate of educational outcomes are important
precursors to the next discussion: developmental mathematics outcomes and progress at LA
North.
Developmental mathematics at LA North. To understand the challenges that students
face as they go through LA North’s developmental mathematics experience, it is important to
highlight the pathway that students must take to complete mathematics courses at the college.
After taking an assessment exam to determine their mathematics skill level, students who assess
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85

below college level mathematics are placed into remedial or developmental mathematics. As
these courses are one to four levels below college-level mathematics, students in remediation can
spend from one semester to two years in the developmental sequence if they do not need to
repeat classes because of course failure or withdrawal; as the number of remedial mathematics
courses that students must take increases, their likelihood of persisting to college-level courses
decreases. Therefore, students who succeed in remedial math are among a small group of
learners who have mastered maneuvering external and internal roadblocks, such as relearning
high school material and questioning one’s skills and abilities. The difficulty of advancing in
remedial mathematics is reflected in the data in Table 7, which focuses on mathematics success
among Black, Latino, Asian, and White students at LA North.
Data in the Table 7 (from LA North’s Office of Institutional Research) shows that
although Black students at LA North comprise the second largest student population at the
college and in remedial math classes, in Spring and Summer 2016, they successfully completed
remedial-level and college-level math at the lowest rate of all four racial and ethnic groups. As a
point of clarification, under the initial study criteria, 22 students (identified by the italicized
percentages and numbers in the table) were eligible to participate in this study. Of the ten
students who engaged in this study, three participants fit this initial criteria.
Table 7: Student E nrollment and Pass Rates in 100-level and 200-level Math During Spring 2016 and Summer
2016 (LA North’s Data)

Spring 2016 Summer 2016

Remedial-level College-level Remedial-level College-level
E nrolled Passed E nrolled Passed E nrolled Passed E nrolled Passed
Black 482 41% (198) 54 30% (17) 149 39% (58) 15 33% (5)
Latino 1455 51% (742) 290 54% (157) 441 61% (269) 78 64% (50)
Asian 49 80% (39) 22 72% (16) 14 86% (12) 9 88% (8)
White 39 67% (26) 15 53% (8) 14 42% (6) 2 100% (2)
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While a review of these data show how Black students’ performance in mathematics compares
with other ethnic groups at LA North, my focus on Black students’ mathematics identities and
success moves readers away from focusing on the gap between the larger Black student
population and other racial-ethnic groups. It is more useful to understand these learners’ within-
group performance and learn how these students’ grades compare to their peers who have taken
these classes. Table 8 shows that from Fall 2013 through Spring 2016, higher percentages of
Black students withdrew from 100-level and 200-level classes than those who completed these
courses. Of those students who remained in the mathematics courses, high percentages of
students either failed the courses or earned Ds, neither of which result in earning course credit.
Table 8: Black students’ grade Distribution in 100-level and 200-Level
Mathematics Courses (Fall 2013-Spring 2016)

A B C D F W
100-level 7% 10% 20% 11% 19% 33%
200-level 10% 12% 19% 12% 18% 29%
These data reinforce that participants in this study are among a small group of students who
succeed in mathematics at LA North, in part because they continue to persist in mathematics
when their peers do not. The data about Tonnelly and LA North, more generally, help readers
understand aspects of the community that are not obvious in other parts of this dissertation.
Now, with an understanding of the larger neighborhood and math remediation outcomes, I offer
an explanation about how I gained access to LA North.
Gaining Access
Administrators at LA North, concerned about gaps in student performance in remedial
math courses and transfer outcomes for their students, contracted to work with USC’s Center for
Urban Education (CUE). With this work, administrators, staff, and faculty intended to learn how
to boost outcomes in math and English and improve overall student success and college
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87

completion, particularly for Black and Latino students. As a research assistant on the project for
approximately 17 months, I worked closely with campus gatekeepers (e.g., mathematics faculty
and institutional researchers) who assisted with the study’s details and helped me gain access to
students who participated in the research.
During a prior study at LA North, I was informed by an administrator that I could not
directly recruit study participants at the college. Instead, I had to use an intermed iary who would
help me contact participants; an assistant research analyst in the Office of Institutional Research
served in this capacity. After discussing the details of my study, I sent her a recruitment email
(see Appendix B) that she sent to students who met these criteria: (a) self-identify as African-
American (b) were placed into remedial math after taking an assessment; (c) successfully
completed the remedial math sequence; (d) successfully completed at least one college-level
math course; and (e) completed a math course during the prior semester. After approximately
three weeks had passed with no response from potential participants, I recognized that I needed
to make another request for participants and change my recruitment strategy. I expanded the
selection criteria to include students who were placed into remedial mathematics and
successfully completed at least two courses; from this effort, three participants (two women and
one man) joined the study.
Following this effort, I employed several methods to recruit the remaining study
participants. I revised the initial email sent to participants and added statements about my
personal interest in the project with the intention of creating a compelling and appealing
argument that would encourage students to participate (see Appendix B). From this effort, two
participants (men)—who fit the initial criteria—agreed to join the study. Next, I contacted three
college-level math instructors whom I had met through a colleague at LA North. Although one
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88

instructor responded and offered to announce the study in her class, no students from her class
contacted me; she did not respond to my request to visit her class to make an announcement
about the study; the other math instructors did not respond. Then, I contacted a counselor who
worked with students in one of the largest majors on campus and was known to have a good
rapport with students. Although he solicited students for the study, no potential participants
contacted me regarding the research. So, using my current resources (study participants and
faculty and administrator connections), I employed snowball sampling (Marshall & Rossman,
1999) as a secondary form of recruiting participants. In these instances, since the administration
requested that I not recruit participants directly, study participants, instructors, or faculty assisted
me; from their efforts, five additional participants joined the study (one woman and four men).
One was recruited by a participant who joined the study at an earlier point, another was recruited
by a student representative from the campus’s Black student union group, and the final three
participants were referred by faculty or staff. I sent the recruitment email to two staff and faculty
members who taught or were otherwise connected with students who took both remedial- and
college-level mathematics. While the administrator and faculty member read the recruitment
email, asked me questions to learn more about the study, and understood its purpose, neither
shared my email message with study participants. Once part of the study, participants who were
recruited by the staff member and instructor informed me that they did not know much about the
study and decided to participate either because they were both surprised and proud that an
instructor selected them for the study (a female participant) or because they wanted to support a
Black doctoral student after learning from the faculty or staff member about my race (one female
and one male). Now, with a clearer picture of the study site, I present the participants who
contributed their stories to create this dissertation.
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Participants
This section contains pertinent details about the ten participants who were interviewed for
this study. The table (Table 9) includes participants’ pseudonyms, ages, gender, major, the year
they began their first community college courses, GPA at each college they have attended, and
the mathematics courses that they have taken.
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90

Table 9: Study Participants’ Demographics
Participant’s Name Age Gender Major Year Started in
Community
College
GPA Math Courses
Currently in 1
st
College-level Math Course
Abdul-Malik Baker 37 Male Mathematics 2015 3.92 (LA North City
College)

Intro to Algebra
Elementary Algebra
Intermediate Algebra
Essentials Plane Geometry
(Trigonometry (enrolled at time of study)
Valerie Baylor

49 Female Business 2013 2.28 (Waylen City
College)
3.17 (LA North City
College)
Elementary Algebra
Intermediate Algebra
Introductory Statistics (enrolled at time of
study)
Ophelia Jackson 26 Female Baking &
Culinary Arts
2015 3.91 (LA North City
College)

Pre-Algebra
Elementary Algebra
Intermediate Algebra
College Algebra (enrolled at time of study)
Maurice Knight 28 Male Animal
Sciences
2013 2.43 (Piston City College)
3.0 (LA North City
College)
Elementary Algebra
Essentials Plane Geometry
Intermediate Algebra
College Algebra (enrolled at time of study)
Completed One or More 200-level Math Courses
Wesley Simon 40 Male Biology 2013—transferred
to a four-year state
college in 2016
3.28 (Piston City College)
3.0 (LA North City
College)

Pre-Algebra
Geometry
Intermediate Algebra
Trigonometry
Pre-Calculus
Calculus 1 (twice)
Calculus 2
Kendon Joseph 24 Male Engineering 2013 2.5 (Waylen City College)
3.24 (Piston City College)
3.0 (LA North City
College)
Elementary Algebra
Geometry
Intermediate Algebra
Statistics
Trigonometry
Pre-Calculus
Calculus 1
Calculus 2 (enrolled at time of study)
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91

Jackson Jacobsen

26 Male Engineering 2012 3.55 (Greystone City
College)
2.96 (LA North City
College)

Intermediate Algebra
Trigonometry w/ Vectors
Pre-calculus
Calculus 1 (twice)
Calculus 2 (twice)
Calculus 3 (enrolled at time of study)
E nrolled in 100-level Math Courses (Developmental Mathematics) at Time of Study
Barry Powell

30 Male Chemical
Technology
2012 2.72 (LA North City
College)
Introduction to Algebraic Concepts
Elementary Algebra
Intermediate Algebra (enrolled at time of
study)
Persia Smith

39 Female Fashion 2015 2.33 (LA North City
College)
Arithmetic
Pre-Algebra
Elementary Algebra
Nicole Vincent

30 Female Early
Childhood
Education
2012 3.66 (LA North City
College)
Arithmetic
Pre-Algebra
Elementary Algebra (enrolled at time of
study)
92

Ethical Considerations
Relationships with gatekeepers facilitated the recruitment process and highlighted the
importance of paying attention to ethical considerations. Addressing these considerations begins
by building “empowering relationships” and connections with participants (Hogan, 1988, p. 12
as cited in Connelly et al., 1990). According to the authors, Hogan (1988) notes that these
interactions develop when there is “equality, caring, and mutual purpose and intention” (p. 12) in
the researcher-narrator relationship. Therefore, in an effort to establish rapport with participants,
I shared about aspects of my life, including my family background and where I was raised, my
interest in and connection with the topic, my experiences of reading about African-American’s
low performance in mathematics, my own struggles with math, and ultimately, my interest in
highlighting their success in remedial and—when applicable—college-level math. To allay any
concerns that participants might have about disclosing any of their statements, I assured them
that they would be assigned pseudonyms and that if they allowed me to audio record their
stories, I would not share the recordings nor interview transcripts with anyone other than my
faculty advisor. I also verbally reassured them (in addition to giving them the statement in the
informed consent document) that they were not required to answer questions if they felt
uncomfortable and that they could withdraw from the study at any time. When participants
discussed sensitive topics, such as challenges that they had with instructors’ behaviors or
pedagogical practices, I was judicious in my responses in an effort not to convey judgement that
might deter them from answering other questions on the topic.
Given the researcher-centered nature of empirical studies, saying ‘thank you’ is an
important part of any study. To show my appreciation for the participants’ time and willingness
to share about their math experiences and subsequently, their lives, I used multiple methods to
93

give back to them. In addition to providing each participant with a $20 amazon.com gift card, I
worked with several participants in more personal ways. For example, I assisted one participant
with creating a resume and assisted another with the transfer application process. Upon
completion of the dissertation, I have also agreed to present study findings to the staff of the
Black Student Union group.
Data Collection
Interviews. Following the convention of narrative studies, a majority of my data
collection included semi-structured interviews with participants. While semi-structured
interviews involve using pre-defined interview questions, they also allow for a line of
questioning that is not pre-determined to arise based on the conversation in the interview
(DiCicco-Bloom & Crabtree, 2006). In total, I completed a minimum of three interviews with
each participant. On occasion, I conducted additional interviews, but only when meeting times
were curtailed because of participants’ schedules. Each interview (30 to 75 minutes in length)
was audio recorded and transcribed by a transcription service. Each session took place in an
open area in the college library, a location that was both central on campus and familiar for
participants. The topics covered in each interview are as follows: (a) experiences in mathematics
courses, (b) factors they believe helped them achieve success in math, (c) how they learn math,
(d) their mathematics instructors’ teaching practices, and (e) their understanding of how these
interactions contribute to their academic success. Each question in the protocol was constructed
using the framing of the new mathematics identity conceptual framework introduced in Chapter
Three as well as knowledge about students’ experiences as learned from my time spent at L.A.
North. For example, when asking about how participants solve math problems, I asked probing
questions using concepts from Pickering’s (1995) Dance of Agency, such as if they mostly relied
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on themselves, peers, or an authority figure when they are attempting to solve math problems or
have difficulties with material. The connections between the research questions, protocol
questions, and literature review are documented in the Literature Matrix (Appendix C)
While an interview protocol served as a guide for the discussion (see Appendix D),
conversations with participants were loosely structured, thus allowing themes to arise that might
not have emerged with strict adherence to the protocol. Additionally, I used pre-planned probes
(Brenner, 2006) as follow-up questions (e.g. “Can you say more about that,” “If I were a fly on
the wall, what would I see you doing?” “So let me see if I get this [then paraphrase what the
participant has said as a means for clarifying any misconceptions]”) because they offer greater
comparability among the data collected. Using both methods (loosely-structured interviews and
pre-planned probes), discussions moved from topic to topic and at times, narrators repeated
stories about significant events, often offering deeper insight into the ways occurrences shaped
their experiences and perceptions of themselves. This method was particularly helpful because
repetition allowed me to observe and note the concepts and ideas that were particularly important
to participants and pay attention to experiences that might contribute to their math identity
development. In an attempt to follow narrative methodology’s guidelines and allow participants
to create detailed accounts of their experiences (Riesman, 2008), I opted not to curtail their
comments or often refrained from redirecting them to the current topic when the conversation
went in a different direction than intended.
Following interviews, I wrote field notes, memos, and created contact summary sheets
(Miles & Huberman, 1994) to identify issues and themes addressed in the interview. I also
reviewed the interview recordings, highlighting the questions addressed during the discussion as
well as those areas where I missed the opportunity to probe for a deeper understanding of their
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experiences. This process helped me to identify the information that was captured, note the
information that was missed, and identify both follow-up and remaining questions for the
subsequent interview. On occasion, when I debated about how to approach a topic or probe for
deeper understanding, I consulted with my faculty advisor or three trusted colleagues to discuss
ways to resolve the issue.
While I informed participants that I would take notes during the interviews, I minimized
the amount of notetaking in an effort to pay attention to the participant’s story, follow their train
of thought, and create a more conversational environment. On occasion, when they enacted
inaudible gestures, I commented on the action verbally, with statements and questions such as,
“You seem surprised” and “What makes you smile about that?” These comments allowed me to
capture participants’ gestures on the audio recording and prompted me to include the gestures in
the written narrative.
Vignette responses. In an effort to gather multiple forms of data that I could triangulate,
I constructed and shared short, fictional vignettes about community college students’ experiences
in math class (see Appendix E). After reading the stories, participants selected and wrote about
the vignette(s) that most closely mirrored their experiences in class and math-related memories.
In an effort to address identity, the vignettes are told in story format, involve a main character (a
student), and tell about a mathematics-related experience. While all the vignettes do not contain
each aspect of the new math identity framework, every vignette contains at least one component
of the framework. As most participants completed the vignette write-up during the first
interview, their responses guided a portion of our discussions in subsequent interviews, these
vignettes served as prompts for more detailed descriptions of actual events in their lives and
offered opportunities to probe further to uncover other aspects of participants’ mathematics
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identity construction. Our discussions about the vignettes also helped to confirm stories that
participants shared previously or offered additional opportunities to ask probing questions to gain
a greater understanding of their experiences and identities.
Math education history maps. A math education history map (see Appendix F) is the
third form of data collection in this study. Using Martin’s (2000) framework as a guide to help
participants recall memories during K-12 and college years, I asked them to share words or
phrases that described their perceptions of their abilities, motivating factors, challenges,
opportunities, and experiences with memorable instructors and peers in math classrooms. As
identity is framed by the stories that individuals hear from others and create about themselves,
we discussed the words and phrases that they used and they linked the statements to experiences
in ways that helped to build an understanding about how their mathematics identities had been
constructed over the years. In general, these math education history maps were completed
during the second interview and the results of the maps, including their accompanying stories
were used to triangulate participants’ responses during the data analysis process.
Academic Transcripts. To confirm participants’ grades and completed math courses,
each participant provided academic transcripts from each of the institutions that they attended.
Typically, we reviewed these transcripts together during the second interview and I asked them
to highlight challenges and successes that they had during each course. In some cases, reviewing
the transcripts and discussing the events that took place around the courses provided fodder for
narrators’ stories, particularly if their grades in mathematics courses were considerably higher or
lower from previous semesters. These stories also served as a way to understand the experiences
that informed their math identity development in each of their community college math courses.
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Data Analysis and Presentation
In a conversation about the relationship of narrative, time, and memory, Riessman (2008)
(citing Frank (1995) and White & Epston (1990)) notes that people “turn to narrative to excavate
and reassess memories that may have been fragmented…or scarcely visible before narrating
them” (p 8). It is through this process that individuals recall the interactions they have had with
others, make sense of their past, and ultimately, construct their identities through the stories they
tell to themselves and the ones that they share. It is from this perspective that I analyzed data for
this study—keeping an eye on the ways that participants discussed their past, the influence that
the past might have had on them in the present, and the ways they see themselves in the future.
Review of Data. Keeping the aforementioned formalistic tension in mind, during the
initial read of interviews, vignette responses, and math educational history maps, I sought to
understand the narrators’ experience without a theoretical lens. During the second review of the
data, I used an inductive approach to determine the ways in which narrators spoke about their
mathematics experiences and resulting identities, sought connections within each participant’s
collected data, and looked for the frequency with which they mentioned aspects of an experience
as this might indicate (1) the relevance the experience has had for identity development and (2)
stories that can be used to build a narrative. At the same time, I searched for the ways that
participants spoke about themselves academically, with a focus on their impressions of
themselves in math-related contexts. During the third review of the data, I slotted quotes from
the transcripts into an Excel coding table that was created using the project codebook (see
Appendices G and H) as an organizing tool. Combined with the contact summary sheets that I
created following each interview, these tracking systems helped clarify which aspects of the
research questions and conceptual framework had been addressed, which aspects still remained,
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which new questions arose, any ‘holes’ or gaps in the data, as well as any inconsistencies that
emerged within the data collection process. For example, if I noticed that I did not have enough
information about engagement between a participant and math faculty, I made a point of asking
about the topic during our next meeting. I engaged in this process throughout data collection and
analysis.
Constructing the narrative. Again, keeping the formalistic vs. narrative tension at the
forefront during analysis, I attended to the task of creating each narrator’s story from the
collected data, and put aside the Excel spreadsheet, which contained results of my earlier coding
process. To guide the construction of the narratives, I used a combination of Labov’s (1984),
Labov & Waletzky (2003), and Polkinghorne’s (1995) guidelines for constructing narratives
(Table 10). I opted to use both authors’ lists to construct the stories because although each has
similar elements, each also contains key components that the other does not have. For example,
Polkinghorne states that the story should be easy to understand and credible while Labov and
Labov and Waletzky does not. Similarly, Labov (1984) and Labov & Waletzky’s( 2003) list
includes a coda, while Polkinghorne (1995) does not make the same suggestion.
Table 10: Polkinghorne’s (1995) and Labov (1984) and Labov & Waletzky’s (2003) Guidelines for Analyzing
Narrative
Polkinghorne Labov; Labov & Waletzky
Highlighting the cultural context where the story
occurs
Abstract: main focus of the story
Narrator’s spatial and temporal location Orientation: as related to time, place, characters,
situation
Narrator’s perspective of the world, including
struggles, purpose, motivations, interests
Complicating action: sequencing of events or plot,
typically includes a crisis or turning point.
Interplay of others who influence narrator’s goals and
actions
Evaluation: point when author ‘appears’ to comment
on the meaning and communicate emotions (Riessman
refers to this as the ‘soul’ of the narrative)
Habits, behaviors, or thought patterns along with their
efforts to create new patterns and actions
Resolution: outcome
Ways in which narrator’s story is distinct from other
narrators.
Coda: ending of the story, which brings readers back to
the present
Story must be easy to understand and credible
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Creating the story. During the course of emplotment, I first considered how I would
order the resulting stories. I wanted to represent narrators’ experiences in ways that would
highlight significant events in their lives and elucidate how their mathematics identity developed
over time. So while I start and end each story in the present—beginning each with our first
encounter and ending each with aspects of our final conversation (in all but one narrative)—in
the middle, I shared about their math-related experiences throughout their academic careers,
touching on their past, present, and futures.
Constructing these stories involved a sequence of steps that began with the transcribed
interviews (each interview ranged between 17 and 39 single-spaced pages in length), vignette
responses, math educational history maps, and transcripts. To understand the order in which
events occurred, I re-read each document, copying and pasting (or typing from vignette
responses) the narrator’s retelling of events (or their quoted statements) in a Microsoft Word
document under these main headers: (a) background, (b) schooling in chronological order (by
school grade level—early years, high school, college), (c) factors contributing to success, (d)
interactions with instructors and (e) other. The ‘other’ section served as a sort of repository for
important information that did not fit into other categories. Adding this level of specificity to the
creation of the stories was important because although the protocol questions addressed
narrators’ math memories during certain periods of time in their lives (e.g., earliest math
memory) as well as particular topics (e.g. factors that contributed to their success), individuals
were not confined to talking only about events that related to the protocol; therefore, our
conversations were not linear. Recalling the non-linearity of the data collection process as I
constructed the stories was particularly important during the latter stages of narrative
construction. After constructing the chronological outline for each narrative, I printed the
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document, making it easy for review, marking up the outline, as well as ‘touching’ each
participant’s story and creating a tactile connection with the data.
While reading the chronological outlines, I sought to answer several questions including:
When did the events that narrators indicate as significant take place? How do the narrators
indicate that the events influence the way(s) they think of themselves as math doers and learners?
Do any of these events happen on multiple occasions? Are there patterns that arise indicating the
need for closer attention to that episode? Answering these questions as I sorted out the story’s
chronology required making sense of the constructed story and editing redundant information
(unless it contradicted other aspects of the story and needed to be clarified—i.e., narrative
smoothing). In cases when I could not make sense of a series of events after reviewing collected
data, I contacted the narrators directly via text message or email, set up a time to speak, and
asked them to help clarify the contradiction. I engaged in this practice of organizing and
verifying throughout the writing process. In each of the stories, I used low-inference descriptors
(Johnson & Christensen, 2012) to help readers experience the narrators’ actual language and
dialect. As such there are instances when narrators use African-American Vernacular English;
this language is not adjusted to fit Standard American English.
Of the ten participants who were interviewed, five participants’ stories are presented in
Chapter Five as narratives. A review of the table in Chapter One shows that those whose stories
are presented completed the remedial math sequence and were either enrolled in their first
college-level remedial math course or completed multiple college-level courses. The participants
whose narratives are not presented in Chapter Six were excluded for one of two reasons: (1)
three participants had not completed the remedial math sequence yet and (2) the key features in
two participant’s stories were replicated in other stories. In the event that participants’ stories are
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not included in Chapter Five, but contain noteworthy information, that information is included in
a relevant table at the end of the chapter.
Analyzing the Narratives. After creating the emplotted narratives, I returned to these
stories to synthesize the themes that emerged across the participants in this study. I presented
these themes in the penultimate chapter of this dissertation in an effort to offer readers a
theoretical understanding of the mathematics identity of Black students who are successful in
remedial mathematics at institutions like LA North. To achieve this, I engaged in the process of
analyzing the narratives (Polkinghorne, 1995), a more formalistic approach. This multi-step
process began with reviewing each narrative (21-43 pages in length) and making notations to
highlight the utterances most closely related to the components of the conceptual framework.
Next, as I reviewed the data from the narratives, searching for common elements, I identified
aspects of the narratives that were common across each story and as such revealed concepts and
categories to be addressed. To keep track of the emerging themes I grouped related quotes
within each theme into a three-ring binder. Putting the documents into a binder made it easy to
restructure the organization of the themes as needed when new categories emerged across the
narratives.
Regarding participants for whom I did not write narratives, I reviewed the excel
spreadsheet that I created from the interview transcripts, searching for themes that emerged in
their interviews; I did the same with their vignette responses and math educational history maps.
At the close of Chapter Five, I include tables that represent all participants’ perspectives and
include the participants for whom I did not write narratives in an effort to offer readers an
understanding of how these participants’ responses fit into the discussion of some of the themes
presented in Chapter Six.
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Trustworthiness
Qualitative studies, particularly when conducted by one researcher, often prompt the
question, “Why should we believe it?” (Bosk, as cited by Riessman, 2008, p. 184). Narrative
researchers are not bound by the same types of external validity as quantitative researchers, nor
do the former intend to establish validity in the traditional sense (Mishler, 1990). Yet it is
important that researchers who use narrative methodology establish trustworthiness in the story
told by the narrator and in the analysis conducted by the researcher (Riessman, 2008). As there
is no one ‘correct’ set of steps that should be employed to establish trustworthiness, researchers
are prompted to make arguments “to persuade audiences about the trustworthiness of their data
and interpretations” (Riessman, 2008, p. 186).
Given the interpretative nature of narrative, and in turn, this study, I employed
Reissman’s (2008) four suggested practices that interpretivists can use to create “credible,”
“valid” and “useful” (p. 183) accounts of communication. I offer these four practices along with
an explanation of how I achieved each of these in this study. First, Reissman suggests that
authors carefully document the process used to collect and document and interpret data. In this
study, this is achieved and discussed earlier in this chapter in the subsections that address data
collection. Next, she recommends that authors rely on detailed transcripts. To fulfill this
recommendation, I employed word-for-word transcription of the recorded interviews. In the
penultimate suggestion, she notes the importance of acknowledging the dialogic nature of
narrative. I achieved this earlier when I described the importance of the ‘back-and-forth’ nature
of conversations between the narrator and author. Finally, Reissman recommends that authors
provide a comparative approach during narrative analysis. In Chapter Six, I achieve this by
discussing aspects of participants’ experiences that are similar and different from each other.
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I also engaged in a member checking (Johnson et al., 2012) process with each narrator to
ensure that my interpretations of their words align with their intentions. To accomplish this,
after writing each narrative, I shared the story with the participant for whom I wrote the story,
gave her or him a few days to read the narrative, and then spoke or emailed with her or him to
obtain feedback on the story. I requested feedback in four key areas: issues of misrepresentation,
adequate representation of their stories, selection of the pseudonym, and agreement/comfort with
details that have been excluded for purpose of story flow. Three of the participants responded
and let me know that the stories were accurate reflections of their lives and as a result, they had
no changes. Two others shared their suggestions for changes in email or in telephone
conversations that lasted approximately 30 to 45 minutes. One participant (a Muslim gentleman)
requested that I change his pseudonym because the name given was not reflective of names that
are allowed in his faith. He shared a website with me so I would know which names could be
used for a pseudonym; I thanked him for this correction and selected a new name. The other
participant, after reading the narrative, made two requests: (1) that I change an instructional
practice that I incorrectly assigned to a faculty member (she provided an alternative example)
and (2) she asked if I had altered her language in the narrative, “in reference to the amount of
slang used (wanna, gettin', cus') and lack of complete sentences.” In response, I sent her a PDF
of a transcript so she could review our conversation and noted that I also used slang in our
discussions. I reassured her that this change in speech pattern is often the result of being
comfortable when speaking with others. Eventually, she agreed to keeping the dialogic patterns
as they were transcribed. In addition to serving as opportunities for member checks, these
conversations and email connections were also chances to learn about updates in the narrators’
lives, including their progress in mathematics.
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Study Limitations
While the learning that can be derived from this narrative study is promising, there are
limitations. In current mathematics identity literature, several scholars have foregrounded
discussions about students’ race or ethnicity and how these influence mathematics experiences
and identity development (e.g., Martin, 2000; McGee & Martin, 2011; McGee, 2013; Zavala,
2014). Although I explored the role of race in students’ mathematics identity development in the
conceptual framework, I opted not to foreground the influence of race or ethnicity in the
interview protocol. Rather, I allowed this topic to emerge during the interviews. Considering
the number of times that the topic arose—unprompted—in the interviews with some participants,
when others did not explicitly mention race or ethnicity, eventually, I followed up with questions
about their race-related experiences in math classes or environments if discussions about race did
not emerge naturally.
Next, while I have provided the context of the neighborhood, seven of the ten participants
in the study were raised in LA North’s catchment area. This limitation can encourage some to
believe that the other participants are not subject to the same challenges as the Los Angeles
natives in this study; this presumption is incorrect. Two of the three remaining participants
currently live in LA North’s immediate neighborhood and like others, shared about their lack of
academic resources as children and/or financial challenges as adults. While the third participant
currently lives in a wealthier neighborhood, the family’s move to a new socioeconomic status
was a recent event at the time of the study. According to the participant, her family had few
financial resources when she was growing up and as such, they moved to California seeking a
‘new life.’
Third, as a Black, college-educated individual who studies the field of education, I
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recognize that I have certain biases that may inform how I interpret participants’ responses. I
was mindful of these biases as I listened to the narrator’s responses, probed for further
understanding, analyzed their interview transcripts, vignette responses, and math education
history maps. Given that my study data represent a small population of students enrolled in
remedial math courses at these institutions, my findings are not intended to be generalizable.
Rather, as a narrative study’s outcomes are “for the vicarious testing of the life possibilities by
readers of the research that they permit” (Clandinin et al., 2000, p. 42), the following narratives
and subsequent themes presented in Chapters Five and Six, respectively, should be interpreted as
exploratory.
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CHAPTER FIVE: NARRATIVES
Introduction to Narratives
The narratives that follow in this chapter tell the experiences of five Black students (one
female and four males) at LA North who have been successful in developmental mathematics.
Each story is divided into a minimum of eight sections that highlight students’ math-related
experiences at different points of their lives and in their academic careers. Each narrative
includes the following:
(1) Background: This section serves as an introduction to each participant, highlighting aspects
of our first encounter, details about their current lives, academic major, and career aspirations
(when data are available). In some cases, I include information about the life trajectory that led
the participant to L.A. North.
(2) Early years: In this subsection of each narrative, readers learn details about participants’
early math experiences, often with a focus on their elementary school years; when information
was provided about grammar and junior high school years, that information was included also.
Stories include memorable mathematics experiences—some positive and some negative—to
provide an understanding of their early history.
(3) High school years: Similar to the information in the early years, this section includes
participants’ math-related high school memories. Again, some have positive recollections and
other memories are negative.
(4) College: This section covers participants’ previous and current college experiences. Similar
to the previous sections, they address key features of their math experiences, but different from
prior sections, they may include non-mathematics related activities (e.g. experiences at the
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tutoring center, family-related episodes, etc.) because these reflect broader facets of participants’
lives and are key in understanding ‘how it is’ for the narrator (Fisher, 1985; Riessman, 2008).
(5) Motivation: Participants tell what encourages them to continue to study math, particularly
when they have difficulty with the subject; this section is not addressed in each narrative
(6) Success: This section includes, participants’ practical, emotional, and relational practices that
have helped them achieve success in mathematics.
(7) Instructors: This section highlights the positive and negative episodes that participants have
had with instructors, focusing on pedagogical practices and relational practices. Two instructors
who are important to note in this section are Professors Rivera and Bhattacharya as they are
participants in LA North's efforts to improve Black and Latino students’ academic outcomes.
(8) Other sections (labeled accordingly): As participants have had different experiences, these
‘other’ sections illuminate key occurrences in their math-related experiences (e.g., racial
experiences, turning points in their math performance, current math experiences, etc.) and how
they have influenced participants’ math experiences and subsequently, their mathematics
identity.
Additional Data
While I do not include all participants’ narratives in this chapter, following their stories, I
present a section entitled, “Suggestions from the Resident Experts” where I feature participants’
suggestions to faculty who teach in developmental math courses; in this section, I include
comments from all of the participants in this study. I chose to include statements from those
whose narratives have not been presented in this chapter because these participants offered
insightful suggestions that readers may find beneficial as they consider these learners’
experiences in developmental mathematics.
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Unlike any other section in this narrative, this section presents the data as a roundtable
discussion between the study participants. I chose this format for two reasons. First, as the
earlier sections of this chapter were presented as narratives, I follow suit in this subsection to
preserve the narrative structure of the presentation. Second, I consider these participants to be
the experts on the types of experiences that would make a difference for students in
developmental education, therefore setting this section up as a roundtable discussion formalizes
the interactions in a way that I would not achieve by simply reporting their comments. An
important aspect to note is although I fictionalized the format of the conversation for the
purposes of this dissertation, the suggestions are the study participants’. As noted earlier, this
section contains comments from all participants who participated in this study, not solely the
ones presented in this chapter’s narratives.
Finally, near the close of this chapter, I provide tables that feature an overview of all
participants’ responses to key themes discussed in Chapter Six. As noted in Chapter Four, while
I present the narratives on five of the ten participants in the sample, these tables include all of the
participants’ responses in an effort to offer readers a comprehensive overview of participants’
beliefs and their experiences as related to the themes addressed in Chapter Six.
Presentation of Narratives
As noted earlier, five participants’ narratives are included in this chapter: Ophelia
Jackson, Wesley Simon, Maurice Knight, Abdul-Malik Baker, and Kendon Davis. Although
ordered randomly, similarities are noted across stories where appropriate. Starting with the only
female participant that is featured in this dissertation, we turn to Ophelia Jackson’s narrative.
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Ophelia Jackson—“You can’t pray for an A and study for a C!”
Background
Ophelia Jackson, a 28-year old professional baking and pastry arts student, came to this
study through Ms. Rivera, a 100-level and 200-level math instructor at LA North. In Ms.
Rivera’s email communication with me, she described Ophelia as, “an excellent student.” On
the day that we are scheduled to meet, Ophelia approaches me as I am writing notes at a table
near the back of the library. She had texted me to say that she was coming, and that I would be
able to recognize her by her uniform: the black and white checkered pants of students in the
culinary arts program. I ask her to tell me about herself.
“My family's originally from Chicago, Illinois. We moved here in ’94 or ’95, after the
earthquake. We’ve been out here since.” She transitions to a conversation about her life
following high school. “After 2006, I attempted to go to college for a little bit. I went to [an arts-
based program] for about a year, but I didn’t take any math courses. It was just mainly culinary,
hands on.” Wondering what encouraged her to return to school, I ask Ophelia. She begins by
sharing about her first stint in college.
I was at a point in my life where I wasn’t taking school very seriously, so I ended up
dropping out to get a job. Then I just started working all those years. Boosted my way up
all the way to store manager of a women’s clothing store, and that’s what I was doing
before I decided that it was time to go back to school. I wasn’t doin’ what I was loving.
Like when you go to work and you’re just like, “I do not wanna be here. Why am I
here?” My fiancé, he was very supportive. He was like, “Quit your job and go to school.
I’ll take care of everything. That’s what I want you to do. As far high up as you wanna
go. If you wanna get your PhD, go ahead.”
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Curious about her future, I ask her plans for school. “This is my last semester to earn my
Associates degree. Then I’m planning on transferring next year. I haven’t really decided on
which college, but I’m in between [California State schools] for business.” We transition into a
conversation about career plans.
I want to eventually open up my own bakery café, but I wanna know the ins and outs of
the business. I want a major in business but a focus in entrepreneurship. I don’t wanna
have to pay someone to basically run my books or tell me how to manage my business or
anything like that. I wanna know everything that there is to know before I jump in it.”
I ask Ophelia if she thinks mathematics is relevant for her chosen career.
It’s definitely gonna be important, because money is important [laughs]. It’s gonna help
me. I have a couple more math classes that I need to take, as far as I still need statistics.
That way, I can learn about the different scenarios and what can happen and go on in the
business. Even if…
12
my café idea doesn’t take off or say it doesn’t go as successful as I
want it to, havin’ a degree in business is gonna help me to at least be able to land a job
somewhere else.
Although Ophelia easily links mathematics with her career now, she did not always have this
perspective. During each of our meetings, we talk about her ups and downs with the subject in
her early years. At the start of our first conversation about her early mathematics experiences,
Ophelia begins with a positive mathematics memory.
The Early Years

12
The ellipse (…) in statements indicates that I have removed words to consolidate two sentences that address the
same idea into one statement.
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Elementary and Middle School: “You would be takin’ an exam, and then you’d be
singin’ the little song in your head tryin’ to get it.” Ophelia describes her elementary school
memories of mathematics as “fun”— she recounts how her teacher, Mrs. Jefferson, engaged
students by “bring[ing] in…real apples, real [jelly]beans, or real candy for you to [count]—she
would try to make it relate and make it fun and interesting so that…you just be like, ‘Really
we’re counting or learning how to multiply?’” Laughing, I ask, “What else did she do?”
Ophelia says, “Oh, she used to make up math songs to try to make you memorize
multiplication…You would be takin’ an exam, and then you’d be singin’ the little song in your
head tryin’ to get it [chuckles].” Ophelia reflects on these times and says, “I think she knew that
[math] is not a subject that everybody likes.” Her teacher’s strategies helped Ophelia to
understand the material and feel good about herself as a learner. “I was pretty good, pretty basic.
I mean, you learn your addition, your subtraction. They start introducing your multiplication,
division, things like that. I grasped those pretty well.” Unfortunately, Ophelia’s sweet memories
of mathematics in elementary school soured once she arrived in middle school.
Ophelia often has a cheerful, even sunny disposition during our conversations; her
demeanor changes when she speaks about her experiences and performance in mathematics
during her middle, junior high, and high school years. Speaking in a tone that was a bit more
subdued, she reveals, “Middle school is when it kinda shifted for me when it came to
math….The deeper into math that we got the more lost that I became. [M]y abilities were poor
and my grades reflected that as well.” With a small crinkle between her eyebrows, showing
displeasure, she talks about her experiences when she had to solve word problems, “I didn't
understand how to do them. If you get a problem and it's asking you to do something, you're like,
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‘I see the instruction, but what is it asking me to do?’” This trend of struggle continued even
after she graduated from middle school and worsened when she matriculated to junior high.
Junior High—“What don’t you get? What don’t you understand? It’s simple.”
Teaching practices influenced Ophelia’s feelings about mathematics and although she does not
blame her instructors for her performance, she shares with me about her sixth grade math
teacher, Ms. Joilet. “She would try to explain it, [but] at least half of us did not get it.” I begin
to think, “What Ms. Joilet would say or do when students didn’t understand the material?” so I
ask Ophelia how her teacher handled these situations. She recalls,
Ophelia: I remember in junior high school, you would ask, “Okay. Well, I don’t
understand it. She’d say, “What don’t you get? What don’t you understand? It’s
simple.” It’s like, okay. Then you get to a point where you just don’t ask any
more questions…You don’t wanna be ridiculed or scolded or made to look—or
be embarrassed in front of your classmates. Like, I don’t really wanna ask,
especially if the person next to you is gettin’ it.
Maxine: Did that ever happen to you?
Ophelia: Oh, yeah. I’d never forget that. The girl sittin’ next to me is like, “Everybody
else is gettin’ it. How come you don’t get it? I understand what’s goin’ on.”
Maxine: How did those responses affect you, if at all?
Ophelia: I didn’t ask a lot more questions after that, honestly. I really didn’t. I did not ask
any more questions. If I was still lost during lecture, I’m not saying nothing. I
didn’t participate much with trying to ask questions and things like that. It
negatively impacted me. I didn’t even think about that until now.
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Her decision to remain quiet, combined with a junior high mathematics ability that she
categorizes as, “poor and basic,” resulted in “a D in math.” To her surprise, “It was at a point in
time where they would just pass you through, cuz they didn’t want you to just stay at a standstill.
You gotta D. You can go ahead and move on to the next grade.” So she did. On the first day of
seventh grade, she walked into her mathematics classroom and saw Ms. Joilet. “I was not happy
when I got to seventh grade and saw I had the same math teacher. I was like, ‘Are you serious?’”
Mrs. Joliet’s toolkit of interpersonal interactions with students and teaching skills had not
changed from the prior year, so Ophelia’s seventh grade mathematics experiences mirrored her
sixth grade experiences. Resting her head on her fist, with a look of chagrin, she mumbles, “I
got a D, and I was able to go ahead and go on.”
In eighth grade, she had a new instructor. I wondered if having a different teacher
helped: “Did this change things for you?” Although Ophelia admits that she “got a little better,”
she also notes, “[W]e had classrooms that were full. You can only spend so much one-on-one
time with students in very full classes.” That year, Ophelia earned a C and then moved on to
high school.
High School—“I felt really stupid. I felt very ignorant.” Our voyage into Ophelia’s
high school mathematics experiences was replete with disheartening stories. She continues to
characterize her mathematics skills as “basic,” and shares about her relationship with
mathematics in ways that reflect her difficulties.
It was horrible. Math was completely, totally, utterly horrible and stressful. Very, very
stressful. If it were a person it prob'ly wouldn't like me either. I gotta do it, and we hafta
find some way to get on. I hafta to find some way to force myself to try to understand
this, to try to get it.
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Ophelia’s high school experiences were not much different from her middle and junior high
school memories. About her ninth grade year she mentions, “I didn't do very well in algebra. I
failed algebra, completely literally failed. I failed algebra I think twice.” With a look of
annoyance, she says, “I didn't understand the purpose, reasoning, or the logic. Who in their right
mind came up with the idea to mix the alphabet and numbers together? And for what purpose?”
Her experience in geometry was different, “Geometry wasn't bad. I got a B. I was so grateful for
the fact that I was able to bypass algebra and then just take somethin' else. I graduated high
school because they allowed me to substitute geometry for algebra.”
During each mathematics course during her early years, Ophelia dealt with confusion
with the material, frustration with her lack of understanding, and disappointment with her
performance. Despite these feelings, she passed classes. At this point, talking about Ophelia’s
motivation to pass classes seems apropos, so I ask about what incentivizes her.
Motivation—“ Let me just get up outta here, so I don't have to deal with [math]
anymore except when I wanna count money” Although Ophelia dreaded her high school
mathematics experiences, a thought motivated her to pass classes and reflected her struggle
during those years. “Let me just get up outta here, so I don't have to deal with [math] anymore
except when I wanna count money…cuz college is optional.” To accomplish this goal, Ophelia
knew she would need help, so she sought out different resources.
Ophelia went to a mathematics teacher for help with course material. “He would [say],
‘Well, come ahead. Stay behind, and we can go over it.’ He would really try. I was just not
getting it.” Ophelia also sought help from her mother, but the outcome was the same. She looks
down at the table and somberly recalls,
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My mother, she was a little disappointed, cuz when she grew up, she was straight A
student. She’s like, ‘I did so good in math, and your dad’s good at math. What’s goin’ on,
honey?’ You’re just like, ‘I don’t know. How come I’m not getting it?’ It made me feel—
I felt really ignorant and just like—just really ignorant and stupid. I just didn’t understand
why I wasn’t getting it.
At that time, Ophelia could not grasp the reasons for her difficulties with mathematics.
We talked about perceptions she had about herself during those years.
Maxine: Okay…Let’s see. How did you feel for yourself—to go back to high school or a
little bit. How did you feel if you didn’t understand a concept or an idea in
math?
Ophelia: Okay. Well, I’m gonna go with my first word when you started saying, that I
was stupid. Yeah.
Maxine: Yeah. Can you tell me—?
In a tone that reflects both the frustration and despondence of those years, she recalls,
Ophelia: I really did. I felt really stupid. I felt very ignorant. It made me feel bad. Like
how come every—how come this person’s gettin’ it and that person’s gettin’ it,
and I don’t understand… I didn’t [even] wanna raise my hand. You already
showed me twice how to do it, and I’m still not gettin’ it. I’m not even gonna
ask you anymore. I’m just gonna try and do what I have to do to just get by.
That’s the attitude I got with it after that.
After many years of “summer classes, afterschool classes, Saturday school just to barely
graduate,” Ophelia finished high school and went to work, happy to get away from the need to
deal with mathematics except to “count money.”
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The elementary, middle, junior high, and high school experiences with mathematics that
Ophelia describes highlight ways that her mathematics learning was at first fun and encouraging,
and then discouraging and disheartening. While Ophelia says that she first began to have trouble
with mathematics in middle school, it is also important to recognize the ways that her instructors
either helped or hindered her learning process. By connecting mathematics with students’ lives
(through food and song), Mrs. Jefferson set the stage for the type of learning that Ophelia would
come to expect and appreciate—one that made mathematics both engaging and relevant.
However, her middle, junior high, and high school teachers (as well as her mom) were unable to
build upon Ophelia’s knowledge, help her “grasp” the material, and connect it with her life.
Even though she went to college after high school, it is important to remember that she
intentionally avoided mathematics classes. As she notes earlier, her time in college was short-
lived, so she went to work.
Almost ten years later, dissatisfied with work, and clear that she wanted to pursue a
career where she could follow her passion—baking cakes and pastries—Ophelia left her job as a
manager of a women’s clothing store and enrolled at LA North to study culinary arts. She was
excited to pursue her dream; however, returning to school also meant revisiting her mathematics-
related challenges.
College Years
“Your Attitude Affects Your Outcome.” When Ophelia returned to school to study
business, she had a stark realization about her relationship with mathematics that helped to shape
how she would experience the subject in college. “There was no way I can get to where I want
to be without math. I can't skip over math. I can't bypass it. If I can't do it well, then I can't get a
job.” These sobering thoughts, combined with her prior experiences and maturity helped
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Ophelia to reframe the situation. She tells me that she said to herself, “Since I can't avoid it then
I need to be able to do it well.” With that thought, Ophelia returned to school with a new sense
of resolve. Recalling her attitude about mathematics from middle school to high school, she
shares about her new approach to mathematics in college.
I was gonna make sure that when I went back I did my best and that when it came down
to math I had no choice. I had to come to a realization that if this is somethin' I wanna do
and I want to do well doin' it, then I need to change my attitude about it because your
attitude affects your outcome.
After taking the assessment exam at LA North, she placed into Pre-Algebra, three levels below
college-level mathematics.
Remedial Math: A Throwback to her Early Years. Even with this new perspective,
Ophelia’s stories about college were similar to those from elementary, junior, and high school,
only now, the challenges were different. She talks about her experiences in Professor Zhao’s Pre-
Algebra class, “A lot of it had to do with me bein’ frustrated…[T]here was some kind of
language barrier, but she also moved very, very fast. She didn’t like to repeat herself at all.”
Reminded of Ms. Joilet’s comments when students would ask for clarification, Ophelia cringes
and says, “If someone asked [Professor Zhao] a question, she’s just like, ‘I don’t understand how
you don’t get it.’” Using an example to illustrate her experience for me, Ophelia explains a
situation when a classmate asked the professor to explain a concept again. “She’s just like, ‘I
don’t understand how you don’t understand.’ It got so quiet in there. Everybody’s like, ‘What?
She said that?’ We were all really shocked.” She describes other occurrences from the class;
they all seem to start and end in the same way.
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She would start doin’ the math problems. She would stop talking. She wouldn’t explain
what it was that she was doing. She was just working. You’re just like, “Wait, how did
you get from that? Why did you do that?” She’s like, “Oh, you don’t understand. Well,
this is…” [sighs and shakes her head]. You’re like, “Wait. What?”
These in-class experiences were paired with comparably disheartening interactions when Ophelia
approached Professor Zhao for extra help.
Recognizing that in-class instruction alone would not suffice if she hoped to pass Pre-
Algebra, Ophelia visited Professor Zhao during office hours a few times with questions about the
lessons. Exasperated, she recalls, “She would try to explain it, but [it was] the same way
she…taught it in class.” Although Ophelia turned to some of her peers for support, she soon
realized that they did not understand the material either. Once she “kept getting D’s and fails on
the exams,” Ophelia had frightening flashbacks. “Oh my god. Here we go back to high school
again.” “Anxious,” “nervous,” and “discouraged,” she wanted to drop the class, but her family
would not allow it. Remembering the experience, she recalls their words and her thoughts,
They were like, “No. Go get a tutor. Figure out what it is you have to do, because you
went back to school for a reason. You need to finish this degree. You have to take that
class. I was so frustrated with myself once I realized I wanted to drop the class, because I
should have maybe brushed up a little bit more or studied a little more, so I would have
placed higher. Maybe I shoulda went to Rate My Professor, and I wouldn’ta took that
teacher or something. Now I would go outta my way to go on Rate My Professor.
Ophelia followed her family’s advice, went to tutoring, earned a C, and moved on to Elementary
Algebra. In this next course, when Ophelia met Professor Juntasa, she quickly recognized that
learning was a two-way street. So although understanding the material required her own effort,
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it also “had a lot to do with instructors, as far as the way they were teaching.” Her classroom
experiences and view of herself as a mathematics learner and doer began to shift.
Turning Point—“She encouraged that if you didn’t understand then to please speak
up right then and there.”
Maxine: Okay. Do you have a favorite math instructor?
Ophelia: Juntasa
Maxine: With a big smile [laughs]! What makes her your favorite?
Ophelia: With her I finally got it. I think that’s what it is with her. I finally got it. With
her I finally understood all those years beforehand, [Pre-Algebra], all the high
school math, junior high school, everything that everyone else had tried to teach
me, or everything else I had tried to try to understand, with her I understood in
no time. She took her time with you. She was a very patient woman, very
thorough in her lectures and understanding.
Using other positive words and phrases such as, “awesome,” “thorough,” and “break[s] it
down,” Ophelia beams when she speaks about her experiences with Professor Juntasa. With a
big smile that reveals deep dimples, Ophelia says,
I love her! When she speaks math talk, it’s like she’s speaking English to me. I clearly
understand what it is you’re saying to me. If I don’t get it, I can raise my hand and ask
about it. She encouraged that if you didn’t understand, please speak up right then and
there…[Y]ou were able to raise your hand without feeling silly.
Professor Juntasa acknowledged students’ feeling with statements such as, “you may be scared to
speak up because you don’t understand, and other people are sitting in the class just like you, and
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they’re afraid to speak up, too.” Ophelia’s long-standing fears about asking questions in class
began to dissipate. Encouraging herself with thoughts like, “If I don't get it, let me just ask really
quick, that way I can follow along correctly. Now I’m kind of getting it. I don’t want to get lost
again, so let me ask now,” Ophelia began to bud as a mathematics learner in college. Her out-of-
class experiences with Professor Juntasa were also an improvement over the experiences in Pre-
Algebra. In a one-on-one experience during office hours, Professor Juntasa found ways to help
Ophelia understand mathematics. Similar to Mrs. Jefferson, her elementary school teacher,
Professor Juntasa used concepts that closely linked with Ophelia’s everyday interests and
experiences to help her understand the material.
[In the textbook], they wanna talk about boats and goin’ upstreams and all this crazy
stuff. She started putting it on my terms. She’s like, “Let’s break it down...If you wanna
go to the mall, and you go to this store, then turn around and go to that one, this distance
is x amount. It’s like, ‘Oh, that’s what they’re trying to say?’
Snapping her fingers, she says, “With her, I understood in no time.” Ophelia smiles as she
pointed to her transcript to show me the A that she earned in Elementary Algebra.
Continued Success—“If I can ace math, then I could ace history, I could ace science.”
Reflecting on the next course in the sequence, Intermediate Algebra, Ophelia shares
about a similar experience when Professor Rivera helped students understand percentages and
interest by relating the idea with a high-interest concept, money. She describes how the
professor explained the concept.
[She’d say] you use this if you were buyin' a car or say for instance you were starting a
bank account and you need to know how long it's gonna take before your money grows
or at what percent is your money gonna grow.
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Nodding as she ponders this example, Ophelia says,
It actually does make it a little bit more enjoyable cuz now you're like, okay, then I wanna
get that because I do wanna know if I put this much money in the bank like how to
calculate when I'm gonna get the amount that I want or should I go ahead and make sure
that my rate percentage increased or what?
In another example of the professor’s ability to demonstrate how to connect mathematics with
students’ interest, she shares,
I remember her using shopping examples when it came to teaching percentages and rates.
She explained how knowin’ this would help when shopping at the mall. For example, if a
pair of jeans cost $29.99 is on sale for 20% off and the store is offering an additional 30%
off everything in the store what would be the price? Would you assume it was
automatically 50%? If you said ‘yes’, would that be correct?
She had also used examples of mortgage rates when purchasing a home and knowing
how interest rates apply to your bank accounts, knowing how much money you will have
after a certain amount of time, so compound interest. That helps you decide which bank
to choose to do savings.
Delighted with her experiences in that class, Ophelia shares that at the end of that semester, she
had earned an A in the course.
These stories highlight how instructors’ teaching styles hinder and help student learning.
On one hand, Professor Zhao’s limited capacity to teach concepts for multiple learners
negatively impacted Ophelia’s learning. On the other hand, Professors Juntasa and Rivera both
capitalized on their knowledge of students’ lives and interests to help learners like Ophelia
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understand, or finally “get” mathematics. For Ophelia, these teaching methods helped to clarify
material and ultimately shifted her impression of herself as a learner,
Oh my goodness. To do well in math? It’s like…It makes me feel really proud and
accomplished to be able to go back, cuz I still have my high school transcripts
somewhere in a box to be able to go back and look at those fails and those D’s. Now to
look at my transcript now. They’re all straight A’s. Even an A in math. When I got my
first A in math, I said, “I have never seen that in my life. I’ve never seen that.” I’m sorry.
I wanna cry [Laughs and wipes away fresh tears]. It made me really proud and really
accomplished
Smiling, she says, “I’m just like, ‘Oh my gosh.’ To go from [pause] when I got that first A in
Elementary Algebra, I’m like, if I can ace math, then I could ace history, I could ace science.”
Ophelia’s ability to connect with Juntasa’s and Rivera’s teaching and communication styles
helped her create positive learning experiences in Elementary Algebra and Intermediate Algebra.
As Ophelia notes earlier, both her performance and impression of herself as a
mathematics student shifted in college; this prompted conversations about her success. So, in
our next meeting, we explore her concept of success and the factors that contribute to her
successful progression in mathematics.
Success in Mathematics: Standard and Alternative Perspectives.
Transitioning into a conversation about mathematics and success, Ophelia and I talk
about the ways that she conceptualizes the term, “success.” With a practical perspective
foremost in mind, Ophelia focuses on the kinds of grades that she associates with success in
mathematics,
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For me? A’s. [Laughter] I think it’s just cuz I set that bar for myself. For now, anything
less than an A is upsetting. It’s like that in any course. I’ve never felt that strongly about
my academics before. If I get a B on an exam, I’m just like, “Oh my God. What didn’t I
do?”
At first glance, I figured Ophelia solely linked grades with success, but then, interrupting my
thought, she clarifies her point, connecting success with an idea that she would discuss
throughout the rest of our meetings, the importance of understanding,
Professor Rivera already knows when I get my exam if something’s wrong on it, she’s
gonna have to stay behind an extra five minutes, because I’m like, “Now we need to go
over it. How did I get this wrong? What did I do? What’s goin’ on with that?” She’ll just
break it down for me. So on the next exam, it’s like it’s gonna be an A.
Ophelia’s need to understand the material emerges later in a discussion about mathematics
ability and success.
In an exchange about high and low mathematics ability, Ophelia shares her definition of
the terms.
Maxine: Can you think about somebody who has a high ability in math?
Ophelia: The only people that I’ve run across that I feel would have a high ability in
math would be tutors that I’ve had. I would say that they’re pretty well off in
math.
Maxine: What does that mean to be “pretty well off in math?”
Ophelia: You’re comprehending. You understand what’s goin’ on. How to go ahead and
solve it, to get to a point where you’re like—well, you actually start likin’ it a
little bit. To me, that makes you well off.
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Then, we speak about her definition of low mathematics ability.
Ophelia: Okay. Low ability in math? They really don’t understand it. It’s also they don’t
want to understand it. They’re not trying. They don’t do very well at math.
Maxine: Let me ask you then. Where do you put yourself? High ability or low ability?
Ophelia: I would say I’m in the middle.
Maxine: Okay. What does that mean?
Ophelia: I’m in the middle. I wouldn’t say I’m necessarily low, because there’s a lot that
I do comprehend, but I wouldn’t say that I’m necessarily high, cuz there’s still a
lot to learn. There’s still sometimes I will go through subjects or certain things
that I’m just like, ‘Okay. I’m not gettin’ this at all.’ Sometimes I’ll even forget
things. Then, I’ll be like, ‘Wait, we did that in [Intermediate Algebra]? We did
that in [Elementary Algebra]? Wait, what?’ I get it. I get it. I comprehend it, and
I understand it.
Her balanced comment about high and low mathematics ability prompts a discussion
about the concept of success in mathematics, the value of grades, the link between the two ideas,
and ultimately, the connection between one’s ability to understand mathematics and success.
Maxine: Do you think success in math can be judged by the grade?
Ophelia: [shakes head] In order to be successful in math, it’s not necessarily [about] this
grade, because sometimes you could just be tryin’ to cheat to get a grade. You
need to make sure that you understand.
Maxine: So let me play devil’s advocate here, if the grade is not the only way you know
if you get it, then how would you know that you get it?
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Ophelia: Even if my grade isn’t an A, [but] I understood the problem, what the question
was asking, how to accomplish it, and the formula, I may not have worked the
problem out correctly, but I understood. For me, that’s being successful. I feel
like if you have that attitude about it, then of course you’re gonna get good
grades. You can’t look at it from, oh, you just want the grade, because you can
get a good grade without knowing anything.
Ophelia’s transition from speaking about grades as her personal marker of success to
understanding as a more reliable demonstration of success, highlights the ways that similar to
others in this study, she does not adopt the traditional, grades-based understanding of the term,
“success.” Intrigued by her statement, “[I]f you have that attitude about it, then of course you’re
gonna get good grades,” I ask Ophelia what shifted her performance in mathematics.
Success in Mathematics
“I’ve Learned to Stop Tellin’ Myself That I Couldn’t Do It.” “Better,” “improved,”
and “good,” “but not great or really good,” are words and phrases that Ophelia uses when
describing her mathematics ability in college. While she recognizes that she is a long way from
where she was in middle or even high school, she shares, “I am still improving [and] [t]here are
some tests that I wanna cry over.” It seems that Ophelia is hesitant to claim victory regarding her
mathematics success. Even with this perspective, she could not scoff at the idea that she has
been successful and attributes her accomplishments to four factors: (a) shifting her mindset, (b)
studying, (c) tutoring, and (d) prayer and her faith. Referring to a conversation that we had in an
earlier meeting about how she viewed herself as a mathematics learner in junior high school,
Ophelia talks about the ways that her mindset ultimately creates her reality.
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Mindset—The First Step to Success. Ophelia first suggests the concept of mindset
when we broach the conversation about why she earned Ds in junior high school. Pausing to
think before speaking, she says, “I think a lot of it had to do with me. Something like, ‘This is
something I really don’t want to do. I don’t really like it. Why do I have to do it? This is stupid.’”
With this attitude, she admits that she used to ask herself, “What point in time is [math] gonna
help me in my life?” Her disconnection from the value of mathematics, coupled with her desire
to “get up outta” middle, junior high, and high school helped her to have some success, but it
was inconsistent; other than understanding geometry, she was not “gettin’ it” or being successful
in mathematics.
Given her grades during the early years and progress in mathematics, before returning to college
Ophelia figured,
[D]oin' well was at least getting a C in math in college. Because at least tryin' like that in
college at a college level, was telling me like, okay, I'm kinda gettin' it. At least I'm
gettin' it better than what it was when I first started off my relationship with math.
Then, after earning her first A in Elementary Algebra and then another in Intermediate Algbra,
she began to trust her mathematics skills. We talk about the moments that helped her create a
new perspective,
Maxine: What was it about passing [Intermediate Algebra] that did it for you?
Ophelia: It was when I would get my exams back, there weren’t that many mistakes on
them. Then I found that the ones where I would make mistakes, they were
simple mistakes. The instructor would tell me, “You mess up on the easiest
ones, but the hard ones you do like this.” [Snaps her finger] I’m like, “Okay. If
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I’m gettin’ hard ones, then that’s tellin’ me that, okay. I’m gettin’ it.” Towards
the end of [Intermediate Algebra], when we got the final, and I didn’t have any
anxiety about it or do anything like that, that’s when I’m like, ‘Okay. I’m really
gettin’ it.’
This point in Intermediate Algebra was Ophelia’s lightbulb moment. This was when she learned
to stop saying, “I couldn’t do it and I didn’t understand” and told herself, “I’m going to do this,
and I’m gonna get it. I’m going to understand.” With new self-talk, she became responsible for
her beliefs about herself and mathematics.
When I adopted a different attitude about [math], it made me start viewing it a little
differently. That’s when I had to come to terms with, “Okay. A lot of that was me.” You
can only put so much on the instructors, cuz I really didn’t want to do [math]. I really
didn’t care about it.
With this new perspective, she thought about her other subjects,
If I can overcome this, there’s nothing in life that I can’t do. I’m not gonna complain
about, “How am I fittin’ to do this English paper?” You just aced math! You should have
no problem doin’ a ten page English paper. Now that’s always a reminder for me when I
start tellin’ myself “I can’t do something,” or “I don’t know how to do that.” Then I start
thinkin’, “You aced math. If you can overcome that, you can do this.”
This new perspective also affects her class participation. Demonstrating her new awareness, she
says, with verve, “All of the sudden, I’m clinged onto the board, really tryin’ to get it. I’ll raise
my hand like, “You know what? Wait, can you go over that again?” A new attitude brought a
new incentive for learning the material, “Then I changed my motivation to where it was like ‘this
is what I want to do… I want to get this. I want to know how to do it. I want to know how to do
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it the best that I can.’” Ophelia’s excitement is contagious. I am excited to learn about how she
does her best, so next, we speak about her studying practice, an important activity that helps her
learn the material and ultimately, achieve success.
Tutoring: “[I]t's kinda like they're right along with you understanding the
struggle.” Our conversation about using campus tutoring services stems from a question that I
ask about the mathematics topics that Ophelia finds most challenging. She responds without
hesitation, “The word problems.” To demonstrate her thought process and where she gets
confused when solving word problems, she offers an example.
I think the question was, “You work for CVS or something. You only have 20 percent of
an acidic solution on file. A customer is asking for 80 percent. What can you get from the
back to mix with that to get an equivalent of 80 percent?” You’re like, “Wait, what am I
supposed to do with that?” Okay. I understand you’re asking me what can I mix with
what, but how am I supposed to break that down into numbers to make it work? For me,
it’s always trying to figure out what it is that you’re asking me. Once I know that you’re
asking me, and I already know the formula, then I can go ahead and put it together. It’s
always the beginning part of trying to figure out what it is you’re asking me to do.
When Ophelia gets confused with the material, she uses multiple methods to figure out the
answer to the problem.
For me personally, what usually works for me is to put it to the side, completely just
ignore it and forget about it. Sometimes I could look right back at it and go through my
notes again and look right back at it. I’m like, “Oh, okay. I got it.” Sometimes it’ll take
me leavin’ it there for a whole day. Then re-go over my notes again. Okay. Oh, that’s
what you’re asking me to do. I’ll get it. If I still don’t get it after 24 hours, then Professor
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Rivera has tutoring hours. Then I’ll go see her before class or after class. Like okay. I
don’t understand this. I really don’t get it. She’ll be like, “Oh, okay.” Then she’ll get her
marker and go to the board and be like, “Okay. Let’s write it down.
Sometimes, when Ophelia visits the tutoring center, she is able to work with Professor Rivera.
Ophelia: A couple of times I’ve been, Professor Rivera was actually there, so that
worked out. That she was actually downstairs.
Maxine: She was tutoring in the tutoring center?
Ophelia: Yeah. Sometimes she’ll do her tutoring in the tutoring center. It’ll be different
students from [her] different classes. She’ll block off a whole space. She’ll just
go in between each table, just back and forth [moves her finger between two
imaginary locations]. I’m just like, “Oh lady, and you have a class after this?”
She has to be so exhausted. [chuckles]
Although Professor Rivera serves as a resource in the tutoring center now, this was not always
the case for Ophelia. In Pre-Algebra, when Ophelia struggled with course material, she visited
the campus tutoring center on occasion and worked with tutors. “I do go to tutoring. [In Pre-
Algebra] I went there a couple times. A lot of the times, I don’t have the time to go, but I’ve
probably gone about four times.” Even though she has only visited a few times, she considers
the tutors to be valuable resources for multiple reasons, including the ways that they teach the
material assistance and the ease with which she is able to communicate with tutors.
When talking about dealing with her difficulties in Pre-Algebra, she shares, “They have
really good tutors downstairs in the tutoring lab. I was talking with them, and they were able to
break it down to me.” Their ability to “break it down” for her was critical when she struggled in
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Professor Zhao’s class. She also shares about the level of comfort that she has when
communicating with tutors and the ways that these relationships support her academically.
The campus tutoring here really helps a lot honestly. I think it's a lot more comfortable as
well. I'm not saying you not comfortable with your instructors, but it's a lot more
comfortable because it feels like you're on a peer-to-peer kinda relationship. Because the
tutors are also students, so it's kinda like they're right along with you understanding the
struggle. We can complain about the same stuff. You can kinda act more relatable to me.
They don't speak to you in just straight out math talk.
In addition to seeking out help, Ophelia works on her own to complete her homework and
understand course material. Beginning with a description of how she arranges her physical
space, she is thoughtful about her environment and her practice.
Studying: “I try to hide my phone, because then I’ll start getting distracted and
going on Facebook and other things.” When preparing to study, Ophelia begins by laying out
all of her ‘tools.’ These include, “a lot of music, snacks, and books, and paper” and exclude
gadgets and practices that can divert her attention, “I try to hide my phone, because then I’ll start
getting distracted and going on Facebook and other things.” Next, she is careful about how she
reads questions, “Make sure you understand what the question is asking you to do…Then just
take my time and practice on a scratch sheet just to make sure that I’m doing the steps correctly,
before I actually work on my homework page.”
Using a combination of her notes, textbook, and old exams, she explains,
I go through my notes first, or through the book. Sometimes they have the examples in
the book and I’ll relook over it. A lot of the times, the practice exams, they’re a lot like
the real exams. The numbers may be different, but it’s still the same kind of problems.
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If she cannot figure out the answer after using these methods, she taps her other resources, “I run
straight to YouTube [and] Google, watch multiple videos, and pick from each.” Pointing and
speaking as though she is talking to the speakers on different YouTube channels and then to
herself, she explains, “I'm gonna do the part how you started off, how you did that in the middle,
and then figure out my own way.” Another resource that is important for Ophelia is her
connection with her study partners.
In addition to working on her own and seeking help from instructors, Ophelia uses a third
study resource: study groups with peers. Referring to her study group from Intermediate
Algebra, she notes, “It was nice to just be able to socialize with other people, who are going
through the same struggle as you. We set goals [for our grades], worked toward it, and helped
each other with tutoring.” Working as a team, they used multiple methods to support one
another, “We would text each other [and if] they had a problem with something, they would send
me a picture of it. I tried my best to work it out, or we’d get on FaceTime and try to work it out.”
For Ophelia, working in a group is “reassuring and comforting.”
You’re not the only one. We all know you’re not the only one goin’ through something.
Logically we know this. You’re not the only one ever going through anything in the
world. It was comforting to know that you had other people who were struggling with the
same thing at the same time.
She shares about experiences when they used the group’s collective knowledge to solve
problems, “If I would remember a part of something, and I didn’t understand something else,
somebody else would understand that part, and we would come up with ways to make it to where
we all understood how to do it.” One other aspect of their relationship that Ophelia found
invaluable was their practice of praying together. “It became this thing where we were this
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prayer circle…we would be in a circle in the hallway praying before we went to go take an
exam.” Our conversation about her prayer circles with her study group was one of several that
we had about the last set of factors Ophelia attributes to her success in mathematics: prayer and
her faith.
Prayer and Faith: “I pray first for understanding, for removing the anxiety, for me
to do my best and accept that my best is good enough.” When I first ask Ophelia about the
factors that contribute to her success in mathematics, she pauses, then answered simply, “Let’s
see, prayer and studying.” Later, she elaborated, “I make sure that I study, pray before I study,
and make sure that I pray before my exams…or before I do my homework and start tryin’ to
study.” After pondering about what she focuses on during prayer, Ophelia calmly says, “I pray
first for understanding, for removing the anxiety, for me to do my best and accept that my best is
good enough.” Reflecting on times when praying during an exam helped her figure out an
answer when she was struggling, she notes,
I swear I’ve been in the middle of an exam, and I’m just like, “I don’t even know what
the heck this is asking me to do.” I’m just like, “Lord, help me.” I flip the page back. I’m
like, “Oh, okay. Oh, thank you, Lord [laughs].
One day, during our walk to the parking lot after a meeting, Ophelia talks about the role that her
faith plays in her life, so I devoted a portion of our last meeting to learning how she developed
the practice of praying before undertaking mathematics-related ventures.
With a smile on her face and her hands clutched against her chest, Ophelia shares, “My
pastor would say, “Don’t ever think that your problems are too small or too big for God to
handle. For you kids in school [with] math homework and you’re not gettin’ it, he’s like, ‘Stop
and pray about it before studying and before doing homework.’” When Ophelia returned to
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college and began to struggle in mathematics, she adopted this practice, and eventually, began to
shift her mindset.
Encouraging students to pray was just the start of her pastor’s suggestions; he also
inspired them to shift the ways that they thought about themselves. She recalls, “My pastor [had]
conversations with the young people about how we hafta change our mindset. He would say,
‘How can you say you can't do something when your God is able to do exceedingly above all?’”
With wide eyes, she turns to me and says, “How can I say that? I can't say, I'm not gonna do it
well and I have all the tools spiritually to get it done.” With the belief that, “You can’t pray for
an A and study for a C,” she developed new and effective practices for studying, completed the
remedial mathematics sequence and entered college-level mathematics in three semesters.
Recognizing success as a combination of a positive mindset, tutoring, effective study
practices, peer support, prayer, and her faith, Ophelia employs psychological, physical,
relational, and spiritual tools to continue to progress in mathematics. Ultimately, these all work
in concert to help her understand the material, feel confident in her work, effectively apply her
knowledge during quizzes, tests, homework, and study sessions.
Current Mathematics Class
Now, in College Algebra, Ophelia is in her fourth mathematics course at LA North. Even
though her view of herself as a mathematics student has shifted drastically, the changes in her
feelings about mathematics are more subtle,
Me and math aren’t best friends. We’re definitely not husband and wife right now. I feel
like we’re acquaintances. I’m still gettin’ to know you. I’m learning to like you. Then
maybe hopefully one day, we’ll be friends [laughs]. Even though I’m in [College
Algebra], it’s still one of those things where I’m learning. There are times when I
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wanna throw my math work against the wall. I’m learning to definitely accept it, and I
think accepting [the] role that it plays in my life and the roles that it will potentially play
in my future helps me to be like, “No. Suck it up. You need to get it. You need to like it.
You need to understand.
Despite the subtlety in Ophelia’s shifting relationship with mathematics, it is clear that she has a
new view of the subject and its instrumental value in her life; this view and her value of
mathematics provide new motivation to engage with the material. This perspective demonstrates
yet another mindset shift that Ophelia has experienced in regards to math. The final shift would
become apparent during our last meeting.
A Final Note
In our last conversation during our final meeting, Ophelia shares what she learned about herself
during our discussions,
In our conversations, you really helped me to look at myself in a different light. To
appreciate where I've come from with math. I mean, I already knew that where I am
today, as far as really appreciating my struggle, and how I overcome those hurdles it's
different. You also helped me to be like, okay, I'm good. I've always been a very humble
person, so I don't really ever be like, “Oh yeah, I'm doin' great or I'm doin' good” or, “Oh
yeah, I'm better than so-and-so.” I'm not that kind of person. Now I'm like, okay, I'm up
there. I think I'm a little bit above average. It's okay to acknowledge that.
Approximately three weeks after our final meeting, Ophelia sent me a screen shot of her final
grades in her classes for the semester; she earned an A in her College Algebra course.

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Wesley Simon-- “I’d better do good, or I’m gonna make us look bad.”
Background
In the elevator on my way to meet Wesley for our first meeting, there is an older Latina
woman and a Black man who seems to be in his late thirties. I smile at both and give him a
simple head nod of recognition
13
. Without breaking his stern look, he nods back. We all exit the
elevator and I begin to scan the lobby for Wesley. Eventually, I text him: “Hi, this is Maxine.
I’m near the entrance in a blue and white striped shirt.” He responds, “Be right there.” I wait for
a few seconds, look up, and notice that the same Black man from the elevator is walking in my
direction. “Wesley?” I ask. With a deep, low voice, he says, “Yes, hello Maxine.” I smile at
him and extend my hand. He returns a bright smile that seems to belie the serious veneer that he
had when we first met in the elevator.
Wesley is a 40-year old, divorcé and single dad who has two teens and a tween and works
as an usher at a local concert venue. Before we discuss what brought him to college, we speak
about his post-high school plans during his teenage years.
Wesley: After high school it was like, “Okay, I’m gonna get a job.”
Maxine: Was there any talk about what you might have wanted do after high school?
Wesley: There was never really too much that she said. My mom, she was like, “You
need to do something, get a job, do something.” It was never anything really
specific, never any talk of higher education, just, “Go apply at the post office,”
or, “Try to get a real estate license.”
Maxine: Okay, then what kind of job did you end up getting?

13
Within Black culture, even if people do not know each other, they often give each other a head nod of recognition,
as if to say, “I see you” or “I acknowledge your presence.”
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Wesley: I worked in a mall, then I worked as a travel agent. I worked in construction. I
did all types of stuff, everything. Yeah. I found that I didn’t like the jobs I was
doing, and I had mediocre, at the most, skills to do anything else. I was like,
“Man, what am I gonna do? I don’t know how to do anything.”
Given what Wesley had just shared, I ask, “Well, what brought you to college?” He looks
towards the window, then back towards me, and starts to tell me about his journey to community
college eight years prior. Following this somewhat pensive pause, he begins with his
employment history.
I would install flat-screen tvs, surround sound systems, Direct TV, Dish network, and
[do] cable installations, terminate phone lines, you know things like that. And I hated
that crap. I thought, "Man, if I had the chance to go back to school,” you know? I hated
doing this. Driving all over the place, I'd just sit in traffic for way longer than I would
work. I just hated it. Three in the afternoon in August. It would just be burnin' hot and
I'd think, "Oh my God. I have to do something else ‘cause I hate this." But I had to take
care of my family. But if I could do something else. And then that time came.
Back in 2010, '11 all construction things came to a halt. People weren't buying things. I
would go out and I would install TVs, $250 apiece. I could do three in a day. Really
good money. Who would make that in a day, you know it's hard. And then, all of a
sudden, I'm in Best Buy parking lot saying, "Hey, you want me to hang your tv?" Then, I
saw a way to get out, so I became a Pharmacy Tech. And that was the beginning of me
saying, "Ok, maybe there's something more, I need more." And once I became a Pharm
Tech, I started reading about drugs and whatnot and became interested in what they do,
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how they work, and it led me to enroll in community college. I needed to know more.
and here we are and I still need to know more.
He pauses for a moment, and leans on the table. Then he fast forwards and begins to talk about
his enrollment into community college, two years later.
Wesley: Since [then], I've been to Piston College. I chose Piston because I heard a lot of
negative things about [LA North]. And as time progressed, I had scheduling
issues trying to work and attend school, so I took classes at Piston and took an
Organic Chemistry class here. And I took the rest of my Chemistry classes here
up to Organic Chemistry 2.
Maxine: Oh, you’ve taken several science classes. What’s your major?
Wesley: Biology
Maxine: And do you have a sense of what you might wanna do with that?
Wesley: I'm learning to be a researcher [so I can do] Alzheimer’s research.
At one point during our conversation, I reflect on Wesley’s multiple jobs and his new career
interests. I wonder what he believes might have inspired his journey to college at an earlier time
in life. From his response, it seems that certain behaviors negatively affected his trajectory after
high school. Now, as an informed adult, he makes different choices to design his future.
Wesley: Planning is such a critical part. If you plan from high school to go into
something, a field or whatnot, it’s so much easier. If you’re going from high
school to, “I don’t know what I’m gonna do ‘cause I’m just gonna do
something,” that’s when anything can happen…If you apply this same thing
here, okay, if you’re planning to go to a certain level then it’s that much easier
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as opposed to, “I don’t know what I’m gonna do. I guess I’ll do this or apply
here or apply there.” There’s no focus. There’s no target.
I always think, “Man, if I would have at that point decided to go the direction
I’m going now, I could have did so much more,” because the things that I was
learning—like I say, I struggled a little bit in the beginning because I didn’t
know how to utilize the tools, but once you learn it, “Okay, I understand now.
Now I can develop.” If I would have take that point at which I was at
understanding what to do and said, “Let’s move forward,” as opposed to, “Okay,
I’m cool right here,” it would have been a lot different.
Maxine: For you, you think it was focus on your part?
Wesley: Yeah. I never got the inclination to say, “Okay, I need to really go into this math
and science thing.”
I am curious if Wesley also engages his children in planning conversations about their futures, so
I ask him about this. As he sits up and straightens his glasses, he replies proudly,
Oh, yeah. We discuss it all the time, “Okay, what are you gonna do now? Why?” They
have plans. My daughter, she wants to be a maxofillio surgeon, but she’s also interested
in dermatology. I said, “Okay, you’ve got something to work with here. You’re way
ahead of where I was when I was your age.”
When I was 13 I wasn’t even thinking about that, you know what I’m saying? I wanted to
go play basketball or whatever. I wasn’t really thinking about, “Okay, what am I gonna
do as an adult or when I finish high school?” I didn’t consider it. She does, and that’s
awesome. She knows where she wants to go.
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Before asking about Wesley’s mathematics experiences during his early years, I return to
an earlier part of our conversation. “So, you’ve been at LA North for two years now?” Wesley
corrects me, “I’ve transferred to a four year.” After a brief conversation, I learn that Wesley is in
his first semester at a California state school. He is the only participant in this study who has
completed the remedial mathematics sequence, earned his Associates degree, and transferred out
of the community college system. I make note of this and then we transition into a conversation
about his pre-school years.
Early Years
Elementary School—“My peers always considered me to be pretty intelligent.” “So,
tell me about your earliest math memories. Could be in school, on the playground, anywhere.”
Wesley pauses for a moment, shifts slightly in his chair, and then shares his thoughts about his
earliest memories of mathematics with his mother.
I already knew how to count and read before I attended kindergarten ‘cause my mom
taught me. She would buy little workbooks and things like that. I remember doing a lot
of tracing of numbers.
Their work together prepared him for some of what he would face in mathematics in elementary
school; this eased his transition. As a result, Wesley has positive mathematics-related memories.
In elementary school and all through junior high, high school, I did good in math. It
wasn't difficult at all. Actually, I did nothing extra, just did classwork and homework, no
more. I just did what I did to get by and usually a B or a C or sometimes a A.
Wondering about Wesley’s in-class experiences as well as his teachers’ and peers’ thoughts
about his mathematics skills, I ask for his perspective about their perceptions: “How do you think
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your peers and teachers in elementary school saw you as a math student?” He leans forward and
laughs quietly. Keeping his voice low, he responds,
Wesley: I think my teachers may have saw that I was of at least standard intelligence.
You know, my peers always considered me to be pretty intelligent.
Maxine: How did you know?
Wesley: We'd talk about it, compare grades. You know if I did better, I'd make fun of
people [laughs].
Maxine: And do you think the way they saw you was accurate?
Wesley: I guess so.
In our next conversation, Wesley shares a memory that indicates why his peers may have viewed
him as “intelligent.” He mentions that in fourth grade, his mathematics skills and competitive
nature were challenged when he met Eve Johnston, the other Black student in his class. He
bows his head, chuckles, and recalls,
My school was in a small town close to San Jose. Not a lot of Black kids there. It was
myself and Eve, who was a Black girl. She was really smart. We would have these 5-
minute tests—you would go from addition, once you were able to pass that, then move to
subtraction, then move to multiplication, then move to division. They were fun. You’d
be in competition with your friends and see who could finish the fastest and who could
actually get perfect. Once you get a perfect you move up to the next level. So we would
kinda compete and you know she would start off and get a headstart on me and then I
catch up and she ended up winning a lot. I don't hold it against her [laughs]. She would
finish fast, and she would always have perfect—I would finish fast, too, but I’d always
have maybe one or two that were wrong, so I had to step up my game. I strutted around
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class the day I won. I was, “Yeah!” [pumps his fist and laughs] That motivated me in
elementary. It was just fun.
He goes on to talk about how his teachers responded to his performance, “I remember in
elementary school, Mr. Malcolm, he'd be like, ‘You know, you're pretty good in math.’ And he
would encourage me.” Opportunities to compete on five-minute tests, the results of these tests,
and Mr. Malcolm’s comments served Wesley well. They motivated him to succeed in
mathematics, fostered his beliefs in his mathematics skills, and encouraged his belief that
without studying for mathematics, he could still be successful. In our conversation about his
high school years, Wesley acknowledges that as he moved up, so did the level of difficulty in
mathematics.
High School—“I wish I would have known better, but I didn’t at the time.” Wesley
transitioned to high school with the study habits that he developed in in elementary school. As a
result, his mathematics experiences during his early high school years were rife with
challenges—“I had some issues. I didn’t really know how to study math because I never did it
before.” He goes on to highlight some of the challenges that he had with mathematics concepts
during those years.
Then there were a lot of different mathematical theories and theorems and whatnot that
you had to consider and had to prove and had to remember. It was all brand new to me. I
didn’t understand the equation of the line. The equation of the line was just madness, and
I could not understand how it worked for a while. I was winging it for a long time. I was
just barely getting by. Yeah, that was a struggle in intermediate algebra, whew, knowing
which side of the line they wanted us to shade in and whatnot—the symbols, knowing the
symbols. It was pretty hard.
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Later, he shares, “In high school, I struggled at first, but I became very good. High school, I had
some issues until I really tried to focus, and then it was fine.” So, once Wesley was able to
focus, he figured out how to be successful in high school math. Before that time though, it was
clear that when Wesley walked into the doors of his high school, he entered a different learning
situation, one where not knowing how to study would no longer suffice if he hoped to have the
level of confidence that he had during earlier years. His comment about his struggle sparks a
thought, and so I ask, “What helped you be able to get through that time?” Almost without
pausing, he replies,
I kept trying. I’d study and keep trying and keep trying and ask for help. Mostly I would
just keep trying and look in the back of the book [simulates flipping pages in a book]
‘cause I’d say, “Oh, no, that’s not my answer.” Then I’d try it again. Once I’d see the
answer, “Okay, I can make adjustment here, adjustment here. That’s why the answer’s
that.” Then after time and time again with that, then all those—it was a process. Boy, I
tell you, it was a process. One day I sat and I was like, “Okay, I’m not getting up from
this table until I figure out what the heck y=mx+b mean. I did not understand it
whatsoever [laughs]. I started in the morning. By the time it was dark I had it [laughs].
During these high school years, Wesley’s burgeoning strategy for understanding course
material—“study and keep trying and keep trying and ask for help”—shaped how he would work
to understand mathematics in college. Perhaps this close connection with his current life is why
he is able to respond to my question without much thought. In this conversation about his
difficulties in mathematics, he turns his focus to the only class that he could really recall during
these years.
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I don’t remember any other class that I took. I just remember the geometry class. I
remember being introduced to proofs in that class, and those were really hard. Having to
use a calculator for math as opposed to just doing it in my head was an adjustment, and it
had to be a scientific calculator which I had never seen before…[T]his thing had all these
buttons and words on top of the buttons and symbols that I didn’t know were math. A lot
of them were letters. Math is numbers, “What’s going on here? I have no idea what this
tool is.” That took an adjustment for me in geometry. I like learning things, but I wasn’t
seeing it being like, “Okay, I can use this later on,” or how it could be a useful tool of any
sorts. I know how to count. I know how to divide. I know how to multiply. I’m good.
Those are my life skills.
Wesley’s last few statements, about his life skills spark my thinking: Had any of his teachers
taught in ways that helped him to connect mathematics with his life? So I ask. He responds
simply, “No.”
Recognizing that Wesley did not connect mathematics with his life or future career in
high school, I jot a quick note to remind myself to ask him a question: “Does he connect math
with future career?” Then, I return to asking about high school mathematics. As we continue to
talk, it becomes clearer that Wesley’s desire to “get a job” after high school was shaped by two
factors: (1) his belief that his life skills were adequate for meaningful employment and that (2)
the mathematics he was learning was disconnected from his future. These views shaped how he
approached mathematics during the rest of his high school career.
When speaking about high school mathematics classes, Wesley shares, “The highest I
went was geometry which I did in tenth grade. Then the next year I didn’t have to take math, so I
didn’t [laughs]” Given the paucity of advanced course options available at some high schools, I
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wonder if his decision was based on a lack of courses choices at his school; Wesley responds to
my thought before I could utter the words.
They had more classes that I could take, but I didn’t see why I should put myself through
the pain [of taking them] because I felt, “What could it do for me?” I had no motivation
and just wanted to pass. “I’m just here trying to get out so I can get some freakin’ job.”
That was my thought. I never even considered a future with math or science.
So, he focused on courses and activities that seemed more important and relevant for his future.
I took work study instead. I only had a half a day of school, and the other half I would
work in a mall ‘cause I had all of the credits required. Math in high school [sighs], I
struggled in geometry. Proofs were a little difficult, but eventually I got it.
Wesley ‘got it’ in Mr. Dawson’s class. Mr. Dawson, the geometry teacher whom he describes as
“very serious about mathematics,” seems to garner Wesley’s respect. “In school you have a lot
of children that not only don’t wanna learn but they’re disrespectful. I would watch [Mr.
Dawson] navigate through the disrespect and non-motivated and whatnot.” So, it seems that Mr.
Dawson had a skill for connecting with students; he was also talented enough to recognize
Wesley’s abilities and advise him about his future.
He would always encourage me, and that I should consider secondary education, you
know. He was one of the few teachers who would tell me that I'm a good student. Like,
“You know, you’re pretty smart. You should consider doing higher education.” I got a B
in his class. He would always tell me, “I know you’re better than a B student.” I probably
was, but, like I say, I wasn’t really seeing any development in this. I’m just trying to get
through. You know, he saw I had potential. At that time, I wasn't even thinking about
going to school. You know, "I don't even know anybody who's doing that." You know
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what I'm sayin'. Now, I know people who do it because I'm in it now. You know, [goin’
to college’s] a story, that's not me. I wish I would have known better, but I didn’t at the
time.”
Almost twenty years later, Wesley took Mr. Dawson’s advice.
Wesley’s early experiences show how memorable and fun mathematics experiences can
soon become challenging, frustrating, and even irrelevant when there are not explicit connections
between mathematics and the futures students see for themselves. While students can certainly
benefit from instructors who offer encouragement, as Mr. Malcolm and Mr. Dawson did,
sometimes these words are not enough to provide direction for learners like Wesley who needed
a different level of support to link mathematics to his life and future. While Wesley remembers
Mr. Dawson’s encouraging words as supportive, his instructor’s confidence in Wesley’s abilities
helped him focus on passing his mathematics class so he could graduate and find a job, not on
exceling in mathematics so he could move on to “secondary education.”
Drawing from Wesley’s comments about “focus” and “planning,” without a plan “to go
to a certain level,” it is easy to understand how his future was driven by thoughts like, “I guess
I’ll do this or apply here or apply there.” This connection is particularly relevant when
instructors view students as promising learners who can advance and succeed, but offer no
direction to help them figure out their futures. With Wesley’s belief that “[goin’ to college’s] a
story, that's not me,” it is easy to understand why he did not attend college until almost two
decades later.
College Years
“The more I know, the more I find out I don't know all the time.” Wesley begins our
conversation about his mathematics experiences in college by listing the collection of classes that
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he has taken at Piston and LA North after assessing into Pre-Algebra, three levels below college-
level mathematics. “I started in pre-algebra at Piston, elementary Algebra, intermediate Algebra,
then it was Trig, then I took geometry, then I took Pre-Calculus, then I took Calculus twice
[laughs], then I took Calc 2 [at LA North].” While he has taken several courses and succeeded
in these classes, his journey has not been easy. I ask about his transition from full-time work to
college, and more specifically, into mathematics. With a combination of emotions, he sighs,
shakes his head and chuckles. Then he tells me, “It was a struggle, it was a big time struggle
because I returned to school and there was a lot of stuff that I never even heard of before in math.
You know, and I didn't learn about that.” Curious about this new material, I ask, “Do you
remember some of the new things that you had to learn when you came into college?” He
pauses, then like counting off items on a grocery checklist using his fingers, he lists topics.
Well, just start with sine, cosine, proofs [laughs]. My high school, the highest level I
went to was geometry, but it was completely different. Integrals, that was completely
loony. How the curves work. I had some experience with the xy-plane, but I didn’t know
how much it meant. I had no idea how much that particular concept meant to
mathematics.
In college, Wesley developed a new perception about math and his skills. He no longer
perceived himself as a student who is “good in math” and has stopped “strut[ing] around class,”
excited about his test scores. In college, he characterized himself differently.
I think I'm at least of average intelligence and I'm striving to get better. The more I know,
the more I find out I don't know all the time. I have moments. I guess I feel I'm capable.
That's my motto as opposed to anything. You know, I'm capable, now we just have to do
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it. That's the hard part. I have all the capability in the world to be able to do this, I just
have to execute. Sometimes I know how, sometimes I have no idea how.
During Wesley’s time in developmental mathematics, the thought, “You know, I'm capable, now
we just have to do it,” seemed to drive how he operated and navigated his pathway through
remedial mathematics in community college. I think about the idea of being “capable,” what
does this mean to Wesley and how does he perceive his own abilities? I decide to ask him about
this, but in an indirect way.
Maxine: So let’s talk a bit about ability in mathematics. How would you describe
someone who has high math ability?
Wesley: High ability is understanding the concept quickly and then being able to apply
that concept to problems.
Maxine: And then you'd say low ability is what?
Wesley: Low ability is not understanding it quickly and having struggle to grasp some
hold on the concept, then being able to proceed to try to practice.
Maxine: Ok, so even if they get it in the end, if they struggle or if they don't get it
quickly, then you consider them to have low ability.
Wesley: [nods] um hmm
Maxine: Ok, so where would you say you fall in that?
Wesley: Oh, I got low ability [laughs].
Maxine: Can you say more about that.
Wesley: I got low ability, and I know that, so that means I gotta work hard.
So if Wesley thinks he has with the idea that he has low ability in math, I wonder how he feels
about the subject, so I ask him.
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I like math. It's one of the cooler subjects. I like it, but sometimes it's like, I don't
understand and then I have to go into my lab, my lab is here [points to his head] and I
have to figure it out. And then it's like, "Oh, I'm the greatest on the planet. I figured it
out. There's no one smarter than me." Until the next class [chuckles].
Progress in Mathematics. In my conversations with Wesley about mathematics in
community college, we begin by discussing his progress in these courses. After assessing into
pre-Algebra, he earned As in each course in remedial mathematics and in Trigonometry, his first
200-level mathematics course. With statements like, “I knew all that stuff before. Just it had
been a long time since I had engaged in it,” when referring to Pre-Algebra then, “That was where
I was introduced to the line” in our conversation about Intermediate Algebra (as a reminder
about his struggles with that material), Wesley demonstrates that in these early courses, he had
mixed experiences.
We proceed to talk about his coursework and the obstacles, challenges, and supports that
he used to learn mathematics. From this conversation, two areas become clear: (1) factors that
contribute to his success and (2) what motivates him to succeed in mathematics.
Success in mathematics: “Man, I got some work to do.” From our discussion about
Wesley’s progress in his college mathematics courses, it appeared that it was relatively easy to
achieve success in some classes and in others, he needed to put in more effort. Curious about the
strategies that he used to be successful, I initiate a conversation with Wesley on this topic. He
responds, sharing about the ways that his challenges with the material were compounded by his
in-class experiences. Wide-eyed and chuckling, he shares this memory.
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Wesley: It was like, “Man, I got some work to do.” [Laughs] Yeah, it would be a lot of
people in there [saying], “I remember doing this in high school.” I would be like,
“I’ve never seen this before in my life. This is completely something new.”
Maxine: What did it do for you when you recognized this?
Wesley: I was like, "Well, I gotta study." In high school I did homework, but I don't
think I spent one second trying to study until I got to college. In college, I knew
I had never been exposed to [some of that material] before.
With this realization, he recognized that he needed to take different steps if he hoped to be
successful in these classes. Later, Wesley admits, “Now, as a student, I get busy, you know I
study all the time.” Soon, we transition into a conversation about his use of a combination of
electronic, physical, and personal strategies to achieve success in mathematics, including online
resources, study partners, study spaces, and his knowledge of mathematics.
Online resources. Our first conversation about Wesley’s use of online resources arises in
a discussion about his studying methods.
First thing I do is I read the chapter. And then try to solve for it. And while I’m reading
the chapter, I'll do the examples, but sometimes you can't do that cause it's too time
consuming. The turnover of when you know the information and when you're getting
tested is fast. So sometimes I still don't know how to do it after doing that and that's
when I'll turn to YouTube and once I YouTube, it's a matter of practicing. Online
sources are awesome. There's nothing new under the sun so everyone has already had
my problem, everyone has already solved my problem. So if I have access to everyone
via Google, Bing, or mathematics blogs, I can run into something in the very same way.
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Before I go into a new subject, I watch videos on it. They got guys on here that, “Okay,
this is the principle behind the whole concept.” It’s a lot of talking, explaining it. “Okay,
what you’re trying to find out here is how the line is changing over time,” or whatever. I
say, “Okay, this is the ultimate goal.” Because I found a lot of times, I perform a lot of
robotic processes, and why am I doing this? What is the goal behind it? What is the
object of the game? You know what I’m saying? It’s hard to play the game if you don’t
know the object of the game….
I wonder how Wesley learned about online resources, so I ask him about that. Wesley turns
towards me and begins to share about peers who soon became his friends.
Study partners. Smiling, Wesley recalls the relationships that he has built with his peers
and how these individuals contributed to his success.
Wesley: I met some guys who were really good math students, the tutors. I’d see them in
my class, and we’d work together to understand things, and then myself also
helping other people. Over the time we became friends, and they taught me
some techniques and whatnot.
Like this guy—I can’t remember his name now. He went to Berkeley. He was
really cool. He really instilled in me—he was like, “Look, YouTube has
everything. Utilize it,” you know what I’m saying? “They’re teaching
everything on here,” you know what I’m saying? He really put that in my head.
I took that to heart.
Maxine: Okay. What did that provide for you, being with others doing math?
Wesley: [A]ccess to people who were really math geniuses compared to myself and
opportunities to work with other people who you know, I’d see in my class, and
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we’d work together to understand things, and then myself also helping other
people. That’s the way to know that you know something is to try to explain it.
The peers whom Wesley met became more than classmates, they were his friends, tutors, study
partners, and overall resources. In these relationships, they supported each other in their quest to
understand course material. While Wesley met some of these peers in the classroom, he met
many in the Math Workshop, the physical space where he would do his work and study.
Study spaces (Math Workshop). Looking for a place to study, Wesley enrolled in a Math
Workshop, or math lab, for each of his mathematics courses. This is where he met many of his
peers.
Yeah, the workshop was a big part of my math... That was where I could sneak away to
study. At first, at this point, I was taking it just to have a place to go where I can just
focus as opposed go in a library and every two seconds you see somebody you
know…When I go into the math lab, everyone was in there doing math, so it was a good
place to be.
Practice of Understanding. Aside from each of these physical components that Wesley
uses to solve math problems, he also makes use of his own knowledge of mathematics to find
answers to the mathematics problems that he faces. In particular, this method came to light when
we talked about whether he prefers rule-based or conceptually-based math instruction.
Wesley: I like to know the rules because if I understand the rules and how it works, I can
come up with my own because like adding and subtraction. Once you start
borrowing and carrying over, you know, that's the rules. You add one here and
add a zero here. I came up with my...I would count the edges of numbers in
order to add up if you know you had a 4 here and a 5 here [demonstrates
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counting the edges]. If I had a 4, I would count from the bottom here, so I'd
count 1, 2, 3, 4 or if I had a 3 here, I'd count 1, 2, 3.
Maxine: Oh, that's interesting
Wesley: Yes, I remember things in weird ways.
Maxine: But they work for you?
Wesley: The stupider it is, the better.
Although Wesley might refer to his method as ‘stupid,’ the reality is that his seemingly
unconventional practices work well enough for him to progress thorough remedial and college
math in community college.
Much of Wesley’s success in mathematics stems from his willingness to use multiple
resources to help him learn material. In addition to using the math lab as a study space, he
learned how to build mutually-supportive relationships with his peers such that they helped each
other achieve success by sharing resources—such as tutoring websites—and knowledge. With
each of these strategies, Wesley became a learner who consistently earned As in his remedial
coursework. Given Wesley’s earlier struggles, what motivates him to be successful in
mathematics? He talks about these motivations, particularly during those times when personal
challenges meet academic challenges.
Motivated to succeed: In our second meeting, my conversation with Wesley turns to a
discussion about his motivation to excel in mathematics when we review his final grade in Pre-
Calculus. A conversation emerges about his personal life and reminds me that student success
often involves dealing with life’s circumstances outside of the classroom.
Maxine: You did the math workshop along with pre-calculus, and got a C in that one.
What would you say happened here?
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Wesley: I had some complicated life things going on [laughs]. That was along the time
my wife and I were—we were going through some really, really rough patches.
Over the next couple of semesters, I was like, “Man.” She was trying to make me
quit school. Just a lot of different external things outside of school began to really
take a toll on me, so it was really difficult.
Then also in that class, Miss Parker—a very nice lady. She, she used PowerPoint.
I would literally be just sitting there, just looking [stares blankly]. I don’t know if
I was looking, actually looking at the slide. I was just there. It just became like,
“This is just killing me.” I hate that mode of teaching.
Although Wesley faced academic and personal challenges in the Calculus series, he passed his
classes—even if he had to retake one course. Curious about his motivation during these times of
academic and personal difficulties, I ask him to share about what encourages him to persist in
mathematics even during difficult times. He shares,
In my field, you gotta be able to analyze data, you gotta be able to organize things. You
know, mathematics is being able to take information and produce a process that leads to a
result […] So it teaches you how to think.
With this response, he answers my question about the connection between mathematics and his
career aspirations. He continues to share his motivations.
Also, I always thought that math was a sort of a measure of how well you'd do in
everything else. Because that's probably one of the more difficult classes, so if I'm doing
well here, then everything else should fall in line. So I'd always be motivated to work
hard in math.
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So, although Wesley connected mathematics with his academics, personal life, and career in
limited ways in high school, he links these clearly now. He is also motivated by his ability to use
mathematics to “figure out” “pretty cool” things, and ultimately shares that classroom
interactions with his peers serve as key incentives for his success in mathematics.
It would make me upset that I didn’t know what [the instructor] was talking about.
There’d be a lot of people there, and they’d be like, “Oh, okay,” and they’d be asking
questions. I’m sitting here, too, and this dude understands and I don’t? I don’t like that. I
feel I’m not as smart as this guy. I have to figure this out ‘cause I can’t let that happen.
That was a lot of motivating.
Wesley’s competitive nature, first introduced in his stories about his elementary school years,
resurfaces and encourages him to use the different study methods, such as online resources, peer
support, and study spaces to help him make sense of coursework. Finally, when Wesley has
challenges, he thinks about some of the difficulties that he has faced in the past; the factors that
brought him to college continue to motivate him to persist despite difficulties.
I figured out, after going through multiple jobs and careers and doing things, like, “I
don’t like doing none of this stuff. It’s just terrible.” I have to better my education. That’s
the only way that I’m knowing. I have to put myself in a better position so I can do
something different than what I’m currently doing or qualified for. I have to upgrade my
education so that I’m qualified for more things, and maybe I can get out of things that I’m
doing now into something that’s less displeasureable,” [laughter].
Wesley’s decision to “better [his] education” and persist in mathematics even when he
has personal and academic challenges is fueled by several factors. His interest in mathematics,
appreciation for the subject, the way it prepares him to excel in other courses, and his
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understanding of the need to create a “better position” for himself all move him through
mathematics and closer to his degree. His ability to connect these areas differently than he has in
the past may be the result of life experiences and maturity, but they also speak to the importance
of having supports that help students make these types of valuable connections at all grade
levels.
Instructors—Race—promoting resistance and offering support
In general, Wesley speaks about his relationships with professors positively, but believes that
their ability to be both supportive and helpful was imbalanced. Starting this description with a
calm tone, as the discussion progresses, there are multiple inflections in his voice, indicating
frustration and even annoyance as he recalls the experiences.
Most of my professors were very willing to help. Some did a great job of explaining, but
that occurred very seldomly. Maybe it was my lack of understanding that didn’t allow me
to even understand the explanation. I remember times I would be sitting in calculus class
and I wouldn’t know what the heck was going on, and I couldn’t even ask a question,
because I didn’t know what to say—I can’t just say, “I don’t get it.” But I’d ask. For the
most part, they interacted well. Some, in the beginning, did not, but I’d keep asking
questions and keep asking questions until, “Okay, you’re gonna have to respect the fact
that you’re gonna have to teach me something. You may as well get it over with.” They
were fine with it.
Following Wesley’s last comment, I ask whether or not he has had an experience where he
believes his mathematics instructors were not supportive or helpful. He nods and says that
although these incidents “mostly happened with science instructors,” there was an experience
with a mathematics instructor.
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Wesley: I may be small-minded. I automatically thought it was a race thing. I’m one of
few [Black students] in the class always, and I see other people getting help.
Then, you go to ‘em, and they’re overdramatic about it, “Oh, you didn’t listen. I
just went over this.” “Okay, well, go over it again. I didn’t get it.”
Maxine: Do you remember a specific time when someone said that?
Wesley: I had one in particular that I remember. I stopped asking a lady for help, actually.
There was something I didn’t understand. I was like, “I’m gonna ask for help.” I
was sitting there. My friend James, he was always saying, “Hey, she doesn’t like
you.” [laughs] I was like, “What are you talking about?” I didn’t pay any
attention to it. I went to ask her about this. It felt like she was trying to put me
down almost.
Maxine: Well, what did she say, or what did she do?
Wesley: She was like, “You didn’t listen to what I was saying? What are you doing?” I’m
looking at my friend. I guess it didn’t really affect me in the way that I felt bad or
anything. I was trying to keep from laughing, because he had just told me that,
that “I don’t think this lady likes you.” I told her, I was like, “Okay, well, the
way you explained it earlier isn’t working for me. Do you have another way of
doing it, or should I go to someone else? Because I’m obviously trying to
understand, but if you can’t help me, tell me.” She stopped for a moment and
thought about it. From that point, she changed—in the way in which she would
approach helping me.
By being persistent about asking his instructor for support, Wesley got the help that he needed.
First though, he had to deal with her seeming reluctance to answer his questions. While he was
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able to resolve this incident and work with this instructor, interactions with other professors were
less comfortable for him and ultimately, affected his classroom experience. Leaning back in his
chair, he shakes his head, and talks about his thoughts during those times.
Wesley: It made me not wanna go [to class]. “I don’t even have a chance here. I’m not
gonna get the benefit of the doubt on anything.” No matter what, a professor gets
the last word, especially in something like math.
Maxine: Any other ways that their behavior might have affected you?
Wesley: It pissed me off sometimes, and I was like, “Okay, I’m gonna show this son of a-
-”[laughs].
Here, he catches himself and stops short, but the meaning was crystal clear. I follow up to learn
more.
Maxine: Yeah, and what did you do to show them?
Wesley: I worked harder, you know what I’m saying? Ask more questions. Come with
pre-prepared questions to ask that would be difficult for them to answer. I’m like,
“Okay, we’re gonna be difficult,” then I’d go find the hard question. I’d come to
class and I’d ask it. “I can’t get into that right now.” “Well, that’s what I wanna
know. You can’t answer the question? What’s going on here?” My revenge was
always, “I’m gonna do better, and I’m gonna ask really, really, hard questions”
As Wesley continues to share about these experiences with instructors, it becomes clear that he
believes their practices are unfair and in some cases, racist. This sparks a thought for me, “I
wonder if he’s had any Black instructors.” So I ask him. Wesley smiles, then shares about a
Black mathematics instructor who was a role model and affirmed his progress in community
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college. We talk about his interactions with her and how they affected his experience of feeling
welcome at the school and overall, his progress as a mathematics learner and doer.
Wesley: [O]ne of my favorite professors, Professor Asimah was his name, he was from
Africa but he went to school in France…Really, awesome guy, very intelligent,
but sometimes I did not understand what he was talking about and I'm like, I
know he's so smart, how could he not explain this to me? [I]t might be
because…there's a communication gap there with their language versus my
language.
Maxine: And how did that impact or influence your learning?
Wesley: Well, I had to find other means…And I would ask him again.
Maxine: Ok, any other memorable professors? Any other Black math professors?
Wesley: My first professor was a Black lady. I liked her a lot. She didn’t take no mess,
though [laughs]. Throughout my progress, I would see her just walking through
campus. She would always, “Hey, how you doing?” Talk to me. “What are you
taking now? Good. You’d better keep it up. Remember everything I taught you.”
I would see her over the semester. She was a very nice lady.
Maxine: What did her words, “Keep going. Remember what I taught you,” even saying
“Hi” to you, how did that affect you?
Wesley: It would make me feel more comfortable. Sometimes, you end up being a face in
a big room. I may have been one of 50 million, but at that one point in time when
we were communicating, I thought, “Oh, she remembers me.” I felt good.
Maxine: Did it also make a difference for you to see somebody who looked like you at
the front of the classroom?
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Wesley: Most definitely. Seeing her was great. I would feel inspired seeing her teaching
and think about what obstacles she had to navigate to get here. That was
inspiring.
Maxine: Anything else you’d say to yourself?
Wesley: “I’d better do good.” [laughs] “I’d better do good, or I’m gonna make us look
bad.” [Laughs]… You know I can't sit up here in this class and be the only Black
dude and fail, you know. I'm gonna make everybody look bad. That's the worst
part, right? I'm gonna make everybody look bad.
Maxine: When I hear you say “I’m gonna make us look bad”, it makes me wonder if
there was any kind of—I don’t wanna put this word on you, but any kind of
pressure that you put on yourself?
Wesley: Yeah. I think it’s a lot of pressure on Black students.
Maxine: In what way?
Wesley: We feel we don’t wanna—if we fail, we believe that we’re being stereotypical.
We can’t just fail and just try again. It’s not that simple. That’s what it feels like,
you know what I’m saying? It’s a tremendous—I was just having a conversation
about this with a guy on my job, a white guy. He was reading something about—
they were comparing results of a test. They turned it into some official test. They
said the Black students did a lot worse than the Whites. Then, they said, “Okay,
this is just”—they didn’t make [the test] formal. Then, they see those disparities
disappear, even though the test is exactly the same. They did this a couple of
different times. I told him, “Black students, we got a lot of pressure.” If I fail,
it’s not just a simple failure, you know what I’m saying? It’s a whole lot more
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involved. That little tweak in your psyche, it can tear you up, you know what I’m
saying? It can really put a barrier on your ability to perform.
Maxine: Did that ever happen for you?
Wesley: Yeah. [laughs] A couple of times. It’s difficult to get over.
Maxine: Then, how did you get over it? ‘Cause, you’ve already transferred. You passed
the math classes.
Wesley: Sometimes, I still deal with it, but I just try to calm down. I eat Reese’s Peanut
Butter Cups, and take a sip of my water. You’re like, “Okay, I prepared for this.
Let’s just do what we did when we were preparing, and hopefully it’ll work out
for the best. You know you knew what you were doing when you were
preparing. Let’s make it happen.” Sometimes, that works. Most of the times it
works; sometimes, it don’t [laughs].
In our conversations about instructors, it seems apparent that Wesley’s experiences in the
classroom influence his behaviors in multiple ways. Whether he believes that he needs to assert
himself to get answers to his questions, retaliate when he feels mistreated, or do well so he can
be a positive race representative, Wesley’s comments highlight that his identity as a mathematics
learner is complex. Creating this identity involves more than understanding material, completing
homework, and passing exams. The process also includes viewing himself as one who must
defend himself, adopt the role as a race representative, and ultimately, engage in self-talk to
“calm down” if he hopes to be successful. That he refers to research that appears to be Steele’s
Stereotype Threat and then connects the conversation about the literature with his experience in
the classroom, further demonstrates that his memories of mathematics have resulted in a “little
tweak in [his] psyche.” While Wesley has found practices that help him to achieve in
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mathematics, his experiences have been marred by memories of multiple challenges and
difficulties.
Despite these challenges, Wesley has been positively influenced by several mathematics
instructors, including a Black math professor with a foreign accent and his first mathematics
instructor, a Black woman. While learning from Professor Asimah was sometimes difficult, and
the presence of the Black female instructor in the classroom sparked a concern that his poor
performance could make other Black students “look bad,” Wesley benefitted from seeing
instructors who look like him at the front of the classroom. Ultimately, he was influenced and
inspired by their presence; all of this encouraged him to be a stronger mathematics student.
The First Comment, Yet Final Reflection
Now, in his first semester at a four-year university since transferring from LA North,
Wesley is not enrolled in a mathematics course. This idea is important because during our first
conversation, I asked why he decided to participate in this study. He shifts in his seat, leans
towards the recorder, and shares these thoughts with me.
Well, higher math and higher sciences have a low frequency of Black students. It's
something I’ve noticed, you know, I can't even be absent because it's very noticeable.
Because I’m the only dark face most of the time. Maybe one or two others, you know,
most of the time they're from foreign countries and you know, they always seem to do
pretty well, but as far as what you would consider African-American, they are not. I
always thought there was something wrong with that.
So, if there's some information that I can provide to help, maybe one or two more will be
there next semester, two more the next and it can grow from there because from what I
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know, African-Americans have a strong past history of science and mathematics and
along the way somewhere it got lost and I don't know why.
Although Wesley is not enrolled in a mathematics course, memories of his experiences in these
classes are vivid and still influence the ways that he perceives himself as a mathematics learner
and doer. Considering that he is the only participant who has transferred from community
college to a four-year institution, it is important to consider how this final statement (actually his
first statement during our initial meeting), though only reflective of his experiences, could shed
light on the experiences of others who have successfully completed remedial mathematics in
community college and intend to go on to four-year institutions.

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Maurice Knight—“I was in love with math”
Background
Maurice, a 29-year old Animal Science major, is a self-proclaimed “lov[er of] math”.
Sporting shoulder-length dreadlocks tied back by a black elastic band, thinly-rimmed spectacles,
black track pants, and a grey long-sleeved pull-over jersey, he arrived early for our first meeting
and kept himself occupied by reading a mathematics textbook in a cubicle. He came to this
study through Professor Rivera, who described Maurice in an email exchange as a student who
“has the potential to get better grades.” Once Maurice and I sit down and begin to talk, he shares
about how he came to study at LA North, his career aspirations, and some aspects of his life.
While Maurice has been at LA North for one semester, he graduated from high school
eleven years ago, and attended Greystone, a local community college, one year later. About this
experience, he shares,
They were classes that I took but didn't pass. Because that was the first year I went
through the first 8 weeks and the 16
th
week. Dropped out, left, [and]…decided I was not
gonna do school for maybe three years [and then] I was workin' at a nice restaurant job.
After some time, Maurice lost the job because he was “negligent,” and decided to return to
college. Sharing honestly about his reason for returning to school, he mentions, “[p]rimarily, the
plan was to return so that I can receive the financial aid [and] keep [my share of the] rent paid at
my apartment.” With a look of surprise and delight, he then shared, “but when I started taking
classes again, I was determined to stay in the game...I was searching for a better outcome in my
life.” Although, he “bounc[ed] back and forth” between different colleges in the area, earlier this
year he transferred to LA North from Piston when he learned that the previous semester was the
“last semester…that you’re required to take geometric plane if you’re going to transfer.” He had
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not passed his Essentials Plane Geometry course during the prior semester, and so transferring
was an opportunity to bypass taking this final developmental mathematics course at Piston
College and enter College Algebra at LA North. With six courses remaining (three mathematics
and three science) before earning his Associate’s degree, Maurice expects to transfer to a four-
year university within the year.
Maurice lives with his mother, younger sister (three years his junior), and his six-year old
nephew; with a hint of sadness in his voice, he also shares about his dad—a tailor and musician.
“My father passed away in June of 2008 around the time my sister was expected to graduate. I
was 20 years old at the time. My mother told me the news the day after he passed.” Although
Maurice has explored several fields, including “accounting,” ”EMT”, and “firefighting,” he has
settled on Animal Science and wants to earn a Bachelor’s and Master’s degree in the field.
Smiling, he tells me that he plans to become a veterinarian or animal nutritionist, open an animal
hospital, and eventually “take part in makin’ a contribution towards the animal area.” Maurice’s
love of mathematics, “made it easy to stay involved in science classes and that inspired [him] to
want to become a veterinarian.” While he works towards his anticipated career, he is also
employed as a server at a local fast food restaurant.
The Early Years
“The Fives is The Easiest, 'Cause You're Goin' by Five.” During each of our
conversations, Maurice shared mathematics memories and the ways different interactions with
family members and teachers shaped who he is as a mathematics learner and doer. Curious
about these moments, I asked Maurice to describe one. His earliest mathematics memory took
place with his “Daddy” in elementary school; he smiles broadly as he recalls these memories of
his father, “He'd sing songs with math. He'd have a table with one times table, two times, three
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times. He'd be like, ‘The fives is the easiest, 'cause you're goin' by five. Twos, you're goin' by
twos. Threes, you're goin' by threes.’” During these tutoring sessions, Maurice’s dad allowed
him to think independently and supported him when needed. Imitating his father by speaking
slowly and calmly, he says,
If he had to go and sew his clothes, he had us in that same room while he was sewin’. He
would, ‘How you doin'? You need help?’ He'll stop, come help us, and then go back to
sew… My dad, he used love to teach us. It was a lot of fun. We'd get extra time to play
outside, if we nailed it. It made me happy.
Maurice juxtaposes stories about his dad with memories of his “Momma’s” teaching practices.
Changing from a gentle to more stern tone, he says, “My momma she was a whole different
story.” He turns up one corner of his mouth and furrows his brow, “Her teaching methods was,
man, it was not my favorite. No. She had a ruler stick. [I called her] Hittin' Sam. She was bangin'
the walls to scare us. She used fear to teach us.” I ask him if he can recall any details from those
moments. He shares, “I’d try and learn somethin'. If I didn't get it, she'd clown me. She'd say,
‘This is why this-and-this is happenin'.’ Man, I did not wanna learn from my mom.” Memories
of these stark differences between his parents’ teaching practices set the stage for what Maurice
would appreciate and dislike about his mathematics instructors and how he would distinguish
between ‘good’ and ‘bad’ teaching and support in college.
Elementary School: “He do just as good at chess as he’s doin’ good at math.”
Maurice’s fondest memories of elementary school mathematics were of Mr. Horn, his chess
teacher who often visited during his mathematics period. “Mr. Horn wasn’t a math
teacher…[but] he loved math [and] was really good friends with my math teacher.” Offering an
example of the kinds of conversations that he overheard between the two instructors, Maurice
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smiles and shares, “[Mr. Horn] and the math teacher would always talk about me, because I was
really good at chess, and I was really good at math in elementary school.” He also recalls Mr.
Horn’s encouraging words, “He’d be like, ‘You know what? He do just as good at chess as he’s
doin’ good at math. Your teacher tells me you are amazing in numbers. It seems like it’s easy to
you.’” Enacting writing gestures midway through his next statements, he continues with Mr.
Horn’s comments, “When the teacher asked you to solve it, you go write on the board, and you
solve it. Your confidence is off the charts. You have very good confidence with numbers and
how you move your pieces on the board.” Later, when he speaks about his elementary school
mathematics teacher (he could not recall his name), Maurice explains the ways his teacher used
words and instructional practices to encourage students to participate and how these fueled his
own desire to engage and learn mathematics.
Maurice’s excitement when he speaks about his mathematics teacher prompts me to ask
him about the ways that the instructor engaged students. “He played games—board games. He'd
bring Sorry, but make it a math version of Sorry. He'd do Monopoly and make it a math version
of Monopoly. Where’s the money? was mathematical problems.” Maurice enjoyed participating
in class, so he was “always up on the board a lot.” He has such excitement in his voice as he
describes mathematics that I ask for a word or phrase to best describe his feelings during that
period. He leans back in his chair, grins, and says, “I was in love with math.” Maurice’s love
for mathematics and his skill made him a favorite among his peers who learned to “rely” on him
for help when they had difficulty with topics in class. Curious about his feelings towards their
responses, I asked Maurice how this attention made him feel. He shares that he was happy to
help because he knew their teacher would give out candy and extend recess time if everyone did
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well. These incentives motivated him to excel and to help his peers succeed; as a result, “The
class was always gettin' very good grades as a unit.”
While Maurice did not have many challenges in mathematics there were times when he
did not grasp all of the coursework. Often, his parents could not help him because they “didn't
know the math I knew.” However, encouraged when they affirmed him with phrases such as,
“’Now you got this’, ‘Your teacher says you're good at math’, and ‘You'll figure this out,’”
Maurice was reassured by their supportive words and trusted in his own abilities to solve
problems. When he did not grasp the material in class, he notes, “I could kinda teach myself.
Only because I had that confidence from the teacher, and my mom, and my dad.”
During these years, Maurice thrived off of the interactive classroom environment, his
ability to help his peers, and the positive comments from his teachers and his parents. Each of
these supports helped him to trust in his mathematics skills, gave him courage to attempt to solve
problems when the answers were not obvious, and ultimately bolstered his view of himself as a
mathematics learner. His trust, courage, and view of himself were valuable when he entered
high school and mathematics became more challenging.
Moving to High School: “It was always the book that really helped me figure out
how to solve all the problems.” Using words like, “quick,” “focused,” and “confident” in high
school mathematics, Maurice said, “I could solve any problem with speed and ease and I knew
how to explain my answers.” Although he was more challenged in Algebra when he “first got
introduced into letters,” it was not impossible to learn the material because (1) his “teachers were
really good” and (2) he “was in love with teaching [him]self math.” Reminiscing about his
experiences, he shares, “Somethin’ about math, it wasn’t mixed with words. It was just numbers.
I just loved learning how different numbers and different tricks gave you the same answer, you
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just solved it differently.” I ask Maurice about his classroom experiences in high school. He
shares that while he continued to teach himself new concepts and develop his love for
mathematics, he also became quieter in class; his behavior influenced his participation and in
turn, how he was viewed by others during his high school years.
Maxine: How did your peers, your teachers, your parents see you as a math student?
Maurice: I think they saw me as distant, only because I always sat in the back of the
classroom. I always found it not as easy for me to listen to the instructor
teaching. It was always the book that really helped me figure out how to solve
all the problems…but every once in a while, I’d look up and confirm with the
teacher. If they were doin’ problems, I would relate to the class and go to
participation, but when she would be teaching the lesson, I always went back
to the book cuz the book…gave me all the steps.
Although Maurice sat in the back of the class and focused on the textbook, his teachers
continued to engage him: “They asked me, ‘Hey, can you solve this,’ and I’d solve it quick, just
like that.” As the material became more challenging, he reached a turning point in his
mathematics studying and practicing. He recalls that he started “skipping problems that seemed
difficult.” “What were you thinking when you were skipping problems,” I asked. Waving his
hand as though he was swatting a fly, he responds, “I’m over it. I’m just not gonna solve it.”
Even when he skipped problems, his teachers still reacted in ways that he found encouraging.
“They’d be like I’m very intelligent, but I choose my problems. I should just do all of the
problems.” By focusing on the work that he completed and not his tendency to skip problems,
Maurice’s instructors began to shape how his perceptions of success in mathematics,
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Maurice: If I only got as far as I needed to, and couldn't figure it out, they're like, "You
know what? You got this far. That's not easy. You got most of the work done."
Then they did this [motions writing on a piece of paper]. "That's all you had to
do." Really, they just [helped to clarify] my awareness. That was more
important, than actually solving the problem, it was my awareness…Class
participation [was] more important to the teachers in my high school, than
actually solving a problem. They're like, "As long you get up and you're on the
board, there's your credit."
Maxine: Okay. How did you respond to that?
Maurice: That gave me the confidence, that even if I got it wrong, what was more
important, was that I was seen goin' up [to the board].
His burgeoning concept of success worked while he was in high school and ultimately helped
him to maintain his confidence in mathematics. However, when he entered college, a new
setting brought new instructors with new behaviors, practices, and expectations. This was the
start of the shift in Maurice’s mathematics performance.
College
In these discussions about his college years, Maurice’s perspectives shift with regards to
instructors, his views of his abilities, and mathematics, overall. Before we discuss this shift,
Maurice conjures positive memories of his experiences in college mathematics.
Linking Mathematics with His Life. During a 100-level course, Maurice had an
interaction that paralleled high school mathematics experiences and supported positive
perceptions of himself as a mathematics learner. I ask for details, so he leans forward and shares
about an interaction with Mr. Jones, his Intermediate Algebra instructor,
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There was a problem the teacher was showin’ the class—he couldn’t figure out. He was
tryin’ to work it out on the board, and I raised my hand, and I was like, “Can I show you
what I did?” I went on the board, and I used synthetic division. He was like, “How’d you
figure that out?” I was like, “Well, I was playing with all of the formulas that I learned
throughout this class so far, and this seemed to have made sense to get the answer.”
“How did Mr. Jones respond?” I ask. Imitating his instructor, Maurice says, “Wow, wow, you
actually stumped me cuz I couldn’t figure it out, but you figured it out.” After that incident, Mr.
Jones engaged Maurice in “small talk” whenever they met on campus. “He got into my personal
life. He was like, “Well, what are you in school for?” We had an in-depth conversation about my
plans for the future. That’s the first instructor that really had any care about my life personally.”
Recalling another positive classroom experience, Maurice speaks about the types of
assignments that his statistics instructor gave.
One of the problems was like, “You’re having a picnic with your family, and you need to
figure out how many so and so’s is goin’ with this and what juices to drink. How would
you create your survey, and what variables would you use based upon your family
members using this T-chart?
Speaking about her teaching style, Maurice says, “She was the only instructor that applied the
stats to the lifestyle, and that’s what really made me get more into depth with stats.” He earned
an A in this course.
Similar to his experiences in high school, there were certain college classes where
Maurice connected with instructors. For him, these connections happened when instructors
sought to learn more about him or found creative ways to connect learning with his life. While
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these positive memories reassured Maurice about his ability to be successful in mathematics, he
also faced challenges that negatively influenced his work practices.
The Downturn—“Why the hell would you mark a train a y?” After reflecting on his
positive interactions with professors in mathematics, I am curious about how Maurice’s
perception of his mathematics ability has developed in college, so I ask him to offer some words
to describe his current mathematics ability. With his mouth slightly twisted to the left and his
lips pouted, he says, “tired,” “frustrated,” and “able.” Even with his frustration, he reflects on his
relationship with mathematics positively saying, “It’s love and hate. I love it when I get it. I hate
it when I don’t get it.” He attributes this perspective and his relationship with mathematics to
two factors: (1) a lack of encouragement from professors and (2) more challenging course
material. Speaking about his interactions with professors he shakes his head, and says,
When I hit college, I’m just like, “Wow. Now the teachers aren’t really givin’ me
feedback. They’re just teaching the class and dismissing everybody.” I don’t really feel
like I’m doin’ a good job or not doin’ a good job so half of my ambition to do math is a
little bit gone. I still have the love for [math], [but] I’m not getting the constant evaluation
that I used to get in elementary school, in high school, in junior high school.
The second issue—more challenging course material—highlights a primary difference that
Maurice discovered between elementary, high school, and college mathematics.
I loved math in high school, [and] elementary school because it wasn’t as specific as it is
in college. The word problems in high school and elementary, I could read it and
understand. The college word problems, you could read it, and think it's multiplication,
but really, there's a variable somewhere in there.
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Frowning, he continues to share, “You couldn't figure that shit out—‘It's a train, so that's why
you mark that a Y.’ I'm sittin' there like, ‘Why the hell would you mark a train a Y?’”
This distinction between elementary, high school, and college level mathematics required
that Maurice spend additional time working out solutions, and even more time if he had
difficulty with the material. He reacted by questioning the connection between the topic and his
future career and ultimately, asks himself, “’When will I use this in my career?’ It’s the reason
why I skip them.” As we talk, it becomes evident that the habit of skipping problems, which he
started in high school, increased in college and eventually, led to skipping homework
assignments over time. When I ask how he feels if he needs to skip questions, he notes, “It just
make me feel like either I need to spend a little more time or focus on asking for help, which is
the hardest thing for me to do.” Leaning back in his chair, he says, “So I make myself believe in
the fact that I don’t really need to solve this problem, and I could skip it.” As Maurice recounts
his different mathematics experiences, he attributes his increased practice of skipping questions
to his experiences in an early mathematics course.
“I don’t really need to solve it if I can’t figure out the way he taught it.” Between
our first and second meetings, the frequency with which Maurice talks about skipping problems
increases, so I ask if he can recall an event or interaction that prompted his behavior. Maurice
pauses, sighs, and then begins to tell me about his experience in his first mathematics course,
Elementary Algebra. “Professor Lieu, wanted us to solve and get the answer that way he was
teaching it, because that’s what he was doing in his exams. I couldn’t get it the way he was doin’
it, but I figured out a way to get the answer my own way, and it wasn’t the way he was
teaching.” Accustomed to teaching himself mathematics and solving problems in his own way,
Maurice “would spend hours and hours doin’ the same steps [the Professsor] did to figure out
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how to do it.” When he could not successfully replicate his instructor’s steps, he would tell
himself, “I don’t really need to solve it if I can’t figure out the way he taught it,” skip questions,
and stop going to the board to solve problems. His instructor, recognizing his reticent behavior
and incomplete work, told Maurice that although he deserved “at least a high B,” he earned a C
in the course. Nodding as he spoke, Maurice shares what Professor Lieu’s told him, “he said,
‘Although you understood the concept of algebra very well, you didn’t show any interest in
participating in the class and you skipped problems.’” I ask Maurice for his thoughts on
Professor Lieu’s comments. He replies, “I knew exactly what he was talkin’ about because I was
distant in the class, wasn’t showin’ up a lot, and there were problems that I skip[ped].” At times,
Maurice seems to be indifferent about skipping problems; however after he becomes comfortable
with me, he is more willing to share about what gets in the ways of completing his homework.
“It's making you feel like you're a sorry-ass mathematician. Forget it.” After sharing
his reflections about our previous conversations, Maurice details what happens in the moments
when he recognizes that despite his efforts, he is unable to solve a problem. First he decides,
“I'm not even gonna deal with it,” rationalizing his decision by telling himself, “You know what?
I don't need to trouble myself with this problem.” Eventually, he says, “[T]here's other
opportunities for me to make up that work with the ones I'm comfortable with.” However, as
Maurice reminds me, that is only his first thought. Grimacing, he shares his next thought.
Then there's that other side of me that's just like, "Damn. You hit a loophole. This is
showing you a sign that you're weak. You don't need to deal with this. You need to stay
powerful…This one right now, don't worry about it. It's making you feel like you're a
sorry-ass mathematician. Forget it.
“’Powerful,’ that’s interesting,” I think. So I ask Maurice to say more about this idea.
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Maurice: When I solve a problem, and I nail the answer, it puts a smile on my face. I
have a certain glow, like, "I got this shit. This is mine." Then there's problems
where it's just like, "Okay, I can get this. I just need to put more time into it."
Then after another 30 minutes, I'm like, "Okay, this is really frustrating me. I
can't figure it out."
Then the next 15 minutes, and it's like, "What the hell's goin' on?" I start talkin'
to myself. That glow turns into maybe a dull grayish skin color. I start to look
flushed. Because I'm like, "Damn." Then I sit back, and I'm like, "Okay, let me
take two minutes. Let me take two minutes. Let me drink some orange juice or
somethin'. Maybe I'm hungry. Maybe I'm thirsty."
I'll go and I'll drink, I'll eat somethin'. I come back, and I'm like, "I still can't
figure this out. Man, the hell with it. I'm not dealin' with this.
Maxine: Yeah, and then in that moment, "The hell with it, I'm not dealin' with this,"
what's your experience of yourself then?
Maurice: It's a partially bad experience, because now I can't stop thinkin' about what
problem put me in my place. Because there's many times I can't go to sleep,
because I'm like, "I couldn’t nail this isotope. What the hell? Why couldn't I nail
this? This is my shit. You know what I mean? Why couldn't I nail this?" Then,
I'll go back and I'll try and solve it again. I'll end up with tears in my eyes. I'm
like, "Shit. I don't need to do this right now." [Bows his head]
In part, Maurice’s frustration stems from knowing, “I’ve always been able to figure out and do it;
[this is] what made me good in elementary school. That's what made me good in high school.
That's what made me good in junior high school.” Eventually, he tells himself, "Man, I only
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have two shots. Stress myself, or give up." I stress myself to a point where it's like if I shed a
tear, if my eyes get watery, I'm just like, "I'm done." For Maurice, after experiencing these
events and conversations multiple times, giving up becomes easier and easier.
After talking about this experience, we discuss what Maurice can do to “push [himself]
even further.”
That means spendin' the time to either go on YouTube and figure out how they do it. Do
it wrongly that way, to get an idea across. Or, to just sit back and just give that problem a
rest. Continue working on another problem. Then come back to it, but don't leave it alone
to marinate, and just disappear on you. Come back and at least attempt it again. If not,
take another break, but come back and attempt it again.
[Also,] I just have to open that door to accept help. Again, it falls on my pride. If I feel
like I couldn’t do it, I wouldn’t even go out for it. That's just me givin' up on the fact that
it's information that could better me. So, I’d tell myself, “Make your mistake, go to class,
ask your teacher, ‘How do you solve this?’” Let them solve it and show you how it is.
Then, at the end of the day you'll know how to solve it.
In what seems to be a lightbulb moment, he shares this seemingly simple strategy:
Even if I know I don't know, I should at least attempt to make a mistake. Even if it's
obviously wrong. The fact that I even put a line, or put a graph, will let the teacher know,
"Okay, he may have been tryin', may not been tryin', but he made an attempt, and that's
most important."
Initially, a periodic practice that began in high school, Maurice’s habit of skipping
problems ratcheted upwards when he met a professor who seemed to take on a one-sided
approach to problem solving. While Professor Lieu might have intended to help students by
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insisting that they follow his step-by-step method, this practice was not effective for Maurice.
Accustomed to teaching himself and directing his own learning, Maurice found his professor’s
rule both restrictive and stifling. Yet, he persisted. Using strategies to maneuver the difficulties
of mathematics and his insecurities, frustrations, and fears, Maurice continues to achieve
success; though, he is often frustrated when studying. He takes these unsuccessful memories
from class-to-class, which ultimately leads to more skipping. Considering Maurice’s pattern of
constantly skipping problems when discouraged, I wonder how he continues to pass his courses,
so we discuss this topic in our next conversation.
Success in Mathematics
“Just past history of learning it.” Curious about how Maurice can skip assignments,
yet understand material well enough to pass courses, I ask for his thoughts on this issue. He
responds simply, “Just past history of learning it.” Able to apply his prior knowledge to his
current mathematics problems, he shares, “I know the general aspect of a problem and what
equation it applies to because I’ve practiced it in the past. That gives me a little bit of confidence
even if I can’t figure it out all the way.” Although Maurice continues to understand course
material, he recognizes that his practices affect his grades. “I just get bored of doin’ the
homework [so] I just don’t turn in the homework. [T]eachers tell me…I’m an A or B student, but
my grades come out Bs and Cs because of my accumulation of points.” Given the collection of
experiences that Maurice shares in our conversations, I wondered about moments when he feels
successful, so I asked him to share one.
Pondering for a moment before speaking, Maurice tells me about the first exam that he
took in College Algebra—his current course—after taking an Intermediate Algebra class one
year prior. He explains, “The first exams are usually the reviews. It reflects off of what you
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learned so far, and I was very pleased with my grade cuz I got an A.” Clarifying why this
moment was so important, Maurice smiles and adds, “Although I didn’t review algebra in such a
long time, it just came to me when it came to takin’ the exam. I was very pleased that I didn’t
lose all of my gifts. It’ just needed retightenin’ and refreshenin’.”
This story highlights that once Maurice learns material, he is able to recall the
coursework for exams; this skill serves him well. To gain a better sense about how he
approaches homework, I ask him to share his step-by-step process when he solves mathematics
problems successfully. This is the focus of our next conversation.
Doing homework: step-by-step. Looking at the table as if he is looking at his textbook,
Maurice takes me through his step-by-step process for completing homework. His use of prior
knowledge of mathematics, his problem-solving skills, and instructions from the textbook to
understand the course material highlights the ways that teaching himself mathematics is still a
practice that he uses regularly. Pointing to the table as though he is pointing to a page in his
textbook, he continues, “They’ll use an exercise, so I’ll read the exercise. I’ll copy it down, cuz I
learn by writing. Then they’ll give you maybe about two or three problems [and] they’ll have
answers. They’ll give you how to break ‘em down.” Shaking his head, he shares, “I won’t even
look at ‘em. I’ll take a piece of paper, and I’ll block it. Then I’ll just look at the problems, work
it out myself.” Then, nodding, he says, “Once I feel like I find the answer, then I’ll look at the
answer. If it’s different, then I’ll see where I went wrong.” Using the examples from the
textbook to test himself—because they have printed answers—he solves problems and compares
his answers with what is in the textbook. He finishes with, “If it’s different, then I’ll see where I
went wrong.”
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Maurice’s strategy for solving mathematics problems appears straightforward: he uses his
prior knowledge along with sample questions and answers to guide his understanding of the
material and then attempts to solve other examples in the textbook. Then, he figures out whether
or not his answer is correct. After learning about Maurice’s performance when he understands
course material, I am interested in his motivation to do the work when his outcomes are not so
positive.
Motivation
“I get frustrated a lot, but at the same time, when I calm down, I’m back in it.”
Given our earlier conversations about Maurice’s lack of motivation to complete problems that
require more of his time, we discuss his incentive for continuing with mathematics as well as
obtaining a college degree; he highlights his “love and hate relationship” with mathematics,
Just knowing that it’s not an easy subject—is what’s keepin’ me inspired to keep playing
with numbers. I get frustrated a lot, but at the same time, when I calm down, I’m back in
it. I’ll get frustrated with it. I’ll not wanna bother with [math] anymore. I’ll say this is it,
but I’ll always be thinkin’ about math [and] wantin’ to go back to math. That is one
subject that I won’t fully understand, but I will try the best I can to understand it.
We also talk about how he continues to persist in mathematics when he needs to retake classes if
he has not done well, initially. His response reminds me of the perspective that he shared about
mathematics success in high school, “My grades my second time around were a lot better than
my first time. Even though I walk out of class with a C, I still got the general idea [of the work].
That, to me, is important.” While Maurice speaks about the factors that incentivize him to
persist in mathematics, he also addresses discouraging interactions with his instructors.
Reflecting on his experience with one mathematics instructor he shares,
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Maurice: “I’ve always had to been like, “I had to figure this out.” I can’t ask him. He’s
gonna make me feel like I ain’t shit if I ask him for it. ” When it comes to
math, I gotta be ready to get emotionally beaten down from it.
Maxine: It’s interesting choice of words—when you say “emotionally beaten down,”
can you say a little bit about that?
Maurice: I feel like [some] math teachers I’ve had have made me feel like shit…The
times I’ve came to them with questions, they’ve been like, “Well, figure it out.
Work it out.” “Do a little bit more practice,” instead of pull a sheet of paper
aside and be like, “Show me where you think you may be goin’ wrong.” I’ve
went to office hours [and] had a couple of ‘em be like, “You know what? I
don’t know how you’re not gettin’ it sometimes. The problem’s right here.
I really feel like in my mind, you’re mentally—you’re emotionally makin’ me
feel like shit. I don’t feel like I can do this math.”
While Maurice’s love for mathematics encourages him to continue to take classes, his
interactions with instructors interfere with his willingness to seek their help and eventually, lead
to skipping problems when he cannot figure out how to solve them. Also influential in
Maurice’s motivation in mathematics is the number of Black students who are in his class;
though what he has to say about the influence is not what I expect.
Race relations: “If I saw like maybe five or six, then it would impact me a little bit
more.” During our conversations about his classroom experiences, Maurice does not mention
racial diversity or discrimination, so I ask about his experiences to learn how they might be
similar or differ from other participants. I did not expect that my question would launch us into a
conversation about motivation in mathematics.
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Maxine: Have you noticed that there are more people that look like you, or fewer
people that look like you, or an equal amount as you move up the ranks in
math?
Maurice: Consistently, there's only been maybe one or two other [African-Americans] in
the class.
Maxine: Okay, does that make you feel any kinda way?
Maurice: It doesn't bother me. It really doesn't bother me. If I saw like maybe five or six,
then it would impact me a little bit more. Because then it'll make me feel like,
"Okay, I have peers in this classroom," but one or two to me is just like any
other student.
Maurice speaks about the lack of Black students in the classroom differently from other
participants in this study. For him, smaller numbers of Black students offer fewer options for
study group partners, “I feel like the more, the merrier. Two is very little to me. Two makes me
feel like I'm kind of by myself. I gotta do things my way. If there was three or four, best believe I
would approach.” He recounts an experience when he was in an African-American studies
course with 11 other Black students, “We had more questions. We had more ideas. We worked
together more…[B]ecause there was 12 of us. If we saw more people, we'd probably do better.
It's just when we're so low, I think it's not very much impact.” I am interested in this idea. On
one hand, Wesley believes that fewer Black students in his mathematics classes make him feel as
though he must succeed or else negatively frame how Black students will be perceived. On the
other hand, the effect on Maurice is different, yet somewhat the same. Although he does not
speak about discrimination or the pressure that Wesley mentions, similar to Wesley’s reaction,
with fewer Black students in Maurice’s class, he tends to focus on his work, and even isolates
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himself. Neither participant talks about this experience of being ‘the only’ or ‘one of the few’ as
appreciated, let alone positive.
Despite his challenges in mathematics, Maurice continues to create success in these
courses. Reflecting on our conversations about his difficulties when he struggles to solve
problems, his strategies for success, and his motivation to succeed, I become curious about how
Maurice defines success in mathematics.
Defining Success: Maurice’s Perspective
“It’s not important for me to perfect with A’s and B’s.” Following our earlier
conversation about success in mathematics, I wonder how Maurice defines this concept of ‘doing
well in math,’ so I ask him about this idea.
Maxine: What does it mean for you to do well in math class?
Maurice: It means I could solve problems.
Maxine: Okay, okay. Do you associate the grade with doing well at all, or no?
Maurice: No. No, I could care less about the grade I get in the class because I learn
somethin’ new. I learned somethin’ new regardless of what grade I get.
Although outside of the scope of this study, I am curious to know whether or not Maurice
connects success in mathematics with his goal to transfer to a four-year university. I intend for
this to be a brief conversation that could offer additional insight on his thought process about
success in mathematics. Little did I know it would alter the trajectory of our discussion.
When I ask how his he believes success in mathematics—and subsequently, grades—
could affect the ability to transfer, Maurice pauses, thinks, and then comments,
I’ve never really thought about it like that, only because it’s like I’m not at the career I
care about—the career that I want…In my mind, what I’m doing right now is somewhat
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important for me to get there, but it’s not important for me to perfect with A’s and
B’s...As long as I get the general understandings of it, I’ll worry about putting more work
into it later on…Once I know I’m two classes away from getting to my career classes,
then it becomes a little more important.
He asserts “grades do not determine the character of a person who’s passionate about their
thing…[so] if a school is lookin’ at my grades to see about my passion, they’re lookin’ at me the
wrong way.”
From this discussion about success and grades, Maurice bounces from conversation to
conversation, as if long-avoided memories were rushing towards him. He wipes away fresh tears
as he talks about difficulties including, his mother’s challenges: “It was really hard on my
momma. Raisin’ my sister and I was really hard on her;” mischievous childhood activities where
he would “mess up a lot;” his difficulty with staying “motivate[d] and inspire[d];” the desire to
be viewed positively: “Look. You can still be proud of me, even though I was a bad kid at
times;” challenges with counselors, “I haven’t had any counselor that has given me any good
feedback. Just straight bad feedback;” and his feelings of inadequacy when comparing himself to
his sister: “I’m three years behind my baby sister…playing catch up.” It was not long before
Maurice begins to share feelings about mathematics that differ from the ways he spoke during
previous conversations. Sighing heavily, he says,
It’s just math has so much work. It’s so much work. You have to constantly do it.
Although I have the gift for it, my patience isn’t there with it any more. Because my
patience isn’t there…I’m sittin’ there like, “Why am I still takin’ this class, even though I
know how to do this?” This is why I feel like it don’t matter what grade I get in math,
because it’s just the same shit to me. The same shit. It’s a frustration.
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My conversations with Maurice about mathematics in college highlight that while he
loves mathematics, sometimes difficulties with course material and his instructors influence how
he views himself as a mathematics learner and doer and in turn, impact his progress in these
courses. These experiences have shaped his perceptions of success in mathematics and become
factors that interfere with his progress. As a result of Maurice’s struggles with mathematics, his
frustrations with the material, and disappointment with some instructors, he engages in some
behaviors that may not differ much from other students who feel ‘stuck’ in the developmental
mathematics sequence (e.g. skipping problems, missing class). Yet, he continues to persist and
succeed. While Maurice points to a number of personal- and classroom-based factors that
influence him, he also touches on the ways that institutional policies affect his progress.
Sometimes Life and Institutional Challenges Get in the Way
“By the time I got my financial aid, I'm playing catch-up in my classes.” Similar to
others in this study, although Maurice lives with his family, he has a part-time job to pay for his
tuition, transportation, and bills at home. As noted previously, earlier in his academic career, he
rented an apartment with roommates while attending school. At the time, although he received a
Board of Govenor’s fee waiver
14
from the state, with this money, only “classes are paid
for…[but] you [can] get more money to you, for your books and stuff like that.” Then, although
“financial aid benefitted [him] financially in school…it didn't benefit [his] personal life with
rent.” Referring to his financial challenges, he says,

14
The Board of Governor’s fee waiver is used to pay for students’ college enrollment fees.
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I was fallin' behind on my rent, and then I couldn’t even—I was takin' out a student loan.
Didn't take out many. I think I took out maybe two different student loans…When I got
the money, things had happened where I had to financially take care of things.
These life issues were compounded by institutional mishaps, beginning with his financial aid
forms.
I filled out a FAFSA in 2006...I made a packet, but they always told me it was
incomplete. Then I said, "Incomplete as—you know what? I don't need this money." That
school was already beatin' around the bush with my financial aid. 'Cause they tell me I
have to fix some stuff, but they were losing my packets. They were losing papers and
stuff…I was lined up in the system for the LA City district, to be as a late-registered
student. They had a group of registered students. For some reason, I was listed as one
who had had to be set up with an appointment to be allowed to schedule classes.
By the time I was allowed to schedule classes, those classes were already almost full. My
[work schedule] had to be shifted.
Due to this administrative system glitch, Maurice was marked as a “late registrant” and received
his financial disbursement two months into the semester. Like a domino effect, the glitch
affected his ability to sign up for classes, the class schedule affected his work schedule, and
ultimately, both affected his study schedule. Frustrated, he shared, “Man, I had to work hella
hard. By the time I got my financial aid, I'm playing catch-up in my classes.” The “late
registrant” notation in his file created difficulties when he tried to register for courses—
By the time I was allowed to schedule classes, those classes were already almost
full…[A]ll they had was night classes. I'm like, ‘I work at night. I need those night
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shifts.’ My work schedule really made it really hard for me to get my homework done at
school…'cause when class was done, the next hour, I had to eat, to go to work, or go
home and do my homework there.
Financial challenges and the need to work impacted Maurice’s study time, forcing him to choose
between studying and working to pay for rent and other expenses. Eventually, he chose to move
home and focused on school.
In this last discussion, Maurice unveils much of what goes unnoticed in discussions about
student success in mathematics—the multiple academic, financial, and institutional challenges
that impact their success. Maurice persists beyond these challenges and continues to highlight
how inefficiencies in the college system can negatively impact students’ progress in these
courses.
Current Mathematics Class
When Maurice talks about experiences in his current class, College Algebra, he primarily
speaks about his instructor, Ms. Rivera. He describes her as “a blessing,” focusing on her ability
to explain the material and seek out students who need help, “She broke everything down… She
reiterates what she wants [us] to learn. There have been many times where students have asked
her the same thing. She switched it up and rewrote it and broke it down.” To demonstrate how
she supports students in an effort to help them succeed, he shares, “She literally came up [to me],
and she was like, "Hey, I know you're missing some work. You could make up some of this
stuff. Just turn 'em in to me." For Maurice, this level of support makes him, “feel like the
teacher’s on my side. Like you feel like the teacher is willing to throw aside her plan and her
syllabus to make sure that I get it. That is very important to me.” After some of his earlier
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negative experiences with instructors and his mathematics-related challenges, this response in a
higher-level mathematics class is encouraging.
Given his positive experiences in this class, I end our discussion with a final question, “If
you could do [this math class] again, what would you do differently?” Maurice smiles, then
shares,
The minute she's done with class, come straight to the library, and get it done. The
homework allowed me to at least go in the next class time, and just sit there, and just soak
in what she had to teach. Because the majority of the class, I was in class makin' up for
work I didn't do. She'd be teaching a new lesson, but I'd be on the previous lesson doin'
the work…It's like when she's done with the class, I'll do everything in my power to at
least stay on the level, or to stay ahead.
Next, he speaks about the need to attend tutoring, “Even if it's one problem, definitely take
advantage of the tutoring, because there's times I went for one problem, and end up stayin' to
finish my homework in there. 'Cause if I was stuck, [the tutors are] right there.”
After the final exam. Maurice shows up for our last interview without a knapsack or
books, only with a broad smile; he just completed his final exam for his College Algebra
mathematics class. After he sits down, we exchange pleasantries and I ask, “How was the exam
for you?” His response reflects disappointment and relief. Sighing, he says,
Taking these finals was—it wasn't easy. [I]t was a reflection of what I've skipped. What I
decided I did not want to learn. What I decided I did not want to put in time to. 'Cause
this math, I knew the majority of it, but there were those I've looked at. "Man, if only I
took that a little bit more time, it woulda gained me that extra confidence…They came
back to haunt me in this final.
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Presenting a side of himself that he had not revealed during our two previous meetings, we
discuss how his realization during this exam compares to his experiences during final exams for
other mathematics classes.
Maxine: It sounds like at some point, you recognized, "These are the things that I
skipped." In previous final exams, have you had that same experience? Of,
"Oh, these are the things that I skipped?" Or does it not even cross your radar?
Maurice: Hell, no! This is the only final I've had for my math where I've actually
reflected back, and was like, “Shit, I skipped this.”
Similar to his experiences when doing his homework, Maurice admits calmly,
I knew how to do the work, but to get the answer was the most hardest part. [T]here was
a formula I needed to get, when doin' the work, to pick it up. I only got as far as doing
the work, and didn't notice the formula, [so] I was able to do half of the work.
He shares that in other mathematics final exams, “There[‘s] another problem…or, another way to
go around it, to get the answer.” That was not the case on this exam. Once we finish talking
about his test, he brings up other realizations that he had since our last meeting,
It’s one thing when you tell yourself something and another thing when you hear yourself
out loud…[t]he second meeting kind of blew my mind. Because it was like, 'You know
what? I made excuses. That was like my excuse meeting.’ I was listening to myself. I
was, "Man, I was tellin' her this and this and this." Which is true, but it sounds like I'm
makin' excuses for me acceptin' failure. I want to be in animal science. Is anybody
gonna trust my ass? Is anybody gonna trust me? If I'm sayin', “This animal's on one leg. I
can't help him.”
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'Cause like, no, I can't live that life. "[This animal] has one eye. He's no use." No. Yet, I
have a dream of opening a facility for these animals, but here I am, half-assin' my life. No
one's gonna come to my facility. "That's the same brother that half-assed on [that math
class]. I don't wanna bring my dog here."
A few weeks following our final meeting, I contact Maurice to ask about his final grade.
The first time I we communicate, he says, “As far as informing you on my grade in Professor
Rivera’s class, I have yet to receive it. I’m waiting on [LA North] to remove a financial hold so
that I may view it.” During our next communication, I ask if he has received the course grade.
He replies, “Yes, she gave me a C for the course.”

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Abdul-Malik—“I stay in the cage with [math] and I come out. You know?”
Background
After sharing about my study with Donnell, a student representative from a campus
group, he says, “Sorry I don’t fit your study criteria, but I’ll see if I can find someone who’s
good for it.” We speak for a few minutes, then he turns and looks a few feet away. “Ay yo’
Malik,” he says to someone. Hearing Donnell call his name, a Black man walks in our direction.
Wearing a black kufi
15
, tunic, long beard, and a puffy down vest, he approaches us. “Yo, which
math you in?” Donnell asks his friend. “Trigonometry,” the Black man replies. Then Donnell
introduces me to Abdul-Malik, a Muslim, and tells him about my study. “She lookin’ for people
who started in 100-level and is takin’ 200-level now.” Soon, it becomes clear to me that Abdul
fits the study criteria, so I ask him if he would like to participate. “Could you send me some
details about your research?” I agree, send him an email with the information later that evening,
and ask if he would like to participate. He responds by the next morning.
Hello Ms. Roberts
After discussing with my family I decided to participate in your study. It sounds very
interesting and I would like to help your cause. We can choose the best time to meet next
week. I can be more certain Monday as to a specific time.
A few days later, Abdul meets me in the library for our first conversation. He approaches
the table where I am sitting and takes a seat across the table from me. “Actually, if you could sit
next to me, that would be easier, so we’re not too loud,” I say. With a calm tone and a quiet
voice, he says, “Ok, then can we sit on the other side of the table, so my back’s not facin’ the

15
A knitted skullcap that Muslim men wear.
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door?” His request reminds me of my cousin who, for personal safety reasons, would always sit
facing the door, so I oblige. He lets me know that because of his study schedule, he can only
meet for 30 minutes, so we quickly settle into our seats and he begins to share about some
aspects of his life.
Born and raised in a major city on the east coast, Abdul is a 37-year old, married,
mathematics major who moved to Los Angeles two years ago. He shares about what prompted
his move.
Maxine: What brought you to California? Why did you come here?
Abdul-Malik: Through life circumstances. I had a friend that was out here and I used to
come see him. It was like a fresh start for me. I can just be like a nerd. It
didn’t happen all of a sudden, but it was just an ease that I can finally find
who I am, as opposed to living in a place to where you have pressures on
you to be a certain thing.
I soon realize that he often speaks using metaphors
Maxine: Did you feel like you could just come here and reinvent yourself?
Abdul-Malik: Gradually. It wasn’t something that was designed. It’s just circumstances,
like the environment [and] circumstances helped that. It’s like if you drop
a seed right here. That seed wasn’t trying to grow. It’s just the soil, the
light, some rain came down. It ain’t just saying, “I’m gonna grow right
here. [points to one spot on the table] I’m gonna be right there.” [points to
another spot on the table]
When Abdul moved to Los Angeles, his friend took an interest in his career and began to speak
with him about his future. Prior to those conversations, Abdul had different plans for his life.
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I was comfortable with what I was doing in my profession just like drivin’ Uber. That
was working for me. I never been to school since I had dropped out of school and I got a
GED, so I was good. I didn’t really care about school…I mean school wasn’t on my
radar, and what I wanted to learn I didn’t have any problem goin’ and learnin’ myself,
readin’ what I wanted to learn.
Leaning towards the recorder, and speaking in a low tone, he shares some of the conversations
with his friend that prompted him to think differently about his life and his plans.
[H]e had a company, a HVAC company and he just got his company. He just got his
contractor license and he said, “You need to come. You should get a trade. You know
you need money you gonna have to take care of your family and all that.” He said, “so
come do some work for me and see how you like it.” I started doing little jobs for him
and I liked it. He said, “If you go to school, you get a degree for that, then I could
possibly pay you more and one day you can be a part of the company.” I said, “Alright.” I
said, “Why not go to LA North, it’s right down the block.”
At that point, Abdul decided to take courses so that he could earn a certificate while working
part-time. He shares about the benefits of coupling employment with classes.
I did one full semester in LA North and in refrigeration major. I did a refrigeration class
and a math—Construction Math I, level one… I did good in the class. I got two As after
the end of the semester. While I was doin’ it—I was doin’ it coupled with working with
my friend, so I was really getting more of an understanding of the job.
Although he understood his work and enjoyed the learning process, there were aspects of his job
that he did not enjoy. With a frown on his face, he describes his on-the-job experiences.
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It just so happened it was in the summer time, so it was so hot. I was coming home hot,
dirty, tired. Being with blue-collar guys with bad attitudes and foul mouths and I figured,
“This is not for me. I don’t like this. I like learning it, but I don’t like doing it.”
Recalling his transition from this type of work and subsequent journey into mathematics, he sits
upright and begins to share about the next step in his educational process.
I came into—it was a rock and a hard place because I’m like do I change my major?
What do I do? After consulting people and gettin’ advice, I had a friend he said “why
don’t you try computer programin’?” I said, “well, I can use my mind and I like
computers.” I took computer programmin’. I took a C++ Class. It almost killed me, but I
got an A.
Then, to be successful in computer programmin’ and computer science major, I had to go
into the math because I got to get my math straight. That was when my first journey of
math started.
His comments about his road towards mathematics prompts me to wonder where Abdul sees
himself in the future, so I ask.
I’m not really sure. I’m thinking as I go on it’s going to be more—I’ll have more
conviction on what I want to do, but I know which direction I want to go. Right now, I’ve
got my sights on being a top mathematician [smiles]. My sights is high.
Although unsure of what he wants to do in the field, Abdul-Malik is clear that he wants to be his
best as a mathematician. Blending in our voices with other low voices in the library, we discuss
the level of proficiency that he wants to develop and his aspirations.
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Abdul-Malik: [M]astering…being able to explain it…I’ve been checking out a few
mathematicians, they went to the university, so I can see myself doin’ that.
Yeah, definitely.
Maxine: Got it. Then where do you want to transfer to?
Abdul-Malik: Well, UCLA has a math program. It’s number eight in the whole world, so
I wouldn’t mind goin’ there or just anywhere really. I think that for me I
want to understand what I’m doin’. I don’t think that it’s in one place. I
think it’s about me no matter where I go I’m gonna get—I’m gonna do my
best. Whatever’s easiest for me, I like to have ease and comfortability in
my life. I wanna transfer and go get my BS, and then get the master’s, and
eventually get the PhD, and all of that. I think there’s a lot of things we
can do with our time. I just like learning math. I don’t necessarily wanna
do it to make money, or do it to be in a corporate where I—I would like
staying in the learning environment, and keep learning.
After learning about Abdul’s history in school and aspirations to be a top mathematician, I am
intrigued to learn more about his early mathematics experiences. So, next we embark on his
journey down his memory lane.
Early Years:
“Growing up, other stuff was what made you more okay ahead of everybody else,
not math.” Different from other participants in this study, Abdul has limited memories of his
school experiences prior to college.
I really had no sound memory of giving math any relevance because growing up other
stuff’s was what made you more okay ahead of everybody else, not math. Use your
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common sense, you have to use survival skills that was what was going on. That other
stuff it really didn’t—I really ain’t pay it no attention.
Thinking there is a story that I should ferret out, I continue to probe.
Maxine: Alright, so we’re just getting back to you as a kid in math. Let me ask you
like this, what’s your earliest memory of math?
Abdul-Malik: Okay, let me see. Okay, my early memory of math. I guess even numbers
is interesting. I memorized stuff like 5, 10, 15, 20, 2, 4, 6, 8 you know
stuff like that.
Maxine: Yeah, and who taught you that?
Abdul-Malik: I don’t know, I just have it in my mind. It just went in to my mind, and I
picked that out right there, yeah.
He continues to search for examples that he can offer and describes them while acting out
scenarios.
Abdul-Malik: My earliest memory in math was okay how much it cost? A pack of
cookies is $.50 or $.25. I got 24 pennies [opens hand and looks at palm]. I
need one more penny. Let me go and tell them, “look, I only got 24
pennies can I bring that back?” That was math, like kid math.
Right [pretends to take something out of his pocket], I got five Now and
Laters
16
, and I got two cousins, and they want one each and I better have
three left.
Maxine: [Laughs]

16
Now & Laters are a type of candy.
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Abdul-Malik: Right. Yeah, and you go by—you got a dollar, you go to the candy store,
the penny candy. You know how much candy you’re going to get. That
was math.
At this point in our conversation, I begin to think that I should steer the conversation towards
learning more details about Abdul’s early years. He begins to share about his experiences during
that time in a different way, focusing more on his life and finding ways to metaphorically
connect them to mathematics.
Maxine: Okay. I remember when you were talking earlier, I asked you a little bit
about you in elementary school and high school and math and you said ‘I
don’t really have a lot of memory around that ‘cuz there were tougher
things that I dealt with in life.’
Abdul-Malik: Right.
Maxine: Can you say a little bit about that?
Abdul-Malik: Well, I think that okay the narrative—my narrative in my life was more, I
think I can say whatever I was into I was into. My life that I was into was
more challenging and more like okay in math you’re learning new
formulas or you have to learn new information, but me living my life I
was learning new formulas and learning new information living life. For
me, I can compare [my life] to math because life you always got new
problems, and you always have new things that’s comin’ at you and you
have to deal with it. For me, my life just living life was math for me. I can
say that. When I see it on paper and it’s more easier because that mistake
that I do I can just erase it, but that mistake in life you got to pay for that.
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Maxine: Okay, I got it because life has a lot more—
Abdul-Malik: Yeah, you gonna have to deal with it. If you mess up one little step, that’s
it. Sometimes you don’t get to learn it’s not in a book, you gotta figure this
stuff out by watching and paying attention and learning it just coming
outta the sky in a sense.
Then, sitting back and gently placing his hands on the table, Abdul turns to me and connects
mathematics with life in a way that clarifies his thoughts about his experience with coursework.
For me, [math is] more lighter to me than actually living life in as far as that how you
compare learning something, and being tested on it, and having a final. In life, you got to
pay if you fail, or if you pass you get something tangible. This math that I’m doing now
it’s lighter. It’s like practice, like life practice.
I wonder about some of the challenges that are in Abdul’s narrative, but honestly, I am
uncomfortable asking about this topic with such little time remaining for our session. Then, in
our future sessions, we focus on other aspects of his life and on mathematics, so I do not create
the opportunity to revisit this topic. Before parting, we schedule to meet again during the
following week and at that time, we start with a conversation about Abdul’s high school
experiences.
High School: If you’re not looking a certain way, you’re gonna get a hard time in
school. I was like, “This is not for me.”
Similar to his elementary and middle school years, Abdul does not recall much about
school during his high school years.
Maxine: Which high school did you go to in [your city]?
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Abdul-Malik: I went to [school A]. I went to [school B]. [Pauses and thinks] Oh yeah,
and I went to [school C] maybe for like a day, and I’m like, “I’m outta
here.”
Maxine: Mm-hmm, what was it about that—
Abdul-Malik: Growing up in [my city], it’s about their style, your clothes. If you’re not
looking a certain way, you’re gonna get a hard time in school. I was like,
“This is not for me.”
Abdul looks in the distance and then turns his gaze towards me. He puts his hands on the table,
and continues. “I was young. I was in the tenth grade or whatever. I went in. I said, ‘I can’t go to
school. I gotta go and make money.’ I gotta come in school looking fly, because that was the
focus.”
Curious about what he just shared, I ask questions to learn more.
Maxine: When you said you had to go make money, what kind of things would you
do to make money?
Abdul-Malik: [B]ack in [my city] we used to sell clothes downtown. I had friends that
would sell clothes. We’d go to Chinatown and we got watches, clothes.
That’s where I started, just some selling clothes downtown. That brought
me enough money, maybe like a hundred-something dollars in my pocket
a day. I was good. I can dress. I can buy clothes. That was good for me.
Maxine: Were you going to class then?
Abdul-Malik: At first, when I was going to [school B] I used to go—after school I would
go downtown and work. After that, I think going to—I went from [school
B], and then I went to [school C]. Then it was just a stint. Even in junior
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high school and going into high school, socially it’s a lot to deal with. I
remember counting money and my friends having a lot of money and
counting—I guess that was the math I seen. Math to me means it’s not
about the numbers. It’s about going through a problem and figuring it out.
To me, that’s how I look at math. It’s not about numbers.
Reflecting on a conversation during our last meeting, I wonder if there’s a way to learn about any
classroom memories that he can share. So, being more focused on the data that I was collecting
for my study than the story that Abdul wanted me to know about himself, I pause the recorder
and tell him that I need to focus our conversations more towards his school experiences. I undo
the pause button on the recorder and reflected on his last statement. With my next question, I
hope to transition into a discussion about any classroom experiences that he can recall.
“Did you have that sense about math and numbers in grammar school and high school, or
is that sense more of a sense that you developed now?”
He turns towards me, leans on the table, and ever so gently and skillfully, checks me.
What’s happening is that, maybe, from this study, I think for my—okay, my profile might
be so different that even it would take somebody that came from the same background as
me, been through some stuff like me, and at the same age and stage of his life, then we
probably can see more of the things lining up. We would probably see a pattern.
Then, I recognize that all that Abdul is sharing is his story about mathematics. So, turning my
focus away from my needs, considering his perspective, and reflecting on our interactions thus
far, I respond to his comment.
Maxine: Yeah, but here’s the thing, is that, just because we don’t have that same
background, I don’t want to say, “Sorry, I can’t match with this.”
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Abdul-Malik: Okay, right. [sits back in his chair]
At this point, I let go of my agenda and listen as Abdul shares his story about mathematics.
The challenges that Abdul experienced during his early years overshadowed his school
experiences and shaped his identity as a mathematics doer and learner both in and out of the
classroom. While his ability to perform calculations was important for maneuvering through his
daily life, the social challenges that he faced in school influenced the value that he placed on
classroom learning prior to his tenure at LA North. While Abdul’s behavior during his college
years would continue to reflect his statement, “I can say whatever I was into I was into,” he gets
“into” mathematics at LA North differently than in his early years as a student in elementary,
grammar, and high school.
College Years
“When I took my GED, I just passed math.” In one of our first conversations about his
mathematics ability just before entering college, Abdul laughs while sharing about his
performance on the GED exam.
When I took my GED, I just passed math [laughs]. I did terrible in math, yeah. I did over
the bar—I did above average on reading. I remember when I took it, they said that my
reading and comprehension of reading is top in the nation, because they compare you
with other people when you take the GED. [But] my math was terrible. I just passed.
Considering the difference between his performance in the reading and mathematics sections on
the exam, I wonder if Abdul was surprised by his score. So I ask.
Abdul-Malik: [I]t didn’t stick out, like me getting that grade on the GED didn’t shock
me. I guess that would prove that that was a normal—something normal
for me… [W]hen I got that grade, I was happy to even just get my GED. I
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was good. Yeah, I guess that would show that it wasn’t nothing—nothing
abnormal to make me be like, “Oh man, I should have did better. Or, “I
should have known that.” I didn’t beat myself up. It was just like, “Oh, I
passed. I’m good.” Right, yeah. I felt good about that. That was an
achievement for me.
Maxine: That doesn’t surprise me, because you said you didn’t really need school,
cuz anything you wanted to learn you could go to the library to get the
book. Do you think, in a sense, that wasn’t the same way in math?
Abdul-Malik: Right, and maybe I just didn’t care about [math].
Maxine: Can you say more about that, like what would have you feel like that
about [math]?
Abdul-Malik: I think it’s the drive, your self-drive, what you feel. Somebody can say this
cup is $1 million, it’s worth $1 million right here, but if it’s not worth $1
million to me, I’m gonna walk right past it. It’s until I say that cup is
worth $1 million that I’m gonna treat it like that.
Prior to entering college, Abdul valued mastering mathematics primarily for what that mastery
offered him: a passing score on the GED, access to higher education, and eventually, a family-
sustaining job. In other words, different from when he was selling merchandise on the street,
mastering mathematics was a means to an end as well as an obstacle that he had to overcome
rather than something to learn or even appreciate. Before we speak about his experiences and
performance in mathematics during his college years, we discuss how his thoughts and feelings
about mathematics have evolved over time.
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Feelings about mathematics: “I guess I fed into the narrative of ‘Math is hard.’”
Given Abdul’s sparse school-based mathematics memories, initially I did not have a clear sense
of how his perception of himself as a mathematics learner and doer had developed over time.
However, all of this became clear through a series of conversations about his views of
mathematics and the factors that have influenced his perceptions. In our previous conversation
about the value that he placed on mathematics during his early years, he spoke about the value
that someone assigns to an object (the $1 million cup) and connects this concept with
mathematics. In that conversation, we just touched on his thoughts. Here, he expands on them.
Maxine: The last time we met, you said that you may not have done as well on the
math portion of the GED because—maybe it’s because you didn’t care
about math. Can you say a little bit about that, like how you felt about math
at that time?
Abdul-Malik: I can say that, for me, I think just, with me, with many people, they look at
math, or we look at math as something that’s just like math. It has its brand.
It’s been branded.
Maxine: What do you think the brand is?
Abdul-Malik: The brand is something that’s a turnoff, only do what you have to. The
brand is something that only smart people can do. It kind of turns people
off. I don’t know who branded the concept, but I think I basically fed into
that brand and I didn’t have no—I didn’t wanna put no—I didn’t wanna
invest in it because I already—I’m lookin’ at it like—I’m feeding into the
narrative of that brand that it has. I just wanted to get through it, and that
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was some basic stuff, now that I look back. That was only percentages and
time, a few word problems.
I am intrigued by this concept of the ‘brand’ of mathematics. On one hand, when Abdul adopted
the negative brand that was placed upon mathematics, he barely passed this portion of the GED
exam. On the other hand, now he is now doing well enough to qualify to participate in this
study. So, it is apparent that at some point his perception of the ‘brand’ on mathematics shifted.
I ask if we can focus on this turning point next in our conversation. He takes me back to an
interaction that he had with a peer after taking Intro to Algebra and enrolling in a computer
science course.
I have one guy—before I started getting into math, maybe a year ago, I was taking a
programming class. At that this time I didn’t know nothing about math. Math was
something to me—like everybody else, it was just a scary—not scary, but just, “I don’t
want to mess with that.”
Then, I spoke to this guy. I was understanding the programming class. He was a math
genius, allegedly, or what he said he was. He looked like it. He looked like a nerd. I said,
“You’re not getting it?” He said, “No, it’s hard for me.” I said, “But you know math.” He
said, “Math ain’t that hard. It’s only nine numbers. It depends on how you look at it.”
With this conversation and much counsel from his Intro to Algebra instructor, Abdul decided he
would take a second mathematics class and then opted to major in the subject. Before we launch
into a full conversation about his experiences in these courses, he offers a vivid metaphor to
describe the shift that occurred for him in mathematics.
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After getting in [the class] and just hanging out, it’s like The Wizard of Oz. They’re
thinking [math is] big, you know. When you lift back the curtain, you’re like, “Oh, it’s
only you back here. I can hang out back here.”
This shift in Abdul’s perception of mathematics from “negative” to something that he could
relate to easily was the start of his transition from one who did not “want to mess with [math] to
one who would later admit, “I fell in love with math.”
How did Abdul fall in love with mathematics? Once we start reviewing Abdul’s
transcript, I begin to learn about how his relationship with mathematics took root. I ask him to
share his thoughts about his experiences and in particular, how he developed an interest in
majoring in mathematics. With his hands folded as he looks towards me, he leans toward the
table and talks about his thoughts after completing Intro to Algebra.
I started in beginning algebra I think, [Intro to Algebra]. After that class, it was feeling
good. I was like, “oh, alright I got an A in Math. Oh, man this is alright.” Then, it was
a—I made a conscious decision that I’m gonna do computer science, so I knew I had to
go all the way up in the math, so I was on that mission. I’m like alright and the teacher
said, “Alright it’s a combo class you can do. You can do [the combo class].” I did some
research, and then I said, “alright, I’m gonna sign up for that.” That was ten units, and
that’s when I fell in love with math, right there in that class. I got an A in that class. I
became a tutor in the class before I even finished.
With his accomplishments in these classes and the opportunity to become a tutor, I could
understand how Abdul might develop an appreciation for mathematics. But love? That was an
interesting word to use, so I ask him to elaborate.
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Well, what I loved about it is that the challenge it gives me, and the feeling you get when
you get the problem. It’s like you have something that’s foreign to you, but it’s to be
respected. At the same time, you can figure it out and other people can’t figure it out.
People’s falling apart, people is dropping the class, but I stay in it and I stay in the cage
with it and I come out. You know?
I am clear about Abdul’s passion for mathematics, so I wonder how he believes others perceive
his mathematics skills, so I ask. Calmly, he shares,
Abdul-Malik: Well, my wife’s always sayin’ why is you always with that math work? Just
put that math book down [laughs]. She know I stay with a math book…So,
that’s how she look at me when it come to math. She call me her
mathematician.
Maxine: Would you call yourself a mathematician?
Abdul-Malik: Hm-mmm. Not yet. One day.
Maxine: Ok, so how do think your peers look at you?
Abdul-Malik: I think a lot of people look at me—not like I look at me—this is not from
arrogance or none of that. I would say others look at me surprised [opens
eyes widely], others look at me for help. To verify, to check certain things
they goin’ “what you got on?” Yeah, I think that’s how they look at me.
Maxine: Surprised? Why do you say that?
Abdul-Malik: When I’m in my class, I’m probably the only brotha in there let alone a
brotha from [my city], that got a certain swag. Even in my own, [from] my
own people, I’m a different category than the average kid that grew up.
Maybe he got a mother and a father or just a mother that never seen nothin’,
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he just going to school. I am 37, so it’s different. I’m just—I don’t know I
think that brings a surprise and thing to them.
Again, Abdul refers to some parts of his youth that may have been challenging. I want to learn
more about his experiences but I know that we have limited time together before he must return
to studying. So, I let go of my question and continue to focus on his perceptions about how
others view him. His response about how his peers view him prompts me to ask for words that
he would use to describe himself as a mathematics student. He pauses to think about the answer
to my question and humbly responds,
Tryin’ to master it. Tryin’ to get my hands around it. Tryin’ to get the process of
learning...I don’t think it’s a math student, I think it’s just you learn it. It’s just math is the
thing that I’m learning. It’s just math is more intricate, so I just I see myself as…
learning how to learn.
As we talk about his love for mathematics, I recall the phrase that Abdul used during our first
interview, “I think I can say whatever I was in to I was into.” On the surface, it appears that
Abdul is simply “into” mathematics and that he is glad to be performing well in his courses, but
viewed from another angle, Abdul is not only “into” mathematics. His shift as a mathematics
doer and learner is prompted by the respect that he developed for the intricacies of the subject.
As he says, he loves mathematics because of the challenge that it offers. These feelings of
respect and love for the challenge guide his interactions with mathematics and in particular, how
he goes about understanding the material and achieving success.
Success in Mathematics
An alternative perspective: “I’d be hard to judge and say who’s a good math learner
because maybe you get the grades, but you don’t know it.” Abdul’s and my discussion about
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his success in mathematics begins with a conversation about his perception of himself as a
student. While other participants offered personal attributes to answer this question, Abdul
responds differently.
Maxine: Do you think you are a good student?
Abdul-Malik: Well, I don’t really care about the student part. I just care about learning
what I’m learning.
Maxine: Do you think you are a good learner then?
Abdul-Malik: Not yet, I’m working on it.
Maxine: Ok, think about somebody who is a good math learner [he looks at the table
and then at me]. What are the characteristics of that person?
Abdul-Malik: Well, okay I don’t really know, I’d be hard to judge and say who’s a good
math learner because maybe you get the grades, but you don’t know it.
Maybe you got the grade but you can’t explain it. I think that for me, what I
gauge what’s a good learner is if I can understand what I’m doin’, and I can
teach others that. That’s my level right now, I wanna be able to understand
what I’m learning. Understand how to use it, and understand to put it in my
terminology and communicate it in any way I want.
I quickly recognize that similar to others in this study, with Abdul’s conceptualization of success,
he shifts the focus from getting high grades and instead, links learning and understanding with
excellence in mathematics. This realization prompts me to dig deeper in my quest to understand
his concept of success.
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Maxine: What I’m wondering is if the grades don’t show your math success, then
what would you say demonstrates math success? When I say success, I
mean like passing a class, passing a test.
Abdul-Malik: I think like, for example, today, I went to meet with my professor and she
was gonna do a review for the test and there was a girl sittin’ outside and I
was askin’ her, “How you doin’” and she was like, “Yeah, I just don’t
understand this one thing.” Then, I was able to say—it was about
bearings—and I said, “You got a protractor?” She said, “No.” I said, “Well,
this is what it’s about and I was able to show her.”…I guess that would be
something how I would gauge how somebody is successful with—not
saying that I’m successful, but if she was able to understand it and I was
able to show it to her and she got it, I think that’s success. Then, she said,
“Well, I’m also having trouble with this.” I just said, “Okay. Just do it like
this, this, this, and that.” Then, she got it. So, I think that, right there,
ultimately, I think that’s what shows that a person know what he doin’ if he
could do that.
Maxine: So, what you did with her, being able to explain it to her in a way that she
can get it and understand it?
Abdul-Malik: Right, and feel comfortable with like basically, they have a saying, I’m not
gonna catch the fish for you, but I can teach you how to fish. If you could
teach a person how to fish and they could catch their own fish, that’s
success, I think.
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Maxine: What happens in a situation—say she understands what you showed her and
then she goes to take the test, but she still doesn’t demonstrate it on the test,
do you think a person who’s not able to demonstrate it on a test can still
have understanding?
Abdul-Malik: Yeah, because I think in real life, when you’re gettin’ these jobs and
whatever, it’s not gonna be a test. It’s gonna be something abstract and you
gotta figure that out and I think that’s the space you need to grow. You can
get better. You can work on it, but if you box somebody in on a test and just
say what’s the answer for that, maybe that pressure, maybe I can’t think
right now, I just can’t do it, but when you’re more relaxed, I think it gives
people space to be creative and come up with the answer.
Maxine: Let’s go back to that conversation about success. Do you think you’re
successful in math?
Abdul-Malik: No, I can never say that.
Maxine: You don’t feel like you’ve ever been successful here?
Abdul-Malik: No, because I don’t wanna get comfortable. I’m too low to be feelin’ like
that. I’m still establishing myself, but I think I would feel a little bit once I
get in to calculus and be able to be comfortable in that. For this, it’s too
early to say.
Abdul’s response encourages me to rethink how I speak with other participants about how they
conceptualize success in math and in particular, how they view their own success. Now, mindful
about how I now use the word ‘success’ with Abdul, he and I transition into a discussion about
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the steps that he takes to learn mathematics. Early in the conversation, reasons for Abdul’s
success in mathematics become apparent.
What influences Abdul’s success?: “I guess with anything, but in particular with math,
I gave it value. It made me want to take my time and invest in it. I feel it’s worthy for me to
take my time and try to understand it.” As I continue to explore Abdul’s journey into
mathematics with him, the importance that he assigns to understanding and learning to gain
mastery over mathematics becomes even more apparent to me. A combination of his personal
characteristics, practices, and beliefs results in how he performs in the subject. More
specifically, Abdul attributes his performance in mathematics to his discipline or the seriousness
that he brings to his work, his study practices, and finally his religious faith and prayer.
Seriousness and discipline. I intend to learn about the factors that influence Abdul’s
success, but then recall that he does not view himself as successful in mathematics. So, I ask my
question differently, but with the same intention.
Maxine: What made it easy for you to learn [math]?
Abdul-Malik: I don’t know, if I had to answer that I would say I can kind of give my
seriousness, my discipline, my basically doing my homework, just doin’
what—it’s kind of like easy. You just follow the syllabus. Do your
homework. It’s kind of like I don’t think it’s set up to where it’s impossible
to get grades or whatever, but for me I really am—now that I’m going high
in math, now it makes me want to understand it more, and understand what
I’m doing more, right.
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I think it’s a stage that went from me just doing my homework and doing
what I got to do, to now I wanna understand it… Not just doing homework
and doing a book. I wanna go deeper in it and understand it.
Seeking clarity about how Abdul demonstrates his seriousness in his work, I ask for an example.
He ponders for a moment and then, begins to speak
I like to be neat. I like to practice and make sure I try to be neat. For me, I take pride in
my work. I don’t want to be writing crazy and ugly, and the teacher take it and want to
just put some coffee and a donut on my work. I want her to see or him to see like, “Hold
on. Let me put this up high.” This is something I took my time on. I like to be neat, take
my time, respect what I’m doing when I’m writing and I’m setting stuff up. Let me see if
I got some stuff and things to see.
Abdul takes his notebook from his knapsack and turns to a page with neatly-printed formulas.
“Look, this is how I like to do my thing right here. These are just notes.” His conversation about
what he needs to know and learn in mathematics prompts a discussion about how he studies and
approaches doing his homework.
Studying. Abdul also shares about some of his study practices.
I would use Purplesmath, some Khan Academy, stuff like that, and I would just do it on
my own. I did maybe two months of that during the break. Then, when I went to class,
the stuff I did, it was already like chapter four and chapter five stuff.
While Abdul focuses on study strategies such as using online resources and the course textbook,
I latch on to his statement, “I did maybe two months of that during the break” and recognize that
Abdul studied for his combo course months before he entered class. I am curious about this
practice, so I ask about his behavior.
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Maxine: What in your past had you say, “Okay, this is how I’m gonna prepare”?
Abdul-Malik: I think I read a lot of strategical—I read a lot about all kind of things. I read
about generals and leaders. One quote that sticks with me is that—it says
that a general does not declare war until he already won the war. That
means he already knows what’s going on over there. He already knows
what he’s gotta do, how much time, he knows the terrain…the weaknesses
and the strengths. He already conquered the war. Then he declared war. I
like to be ahead. That helps me. A wise general, he don’t declare war until
he already won the war
This comment reflects the strategic way that Abdul approaches mathematics and prepares for
whatever academic challenges he may encounter. With an image in my mind of Abdul using his
textbook, online resources, and notebook—like a battle plan—to determine how he will win the
war against mathematics, I ask “How do you approach studying.” He begins to describe his
process metaphorically, connecting studying with the process of baking a cake. He talks about
adding “eggs,” “flour,” “milk,” and other ingredients. While I appreciate the metaphor, I need a
clearer description, so I change my question.
Maxine: If I were to watch you, if I’m a fly on the wall and I’m watching you
studying, and you’re coming up against something that you’re not quite sure
how to do, what do you do with it?
Abdul-Malik: All right, I’m in a section. Okay, look, let me show you. For example, I’m
at this section right here [Flipping pages]. Then you’re right here. Yeah,
it’s six point—I’m looking at it. I say, “Equations involving inverse
trigonometry functions.” I start reading. It says, “Solve Y = 3 cosign 2X for
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X where it’s restricted in the interval 0 to pi.” I’m taking out what I know
already know.
Hunched over his textbook, looking at the problem, Abdul identifies “who’s the threat” and
“who I’m gonna focus on.” Step-by-step, he describes his process for understanding and
ultimately learning the material. Also telling, is Abdul’s rationale for why his studies.
What I can say on this is that I had to make a decision, and I noticed quick that you’re not
going to learn—like me I learn maybe less than five percent, maybe five to ten percent
from the professor. I like to go home, just me and my book. Then I use supplements to
help me whether it’s the Internet, YouTube, ask the teacher, hand math. [L]earning the
way that I’m formulating it and the way it’s designin’ is like 80 percent from the book
‘cuz then I have time, and I can just meditate with the book. That’s how I like to do it.
From his descriptions of his mathematics doing and learning practices, it is apparent that Abdul’s
love for mathematics inspires him to study in ways that ultimately help him to be successful.
The final set of tools in Abdul’s knapsack that help him to achieve success in mathematics is
more fundamental to who he is as a person, his Islamic faith and prayer.
Faith and prayer. Following our discussions about his strategy and accomplishments in
mathematics, I wonder if confidence in his abilities might play a role in Abdul’s success, so I
ask.
Maxine: [W]ould you say you have confidence in yourself around math?
Abdul-Malik: Well, I don’t know if it’s confidence around myself in math. I have
confidence in some—okay, whatever this is [points to his textbook], this is
a book and there’s instructions in it…[B]asically, I have confidence that I
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know how to read some directions. I have confidence that I know how to
read over and over and over and over and over and over till I get it.
Maxine: Yeah, yeah. It’s almost like, “Dang, how can we bottle that and have other
students have that view of themselves?” From your life experiences, what
has you have that perspective about yourself and your abilities? Is there
anything you can point to in particular?
Abdul-Malik: A lot of it comes from my faith and understanding my relationship with my
creator, and understanding the relationship with others, and understanding
the relationship with me and this life, and understand that it’s life. You’re
gonna go through tests. Nobody can escape it.
For example, I listened to this lecture and they were saying that we come
into this world, and a baby—even a baby is going through hardship,
because it come—it leaves a warm place that it knows. Then it’s crying.
Then it gotta go through teeth. That’s hard. They gotta learn how to crawl.
That’s hard. It falls down and that’s hard. They got learn how to eat real
food and that’s hard. Basically, life is nothing but—to me, it’s nothing but
going through stuff. That’s what math is. I’m on a new section. Oh, I gotta
go through it. If I embrace it and I just bust through it, that’s how I look at
it. What I’m learning how to do is bust through stuff. Right. It can happen
too. It’s just a matter of time. That’s all it is.
Both inspired and curious about Abdul’s comments, I ask him to share how he links his faith
with the study of mathematics. He takes out his phone, fiddles with it for a moment, and says, “I
have something maybe I can show you.” Once he finds what he is looking for, he begins to
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explain that before taking on any important venture, he says a prayer. He looks at his phone and
begins to read from it.
Oh, Allah, I seek your guidance in making a choice by virtue of your knowledge and I
seek ability by virtue of your power, and I ask you of your great bounty, you have power,
I have none, and you know, I know not. You are the knower of hidden things. Oh, Allah,
if, in your knowledge, this matter—”
He looks at me and says, “I mention the matter, whatever it is, but in this case, it’s to take this
precalculus class during the winter.”
If this matter is good for me both in this world and the hereafter, or my religion, my
livelihood, and my affairs, then ordain it for me. Make it easy for me and bless it for me.
If, in your knowledge, it is bad for me and my religion, my livelihood, and my affairs, or
for me both in this world and the next world, then turn me away from it and turn it away
from me, and ordain for me the good, whatever it may be, and make me pleased with it.”
So, before I take on a task, I say a prayer like this.
Abdul places his phone on the table, sits back, and then explains the importance of his faith.
For me, for my way of life, it’s very important to me that I do something…that’s pleasing
to my Lord… to choose things that is lawful for me to do…. Mathematics, I like it
because it’s lawful, it’s allowed, you learn, and again, I think, how it helps in the
relationship with my faith. In Islam, we learn to be very patient and we understand that
we’re gonna go through tests and trials through our life and you be patient. You seek the
aid of your Lord. It seemed like with me with mathematics, I’m still learnin’ and
discoverin’, but I find peace in it because it’s me and math. It’s not me and a lot of people
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involved in it. It’s just me and my relationship and my abilities and the work I put in it
has a effect on what my outcome is.
While Abdul and I speak more about his faith, its importance in his life, and his inspiration for
reverting
17
to Islam, we did not speak more about how his faith connects with mathematics. In
reality, we did not need to speak more on the topic. It is clear that Abdul’s faith provides him
with a sense of peace that guides him through his studies, even during the challenging times.
While it seems logical to think that Abdul’s success in mathematics is fueled by his
discipline and use of study practices and online resources, similar to Ophelia, his behaviors
emerge from something that is grander than these practices—his faith. Abdul uses his faith to
guide his choices about which mathematics courses he will take, and as a result, he is able to
engage with the subject from its physical components: a “book” and “instructions.” Keeping this
in mind, he knows that if he is willing to put in the work to learn and understand the material, he
can be successful in mathematics.
Motivation: “I wanna go to the Waldorf— in math.” With my sense that Abdul is
highly motivated to excel in mathematics, I become interested in knowing what inspires him to
study, particularly when the work becomes challenging. Offering more metaphors that need
little to no explanation, he shares his thoughts.
Well, I’ve got my sights on being a top mathematician. My sights is high. My sights is to
go where the best—okay you know in [my city] you can go to a restaurant at McDonald’s
or they used to have one called [upscale restaurant], or you wanna go to the Motel 8 or
you wanna go to the Waldorf? I wanna go to the Waldorf— in math.

17
“Reverting,” rather than converting to Islam refers to the concept that everyone is born with a belief in God.
Muslims refer to themselves as ‘reverts’ to indicate that they have a “pure faith” in their creator (About Islam, 2017)
islam.about.com/od/converts/g/revert_gt.htm
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From this statement, I recognize that Abdul’s desire to be the best incentivizes him to persist
even when faced with difficulties. At a subsequent meeting, I ask whether he has noticed
differences in the numbers of Black students in mathematics as he advances from course to
course. He nods and then shares how this difference inspires him to continue to persist.
[T]he look that I get when [people in class] see me, yes, that’s interesting too. I could tell,
when I’m going up higher and higher, that means I gotta know my stuff, because I
gotta—I can’t be playing, because just who I am and just what I represent or what I might
look like I represent, I can’t be playing…I ain’t come to play.
Abdul’s love for mathematics combined with the future that he sees for himself in the field,
inspires him to do his best to succeed. Similar to Wesley, who believes that he cannot perform
poorly in mathematics or else make “all of us look bad,” the dearth of Black students in upper-
level mathematics courses influences Abdul to succeed and progress in these classes. However,
unlike Wesley who admitted to being affected psychologically, Abdul does not share negative
ramifications from his thoughts.
Instructors: Influencing students’ experiences
Professor Rivera—“She said, basically, ‘you’re capable, you can do it.’” During our
first two interviews, Abdul did not speak much about his interactions with mathematics
instructors, so I devoted a majority of our final meeting to his relationship with faculty. This is
when I learn that since Abdul started to take mathematics at LA North, he has had two
instructors—Professors Rivera and Bhattacharya—both whom “got high ratings on [the] Rate
My Professor” website. Similar to other participants, faculty’s behaviors and practices influence
Abdul, but as is typical in my discussions with him, he offers a slight, yet meaningful twist on
his instructors’ impact and as such, sheds light on the topic from a different perspective.
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After taking the assessment exam and placing into Intro to Algebra, Abdul met Professor
Rivera. In our first conversation about her, he focuses on the ways that the format of her
assignments influenced his understanding of mathematics.
Ms. Rivera, she had online homework, and I didn’t have to engage with the book because
[if you] got it wrong, it would show you where you made a mistake, and it would help
you, and basically guide you until you got the right answer. I seen the mechanics of it.
Given Abdul’s inclination to take out his textbook and walk me through his practice when I
asked about his studying habits, I wonder about his connection with online homework.
Consistent with prior responses, he uses a descriptive metaphor to compare his experiences in
courses that use computer-based versus textbook-based instruction.
[T]hat experience for me was like being a sharpshooter. You don’t gotta get up close to
nobody…[I]t’s easier to be a sniper. You don’t gotta get nothing on you. It’s not
emotional, you don’t see, you don’t feel the person, the heartbeat. You don’t get to look
in the eyes, none of that. That’s the correlation of doing online homework. When you
doing that book homework, that’s up close, hand-to-hand combat. Because you gotta deal
with that book. You gotta deal with that eraser. You gonna be going through a lot of
paper. The eraser’s getting all over you. It’s more gruesome. When you’re doing your
homework out of the book, that’s up and close…I started really, really running through
scratch pads and running through erasers, running through pencils, it’s really—I guess I
got more invested and more involved in my work….Cuz you can’t turn that next page
until I understand. I can’t go to problem 22 or 23 unless I got 21. I can skip it, but I’m not
gonna complete my work. It’s more graphic, I think. Now that I’ve been trained like that,
I feel like I’m more dangerous with my math.
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Abdul’s explanation of his appreciation for more tactile engagement with mathematics is a
reminder that although some students can perform well using both online and tactile methods for
learning, for some, one method can be more effective than another. Abdul’s words also
foreshadow behaviors that he would come to appreciate in his next instructor, Professor
Bhattacharya. Before Abdul and I speak about Professor Bhattacharya, he describes the ways
that Professor Rivera supported him when he was deciding about his next mathematics course.
Upon completing Intro to Algebra, Professor Rivera recommended that Abdul enroll in
“combo course”, a ten-unit course that was “intense,” but would allow him to complete two
courses in one semester. Although he had trepidation about this course, Professor Rivera offered
words of support.
I would be very skeptical about it. I didn’t really know if I was able to do it…Because
that was a combination class, and that was worth ten credits. That was a lot riding on it,
with your GPA and a lot riding on the workload…but Ms. Rivera said, “You can do it.”
She encouraged me to sign up. She said, basically, “you’re capable, you can do it.”
I would keep going to her to reaffirm it from her…She encouraged me the whole way to
sign up for it…I asked her can she give me any websites or any—can she refer me to
some websites that I can start and prepare for the combo class. I think she even emailed
me back some websites.
With his professor’s encouragement, Abdul enrolled into the combo class. There, he would meet
Professor Rivera’s “good friend,” Professor Bhattacharya, the mathematics instructor with whom
he would deepen his love for mathematics over four consecutive courses.
Professor Bhattacharya: “[I]f it was a lion, she goes in there and handles the lion, and
then basically shows us how to tame the lion.”
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When Abdul speaks about Professor Bhattacharya, I can sense the admiration that he has
for her as a person, an instructor, and a mathematician. I ask for a description of some of her
characteristics and he says words and phrases such as, “mentor,” “somebody that I look up to, as
far as the math studies,” and “ I look at her and she inspire me.” Then, after think ing some more,
Abdul leans his head to the right, and says, “What I liked about Ms. Bhattacharya is that she’s
sincere in caring about her students and her class.” I ask him to describe how she demonstrates
her ‘care’ and he shares about a time when she conducted a study session with students from
multiple-level courses. Although he started speaking about her structured tutoring session as a
demonstration of care, I noticed something else in his communication.
Abdul-Malik: Recently I was in Ms. Bhattacharya’s class and it was a few of her students
in there. She had different levels of students. She was doing a review for
them. A girl had a baby in the class, a baby stroller. They had one guy
rapping on the desk, rapping about math. They had old dudes goin’ back
and forth, so I was just like how does she do it?
Maxine: How did she handle that? [chuckles]
Abdul-Malik: She didn’t know how to handle it. She [laughs]. She looked at me and gave
me eye contact and seen me laughing, and we kinda—she kinda looked at
me and laughed at me. She know what I was thinking. Cuz she probably
like—he probably thinking like they are crazy [laughs]. You know, those
are her kids. It’s more than a math teacher. It’s like a psychologist, a mother
or a father, if you a man, probably. It’s a lot going on with that.
Abdul and Professor Bhattacharya seem to have a special relationship, but I do not understand all
of the aspects of their connection. Rather than interrupt his stories about his professor to ask for
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clarification, I continue to listen to his descriptions of her interactions with her students. Soon
enough, Abdul transitions to a story about her ability to encourage students’ efforts to learn
mathematics by building their confidence.
What’s interesting is to see her be able to make it look like it’s easy. For us, it’s hard. She
can do it and be like oh, that’s a piece of cake. It…would make me look at it like okay, if
she’s saying it’s a piece of cake, that means it isn’t a piece of cake. It’s possible, it’s just
it’s gonna take time or I gotta do practice more. [B]asically, if it was a lion, she goes in
there and handles the lion, and then shows us how to tame the lion. She says, “See, it’s
not bad.” And open his mouth and mess with its teeth. Then everybody like, “What are
you doing?” and she’s like, “No, you can do it, too.” Then you like, “Okay,” and then
you just gotta trust her, and do your homework, and do everything she said to do.
With this metaphorical description, Abdul shows how Professor Bhattacharya’s demeanor and
mathematics skill puts him at ease. To offer an example of her interactions with him, Abdul
shares about two instances: a recent visit to her extra help session and a moment in the
classroom.
I was having trouble with a concept, and I went to her office. She took her time with
everyone and explained it to me. She would say, “Try it. Try it.” Then she would just
take her time. She gave me a stack of scratch paper, and she would just get through the
examples.
Then he offers the second example of his interaction with his professor.
Right, sometimes, when we in class, she would use me as an example and say “Yeah,
Abdul, he was in class with me, and remember we did that?” She would use my notes and
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say, “You got nice notes” and refer to me and say, “Let me see your notes, because I
want to show people we went over this.”
While Abdul speaks of this professor positively, all of his interactions with her were not positive.
The incident. In a story about their first class together, Abdul tells about a time when he
asked her to repeat a concept she had explained multiple times. She did not respond positively.
She said, “No, I said it already. If you didn’t get it, too bad.” She had an attitude with me.
I said, “That’s your job. You need to say it again.” Then, she got all upset like, “Oh,
that’s not my job. That’s disrespectful. I could get you thrown out my class.”
In that moment, Abdul left the class and went to the tutoring center, but as he notes, the story did
not end there.
[T]hen some students came to me and they said that, “Oh, no, when you left, it was a big
thing in the class. All the students stood up for you and was like ‘No, he’s a quiet guy. He
don’t ask for that. He do his homework. He don’t bother nobody. He was not trying to
ask you that outta’ bein’ a troublemaker. He really wanted to know.’” They stood up for
me and the professor sent me a email, like she apologized, and I said “I apologize. I
wasn’t sayin’ it to offend you.” Ever since then, we was cool. I think she seen that I
really wanna learn and a lot of students don’t ask questions, but like I said, I’m not here
to be the teacher’s pet. I’m here to understand, so if I ask a question—I don’t ask
questions, I don’t say silly stuff in class—so if I ask a question, you should answer that.
There was others in there that make stupid comments, and you don’t get on them, but
when I wanna ask a question, you wanna get on me? I said, “Nah, that’s your job.”
I ask if he can recall any details from his interaction with her or how he felt after he received her
email. He shares both. Again, fiddling with his phone, Abdul finds the email exchange and
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shares the messages with me. Soon, it becomes clear that he initiated the email communication
between the two of them, but that trivial detail seems less important to him than her response.
He starts by sharing the email message that he sent to her.
Hello Mrs. Bhattacharya. I want to say I apologize for today. I sincerely was not trying to
offend you. I highly respect you, and I have learned so much and continue to learn every
day. You have inspired me to become a math professor like you, so I ask questions to—
really understand, not to cause trouble. I am enrolled in your geometry in the summer,
and trigonometry in the fall. I would take others if you teach them in the future,
pertaining to my degree. I want to stay in your favor and to continue to benefit from your
knowledge…Once again, I apologize, and if you have any suggestions or tips on how I
can better approach you to ask a question in the future, please let me know.
He follows with her response to his message.
She said, “I have apologize to you. You are a very good student. When I said I explained
five times and I did, as you know, then you said explain the sixth time. That’s why you’re
here. That made me a little upset that I am trying my best to help everyone. My apologies
to you, also. I feel that me and my students are just one team. Do not hesitate to ask any
questions. Say, like you said, the sixth time.”
In response to my question regarding his feeling about her message, he says, “Well, I guess I was
still getting to know her in that state, because that was my first—that was my first class with
her.” From his response, it does not seem as though her message affected him greatly.
However, combined with these final thoughts about his instructor, it is not difficult to understand
why Abdul connected with Professor Bhattacharya, completed the developmental mathematics
sequence with her, and enrolled in her 200-level mathematics class. Laughing as he recalls some
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of her practices, he shares some of her behaviors, how they influence him as a mathematics doer
and learner, and how these result in him viewing her as a role model.
Abdul-Malik: Since she got a three-hour class, she don’t spare one minute and she gonna
go over the time. She writes faster than she talks. Her level of teaching is
very, very—from what I seen—I ain’t been around too many teachers, but
it’s a high level, high quality, I would say. You would have to basically
bring a lot to the table on your own, like your own resources. Whether
going home, doing work, research, going home and doing homework,
contemplating about it, [or] understanding it. If our class supposed to end at
10:00 a.m., she’s still trying to teach another concept. She used all the
board. She could fill up the whole—she could fill up one, two, three, four—
four boards in less than maybe 15 minutes….Yeah. I think that—yeah,
that’s what I would say. She gonna give you your money’s worth, and give
you more. Like you go to buy bread from the—they gonna stuff your bag
over. They give you more than what you—you pay for something for a
dollar, and she give you more than a dollar, every day.
Maxine: What were the characteristics that she had, that had you say, “You know
what, I wanna be like her or ‘I look up to her?’”
Abdul-Malik: Well, I think when you—the respect that, once you start doing math, the
respect you have for it. The respect that you gain from how the process of
learning the new concept and how it develops, then you look at a person
that’s teaching you it, it makes you respect them more. Because I would
look at—before college, I just look at a person teaching, like they don’t
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know nothing. They just a teacher. Or they just an instructor. So what?
After seeing—after going through a little of this, I’m like whoa, I got a
whole new life, a whole new respect for anybody that go to school. Whether
you got an AA, BS, BA, master’s, this is no joke….I got respect for all
teachers. It change my outlook…Basically, for me, a person that likes math,
and this is my resource in front of me, my closest resource. I guess that’s
automatic. A mentor, basically.
With his next statement, Abdul reminds me of his distinction between computer-based and
textbook-based learning. His appreciation for textbook learning begins to makes sense to me.
She’s training me on the level of dealing with the book and doing all the homework, and
having a fast pace and not being apologetic about it. She’s very tough. I guess that would
make me who I am today as a math student. Because she ain’t no joke with her teaching.
That’s what I like…she trained me on a level that I think it’s gonna carry me a long way
to success because the work ethic.
Inspired by his professors’ encouragement, care, and knowledge of mathematics, Abdul
continues to be motivated to become a mathematician. However, different from the other
participants in this study, he does not simply point to professors’ practices or behaviors when
considering the ways that they facilitate his learning. Instead, his “respect” and “love” for
mathematics create a foundation for him to appreciate Professor Bhattacharya’s work ethic and
personal qualities. With this appreciation for mathematics, his discipline, studying, faith, and
prayers, Abdul’s earned three As and a B in his developmental mathematics courses.
Personal impressions can get in the way of learning: “[W]hen they used to see me,
people used to be shocked, like, “You a tutor?” Earlier in our conversations, Abdul
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recognizes that he cannot offer many in-class mathematics experiences for this study, so he opts
to tell about other stories that are relevant to his experiences at LA North: his experiences as the
only Black mathematics tutor and one of two Black students in his current Trigonometry course.
When I was a tutor, [it] was interesting because my job was to go walk around. I have
my ID [pointing to his chest] and then I would say, “Do you need any help with
anything?” Then, some would be like, “Nah, I’m alright. I’m alright.” Then, some would
be like, “Yeah, sure, I need help.” I was the only brotha tutor and it was Mexicans and
one white guy, but when they used to see me, people used to be shocked, like, “You a
tutor?” [opens eyes wide and pulls head back in surprise] I be like, “You don’t need
help? Alright, bye. Fine with me. I’m chill.” If I could chill, I’m good. I don’t gotta prove
nothin’ to you.
In another story about his experiences as a tutor, Abdul shares about a student that he connected
with in a meaningful way.
Abdul-Malik: There was one guy. He was an AfricanAmerican guy, older guy, and he was
hood, a hood guy, and I had to talk to him. Nobody in all the…tutors in
there, nobody liked him because he was too aggressive, he too loud, he too
unpolished. But I know how to deal with him, so I said, “I’ll go help him.” I
said, “Yo, what’s up?” He’s like [changes to a stern tone], “Yeah, man, the
teacher—.” I said [hold hand up, motioning to stop], “Hold on, hold on,
relax. Let me do this. Just chill. You wanna do this or you want me to do
it?” Then he said, “Alright, go ahead, go ahead” [relaxes shoulders]. Then I
would just communicate with him in the best of manners…He used to say,
“Yeah, I was out there. I was gettin’ money. I was doin’ this. I had the
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hood.” I said, “Look, you lettin’ these teachers chase you around. You
gettin’ chased in the math class and you used to be chasin’ people around in
the street. You better get it together. Why you doin’ that? Why you lettin’
math chase you around?” He like, “You right. You right. I needed that
conversation. I needed to hear that.” Basically, I was just givin’ him
positive advice on how to—you could do it.
Maxine: When you say that he was hood, can you say a little bit about that? How
would you define hood?
Abdul-Malik: Well, it seemed like he used to get money. He probably was getting a lot of
drug money in the neighborhood and he probably was a boss, which mean
he controlled people, a lot of young people, had people working for him,
very successful. He had a lot of gold chains on and all that…
Maxine: He did? When you saw him?
Abdul-Malik: Yeah, so I could tell that’s why it’s hard to teach somebody like that
because they already successful in their little world, so now they lookin’ at
my world and they don’t understand these other worlds, so I had to tell him
listen, okay, now you was a boss in that world, but now you a soldier now
in this world, and one of the things that’s givin’ you problems is this math,
so you need to be—whatever you was doin’ in that, you need to bring that
over here. Do it with your studyin’ and your homework and your learnin’,
not necessarily with your guns and your manpower. In this world, you gotta
use your brains and your studyin’ and your pencil and your pen. That’s
what I would tell him. Then, a lot of times, I would help handicapped
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students. They were very inspiring because some of them, they couldn’t
even write. Some of them, even you’d tell ‘em two plus two is four and you
keep tellin’ them and tellin’ them and tellin’ them, they don’t get it, but they
still come every day and they still want help and they used to still come.
This one guy, he used to come lookin’ for me. He’d be like, “I need help.”
He used to drain me. It was very draining, but I always helped him. That
was no joke.
Maxine: It is no joke cuz then you gotta pull on all kinds of your own talents.
Abdul-Malik: Right, but I like helpin’ them.
Eventually, Abdul stopped working at the tutoring center. Reflecting on his experiences after he
stopped working there, he turns to me and shares what happens now when he is on campus.
I can’t even walk nowhere, cuz everybody always asks me, “I didn’t see you [at the
tutoring center], when you coming back?” A lot of the people I used to tutor. I’m like,
“Oh man.” I can’t even go to the library and do my work!
In that moment, as I think about those who benefitted from his knowledge, patience, and passion
for math, as well as those who questioned his role as a tutor at the tutoring center and recognize
that they missed the opportunity to work with him. Speaking to me, with his eyes open wide, he
brings me out of my sidebar thoughts and begins to comment about students at the tutoring
center who are least likely to request his assistance. He seems surprised as he shares this story.
What was interesting is my own people, a lot of people that look just like me, they didn’t
want—I couldn’t help ‘em. Mmmm-hmm, they wouldn’t go to me, but other people, I
would go help them and they would always come to me. They’d be like, “C’mon, I need
help.” I mean they would come lookin’ for me. But I guess that my own people were
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lookin’ at me, maybe they see theyself, like, “Oh, he don’t know. I definitely ain’t goin’
to him. He’d be the last one I’m go to if I need help.” Aww, that was funny [leans back
in his chair and laughs]. I’m like, “Wow.”
I ask, “What was that like for you?” Again, Abdul laughs and tells another story about a similar
experience in the classroom. He does not answer my question, and perhaps he did not hear it at
all. I am so focused on the next story he is telling that I forget to ask my last question again.
In class, I would take the role of being quiet [so] nobody knew my capabilities. It wasn’t
until later in the semester when people start—after one or two months, then naturally the
walls start breakin’ down and people start talkin’ and the teacher might put you in
groups…I remember one time, we was in a group and everybody’s in their groups and I
had my group. I could tell that the group I was with, they lookin’ at me like “He don’t
know nothin’.” Then, when I was like—I was just relaxed cuz I already knew it. I said
oh, [moves his finger across the table to mimic showing how to solve a problem] that’s
this, this, and that. There was one girl and her friends over there and she was like [drops
his jaw and opens his eyes wide]—and I showed her, and then she was just lookin’ at me.
The next table was lookin’ like “He know that?”
Curious I ask, “What were their ethnicities?” Abdul responds, “All Latinos. Then at another
table was one Black sister and some other Latinos and I said the answer’s this. They was just
shocked.” [laughs and places his palm on his chest]. “What has you laughin’?” I ask.
Because people underestimate people. That’s why I laugh because I know what I’m
doin’. I like to be quiet so, they didn’t know that I knew. Then, our group, I was helpin’
everybody in the group and then I became the go-to guy. They’d be like, “Can you help
me with this? Can you help me with that?” I just be like, “No problem.”
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I think about Abdul’s response and ask, “Did it bother you that they had that perception of you?”
Smiling, he shakes his head and says, “I like that, though. I like when people underestimate me.”
From Abdul’s somewhat casual response, it seems that he is unaffected by his peers’ responses;
for the most part, he probably is. However, he is not blind to the discrimination that he faces in
the classroom and as such, responds as best as he can.
The look that I get…when they’re seeing me…that’s interesting too. I could tell, when
I’m going up higher and higher. That means I gotta know my stuff, because I gotta—I
can’t be playing, because just who I am and just what I represent or what I might look
like I represent, I can’t be playing. I can’t be playing around. That’s why I might not feel
comfortable going to a tutor or going to the professor, because it’s something there
As Abdul shares these stories, I wonder what inspires his peers’ responses. Is it race, his
religion, or something else? He sums it up, attributing their behavior to underrating his abilities.
Fortunately, their beliefs do not align with his positive beliefs about himself and his abilities, nor
do they interfere with his personal view.
Current Class: “I’m askin’ questions. I’m answerin’ questions. I’m engaging with her.”
Recalling Abdul’s comments about his behavior in class, I remember that he described
himself as “quiet” several times during our conversations. Still, I wonder if there is anything else
to learn about his behavior, so I ask more specific questions. “When you’re in class with her, do
you ever—do you ask questions? Or do you mostly take notes? How do you participate in
class?” Leaning towards the table, he turns his head towards me and speaks into the recorder.
Oh no, I’m right there with her. I stay right there with her. Yeah, I’m hangin’ in, I’m
joggin’. Like if we joggin’, and she runnin’—she has more stamina, but I be right there
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with her. I’m askin’ questions. I’m answerin’ questions. I’m engagin’ with her. If I don’t
understand, I’m not shy about askin’.
Of the “40, or maybe less” students in the class, Abdul’s behavior mirrors “maybe less than three
or four people [who ask] questions or answer questions or engage.”
Near the end of our final meeting, Abdul shares that he will take pre-calculus at nearby
Piston College during the winter session because LA North does not offer the course at that time.
He scratches his head and then shares, that after looking on the Rate my Professor website,
I went and spoke to [the professor] about a month back. I like to know who I’m gonna
get and know and see what other students think about them. Then I go meet them and
look in his eyes and talk with him to feel him out. I got my [text]book coming already.
I’m already reviewing right now.
Unsurprised, I chuckle.
Approximately one week after our final interview, I connect with Abdul and we engage in a
short conversation. At the end, I remember to ask a question that I ask each participant after the
study.
Maxine: Oh, did you get your grade back from Trig?
Abdul-Malik: Oh yeah, I got a B.
Maxine: Oh, okay. Are you pleased with that?
Abdul-Malik: Oh yeah, I’m thankful. I’m thankful for my work and my efforts. I just say
alhamdulillah, or praise to Allah.

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Kendon Joseph—“I definitely want a great career for myself.”
Background
As I walk into the chatter-filled library, Kendon and I spot and approach each other with
slight hesitation, trying to figure out if we are the two strangers scheduled to meet at that time in
that place. “Hi, Kendon?” I ask. “Yes, hi Ms. Roberts.” Wearing red sweatpants, a red
sweatshirt, and red and white basketball sneakers, Kendon smiles, extends his hand to shake
mine, and says, “It’s great to meet you.” Although he only spoke a few words, I hear the familiar
cadence of a West Indian accent and through a casual conversation, learn that Kendon moved
with his family from Trinidad 21 years ago—“I believe '95, that's when my family moved and
we came to the US. I was about 4 or 5.” At 24 years old, Kendon is the youngest participant in
this study.
A college student for four years now, Kendon has taken courses at three different
community colleges in Los Angeles. Although he began college with the intention of earning an
Associate’s degree and then working at the local refinery with his dad and brother, Kendon soon
decided to pursue a Bachelor’s degree in engineering. His career choice is a decision that offers
his parents opportunities to brag about him to their friends. Smiling, he shares that he often
overhears them saying, "You know, my son is studying engineering." Although he has earned
enough credits to transfer to a four-year university, Kendon has opted to remain at LA North for
another two semesters.
They offer the majority of the classes here and a lot of internet courses as well. Plus, I
get a fee waiver [at LA North] compared to going to a university where I have to pay for
the classes. I wanted to take them here, get them out of the way, get it done, then transfer
out. That way I can be more competitive since I have more classes done.
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Curious about his life outside of college, I ask if Kendon has a job other than school. He
shares that other than his schoolwork, he has “no responsibilities.” “My parents tell me to focus
on school and they'd take care of everything else.” Their generosity gives him the freedom to
schedule his time as needed for his studies and other activities. After we talk for a short time
about his family life and his aspirations, we take a journey into his past and discuss his
mathematics experiences in grade school.
The Early Years
“Math wasn’t important at the time.” Once Kendon’s family settled in Los Angeles,
his dad found a job at a local refinery and Kendon’s mother chose to stay at home to take care of
him and his four older siblings. She also served as his first mathematics tutor in elementary
school, sometimes getting frustrated with him during their homework sessions. Scratching his
chin and with a smirk on his face, he recalls, “If I wasn't quite understanding it, she'd hit me or
stuff like that because I should know it already ‘cause we went over something similar.” He
laughs, and quickly follows with, “My mom cared about me though and she wanted me to learn
the material, but it can be frustrating, cause kids they just wanna play and they don't wanna do
homework. It made me focus even more.” While Kendon focused at these times, he did not
connect with, nor really understand the material. “I wasn't fond of it—like everyone else, I
thought, ‘Who invented the stuff? Why does it have to be so hard?’ I wasn't a very good student
in math ‘cause I didn't pay attention.” On one hand, Kendon’s mom incentivized him to focus
during their sessions. On the other hand, even with her strategies, she could not help him
recognize the importance of doing well in school, let alone continue to plow through course
material when he had difficulty with the mathematics. He attributes his disconnection from
mathematics and education to his family’s lack of emphasis on both areas.
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“Math wasn’t important at the time, because they didn’t really drill education in my
household—they wasn't encouraging me to stay focused.” Puzzled about why Kendon perceives
that his family did not stress the importance of education, I ask him about this idea.
Maxine: It’s interesting that you say, “they didn’t drill education,” ‘cause some might
think that by helping with homework your mom was tryin’ to set an example.
What do you think?
Kendon: I mean, of course they wanted my best interest, but they didn't like instill
‘school is very important’ and ‘stay focused’ and ‘get good grades’. They
could've pushed me more and tell me that education is important and you could
have a great life….they didn't think that we probably were gonna go to college.
We probably were gonna start working or something like that. Probably
because they didn't go to college either, so that probably played an effect.
Kendon’s impression about the value that his family (more specifically, his parents) placed on
school affected his view of mathematics and its importance. Shrugging his shoulders as he
recalls his cavalier behavior he says,
To me, it wasn’t really a big deal, because at the time math wasn’t really important. So
it’s like just do it and if I don’t do well or if I—it’s just not a big deal, I guess. …It wasn't
until I got to college that I realized, this thing is real [opens his eyes wide].
Before Kendon got to college and figured out the ‘realness’ of school, he continued to struggle
when he moved into middle school. This is where his lack of focus on school and on
mathematics would soon catch up to him and affect his ability to graduate.
Transition to Middle School: “I was doing bad in his class and wasn’t gonna
graduate middle school.” Kendon mathematics challenges increased when he moved to middle
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school. Shaking his head, he recalls his difficulties, “I wasn’t really too focused in math, I
struggled and I didn’t understand [math] concepts.” Luckily, Mr. Watson, his mathematics
teacher, found ways to motivate his students. Chuckling and bowing his head as he recalls a
memory, he says, “Sometimes I would put more effort to receiving rewards.” He laughs as he
remembers one tactic Mr. Watson used to encourage him and his classmates,
Kendon: He used to give candy if you answer something correctly [smiles broadly].
Maxine: So, did you get a lot of candy?
Kendon: I was able to get a lot of candy [laughs].
Maxine: So you used to do pretty well...
Kendon: Yes, so that encouraged me to do the work as well. That motivated me to
answer some of the questions, ‘cause all the kids, they wanted candy in the
class. It made my math ability a little bit more better in a way.
In middle school, Kendon’s mom continued to tutor him in math, but despite her efforts
and Mr. Watson’s sweet rewards, he struggled.
My mom, she seen that I was doing bad in his class and wasn’t gonna graduate middle
school. We went up to [the school] and spoke to him.” I was doing bad in his class. I
wasn’t gonna graduate middle school, but he gave me a bunch of assignments to do in
order to catch up. At first, he wasn’t necessarily willing. He wanted me to probably
retake it. I can’t remember. I’m glad that it worked out for him to give me the
assignments to be able to graduate, but at first he wasn’t necessarily willing. He showed
sympathy in not holding me back.”
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Kendon mentions no memories of mathematics in junior high, so next, we speak about his move
to high school. This transition brought a change in his school environment and his incentive to
succeed.
High School: A New Level of Independence Brings a Shift in Priorities. Worried
about his safety in their neighborhood’s designated zone school, Kendon’s parents recognized
that his high school choices were limited; his mother sought out an alternative educational
experience.
When I graduated from middle school, I lived in South Central LA, so the high school, it
wasn't a good school based on crime activities, gang violence, and things of that nature.
So my mom, she enlisted me into home school. So I went to [name of school] and that
was basically where I did my whole high school.
Not only was Kendon in school with students who were much older than he was, but his
high school years were drastically different from other teens with more conventional high school
experiences. Turning up one corner of his mouth while shrugging the opposite shoulder, he
notes, “Unfortunately, I wasn't exposed to chemistry, biology, you know like the stuff that they
teach in regular high school and like prom and stuff like that.” Despite these differences—or
perhaps because of them—Kendon’s priorities changed, he began to view some aspects of school
differently, and behaved differently. Adjusting his posture as he sits upright, he recalls a shift in
his behavior.
That's when I started developing better math skills because the teacher forced me to learn
the material--in a good way--because we were quizzed on it. Basically, I had to go once
a week to the location, they assign you a day, Monday or Wednesday, whatever, so they
gave me whole week's of work, I get it done at home. My mom would help me out and I
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believe at the time, I had about probably 3-4 classes at a time. I became a bit more
focused, because I know in high school in order to graduate and get a diploma, you have
to pass the high school diploma test.
While this new understanding changed his perspective about school, the revelation did not
change his mathematics performance right away.
Kendon links his ongoing struggles with mathematics with his beliefs about his ability to
understand the material. Leaning back in his chair, he says,
In high school, to me at the time I didn't understand the concept and stuff. I just thought
math was math and I thought it was gonna be difficult and I wasn't gonna really
understand it, so I took it lightly.
Earnestly, he adds, “Of course I was trying to get a good grade in the class. I just wanted to pass
the class with a B or higher.” During our second meeting, he recalls some of his high school
mathematics experiences and while he rarely mentioned classmates (there were approximately
four other students in class each year), he speaks fondly of Mr. Hobbes, one of his two teachers
during those years.
Mr. Hobbes: “He was just a great motivator.” Mr. Hobbes, whom Kendon
characterizes as, “kind and he cared about us understanding the work,” kept students on their
toes and “forced” him to learn the material by giving weekly quizzes. Smiling and nodding as he
remembers his teacher’s efforts, he adds, “He was always willing to work with the students and
help them, one-on-one. If we had any questions, we just had to go up to him and he would come
to us and showed you step-by-step.” Mr. Hobbes, Kendon’s sole math teacher during his high
school years, provided the support and consistency that Kendon needed to develop as a
mathematics learner. “Mr. Hobbes, he was my math teacher the whole time. That’s why I built a
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great relationship with him. He was just a great motivator. That’s what motivated me to do
well.”
Mr. Hobbes’s willingness to support students and the consistency of his classroom
practices (e.g., weekly exams), helped Kendon to pass mathematics despite his struggles with the
subject. While his connection with Mr. Hobbes was valuable for his development as a
mathematics learner, ultimately the structure of his learning environment shaped how he engaged
with his work and dictated his work practices.
Early Work Habits Foreshadow College Practices. In high school, Kendon enjoyed
activities that were similar to other teenagers his age, so while he was interested in earning a
diploma, academics were not always his primary focus. “In high school, I used to play video
games and stuff…like a typical kid, I wasn't too worried about school.” The freedom provided
by the less-structured school environment offered him an opportunity to manage his own
schedule and this set the stage for some of the challenges that he faced during these years.
I had to do a lot of self-learning since it was homeschool. That’s what also played a factor
in me having challenges, ‘cause I had more time to myself. I only went once a week, so
basically for the majority of the week, I was playing video games, hanging outside with
my friends. A couple days come closer to my time to go to school, that’s when I started
doing my work.
Like the bricks used to construct a building, Kendon’s middle and high school
experiences helped him to create study and work practices that he would use later, in college.
For example, taking initiative to complete homework and prepare for weekly quizzes for Mr.
Hobbes’s class helped him to learn to manage his schedule; as an adult in his first remedial
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mathematics class in college, these skills were invaluable and ultimately, led to his success in the
course.
College Years
From Mathematics Struggler to Mathematics Learner. After graduating from high
school, Kendon found part-time work as a driver for UPS and worked there for two years. His
plan to leave the company and work at a refinery with his father and older brother was derailed
when Kendon learned that LA North offered a certificate in Process Plant Technology; he opted
to go to college to increase his earning potential. With this decision, he changed the trajectory of
his career and his view of education. Excited about this memory and with wide-opened eyes, he
recalls with a smile,
I achieved the degree, the two years went by so fast and the courses were fun and easy,
the teachers were pretty good. I said, “I love going to college and this is fun. It’s not bad
after all.” A Bachelor’s only takes about four years, and two additional years a Master’s
degree. That’s not bad. Then the PhD…I just said, “Spend about eight or more years
pursuing a PhD is better than working for the same amount of time.”
He took the mathematics assessment and entered Pre-Algebra. This class became the turning
point that shifted how Kendon viewed himself as a mathematics student—he was more than a
student who struggled with mathematics; here, he became a mathematics learner. Chuckling, he
says, “I didn't know that I was that great at math. I understood the material he was covering very
well and had a high A in the class. I started to understand the concept…That's when I began to
love math.” This newfound love even inspired a change in his work practices, “I was doing all
the homework assignments. The teacher would normally assign the odd [numbered
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questions]…but I did the odd and the evens.” With every assignment, he continued to
understand the material and grow as a mathematics learner.
Kendon recognized his prowess as a mathematics learner and so did his peers and his
professor, Mr. Davis; classmates often asked him to explain course material and Professor Davis
would call on him to solve problems in class. Soon, his confidence increased. Adding emphasis
to clarify his feelings, he says, “I felt more comfortable and confident with students approaching
me, asking me questions. That’s how I first started beginning to love math, because I liked how
students used to come up to me to ask for help.”
With a flood of fond memories from his experiences in this class, Kendon also shares
about his interactions with Professor Davis. In fact, he even shares about an interaction with his
professor to highlight Mr. Davis’s teaching style and demeanor. “I approached him to ask him
more about the complex fraction and how to better solve it. That’s when he showed me and he
gave me a different example so I could work on it myself.” Using words like, “patient” and
“positive,” Kendon remembers “He wasn’t like, “You don’t do it this way,” or, “You’re doing it
wrong.” If you get stuck, then he’ll help you get through it.” Professor Davis’s response elicited
Kendon’s best and encouraged him to continue to develop his skills.
In this first remedial mathematics course, Kendon became a new type of learner who
shifted both his practice and his perception of himself as a learner. By becoming a diligent
student who went beyond what his instructor required, his understanding of mathematics began
to emerge. Combining his new aptitude for mathematics, a “patient and positive” instructor, and
a belief about how he could be successful in class, Kendon developed a newfound and
unexpected love for the subject.
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Connecting with Mathematics. After taking Pre-Algebra, Kendon began to understand
how to achieve success in class and shifted his perception of his mathematics abilities and
feelings about the subject. “I’m a better math student,” “I love math,” and “I definitely have a
connection to math” are the phrases that he uses when talking about his relationship with
mathematics in college. “Like before I wasn’t really giving it a chance, but now that you come
to college and you gotta get this stuff done. That just made me love math.” Beaming with pride,
he says, “I just love that I’m able to understand it and help others.” With this newfound
confidence and an understanding of his own struggles in mathematics, now Kendon focuses on
helping his classmates understand the material and tutoring other students. “In my free time, I
spend a lot of time at the tutoring center and I volunteer there.” Later in our conversation, he
says, “The [Director of the tutoring center], wants to hire me, but I don't do it for the money, I do
it because I enjoy math and I'm passionate about it and I love to help people. I understand and I
was once in their situation.” Kendon also uses his skills to help younger family members who
need support—he tutors his nephews after school. As a result, he has also shifted his family’s
perceptions of his skills. “They definitely look up to me more…They're shocked that I know the
material so well.”
By improving his own mathematics skills, volunteering at the tutoring center, and helping
his nephews to develop their own understanding of mathematics, Kendon improved his progress,
feelings towards mathematics, and his connection with the subject. Within one semester, he
went from viewing himself as a student who “wasn't too worried about school” to a learner and a
tutor who is successful and respected for his knowledge.
Success: How did He Achieve the A?
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Campus Support and Online Resources. Kendon’s stories about his development as a
mathematics learner leaves me wondering what shifted in his experience and helped him to excel
in this course, so I ask for his opinion. He ponders for a few seconds and then shares that during
the Pre-Algebra course, he visited the campus tutoring center; there he learned about the worlds
of learning available through the Internet and textbook resources; these would help him to make
sense of mathematics. While simulating typing, he elaborates, “I’d go on Khan Academy, or
YouTube, or Chegs Solutions. [Chegs Solutions] has the step-by-step solution to many book
problems.” Then, Kendon pulls out his binder organized with color-coded tabs to show me some
of his other resources. Flipping through the pages, he lands on the calculus tab and points to
printed sheets with formulas,
Maxine: Oh, so you have formula sheets.
Kendon: Having formula sheets is very, very helpful because if you forgot something
you can just easily access it.
Maxine: Oh, so they give you formula sheets—
Kendon: Yeah. In the tutoring center they have a lot of it.
Maxine: Oh, so the tutoring center gave you that, not the math instructor?
Kendon: Not the math—actually, my math instructor, he’ll give us a formula sheet if
there’s something that he don’t want us to memorize. Like if it’s a quiz and if
it’s like a lot of things that’s going on, like a lot of different formulas, he’ll
provide it for us. However, at the tutoring center, they provide a lot more
formula sheets on the different topics.
Kendon’s notes are neatly printed by hand with colored pencils that match the markers his
instructor uses to write on the board and organized for easy access. While he uses human,
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electronic, and paper-based resources, Kendon also includes another valuable asset to create
success: his own class participation and tenacity.
Creating Success from Within: Participation and Persistence. After we talk about the
collection of external resources that Kendon uses to make sense of mathematics, he mentions a
practice that also helps him to create success. He smiles and raises his hand as though he is in
class, “I’m always participating. I’m always in-tune in the class. Even if I have the wrong
answer, I still participate.” Knowing that he can access resources and ask questions when he is
unclear, Kendon is rarely, if ever, discouraged when he faces problems that he does not know
how to solve. This understanding helps him to persist even when he has difficulties.
In high school, and in middle school, I wasn't too keen on math, so sometimes I used to
get discouraged. In college, I haven't really been discouraged because I realized that the
material can be challenging, so you just have to fight through it [and] just keep trying or
look at another example.
In our final discussion about the techniques that he uses to be successful, Kendon shares a three-
part strategy that he believes is important for academic success—he even created a PowerPoint
presentation to motivate himself with these reminders: “[R]ead the chapters that the professor
covers in class, do the homework that the professor assigns, and study before exams.”
Combining strategies such as on-campus tutoring, online support, clear note-taking, and
persistence helped Kendon earn an A in Pre-Algebra. Since then, he identifies himself as a
student who is “bright,” “knowledgeable,” and can achieve success in mathematics. These
positive perceptions about his abilities help him to believe that he can be successful even when
he has academic difficulties. Curious about the factors that incentivize him to persist when he
has difficulty with mathematics, I ask Kendon to share his motivation with me. Our next
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conversation sheds light on the ways that being a mathematics learner involves more than
knowing how to manipulate numbers and formulas.
Motivation to Succeed
The Value of Friendships. In part, Kendon attributes his desire to advance in
mathematics to his relationship with fellow engineering majors whom he met in an entry-level
engineering class; since then, they have taken multiple courses together, including mathematics.
Seeming fond of these relationships, he leans toward me, smiles, an says,
Kendon: As we go up, you understand that it’s important to build relationships with
people, especially in the engineering world.”
Maxine: Would you tell me a little about these relationships
Kendon: “Well, we’re in similar courses or we take them in the same semester, that way
we can help each other to do good.”
Further explaining this idea of reciprocity, he says, “Sometimes I’m not able to understand the
concepts, so I go to them, and if they don’t understand something, they come to me.” These
relationships with peers have also been pivotal for Kendon and encouraged him to change his
work habits when he realized that he was struggling in Essentials Plane Geometry (and risked
getting left behind) if he did not improve. With a furrowed brow, he speaks of his motivation to
succeed in the course, “At that point, I was just trying to pass the class because my friends were
taking it too, so I wanted to continue on the same—taking the courses with them.” With these
thoughts and a shift in his work practices, he achieved his goal, passed the class, and moved on
with his friends.
As Kendon points out to me, interactions with his peers are more than just friendships
with classmates. These relationships serve as reason, or motivation, for him to succeed in
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mathematics; they are also the supports that he uses to push himself when he struggles with
material. In our next discussion about motivations, Kendon focuses on his desire to be an
engineer and the ways that this desire influences his performance in mathematics.
A Focus on Career and Its Relevance to Mathematics. Kendon’s interest in being an
engineer seems to be his primary motivation for succeeding in mathematics. With fervor, he
says, “I want my engineering degree…I'm definitely not gonna stop.” His belief about what an
engineering degree and career can provide motivates him to put in extra work when he begins
struggles in mathematics. “I definitely want a great career for myself…my goal is to obtain a
PhD in engineering, so I can be prestigious and have my family and friends proud of me.” Given
his earnestness when he speaks about obtaining an engineering degree, I ask what inspired his
interest in the area.
As I mentioned earlier, Kendon was prompted to pursue engineering after earning his
Associates degree in Process Plant Technology at LA North. While some of his cousins and an
uncle have engineering degrees, none of his siblings have pursued the field; he also believes that
obtaining a degree in engineering is an opportunity to “do something fantastic with [his] life.”
On a more practical level, when talking about the value of mathematics in engineering, Kendon
speaks in general terms about the connection between the two. “Math plays a huge part because
you have to work with a team and develop equipment. As well as financially, when it comes to
traveling, math plays a huge part.” In this conversation, Kendon makes more connections
between mathematics and his personal life than the role it would play in the day-to-day
operations in his career. “Especially as an engineer, you have to know how to calculate to make
sure you're making the correct earnings or put overtime into play, and also traveling. You have
to do math to see how long you'll be out of state or to see if that job is right for you.”
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For Kendon, the prospect of a career in engineering incentivizes him to succeed in
mathematics in ways that his mother and teachers could not encourage him during his middle
and high school years. At the same time, his understanding about the connections between
mathematics and engineering helps him to persist when he has difficulties in his courses.
Instructors Impact Students’ Experiences
“I've never been suspended in life, so it made me very emotional.” In many of our
discussions about mathematics faculty and the ways that their instructional practices and
behaviors affect his learning, Kendon shares mostly positive experiences. However, one
situation, though memorable, was not positive. It took place in Intermediate Algebra at nearby
Piston Community College and was the only negative experience that he could recall.
Kendon: One day [the instructor] was going over the square root. When you have a
negative number in a square root, it turns into an imaginary number. I thought
that was interesting because it was my first time seeing that. Then during class,
he put us in groups to work on assignments and he called me outside--I'm
thinking he called me to tell me I'm doing a great job. However, it was opposite.
He told me he was gonna suspend me for a couple days. The class was three
times a week, then he told me I'm disrupting the class, you know. He was just
accusing me of things I wasn't doing. There was students who was being
obnoxious, who was being loud and was really disrupting the class, I guess he
thought I was being sarcastic, but I took my college classes very seriously. So,
when he told me he was gonna suspend me, I was shocked…I've had many
classes and the students are disrespectful and very loud and the teacher talk to
them over and over and I've never seen a teacher suspend a student. I've never
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been suspended in life, so it made me very emotional. I was just in shock. I
couldn't even tell my family.
In general, Kendon’s demeanor during many of our conversations was calm and cheery;
however, during this discussion, his voice is louder than normal and he sounds agitated. It was
clear that even retelling the details about this situation disturbs him. While he did not identify
the issue as racially-motivated at first, given my discussions with other participants in the study,
I asked if he thought there might be a connection. Initially, Kendon seems reluctant to say the
situation has racial undertones, but then shares his honest perspective.
Maxine: So why do you think he did that?
Kendon: Um, I mean it was a White gentleman. Obviously, I wasn't doing anything
wrong. I found it interesting because I liked it, the math that he was explaining.
It's not like I blurted it out, I just said it at a pretty low tone. He probably took
offense to it or something.
Maxine: You bring up that he was White, do you think it was race-related?
Kendon: Indeed, because there was only a few Black students in the class and a majority
was White and Hispanic. He was picking on this other Black kid as well. He
suspended him as well.
At the time, this incident was problematic for Kendon, because as he notes, the class took place
three days during week; he was suspended for two days and an exam was scheduled for the third
day. In an attempt to advocate for himself, he went to the mathematics department.
Kendon: I went to the chair and that didn't work out, she was on the teacher's side. So
anyway, since nothing worked out, I went on the 3rd day to take the test and he
said what am I doing here, do I have a paper to return back to class and I didn't
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know I needed a paper to return back because he said I was suspended for 2
days. So I went to try to get the paper and the lady was out of town. So I had to
miss the test.
Concerned about his grade and passing the course, Kendon shares that the incident, “made me
have to work harder to prove him wrong and to pass the test.” Kendon offers an example of
another experience that he defines as “daunting.” “Throughout the semester, the things he'd give
students partial credit on, he wasn't giving me credit. It was pretty daunting and it made me have
to work harder to prove him wrong.” “So what was your final score,” I ask. “He ended up
giving me a B in the class when I deserved an A.”
This situation, both negative and upsetting for Kendon, shows that even through tough
interactions with instructors, he persists and can succeed in mathematics. Once he completed
Intermediate Algebra, he finished the developmental mathematics sequence and was ready to
move to college-level mathematics courses. Because of his interactions with the instructor—and
at the recommendation of a friend—he decided to take his remaining mathematics classes at LA
North. There, he met Professor Blaze, the calculus-series instructor with whom he would take
his next several calculus classes.
“My math instructor is hard.” Kendon smiles when he first mentions Professor
Blaze’s name, “Dr. Kenneth Blaze. Well, I'm not sure if he's a doctor,” he chuckles. “Fantastic
math professor, I plan to take Calculus 3 with him as well.” Kendon first learned about
Professor Blaze from a friend who had taken a calculus course with the instructor. He heard that
Professor Blaze was “challenging” and one who would have “you know your stuff.” While
Kendon cannot recall many details about his other college mathematics instructors, he shares that
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this professor was a “tough teacher” who “wants the best interest for the students” and with this
combination, he prepares students for the ‘real world’. Grinning, he says,
He gives pop quizzes, so you never know when to expect them, you always have to stay
on top of the material. So people say, ‘You know, he's hard...The pop quizzes it's crazy’
but I look at is as a positive. As he told us, you know, ‘When you get into the workfield
or life, things are gonna appear out of nowhere and you have to know how to handle it.’
So this is preparing us.
Kendon’s greatest complaint about Professor Blaze is the same characteristic that he most
appreciates about him: his level of rigor. After we discuss his final grades in each of his courses
with this professor—he has earned Cs in each course—he discusses his rationale for continuing
to take courses with Professor Blaze.
He's a great professor because he expects perfection, and he's pretty challenging. That's
what I like about him because you want to be an engineer, you have to know your stuff.
Compared to taking an easier professor, yeah, you could get the A, but what do you
learn? How is that gonna help you? I have friends that take easy professors just to get
the As to make their transcript and their GPA look good, but what are they learning when
it comes to the GRE or these tests to take to get in a master's program? They're not gonna
perform well on it because they don't have a strong background in math.
This idea of greater learning through harder–rather than easier—professors is why Kendon
continues to take courses with Professor Blaze. Tapping the table to emphasizes his points, he
says,
I wanted to take the harder route by taking this professor because he really pushes you.
When I was taking this class, I tried to do well, but I didn't know what to expect because I
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didn't know he was that picky about notations and expecting perfection. He don’t care
about having the correct answer [laughs]. You could have all the correct answers and you
could fail the test even though you have the correct answer—he cares more about the
steps.
Ultimately, Kendon appreciates two aspects of Professor Blaze’s teaching style: his rigor and
high expectations of students. When I ask him about his views on the professor’s coursework,
laughing, he says, “it's challenging because it's math, and it's calculus.”
These stories about the ways that instructors’ practices influence Kendon’s mathematics
experiences are important because they highlight the need to look beyond students’ knowledge
of mathematics and their study habits to understand the factors that influence their success. In
general, although Kendon’s experiences in the three professors’ courses incentivize him to do his
best to succeed, it is in Professor Blaze’s class that he feels like he can achieve in a safe and fair
environment; it also appears to be the reason that he continues to take courses with him. As part
of our discussion about success, Kendon speaks about the connection between learning and
achievement as he explains his concept of success.
Defining Success: Kendon’s Perspective
Kendon’s experiences with Professor Blaze have helped him recognize that success in
mathematics is not solely about getting the right answer, rather it is about demonstrating your
learning or “showing the steps” when solving problems. On several occasions during our
meetings, Kendon shares that his instructor deducts points for incorrect notations and missed
steps. From our next conversation, it seemed as though Professor Blaze’s practices and
expectations have shaped how Kendon conceptualizes success. To gain a better understanding of
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his idea of success in mathematics, we talk about the idea of success, how he defines the term,
and how he knows if one is successful in mathematics,
Maxine: Some people base success on grades. What do you base success on?
Kendon: I base success on how well you understand the material that you learned or how
well you understand the class.
Maxine: Well, then do you consider yourself successful in math?
Kendon: I consider myself probably about 70 percent successful in math. For you to
consider yourself successful, you have to understand the material. If you
understand the material, if you know how to do the work, then you're successful.
I'm partially successful because I get the work done, but do I fully understand it?
Sometimes, I don't.
Curious about the ways that he views himself in relation to this concept of success, I ask Kendon
to tell me what makes him believe that he is “70 percent successful in math.” He shares four
examples: (1) his peers seek him out when they have trouble with material; (2) of more than one
thousand people who took a mathematics-based exam for a position at the refinery, he was one
of 20 offered a position; (3) his recent scores in his calculus exams (he earned an A); and (4) his
willingness to try even when he does not know the answer. His response to this question helped
me to gain a better understanding about his newly-developed tenacity in mathematics.
Kendon’s conceptualization of success is useful for his development as a mathematics
learner; while it shows him where he does not always ‘meet the mark’ as a successful student (by
his description of the term), the definition helps him to locate himself amongst students who are
successful. As such, he can recognize his achievements, identify as a successful mathematics
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learner, and persist even when he struggles with coursework. During our final meeting—one
week before his final exam—we talk about how he plans to study for the exam.
Currently in Mathematics
In our final meeting, Kendon appears to be of two minds—he is concerned about his
upcoming quiz and final exam, yet he seems confident because he has been studying for the
upcoming quiz and exam and is hopeful about how he will perform. Reflecting on his upcoming
exam, he says,
I spend a lotta time studying for math, so with math you just never know what to expect,
never know what approach to take or what formula to use until you have to really think
about it or see it and you go from there. I think the main thing with me is when I study I
have to figure out a way of retaining the information that I study. But, I'm definitely
doing much better on the quizzes, and I got an A on the midterm, so this next test coming
up on Wednesday, I'm gonna try to get an A on it as well.
Seeming even more confident about his final, he says, “Then I’ll try to get an A on the final
[and] hopefully get an A in the class.” Smiling as he reflects on his performance on his prior
exam, he shared, “I got a 98 on a test. On the quizzes I’ve been doing well—in the beginning I
wasn’t doing so well, but I picked it up because I anticipated [a quiz] was coming, so I started
studying and reviewing.” He seems determined as he discusses his study plans for the final, “I’m
definitely gonna study hard and go over [the course material] because the final’s gonna be based
on the nine quizzes we had and also the two exams.” Curious about his study plan, I ask him to
share his strategy. “I’m gonna read it over ten times to make sure I understand everything. That
way when I take the final it could be a breeze.”
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After our meeting, Kendon mentions that he is going to the tutoring center to study; I see
him there when I leave and wave good-bye. A few weeks after our final meeting, I follow up
with him to ask how he is doing and to ask about his final exam score. As we end our
conversation, he says, “By the way, I ended up getting a C in Calc 2. I believe I deserve better.
Dr. Blaze grades too harsh.”

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Data from All Study Participants
As noted at the beginning of this chapter, in this section I present data from each of the
participants in this study to introduce information that I analyze in Chapter Six. The tables
featured present the following: (1) Table 11: participants’ mathematics identity as categorized by
the new mathematics identity framework—academic ability, instrumental value, obstacles,
support, motivation, approach, and sense of belonging in mathematics; (2) Table 12: participant-
identified turning points in their college-level math performance; (3) Table 13: academic
resources that participants use to achieve academic success; and (4) Table 14: quotes that
exemplify participants’ sense of belonging in mathematics.

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Table 11: Participants’ Beliefs about Their Mathematics Identity
Ability
(Academic)
(One Option)
Instrumental Value
(Multiple Choices)
Obstacle
(Multiple Choices)
Support Motivation Approach
(Multiple Choices)
Sense of
Belonging
Low Med High Work Life A P A P Online Textbook Peers
Abdul-Malik
Baker
+ + + + + + + +
Valerie
Baylor
+ + + + + + +
Ophelia
Jackson
+ + + + + + + + + + +
Jackson
Jacobsen
+ + + + + + + +
Kendon
Joseph
+ + + + + + + + + + +
Maurice
Knight
+ + + + + + + + + +/-
Barry Powell + + + + + + + +
Wesley
Simon
+ + + + + + + + + + +/-
Persia Smith + + + + + + + + +/-
Nicole
Vincent
+ - + + + + + + + + -

+ Participant addressed their beliefs about this aspect of Mathematics Identity in a way that demonstrated their agreement with this component
- Participant addressed their beliefs about this aspect of Mathematics Identity in a way that demonstrated their disagreement with this
component
A: Academic: Participant addressed their beliefs about academic obstacles or supports to their math success (e.g., instructors, peers, etc.)
P: Personal: Participant addressed their beliefs about family, friends, peers as obstructing or supporting their math success
Empty: Participant either chose another category or did not speak about these aspects of mathematics identity (e.g., ability).

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Table 12: Participants Who Identified A Turning Point in Their College-level Math Performance
Participant Abdul-
Malik
Baker
Valerie
Baylor
Ophelia
Jackson
Jackson
Jacobsen
Kendon
Joseph
Maurice
Knight
Barry
Powell
Wesley
Simon
Persia
Smith
Nicole
Vincent
Identified
turning
point
X X X X

X X X

Table 13: Academic Resources That Students Use to Achieve Success
By the Book Beyond the Book
Studying
with Peers
Homework/
Textbook
Tutoring Online Sources Seeks Help
from
Instructors
Spiritual Faith &
Prayer
4 10 7 5 8 5

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Table 14: Quotes that Reflect Participants’ Sense of Belonging in Mathematics
FE MALES MALE S
Components
of Sense of
Belonging
Ophelia Valerie

Nicole Persia Abdul-Malik Kendon

Barry Wesley Maurice Jackson
a) Belief (s)he
is part of the
group of math
learners
We would text each
other [and if] they
had a problem with
[a math question],
they would send me
a picture of it. I
tried my best to
work it out, or we’d
get on FaceTime
and try to work it
out.
N/A Interviewer: Do you
ever work with
classmates?
Nicole: I haven’t
before cause…if I'm
wrong or don't know
what I'm doing, I
don't want to stop
them or slow them
down. So I haven't
really worked with
anybody.
N/A They’d be like, “Can
you help me with
this? Can you help
me with that?” I just
be like, “No
problem.”
We’re in similar
courses or we take
them in the same
semester, that way
we can help each
other to do good.
Interviewer: And do
you usually study
math with other
people or usually by
yourself?
Interviewee: By
myself. In high
school, I studied with
other
people…Now…peop
le might be in
different places, so I
don't wanna hold up
anybody and I don't
want them to hold me
back, so that's why I
study by myself .
Yeah, the [math]
workshop was a big
part of my math...
That was where I
could sneak away to
study. At first, at this
point, I was taking it
just to have a place to
go where I can just
focus …When I go
into the math lab,
everyone was in there
doing math, so it was
a good place to be.
Interviewer:Do you ever
do math with your
classmates or anything like
that?
Interviewee: No, t’s just
me and math. I feel like to
talk to another person, my
mind has to be focused on
math…When it comes to
doin’ math, the students
I’ve talked to about maybe
working with math, they’re
really standoffish when it
comes to math. They like
to be by themselves. In my
mentality, I’d rather [work]
by myself. There’s no one
who would work math with
me, so I may as well learn
to do it by myself.
Interviewee: I realized
that study groups are a
necessity. It wasn’t the
instructor, but the fact
that the people in that
study group felt like I
can contribute to that
study group or it
would be best if I stay
in that study group and
still do it. They were
reinforcing getting
good grades or passing
a class, reinforcing
that I have the
potential to pass this
class, or understand
the material to pass.
b) Belief
about ability
to be
successful in
math
You aced math. If
you can overcome
that, you can do this
I finally realized, oh,
wow, I can do this.
It’s…a strength in just
knowin’—just not
givin’ up. Just knowin’
that I can do
everything.
I think if I just
practice and refresh,
it can get better.
Interviewee: I feel
I’m capable.
Interviewer: What
has you say you’re
capable?
Interviewee: It’s just
me knowin’ and
believin’ in
myself…Once I
collectively have
everything—man, I
see my future being
very bright.
I have confidence
that I know how to
read some directions.
I have confidence
that I know how to
read over and over
and over and over
and over and over till
I get it
I consider myself
probably about
70 percent
successful in
math.
[I can solve anything
that's put before me.
Some people, if they
get a math problem,
they might get
frustrated…but I
have an
understanding that I
can do it . I can do
this problem.
I like [math], but
sometimes it's like, I
don't understand and
then I have to go into
my lab, my lab is
here [points to his
head] and I have to
figure it out. And
then it's like, "Oh, I'm
the greatest on the
planet. I figured it
out. There's no one
smarter than me."
Until the next class
[chuckles]
There's problems where it's
just like, "Okay, I can get
this. I just need to put more
time into it." Then after
another 30 minutes, I'm
like, "Okay, this is really
frustrating me. I can't
figure it out…"
I'll go and I'll drink, I'll eat
somethin'. I come back,
and I'm like, "I still can't
figure this out. Man, the
hell with it. I'm not dealin'
with this."
Interviewer: What has
you continue taking
math classes, going
towards engineering?
Interviewee: Believing
in myself, seeing that
other people are like,
“Hey you can do this
crazy major,” and
seeing that people
believe that getting an
A in [that math
course], seeing that if I
do put time and effort
into something and I
could achieve.
c) Level of
comfort in
math
Me and math aren’t
best friends. We’re
definitely not
husband and wife
right now. I feel like
we’re
acquaintances. I’m
still gettin’ to know
you. I’m learning to
like you. Then
maybe hopefully
You know, you connect
with a person? Oh, we
were friends right
off…That’s the way it
is for me with math. I
can connect real quick
Interviewer: What
would you say are
your feelings towards
math?
Interviewee: Ugh.
N/A I fell in love with
math
I love math, and I
definitely have a
connection to
math
I enjoyed doing this
math.
I like math. It's one
of the cooler subjects.
Interviewer: What would
you say are your feelings
towards math?
Interviewee: It’s a love and
hate relationship. I love it
when I get it. I hate it when
I don’t get it

Interviewer: What are
your feelings about
math?
Interviewee: What are
you? What is math? I
don’t understand what
is the meaning of
conceptualizing math?
What are we
conceptualizing? How
do we know
everything we’re
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one day, we’ll be
friends
doing is true. What
does it mean to
understand math as far
as going up to calc III
or differentials or
linears?
Interviewer: So,
would you say
curiosity?
Interviewee: Yeah.
Curiosity
d) Belief
about level of
support from
peers and
instructors

If I don’t get it, I
can raise my hand
and ask about it.
She encouraged that
if you didn’t
understand, please
speak up right then
and there…[Y]ou
were able to raise
your hand without
feeling silly.
Professor Juntasa
is…showing you how
to get it…She says,
“Some of you guys may
have this kinda
computer. You gonna
have to go into here.”
She’s really just—it’s
good, walking you
through it.
[W]e had to get into
groups and I was like,
"I really don't wanna
do this. I'm gonna be
with these people
who know what
they're doing and
they're gonna be like,
'what are you doing?
You’re slowing down
the group."
Interviewer: How
would you describe
his reaction?
Interviewee: It was
very negative…I felt
like he tried to
embarrass me. I said,
“Malissa, he doesn’t
care for you.”
I was having trouble
with a concept, and I
went to her office.
She took her time
with everyone and
explained it to me.
She would say, “Try
it. Try it.””
He's a great
professor because
he expects
perfection, and
he's pretty
challenging.
That's what I like
about him
N/A I met some guys who
were really good
math students, the
tutors. I’d see them in
my class, and we’d
work together to
understand things,
and then myself also
helping other people.
Over the time we
became friends, and
they taught me some
techniques and
whatnot.
My elementary school
teacher…He’d be like,
‘You know what? [Mauice
is] just as good at chess as
he’s doin’ good at math.
Your teacher tells me you
are amazing in numbers. It
seems like it’s easy to
you.’”
[My instructor] didn’t
give up on me. She
always pushed
me…She would
always say like, “Look
you can do this. You
got this. Just put time
into it.”… She would
always tell me like, “If
you wanna be an
engineer you have to
understand this stuff.
I want you to be who
you wanna say you
wanna be, so master
math.”
e) Tendency
to participate
in math
groups
Interviewee: I am
the quiet person in
math class…with a
focused stare face.
Every now and then
if it’s something
that I’m 100 percent
confident that I
know, and it’s
something that
everyone knows but
nobody just wants
to speak, then I’ll be
like, oh, well, yeah,
we do this. Yeah,
we do that. She’s
like, yeah, exactly.
Most of the time I
don't say nothing. I
sit right up front,
and I don’t say
nothing.
I ask questions. I even
try to answer ‘em to
keep givin’ myself a
better understanding.
You know, and if my
teacher is talkin’ about
somethin’, I’ll say, you
know, I’ll raise my
hand, I’ll say, okay, so
if I do this, this and
that, and if I use this
and carry this, you
know, bring this over
here—and then she’ll
say, yeah. That helps
me understand.
I do ask questions.
I’m not afraid to now
as an adult cuz I
realize if I don’t ask,
I might not remember
to ask later.
N/A I’m answerin’
questions. I’m
engagin’ with her. If
I don’t understand,
I’m not shy about
askin’
I’m always
participating. I’m
always in-tune in
the class. Even if
I have the wrong
answer, I still
participate
If I have a question, I
speak up cause the
teacher is going along
with the problem and
if he has something
that I don't
understand, then I
have to stop him
cause I don't
understand, so I have
to catch what I
missed.
Maxine: Okay. What
did that provide for
you, being with
others doing math?
Wesley: [A]ccess to
people who were
really math geniuses
compared to myself
and opportunities to
work with other
people who you
know, I’d see in my
class, and we’d work
together to
understand things,
and then myself also
helping other people.
That’s the way to
know that you know
something is to try to
explain it.

Interviewer: Are you
comfortable sharing [your
math in class]?
Interviewee: I’m
comfortable with sharing
with most of my math,
stuff that I get. When I’m
not comfortable sharing,
I’m open to learn

Interviewer: What
kind of interactions
did you have in study
groups?
Interviewee: Actually
calc one in the winter
we had a good student
group too. Piecing the
problems like I
understand the first
part, but then the next
person is like, “Oh but
this is how you finish
it.” Then things like
that or another student
like, “We got through
that problem. Now
we’re on the next
section and we’re
lost.” This one student
was like, “Oh I got
this. Here this is how
you do this part.
Thanks for helping in
the last one,” things
like that.
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f) Likelihood
of engaging in
practices to
achieve math
success
I go through my
notes first, or
through the book
…I run straight to
YouTube [and]
Google, watch
multiple videos, and
pick from each
Interviewer: What do
you think helped you be
successful in math?
Like even now?
Interviewe: Tutoring
and studying. If I
wouldn’t have had
tutors, I wouldn’t have
been successful.
I go to tutoring
Monday through
Thursday and I'm
here every morning
on Saturday from 8-
12…
I study, so I’ll study
and really try
Interviewer: Do you
ever study with any
other people?

Interviewee: Yes, my
daughter. If there's
anything I don't
know, I'm like,
"Look, I need you
today." Normally, I
just stress her when
it's test time. Cause I
tried to hire a tutor
and he was showing
me stuff the wrong
way and I was like, "I
can't do you."
I would use
Purplesmath, some
Khan Academy…and
I would just do it on
my own. I did maybe
two months of that
during the break.
Then, when I went to
class, the stuff I did,
it was already like
chapter four and
chapter five stuff.
I’d go on Khan
Academy, or
YouTube, or
Chegs Solutions.
[Chegs Solutions]
has the step-by-
step solution to
many book
problems.
Interviewer: When
you don't know how
to solve a math
problem, what do you
do?
Interviewee: I go
back and look at the
rules at the beginning
of the chapter. It
answers it all right
there. So if they give
us a problem, they
give us the answer to
these problems
First thing I do is I
read the chapter.
And then try to solve
for it. And while I’m
reading the chapter,
I'll do the examples
…I'll turn to
YouTube and once I
YouTube, it's a
matter of practicing.
Online sources are
awesome. There's
nothing new under
the sun so everyone
has already had my
problem, everyone
has already solved
my problem. So if I
have access to
everyone via Google,
Bing, or mathematics
blogs, I can run into
something in the very
same way.
Interviewer: I’m wonderin’
when you have a math
problem that you don’t
know how to solve, what
do you do?
Interviewee: Go on
Google. Do YouTube.
That’s pretty much it.
Every once in a while, if
it’s like one problem, I’ll
go to the tutoring center.
I’ll ask for that one
problem. If it goes passed
maybe two problems, I
wouldn’t hit the tutoring
center. I’ll just skip the
damn thing. Yeah, cuz if
it’s 2 problems out of 15
problems, then it’s little to
me. Don’t worry about it.
When I first took
college math, I already
came in with the
intention of doing
what it takes in order
to transfer, so when I
studied, I made sure
that I did all the
homework. I didn’t
cheat. I didn’t go to no
solutions menu or
anything like that. I
tried my best to
understand the
concepts and stuff and
just did every
homework problem,
and that’s how I was
able to get an A.
g) Intention to
take higher
level math
courses
I have a couple
more math classes
that I need to take,
as far as I still need
statistics.
I need to get it for
myself where you
know, everybody say,
"As long as you can
add" No, there's more
to it… It's so many
forms and I need to
understand it. That's
why I make sure I'm
getting it, because I
need to understand it
for me.
If they told me
tomorrow, "You don't
have to take anymore
math classes” I
probably wouldn't
Interviewer: So,
would you say that
you're gonna keep
takin’ math? Do you
think you'll need it
for the future?
Interviewee: I need it
for fashion, period.

I’ve got my sights on
being a top
mathematician. My
sights is high.
I want my
engineering
degree…I'm
definitely not
gonna stop
N/A N/A Interviewer: How much
time do you have left here
at [LA North]?
Interviewee: Well, I have
maybe three math classes
left to take and maybe two
or three science classes left
to take.
If I wanna stay in
education, then I think
math would be pivotal.
Because that's what I
would think I will be
teaching in…
math is very
important if I want to
get my degree. As far
as in order to obtain
my bachelor's degree,
master's, PhD, I need
to get to differentials
or linear, whatever
extra math I need a
take. I think math is
very important to the
student, in getting
their degree. I think
math is very
important.
259

The Final Meeting: Suggestions from the Resident Experts
18

On a rainy afternoon, I meet the study participants in a private room in the library for our
first and only group meeting. During this session, many meet each other for the first time; others
who knew one another before the study chatted about which classes they would take next, and
together, we ate lunch. After I distributed their gift cards to thank them for their participation,
we settled in for a conversation. “Thanks for being here, everyone,” I say. I pause to turn on the
recorder and then continue.
So, we’re at the end of the study. I just wanted to get everyone together for some lunch
and to ask a few final questions while we eat. With all of the knowledge that you have
about being a student who has been successful in developmental math at LA North, what
would you suggest to instructors about how to improve the way they teach and engage
with students?
The group is quiet for a short time, likely thinking of the types of instructors they might have
wanted to have in their math classrooms. Then, they speak insightfully about what can make a
difference for learners who take developmental math courses.
Relational Practices: The Importance of Care and Encouragement
First to respond, Kendon raises his hand and says, “The care definitely makes a
difference because if the students see that the professor really cared, then that’s gonna encourage
[them] to do better.” I remind them that this is an informal conversation, so they don’t have to
raise their hands. Then Maurice jumps in, “Oh, in that case, I’ll say be more engaging with your
students, especially the ones you see… having some troubles…We could be grown, old people.

18
As a reminder, although this lunchtime meeting did not actually occur, all participants’ suggestions are factual.
260

If we have somebody that cares, we keep moving forward.” I see Nicole and Barry nodding in
response from the corner of my eye. “So how would they show that they care,” I ask. Kendon
replies, “Consult with the student and encourage them to come to their office hours. Be
concerned about the student. If they’re slacking off, tell ‘em. [This] starts from the beginning of
the semester.” Maurice chimes in again, “There’s nothing wrong with pulling the students aside
and having a talk with them… They’re not gonna listen to the teacher and then go back…to the
same way.” He goes on, “You don’t have to understand what a student’s going through, but be
more engaging in what you want your student to accomplish. Don’t let them leave the class if
you know they’re walkin’ out with a D, because they’ll walk out.” Persia, the only fashion
design major in the group, shares her thoughts on the importance of care, “For the ones sittin’
there that you know are behind…They may’ve had a day, hard week, hard month, hard year.
They just needed you to come, be more caring…When we succeed, they succeed.”
Quiet up until this point, Ophelia’s initial response is short and to the point, “Be
encouraging.” She goes on to share about her experiences with Professors Rivera and Juntasa
who told her, “You can do it. No, you can do it. You have it. Stop doubting yourself.” Perhaps
recalling his own experience with Professor Rivera, Maurice nods in agreement. Then, Ophelia
goes beyond the importance of providing encouragement for coursework and suggests that
instructors, “Encourage students to go ahead and try for their Associates, versus ‘just get your
certificate...[I]t’s important for the instructors of the trades to encourage students to go ahead.”
Sitting next to Ophelia is Nicole—she nods in agreement, then changes the focus of the
encouragement back to the classroom. She says, “[I’d say] ‘Please don’t discourage us, because
not all of us are gonna say, Forget you,’ and keep going. Some of us will take your word
seriously and not follow through or leave.” Sharing both the value and the sting of instructors’
261

words from her experiences, she adds, “We still look up to teachers. They’re still role
models…My teacher told me I couldn’t do it, and I really believed you…Words do hurt, so when
you tell somebody just give up, they start to believe.” Then, as though sending a message
directly to instructors she turns to me and adds, “If you get to that point where you’re telling
people to just give up, you need to give up. You don’t have any passion or spark about what
you’re doing if you think telling someone to give up is great.” A few participants applaud to
acknowledge the realness of her statement. “Amen to that,” Valerie adds.
Pedagogical Practices: Making Math Make Sense and Expecting the Most from Learners
“Ok, what else,” I ask. Changing the focus from the ways that instructors interact with
students, Valerie starts talking about the pace at which instructors teach in the classroom, “[We
have to] get that concept, you can’t keep goin’ forward if someone’s stuck…sometimes, they
have they schedule in this week, but if you take one more day to explain somethin’, I think that
[the student will] get through the next day.” She adds, “Don’t skip steps…If you’re doing these
problems, don’t leave anything out, ‘cause you’re confusing the students.” Likely recalling one
of the experiences that she shared with me during one of our conversations, she says, “When
someone can’t understand, instead of getting agitated with them because you know it…keep in
mind that the people you’re talkin’ to does not know what you know. Just because you know it
that way, you can’t teach it that way.”
Ophelia offers another suggestion, this time for teaching course material. “Don’t speak, I
call it ‘mathematical talk.’ Just remember that we’re not at that level quite where you’re at, so
when you’re speaking it would be nice to use terms that the general population would
understand.” Wesley and Abdul engage in a sidebar conversation, so figuring they have their
own words of wisdom to add, I ask them for their suggestions. Wesley responds first, and talks
262

about what happens during homework. Abdul follows with an innovative way to deal with
course assessment.
Focusing on homework assigned, Wesley suggests instructors make homework more
rigorous. “I would give less problems, but more challenging problems. Go about it that way…if
you’re doing a bunch of easy problems, you’re being a robot.” Explaining his experience when
he was given these ‘easy’ homework assignments he says, “I hate the easy—when I start doing
problems, and every single one is easy, I’m like, I’m uncomfortable.”
Near the recorder, Abdul leans on the table to ensure he can be heard. With his focus on
assessing students’ knowledge, he speaks about the importance of employing new testing
practices. “For my final, interview me.” Simulating writing on the whiteboard, he says, “Let me
get up and put some stuff on the board and let me explain to you what that is. Let me give a
presentation. Let me teach, and then grade me on that.” “Ok,” I say, “I’m gonna play devil’s
advocate here cuz I think that’s a great idea cuz then we’re really seeing what people can do.
What about the person who says, ‘Well, I have 45 students in the class. I can’t do that.’?” Abdul
pauses and looks at me with his head slightly cocked to the left and says,
Well, you know math. I would say divide it by five. Get five chalkboards…and you could
sit back and have this one working on that, and just sit back and watch...Then, the next
group go up, like that…That would make people more strong…it’s more engaging, I
think, than just you and that paper and your head.
While some participants laughed at Abdul’s comment, others simply nodded in agreement. As
we ended the session, Nicole asked, “Will this be part of the dissertation too?” “Yes,” I said.
This will be in a section of a chapter with your suggestions.”

263

CHAPTER SIX: THEORETICAL IMPLICATIONS
The primary focus of this dissertation is to bring attention to a group of learners who are
often neglected in community college remedial math literature: African-Americans who succeed
in these developmental courses. Most of the previous research on Black students in remediation
has addressed these learners’ failure in these courses, and so, presents them from a deficit lens.
In contrast, I focused on the experiences of ten African-American students who have been
successful in remediation to learn (a) how these participants describe their mathematics identity,
(b) how they describe the ways they achieved success, and (c) how these learners perceive the
role of instructors and classroom practices in their success. I combined Martin’s (2000)
mathematics identity framework with sense of belonging in mathematics (Boaler et al., 2000;
Good et al., 2012), and used narrative methodology (Bruner, 1987, 1991; Clandinin & Connelly,
2000; Fisher, 1985; Polkinghorne, 1988, 1991, 1995; Riesman, 2008) to study this topic.
In this chapter, I draw out themes that emerged from the narratives in Chapter Five, to
illuminate how mathematics identity, success, and instructors’ behavioral and pedagogical
practices influenced participants’ progress in remedial mathematics. In the following sections, I
examine emergent themes with three considerations in mind: (1) the frequency with which
participants discuss ideas, experiences, or concepts across narratives; (2) the relation of the
themes to the literature reviewed in Chapter Two; and (3) the ways these themes answer the
research questions. Said another way, discussion of every theme includes quotes from two to
three participants who spoke about related experiences. I present these themes using the
categories delineated in the new mathematics identity conceptual framework introduced in
Chapter Three and address emergent themes about instructors’ practices and learner success. As
a reminder, the New Mathematics Identity framework features the categories from Martin’s
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(2000) mathematics identity framework (ability, instrumental value, obstacles and supports, and
motivation and approach) along with the sense of belonging in mathematics framework (Good et
al., 2012). When analysis of the narratives revealed connections between different components
from the new mathematics identity framework and the other research questions, I combined the
categories for ease of discussion (e.g. instrumental value is linked with motivation, success is
linked with approach, and instructors is linked with approach). As I am an interpretivist
researcher, I acknowledge my own subjectivity as I connect participants’ experiences to the
literature reviewed and answer the research questions. While a majority (and in some cases, all)
of the participants addressed the themes presented in this chapter (unless otherwise stated), I
selected examples with connections that strikingly corresponded with or contrasted each other.
Ability
As noted in Chapter Three, identity, from the sociocultural perspective, relates to the
ways that individuals “know and name themselves” (Grootenboer, et al., 2006, p. 612) and is
based on social interactions with people in their home, school, and social environments. These
participants’ experiences show that this definition of identity is not just a conceptualization.
Rather, their retelling of their experiences highlighted how perceptions of one’s ability are
always under construction, are shaped on a daily basis, and influence how these participants view
themselves as math learners and doers.
Ability: Then, Turning Point, and Now
As participants’ personalities and life experiences varied, so did their beliefs about their
math-related abilities. While some classified their current math ability as “low” and few
categorized themselves as having “high math ability,” a majority of participants placed
themselves ‘in the middle’ (see Table 11 in Chapter Five) based on their own definitions of
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“low” and “high” math ability. In some cases, participants shared beliefs about their current
abilities that differed from the labels they gave themselves in their early years; this difference
prompted me to explore classroom experiences, instructor interactions, and other events that may
have influenced their views of themselves as “low,” “middle,” or “high” ability students. In the
first section of ability, I explore the ‘Then’ period, or early years, in participants’ math
experiences to show the ways that early math progress and classroom interactions influenced
students’ views of their abilities. The second section addresses the turning points in
participants’ math experiences and how these experiences influenced their math trajectories.
Lastly, the ‘Now’ section features the ways that participants perceived their math abilities at the
time of the study. Each section contains a discussion about the ways math-related events during
different periods in these learners’ lives shaped their experiences in math and their views of
themselves at that time.
Then: Classroom Interactions Shaping Experiences
Ophelia and Wesley viewed their elementary school memories in mathematics positively
as evidenced by the affirmative ways they spoke about their ability. In Ms. Jefferson’s class,
Ophelia had her earliest math memories, which she described as “relat[able]” and “fun;” she
classified her ability as “pretty good.” With similar positive math experiences, Wesley described
himself as a student with “good math skills” who enjoyed the subject. Recalling the ways he was
able to show off his math skills to his peers when he won the five minute test challenge, he said,
“I strutted around class the day I won [the math test]” [and] “If I did better, I'd make fun of
people.” In other words, he was proud of his performance and demonstrated this to his peers.
Similarly, six other participants recalled positive math experiences during their elementary,
middle, or high school school years.
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By relating these experiences with positive perceptions about their math ability, Ophelia,
Wesley, and six other participants reflect what authors posit about the ways positive math
performance influences learners’ math identity development (Berry et al., 2011; Boaler et al.,
2000; Martin, 2000; Stinson, 2008). Said simply, these students had enjoyable and positive math
memories and these experiences prompted positive perceptions about their math ability.
Like Ophelia, Wesley demonstrated that positive interactions with teachers influence how
students view themselves. In one of his earliest school-related math memories, he recalled
positive words from his teacher, Mr. Malcolm, “You know, you're pretty good in math…he
would encourage me.” Here, Wesley demonstrated the ways that affirming exchanges with
instructors can encourage students. Ophelia’s and Wesley’s memories of positive interactions
with teachers and classmates contributed to their views of their math ability and highlight how
interactions with instructors along with classroom experiences shape learners’ perceptions of
their ability and interest in math (Berry, 2008; Jackson, 2009; Martin, 2000, 2009; McGee &
Martin, 2011a, 2011b; Stinson, 2009). Ophelia’s and Wesley’s classroom experiences continued
to influence them into their grammar, middle, and high school years, though the outcomes of the
next set of interactions were not as positive.
Ophelia’s middle school experiences with Ms. Joliet and peers prompted her to describe
her ability as “poor and basic” during those years; she thought of herself as “lost.” Although
Ophelia’s math experiences improved in high school when she took geometry, the idea that she
was not skilled in math had already taken root. This was evidenced by what motivated her to
pass math during those years, “Let me just get up outta here, so I don't have to deal with [math]
anymore except when I wanna count money.” In high school, although Wesley said he
“struggled at first, but…became very good,” becoming “very good” was not enough to
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encourage him to take upper-level math courses. Thinking, “I’m just here trying to get out so I
can get some freakin’ job,” Wesley left school and went on to find a job, leaving behind
memories of his experiences with mathematics. As with Ophelia and Wesley, three of the six
participants with positive early math memories eventually discussed negative experiences in
junior high school, high school, or college.
From Ophelia’s, Wesley’s, and others’ explanations of their interactions with teachers,
peers, and coursework in elementary, grammar, and high school math, it is not difficult to see
why their views of their abilities and desire to continue studying mathematics took downward
turns during these early years. The idea that teacher practices shape Black students’ math
identities over the short and long term has been discussed by a number of authors (e.g., Berry,
2008; Jackson, 2009; Martin, 2000, 2009; McGee & Martin, 2011a, 2011b; Stinson, 2009). The
importance of teacher behaviors is not unique to math, as authors have also found that this
concept exists in science classrooms with Black students (Kane, 2009, 2012a; Varelas et al.,
2012). Additionally, when students do not have positive math experiences, they mostly view
math as important for its current purposes (e.g. testing and homework), not as part of their future
goals (Martin, 2000; 2007). They are also less likely to take more than the minimal number of
math courses to complete their diploma, certificate, or degree (Martin, 2000; 2009). As such,
students like Ophelia and Wesley, shaped by their experiences, leave their early years with
strong beliefs about their ability to succeed (or fail) in mathematics. Those who go to college
carry these memories like an albatross, are placed into remedial math, and hope for the best.
While some students struggle in math remediation or do not complete the sequence, others—like
several participants in this study—have a turning point in their math experiences that shifts their
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view of themselves and their math abilities; ultimately, these shifts influence their academic
performance.
Turning Point: Events Result in a Shift
Seven of the ten participants spoke of a moment or series of events that altered their
perceptions of their math abilities and encouraged them to know themselves in new ways as
math learners. With this new perception, they began to perform differently in math; for most,
their new performance was a welcome surprise. This section highlights the experiences that
served as a shift or turning point in Kendon’s and Maurice’s experiences in remedial
mathematics.
As noted in Kendon’s narrative, he had his turning point in his first college remedial math
class. This experience was prompted when Kendon began to understand math and changed his
work habits, “I started to understand the concept…That's when I began to love math…[then] I
was doing all the homework assignments.” These new practices encouraged new interactions
with his peers. ”I felt more comfortable and confident with students approaching me, asking me
questions.” Although Kendon’s math faculty helped him understand course material, his
instructor’s efforts were not the only reason he viewed himself and his math abilities newly and
changed his work practices; he benefitted when his peers acknowledged his math skills. Peer
recognition positioned Kendon as a capable math learner and doer, influenced his status in math-
related settings and conversations, and motivated his positive mathematics identity development
(Stinson, 2008; Varelas et al., 2012). In other words, the acknowledgement that he received
reinforced his beliefs in his academic ability, encouraged him to change his work practices, and
ultimately, improved his math performance.
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Research on Black college student success supports Kendon’s experiences by showing
that Black students’ peer groups play a critical role in their academic progress and success
(Palmer et al., 2011); these results match findings on the influence peer groups have on positive
mathematics identity development (Berry et al., 2011; Grant et al., 2015; Stinson, 2008).
Kendon’s new understanding of math brought new behaviors, as evidenced by the ways that he
worked to complete homework and support his peers. His actions demonstrated his new level of
accountability (Grant et al., 2015) in math class. This new accountability, paired with an
improved perception of his ability, reflects Kendon’s strengthened mathematics identity.
Kendon’s positive turning point experience is reflective of most, but not all participants in this
study; Maurice’s turning point highlights the ways that instructors’ expectations can hinder
students’ advancement.
Although nine participants improved or maintained their progress in math from their
early years, Maurice’s mathematics progress declined in college; as a result, so did his beliefs
about his abilities. According to Maurice, his experience of and love for mathematics changed
when his professor “wanted [them] to solve and get the answer that way he was teaching it,
because that’s what he was doing in his exams.” His inability to solve the problems using his
professor’s steps was particularly frustrating because since his early years, Maurice self-
identified as a student who has “always been able to figure out and do [math].” This was his
turning point in mathematics and is reflective of Howard and Whitaker’s (2011) reports that
negative and positive turning points in students’ math experiences contribute to a shift in
mindset, views of their own math-related abilities, and ultimately their math performance. A
review of Table 12 (in Chapter Five), shows the participants who identified turning points in
their math-related experiences.
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A closer look at Maurice’s turning point experience shows that in Professor Lieu’s
course, Maurice knew how to solve the math problems, but he struggled with the course material
primarily because of his professor’s requirements; as a result, he continued skipping problems
and became frustrated. Eventually, as he advanced in remedial math, he felt despondent about
his progress and the need to relearn material that he had learned in high school. Maurice’s
feelings and subsequent behaviors reflect those students who are placed into lower-level
remediation courses even after succeeding in high school (Attewell et al., 2006; Ngo, 2017;
Scott-Clayton et al., 2014) and the ways that repeating these courses can be detrimental to
student progress. In addition to the difficulties associated with repeating courses, like others who
have similar experiences in remediation, Maurice’s underlying frustration and self-concept
appeared to sabotage his educational goals (Cox, 2009).
These participants’ turning points in math performance link with their views of their
abilities and more importantly, reflect the ways in-classroom and peer experiences along with
institutional glitches and administrative issues shape learners’ perceptions of themselves and
their math ability as college students. This is the next and last focus of these participants’
perceptions of their math ability: students’ current perceptions of their ability.
Math Ability Now: The ABCs of Perception of Math Ability: “Average,” “Basic,”
and “Capable.” When asked for their thoughts about their ability, several participants
responded in ways that seemed to belie their achievements; they considered themselves to be
“average,” “basic,” or “capable” math learners. In other words, although they were successful in
remedial math, eight of the ten participants did not view themselves as high performers. In fact,
of those who perceived their ability as “low” (three of ten participants) or “in the middle” (four
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participants), Wesley had the most positive assessment of his math ability. “I think I'm at least
of average intelligence and I'm striving to get better…I guess I feel I'm capable.”
Although Abdul did not use the words ‘average,’ ‘basic,’ or ‘capable’ when he described
his math ability, he embraced a sentiment similar to Wesley’s. What is interesting is that he had
this perception of himself despite earning As and Bs in mathematics and computer science at LA
North after dropping out of high school and doing “terrible” on the math portion of the GED.
When asked if he was a good learner and if he thought he was successful in math, he responded,
“No, I can never say that…I’m too low to be feelin’ like that…I think I would feel a little bit
once I get into calculus.”
Ophelia’s beliefs about her math ability as an adult changed marginally from her junior
high and high school years. In her discussion about her math ability, she shared that she thought
she was, “Better,” “improved,” and “good,” “but not great or really good,” “I am still
improving.” Ophelia has this perspective despite primarily earning As and one C in the remedial
math sequence and performing well enough to earn an A in her most recent math course.
These and other participants’ perceptions about their math ability beg the question, “Why
do these students believe they are ‘average,’ ‘basic,’ ‘capable,’ and ‘good, but not great or really
good when they are persisting and succeeding in remedial math courses while others do not
complete the sequence?” Perhaps a review of the ways that these students define low and high
mathematics ability offers some perspective.
Wesley defined high math ability as “understanding the concept quickly and then being
able to apply that concept to problems.” Ophelia also connects high math ability with
understanding, noting, “You’re comprehending. You understand what’s goin’ on. How to go
ahead and solve it…[Y]ou actually start likin’ it a little bit.” With a similar sentiment, Abdul
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says, “I gauge what’s a good learner…if I can understand what I’m doin’, and I can teach others
that.” Wesley defined low math ability as “not understanding it quickly and having struggle to
grasp…the concept.” Ophelia used similar words, noting that those with low math ability “don’t
understand it…don’t want to understand it…[and] don’t do very well at math.” Abdul did not
provide a definition, but his understanding of low math ability can be implied from his definition
of high ability. As marked in Table 11 (in Chapter Five), Wesley and Ophelia identified their
math ability as low- and mid-level, respectively; Abdul did not offer a self-assessment. So,
perhaps these participants’ beliefs that those who solve problems quickly, understand math, like
the subject, and can teach math to others have shaped their view of how math should be done.
To some degree, Wesley and Ophelia extol ease and facility in math in the same ways that speed
and correct answers are valued in dominant mathematics-related discourses (Boaler et al., 2000).
In turn, the struggles that Wesley and Ophelia had with math at different points in their schooling
likely shaped their views of low, medium, and high math ability and reminded them of their
struggles. In this view, they have led themselves to believe that they do not have high math
ability, despite their academic success.
According to math education scholars who study instruction, Wesley’s, Ophelia’s, and
Abdul’s perceptions about math ability may derive from K-12 math classroom learning
experiences (Mesa et al., 2014). They argue that early classroom experiences can embed negative
and “deep-rooted misconceptions” (p. 175) about what it is to be a ‘good’ math student. This is
another example of the ways that learners bring their prior experiences into their college math
classrooms.
Did these participants simply carry self-perceptions of their math ability from the early
years into college despite their success in this new environment? For example, Ophelia, Wesley,
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and Abdul knew themselves as students with certain math skills prior to enrolling at L.A. North.
Despite experiencing turning points that led to greater success throughout their remedial
coursework, they did not assess their math abilities as ‘high.’ As identity is defined as the ways
that one knows and names herself or himself, do Ophelia, Wesley, and Abdul simply need more
positive experiences and successes to continue shifting what they know about their abilities? If
yes, then this is further evidence that students’ math experiences and the stories they tell
themselves about these experiences are key for cultivating positive mathematics identity.
Obstacles
When asked about the obstacles that hampered their progress in math classes, participants
cited multiple in-and-out-of-classroom experiences on their respective roads to success. This
section highlights three themes that emerged in these discussions about math-related obstacles
and shows how participants navigated through these challenges to achieve math success. The
first was an issue with multiple languages in the classroom, the second were racialized math
experiences that participants dealt with on a daily basis, and the third obstacle was the
institutional challenges that became barriers and affected one student’s efficiency and
effectiveness.
Two languages in the math classroom. Four of the ten participants talked about the two
languages in the classroom and how these resulted in difficulties: the languages of accented
American-English and the mathematics language. While some participants spoke about
difficulties understanding their instructors’ foreign accents, the real obstacle emerged when these
instructors were unwilling to clarify material. For instance, Ophelia shared this about Professor
Zhao, “[T]here was some kind of language barrier, but she also moved very, very fast. She didn’t
like to repeat herself at all.” Though other students had difficulty understanding their instructors,
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not all faculty were unwilling to explain material multiple times. About Professor Asimah,
Wesley said, “…sometimes I did not understand what he was talking about.” In these cases, he
“…would ask him again” and then received the help that he needed.
These participants’ challenges exemplify that for some students, difficulty with course
material is secondary to challenges that they have when instructors who do not speak American-
accented English refuse to clarify themselves. For those who struggle with math, the subject can
be considered a ‘different’ language on its own and understanding the material can seem
impossible. When instructors take issue with students’ requests for further clarification (as in
Ophelia’s experience), learners’ math-related difficulties can be exacerbated. Said another way,
learners’ difficulties continue to grow when they do not get the help they need to make sense of
what is happening in their classroom experience.
Racialized math experiences: “The group I was with, they lookin’ at me like “He
don’t know nothin’.” As in other math identity-related studies (e.g., Martin, 2000; McGee et
al., 2011), participants in this study identified racialized math experiences or some form of
discrimination in the classroom or math learning environment. Wesley recalled an experience
with a math teacher who seemed to scoff at his request for help, “I may be small-minded. I
automatically thought it was a race thing…you go to ‘em, and they’re overdramatic about it, ‘Oh,
you didn’t listen. I just went over this.’” Kendon’s experience with discriminatory behavior was
“daunting” because not only did his instructor falsely accused him of behaving inappropriately in
class, he also treated him differently from his peers, “[T]he things he'd give students partial
credit on, he wasn't giving me credit.” Abdul expressed similar sentiments about the ways that
peers—who were unaware of his mathematics prowess—treated him in the classroom. “The
group I was with, they lookin’ at me like “He don’t know nothin’.” Once Abdul showed that he
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understood the material, his peers (majority Latino) reacted differently, “The [students at the]
next table was lookin’ like ‘He know that?’” Two other male participants shared similar
reactions of seeming shock or disbelief from Latino classmates when we spoke about others
learning about their math-related skills.
The math classrooms were not the only places where these students experienced hostile
treatment. Abdul recalled moments when his “own people” refused his assistance at the tutoring
center. In this case, while not a racist situation, it was clearly discriminatory, “I guess that my
own people were lookin’ at me, maybe they see theyself, like, ‘Oh, he don’t know.’” Although
each of these participants shared similar racialized or discriminatory math experiences, the ways
they chose to deal with the situations differed.
Reactions to these experiences. In response to these racialized experiences, Wesley
persisted and resisted discrimination by “work[ing] harder…Ask[ing] more questions. [Coming]
with pre-prepared questions to ask that would be difficult for them to answer.” Responding
similarly, Kendon recognized that the experience “made [him] have to work harder to prove [the
instructor] wrong.” Whether responding by challenging instructors or working harder to prove
others’ race-related or discriminatory perceptions incorrect, Wesley and Kendon, enacted their
own forms of stereotype management in the face of the threats they experienced regularly with
faculty and peers in math classrooms. McGee & Martin (2011) define stereotype management as
behaviors that are prompted by the omnipresence of stereotypes. As a result of these stereotypes,
individuals engage in achievement-driven performance in an effort to dispel negative
stereotypes. Individuals engage in ongoing management of these stereotypes as they deal with
“everyday micro-aggressions inside and outside the classroom” (p. 1355). Whereas many of
these participants experienced frustration or anger, initially Abdul responded differently. First,
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he laughed. Then he said, “[P]eople underestimate people…I know what I’m doin’.” Later he
spoke about the same type of discomfort as others and shared, “That’s why I might not feel
comfortable going to a tutor or going to the professor.” While students like Abdul are able to
achieve success by teaching themselves, others who react to this type of situation in the same
way but do not have his skill set could be at a disadvantage if they choose not to visit the tutoring
center or a professor when they need academic support.
These participants’ responses reflect the literature about Black students’ racialized math
experiences. Researchers contend that when Black students face racialized experiences in math-
related environments (Martin, 2006, 2007; McGee et al., 2011; Stinson, 2008, 2009), these
episodes signal to them who can and cannot succeed in math. McGee and Martin (2011)
reported that when Black math and engineering students in a four-year college dealt with
racialized experiences on campus, they responded by excelling in math in an attempt to prove
others wrong. As participants in this study spoke about their own racialized experiences in math,
it was clear that their frustrations encouraged them to work harder to cope with their concerns
about discrimination and stereotyping in the classroom and in the tutoring center.
However, before some readers label these racialized experiences as positive forms of
motivation for these Black students, they should consider an argument put forth by McGee and
Martin (2011),
[While] stereotype management facilitated success in these domains, the students
maintained an intense and perpetual state of awareness that their racial identities and
Blackness are undervalued and constantly under assault within mathematics and
engineering context (p. 1347)
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These participants’ experiences highlight this concept in multiple ways. Whether Black students
believe that they need to retaliate when they feels mistreated (Wesley), that they have to do well
to prove others wrong (Kendon), or that they should not ask tutors or instructors for assistance
(Abdul), their identities as mathematics learners are complex. As exemplified in Wesley’s
narrative, these learners’ mathematics identities require that they do more than engage in math-
related practices to learn material. It also requires that they learn to navigate and survive in
contentious math environments and learn to deal with the “tweak in [their] psyche” (Wesley).
As Wesley notes, these “tweaks” can affect the ability to perform and eventually become barriers
to math success. These participants’ math-related experiences and their responses reflect a
sentiment put forth by Grootenboer and Zevenbergen (2007). These authors argue that, “[What
happens in] the classroom community is temporal, and it will be the mathematical identity (the
connection between student identity and mathematics) that will remain.” (p. 245). So, while
these racialized experiences in classrooms and tutoring centers may last for a moment, they
become ongoing obstacles with which these students and other Black students who have similar
experiences must contend as they strive to achieve in mathematics.
Institutional challenges. For one participant, obstacles extended beyond the classroom
practices and the tutoring center and reflect the larger institutional barriers that can impede
students’ progress in mathematics. Although only one participant spoke about institutional
bureaucracy-related barriers, mentioning his experience is important because his story
illuminates the challenges that often go unnoticed in larger conversations about student success
in mathematics.
A focus on Maurice’s narrative shows that a number of his obstacles were related to
institutional, not academic challenges. Maurice’s stories about his troubles with financial aid
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illuminate the ways that inefficiencies in the school’s financial aid office delayed his registration
for classes and as such, interfered with his work and study schedules. As a reminder about the
ways that glitches in the financial aid office affect student progress, Maurice shared, “That
school was…losing my packets [so] I was lined up in the system…to be as a late-registered
student. By the time I was allowed to schedule classes, those classes were already almost full.
My [work schedule] had to be shifted.” This shift in schedule impeded on Maurice’s study time.
This limited study time resulted in bigger issues, because as his coursework became more
challenging, he had less time to focus on new and more complex topics. While the root of
Maurice’s challenge was lost paperwork in the financial aid office, this difficulty points to larger
issues that pervade institutions and in turn, affect student progress and success.
As stated in Chapter Two, much of the remediation literature focuses on student progress
in these courses from a deficit perspective by highlighting students’ failures; few consider the
ways that institutional culture and staff and faculty practices set off a chain of events that affect
learners’ academic outcomes (e.g., Deil-Amen et al., 2001). In Maurice’s case, certainly a
portion of his challenges related to his habit of ‘skipping problems’ that appeared too time-
consuming. A closer look at the situation, however, highlights “deficits at the institutional level”
(Baumann, Bustillos, Bensimon, Brown, & Bartee, 2005, p. 2) and the ways that such issues
intensify already-existing difficulties as students navigate mathematics in the community college
system. The intent here is not to shift the blame from students to institutions, but rather to shed
light on campus practices that co-exist with and can exacerbate student difficulties. For learners
like Maurice who have to fit in multiple visits to the financial aid office to resolve issues while
maintaining work and school schedules, sorting out these issues and being efficient with study
time can be challenging. This situation is particularly troublesome knowing that Maurice’s
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inclination to identify himself as “a sorry-ass mathematician” stems from having too little time to
study, understand material, and complete homework.
Instrumental Value and Motivation
For many participants, the return to college and ultimately, the pursuit of math was
prompted by their professional and personal interests. Some sought to earn credentials to boost
their knowledge and salary in an already existing career, while others recognized that a college
education could help them fulfill on a newly adopted dream or desire. Regardless of their reason
for returning to college, these participants knew that they needed to complete the remedial
mathematics sequence to achieve their goals. As participants talked about why they continued to
persist in mathematics, three themes emerged: (1) the purpose that math served for their future
career plans (seven of 10); (2) the way(s) that they linked mathematics and money (three of 10);
and (3) the respect that they developed for the subject (two of ten). A review of the data showed
that the instrumental value that students assigned to mathematics also served as their motivation
to persist, particularly when course material became more challenging. To reflect this link, these
two categories from the new mathematics identity framework—instrumental value and
motivation—are combined in this section. To understand how these participants’ thoughts about
the benefits of math evolved, this section begins with three participants’ early beliefs about
math’s role in their lives and the ways these perceptions developed over time.
Instrumental Value in the Early Years
Although Ophelia, Kendon, and Wesley differ in age, school major, and career interests,
one idea was consistent: after high school, they all viewed math as unimportant in their careers.
Ophelia’s motivation to learn math and the value the subject had in her life were summed up
with the idea, “Let me just get up outta [high school], so I don't have to deal with [math]
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anymore except when I wanna count money.” With this view, she took minimal math classes in
high school, graduated, and pursued a career that involved basic math skills. Wesley held a
similar perspective after passing high school geometry, “What could [math] do for me?” “I’m
cool right here.” Wesley’s views of mathematics were compounded by his mother’s requirement
that he find a job; eventually, finding a job became Wesley’s focus, not pursuing higher-level
math classes. He thought, “I’m just here trying to get out so I can get some freakin’ job” because
as he shared, “I never even considered a future with math or science.” Kendon’s beliefs in
math’s unimportance stemmed from interactions with his parents, “Math wasn’t important at the
time, because [my parents] didn’t really drill education in my household—they wasn't
encouraging me to stay focused.” Eventually, he believed, “So it’s like just do it and if I don’t
do well…it’s just not a big deal.” One could say that the difficulties these participants had in
their math-related experiences, coupled with the lack of connections that they made between
math and their lives, limited the instrumental value they placed on the subject and increased their
desire to ‘escape’ from math. Once Ophelia, Wesley, and Kendon grew older and gained life
and work experiences, their perspectives about math and its value in their lives changed.
Math Success = Career Success
Each of these three participants worked for a period of time and then decided to return to
school. At the time of this study they were well into the coursework for their majors, had new
views of math, and held beliefs such as, “[t]here was no way I can get to where I want to be
without math…If I can't do [math] well, then I can't get a job” (Ophelia); “In my field, you gotta
be able to analyze data, you gotta be able to organize things…So [math] teaches you how to
think” (Wesley); and “as an engineer, you have to know how to calculate” (Kendon). Each
adopted a new view of math’s instrumental value in their lives as it relates to the career that they
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envision for themselves. This link with an important part of their futures (their careers), helped
them connect with math in tangible and important ways, but also brings forth another aspect that
they deemed important for their lives.
When considering the new importance that math has in their lives, Ophelia and Kendon
linked success in math with a personal benefit: money. Ophelia said, “[Math is] definitely gonna
be important, because money is important” and Kendon shared, “[A]s an engineer, you have to
know how to calculate to make sure you're making the correct earnings or put overtime into
play…” Their sentiments reflect Martin’s (2000) research showing that many of the parents of
the junior high school students in his study recognized the connection between math success and
financial gain from employment opportunities only after they became adults. Those who had
recent math success altered the ways they viewed math and their aspirations for their children.
In some sense Ophelia’s, Wesley’s, and Kendon’s experiences and perceptions about math
success closely aligned with the views of the parents in Martin’s study; as adults, several
participants in this dissertation study viewed math’s importance differently. In essence, they
have applied a popular belief to their own trajectories: that math success offers access to ‘good,’
‘high-paying’ jobs and can result in higher salaries.
Because of their own life experiences, Ophelia, Wesley, and Kendon had different
reasons for returning to college and persisting in mathematics. Math had become valuable in
their lives and this value motivated them to persist. Said another way, their desire for better
careers and money drew them to math-related careers because they believed that mathematics
had the power to help them fulfill their desires. Career opportunities and money were
particularly important for some participants in this study; however, for others, respect for
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mathematics and an appreciation for the subject outweighed all other reasons to persist in the
face of academic challenges with the subject.
Respect, personal value, and love of the challenge
Those who had a deep-seated love and appreciation for mathematics and valued the
subject were motivated to persist in the face of difficulties (two participants: Maurice and
Abdul). Of all students in this study, Abdul most expressed a deep appreciation for mathematics.
His appreciation for the subject served as his motivation to persist and superseded any incentives
around the financial gain that math success might offer.
Abdul talked about a new perspective that he developed in mathematics and associated
this view with his sense of respect for the subject. “I gave it value. It made me want to take my
time and invest in it.” Now, recognizing the value of math in his life, Abdul approaches
mathematics differently. “[N]ow I wanna understand it… Not just doing homework and doing a
book. I wanna go deeper in it and understand it.” As a result of Abdul’s academic experiences in
his early years, he did not place much value on math beyond the immediate purpose that it served
in his life. While the ability to care for his family sparked his interest in attending college, he
was motivated to pursue learning and to be successful in math when he experienced challenges
with the subject. “Well, what I loved about it is that the challenge it gives me, and the feeling
you get when you get the problem… you can figure it out and other people can’t figure it out.”
Abdul’s ability to understand math when others were “falling apart [and] dropping the class”
continued to inspire him, not only to persist but to excel in his classes. In other words, the new
value that he placed on math helped him to put forth his ‘best self’ in his math-related endeavors
and take pride in his work; each of these reflect his positive math identity development and in
turn, contributed to his success (Berry et al., 2011).
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With Abdul’s new math-related thoughts and actions, he identified as a math student and
demonstrated his identity through his participation in mathematics in college. When students
seek ways to participate in math-related activities, look to themselves and peers for answers
rather than a classroom authority figure, and appreciate the challenge that math offers, they have
a greater chance of developing strong mathematics identity (Berry et al., 2011; Grant et al.,
2015). As Abdul embodied these different practices and embraced the challenge, he gained a
deeper love and respect for the subject. His growth and development as a math student,
willingness to invest time and effort into his work, and desire to help others learn math through
providing informal assistance and tutoring services showed that at LA North, Abdul embraced a
new identity as a math participant, learner, and doer.
Success and Approach
In our conversations about success, participants shared a host of practices that they use to
achieve in mathematics. Review of the narratives in Chapter Five showed that they discussed
success in three ways: (1) they redefined academic success, valuing understanding over grades
(five participants); (2) they discussed by the book strategies that they used to achieve success (all
participants); and (3) they shared beyond the book strategies that they used and how these helped
them to be successful (five participants). By the book strategies refer to the traditional and often
standard methods that students used to learn material and achieve success, such as studying with
peers and visiting the tutoring center; beyond the book refers to the faith-based practices and
beliefs that students employed to help them achieve success. Similar to other sections in this
chapter, analysis of the narratives showed that the practices they used to succeed linked with
their approach to studying mathematics, thus these two categories are presented as one in this
section, exemplifying that success in math requires identifying and employing effective
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approaches when one faces difficulties. Table 13 (in Chapter Five) shows the by the book and
beyond the book resources that students used to achieve academic success and the number of
students who employed each type of resource.
Redefining Academic Success
When speaking about what qualifies as academic success, one participant whose narrative
was not included in Chapter Five noted, “Cs get degrees.” More than just a catchy rhyme, this
phrase highlights that for these participants, grades were not of primary importance when they
determined their math success. When asked how he defines success, Kendon shared, “I base
success on how well you understand the material that you learned.” Abdul’s response was
closely aligned. “I’d be hard to judge and say who’s a good math learner because maybe you get
the grades, but you don’t know it…a good learner is if I can understand what I’m doin’, and I
can teach others.” At first glance, one might perceive these participants’ ideas of success, rooted
in understanding rather than grades, as ways to mask that some had passed classes with Cs.
However, with a closer look at aspects of some of their stories, readers gain a deeper
understanding of the thinking behind this alternative definition of success. Kendon’s interest in
working with Dr. Blaze, despite his “harsh” grading methods encouraged him to stay in the class,
learn the material, and earn a passing grade, even if was not the highest in the class. Ophelia
admitted that she had been “passed through” grades in her early years even when she did not
know the material. So, it is possible that Ophelia gave more credence to math knowledge and
understanding than grades. Whether the instructors’ requirements for success or memories of
receiving passing grades despite not learning course material served as impetuses for
understanding, these participants recognized that knowing answers without understanding course
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material is useless. Because they wanted more for themselves, developing the ability to
understand mathematics became their priority.
By the Book: Studying with Peers
Strategic in his study practice, Wesley paired each of his math courses with the “math
workshop” because as he noted, it was where he would “sneak away to study.” Prior to
attending the math workshop, Wesley admitted, “It would make me upset that I didn’t know
what [the instructor] was talking about.” As a student who excelled in elementary and middle
school, and struggled, but then succeeded in high school, not knowing was uncomfortable for
Wesley. Displeased with his lack of knowledge of course material, Wesley shared, “I have to
figure this out ‘cause I can’t let that happen.” Then, he began attending the Math Workshop and
interacted with peers in ways that were instrumental for his success. In the workshop, even
though Wesley studied alone, he also met with classmates, “[W]e’d work together to understand
things, and then myself also helping other people.” Here, even if he struggled with math, he was
comfortable to turn to peers for support without concern for how he might be perceived. He also
became a student who could be viewed as knowledgeable—a different experience than in the
math classroom in college where he thought, “I feel I’m not as smart as this guy” if he could not
answer questions.
For Wesley, the math workshop became a “math space” (Walker, 2012, p. 67), or place
where he joined a community of math learners and doers and developed his math knowledge.
Walker (2012) acknowledges that these math spaces are where “relationships or interactions
contribute to the development of a mathematics identity” (p. 67). These experiences in the math
workshop were particularly important as they signaled that Wesley could demonstrate success in
a safe space after recognizing that his skills were lower than his classmates and struggling with
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course material. In this math space, Wesley’s developed his math identity and cultivated his
ability to be successful in remedial math.
By the Book: Textbook Resources
In conversations with participants about their math-related success, all narrators spoke
about using the course textbook during homework sessions. Ophelia, Maurice, and Abdul spoke
in more detail about how they used the textbook to learn material. “I go through my notes first,
or through the book. Sometimes they have the examples in the book and I’ll relook over it,”
Ophelia said. Maurice provided more detail, “I’ll read the exercise [and] I’ll copy it
down…[and] work it out myself.” He avoids the textbook’s answers until he thinks he has
solved the problem. “Once I feel like I find the answer, then I’ll look at the answer. If it’s
different, then I’ll see where I went wrong.” With a step-by-step process, similar to his early
years, Maurice uses the textbook as his personal guide for learning course material.
Becoming “more dangerous with [his] math” when he transitioned from learning math on
the computer to the textbook, Abdul spoke about becoming “more invested and more involved”
in math. While he never used the phrase, ‘hands-on learning,’ his description of his math
learning seems to fits the idea. “When you doing that book homework…you gotta deal with that
book. You gotta deal with that eraser. You gonna be going through a lot of paper.” For Abdul,
this hands-on engagement with math was exciting, and more fulfilling than the online homework
system used in a previous class where the software would guide students toward the answer. His
strategy for learning course material required that he sit—and sometimes struggle—with
material. Of the nine other participants who spoke about using the textbook, no one else spoke
about the discrepancy between learning from the computer and the textbook.
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Abdul’s preference for learning math via textbook rather than computer might be linked
to what researchers have to say about math learning and identity development. In math identity
and learning research, scholars report that in the classroom, learning goes beyond cognitive
thinking (Boaler et al., 2007); how one “learns a particular set of knowledge and skills, and the
situation in which a person learns, become a fundamental part of what is learned” (Putman &
Borko, 2000, p. 4). A review of Abdul’s narrative and the transcripts of several of our
conversations shows that he expressed his goal of achieving “master[y],” “being a top
mathematician,” and earning his PhD in mathematics. That said, he also considered himself to
be at a “low” level in the number of courses that he had completed. Therefore, when considering
how involved he became with math in his textbook learning experiences, it is understandable
why he prefers the textbook over the computer. Unlike the computer programs used to teach the
subject in one class, the textbook required that he get acquainted and engage with the book in
ways that were not available with the computer. The situation in which he learned textbook
mathematics helps him develop the skills to “stay in the cage” with mathematics while his peers
struggled in class. With the goal of being a top mathematician, Abdul recognized that he has a
long way to go to develop his math skills; while he uses other modes of learning (e.g., the
internet and instructor support) the textbook is his preferred method.
By the Book: Tutoring and Online Resources. Like Ophelia, six other participants visited the
tutoring center for academic assistance when they needed support. Ophelia shared, “[C]ampus
tutoring here really helps a lot honestly…it feels like you're on a peer-to-peer kinda relationship.
Because the tutors are also students, so it's kinda like they're right along with you understanding
the struggle.” Maurice shared, “[D]efinitely take advantage of the tutoring, because there's
times I went for one problem, and end up stayin' to finish my homework in there…if I was stuck,
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[the tutors are] right there.” These participants’ comments serve as a reminder that during peer
connections in math environments like the tutoring center, learners meet others with similar
aspirations (Martin, 2000; Seymour & Hewitt, 1997; Solomon, 2007; Treisman, 1992) who help
them learn material in a collegial environment (Grant et al., 2015; Treisman, 1992). Success in
these environments help to foster learners’ positive math identity development.
While some participants discussed using textbooks, tutoring, and online math resources
to tackle their difficulties, others spoke about using online resources prior to course enrollment to
ensure that they set themselves up for success. “She got high ratings on Rate My Professor,”
Abdul shared when speaking about his favorite math professor at LA North. Ophelia said, “Now
I would go outta my way to go on Rate My Professor,” when we talked about difficulties that she
had with an instructor in class. These out-of-classroom guides for academic success help these
learners continue to find innovative ways to ‘take charge’ of their learning and academic success.
Beyond the Book
When most participants spoke about the reasons that they were successful, they focused
on the academic practices that they employed to learn math. Ophelia and Abdul offered similar
ideas, highlighting their study practices and academic resources; however, they were two of the
five who also spoke about the importance of two other resources in their success toolkits: their
spiritual faith and prayer. When speaking about the factors that have shaped her success,
Ophelia’s first response was “prayer.” She followed by saying, “I…pray before I study, and
make sure that I pray before my exams…or before I do my homework.” Her faith was
particularly important for her because during a majority of her early years, she struggled with
math and believed she could not be successful. Her pastor’s words, “Don’t ever think that your
problems are too small or too big for God to handle,” helped her to reframe her thoughts. Soon
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she began to believe, “I can't say, I'm not gonna do it well and I have all the tools spiritually to
get it done.”
Abdul echoed Ophelia’s sentiment about the influence that his faith has had on his
progress and success in math; although he attributed what I initially thought was confidence in
his ability “to read[ing] some directions,” it seemed as though his “faith and understanding [and
his] relationship with [his] creator” made the difference for his progress and success. Because of
his faith, he knows that in life, “You’re gonna go through tests.” With this in mind, before
studying for a test, doing homework, or taking on a new academic endeavor, both participants
take time to pray for guidance along their academic paths. Ophelia shared that when she has
difficulty during an exam she stops and says, “Lord, help me;” with these words, she re-centers
herself and is able to solve the problem. For Abdul, his faith is more than a way to achieve
success, his appreciation for math is connected with the lawful nature of mathematics in relation
to his faith. When we spoke about the importance of mathematics in his life, he said, “For me,
for my way of life, it’s very important to me that I do something…that’s pleasing to my
Lord…Mathematics, I like it because it’s lawful.”
These faith-based activities reflect Ophelia’s and Abdul’s spirituality and illuminate
something else that took place in their identity development: a shift in their mindset about their
math abilities and in turn their math study practices. Similar to the work of other scholars (e.g.,
Wood & Hilton, 2012), a closer look at Ophelia’s and Abdul’s narratives reveals that their
spirituality helped one or both of them develop confidence, learn how to deal with barriers, and
discover a purposeful path in life. With bolstered confidence and the ability to address the
barriers in math that seemed to hold her back for many years, Ophelia shifted her perspective
about herself as a math student and began to learn how to create a mindset to promote success.
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“I adopted a different attitude about [math], it made me start viewing it a little differently. That’s
when I had to come to terms with, “Okay. A lot of that was me.” This realization that she was a
culprit in her math-related difficulties was empowering. With this knowledge, she began to tell
herself a new story, “If I can overcome this, there’s nothing in life that I can’t do.” This new
story helped her construct a new identity. Once Abdul began his math classes and coursework,
his mindset also shifted, “After getting in [the class]… it’s like The Wizard of Oz. They’re
thinking [math is] big, you know. When you lift back the curtain, you’re like, “Oh, it’s only you
back here. I can hang out back here.” With these perspectives, Ophelia and Abdul used their
respective faiths to tell themselves a new story about their math abilities and as such, began to
create a new mathematics identity.
Instructors and Supports
As noted in Chapter Two, instructors play an important role in the stories that students
create about themselves, the math identities that they develop, and learners’ progress in
remediation. A review of the narratives in Chapter Five showed that instructors’ behaviors were
both helpful and harmful for students’ progress. Instructors showed their support for students
when they (a) built up students’ confidence (five participants) and (b) taught in ways that helped
students develop an understanding of material (seven participants); some instructors’ practices
were harmful for students’ progress, particularly when they taught in ways that indicated learners
should already know the material taught in class (six participants). Participants also discussed
the importance of Black professors (four participants) and their own family members as part of
their support structures (six participants). As in previous sections, similar themes emerged
related to instructors and student supports, and so I have combined them in this subsection of this
chapter.
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Instructor Practices Help Create New Stories
After seeing her own role in her academic success, Ophelia recognized that student
success also has “a lot to do with instructors, as far as the way they were teaching.” Beyond
teaching strategies, participants also talked about instructors’ behaviors and the pivotal role they
played in the learning process. Before discussing instructors’ different practices, and their
influence on these learners’ progress, it is useful to mention that several participants have had the
same instructors for different courses. As such, readers will notice that different students
mention the same instructors’ names in the narratives and this section.
Building them up. When deciding if he would take a “combo class” after his first math
course, Abdul had some trepidation. Aside from knowing that he had just completed his first
course, the combo class “was worth ten credits” and “a lot was riding on it” in terms of the
amount of work expected and how the course might affect his GPA if he did not score well. He
spoke with and emailed Professor Rivera to ask her opinion about his decision multiple times
and she “encouraged [him] the whole way,” saying “You can do it” and “[Y]ou’re capable.
Abdul spoke about Ms. Rivera’s ability to encourage students; Ophelia and Maurice praised her
ability to know what students need and inclination to reach out to them as though she knew when
her support was required. Ophelia and Maurice shared about the professor’s willingness to
support and her ability to “break it down,” referring to her ability to “switch [the explanation]
up” and “reiterate what she wants [them] to learn” (Maurice). With these abilities and skills,
Professor Rivera helped Maurice learn math in ways that connected with his ability to teach
himself and in ways not always reflected in the textbook. Her willingness to meet them where
they were as students helped them to connect with her. As Maurice noted, “You feel like the
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teacher is willing to throw aside her plan and her syllabus to make sure that I get it. That is very
important to me.”
Teaching for learning. Kendon described Professor Blaze’s grading practices as
“harsh,” but he could not deny that he was forced to learn in his class and supported as he
engaged in the process. “You could have all the correct answers and you could fail the test
[because]…he cares more about the steps.” With this understanding about his math instructor’s
teaching practices and expectations, Kendon trusted that he would “know [his] stuff.”
Next, Abdul recalled that during office hours, Professor Bhattacharya would patiently
explain the problem, “She would say, ‘Try it. Try it.’ Then she would just take her time.” With a
focus on her professor’s ability to make subject matter relevant for her life, Ophelia shared that
Professor Juntasa taught in ways that made complex language understandable by taking concepts
about “boats and goin’ up streams” and linking them with situations closer to Ophelia’s life, such
as “go[ing] to the mall,” “go[ing] to this store,” and calculating that “this distance is x amount.”
Professor Rivera’s ability to use “shopping examples when it came to teaching percentages and
rates” contextualized math in ways that helped Ophelia make sense of course material and
connect it to her everyday life. Wang and colleagues (2017) define contextualization in math as
not only weaving mathematics into courses from other subject matter, but also “teaching [math]
knowledge and skills with immediate reference to real-life examples” (p. 429). Professors
Juntasa’s and Rivera’s ability to connect math to Ophelia’s everyday life helped her learn the
course material, appreciate the subject, and crave a new level of understanding.
In each of these cases, participants spoke about Professors Rivera’s, Blaze’s,
Bhattacharya’s, and Juntasa’s, abilities to provide encouragement, make themselves available
for extra academic support, tend to learners’ emotional and academic needs, push students’
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mathematical comprehension, and teach with attention to what facilitates students’
understanding. Their words reflect what is in the literature about Black students who know their
instructors have high expectations of them and feel supported by faculty’s behaviors. These
students appreciate their instructors’ efforts (Guiffrida, 2005), believe in their own ability to be
successful (Hagedorn et al., 2001), and have a higher likelihood of developing a strong
mathematics identity (Berry et al., 2009; 2011; Stinson, 2009; Walker, 2012). These instructors’
ability to balance emotional and academic support and provide an extra push that some
participants did not received in their early years gave these learners a sense of hope that they
could not just pass math classes, but they could excel in them. This sense of hope laid the
groundwork for some to reframe their previously negative math identities and begin developing
more positive math identities.
Although Ophelia was the only participant who referenced her professors’ ability to
contextualize math in the classroom, her emphasis of their practices warrants mention in this
section. That she was the only one to highlight instructors’ ability to contextualize basic skills
mathematics and help her gain a greater understanding of course material may speak to the high
percentages of students who withdraw from or fail developmental math courses. This is
particularly disturbing because researchers have noted that contextualizing math helps students
understand mathematical processes, not just content and as such, helps them to succeed in
remediation (Cox, 2015; Wang et al., 2017). This greater understanding “facilitate(s) authentic
math learning by helping students both retain math knowledge in a meaningful way and extend
their newly gained knowledge into other learning settings” (Wang et al., 2017, p. 429).
Considering the ways that students benefit when they perceive that math is useful in their lives
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(i.e., instrumental value), finding innovative and creative ways to contextualize math into the
lives of those in remediation is both important and valuable.
You Should Already Know. As noted in the participants’ narratives and in earlier
sections of this chapter, not all faculty’s behaviors and practices were positive and affirming.
Aside from enduring racist and discriminatory practices, participants spoke about instructors’
general classroom behaviors, particularly when faculty made it seem as though students’ lack of
knowledge was problematic (six participants). Describing an experience during office hours,
Maurice talked about challenges when he brought questions to his professors. Instructors told
him, “Well, figure it out. Work it out. Do a little bit more practice.” Others said, “You know
what? I don’t know how you’re not gettin’ it sometimes,” when he just wanted them to sit with
him and say, “Show me where you think you may be goin’ wrong.” He described the experience
as one where he has been “emotionally beaten down” and thought, “I don’t feel like I can do this
math.”
Frustrated and disappointed with instructors’ practices, Maurice was quiet about his
feelings. Other students were not silent though. Abdul decided that he would not squelch his
frustration when Professor Bhattacharya, annoyed with the request to clarify the material a sixth
time, refused to explain the material to him. “She had an attitude with me. I said, ‘That’s your
job. You need to say it again.’” The professor threatened to throw him out of class, and so he
left and diffused the situation. As a reminder, Abdul and his instructor apologized for their
behaviors and resolved their disagreement; however he was the only participant who spoke about
resolving a contentious situation with an instructor.
Abdul’s negative interactions with faculty shed light on an important issue in community
college math remediation: some instructors’ lack of effective pedagogical practices and how their
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teaching difficulties can cause problems for both students and instructors. Kozeracki (2005)
reported that often, instructors who teach remedial courses have been trained in their discipline,
not in instructional practices; nor are they prepared to be instructors in remedial courses. As
noted in the literature review, faculty who are ill-equipped to teach these courses can become
frustrated when their instructional practices are not effective; students are often the ones to deal
with the outcome of their reactions. For students like Maurice who do not express their
frustration to their professors, experiences with instructors who behave in these ways make
learners question their choice to persist; ultimately, other aspects of their mathematics identity---
which are noted in Chapter 5 and in this chapter—encourage them to continue in these classes.
However, as represented in Table 7 in Chapter Four on student progress in remediation, a
majority of Black students are not able to withstand their instructors’ toxic responses and other
obstacles in their pathways. These students either fail or withdraw from these courses and as
such, do not complete the remedial sequence. Those like Abdul who are more vocal about their
frustration also have to contend with more than learning mathematics. When they decide to
speak up for themselves, they take a chance on being reprimanded or punished for disagreeing
with the instructor, which can result in contentious relationships with instructors and add a layer
of challenge to their math learning process. Readers will recall earlier in this section that while
Professor Bhattacharya’s patience during office hours supported Abdul’s understanding of
course material, their interaction in the classroom contributed to his frustration. Their
experiences together remind readers that student-instructor relationships, like math learning, are
complex and take time to cultivate.
Seeing Yourself at the Front of the Room: The Importance of Black Faculty.
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Of the ten participants in this study, four had Black instructors during their community
college experience at the time of the study; three had Black math instructors. In this section, I
address Wesley’s experience because he was the only participant with a narrative in Chapter Five
who had Black instructors for remedial math. These instructors’ pedagogical practices and
presence made a difference for him and his progress in remedial math. He spoke more in-depth
about one instructor than the other, so this section focuses on his perspectives of his interactions
with the Black female instructor.
“I liked her a lot. She didn’t take no mess though,” Wesley shared about his first Black
professor. When speaking about her, he focused more on the out-of-class connection that she
made with him, noting, “I would see her just walking through campus. She would always, “Hey,
how you doing?” Talk to me. “What are you taking now? Good. You’d better keep it up.
Remember everything I taught you.” Her effort and willingness to speak with him helped him to
connect with her outside of the classroom. While Wesley appreciated his instructor’s willingness
to speak with him outside of class, it was seeing a Black faculty member at the front of his math
class that inspired him.
Wesley’s comments about the importance of having Black math professors echoes
researchers’ findings that Black students benefit when they interact with Blacks who have been
successful in higher education (Sedlacek, 1987; Willie et al., 1972). Under this instructor’s
tutelage, Wesley had positive interactions (Chang, 2005; Wood & Ireland, 2014), felt validated
(Acevedo-Gill et al., 2015; Rendon, 1994), and was inspired when he saw an individual who
looked like him at the front of the classroom. A majority of participants (seven of ten) in this
study either did not have Black math instructors during their academic career or they had Black
math teachers when they were very young, and had no recollection of the value that these
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individuals had on their lives (one participant). By highlighting Wesley’s experience with a
Black math instructor, I do not disregard the positive experiences that he and other participants
had with math instructors from other races or ethnicities. As noted in the narratives, faculty from
different races and ethnicities positively influenced these students’ lives. However, one cannot
deny the power of Wesley’s words when he said that his Black instructor’s presence in class
helped him, “feel inspired seeing her teaching and think about what obstacles she had to navigate
to get here.” For students like Wesley who have struggled with math at some point in their
academic career, being in class with instructors who look like them provides a powerful image of
success and fosters their identity as Black students who can excel in mathematics.
Making a difference outside of class. When participants spoke about support, they also
included people who were not in classrooms with them regularly: peers and family members (six
participants). Wesley spoke about his interactions with peers and the difference that these
interactions made for him as he sought new study practices. Telling about a conversation during
a study session at the math workshop, he said a peer offered valuable information that he still
uses, “YouTube has everything. Utilize it;” now he lists the website as one of his academic
resources. Talking about a different group that offered support, Ophelia recalled how her family
pushed her when she considered dropping out of her first math course at LA North. They told
her, “You went back to school for a reason. You need to finish this degree. You have to take that
class.” Ophelia was frustrated with the situation, but followed their advice and passed the course.
Abdul also discussed support from his family, but mentioned this in a more subtle way. “She
call me her mathematician,” he said when referring to his wife. This is particularly important for
two reasons: (1) when asked about his perception of himself, Abdul said he did not view himself
as a mathematician and (2) this comment was not included in Abdul’s original narrative; he
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asked that I add the statement during the member check process, showing that his wife’s
affirmation of his identity as a mathematician was important to him.
These out of classroom and in some cases, out-of-school supports were pivotal parts of
the ways these students envisioned themselves as math doers and learners and the practices that
they used to learn material. Said another way, through peer-to-peer information sharing, high
expectations for success, and affirming conversations about their abilities, these participants’
peers and families recognized and interacted with them from what they expected that they could
achieve and encouraged them to use the resources they needed to be successful. Peer and family
behaviors helped students identify resources to progress as math students, push themselves to
persist when they had difficulties, and reminded them of who they could be. These supportive
people were also pivotal because they helped these participants envision themselves as math
students and as such, contributed to their positive math identity development (Berry et al, 2015;
Stinson, 2008; Walker, 2012).
Sense of Belonging in Mathematics
As a reminder, ssense of belonging in mathematics—an additional component of this
study’s mathematics identity framework—highlights the connection or sense of membership that
students have with mathematics. With this study’s focus on Black students who are have
traditionally been marginalized in math, but are now succeeding, experiencing a sense of
connection, or belonging is not only important for their math success, it is imperative. From
these participants’ narratives it is evident that while their sense of belonging with mathematics is
not uniform, there are few differences between males and two of the four female participants.
As a brief review of the components of sense of belonging in mathematics, students
exhibit a sense of belonging in mathematics when they: (a) perceive themselves as part of the
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group of math learners (b) believe they can be successful in math-related settings; (c) enjoy and
are happy and comfortable in the math-related setting; (d) believe their peers and professors
support their success; (e) engage in the learning community rather than being ‘invisible’ in
learning settings; (f) engage in practices to achieve math success (e.g. attend study groups and
office hours) and (g) intend to take higher level math courses (Boaler et al., 2000; Good et al.,
2012).
Belongingness in College-Level Math
Contrary to extant literature on women’s sense of belonging in mathematics (e.g., Good
et al., 2012), female and male participants in 200-level math show little difference in their sense
of belonging in mathematics (See Table 14 in Chapter Five). The greatest discrepancies in sense
of belonging in mathematics appear between female students in 100-level mathematics (two
participants) and the other students. Although the female participant with a narrative featured in
in 200-level math did not comment on each aspect of sense of belonging, her responses closely
reflected those of the male participants.
Even with these similarities, some participants’ responses about their experiences with
the components of sense of belonging in mathematics varied. For instance, when discussing
their level of comfort in and affinity for math, Abdul and Kendon spoke about their “love” for
the subject. While Ophelia did not express “love” for math, at the end of our final interview, she
demonstrated that her relationship with mathematics changed in positive ways and that she had
hope that she could continue to improve. By the end of our final interview, Ophelia showed that
she is certainly not where she used to be with math in junior high or high school, rather she is
‘warming up to math,’ and “hopeful” about her future connection with the subject.
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So, without presuming that all women in math-related situations will have a reduced
sense of belonging as compared to their male counterparts, one might wonder what could have
made the difference for Ophelia’s sense of belonging with mathematics. In particular, what may
have helped her to have a sense of belonging with mathematics that is on par with male
participants in the study? To answer this question, one can turn to the literature on sense of
belonging in mathematics along with Ophelia’s narrative. Good and colleagues (2012) reported
that when women perceived that math ability is malleable or that it can be learned, they were
able to “maintain a high sense of belonging in math.” (p. 1). While Ophelia did not indicate that
anyone told her that math ability could be acquired, she espoused that her pastor’s words, helped
her to believe in herself and know that she has the capability to learn mathematics and in turn, to
excel in her classes if she studied and worked hard. In this sense, perhaps it is her spiritual faith
that influences her sense of belonging with mathematics. As Ophelia is the sole female
participant whose experiences were narrated in this dissertation, further study on sense of
belonging in mathematics for Black women in developmental math would be useful; I suggest
this as a future research topic.
Suggestions from the Resident Experts
As discussed in the findings during the final discussion with participants, these students
offered suggestions to help math instructors understand how to support learners in math courses.
While these participants responded regarding their math-related experiences, a majority of their
comments relate to experiences that would benefit students in other courses. As noted in Chapter
Five, their comments fell into one of two categories: relational practices and pedagogical
practices.
Relational Practices
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With statements such as, “The care definitely makes a difference because if the students
see that the professor really cared, then that’s gonna encourage [them] to do better” (Kendon)
and “If we have somebody that cares, we keep moving forward” (Maurice), participants’ words
reflect the sentiments of scholars like Noddings (1984; 1992), Rendon (1994; 2002), Valenzuela
(1999), and Acevedo-Gill and colleagues (2015) who address the importance of employing
validating and caring practices, particularly when working with students of color in remediation.
These participants emphasized the value of creating personal relationships with faculty and
highlighted the difference that these types of experiences made for them as learners. Maurice’s
words, “be more engaging in what you want your student to accomplish,” highlights
opportunities for faculty to learn about students’ interests and to help learners connect that
interest with mathematics; this can help learners develop the instrumental value that they
associate with mathematics and in turn, strengthen their mathematics identity. As most students
in community college spend much of their time in the classroom (Bickerstaff et al., 2012), these
conversations may represent just a few of the discussions that they will have about their career
interests in an academic setting.
Pedagogical Practices: Making Math Make Sense and Expecting the Most from Learners
The three most common themes in this group of suggestions revolved around making
math comprehensible, bringing rigor to assignments, and innovation to testing. These
participants offered instruction- and assessment-based suggestions, which reflect research on
pedagogical issues in remediation (e.g., Kozeracki, 2005). With requests that instructors explain
material, clarify math-based language, elevate rigor, and assess students orally to demonstrate
their knowledge, in essence these participants are requesting that instructors prepare them on
multiple levels. Not only do they want to be able to understand material and perform well in
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these classes, they want to be ready to use their math knowledge for employment, transfer to
four-year universities, and to develop their own academic interests. Thus, these participants’
responses in this final discussion were not simply about what can be done to help students “get
good grades.” They were about what learners need to be successful as they move from course to
course and eventually into the workplace, into academia, and even beyond these environments.

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CHAPTER SEVEN: CONCLUSION
As noted earlier in this dissertation, many studies, reports, and policy briefs that address
Black students’ performance in mathematics often present these learners as under-performers
who rarely persist or succeed in mathematics-related contexts (Berry, Ellis, & Hughes, 2013;
Ladson-Billings, 1994; Martin, 2000; 2009). By continuing to focus on these students’ failures
in these courses, scholars diminish the achievements of those who succeed, influence beliefs
about their ability to perform, and downplay these learners’ success in mathematics (Ladson-
Billings, 1994; Martin, 2000; 2007; Tate, 1995). Also, a review of data about student enrollment
into higher-level mathematics and science courses shows that African-Americans enroll in these
courses at lower rates; this is troubling because these courses are necessary for entry into high-
demand careers. This ongoing juxtaposition of reports about Black students’ underperformance
in mathematics with stories about their low enrollment in upper-level mathematics courses are
cause for concern. The concern is exacerbated when one considers the trend for Blacks in
community college remedial mathematics courses: these students over-enroll into these non-
credit courses, which often become barriers to their math success and degree attainment.
Using narrative methodology to understand participants’ experiences, in this dissertation,
I studied Black students’ progress in community college developmental mathematics in a way
that diverges from typical mathematics-related research on this topic: I focused on learners who
succeed in these courses. At the start of this study, I set out to explore and understand how these
students (a) describe their mathematics identities; (b) explain how they achieved success; and (c)
perceive the roles of faculty members, peers, and classroom practices in their math success. To
conduct this study, I recruited ten participants: three who were enrolled in developmental math
courses, four who were taking their first college-level math course, two who had completed
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multiple college-level math courses, and one who had already transferred to a local four-year
college.
Using a combination of interviews, math educational history maps, and responses to
vignettes, I gathered information about these students’ math histories along with positive and
negative interactions with faculty and peers from their K-12 and college years. With these data, I
constructed narratives for five of the ten participants and then analyzed the narratives using the
components of the New Mathematics Identity Framework (comprised of Mathematics Identity
and the sense of belonging in mathematics conceptual frameworks). In this final chapter of the
dissertation, I begin with a discussion about the events to which participants’ attribute their
mathematics identity development. Then, I highlight the study’s contributions to scholarship on
developmental education, and where appropriate, link these learnings to issues that are important
and relevant for learners in remedial mathematics and developmental education, more generally.
Next, I address the strengths and limitations of the New Mathematics Identity conceptual
framework. Finally, I close the chapter with implications for practice and future research.
Mathematics Identity Construction
According to identity theorists, mathematics identity construction is a result of the events
that occur in math-related settings, interactions with classmates and instructors, the ways these
interactions affect students’ beliefs about themselves, and ultimately, the stories they tell
themselves about who they are as math learners and doers (e.g., Anderson, 2007; Grootenboer, et
al., 2007; Martin, 2000; Nasir, 2002a). The participants in this study had diverse math
experiences which included events that supported their identity development and others that
negatively influenced their development; this combination of events and experiences influenced
the ways these students performed in mathematics. Given what we know about the ways that
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environments attribute to student performance, I offer a review of the experiences that influenced
the mathematics identity development of participants in this study.
With memories of mathematics from their early years, students who participated in this
study walked into remedial math classrooms toting notebooks filled with stories about their math
abilities. Depending on their interactions with instructors and classmates in these learning
environments, their stories were reinforced, challenged, or dispelled. Some participants’ math
identities were cultivated by caring professors and fostered by classmates who were helpful and
collaborative; others’ math identities were encouraged when they took classes with Black
instructors. In contrast, in other classrooms and math-related settings, learners contended with
insults from their instructors, glares from classmates, and questions about their capabilities.
They learned to navigate oppositional faculty and administrative difficulties and strategize and
defend themselves in racially-hostile math learning environments. In many of these cases,
problems arose when math learning was not solely about learning mathematics, but when it
became about navigating contentious learning landscapes that negatively affected participants’
math progression and ultimately shaped their views of themselves as math learners and doers.
So, while the findings of this dissertation study reinforce the idea that math learning in
remediation classrooms (and in many classrooms, for that matter) can be affirming experiences
for some students, they also show that for others, learning in these environments is challenging
and even problematic. Despite these difficulties, these participants found ways to put aside
discouraging experiences, comprehend course material, pass exams, and ultimately, persist to the
next course. That said, these participants’ experiences—whether negative or positive—
contributed to their ongoing math identity development.
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Contributions to Literature
This study makes two contributions to the developmental education literature: (a) the
significance of race in remediation and (b) the ways that study participants reconceptualized
success in mathematics. In this section, I discuss both topics as they arose in the study and how
they relate to relevant discussions in scholarship.
Significance of Race in Remediation
This study’s findings build on learning from prior research about the factors that shape
Black students’ mathematics identity development, particularly the racial and discriminatory
experiences that they endure in math-related settings (e.g., Martin, 2000; McGee et al., 2011).
As noted in this dissertation’s literature review, Black students’ racialized math experiences have
multiple outcomes. These include encouraging these learners to withdraw from math courses,
discouraging them from completing more than the minimum number of math courses that are
required for graduation, deterring their participation in upper-level mathematics, and in some
cases shaping their beliefs about their inability to achieve in mathematics-related contexts. Black
students who refuse to adopt these negative stereotypes and develop the ability to navigate these
experiences achieve success despite their challenges; they can persist to higher-level courses.
But before readers adopt the idea that perseverance and passing grades make Black students who
persist in mathematics ‘better,’ ‘more resilient,’ or ‘more prepared’ than those who do not, they
should recall that several participants in this study alluded to the ways that they experience harm
in these math environments during their interactions with instructors, classmates, and peers from
other racially-minoritized groups. So, on one hand, African-American students who persist and
achieve in developmental mathematics increase the likelihood that they will earn degrees and
become gainfully employed in high-demand math-related fields. On the other hand, they
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increase their exposure to learning environments that could be emotionally troubling, and in
some cases, even damaging. The interplay between race in math learning environments,
mathematics identity, and academic outcomes (Jackson e al., 2012; Martin, 2000, 2006) calls for
discussions about the challenge of race in remediation, how race manifests in the classroom and
between minoritized groups, as well as the role of race in current developmental education
reform efforts.
The challenge of race in remediation. Considering the ways enrollment in remediation
delays or disrupts students’ college completion, the high percentage of Black students in
community college remedial math courses is cause for concern. Combining these enrollment
rates with statistics about these students’ withdrawal from or failure in these courses, illuminates
the realization that large percentages of Black students enter, but do not leave remediation. As
noted earlier, lack of math achievement in these courses results in Black students’ reduced
enrollment into upper-level math courses, a paucity of Blacks in math-related majors, their
exclusion from high-demand careers, missed opportunities to enter fields that influence research,
and the inability to influence the race-related policies that stem from such research (Tate, 1995).
For these reasons, the number of racialized math experiences that participants reported in
this study was particularly disturbing because these experiences can negatively affect student
persistence in these courses. Important to note in my conversations with participants about
math-related racial discrimination is that I did not initially include interview questions about
racially-charged math environments in the interview protocol. In other words, several
participants’ comments about their experiences prompted our discussions about racial
discrimination and race-related maltreatment from instructors, classmates, and students and staff
at the tutoring center. These issues, seemingly at the forefront of their minds, reflect a racial
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knowing that is present for some of these learners and highlight that participants faced
difficulties that that are unrelated to course material. As noted in Chapter Six, these types of
experiences add a level of complexity to the math learning environment, making these settings
psychologically and emotionally unsafe learning spaces. Expecting students to thrive and persist
in these virulent environments is both unrealistic and impractical.
Black and Latino race relations. Important to note in this study are the discriminatory
experiences between some Black participants and their Latino peers and faculty. Such
occurrences interfered with these participants’ math engagement, their math identity
development, sense of belonging in mathematics, and ultimately, their progress in mathematics.
In a discussion about race relations in the United States, Mindiola, Niemann, and Rodriguez
(2002) note that “much of the history of the…study of intergroup relations has focused primarily
on Blacks and Whites” (p.2). However, in this study, participants addressed a topic that has not
been fully explored: minority-minority relations and discrimination in developmental education.
Similar to prior research on Black and brown relations in America (e.g., McClain and Associates,
2006; Mindiola et al., 2002), these participants highlighted the mistreatment that they
experienced during interactions with their Latino classmates and instructors. Not only do these
experiences uncover additional obstacles that students must address in math classrooms, they
also reveal the reality that discussions about racial discrimination are not reserved for the Black-
White binary.
Cities such as Los Angeles—where this study was conducted—reflect the reality of a
demographic shift that continues to increase in the United States: the population divide between
Blacks and Latinos (United States Census Bureau, 2000, 2010, 2017). As the percentage of
Latinos continues to grow in cities such as Los Angeles, Houston, and Atlanta, there is a
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potential for greater population and racial divide between Blacks and Latinos. As such, one
cannot help but wonder whether or not there will also be an increase in reports of minority-
minority discrimination from students who enroll in remedial math courses. If this is the case,
then students—such as those in this study—may face additional hurdles as they navigate their
educational paths and attempt to succeed in remediation courses.
Race-blind remediation reforms. In a 2017 speech entitled, Making Higher Education
Just, Bensimon (2017) focused on the absence of race, ethnicity, and racism in publications that
suggest reforms to address low developmental education success rates. She identifies several
reasons why ignoring race, ethnicity, and racism in these documents is problematic including, the
high percentages of students of color in remediation and the frequency with which authors used
race-neutral terms, such as “first-generation,” “low-income,” and “demographic forces” in their
plans. The use of these terms is particularly key because as she notes, authors often use these
phrases as substitutes for students from minoritized racial/ethnic groups. So, in a sense, authors
indirectly name these student group in these documents, yet they do not design reforms to
address these learners’ needs.
In addition to the rationale that Bensimon (2017) offers for her contention with these
race-blind reforms, I propose two additional reasons why the erasure of race in these reforms is
problematic. First, given the racialized math experiences that participants in this study endured,
it is clear that racism is not absent from developmental math classrooms. In fact, I assert that
racism and racial discrimination are prevalent in the classroom experiences of students from
racially-minoritized backgrounds who enroll in remediation. As such, if authors and
policymakers who design remediation reforms acknowledge the presence of race, ethnicity, and
racism in developmental education, there is a greater likelihood that they would impleme nt
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reform efforts to address racial/ethnic inequities in remediation. Such reform efforts and
practices could include, disaggregating success data by race/ethnicity to clarify the efficacy of
reform efforts; implementing race-focused professional development workshops to help
practitioners identify and address their thinking and beliefs about students in remediation; and
infusing culturally-relevant pedagogy into classrooms to help students connect with course
material in meaningful ways. Including these types of practices would start to address the needs
of the racial/ethnic groups that are most disenfranchised in the current remediation system and
would be instrumental in producing effective change. Erasing race from these reforms distracts
from the need to focus on the importance of these types of practices and reform efforts.
My second reason for taking issue with the absence of race, ethnicity, and racism in
reform efforts is more practical. Philanthropists and policy makers with an interest in
developmental education (e.g., Bill and Melinda Gates Foundation, Kresge Foundation,
California Community Colleges Chancellor's Office) have given millions of dollars to support
initiatives such as Guided Pathways and the Basic Skills Initiative. Considering the high rates at
which racially-minoritized students are placed into remediation and the financial benefits that
institutions gain from these private and public funders, the lack of attention to race-focused
reforms is disappointing. Institutions and organizations that garner funding to improve
developmental education should implement reform efforts designed for learners who enroll in
remediation at higher rates and those who are most disproportionately impacted in these
courses—students from minoritized racial/ethnic groups.
Student Success Reconceptualized
As discussed in Chapters One and Two of this dissertation, much of the literature on
mathematics and developmental education highlights Black students’ failure in these courses, not
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their success. In contrast, in this study, I present findings which are simple, yet important: Black
students in developmental math are successful. Juxtaposed with this study’s definition of
success, which is based on traditional markers of achievement (course advancement and passing
grades) these participants’ conceptualizations of academic success differ from the grade-focused
ideas that are typically highlighted in academia. For these participants, understanding material,
not simply earning high grades qualifies as success. By ranking comprehension over grades,
these students require that their instructors go beyond teaching learners how to get “good”
grades; they want faculty to teach to ensure students can understand course material. This style
of teaching requires that community college faculty know how to use effective pedagogical
practices and employ multiple instructional methods to help students learn course material. This
finding links with results from recent reports and studies on reforms in developmental education,
which show that when faculty use certain instructional practices (e.g., conceptual versus
procedural instruction, culturally-relevant pedagogical practices, and contextual instruction),
students have greater success comprehending material and achieving successful outcomes (e.g.,
Cox, 2015; Preston, 2016; Wang et al., 2017). In this sense, instructional practices that are
designed to improve students’ comprehension in remediation are garnering attention in the
literature. These scholars’ attention to instructional practices paired with these students’ interest
in developing a true understanding of math encourages researchers and practitioners to attend to
the types of teaching practices that help learners comprehend material, not just pass courses.
This type of learning for understanding—not just attaining grades—has the potential to help
students recognize the value of learning math and in some cases, encourage them to find their
own connections with the subject.
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Strength and Limitation of the New Mathematics Identity Conceptual Framework
One key benefit and one hindrance to using the mathematics identity conceptual
framework arose in this study. The benefit to using this framework is that it provided an
opportunity to study Black students’ progress and success in developmental math without a focus
on their academic outcomes. In other words, looking at these students’ beliefs about the
components of math identity (abilities, instrumental value, obstacles and supports, and
motivation and approach), their interactions with instructors and peers, and how these are related
to learners’ progression in mathematics offers researchers a new way to understand these
students’ success. When researchers primarily study students’ developmental math course
placement, grades, and ability to ‘get out’ of remediation, they miss the opportunity to
understand which factors and experiences can attribute to student success and how these could
make a difference for other learners in these courses.
The hindrance with using mathematics identity is that on its own, the framework does not
include a race-focused component and as such, does not directly address race. According to
Martin (2000; 2006; 2009), because Blacks have faced sociohistorical injustices, discrimination
in academic settings, and exclusion from math-learning environments, researchers should include
conversations about race in math identity-related discussions. As such, the mathematics identity
framework would benefit from including a critical lens. With this component, researchers can
learn new ways to conceptualize African-American students’ math-related experiences as distinct
from the math experiences of learners from other ethnic and racial groups. Martin (2000)
accomplishes this in his study by exploring the sociohistorical and community forces that
influence the lives of students in his study. However, on its own, the mathematics identity
framework does not accomplish this task.
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In this study, sense of belonging in mathematics (Boaler et al., 2000; Good et al., 2012),
used to understand learners’ “feelings of membership and acceptance in the math domain” (Good
et al., 2012, p. 1), is valuable when seeking to understand students’ beliefs about their own
connection with and value in math-related settings. Beyond using the conceptual framework to
understand differences between women’s and men’s belonging with math, this aspect of the
conceptual framework can also be used to learn about belonging in math as it relates to different
racial-ethnic groups of students. Good and her colleagues (2012) spoke about this idea more
broadly when they noted, “the issues addressed…easily apply to members of any group who face
messages of limited ability in an achievement domain” (p. 16). Therefore, the sense of
belonging in mathematics framework can be used to address “a disturbing crisis in the
educational welfare of Black and Latino Americans” (p. 16). As sense of belonging in
mathematics can be beneficial in studies with these student groups, it has the potential to capture
nuances that are present in these learners’ experiences in the math classroom; however, the
framework could benefit from including an explicit focus on race and ethnicity.
Keeping ideas about ways to develop mathematics identity and sense of belonging in
mathematics in mind, the framework used in this study could be enhanced by:
• Including explicit questions about race and ethnicity
• Asking participants to give examples where as a person from a specific racial or ethnic
group, they have felt as though they have (or do not have) a connection with mathematics
• Adding a racial or ethnicity-focused lens to questions about the seven areas of sense of
belonging in mathematics:
o perceptions of themselves as part of the group of math learners
o beliefs that they can be successful in math
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o feeling comfortable and happy in math
o beliefs that peers and instructors support their success
o actively participate in the group
o engage in practices to achieve math success
o intend to take higher-level math courses
Adding a race/ethnicity lens to the framework can help researchers learn about the connection
that students make with math, particularly those who are marginalized in academic settings.
Implications for Practice and Research
In this section, I offer suggestions for institutions that are interested in creating
environments that strengthen students’ mathematics identity development. Implications for
practice are categorized by classroom-level and administrative-level approaches and implications
for research focus on student-level studies. The implications for practice and research are
designed to further what we know about Black students in remediation, their mathematics
identities, and their experiences of belonging in math-related settings.
Implications for Practice
Students who bring speed-focused math-related beliefs cultivated during their K-12 years
to their college math courses link strength in math with the ability to solve problems quickly and
with minimal errors. This belief can become problematic when learners need to take more time
to understand new or complex material. To help dispel this myth, faculty could teach students to
value process over speed when solving math problems. By helping students develop a new
perspective about what qualifies as “strength” in math, students in remediation can create new
and positive perspectives about their abilities; these positive perspectives foster positive
mathematics identity development.
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Students who have trouble connecting math learning with their lives can lose motivation
to study mathematics. To help students make these connections, faculty may consider linking
math concepts with relevant situations in adult students’ lives (e.g. calculating interest to
determine where they should save their money and figuring out percentages to calculate
discounted prices during sales). Making these links can help students find purpose for learning
and doing mathematics and recognize the subject’s instrumental value in their lives. This
realization can help them persist, particularly when they have math-related difficulties.
Next, students who study in groups have opportunities to demonstrate their skill set and
receive peer support. Faculty might consider finding meaningful ways to incentivize students to
participate in group support sessions. This effort can help learners connect with other peers as
they demonstrate their knowledge in ways that can boost their views of themselves as math doers
and learners.
Black students who have racialized experience in math-focused settings are at a
disadvantage as compared to peers who do not contend with these issues. Administrators can
help faculty and counselors learn to identify racial microaggressions, which are “brief,
commonplace, and daily verbal, behavioral, and environmental slights and indignities directed
toward Black Americans, often automatically and unintentionally” (Sue, Capodilupo, & Holder,
2008, p. 329). Instructors could benefit from understanding how they might be perpetuating
these microaggressions, learning how to recognize these aggressions, and figuring out ways to
support students who may have experienced microaggressions in the math classroom and in
other on-campus environments.
Next, to foster positive mathematics identity development among students, faculty
members can examine remedial math course objectives to assess whether course goals focus on
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learners’ positive mathematics identity development. In the event that positive math identity
development is not included in the course goals, faculty can determine effective ways to build
these concepts into the course materials.
The need for an increase in Black faculty members highlights the importance of working
with campus hiring teams. These groups might consider conducting national searches for Black
math faculty to fill teaching positions at community colleges. Because hiring committees often
argue that there is a low number of eligible Black candidates for instructor positions, these hiring
committees might consider focusing search efforts on recruiting graduates from Historically-
Black Colleges and Universities (HBCUs) which are known nationally for producing African-
American mathematicians and engineers at the highest rates of all US colleges and universities.
Just as efforts are in place to create partnerships between community colleges and HBCUs to
facilitate and improve student transfer, similar measures can be enacted to boost the numbers of
Black math faculty in community colleges.
Finally, the need for strong and positive classroom interactions between students and
faculty members highlights the importance of training faculty to interact with students positively
and effectively. Administrators can use this study’s participants’ suggestions about helpful
relational and pedagogical practices (in Chapter Five) to create faculty observation protocols.
With this information, these protocols would go beyond highlighting what administrators want
students to learn in the classroom and focus on helpful and valuable strategies that contribute to
learners’ success (as suggested by students who have been successful in these courses).
Implications for Research
The implications for research involve further exploring the mathematics identity
conceptual framework used to analyze data in this study, the ways that institutional barriers
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shape learners’ progress, sense of belonging in developmental mathematics, and racial
discrimination in remediation.
First, these participants’ beliefs about who they are as math doers and learners call for
further study about Black students’ mathematics identity development. However, it would be
useful to understand how these students’ beliefs about themselves as math learners and doers
have developed over time. Additionally, it would be valuable to understand the roles that
experiences in their early years (e.g., elementary school, grammar school, high school) play in
their current mathematics identity.
Next, given Wesley’s position as the only participant in the study who transferred to a
four-year university at the time of data collection, a study about the mathematics identity of other
Black students who have succeeded in remedial math and transferred to four-year colleges could
inform our understanding of these students’ experiences. Findings from that research could offer
an understanding about how to improve success rates for other students in community college
remedial mathematics.
Third, recall that some of Maurice’s academic challenges resulted from institutional
policies and inefficiencies in the financial aid office. A study focusing on the ways that
institutional policies shape the outcomes of Black students who are succeeding in remedial
mathematics would provide a deeper understanding about the ways that such policies (e.g.,
financial aid, enrollment management, grading systems) and practices contribute to students’
academic progress.
Next, Ophelia’s position as the only female participant with a written narrative in this
study provides limited opportunity to understand the experiences of Black women who succeed
in community college developmental mathematics classes. To gain a greater understanding
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about this population, I suggest conducting a study on sense of belonging in mathematics with
this student population. Findings from this research can help practitioners, researchers, and
policymakers learn the factors that affect these students’ belonging in these classes, what
impedes and propels their progress, and ultimately, how to support their success.
Finally, given the prevalence of participants’ racialized math experiences in this study, it
would be valuable to further explore Black students’ experiences with racism in developmental
math-related contexts, how these racial experiences shape their perceptions of their positions in
these math settings, and the influence on their mathematics identity.

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EPILOGUE
As suggested by narrative methodologists Connelly and Clandinin (1990), and as part of
my own personal interest in these participants’ development, I have reached out to participants at
least twice following the official data collection process: (1) to request their feedback on the
written narratives and (2) to ask how they were progressing with their studies and life, in general.
I have met with some participants in person and followed up with others via text, email, or
phone. With a follow-up question such as, “How are classes progressing?” or an inquiry about
something more specific that they may have mentioned as part of an ongoing conversation, I
often sought to learn about their math and coursework progress as well as relevant life details
that are important to them. For instance, in my final interview conversation with Abdul, he
mentioned that he was going to take a math class at another local community college. So, in one
of my follow-up messages, I asked about his experience in the course. The conversations with
other participants were similar, some offered unsolicited reflections about their experience as
part of the research study and others simply answered the questions that I asked. Now, in this
final part of the dissertation—the epilogue—I present segments of email communications with
each of the participants for whom I wrote narratives to highlight aspects of their lives following
the study.
Ophelia
As I noted in Chapter Four, Ophelia initially requested that I change two aspects of the
narrative and asked a question: “[D]o I really speak that way? In reference to the amount of
slang used…and lack of complete sentences. I'm not sure if it were emphasized for the purpose
of the writing…” I sent her a transcript from one of our conversations to confirm that I did not
alter her speech pattern in the narrative. In response to my second inquiry (a general question
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about how her coursework was progressing), she responded by sharing about recent and
upcoming events. “I was just thinking about you at my Black Graduation Celebration. When I
think of my accomplishments and how far I've come I think of you. She went on to share, “My
graduation from [LA North] is soon and I'm super excited for that…This summer I will be taking
courses and officially deciding on a major and schools to apply to for my transfer.” After
reading her note, I wondered about the comment, “When I think of my accomplishments and
how far I've come I think of you,” and so I asked her about it. She responded saying,
What made me say that was remembering the conversation we had about my
accomplishments. When you told me to not sell myself short because statistically at my
school I'm doing very well. This was something I hadn't even considered or thought of.
One of the speakers at the graduation celebration said, "no matter how big or how small,
you all should be proud of your accomplishments." This made me think of math and my
past struggles and how I overcame them. Instantly there was a sense of pride within me
and I thought of you and how having these conversations with you made me realize that
I’m doing pretty darn good and I should allow myself to be proud of that! And this goes
beyond math. I guess, somehow I had this concept about humility and proudness. To be
proud was to lessen my humility somehow. I know it may sound silly, and don't ask me
where I even came up with that concept, I'm not even sure myself. But I've realized I can
be proud of myself and my accomplishments and still remain a humble person, the key is
not to be boastful in my pride. Being proud doesn't have to have a negative association all
of the time, I am proud of you and your accomplishments and that doesn't make me any
less of who I am to have pride in others or myself. So, I thank you for that.
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I thanked her for her response, let her know that I would attend the graduation (another
participant had invited me to the celebration), and offered to support her with the transfer
process. She seemed grateful and responded, “I am sure I will reach out to you when it is time to
start those applications and obtain some advice from you. Still not sure about where to apply but,
I'm not going to limit myself; why not apply everywhere I can?” She went on to share some of
her future plans, “I am planning on taking courses this fall…Once I meet with a counselor and
the transfer office this summer I will decide which courses to take. I'm trying to make my
transfer as seamless as possible…” In her final note, Ophelia wrote,
Maxine, I am happy that you continue to stay in touch. I really am. I've really enjoyed our
conversations about math and otherwise. It's nice to have someone I can look up to, who
has accomplished so much and beat the odds herself. Just know that you set an example
for me to keep going forward. Who knows maybe one day I'll have a dissertation of my
own.
Maurice
After Maurice read the narrative he sent me a short note to share his thoughts. In
response to my question about whether or not he thought the narrative was an accurate depiction
of his story, he said, “I love how I feel after I read this story…It made me smile and tear up at the
same time because I realize how much potential I have and how proud I should be of what I've
overcome.” He finished the note with one statement, “Thank you for inspiring me not to give up
on myself.”
In my next communication with Maurice, I asked how he was doing and in particular,
how his coursework was progressing. In addition to telling me about his math coursework, he
shared about his new academic interests and plans, “This Spring semester, I’ve taken Geometry
322

so that I can finish math completely [next semester]… with Trigonometry. I’ve also taken
Philosophy 1 and have fallen in love with the concept. My favorite philosophers are Epicurus
and Epictetus, lol.” He went on to share about some of the personal interests that he developed
noting, “I’ve also taken Voice Fundamentals…[S]ince our meetings last semester, I’ve been
writing and singing.” He ended the discussion with an update on his plans for veterinary study.
“I plan on inquiring about a Veterinarian technology program that [a nearby] college is offering
to help give me an idea of what I’ll be getting into on the field when I become a Veterinarian in
the future.” He also noted, “School is treating me well and I’ve noticed that I’m good to transfer
based upon the…transfer checklist, but I’ve decided to stay on campus another two semesters to
give me time to get this transfer process done right.”
Abdul
When I shared the narrative with Abdul, he asked me to make minor adjustments and
then like Ophelia and Maurice, shared his reflection about the piece, “I think the piece is
great…Just reading the piece gave me extra inspiration. It’s kind of surreal for me just
knowing where Allah has brought me from.” Unlike the other participants, Abdul and I
communicated somewhat regularly after the study. At his request, I sent him information about
math-based scholarships, he sent me a news article about a math after school program for middle
schoolers, and then he contacted me to share his Pre-Calculus grade (he earned a B in the
course). He also asked if I could assist him with his next endeavor, the transfer process.
So I just had a meeting with my transfer counselor Mr. [John Espinosa] in the College
transfer center. After he spoke with me an accessed my grades he said it's not only make
senses that I go to USC, but its very much possible to get a merit scholarship that will pay
for all my expenses due to my gpa. So he said he gonna help me and we should apply
323

2018. He advised me to go to the school and talk to an admissions counselor or the like to
see what I will need and make some contacts to help get accepted. [This can help with]
setting me up for my ultimate goal getting a PHd degree in Applied Mathematics
That's everything in a nutshell, hopefully you can grasp what im trying to accomplish and
give me some advice on this I would really appreciate your input.
Thanks again have a good day.
In response to his message, I connected Abdul with a colleague in my program who had
transferred from LA North to our PhD program. They have since met and outlined his next steps
for successful transfer. Since that time, Abdul and I have had several other conversations, some
in person, but mostly via email. In one of our communications, he stated something that caught
my attention, “Again Thanks again for all your help. Im really getting to see as I go higher in my
studies the less help is available. You are a major asset. Im really blessed.” Interested in what he
meant when he said, “as I go higher in my studies the less help is available,” I asked him about
this in my response to his message. He responded by describing an experience that was not
much different from the experiences he had previously in math courses.
What I have been noticing in the stem field most of the class demographics are Asians,
Mexicans, white people and very few brothers and sisters
19
. What seems to happen, is
every race generally seems to huddle together and assist each other. The professor gives
his lecture and expects everyone to understand and deliver. So these different
communities gather to help each other to a degree. So where does that leaves the only
brother in the class? That the new dynamic of what I have been encountering. It is a little

19
The term “brothers and sisters” refers to Black men and women.
324

troubling, but now that I can identify my new adversary, I Can develop a strategy of
success.
Which lead to my making that statement, “Again Thanks again for all your help. Im
really getting to see as I go higher in my studies the less help is available. You are a
major asset. Im really blessed.”
Im really getting a view of what its going to take to be successful. I think genuine help
and support is important. Also being comfortable with that fact that the majority of the
time I am going to be out numbered and have to pro form at the same level as everyone
else and even greater. So I am getting more relaxed with that idea, and making the
proper adjustments and fortifications. Its an interesting journey. I love the challenge….
In one of my last communications with Abdul, he let me know that he returned to his job as a
tutor at the Tutoring Center and planned to apply for transfer for Fall 2018.
Kendon
After reading the narrative story, Brandon responded simply, “I enjoyed reading about
my experiences in math. I’m glad I have something tangible to reflect on.” He went on to say,
“Thank you so much, it was a pleasure being a part of your study. I'm always willing to help, so
definitely contact me anytime the opportunity arises.” When I asked about his current progress
in school and plans for the summer, he noted, “I'll be having my physics final on Thursday, calc
3 Friday, english Sat. Then next Monday I'll have my last final for c++.” About the summer
plans, he added, “When summer session start I may take two courses or just one and do work
study. I haven't decided yet however I am already registered to the courses to secure my spot.”
Wesley
325

After reading the narrative, Wesley responded with appreciation and comedy, “You are to
kind. I like the Wesley a lot. We need more like him. I have no changes.” During my writing
of the dissertation, although Wesley responded to my clarification questions, after
communicating with me about the narrative, I did not hear from Wesley again.

326

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APPENDICES
APPENDIX A: Table 3: Alternative Math Identity Definitions and Relevant Constructs

Table 3: Alternative Math Identity Definitions and Relevant Constructs
Scholars Who Use Martin’s (2000) Framework
Stinson (2007) Berry, Thunder, & McClain
(2011)
Zavala (2012) Borum, Hilton, & Walker, 2016 Larnell (2016)
Scholars Who E xpanded Martin’s (2000) Framework
Author(s) Other Versions of
Mathematics Identity
Definition
Boaler & Greeno (2000) Participation in the social
practices of the math classroom
“Discourse practices” (p. 172) in which students use math concepts and methods to make sense
of and solve math problems. Students can engage in these practices in groups or alone.
Boaler, William, &
Zevenbergen (2000)
Math as a sense of belonging Identity in the math classroom is comprised of three components: (a) a sense of belonging with
a group; (b) a sense of achievement within the group’s norms; and (c) behaviors associated with
belonging to the group
Nasir & Saxe (2003) Math Identity as linked with
cultural practices
Identity developed in areas such as math is a result of cultural practices —activities linked with
community norms and values.” Through these cultural practices, identities are formed, built,
and negotiated” (p. 14)
Anderson (2007) Faces of Math Identity
Development
Practices that students use when participating in math classrooms. The four faces are:
engagement (students imagine themselves as successful in math); imagination (students connect
math with life experiences beyond the classroom); alignment (students engage in math practices
that help fulfill the ways they imagine their future engagement with math); and nature (the view
that students could perceive math learning and understanding are linked with genetics or
biology—Anderson encourages readers to support students’ identity in the math classroom by
building the first three faces of identity)
Grootenboer &
Zevenbergen (2007)
Three Dimensions of the
Learning Classroom
Focusing on interactions in the math classroom, authors identify three key aspects of the
classroom: (a) How math is taught (Discipline of math); (b) Instructors, peers, and the learners
341

and how they interact with each other (classroom community); and (c) the learner who enters
the classroom with prior experiences that shape their math identity (student)
Solomon (2007) Math identity as beliefs about
math and beliefs about one’s self
Mathematics identity includes the following: (a) beliefs about oneself as a math learner; (b)
perceptions of the ways others perceive him or her as a mathematics learner; (c) beliefs about
math, math engagement, and perception of one’s self as a participant in math
Cobb, Gresfaldi, &
Hodge (2009)
Analytic approach for addressing
math identity
This approach explores the “microcultures” (p. 41) that exist in math classrooms and how they
influence development of students' personal identities in class.
The definition involves three components: (a) how students understand math activity in the
classroom; (b) how they define what it means to know and do math; and (c) whether and why
they identify with, comply with, or resist engaging in classroom activities.
Cass, Hazari, Cribbs,
Sadler, & Sonnert (2011)
Student beliefs Students’ “beliefs of themselves with respect to mathematics” (p. F2-H2)
Bishop (2012) Math identity as behaviors and
beliefs
One’s ideas about who (s)he is with regards to math and math-focused activities. These include
how an individual speaks and behaves as well as the ways others perceive an individual with
regards to math.
Benken, Ramirez, Li, &
Wetendorf (2015)
N/A Authors use Bishop (2012) framework
Grant, Crompton, &
Ford (2015)
Identity as Participation Authors define math identity as Participation (a combination of Agency and Accountability).
Agency, taken from Bandura (2005), is defined as intentionally influencing “one’s functioning
and life circumstance…[by being] self-organizing, proactive, self-regulating, and self-
reflective” (p. 9). Accountability answers the question, “to whom or what are students
accountable” and can be used to explore students’ sense of competency in class
Kennedy & Smolinski
(2016)
Math identity in ‘math circles’
(community where students
engage in problem solving and
math-focused discussions to solve
problems and create new
knowledge)
Mathematical identity is associated with students’: (a) positive intrinsic and extrinsic
engagement in mathematics; (b) expectation they will be successful and enjoy math tasks; and
(c) an increase in voluntary engagement with math
Scholars Who Use Other Constructs in Math Identity-Related Context
Author(s) Relevant Framework Definition
342

Lesko & Corpus (2006) Perceptions of one’s abilities and
the importance of their math
ability (Spencer, Steele & Quinn,
1999)
Math identity is based on students’ perception of their math ability and the importance of being
good at math
McGee & Martin
(2011a)
Mathematics identity coupled
with Stereotype Management
(Harpalani, 2007).
Students’ ability to use to manage racial stereotypes, offset the influence of Stereotype Threat
(Steele, 1995), and use the stereotypes to motivate them to achieve academic success.
343

APPENDIX B: Recruitment Email Messages
Hello Professor Rivera,
Thank you so much for responding--I also reached out to Professor Bhattacharya last week. The
4 students that you suggest would be perfect. Can you refer me to faculty who teach
precalculus?
Here is the note that I am sending to students who are interested in participating. Please feel free
to share it with students who are interested in participating:
----------
Hello,
My name is Maxine Roberts and I am a Black graduate student who needs your support. I am
doing a study to learn about what helps Black students--like you--to achieve success in math at
LATTC. To say thank you for your participation, I will give you a Visa gift card or gift
certificate (your choice) to the campus bookstore at the end of the study.
I am passionate about this topic because I have heard too many times that Black students are not
successful in math and in school overall. Many of my friends in grammar and high school were
successful in math, so I know the stories that are out there don't tell the full story about our
abilities. I am committed to learning about and telling your story of math achievement.
By participating in this research, you will help me complete my study, but more importantly, you
will help break the stereotype about our lack of success in math and help people learn what they
can do to help other students be successful.
If you choose to participate in this study, we will meet 3 times for 45-60- minute interviews. I
will ask questions about: (1) your experiences in math courses, (2) the factors you believe helped
you achieve success in math, (3) how you learn math, (4) your math instructors’ teaching
practices, and (5) your understanding of how these interactions contribute to your academic
success. These interviews will take place at LATTC.
Also, I will ask you for an unofficial transcript to confirm the math classes that you have taken
and to write short responses to two to three short passages that you will receive during our first
meeting. These will be useful as we talk about what has contributed to your math success.
To participate, please email me at mtrobert@usc.edu. I would really appreciate your time and
the opportunity to learn about your success. I look forward to hearing from you.
Sincerely,
Maxine Roberts

344

Appendix B (continued)

Second message
Hello:

My name is Maxine Roberts and I am a Black graduate student who needs your support. I am
doing a study to learn about what helps Black students (like you) to achieve success in
mathematics. You are someone who has proven to be successful in math and I would like to
learn from you how you made your success possible. Learning about your experience is
important because it can help other Black students learn how to be successful in math. By
participating in this research, you will help me complete my study, but more importantly, you
will help break the stereotype about our lack of success in math and help people learn what they
can do to help other students be successful. I know that your time is valuable and in order to
thank you for your participation, I will give you a Visa gift card or gift certificate (your choice)
to the campus bookstore at the end of the study.

I am passionate about this topic because I have heard too many times that Black students are not
successful in math and in school overall. Many of my friends in grammar, high school, and
college were successful in math, so I know the stories that are out there don't tell the full story
about our abilities. I am committed to learning about and telling your story of math
achievement.

If you choose to participate in this study, we will meet 2 to 3 times for 45-60- minute
interviews. I will ask questions about: (1) your experiences in math courses, (2) the factors you
believe helped you achieve success in math, (3) how you learn math, (4) your math instructors’
teaching practices, and (5) your understanding of how these interactions contribute to your
academic success. These interviews will take place at LATTC.

Also, I will ask you for an unofficial transcript to confirm the math classes that you have taken
and to write short responses to two to three short passages that you will receive during our first
meeting. These will be useful as we talk about what has contributed to your math success.

Up to now I have interviewed 8 students and based on their feedback they enjoy being part of the
project and have said that talking with me helps them reflect on their experiences

To participate, please email me at [email address] or send me a text/WhatsApp message
at [phone number]. I would really appreciate your time and the opportunity to learn about your
success.
Thank you,
Maxine Roberts

345

APPENDIX C: Literature Matrix
This appendix provides a literature matrix to offer readers a greater understanding of how the
research questions link with the protocol questions and literature reviewed for this study. As a
reminder, the research questions are as follows:
• How do Black students who are successful in developmental math courses describe their
mathematics identities?
• How do these learners describe how they achieved success?
• How do these learners perceive the role of instructors and classroom practices in their
success?
Research Question Connection with Interview
Guide
Major Section in
Literature Review
How do Black students
who are successful in
developmental math
courses describe their
mathematics identities?
2a, 2c, 2d, 2e, 2f, 2g, 2h, 3b, 3c Mathematics Identity and
Student Success:
Characteristics of students
who positively identify with
math, Characteristics of
students who negatively
identify with mathematics,
Students of Color in
Community Colleges and
Remedial Courses: Black
Students in Community
College, Black males in
community college,
Students’ Characteristics and
Concerns: Students’
Backgrounds, Beliefs, and
Attitudes,
How do these learners
describe how they achieved
success?
2b, 2c, 3a, 3b, 4a, 4c, 4d, 5d Recognizing the Importance
of Culture in Pedagogy:
Culturally-Relevant
346

Pedagogy, Culturally-
Sustaining Pedagogy:
Culturally-Relevant
Pedagogy 2.0.,
How do these learners
perceive the role of
instructors and classroom
practices in their success?
2h, 2i, 4e, 5a, 5ii, 5b, 5c, 5d, 5e,
6a, 6b, 6c
Students’ Backgrounds,
Beliefs, and Attitudes:
Learners’ beliefs about
classroom instruction, The
need for effective
instructional practices:
Mathematics Pedagogy,
Instructor’s Training
The Value of Interacting
with Black Faculty in the
Classroom

347

APPENDIX D: Interview Protocol
Interview Protocol
Thank you for your time. My name is Maxine Roberts and I am a Research Assistant with the
Center for Urban Education at the University of Southern California. The purpose of this
interview is to understand your views of math instruction at LANCC and whether or not it helps
you to be successful at LANCC. I’ll cover three areas in this interview: (a) your interactions
with faculty, (b) your relationships peers, and (c) your math instructor’s teaching practices
actions here at LA North to learn how each helps you to learn math. I will also be asking
questions that are related to your classroom experience in your Math course.
I will make every effort to keep your responses confidential. Your responses could be used in a
research publication or conference presentation.
Here is an informed consent form for your review. Please take you time to look over the form. I
am happy to answer any questions you might have regarding the information contained in this
informed consent.
Here is my card [hand over business card] in case questions arise after the interview is done.
[Pause to let participant read and sign consent form.]
Before we begin, I would like to ask for your permission to tape record this interview. As a
reminder, I will keep any information that you share with me confidential and your participation
is voluntary. You may stop the interview at any time if you feel uncomfortable.
The interview will last no more than one hour. During this time, I have several questions that I
would like to cover. At this point, do you have any questions?
Bank of Questions
1. General Questions
a) What’s your name?
b) How long have you been a student at LA North City College?
c) Tell me, which math class are you currently enrolled in??
d) What is your major?
e) Why did you say ‘yes’ to the request to participate in this study?

2. Math Identity and Success
a) Tell me about your earliest math memory. Probe for home and school memories.
b) Tell me about a time that you felt successful in a math class.
c) Tell me about a time that you felt discouraged or frustrated in a math class.
d) When you think about yourself as a math student in elementary school and junior
high school and in high school, what are words you would use to describe yourself?
348

e) How would you say that others, like your peers, or your teachers, or your family
members saw you as a math student?
f) When you think about your future career, which subjects are most important for you
to learn? Probe to explore importance of mathematics in future career.
g) How do you define low, medium, high math ability? Which best describes you math
ability?
h) If I were to watch you in class, what would I see you doing during lessons?
i) Can you share about a time you thought your race might have played a role in math
class for you.

3. Sense of Belonging in Mathematics
a) Can you share about a time when you felt like you ‘fit in’ or did not ‘fit in’ your math
class?
a. Would you link this feeling with something that your instructor did, your
peers did, or neither? Please explain.
b) Have you heard of the terms being an ‘insider’ and being and ‘outsider’?
a. How would you describe these terms?
b. Would you consider yourself an ‘insider’ or ‘outsider’ in math settings?
Why?
c) Can you share about a time when you have noticed students (including yourself)
being respected/disrespected in a math classroom?
d) If I observed you in math class, what would I see you doing?
e) How would you describe your level of comfort in math class?

4. Solving Math Problems
a) When you have a math problem, that you don’t know how to solve right away, what
do you do? Probe for steps to solving problem. Do they involve collaborating or
working alone?
b) Can you tell me about times when you have difficulties with math?
c) What keeps you going when math becomes difficult?

5. Culturally-Relevant Experiences
a) Tell me about at time when you felt like you could relate to the material in the course.
b) If this has not occurred then c. If this has occurred, but not in math, then d
c) How did you stay motivated in the course?
d) Have you ever had this experience in math class? If yes, what difference did this
make for you and your learning?
e) Do you ever find that teachers teach math in ways that help you see how math is part of your
lifestyle?
6. Instructors & Class Experiences
a) Tell me about your most memorable instructor. What made her/him memorable?
i. If not a math instructor, then ii
ii. Can you tell me about a math instructor who acted the same way?
349

b) Can you tell me about an interaction that you had with a math teacher, either one that
was helpful or not helpful for you?
c) Describe a ‘typical’ math class at LATTC
d) Now describe your best math class
e) If you could make suggestions to math faculty about how to improve the ways they
work with students and help students be helpful, what would you suggest?

7. Black Instructors
a) Have you ever had a Black math instructor (distinguish between K-12 and college
years)
b) What difference (if any) did this make for you?
c) Please share about any role models of color who were successful at math.
8. Is there anything you’d like to add that I haven’t asked?

That concludes the interview. Thank you again for your time. Would it be OK to follow up with
you if I have any additional questions?

350

APPENDIX E: Vignettes
Instructions:
Each of the short pieces below describes four students’ math memories or classroom experiences
in a fictional math class in a community college. Please read each piece, select the student
whose story most closely connects with your math experiences, and answer the following
questions on the notepad provided:
(1) What memories does it bring up for you?
(2) In what ways does this student’s story mirror your own experiences in math? In what
ways does the story not match your experience?
Student #1: Tanya
Tanya sits in the second row of her math class and is retaking Algebra 1 during her third
semester in community college. Although she’s having some challenges with the material, she’s
is ready to start the second week of the semester and hopeful that this semester will be different
from her last one. Mr. Davidson, her math teacher, sits at his desk waiting for the clock to tell
him when to start class, then stands up and begins teaching. Funny enough, whenever Mr.
Davidson, teaches with his back turned to the class, speaks in a flat tone, and scribbles on the
board, he reminds her of her high school Algebra teacher, Mrs. Schultz. Instantly, Tanya
imagines herself in high school again where she worked hard to understand the math material
because her teacher didn’t always do a great job of explaining the topics.
After explaining binomials, Mr. Davidson writes a math problem on the board and asks students
to solve it in their notebooks. Looking at the example Mr. Davidson wrote on the board just a
few minutes earlier, Tanya attempts to solve the problem and isn’t sure if she has the right
answer. Because of her lack of confidence in her math work and memories of Mrs. Schultz’s
class, Tanya was uncomfortable to share her solution with the class when Mr. Davidson asked
for a volunteer to work out the problem on the board, so she didn’t raise her hand. After her
classmate, Nikki, solved the problem on the board, Tanya realized that her answer was correct.
Student #2: Daniel
On the first day of college, Daniel finds his math class and is glad that he arrived early. On the
hour, his math teacher, Ms. Kuchera, introduces herself, and begins passing out the course
syllabus. As she goes page by page and tells the class what they will cover during the semester,
Daniel thinks, “I learned this stuff in high school already! How did I end up here when I’ve
always been good in math?”
A few weeks later, Daniel is bored in class because the work is too easy, but he isn’t able to
transfer to a higher math course. Some friends told him that they were re-taking the class for the
second time and he vows that he will not retake the course. Daniel puts some extra hours into
studying, refreshes his memory on the material they will cover next during the semester, and
351

reminds himself that although it might seem like a waste of time to redo work he’d completed in
high school, this class brings him one step closer to his degree.
Student #3: Kim
Given the choice of what to study, Kim always chose math. She knew math formulas like the
back of her hand, helped her friends understand math concepts when they had questions about
the material, and thought of herself as someone who could ‘get’ math quickly. Unlike English,
history, or even gym class, Kim thought math was fun. So, when she had to choose a career, it
wasn’t hard to imagine that she would choose something that was math-related. Much of the
ways she thought about math were influenced by her early classroom experiences.
Kim’s positive thoughts about math were influenced by the success she had in fifth grade. See,
her fifth grade teacher, Mr. Jackson, wasn’t like other math teachers who told students that math
was something they were “either good at or not.” Mr. Jackson talked about math differently,
telling students that they could learn anything if they worked “hard enough” and he would work
with them to be sure they understood the material. He also helped students to be successful in
math by creating a classroom environment where their mistakes were welcomed and they
received support without being ridiculed. As a result, Kim believed that she could succeed at
math and proved herself right in each of her math classes over the years.
Student #4: Jerome
Math wasn’t Jerome’s best subject, but it wasn’t his worst subject either. By the time he’d
arrived in community college, he figured out how to study for math. So, even if he had a hard
time with some ideas and topics, with some ‘hard work’ and a ‘bit of luck’ (as his mom called
it), he could be successful.
When he entered Mr. Smith’s math class, he had a collection of activities that he did to make
sure he understood a topic:
• take notes on the topic in class
• study class notes on the topic(s)
• do the homework
• go to the professor’s office hours
So, while Jerome didn’t always get As, he did all that he knew to do to be successful.
Students #5: Reggie
This year was Reggie’s second time taking Elementary Algebra. After his first bad experience
with his math instructor in the Elementary Algebra class during the previous semester, he
352

decided to take notes, do his homework, and study with the hope of being successful the second
time around.
Although he eventually passed the class, it was difficult for Reggie to develop a level of
confidence to ask for help when he had math difficulties. This was because the first time he took
Elementary Algebra, his instructor made insulting and seemingly discriminatory remarks when
students did not know the answers. Although the comments were not directed at Reggie, he felt
unwelcomed and unwanted in class and felt like an outsider. During that semester, Reggie
struggled in math, by the end of the semester he was glad to be ‘done’ with the course.
353

APPENDIX F: Math Education History Map
Elementary & Middle
School
High School College
Math Ability
Motivating Factors
Challenges
Opportunities
Memorable Instructors
or Peers (positive or
negative)

354

APPENDIX G: Codebook (Sample)
Codebook (developed from the New Mathematics Identity framework and research
questions)
Code Definition
Research Question #1: How do Black students who are successful in developmental mathematics
courses describe their mathematics identities?
Ability: capable
Concepts/Rules—refer
to the ways they like
to learn math:
Learning math using a
step-by-step process or
conceptual
understanding of
material
Concepts: student views herself/himself as a math learner who comprehends
mathematical concepts very well and so, can solve math problems easily
Rules: student views herself/himself as a math learner who memorizes
mathematical rules very well and so, can solve math problems easily

Ability: capable—
overall ability
Overall ability: student views herself/himself as a math learner who
comprehends mathematics very well and so, can solve math problems easily
Ability: average
Concepts/Rules—refer
to the ways they like
to learn math:
Learning math using a
step-by-step process or
conceptual
understanding of
material
Concepts: student views herself/himself as a math learner who may have
some difficulty comprehending mathematical concepts and solving math
problems
Rules: student views herself/himself as a math learner who may have some
difficulty memorizing mathematical rules solving math problems

Ability: average—
overall ability
Overall ability: student views herself/himself as a math learner who may have
some difficulty comprehending mathematics and so, has difficulty solving
math problems
Ability: poor
Concepts/Rules—refer
to the ways they like
to learn math:
Learning math using a
step-by-step process or
conceptual
Concepts: student views herself/himself as a math learner who struggles to
comprehend mathematical concepts and solve mathematical problems
Rules: student views herself/himself as a math learner who struggles to
memorize mathematical rules and solve math problems

355

understanding of
material
Ability: poor—overall
ability
Overall ability: student views herself/himself as a math learner who struggles
to comprehend mathematics and so, has difficulty solving math problems
Ability: struggle memories of ongoing struggle in mathematics courses
Ability: developing
ability
does not view self as strongest student, but acknowledges her/his developing
math ability
Ability: consistently
strong
indicates student always achieved success in math
Ability: judgment,
self-image/confidence
(positive)
student has positive impression of math abilities
Ability: helping others student uses her/his mathematics ability to help others
Ability: judgment,
self-image/confidence
(negative)
student has negative impression of math abilities
Instrumental value:
connection with career
identifies a direct connection between math and career
Instrumental value:
disconnected with
career
does not identify a direct connection between math and career
Instrumental value:
connection with life,
but not career
identifies a connection between math and life, but not with future career
Instrumental value:
connection with career
and life
identifies a connection between math, career, and life
Instrumental value:
hopeful about future
connection
does not identify a direct connection between math, life, and career, but
hopeful
Obstacles: emotions negative feelings about math becomes obstacle
356

Obstacles: difficulty
understanding subject
student has challenges understanding material
Obstacles: difficulty
understanding faculty
student does not comprehend math faculty’s teaching methods
Obstacles: faculty
accents
student does not comprehend math faculty’s accent
Obstacles: lack of
access (math)
student recognizes that poor educational access influenced her/his ability to
be successful in math
Obstacles: tutoring lack of effective tutoring has affected student’s success in math
Obstacles: personal
challenges
challenges in student’s life affected her/his performance in class, including
math
Obstacles: instructor-
related
student has difficult relationship with math instructor, which they believe
affects her/his understanding or grades in math.
Obstacle: Concern
about representing
race
Concern about representing race becomes obstacle for success
Supports: access to
tutoring
student believes (s)he has ready access to tutoring
Supports: materials student has access to math-related materials to learn the math
Supports: role model student has identified a role model as supportive; individual may have
provided verbal, emotional, or math-related support
Supports: instructors student has identified an instructor as supportive; individual may have
provided verbal, emotional, or math-related support
Supports: peers student has identified peers as supportive; individuals may have provided
verbal, emotional, or math-related support OR
Offers support to peers
Supports: family student has identified family members as supportive; family may have
provided verbal, emotional, or math-related support
357

student has identified family members as unsupportive; family has not
provided verbal, emotional, or math-related support
Supports: None student identified no supports who were instrumental in math success
Incentive: desire for
‘better’ life
student believes being successful in math will help her/him to earn a degree,
get a higher-paying job, and then create a ‘better’ life
Incentive: role model student identified a role model who has either encouraged success or helped
her/him understand math-related concepts
Incentive: earning
degree
student is focused on earning a degree, so (s)he views success in class—in
this case, math—as important
Incentive: time student is concerned about the amount of time (s)he will stay in school; lack
of success in math results in spending more time in college
Incentive: good grades earning ‘good grades’ is important to the individual
Incentive: bragging
rights
student earned bragging rights by being successful
Incentive: pride student believes her/his success in math would make others proud
Incentive: race
representative
needs to make sure blacks are represented well
Approach: using
textbook
student uses a math textbook first when (s)he has difficulty with mathematics
Approach: I can solve
this
student is encouraged by positive beliefs about her/his ability to solve
mathematics problems
Approach: I can’t
solve this
student is discouraged by negative beliefs about her/his ability to solve
mathematics problems
Approach: conceptual
knowledge of math
student uses conceptual knowledge of mathematics to solve problems
Approach: knowledge
of math rules
student uses knowledge of mathematics rules to solve problems
Approach: online
support
student uses online sources, such as YouTube, Kahn Academy, etc. for
academic support when (s)he has difficulty with mathematics
358

Approach: faculty
support
student seeks support from math faculty when (s)he has difficulty with
mathematics
Approach: work with
peers
student seeks assistance from peers to solve mathematics problems
Approach: work on
my own
student works on her/his own to solve mathematics problems and does not
seek help when they have difficulty with mathematics
Sense of Belonging
with Mathematics:
positive classroom
experience
student is comfortable because of experiences in the mathematics classroom
Sense of Belonging in
Mathematics: negative
classroom experience
student is uncomfortable because of experiences in the mathematics
classroom
Sense of Belonging in
Mathematics: positive
beliefs about math
Student has positive beliefs about mathematics (subject)
Sense of Belonging in
Mathematics: negative
beliefs about math
Student has negative beliefs about mathematics (subject)
Sense of Belonging in
Mathematics: positive
connection with peers
student has created collaborative experience with peers and feel comfortable
in the mathematics classroom
Sense of Belonging in
Mathematics: poor
connection with peers
student is uncomfortable with peers in the mathematics classroom
Sense of Belonging in
Mathematics: positive
connection with
instructors
student has created collaborative experience with peers and feel comfortable
in the mathematics classroom
Sense of Belonging in
Mathematics: poor
student is uncomfortable with peers in the mathematics classroom
359

connection with
instructors
Sense of Belonging in
Mathematics: positive
community
engagement
student is an active participant in the classroom
Sense of Belonging in
Mathematics: lack of
community
engagement
student does not actively participate in the classroom
Sense of Belonging in
Mathematics: future
math course plans
(yes)
student plans to take future college math courses
Sense of Belonging in
Mathematics: future
math course plans (no)
student does not plan to take future college math courses

Research Question #2: How do these learners describe how they achieved success?
Success: belief in self believes in her/his ability to be successful in math
Success: hard worker believes in her/his willingness to continue to work when facing difficulties
Success: figure it out uses a combination of knowledge and rules to be successful
desire to learn math
Success:
learning/implementing
rules
success is achieved by learning/implementing rules
Success:
learning/implementing
concepts
success is achieved by learning/implementing concepts
Success: drive success is achieved by pursuing a goal, despite opposition
360

Success: time student attributes success to the need to ‘hurry up’ and complete the
degree/course
Success: strong
abilities
belief that success is the result of strong math abilities
Success: achieve
despite struggle
(academic)
speaks about ability to be successful in school despite challenges in school
(e.g., learning difficulties, interactions with faculty)
Success: achieve
despite struggle
(personal life)
speaks about ability to be successful in school despite challenges in personal
life (e.g., lack of resources, family struggles)
Success: based on
grade
success based on math on grades
Success: secondary
perspective
success based on something other than grades
Success: prior
knowledge
success is attributed to previous knowledge

Research Question #3: How do these students perceive the role of instructors and classroom practices
in their success?
Instructor: practices Helpful: student identifies instructional practices that are helpful for their
learning
Unhelpful: student identifies instructional practices that are not helpful for
their learning
Instructor: behaviors Caring: student identifies instructor’s behavioral practices that they perceive
as helpful
Uncaring: student identifies instructor’s behavioral practices that they
perceive as unhelpful
Helpful: instructor behaviors identified as helpful
Unhelpful: instructor behaviors identified as unhelpful
361

Instructor: teaches
using rules
Instructor teaches with a focus on rules or steps
Instructor: teaches
using concepts
Instructor teaches with a focus on conceptual instruction
Instructor: instructions Student views instructor’s teaching (words or instructions) as important
Instructor: not
supportive
perceives mathematics instructors’ as unsupportive
Instructor:
encouraging words
perceives mathematics instructors’ words as encouraging
Instructor: strict perceives instructor as strict—views this positively
Instructor: makes sure
student understands
perceives instructor’s ability to ‘make sure students understand’ supports
her/his success
Instructor: makes
learning fun
perceives instructor’s ability to make learning fun supports her/his success
Instructor: connection Connects material with students’ lives
Classroom experiences
with peers: positive
experiences
student recalls positive experiences with peers in the mathematics classroom
that have contributed to her/his mathematics identity
Classroom experiences
with peers: negative
experiences
student recalls negative experiences with peers in the mathematics classroom
that have contributed to her/his mathematics identity
Other Codes
Race racial issue affects students in math-related context
Math at home student connects math-related activities with home life
Math—favorite
subject
identifies math as favorite subject
Aspirations Math-related aspirations
No connection needed Does not require a connection between math and life

362

APPENDIX H: Analysis (Sample)
Code
Heading
Participant Quote Interview Sub-section
Ability Maurice
Interviewer: What kind of grades did you get in high school and in
elementary?

Interviewee: Really, it was B’s and A’s. B’s and A’s. I was in love
with teaching myself. Yeah, never really read books. I love comic
books, but somethin’ about math, it wasn’t mixed with words. It
was just numbers. Used all the digits from zero to ten, and I just
loved figuring out—just learning how different numbers and
different tricks gave you the same answer, you just solved it
differently.
1 capable (child)
Ability Ophelia
Interviewee: Better. Improved. I feel like I wouldn’t say great or
really good, cuz I’m still improving. There’s some tests that I
wanna cry over. I have my moments every now and then with
some stuff, and I’m like, “Wait. What? What did you just say?”
Most definitely a lot better and improved.
1
average/capabl e
(adult)
Ability Nicole
Interviewer: Can you tell me about a time when you actually felt
successful in math.
Interviewee: Well, the other day in class I felt really good because
usually I'm just taking the notes and I don't get it. And later, it
clicks and it takes a while. But this was different, I got it. And
before anyone else. Not like it was a competition. So yes, that was
a feel-good moment.
1
developing
ability
Ability Wesley
It was a struggle, it was a big time struggle because I returned to
school and there was a lot of stuff that I never even heard of before
in math
1 struggle
Instrumental
value
Abdul
Then, to be successful computer programming and computer
science major, I had to go in to the math because I got to get my
math straight.
1
connection with
career
Instrumental
value
Jacob
Interviewer: What role do you see math playing in your career, and
just in your future?

3
connection with
career
363

Interviewee: Depends on what path where I take. If I wanna stay in
education, then I think it would be pivotal. Because that's what I
would think I will be teaching in. If I do the education role. If I am
doing engineering, one story I got, one of the teachers said that the
only reason why her husband was a great engineer. Was because
he actually could master the core and all that.
Obstacle Nicole
One instructor, when you’d ask him, “Can you repeat that?” “You
didn’t hear me?” It’s like, “No, I didn’t hear you. I really didn’t
hear you.” Or, “I don’t understand what you’re saying.”
2
faculty
member’s
reluctance to
re-explain
material
Obstacle Persia
That's the confusion part--the words. When you go from Algebra
1 to Algebra 2, they're saying even Calculus, I'm hearing it's the
words. That's what I want to identify. You know, this words
means this.
1
Difficulty
understanding
course material
Obstacle Valerie
I believe it is more—I believe that it’s more of us dropping these
classes cuz the teachers, some of them are really—some of them
do show their little racism.
2
Racial
discrimination
Obstacle Barry
You could be in a classroom. I could ask a student of another race
a question or just—ask 'em a question or when it's time to work in
groups, they all segregate themselves. They're all in one group and
the blacks are left to work with each other. It could be in the
beginning of the semester or something, and no one knows each
other, but if they repeat 00:33:51 the class, they segregate
themselves. I can ask a person of another race for help with a
problem, and they can tell me simply, "Oh, I don't know" or—you
know?—somethin', but they help each other
2
Racial
discrimination
Support Maurice
Those were the times when my mom and dad were always bringin'
me up. They're like, "Now you got this. Your teacher says you're
good at math, so you got this. You'll figure this out." We didn't
really have tutors in elementary school. If I needed help, I'd have
to wait till the next class time, to ask the instructor.
3 Family
Support Ophelia
Interviewee: Mm-hmm. I do go to tutoring. I’ve been there a
couple times. A lot of the times, I don’t have the time to, but I’ve
probably gone about four times. A couple of times I’ve been,
1
Instructors
(extra help)
364

Professor Rivera was actually there, so that worked out. That she
was actually downstairs.

Interviewer: She was tutoring in the tutoring center?

Interviewee: Yeah. Sometimes she has her tutoring. She’ll do her
tutoring in the tutoring center. It’ll be different students from
different ones in her class. She’ll block off a whole space. She’ll
just go in between each table, just back and forth. I’m just like, oh
lady, and you have a class after this.
Obstacle
Support

Persia
Well math—they didn’t care. To me they didn’t care if I knew or
not. I failed the second grade. I had to take it over ‘cuz my mom
moved me from one to school to this school. It was new. It’s just
like—a new teacher, new people. I didn’t do good.

When she made me take it again, my grandmother started tutoring
me. My grandma started tutoring me. It got me through it. I still
was daydreamin’. I was still not—when I mean hard on me it’s
like they were mean. They have money, and I don’t. I kinda feel
like they didn’t relate to me in that way
2

Personal
Challenges
Family

Incentive Nicole
It has me continue to go because I know I need these math skills to
get to another level of education. I know I need math skills to
better my future. I know I need math to do a lot of things. That’s
what keeps me going.
2
Academic
advancement
Incentive
Success
Ophelia
What motivates me to do well in math? I think it’s more so now
that when we start comin’ up with new topics and new subjects
that I don’t get, it’s wanting to understand them—is what
motivates me now. Now I want to learn, and I want to get it,
because I discover that if I put my mind to it and I stop telling
myself that I can’t do it, then I can. Now that’s motivation for me.
Knowin’ that I can, because I’ve done it. Now it’s like, okay.
We’re entering a domain, and you’re lookin’ at her while she’s
teaching. You’re like, “What the heck are you talkin’ about?” It’s
like, “No.” I can do this. I can be successful in this. I’m gonna get
this, kind of a thing.
1
Desire to
understand
Belief in
abilities
365

Approach
Ability
Barry
Interviewer: What do you think has you be successful in math?
Interviewee: Just the understanding. An understanding that with
the rules, and the problem, I can solve anything that's put before
me. Some people, if they get a math problem, they might get
frustrated and they don't want to complete the work, but I have an
understanding that I can do it. I can do this problem.
Interviewer: Is it just I have the belief I can do this problem or do
you draw on other memories of how you did math?
Interviewee: I have a belief I can do it. Cause math is 1 + 1 =2.
And it fits every time, so just knowing that understanding that I
can solve any problem.
1
Belief in self
Capable
Approach Ophelia
Hiding my cell phone, pulling down the laptop. They can be such a
distraction. Yeah, I’ve had moments where I got seriously
distracted and before you know it, two hours have passed by and
I’ve just been doing a whole bunch of other stuff. I’m just like, oh
my gosh. I haven’t even been paying attention. Definitely getting
rid of all of the distractions and really take my time, really, really
study, and research, and go over my notes. If I don’t understand
something, then go to Google or try to find some way to make sure
I get it, and then do a lot of practice questions. A lot of the times,
especially when you start having your exams and things like that,
what I found is a lot of the times if you did the practice exams,
they’re a lot like the real exams. The numbers and everything may
be different, but it’s still the same exact kind of problems
2 Strategies
Sense of
Belonging with
Mathematics
Nicole
Because before I really was not a science or math which is how I
ended up leaving those areas to the end of my schooling here.
1
Lack of
connection with
math
Sense of
Belonging with
Mathematics
Abdul
At that this time I didn’t know nothing about math. Math was
something to me—like everybody else, it was just a scary—not
scary, but just, “I don’t want to mess with that.”
2
Negative
beliefs about
mathematics
Sense of
belonging in
mathematics
Barry
Interviewer: How do you think your peers view your math skills?
Interviewee: I'm just sayin' far as the other students of the class. I
don't know how they thinkin', but I'm assumin' they're like, "Well,
if he can get the answer, so can I." You know?
2
Peers’ positive
perception of
math skills
366

Sense of
belonging in
mathematics
Valerie
If I had to tackle another math class at this university, I’ll do it,
and I won’t be afraid. Because this is a different kind of math, so
different from the regular, so I believe that after this, you know, I
would be at that high to where I’m not gonna even blink when it’s
time for math. Just like bring it on.
2
Positive beliefs
about self
Instructors Maurice
In math, I don’t get the math teachers that care. That is a very high
subject. That’s a very thorough subject. You have to be on your A
game when you’re in that subject. The teachers are in their A
game, but the teachers lack patience and just the ability to care
about what their students are goin’ through to at least help them
move forward.
2 Lack of support
Instructors Ophelia
She’ll show you. She won’t just say, “Oh, no, no, no. You can’t.”
She’ll show you why. “Okay. Let’s try it and see what happens.”
For the most part, if you can get it, and it’ll work for all problems,
then go ahead, if that’s the way to work out for it.
2
Encouraging
and helpful
Success Abdul
Interviewer: What would you say, from your life experiences, has
you have that perspective about yourself and your abilities? Is
there anything you can point to in particular?

Interviewee: A lot of it comes from my faith and understanding
my relationship with my creator ,and understanding the
relationship with others, and understanding the relationship with
me and this life, and understand that it’s life. You’re gonna go
through tests. Nobody can escape it.
2 Faith
Success Valerie
Very few to me, of the instructors, view success on learning it,
learning the work. They view success on the A you get in their
class, regardless of how you get it. A lot of them—I’m not gonna
say all, cuz that’s not good to say that cuz it’s not true. For the
most part, all of my teachers, there’s been very few that would
view that to be—just getting an A in their class.
3
Alternative
perspective
Success Barry
Interviewer: What do you think has you be successful in math?
Interviewee: Just the understanding. An understanding that with
the rules, and the problem, I can solve anything that's put before
me. Some people, if they get a math problem, they might get
1 Belief in self
367

frustrated and they don't want to complete the work, but I have an
understanding that I can do it. I can do this problem.
Interviewer: Is it just ‘I have the belief I can do this problem’ or do
you draw on other memories of how you did math?
Interviewee: I have a belief I can do it. Cause math is 1 + 1 =2.
And it fits every time, so just knowing that understanding that I
can solve any problem.

Abstract (if available)

Abstract Research on community college students tends to focus on their deficits and failures rather than assets and achievements. This narrative study focuses on African-American community college students and their remedial math achievements. Research questions addressed participants’ descriptions of their mathematics identity (Anderson, 2007

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Asset Metadata

Creator Roberts, Maxine Tracey (author)

Core Title Mathematics identity and sense of belonging in mathematics of successful African-American students in community college developmental mathematics courses

School Rossier School of Education

Degree Doctor of Philosophy

Degree Program Urban Education Policy

Publication Date 04/03/2018

Defense Date 02/20/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag African-American,Black,community college,developmental math,mathematics identity,OAI-PMH Harvest,student success

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Bensimon, Estela Mara (committee chair)

Creator Email maxtr45@gmail.com,mtrobert@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-490056

Unique identifier UC11267342

Identifier etd-RobertsMax-6137.pdf (filename),usctheses-c40-490056 (legacy record id)

Legacy Identifier etd-RobertsMax-6137.pdf

Dmrecord 490056

Document Type Dissertation

Rights Roberts, Maxine Tracey

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA