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The role of secondary mathematics teachers in fostering the Algebra 1 success of African American males

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The role of secondary mathematics teachers in fostering the Algebra 1 success of African American males

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Content Running head: ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 1
THE ROLE OF SECONDARY MATHEMATICS TEACHERS IN FOSTERING THE
ALGEBRA 1 SUCCESS OF AFRICAN AMERICAN MALES

by
Darius Frelix

A Dissertation Presented to the
FACULTY OF THE USC ROSSIER SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF EDUCATION

December 2016

Copyright 2016 Darius Frelix
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 2
Dedication
This study is dedicated to my two boys, Christopher and Caleb. May you take your
rightful place in this society as men, and make lasting contributions to improve the quality of our
day-to-day lives. You have inspired me to persevere through the challenges presented by the
pursuit of a doctoral degree so that I may be an example of what you can accomplish through
your own dedication and perseverance. The task may at times seem insurmountable, but you can
always call on God to equip you with the fortitude to reach your desired goals and dreams. I also
dedicate this study to my grandmother, the late Willie Ann Snead, and my father, the late
Solomon Frelix. You have instilled in me the spiritual sense as well as the humility that is
necessary to take on such a worthy challenge. I dedicate this study to my father-in-law, the late
Willie “Bill” Bilbrew. I will always cherish the times that we shared, and I am blessed to be a
part of the Bilbrew family.

ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 3
Acknowledgements
“Anyone who listens to the word but does not do what it says is like someone who looks
at his face in a mirror and, after looking at himself, goes away and immediately forgets what he
looks like. But whoever looks intently into the perfect law that gives freedom, and continues in
it—not forgetting what they have heard, but doing it—they will be blessed in what they do.”
(NIV, James 1:23-25)
I am thankful to God for providing me with the strength to make it through this process. I
would like to thank my dissertation committee: Dr. Rousseau, Dr. Carbone, and Dr. Hasan, for
their guidance, patience, and for sharing their expertise. I am thankful for having Dr. Rousseau
as my dissertation chair and grateful to Dr. Rousseau for her constant feedback, commitment,
and encouragement in seeing me through this process. It was such a wonderful privilege to have
Dr. Rousseau chair my dissertation committee, and I will always cherish the experience. To the
members of my thematic dissertation and cohort groups, as well as my peers in the TEMS
concentration, I thank you for your support, advice, and encouragement.
To my co-workers at Peary, thank you for your contributions, cooperation, and
understanding, as many of you have selflessly overlapped your responsibilities into areas that
were defined by my job tittle during the years I have pursued a doctorate. You are very much
appreciated. I am thankful to my two brothers, Kenric and Quinlan, and my sister DeAnna for
always being in my corner. I appreciate all that my sisters-in-law, Marina and Nicole have done
to assist in my completion of this project. I am also very much appreciative of my mother-In-law,
Candon, and Granny Judy for all of their help. I would like to thank my mother for her strength,
wisdom, and courage, as she has always been my inspiration. She has led by example and shown
me the importance of seeking God first and remaining steadfast in His word. Thank you to the
Frelix and Williams families for your thoughts, prayers, and cheers.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 4
To my wife, Dawn, I thank you for all you have done to push and pull me through this
process. I could not have made it through without you. Words could not express how grateful I
am to you and how blessed I am to have had you beside me throughout the challenge that was
presented in completing this doctoral program. I am truly grateful and thank you from the bottom
of my heart for all that you have done. You are my hero!
Thank you to all of my professors, instructors, teachers, and coaches from pre-school to
college, as well as all of my General, Tiger, Laureate, Trojan, and Leopard classmates and
teammates for your help, input, and encouragement in providing me with the foundation that I
needed for successful academic and professional endeavors. I am thankful to my New Philly
family and friends for your thoughts and prayers.

ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 5
Table of Contents
Dedication 2
Acknowledgements 3
List of Tables 8
List of Figures 9
Abstract 10
Chapter One: Background of the Problem 12
Statement of the Problem 16
Purpose of the Study 17
Significance of the Study 18
Limitations 19
Delimitations 19
Definitions 20
Chapter Two: Literature Review 22
Mathematic and Algebra 1 Achievement for African American Male Students. 22
Brief History of Denial of Opportunities to Learn for African Americans 23
African Americans Males and Mathematics: A Mixed Story 25
Racialized Narratives 27
Structure of California Mathematics and Reform Efforts 29
California Math Reforms 29
California High School Exit Exam 30
Common Core 32
Reforms Versus Revisions 33
Reforms and African American Males 35
Critical Race Theory 36
Racial Stereotypes 37
Micro-aggressions 39
Institutional Agents 41
Special Education Placement 41
Teacher Education 43
Pedagogical Content Knowledge 44
Mathematical Content and Pedagogical Knowledge 46
Culturally Relevant Education 48
Culturally Relevant Mathematics 49
Teacher Qualifications for Teaching Math 52
Inequities in California Teachers’ Qualification. 53
Principles of Learning Math 54
Sociocultural Theory 57
Mathematics Identity Development 59
Positive Math Identity 60
Math Self-Concept 61
Mathematics Experiences and Mathematics Identity 61
Self-Efficacy 64
Teachers and Self-Efficacy 64
Math Self-Efficacy for African American Males 65
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 6
Summary 67
Chapter Three: Methodology 68
Purpose 68
Research Design 70
Sampling and Population 70
Data Collection 72
Instrumentation 74
Data Analysis 75
Credibility and Trustworthiness 76
Clarification of Biases 76
Presentation of Negative or Discrepant Information 76
Ethical Considerations 77
Chapter Four: Findings 78
Participants 79
Equations and Functions 81
Themes for Research Question 1 81
Content Knowledge Beyond Algebra 2 83
Fixed Versus Growth Mindset Pedagogy 101
Interactive Environments 112
Themes for Research Question 2 125
Theme 1: Relevancy 125
Theme 1 Summary 136
Theme 2: Repetition 138
Theme 2 Summary 144
Theme 3: Relationships 145
Theme 3 Summary 156
Chapter Four Summary 158
Math Content Beyond Algebra 2 158
Fixed Versus Growth 158
Interactive Environments 159
Relevancy 160
Chapter Five: Discussion 162
Research Questions 162
Summary of Findings 162
Math Content Knowledge Beyond Algebra 2 163
Fixed Versus Growth Mindset Pedagogy 163
Interactive Environment Pedagogy 164
Implications for Practice 166
Recommendations 167
Recommendation 1: Continuously Support Algebra 1 Teachers in Developing and
Maintaining Deep Content Knowledge of Algebra 2 and Beyond 167
Recommendation 2: Develop Lessons That Are Relevant to The Social Lives and
Culture of African American Males 168
Recommendation 3: Algebra 1 Teachers Should Consistently Reflect on Algebra 1
Pedagogy for Biases and Culturally Insensitive Practices 169
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 7
Recommendation 4: Consider Purposeful Repetition, especially in the Early Grades,
As A Way to Promote the Background Knowledge Students Need to Construct
Mathematical Concepts 169
Recommendation 5: Recruit African American Math Teachers 169
Recommendation 6: Future Research 170
Conclusion 170
References 172
Appendix A: Student Interview Protocol 196
Appendix B: Interview Questions (Algebra 1 Teacher) 199
Appendix C: Teacher Observation Protocols 202

ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 8
List of Tables
Table 1: 8th Grade Math NAEP Scores 15
Table 2: California Standards Test Scores 8
th
Grade Algebra 1 Students Scoring Proficient or
Higher 16
Table 3: Methods 74
Table 4: Student Participants 79
Table 5: Teacher Participants 80

ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 9
List of Figures
Figure 1: Graphical Models 87
Figure 2: Mind Map 88
Figure 3: Final Exam Topics 89
Figure 4: Mr. Zody’s Board 1 96
Figure 5: Mr. Zody’s Board 2 97
Figure 6: Mr. Zody’s Board 3 97
Figure 7: Mrs. Rivers’ Board 1 103
Figure 8: Mrs. Rivers’ Board 2 104
Figure 9: Mr. Zody’s Board 4 106
Figure 10: Mr. Zody’s Room 1 118
Figure 11: Mr. Zody’s Room 2 118
Figure 12: Mr. Zody’s Room 3 119

ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 10
Abstract
This study examines the experiences of mathematically successful African American
males in secondary Algebra 1 courses through the lens of critical race theory (CRT). The
purpose of this study was to contribute to the knowledge of how to promote their success in
mathematics, particularly Algebra1, when there are structures in place that impede their
mathematics success. Further, this study aims to determine how teachers’ pedagogy may or may
not have contributed to African American males’ Algebra 1 success. Qualitative methods were
used to collect data from the interviews and classroom observations of 10 participants. The 10
participants include six African American males and four high school Algebra 1 teachers. The
data was then transcribed and coded for analyzing in relationship to the following research
questions: (1) What pedagogical content knowledge do secondary math teachers believe is
necessary for teaching Algebra 1 to African American males? (2) How can Algebra 1 teachers’
pedagogy support African American males in developing a positive mathematics identity?
Findings from this study suggest that teachers’ math content knowledge for teaching
Algebra 1 be beyond that of Algebra 2 with some knowledge of calculus. In addition, Algebra 1
teachers should be able to foster a growth mindset for African American males who have not
developed a positive mathematics identity, and they should be able to create an interactive
classroom environment for teaching and learning Algebra 1. Further, Algebra 1 teachers should
be able to provide Algebra 1 instruction that is relevant to African American males’ daily lives
and culture, provide opportunities for students to practice skills and develop strong factual
knowledge, and create a classroom environment that is inviting of student-teacher interaction as
well as student interaction with their peers.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 11
The implications of this study is that teacher education programs as well as in-service
professional development should prepare teachers for teaching math by equipping them with the
proper content knowledge and monitoring them to ensure that they maintain the level of content
knowledge. In addition, teacher education programs as well as in-service professional
development should teach cultural and social perspectives of math, including Algebra 1, and
reinforce this knowledge as part of an ongoing teacher development process. Finally, schools
should implement small-group settings or Algebra 1 support courses into the school curriculum
to supplement Algebra 1 content learning and help negate African American males’ reliance on
tutoring in order to benefit from their Algebra 1 instruction.

ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 12
CHAPTER ONE: BACKGROUND OF THE PROBLEM
African American males are overrepresented in negative categories of educational
outcomes such as dropout rates, underachievement, school suspension and expulsion, and special
education programs, but underrepresented in reports of positive categories such as honor roll and
gifted and talented programs. Due, in part, to negative educational experiences and academic
preparation, African American males are the most likely to be unemployed in many U.S. cities
(Noguera, 2003). Further, they are more likely to be arrested, incarcerated, and convicted than
their White peers (Noguera, 2003). While experiencing disproportionate levels of punishment
and academic failure in schools, these males are both loved and loathed for setting standards in
social areas such as hip-hop culture and athleticism (Davis, 2003), but not for academic
achievement.
Although African American males represented only 3.6% of undergraduate students in
2009, they represented 55.3% of basketball and football players in NCAA Division 1 institutions
(Harper, 2012). The disproportionate levels of punishment and academic failure, along with
inconsistent displays of appreciation for certain aspects of their culture and identity, such as hip-
hop and sports, has led to a range of behaviors and strategies within schools that has set the tone
for African American males’ overall problematic educational experiences (Davis, 2003).
African American males are more likely than any other group to be suspended or
expelled from school (Delpit, 2012). In addition, they are more likely to be classified as mentally
retarded or as suffering from a learning or an emotional disability, and consequently, placed in
special education (Delpit, 2012). African American students, which includes African American
males, represent approximately 17% of students attending public schools, but make up 33% of
students with a mental disability, 27% of students with serious emotional disturbance, and 18%
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 13
of students with a specific learning disability (U.S. Department of Education, 2000). As a result
of such negative educational experiences and unfavorable academic outcomes, African American
males are likely to doubt their own competence, resulting in behaviors that teachers often
misunderstand as unmotivated, uninterested, or disruptive (Delpit, 2010). Further, African
American males have a lower threshold for engaging in behaviors deemed as disruptive and/or
contrary to actions that many educators consider to be conducive to the learning environment
(Howard, 2015).
In 2011, an average of 16% of African American students were suspended as compared
to only 5% of White students (U.S. Department of Education, 2014). African American males
represented two out of three suspensions in 2011 (U.S. Department of Education, 2014). While
African American students represented 16% of student enrollment in 2011, they represented 32%
to 42% of students suspended or expelled, 27% of students referred to law enforcement and 31%
of students subjected to a school-related arrest (U.S. Department of Education, 2014). White
students represented 41% of students referred to law enforcement, 39% of school-related arrests,
and 31% to 40% of students suspended or expelled while representing 51% of enrollment (U.S.
Department of Education, 2014).
Disproportionate levels of suspensions and expulsions lead to lost opportunities for in-
school learning, as students who are suspended or expelled are typically not provided the
opportunity to make up for lost mathematics instructional time (Townsend, 2000). Mathematics
instructional time is of greater importance for African American males when their history of
mathematical underachievement is considered (Townsend, 2000).
When African American males’ educational experiences are reversed to include greater
access to highly qualified and culturally competent teachers, culturally relevant pedagogy,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 14
greater representation in the curriculum, and asset-based instruction, they have more equitable
opportunities to learn (Ladson-Billings, 1997). School structures and practices that intentionally
include African American males in honors classes, gifted and talented programs, and co-
curricular activities, could present a chance to reverse the negative outcomes that are associated
with African Americans’ academic achievement, including mathematics (Ladson-Billings, 1997).
Negative cultural messages carry over into schools and have an influence on the ways
young African American students are treated, positioned, and distributed opportunities to learn
(Davis, 2003). African Americans are often negatively constructed in the media and perceived in
everyday life (Davis, 2003). These images portray them as violent, disrespectful, unintelligent,
and threatening (Davis, 2003). It is likely that many Americans are familiar with the plight of the
African American male that includes unemployment, delinquency, crime, imprisonment, and
educational deficits (Stinson, 2006). Although sources that recount this plight are often
inaccurate, the extensive amount of these sources coincide with the popular media’s frequent
portrayal of them as lazy, hostile troublemakers, gang members, and drug addicts (Stinson, 2006).
From the institution of African Americans in slavery to the 1896 Supreme Court ruling
that segregated schools were constitutional, African Americans experienced inferior schooling
that lacked infrastructure and adequate funding in comparison to schooling for White students
(Harmon & Ford, 2010). African Americans’ poor performance in academics, including
mathematics, continued throughout the twentieth century, and is still prevalent in the twenty-first
century (Harrison & Ford, 2010). African American students are less likely to have access to
resources such as computers and mathematical manipulatives for deeper understanding of
abstract mathematical concepts (Flores, 2007). In addition, African American students are less
likely to have qualified and experienced teachers who emphasize class discussion and non-
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 15
routine problem solving than White students (Flores, 2007). Further, the least prepared teachers
are disproportionally found in under-resourced schools where African Americans typically attend,
located in central cities and rural areas (Flores, 2007; Darling-Hammond, 2010).
The 1954 ruling in Brown v. the Board of Education led to desegregation, but African
Americans continued to struggle. According to some scholars, their struggle is rooted in a
Eurocentric curriculum and teaching pedagogy that disregards their culture and history (Harmon
& Ford, 2010). Rather, the school experiences are demeaning of African and African American
culture. Positive images reflecting the contributions of African Americans to American life are
rarely promoted. Thus African American students go unaffirmed in their schooling experiences.
During recent history, African American males continued to underachieve academically,
particularly in mathematics. The national average scaled score in 8th grade math on the 1996
National Assessment of Educational Progress (NAEP) for White students was 281, and, for
Black students, it was 240 (Moses-Snipes, 2005). In 2003, the average NAEP 8
th
grade score was
288 for White students and 252 for Black students (Moses-Snipes, 2005). In 2013, the national
average NAEP scaled score was 294 for White students, and 263 for African American students.
In California, the average scaled score was 291 for White students, 263 for Hispanic students,
and 258 for African American students (National Center for Education Statistics, 2013)
Table 1
8th Grade Math NAEP Scores
Year 1996 2003 2013
White Students 281 288 294
African American Students 240 252 263

Although methods for teaching math have moderately changed over time, African
American students continue to perform below their White peers on math achievement tests
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 16
(Ladson-Billings, 1997). In 2005, on the California Standards Test (CST) in 8
th
grade Algebra 1,
14% of African Americans scored proficient or higher while 49% of White students did so. In
2010, 29% of African Americans scored proficient or higher on the CST in 8th grade Algebra 1,
while 58% of White students did so. From the mid 1990’s to 2013, the mathematics achievement
scores of African American students consistently remained below that of White students.
Table 2
California Standards Test Scores 8
th
Grade Algebra 1 Students Scoring Proficient or Higher
Year 2005 2010
White Students 49% 58%
African American Students 14% 29%

Statement of the Problem
According to the recent California Assessment of Student Performance and Progress for
2014 (CAASPP), 60% of African American students did not meet the Common Core
mathematics standards for 8th grade while 25% of White students did not meet the standards
(California Department of Education, 2015). While standardized testing may not be the only way
to assess students’ academic achievement, they are a significant indicator that demonstrates a
disparity between African American and White students.
Students who are not successful in academics, particularly math, are also more likely to
drop out of school (Rumberger, 1995). In 2013-2014, the cohort dropout rate was 4.5% for Asian
students, 7.6% for White students, 13.9% for Hispanic students, and 20.3% for African
American students (California Department of Education, 2014). These data are consistent with
the math achievement test scores. White students scored higher than Blacks and Latinos in
Algebra 1 on the CST for 2013, and Latinos also scored higher than Blacks in Algebra 1 on the
CST for 2013.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 17
African American male students have consistently scored lower than their peers of other
ethnic groups on 8
th
grade math achievement tests in California. This is a problem because only
33% of the African American students who were tested scored proficient or higher in Algebra 1
on the 2013 CST in the 8
th
grade while 78% of Asian students, 61% of White students, and 40%
of Hispanic students scored proficient or higher (California Department of Education, 2014).
These data support the notion that African American students have consistently achieved lower
on Algebra 1 achievement tests than their peers of other ethnic groups in California. This
problem has a negative effect on the state’s goal to prepare all students for high school and
college mathematics. Since many jobs in technical fields such as STEM areas require college
degrees, and African American males’ Algebra 1 achievement test scores are below those of
their peers, they are less likely to be hired than their peers of other ethnicities (Noguera, 2003).
Purpose of the Study
The purpose of this study is to contribute to the knowledge about how to promote African
American male students’ success in mathematics, particularly Algebra 1. Based on this purpose,
two research questions were developed. The purpose of these research questions is to determine
the necessary course of action for improving this population’s mathematics and Algebra 1
achievement.
1. What pedagogical content knowledge do secondary math teachers believe is necessary
for teaching Algebra 1 to African American males?
2. How can Algebra 1 teachers’ pedagogy support African American males in developing a
positive mathematics identity?
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 18
Significance of the Study
Math teaching and learning is one of the most serious issues in education (McCoy, 2005).
Many educators perceive students’ achievement in Algebra 1 as a pivotal issue in K-12
mathematics, state graduation requirements, and students’ ability to meet college admission
requirements. California includes at least a year of algebra, but Algebra 1 is also a prerequisite
for higher levels of mathematics and science. On the basis of an examination of the National
Educational Longitudinal Study, Atanda (1999) found that 8th grade students who studied
algebra were more likely to study high-level mathematics in high school and more likely to apply
to college than were 8th graders who did not (McCoy, 2005). Further, according to (Ing, 2014),
students who attend college with low math achievement scores may not have the requisite
knowledge to pursue a career in the areas of science, technology, engineering, and mathematics
(STEM). Individuals with knowledge in the STEM areas are needed to develop and support a
competitive national workforce in the global marketplace (Ing. 2014).
Due in part to the lower graduation rates and diminishing opportunity for college and
university access, African American males in the United States are lagging behind students in
European and Asian nations in educational attainment (Darling-Hammond, 2010). While the
United States graduated just under 70% of its students from high school in 2000, many
previously underperforming nations graduate over 90% of their high school students (Darling-
Hammond, 2010). These nations include Greece, Norway, Germany, Czech Republic, and Korea
(Darling-Hammond, 2010). Further, about 35% of a 9th grade cohort gains a college degree in
the United States, while 50% of European 9th grade cohorts do so. Only about 17% of African
Americans between the ages of 25 to 29 earned college degrees in 2005, compared to 34% of
White youths ages 25 to 29 (Darling-Hammond, 2010). By the year 2025, it is estimated that the
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 19
majority of United States’ public school students will be young people of color, but the nation’s
investment in education remains highly unequal, inequitable, and inadequate for this population
(Darling-Hammond, 2010).
As the average schooling level for students in the United States trends downward while
students of some European and Asian nations trend upward, it is important to note that there is a
corresponding increase of 3.7% in long-term economic growth for every year that the average
schooling level of a population is raised (OECD, 2008). Therefore, African American males’
continued underachievement in mathematics is detrimental to the United States’ future economic
growth.
Limitations
This study is qualitative and data were collected through interviews and observations.
Due to scheduling problems that sometimes prevented the researcher from matching the teachers
interviewed with the students interviewed in all cases, some of the responses students provided
in the interviews related to their experiences with teachers who were not teachers interviewed or
observed in this study. Data were collected over a period of one month. Therefore, this study is
not as comprehensive as a longitudinal study. Further, this study was limited to 10 participants.
Delimitations
This study focused on six students and four teachers. Although the students and teachers’
schools may differ, it covered only two high schools. Therefore, the results of the study may not
be widely generalizable. Further, this study focused on how teachers’ knowledge and pedagogy
may or may not be consistent with the literature about what contributes to African American
males’ achieving math identities. The inclusion of school-wide tutoring programs, interventions,
and assistance from other staff members that may have led to their mathematics achievement was
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 20
not considered. In addition, the possibility that interdisciplinary lessons and/or projects from
teachers of other academic disciplines, which may have contributed to African American males’
success, were not considered. The only school personnel who were interviewed and/or observed
were mathematics teachers.
Definitions
Four-year Adjusted Cohort Dropout Rate - the rate of students who enter high school together
and leave the 9-12 system of instruction without obtaining either a high school diploma, GED, or
special education certificate of completion, and do not remain enrolled after the end of the 4th
year (California Department of Education, 2014).
Discourse - frameworks for thought and action that groups of individuals draw upon in order to
speak and interact with one another in meaningful ways (Marsh, 2002)
Mathematics Identity - beliefs about one’s mathematics ability, importance of mathematics,
opportunities presented through mathematics ability, existing constraints in developing
mathematics knowledge, and motivation to learn math (Martin, 2000).
Micro-Aggressions - acts of disregard that stem from unconscious attitudes of White superiority,
constituting a verification of Black inferiority (Davis, 1989).
Pedagogical content knowledge - knowledge of how particular subject matter topics, problems,
and issues can be organized, represented, and adapted to the diverse interests, abilities, and
cultural experiences of learners (Magnusson et al. (1999).
Racialized Narratives - dynamic cultural artifacts that students appropriate and deploy in
processes of identification and positioning (Nasir & Shah, 2011)
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 21
Sociocultural Discourse - appropriations of historically, socially, and culturally specific ways of
thinking, speaking, and interacting within the context in which individuals are situated (Marsh,
2002).
Trends in International Mathematics and Science Study - An international assessment of
math and science at the fourth and 8th grades conducted every four years since 1995. (TIMSS,
2011).
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 22
CHAPTER TWO: LITERATURE REVIEW
Although several reform efforts were initiated to improve California mathematics
education with a goal of changing what has been described as an achievement gap between
African American and White students, African Americans continue to underachieve in
mathematics (Zamani-Gallaher et al., 2012; Howard, 2014). The average 2013 CST score for
African Americans in 8th grade Algebra 1 was 43% proficient or advanced as compared to 68%
proficient or advanced for White students (California Department of Education, 2013).
This chapter is a review of the literature that discusses possible underlying causes of the
perceived mathematics achievement gap between African American and White students in
California. Related topics discussed in order to understand this gap include the structure of
California schools, teacher education programs, math identity development, and the self-efficacy
of teachers and African American male students. Since access to Algebra 1 is recognized as the
gatekeeper for future educational and employment opportunities (Ladsen-Billings, 1998), it is
necessary to determine underlying causes of underachievement as measured on achievement
tests in mathematics, student grades, and mathematics course-taking patterns.
Mathematic and Algebra 1 Achievement for African American Male Students.
There continues to be a considerable gap in Algebra 1 test scores between African
American and White students. Further, African Americans are the only ethnic group in which
their female counterparts outperform their male counterparts in mathematics achievement
(Lubienski & Copur, 2009). African American males’ consistent underperformance in
educational achievement, including mathematics, can be traced to the mindset about African
Americans reflected in the institution of slavery that caused the White slaveholder to deny
African Americans access to even the most basic schooling (Jemmes, 2007). An informed
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 23
African American male has always been viewed as the greatest threat to the myth of White
supremacy.
Brief History of Denial of Opportunities to Learn for African Americans
The denial of access to education has had lasting effects on African Americans’
relationship to formal education. During slavery, most African Americans were prohibited from
learning to read or write, largely due to slave owners’ fears that education would inspire
rebellion (Woodson, 1915). Keeping the slave ignorant would serve to confirm their construct of
an intellectually inferior Black identity. However, there were opposing ideas between the North
and South on the education of African Americans (Jeynes, 2007). Those who favored the
liberation of African Americans viewed education and emancipation as inseparable and saw
education as a necessary step toward their freedom and citizenship. In New York, for example,
equal numbers of African American children and White children attended school (Bergman &
Bergman, 1969). At the same time, in Southern states, laws were passed in the 1830s and 1840s
that forbid African Americans from attending schools (Bullock, 1967; Wilson, 1977). It is
estimated that, by the end of the Civil War, African American literacy in the South was no higher
than 10% (Jennes, 2007). Over time, however, de facto segregation in the North mirrored the de
jure segregation of the South (Jennes, 2007).
Although literacy rates among African Americans in the North were nearly 90% during
the late 1800s, lack of job opportunities were due to views of African Americans as ignorant and
lacking in mental capacity (Tyack, 1974). Since jobs that required higher literacy skills and
competency in areas of mathematics such as algebra were not open to African Americans, it was
questionable whether the institution of education should adequately prepare African Americans
for jobs that required higher levels of education (Tyack, 1974;). Thus, as educational attainment
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 24
increased for African Americans, satisfaction with jobs decreased (Tyack, 1974). African
American’s attendance in schools began to drop which, in part, led to decreases in African
American literacy rates (Jennes, 2007; Tyack, 1974;).
Mathematics learning and literacy are connected. Falle (2004), and Meaney & Irwin
(2005) assert that mathematics learning is mediated through language. Low literacy rates affect
the development of mathematics understanding. Literacy and mathematics are inseparable. In the
context of mathematics, there is a social language (Bakhtin, 1986) that consists of the specialized
words, terms, and words from non-mathematics contexts that have mathematical meanings
(Khristy & Chval, 2002).
In order to have students understand and engage in the mathematical discussions that
develop higher levels of thinking and comprehension, teachers must be able to foster the social
interaction in mathematics classrooms that mediates students’ mathematical thinking and
learning (Vygotsky, 1978). Mathematical language is developed in context through meaningful
and active use of the mathematical words as they are used and heard in context (Khristy & Chval,
2002). Thus, Southern laws in the 1800’s that prohibited the education of African Americans had
a profound effect on the development of literacy, which, in turn, had an effect on African
American’s mathematical language development. This connection between literacy and
mathematics, though often overlooked, still exists.
Although Southern laws in the mid-1800s prohibited the education of African Americans,
some African Americans in the South were introduced to mathematics through such business
practices of the plantation as record-keeping and purchasing provisions (Bullock, 1967). They
demonstrated levels of math proficiency through daily tasks, although they did not have formal
education. Further, African Americans performed mathematical tasks such as weighing and
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 25
measuring rations, doing carpentry, and building machines and devices used for harvesting and
cultivating crops (Bullock, 1967). African Americans in the South, at times performed tasks that
indicated mathematical knowledge and understanding, although African American access to
formal education was denied (Bullock, 1967). They were able to learn mathematics despite the
denial of formal education.
African Americans Males and Mathematics: A Mixed Story
Although much literature discusses negative mathematical outcomes for African
American males, which include a history of denied access to formal education, there has been
little literature on the successes of African Americans, particularly males, in mathematics
(Ladson-Billings, 1997). Taylor (1999) asserts that the narrative about African American male
negative outcomes has been so intertwined in the mindset of educators, that African American
male success outside of athletics is almost surprising and unexpected. Frequently absent from
this view are stories of African American males’ academic success and the discourse that makes
known that the majority do not drop out of school, nor that majority are not imprisoned (Howard,
2010). Many of these students do experience varying degrees of success and are disciplined and
hardworking (Howard, 2010).
Howard (2010) suggests the current narrative of the underperforming, unmotivated,
undisciplined African American male must be shifted to uncover how certain school cultures and
pedagogical practices are able to create atmospheres of success for them in spite of data and
reports that focus on low performance. Since Ladson-Billings’ (1997) call for research on
African American students’ mathematics success, a small number of scholars labored to refocus
the discussion by documenting the life and schooling experiences of those who are
mathematically successful (Stinson, 2013).
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 26
Lubienski and Bowen (2000) concluded that researchers tend to look primarily at
negative outcomes for African American males and rarely examine how schooling experiences
contribute to these outcomes. Gutierrez (2008) suggests a greater focus on the advancement,
excellence, and gains within marginalized communities, and less on gaps in achievement
between historically marginalized communities and their White counterparts is in order. In
addition to identifying successes among African American males, it is important to identify the
underlying structural and institutional causes of mathematics underachievement, which are rarely
captured (Gutierrez, 2008).
Stinson’s (2008) study examined the lived experiences of four African American males
who demonstrated achievement by focusing on their persistence in high school mathematics.
Stinson found that the four participants successfully negotiated discourses of deficiency and
rejection, while reconfiguring the White male-math-myth and the cool pose theory commonly
promoted. The discourse of deficiency focuses on the perceived deficiency of culturally oriented
schooling, and life experiences of African American children. Stinson’s (2008) participants
negotiated the discourse of deficiency through their beliefs that hard work and a strong drive will
foster success in spite of structural deficiencies and inequalities. The discourse of rejection is
based on the notion that African American males systematically reject academics. The
participants in Stinson’s (2008) study negotiated the discourse of rejection with assertions that
the discourse of rejection is inconsistent with their views that mathematics learning and
understanding is vital to the pursuit of positive academic outcomes.
The participants in Stinson’s (2008) study negotiated the White-male-math-myth, which
suggests that mathematics is a White, middle-class-male domain, due, in part, to the participants’
beliefs in their own abilities to learn and perform well mathematically. African American male
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 27
mathematical success opposes views that math is not pertinent to their culture. Participants in
Stinson’s 2008 study developed beliefs in their abilities to perform mathematically, in part, by
identifying with friends and relatives who also performed well mathematically, and received
college degrees. The participants attributed their relatives’ positive academic outcomes to
mathematical understanding.
In addition to negotiating the White-male-math-myth, the participants in Stinson’s 2008
study reconfigured the cool pose theory, which suggests that some African American males
develop ritualized forms of masculinity that are oppositional to school success. These behaviors
include scripted behaviors, physical posturing, impression management, and carefully crafted
posturing that present messages of pride, strength, and control (Majors & Billson, 1993; Majors
& Gordon, 1994), but often result in disciplinary actions (Howard, 2015). The participants
reconfigured the cool pose theory by developing strategies that allowed them to engage in cool
pose behaviors while limiting the negative impact on the participants’ school and academic
success.
Racialized Narratives
Ladson-Billings (1997) suggested that African American males’ math experiences might
be different if African American males did not have to spend so much energy–intellectual and
physical–negotiating a plethora of sociocultural discourses and racialized narratives, that unjustly
construct them as less capable of mathematics success than their White male counterparts
(Stinson, 2013).
Nasir and Shah, (2011) explored the role of racialized narratives such as Asians are good
at math, and found that students made sense of such narratives in ways that linked perceptions of
Asian Americans as mathematically gifted to perceptions of African Americans males as
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 28
intellectually inferior. Further, racialized narratives describe Asian Americans as being
successful in school because they work hard and come from cultures that believe in the value of
education (Lee, 1994,) in contrast to African Americans. In order to position themselves as
mathematically competent, African American males in Nasir and Shah’s study attempted to
repurpose racial narratives in order to positively identify with mathematics (Nasir & Shah, 2011).
Repurposing racialized narratives consisted of focusing on the notion that there are many
mathematically successful African American males who work hard and value education (Nasir &
Shah, 2011). Racialized narratives tend to be slightly covert, and although many school settings
rarely take up issues of race in an explicit manner, race continues to be a key aspect of students’
mathematical experiences from pre-school through high school (Schafer & Skinner, 2009). In
light of the issue of racialized narratives and unfavorable math experiences and poor
mathematics outcomes for many minorities, Schafer and Skinner (2009) performed an
ethnographic study of 8- to 11-year-olds in four 4th grade classrooms in the Southeast United
States.
Schafer and Skinner’s 2009 study contributed to the research that shows that students
from pre-school to high school actively engage in race as a meaningful system of difference and
power within educational institutions that produce and reproduce social hierarchies of race,
gender, and class. Ferguson (2000) shows how specific disciplinary techniques can construct
African American males as bad boys and naturalize a racial order that privileges those who
conform to White middle class social norms.
Perry (2001) implicates school structures and practices that help construct and reinforce
whiteness and demonstrates how White students represent an unmarked norm against which
others are judged. Schools can and do perpetrate inequalities based on race, gender, ability level,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 29
and class through tracking and labeling practices, racial disparities in enrollment in gifted and
special education classrooms, biased disciplinary practices, as well as other aspects of
programming and hidden curricula (Schafer & Skinner, 2009). These and other systemic barriers
make it difficult for large numbers of African American males to be successful in mathematics
(Zamani-Gallaher & Polite, 2010).
Structure of California Mathematics and Reform Efforts
It is essential to consider the performance of African American males’ mathematics
learning and achievement in the context of developments in mathematics teaching and course
offerings. Over the last several decades, U.S. schools have dramatically intensified high school
mathematics curricula in an attempt to improve U.S. mathematics achievement (Domina &
Saldana, 2012). The state of California attempted to further intensify mathematics curricula
through reforms and initiatives aimed at increasing all students’ mathematics performance.
California Math Reforms
The California legislative reform package known as Senate Bill (SB) 813 in 1983
consisted of more than 80 initiatives which included increased high school graduation
requirements, merit pay and incentives for teachers, and a curriculum overhaul (Causey-Bush,
2005). SB 813 included increased graduation requirements aligned to the California State
University and University of California systems (Honig, 1988). The legislation attempted to base
student learning on curriculum content standards and use of a variety of assessments to hold
schools accountable (Causey-Bush, 2005) for improving students’ achievement in content areas,
including mathematics. Although Algebra 1 test scores increased for California’s students from
2003 to 2010, African American males continued to underperform in comparison to their peers
of other ethnicities (Williams et al., 2011). The number of students who scored proficient or
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 30
higher on the CST in 8
th
grade Algebra 1 rose from 39% in 2003 to 46% in 2010 (Williams et al.,
2011). The number of African American students who scored proficient or higher on this test
rose from 17% in 2003 to 29% in 2010 (California Department of Education, 2010). Although
African Americans made considerable gains in Algebra 1 achievement from 2003 to 2010,
African Americans continue to lag behind their peers of other ethnic groups in Algebra 1
achievement.
California High School Exit Exam
The state legislature attempted to increase accountability for raising the achievement
among low performing students by introducing the California High School Exit Exam
(CAHSEE), which was authorized in 1999. All students were required to pass the CAHSEE in
order to receive a high school diploma (Causey-Bush, 2005). Nevertheless, African American
males continued to underperform in middle school mathematics as many of the reforms were
developed without addressing African American males’ needs (Berry et al., 2014). African
American males’ low middle school performance negatively impacted high school academic
achievement and performance on the CAHSEE.
Other attempts by the state to reform mathematics also produced mixed results.
California was at the forefront of the Algebra-for-All movement, and, in 2008, the state moved to
make Algebra the accountability benchmark test for 8th-grade mathematics (Domina & Saldana,
2012). Although the Algebra-for-All movement provided access to 8
th
-grade Algebra 1 for many
African American males, and African Americans continued to have increased Algebra 1
achievement test scores overall, they continued to underachieve on Algebra 1 achievement tests
in comparison to members of other ethnic groups. In 2009, 26% of African Americans students
scored proficient or higher on the CST in Algebra 1, while 74% of Asian students, 56% of White
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 31
students, and 33% of Hispanics did so (California Department of Education, 2009). In 2011,
29% of African American students scored proficient or higher on the exam while 76% of Asian
students, 58% of White students, and 37% of Hispanic students did so (California Department of
Education, 2011).
Domina and Saldana (2012) studied the effects of increasing 8th-grade Algebra
enrollment rates on 10th graders’ performance on the mathematics portion of the CAHSEE.
Domina and Saldana (2012) found that enrolling more students in advanced courses had negative
average effects on students’ achievement (Domina, McEachin, Penner, & Penner, 2014). In 2008,
the year that Algebra-for -All began for 8th grade students, 78% of California’s 10th grade
students passed the CAHSEE (California Department of Education, 2008). By 2012, the number
of California’s 10th graders who passed the CAHSEE had decreased by seven points to 71%.
Further, Algebra-for-All did not improve the CAHSEE scores for African American
students in comparison to students from other ethnic groups. While 71% of all 10th graders
passed the CAHSEE in 2012, 88% of Asian students, 83.5% of White students, 62.9% of
Hispanics, and 68.9% of African American students did so (California Department of Education,
2012).
African American males’ low scores on standardized testing in mathematics reinforces
existing negative constructs of African American identity and fuels the belief that African
American males are incapable of learning mathematics. For instance, the CAHSEE is based on
California Content Standards for grades 6, 7, and 8 as well as Algebra 1 (California Department
of Education, 2014). Yet, in 2014, 72 % of 10th grade African American students passed the
math section of the CAHSEE as compared to 97 % of Asian students, 80 % of Latinos, and 92 %
of White students (California Department of Education, 2015). When African American males
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 32
do not perform well on standardized tests, they pay a heavy price in terms of their future. Since
access to higher education is linked, in part, to mathematics achievement and the pursuit of
careers in higher-paying STEM-related fields, low performance on standardized tests such as the
CAHSEE may reinforce perceptions of African American males as mathematically incapable,
which, in turn, may have a negative impact on their potential to higher education and access to
higher-paying careers.
Common Core
Tienken (2012) argues that the adoption of the CCSS could be one of the largest social
experiments undertaken on children, as it was adopted with little empirical evidence for support.
In contrast to these objections, Conley et al. (2011) published a report called Reaching the Goal:
The Applicability and Importance of the Common Core State Standards to College and Career
Readiness, suggesting that the CCSS will prepare students for college and careers.
Banks and Lafors, (2015) assert that the new CCSS elevate expectations of teachers to
improve their pedagogy, and, therefore, it can be expected that students’ mathematical outcomes
will be favorable. This increase in teacher and student expectation is significant for African
American males, a group who has consistently performed below grade levels (Banks & Lafors,
2015). Increased expectations resulting from the CCSS for mathematics has the potential to
improve instruction for all students, including African American males, while also preparing
students for college level math and employment in the workforce, which includes STEM-related
fields (Banks & Lafors, 2015). However, improvement in instruction and mathematics
performance for African American males requires more than higher expectations.
Many districts, schools, and teachers are not prepared for the Smarter Balanced
Assessment Consortium, which requires assessments aligned to the CCSS for mathematics
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 33
(Banks & Lafors, 2015). The CCSS do nothing to change the circumstances of underprepared
teachers and poorly administered schools (Banks & Lafors, 2015). Failure to align curriculum,
instruction, and assessments, in addition to the wide use of teacher pedagogy that is not relevant
to African American males’ culture, are factors that continue to contribute to low performance in
mathematics (Ladsen-Billings, 2009).
The 2010 NAEP for 8th grade mathematics indicated that African American students,
who made up 16% of the overall 8th grade population, were overrepresented in the lowest
quartile of score bands, comprising 28% of the lowest quartile score bands, and 5% of the
highest quartile score bands (National Center for Education Statistics, 2011). These data
demonstrate that African American students, males in particular, continued to underperform
despite the passage of legislation, as legislature and reforms continue to fail to focus on equitable
ways to meet African American males’ needs (Berry et al., 2014).
Reforms Versus Revisions
Reform raises questions about the core beliefs underlying mathematics education and
teaching, moving schools to restructure thinking about the nature of mathematics, how it is
taught to all students, including African American males, how it is learned, and what is the
definition of success (Ellis & Berry, 2005). True reform is transformative and leads to redefining
the necessary epistemological stance towards mathematics learning (Ellis & Berry, 2005).
On the other hand, revisions can be characterized as renewal efforts that capture
educators’ attention for a short period of time but fail to address underlying causes of students’
mathematical difficulties (Ellis & Berry, 2005). Revisions appease educators, administrators, and
voters, although in many cases they are simply adapting new components to fit within the
boundaries of the accepted mathematics educational paradigm. These surface level
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 34
modifications do little to alter deeply held beliefs about the nature of mathematics, how it is to be
taught to all students including African American males, the type of learning that is valued, and
how success is determined (Ellis & Berry, 2005).
Throughout the last century, mathematics education in the United States has seen a series
of revisions under the guise of reform movements that failed to question traditional assumptions
and beliefs about mathematics teaching and learning. These revisions lacked the epistemological
changes necessary to foster successful mathematical outcomes for African American males as
well as other students (Ellis & Berry, 2005). African American children, particularly African
American males, have not benefited from previous efforts to promote mathematics reforms,
which are often products of social and political pressures. Past mathematical revisions included
graduation standards, new curriculum frameworks to guide instruction, new assessments to test
students’ knowledge, high stakes testing, and accountability mechanisms. In addition, voucher
programs and charter schools were created to present new options for students’ schooling and
educational experiences (Darling-Hammond, 2000). While many of these efforts were useful
and led to some positive educational outcomes and experiences for African American males in
mathematics, overall, these efforts failed to address issues such as quality of teaching in
underserved schools, the lack of culturally relevant curriculum, and inequality in education
(Darling-Hammond, 2000).
According to the TIMSS 2011 report, past reform movements and policy have not
yielded favorable results for the United States’ 8th grade students in mathematics when
compared to the top performing nations. Four of the top performing nations in 8th grade
mathematics on the TIMSS were Korea, Singapore, Chinese Taipei, and Japan. In addition to the
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 35
four top scoring nations, the Russian Federation, Israel, and Finland all out performed the United
States in 8th grade math.
As a result of the United States’ lagging behind other nations such as China in
mathematics achievement, United States Ph.D. programs are now dominated by graduates from
other countries (Darling-Hammond, 2010). The year 2006 became the first year that the top
producers of U.S. students in doctoral programs were Tsinghua and Bejing universities (Darling-
Hammond, 2010). Further, more than one-third of the U.S. doctoral recipients in science and
engineering come from countries other than the United States (Darling-Hammond, 2010).
Reforms and African American Males
The underlying narrative of America’s past educational reforms and initiatives focused
on national security, technological interests, social efficiency, and the perpetuation of White
privilege. Reform debates focus on curriculum, teaching, learning, and assessment, although the
focus is often superficial, and rarely focus on understanding the realities of children’s lives. They
do not address inequitable opportunities to learn, generational segregation, unequal quality of
teachers, cultural differences, limited resources in urban schools, the biases against males in
schooling, as well as other significant factors (Berry et al., 2014). Reforms have not yielded big
improvements for math teaching in general (Mullis, 2012). Therefore, when considering some of
the social and economic challenges African American males face, the results are devastating.
As a result of a lack of focus on African American males’ needs in mathematics and
perceptions of their inadequacies, they experience the following conditions: reduced access to
advanced math courses, routine exposure to activities that focus on rote memorization, and
disproportionate access to qualified teachers (Ellis & Berry 2005; Flores 2007; Gutierrez 2008a;
Martin 2007). Berry et al. (2011) used a historical-critical race theory to argue that African
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 36
American learners have not benefited from attempted reforms in mathematics education, which
are most often designed and enacted from the perspectives of the dominant society.
Critical Race Theory
Critical Race Theory (CRT), which emerged, in part, as a result of a legal movement
called critical legal studies (Ladson-Billings, 1998), provides a perspective on African American
males’ low academic performance, including their performance in mathematics. CRT describes
racism as so entrenched in the mindset of America’s culture that it is normal in American society
(Ladson-Billings, 1998). CRT also provides a lens for a discourse about race, gender, and class
as a centerpiece in analyzing African American males’ mathematical underachievement (Howard,
2014). Racism in American society influences the way African American males’ experiences in
mathematics instruction are shaped and made available as opportunities to learn math (Ladson-
Billings, 1998).
Although there is data that describe African American males as underperforming and
mathematically incapable, there is little effort to dispute these data (Bell, 1991). As a result, the
narrative of African American males as mathematically incapable is reaffirmed while there is
little effort to fix a system of education that perpetuates a racial hierarchy that views African
Americans as inferior and incapable learners. Instead, African American males are used as
scapegoats and the burden of creating an equitable system of education (Bell, 1991; Ladson-
Billings, 1998) where African American males could be viewed as mathematically capable is
removed.
Ladson-Billings and Tate (1995) state that there would be more examples of African
American males’ success in education if racism were expressed in merely isolated and unrelated
individual acts. Instead of educational success, African American males rarely find success
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 37
inside the school except moderate to extensive success in areas such as athletics and
entertainment (comedy, singing/dancing, acting). Sometimes, they find success in church,
neighborhood parks and recreational facilities as well as in their families (Howard, 2014). These
informal experiences with success are often facilitated by people in leadership positions (Howard,
2014). Coaches, clergymen, relatives, and other adults have often fostered African Americans
males’ positive and successful experiences outside of school; they are a potential source of
insights for educators who struggle to develop these students’ academic potential (Duncan-
Andrade, 2010).
Racial Stereotypes
Steele and Aronson’s (1995) work reveals that racial stereotypes are deeply woven into
the fabric of U.S. society, yet daily effects of racial stereotypes are often misunderstood. Steele
and Aronson (1995) assert that stereotypes may interfere with African American students’ ability
to achieve high scores on standardized tests. Racial stereotypes about intelligence and academics
are particularly important to investigate, because they can have detrimental effects on the
academic performance of students from negatively stereotyped groups (Steele, 1997).
Stereotype threat research showed that, when children are reminded of a negatively
structured identity based on stereotypes, they, as members of the stereotyped group, perform
worse on achievement tests than they do when the stereotypes are not embedded and exhibited
through the mindset and behavior of the educator (Schmader et al., 2008). Some of the most
studied academic stereotypes in childhood and adolescence pertain to African American males,
who are stereotypically portrayed as caring less about school or as being less intelligent than
their White male counterparts (Okeke et al., 2009). The range of racial stereotypes documented
run from openly negative characterizations to more unintentional biases (Sue et al., 2007), which,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 38
nevertheless, may constrict children’s aspirations and shape future academic goals and identities
(Spencer & Markstrom-Adams, 1990; Way et al., 2013).
African American males’ low achievement in mathematics is a function of attitudes,
policies, and practices in urban schools, particularly low educator expectations, deficit thinking,
irrelevant curriculum, culturally incompetent educators, and/or few or no resources (Ford &
Moore, 2013). The term urban is often associated with negative connotations about poverty,
apathy, crime, and violence, which further promote deficit-oriented stereotypical perceptions of
African American males such as lazy, resistant to learning, and incapable or unwilling to think
critically (Ford & Moore, 2013).
When these deficit views are held among school personnel, it is difficult and nearly
impossible for African American males to utilize the energy, commitment, and resources
necessary to challenge those in authority, and achieve success in mathematics (Ford et al., 2006;
Moore & Owens, 2008). In addition to structural challenges that African American males face in
schools, classroom challenges such as teachers’ lack of racial awareness, cultural ignorance
among school personnel, apathetic teacher attitudes, and poor quality instruction are also
apparent (Howard, 2008; Milner, 2008).
The Pygmalion effect, which can happen as early as kindergarten, suggests that teachers’
attitudes and expectations can influence the academic achievement of middle school students
(Howard, 2010). Poor educational outcomes, particularly low Algebra 1 achievement, can
become a self-fulfilling prophecy when students internalize negative teacher attitudes and deficit
thinking (Howard, 2010). Further, issues stemming from deficit cognitive frames (Bensimon,
2005) present topics that are difficult for urban educators to discuss, admit, accept, and share
responsibility for (Ford & Moore, 2013). Thus, African American males often lack the support of
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 39
institutional agents who can provide the necessary resources for success in Algebra 1 (Stanton-
Salazar, 1997). In addition to other resources, institutional agents can offer the moral and social
support that is necessary to enhance and empower their educational experiences (Stanton-Salazar,
1997). African American males often lack the social and moral support from institutional agents
that is necessary to foster success in Algebra 1, due in part, to deficit thinking and prejudiced
attitudes among educators that view African American males as incapable of producing positive
mathematical outcomes.
Micro-aggressions
Micro-aggressive attitudes among educators, particularly mathematics teachers, can have
detrimental effects on the pursuit of favorable mathematics outcomes for African American
males (Davis, 1989). Davis (1989) defines micro-aggressions as stunning acts of disregard that
stem from unconscious attitudes of White superiority, constituting a verification of Black
inferiority. For African American males, racial micro-aggressions from classroom teachers can
manifest themselves in numerous ways.
Suspicion or surprise about African American males’ academic success, common
acceptance of their underachievement, lack of positive re-enforcement for their accomplishments,
differential forms of punishment, demeaning comments, failure to place them in leadership
positions, and reluctance to refer them for advanced classes are the contexts in which conscious
and/or unconscious micro-aggressions communicate deficit thinking and low expectations for
African American males among educators in urban schools (Davis, 1989). African American
males sometimes adopt these same perceptions about themselves, which lead to a fear of failure
or lack of interest in learning (Smith, 2010).
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 40
Forms of micro-aggressions such as colorblindness, denial of racism, ascription of
intelligence, and the myth of meritocracy all serve to create a hostile and/or derogatory
environment for African Americans, particularly African American males (Sue et al., 2007). It is
likely that acts of racial micro-aggressions will occur when there are interracial encounters (Sue
et al., 2007) such as those that may exist in diverse, urban classroom settings. Acts of micro-
aggressions often go unnoticed as neither the perpetrator nor the victim is aware that an act of
micro-aggression has occurred.
In short, racial micro-aggression is commensurate with unconscious racism or an
uncritical habit of mind that justifies inequity and exploitation as the status quo as acceptable
(King, 1991). Many African American males are forced to negotiate through racial micro-
aggressions, which may be based in school policies, curricular programs, and teacher practices
(Howard, 2008). Micro-aggressions can cause stress in the form of racial battle fatigue (Smith,
2010) or the psychological, physiological, emotional, and behavioral toll placed on African
American males as they respond to daily racial micro-aggressions. The phenomenon of racial
battle fatigue could provide one of the explanations for African American males’ low academic
performance overall, and specifically, in mathematics.
Racism plays out in daily micro-aggressions within educational institutions. Solorzano et
al., (2000) define micro-aggressions as subtle insults (verbal, nonverbal, and/or visual) directed
towards people of color, often automatic and unconscious. Racial micro-aggressions result in a
negative racial climate, and inside this kind of climate, African American males struggle with
feelings of self-doubt and frustration, as well as academic isolation (Solorzano et al., 2000),
which may have an effect on African American males’ pursuit of mathematical success in the
classroom. Racial micro-aggressions, although pervasive, are seldom investigated (Solorzano,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 41
1998), yet they affect the environment in which African American males are expected to learn
mathematics.
Institutional Agents
The lack of social support from institutional agents who are capable of addressing the
need for educational resources that may empower or encourage African American males to be
successful is systematically problematic (Stanton-Salazar, 1997). White male students tend to
have access to the institutional agents who can offer and assist with students’ healthy human
development and general well-being, Algebra 1 success, mathematical identity development, and
the social integration for positive educational outcomes in Algebra 1. However, African
American males frequently lack access to those same institutional agents (Stanton-Salazar, 1997).
The need for institutional agents to support African American males may also be illustrated
through their underrepresentation in gifted and talented programs as well as their
overrepresentation in special education.
Special Education Placement
Racial, gender, cultural and linguistic biases remain integral aspects of the special
education process, particularly for African American males (Harry et al., 1994). The entire
special educational process is seriously biased against them from their first experiences in
schools through their disproportionate referral to, assessment for, and placement in special
education programs (Harry et al., 1984). In 2007, African Americans represented 12% of the
total population in the United States, but 20% of those aged 6 to 21 who were identified with a
disability, such as a specific learning disability, speech or language impairment, mental
retardation, emotional disturbance, autism, hearing impairment, and/or visual impairment.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 42
Whites represented 66% of the United States population in 2007, but 57% of those identified
with a disability (National Center for Education Statistics, 2010).
African American males are more likely to be classified as mentally retarded or suffering
from a learning disability and placed in special education than African American females as well
as peers of other ethnicities (Noguera, 2008). Special education placement is a serious matter for
two reasons: the stigma attached to being designated disabled and the likely detrimental outcome
of being removed from the mainstream of education and thereby losing the opportunity to catch
up or return to the general education classroom (Howard, 2014). African American males who
are placed in special education are often denied high-quality instruction, particularly in
mathematics and enrichment activities that are beneficial for students who often are already
behind academically (Howard, 2014).
The 2005 NAEP mathematics assessment showed that 43% of grade 4 students with
learning disabilities scored below basic compared to 17% of grade 4 students without learning
disabilities. Berry et al., (2011) assert that the development of computational fluency by third
grade is key in shaping a positive mathematical identity. Low math achievement on the 4th grade
NAEP may be the consequence of the inability or lack of effort of educators to foster a positive
mathematical identity by the 3rd grade for African American students with learning disabilities.
Further, special educational learning experiences are not providing opportunities for students to
meet state standards assessed in standardized testing.
African American males are disproportionally diagnosed with learning disabilities during
the primary grades, which represent crucial stages for the development of a positive
mathematical identity (Arnold & Doctoroff, 2003; Harry & Anderson, 1994; Judge & Watson,
2011). Students who are diagnosed with a learning disability not only suffer from the
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 43
development of a negative identification with mathematics, but they also often lack the proper
resources, instruction, and support necessary for success in mathematics (Judge & Watson, 2011).
African American males’ disproportionate placement in special education and the failure of
special education to ameliorate their real or perceived deficits represent another set of outcomes
that supports critical race theorists’ assertion that an inherently racist system of education in
America has failed to foster African American males’ mathematical success (Howard, 2014).
Teacher Education
Teacher education programs in the United States struggle to prepare teachers to meet the
mathematics needs of secondary students, including African American males (Milner et al. 2013).
Although the field of education made progress toward effective pedagogy and math teacher
preparation, it has not made sufficient progress in understanding education’s responsibility
toward students of color, particularly African American males. Reasons for this struggle may
include cultural differences, rapidly changing sociocultural landscapes in K-12 public schools,
and instructional practices of teachers. Some teacher educators and teacher education programs
have not adequately equipped teachers with the necessary pedagogical skills to teach middle
school mathematics in diverse classrooms (Milner et al., 2013).
One of the challenges faced by teacher education programs is the inconsistent transfer of
theory taught in teacher education programs to in-service practice. Flaxman & Passow (1995)
stated that during the previous 10 years, America had grown in diversity, and increased in single-
parent households, the number of children living in poverty, and the number of children with
parents who did not completed high school. Since some of these issues may continue to be
apparent in African American males’ households, the challenge teacher education programs face
is finding ways to encourage prospective teachers to consider these issues without developing a
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 44
deficit mindset (Flaxman & Passow, 1995), as teachers’ prior experiences and beliefs can affect
how they provide opportunities for their students in K-12 settings (Howard & Terry, 2010;
Milner, 2010). In addition, it is necessary to modify and reform schools and curriculum to
improve educational conditions, opportunities, and experiences without maintaining oppressive
attitudes, behaviors, and biases (Flaxman & Passow, 1995).
African American males’ mathematics experiences could benefit from a reform in teacher
education programs that includes the development of pedagogical skills and content knowledge
necessary to increase the depth of knowledge and conceptual understanding for all students
(Shulman, 1987; Kinaard & Kozulin, 2008). Teachers need to adopt pedagogy based on an asset
view of African American students’ capabilities instead of a deficit view.
Pedagogical Content Knowledge
Milner et al. (2013) discussed the content knowledge, as well as the pedagogical
knowledge that teachers should begin to develop in teacher education programs in order to be
prepared for diverse students. Ball et al., (2008) assert that this includes the knowledge of
content and the knowledge of content-specific pedagogy. Further, Ball et al. (2008) suggest that
teachers are not likely to be able to help different kinds of students learn if they do not know the
content well. Shulman (1987) states that, in addition to content knowledge, the teacher must
have knowledge of and adopt pedagogy that specifically facilitates student learning related to the
content. Magnusson et al. (1999) define pedagogical content knowledge as a teacher’s
understanding of how to help students grasp specific subject matter, which includes knowledge
of how particular subject matter topics, problems, and issues can be organized, represented, and
adapted to the diverse interests, abilities, and cultural experiences of learners. African American
males, who have consistently underperformed mathematically, should have access to teachers
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 45
who possess the mathematical content knowledge to present math in meaningful, descriptive
ways (Vygotsky, 1978), in part, by emphasizing reasoning, and using technology for simulations
and applications (Flores, 2007). African Americans unfortunately are less likely to have math
teachers who have at least a minor in mathematics.
In 2005, schools with 91-100% minority populations had an average of 16% math
teachers who were underprepared and lacked the necessary content knowledge to foster
conceptual mathematical understanding, while schools with 30% or less minority populations
had an average of 4% underprepared math teachers (Flores, 2007). In order to improve the
African American males’ mathematics achievement, it is important for underserved schools with
large populations of minorities to have qualified teachers who possess the mathematical content
knowledge that will present opportunities for these students’ success at higher mathematics
levels (Flores, 2007).
In an extension of Shulman’s (1987) studies, Ball et al. (2008) attempted to apply
pedagogical content knowledge to the teaching of mathematics. In a qualitative study, Ball et al.,
(2008) sought to answer three research questions: “What are the recurrent tasks and problems of
teaching mathematics? What do teachers do as they teach mathematics? What mathematical
knowledge, skills, and sensibilities are required to manage these tasks?” (p. 395). Mathematics
teachers need to know mathematics in ways that allow teachers to make mathematical sense of
student work, and are able to choose powerful ways of representing mathematics so that it is
useful to a range of students.
The knowledge of math content and how students learn content (KCS) represent teachers’
conceptual understanding of mathematics in connection with the manner in which students think
about, know, or learn mathematics (Hill et al. 2008). In a problem such as the addition of 43 + 7,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 46
the math teacher may have the conceptual understanding of the addition of 43 + 7, but students
without this same conceptual understanding may add the “7” to the “4” in 43 and reach the sum
of “113.” Teachers’ KCS represents both the teachers’ own conceptual understanding of the
addition of 43 + 7, in addition to students’ potential misconceptions of the addition of 43 + 7
(Hill et al., 2008). Therefore, it is important for teacher education programs to prepare math
teachers for urban schools by providing them with the necessary practice for developing the
content knowledge, pedagogical content knowledge, and knowledge of students’ metacognition
for teaching mathematics. Subject matter courses in teacher education programs tend to be
extensively scholarly and irrelevant to the practical day-to-day teaching of mathematics, and are
not aligned with the necessary content knowledge for teaching mathematics (Ball et al., 2008).
Mathematical Content and Pedagogical Knowledge
In addition to pedagogical content knowledge, prospective teachers seeking qualification
to teach secondary mathematics need to have mathematical content knowledge, or adequate
knowledge of disciplinary facts, procedures, and concepts (Hill, 2007). Studies have shown that
throughout the United States, many teachers of African Americans students, particularly males,
do not have the necessary content knowledge to effectively teach diverse groups of students.
Empirical research suggests that common knowledge of mathematics is related to, but not
equivalent to, specialized and advance knowledge of mathematics (Hill et al., 2004). Ball and
Bass, 2000; Leinhardt & Smith, 1985; Ma, 1999; Thompson & Thompson, 1994) identified
specific classroom situations requiring teachers to have deep content knowledge to facilitate
diverse students’ mathematics understanding of topics such as fractions, multiplication, division,
and rate or ratio to teach these topics to children. Teachers may, for instance, not only teach
students the procedure for reducing fractions (3/9 = 1/3) but also explain why the procedure
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 47
works (Leinhardt & Smith, 1985). The ability to explain in a language that is familiar to the
students is important.
Teachers need mathematics content knowledge as well as pedagogical knowledge to be
able to represent mathematical procedures and ideas using pictures and/or manipulatives.
Moreover, teachers need math content knowledge to appraise unusual or culturally familiar
student methods for solving computational problems and determine whether such methods would
be generalizable to other problems. In addition, teachers must inspect each student’s work,
determine what method the student is using to solve a mathematical problem, and then decide
whether these methods would transfer to other mathematical problems and challenges (Leinhardt
& Smith, 1985).
African American males tend to populate schools where teachers are the least qualified to
teach mathematics because of their weak content knowledge. Darling-Hammond (2010) and Hill
et al. (2004) sought to answer the question as to how teachers’ mathematical knowledge for
teaching is organized, and whether teachers’ mathematical knowledge for teaching can be
measured accurately. Some studies show that a teacher one standard deviation above average in
mathematical content knowledge would significantly boost his/her students’ mathematical
understanding.
Hill et al. (2004) showed that content knowledge for teaching mathematics consists of
more than the general knowledge of mathematics held by most educated adults. General
mathematics knowledge that is held by most adults is necessary for teaching math; however,
there is much more mathematical depth needed for teaching math than the depth of which most
adults possess. Further, Hill et al. (2004) assert that math teachers should know why
mathematical statements are true, how to represent mathematical ideas in multiple ways, how to
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 48
identify the math that is involved in conceptualizing and making meaning of definitions and
terms or concepts, and methods for evaluating or appraising mathematical methods,
representations, and solutions. In addition to deep mathematical content knowledge, knowledge
of students’ mathematical metacognition, and pedagogical content knowledge, teachers need
knowledge of students’ individual cultures to be able to recognize students’ cultures as assets in
developing positive mathematical identities (Milner et al. 2013).
Culturally Relevant Education
Cultural knowledge is derived from experiences, traditions, and social relationships that
students and teachers possess. It is directly related to various aspects of a person’s identity
including race, class, gender, sexual orientation, and religion (Milner et al., 2013). Culturally
relevant teaching involves pedagogy that allows students to develop intellectually, socially,
emotionally, and politically by using cultural referents to import knowledge, skills, and attitudes
(Ladson-Billings, 2009). The primary aim of culturally relevant teaching of African American
males is to assist them in maintaining their African American male identity while choosing to
excel mathematically (Ladson-Billings, 2009). Research in education suggests that there are
sociocultural, sociopolitical, and socio historical issues inherent to the incongruence between the
disproportionate number of Caucasian teachers and the increasing ethnic population, which may
decrease the opportunities for these students to receive culturally relevant mathematics
instruction (Graham & Erwin, 2011).
Milner & Smithey, (2003) found that teacher education students’ responses to discussions,
assignments, and activities centered on race at a classroom level ranged from being receptive to
the discussions, assignments, and activities, to reporting new levels of insights and consciousness
for their P-12 student needs. Some teacher candidates’ responses included being resentful and
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 49
not understanding why or how programs or accommodations for historically marginalized groups
are necessary. Teacher candidates often show resentment to the development of adequate racial
and cultural knowledge, and there is a lack of interest in class discussion and activities regarding
race and culture (Brown, 2004).
Some teacher candidates and teachers favor the infusion of cultural knowledge, as well as
tenets of culturally relevant education (CRE). However, standardized curricula and testing may
have marginalized CRE due in part to a failure to consider students’ culture, particularly African
American males, when adopting or developing curriculum and subsequent testing material.
Further, mathematics teachers find it challenging to embed culturally relevant mathematics into
their classroom curriculum due to a lack of exposure to concrete examples of such practices
(Aronson & Laughter, 2015). Aronson and Laughter (2015) attempt to address the need for
examples of CRE in a synthesis of culturally responsive teaching (Gay, 2010) and culturally
relevant pedagogy (Ladson-Billings, 1994) ideologies by sharing four markers for CRE based
on: “use of constructivist methods to create bridges that connect students’ cultural references to
academic skills and concepts, particularly mathematics, building on the mathematical knowledge
and cultural assets all students bring into the classroom, engaging students in critical reflection
about their own lives and societies, explicitly unmasking and unmaking oppressive systems
through the critical discourses of power” (pg. 5). However, it remains unclear how Aronson and
Laughter’s assertions apply to middle school mathematics for implementation in classroom
settings that include African American males.
Culturally Relevant Mathematics
Gay (2010) provides examples of CRE for mathematics. Culturally relevant mathematics
tends to incorporate interdisciplinary content into mathematics such as literacies and language,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 50
social studies, and technology. Culturally relevant mathematics utilizes cultural sites and sources
such as construction crafts, urban forms of transportation, taking trips, hair braiding, shopping,
star navigating, pattern designs, music, art, cooking, and games for teaching mathematical
knowledge, concepts, and skills (Gay, 2010). Students in these classes are encouraged to make
sense of math practices, address probing questions for deep thinking, embed imaginations, and
view mathematics from multiple perspectives (Gay, 2010). Unfortunately, as these suggestions
may add clarity to CRE practice, they do not address issues of the educators with deeply
embedded deficit mindsets and lacking the desire to implement activities that may enhance the
mathematical experiences of African American males. Further, these suggestions do not address
the issue of inadequate teacher preparation and/or teacher transfer of theories from pre-service
training to in-service practice. Increased emphasis on testing has also limited the amount of time
teachers have to implement culturally relevant mathematics.
There is a need for Algebra 1 teachers to consider social perspectives of mathematics
with cultural perspectives of mathematics. In addressing the perceived achievement gap between
African American males and their White peers, social and cultural perspectives are often missing,
which results in teaching more mathematics using previous strategies that are Eurocentric in
nature and fail to consider these students’ cultural assets (Kress, 2005). Considering the social
and cultural perspectives of Algebra 1 can offer access to Algebra 1 as it relates to other
academic disciplines (Kress, 2005).
The Algebra Project, which was developed by Moses and Cobb (2001), demonstrates the
effectiveness of connecting social and cultural perspectives of Algebra1. In the Algebra Project,
math teachers build on students’ social and cultural assets and develop lessons that are
interdisciplinary (Kress, 2005). An example of an activity from Moses and Cobb’s (2001) project
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 51
is the use of students’ knowledge of a city’s subway system. Lessons are designed around the
subway system, and connections are made between students’ prior knowledge of the subway
system to the algebraic analysis of the subway systems through the language of algebra (Kress,
2005; Moses & Cobb, 2001).
Moses and Cobb’s (2001) Algebra Project curriculum consists of five steps. First,
physical events include a trip to a place that is familiar to students. These trips may include a
transit system, students’ communities, or a city bus tour. Second, pictorial
representation/modeling includes a series of linked but abstracted representations of the physical
event. Third, intuitive language/people talk includes a discussion and/or report about the physical
event in the students’ common language. Fourth, structured language/feature talk refers to
selecting aspects of the experience and building the mathematics around those aspects of the
experience. Fifth, symbolic representation occurs when students construct symbols to represent
their ideas. In order to accurately implement the Algebra Project, teachers must rethink their
pedagogy, as they cannot implement direct teaching and/or superficial pedagogy that rely on
techniques to enhance rote memorization and mathematical shortcuts (Moses & Cobb, 2001).
Zeichner (2011) asserts that much of the research on diversity in teacher education in the
United States consists of individual studies by teacher educators about their own teaching
(Zeichner, 2011). Due, in part, to the need for extensive studies on the successful preparation of
math teachers for urban schools, and also to the inconsistent transfer of theories from teacher
education programs to the classroom setting, prospective teachers are ill-prepared to teach
mathematics to a diverse group of students (Zeichner, 2011). Some math teachers in California’s
public schools have neither the pedagogical aptitude nor an equitable cognitive mindset
(Bensimon, 2005), to address the mathematical characteristics of African American males who
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 52
struggle with mathematics (Graham & Erwin, 2011). Teachers implement pedagogy and
classroom behavior consequences from a Eurocentric and a deficit perspective toward African
Americans, and rarely make modifications or adjustments due in part, to a lack of cultural
competence (Ladson-Billings, 1994).
Teacher Qualifications for Teaching Math
United States secondary schools, particularly low-achieving schools and schools that
service African American males, have difficulty attracting and retaining high-quality math
teachers (Loeb & Reininger, 2004). These schools tend to systematically employ less-
experienced teachers with low levels of content knowledge for teaching math. Teachers in
schools that serve the greatest number of minority students tend to be the least qualified by
measures of certification, subject-matter background, pedagogical training, selectivity of college
attended, test scores, and/or experience (Darling-Hammond, 2010, pg. 43).
In a 2007-2008 Schools and Staffing Survey, high school teachers were asked whether
they were certified in, and if their major was associated with the subject they taught most often.
Twenty-five percent of the math teachers surveyed from schools with at least half African
American student enrollment reported having neither a certification nor major in mathematics,
while only 8% of the math teachers surveyed from schools with at least half White enrollment
reported having neither certification (U.S. Department of Education, 2010).
Ferguson (1995) found that Texas teachers’ examination verbal scores were lower in
heavily African American districts. Loeb and Reininger (2004) found that, within New York
City, only 16% of White students had teachers who failed the general knowledge certification
exam on their first try, whereas 26% of non-White students had such teachers. Ferguson’s (1995)
as well as Loeb and Reininger’s (2004) studies show that African American students are further
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 53
disadvantaged by inequities in the resources teachers bring to their classrooms. Hill’s (2007)
study that focused specifically on mathematics, which plays a key gatekeeping role for academic
and occupational advancement, found that math teachers with more mathematical course work, a
subject-specific certification, and high school teaching experience tended to possess higher levels
of mathematical content knowledge for teaching.
Inequities in California Teachers ’ Qualification.
Powers’ (2004) examination of California school data revealed that high-minority schools
had fewer fully credentialed teachers, more teachers teaching out of field, and less experienced
teachers than do low-minority schools. Further, evidence regarding California from the 2003
NAEP data (National Center for Education Statistics, 2011) shows that White students are
significantly more likely than African American students to have a teacher with a standard
teaching certificate. Only 2% of White 4th graders in California had teachers who reported
having an emergency credential, while 10% of African American students had these teachers.
These percentages at the 8th grade level were 6 % for White students and 19 % for African
American students based on the 2003 NAEP data.
African American males in urban schools are more likely to be taught by math teachers
who are unqualified, poorly qualified, lack proper certification, or teach out of field. They are
also the teachers with the fewest credentials and lowest college grades and test scores (Barton &
Coley, 2009; Moore & Lewis, 2012). In schools with a large African American population,
nearly 30% of teachers do not major or minor in the subject area they teach (Ford & Moore,
2013)
Inexperienced or novice teachers with fewer than 5 years of classroom experience are
more likely to teach in urban areas where high percentages of African American males are often
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 54
located and segregated (Ford & Moore, 2013). Teachers who lack qualifications for teaching
mathematics tend to have difficulty in teaching math to African American males, and are less
likely to increase their mathematics achievement because they do not have adequate training and
cultural competence. Inexperienced teachers, except in rare cases, adversely affect the quality of
mathematics instruction for these students, contributing to their low mathematics achievement
(Ford & Moore, 2013).
Inequities in teachers’ mathematical knowledge across student populations play a role in
partially explaining some of the perceived achievement gap because mathematically
knowledgeable teachers produce more mathematically knowledgeable students (Harbison &
Hanushek, 1992). Some middle and high school teachers’ lack of a fundamental understanding
of mathematics has led to inferior instruction (Hill and Lubienski, 2007). This lack of knowledge
is most likely the result of substandard preparation in their pre-service programs (Ma, 1999).
Teachers who lack adequate content knowledge for mathematics instruction, many of whom
teach African American male students, begin perpetuating the cycle of inferior mathematics
knowledge by producing generations of African American male students lacking the
fundamental concepts.
The research literature documents that teachers’ mathematical knowledge is positively
correlated with student achievement (Hill et al., 2005; Robichaux & Guarino, 2013). Since
African American males tend to populate schools where teachers are the least qualified to teach
mathematics, it is necessary for teacher educators to rethink the teacher education programs that
are responsible for equipping teachers with the necessary pedagogical content knowledge and
mathematics content knowledge.
Principles of Learning Math
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 55
Principles associated with learning math that should be presented to prospective teachers
of urban school students during pre-service teacher education are: engaging prior learning of K-
12 students, developing student understanding, knowing the role of factual knowledge and
conceptual understanding, and the importance of student self-monitoring or metacognition
(Donovan & Bransford, 2005). The mathematics understanding that K-12 students bring prior to
the start of their schooling can have a significant impact on their mathematics learning. When
students can connect what they are currently learning to accurate and relevant prior knowledge,
they learn and retain more (Ambrose et al., 2010). Many African Americans can engage in
informal mathematical problem solving when engaging in tasks such as shopping, analyzing
sports, cooking, and dieting, but are often unable to solve similar problems presented in the
context of the mathematics classroom (Donovan & Bransford, 2005). Instruction that bridges the
two worlds of home and school may lead to positive outcomes for African American males.
These practices are aspects of culturally relevant and responsive pedagogy.
African American males, as they are presented with the challenges of overcoming racial
prejudice, micro-aggressions, and teacher pedagogy that lacks cultural relevance, also face the
challenge of transferring informal mathematics success to the context of the mathematics
classroom. African American males possess mathematical-problem-solving resources in the form
of informal strategies and mathematical reasoning that could be applied to formal mathematics if
the link between informal and formal mathematics is provided through teacher pedagogy
(Donovan & Bransford, 2005). This is an important way to create a more familiar cultural
context for learning mathematics.
When the link between informal math and formal math is missing, individuals’ prior
learning through the development of inaccurate preconceptions can act as barriers to learning.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 56
Preconceptions are difficult for teachers to change because preconceptions may generally work
in certain contexts, although they may not necessarily be accurate (Donovan & Bransford, 2005)
If students’ preconceptions are not addressed directly, students often attempt to memorize
content, yet revert back to experience-based preconceptions (Donovan & Bransford, 2005).
Common mathematical preconceptions are: mathematics is about learning to compute,
mathematics is about following rules to guarantee correct answers, and some people have the
ability to do math and some do not. The preconception that some people have the ability to do
math and some do not is a serious widespread preconception in the United States and can
become a self-fulfilling prophecy, especially for African American males (Donovan & Bransford,
2005) whose experiences already cast doubt on their ability. Further, ability is assumed to be
more important than effort in the United States, and African American males are perceived to
lack the mathematical ability for success in mathematics (Donovan & Bransford; Ladson-
Billings, 1997; Stinson, 2013; Nasir & Shah, 2011).
Factual and conceptual knowledge are two components that lead to the necessary
conceptual understanding for success in mathematics (Donovan & Bransford, 2005). Conceptual
understanding does not occur with either factual knowledge or conceptual knowledge alone. In
order to develop mastery or a high degree of competence in mathematics, students must be able
to acquire factual knowledge, practice integrating the factual knowledge with conceptual
knowledge, and know when to apply what they have learned (Ambrose et al. 2010).
Students’ metacognition refers to their understanding of themselves as learners as they
process new information and build conceptual understanding (Donovan & Bransford, 2005).
Students must be able to assess the demands of a task, evaluate their knowledge and skills, plan
their approach, monitor their progress, and adjust their strategies accordingly in order to be
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 57
successful in mathematics (Ambrose et al., 2010). Unfortunately, these skills are neglected in
many schools and mathematics classes where African American males attend, due in part to the
prevalence of inexperienced, ineffective, under-qualified, teachers (Ladson-Billings, 1995).
Sociocultural Theory
Math education research often focuses on the individual acquisition of mathematics
knowledge outside the dynamics of the sociocultural context (Lerman, 2000), yet the
sociocultural structures in which mathematics teaching and learning are embedded can
significantly affect African American males’ mathematics achievement (Berry III, 2008; Khisty
& Chval, 2002; Weissglass, 2001). Algebra1 teachers who encourage students to explain and
justify their thinking in mathematics incorporate a sociocultural approach to teaching and
learning (Khisty & Chval, 2002; Steele, 2001).
When teachers’ pedagogy consists of direct teaching in a teacher-centered environment,
and students’ learning is reliant upon the teacher as opposed to a sociocultural approach where
students and their peers share their thinking and algebraic reasoning, the teacher’s views, biases,
and problem-solving strategies are forced on the students (Freire, 1993). Students within a
sociocultural approach share their algebraic reasoning while listening to their peers share their
thinking. In this sociocultural context, an algebraic culture for learning in the classroom can be
created (Steele, 2001).
An algebraic culture for African American males can be created when teachers present
an atmosphere where they can internalize the algebraic language, and openly function as
algebraic thinkers as they learn the algebraic discourse (Gee, 2001; Khisty & Chval, 2002; Steele,
2001). The connection between language and learning mathematics is apparent in this kind of
setting.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 58
Students, especially African American males who are seen as the other, need teachers to
socialize them into discourses of algebra learning. Classroom discourses are a means for
apprenticing them into receiving and producing the language of algebra as opposed to only
acting as consumers of the language (Gee, 2001). Stinson (2006) studied the sociocultural
discourses involving the agency of four African American men who were relatively successful in
K-12 mathematics. In their pursuit of mathematical success, the four African American males
from Stinson’s 2006 study were able to negotiate their learning through classroom sociocultural
discourses that viewed African American males’ mathematical success as normal.
The social language of mathematics used in the context of a mathematics classroom is a
specialized mathematics discourse that is not heard or used in the same context outside a
mathematics classroom. It is important for mathematics teachers to strategically select
mathematical words and place them in the correct mathematical contexts for their students
(Khisty & Chval, 2002). Algebra teachers cultivating the pedagogical discourse for algebra can
assist students in speaking and understanding the language of algebra (Khisty & Chval, 2002).
The development of a discourse for algebra is often missing in schools and classrooms for
African American males (Khisty & Chval, 2002). Teachers will need some understanding of
African American language to make the appropriate connections (Dyson & Smitherman, 2009).
In their 2002 study of the pedagogical discourses of mathematics teachers, Khisty and
Chval (2002) discussed the pedagogy of Ms. Martinez, a fifth grade mathematics teacher. Most
of Ms. Martinez’s students entered the class one to two grade levels below average in math, but
exited the class one to two grade levels above average. Ms. Martinez created a learning
environment that was conducive to the development of a mathematics discourse. Ms. Martinez
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 59
encouraged students to actively engage in problem solving through collaboration, oral and
written communication, justification, and independent thinking.
In addition, Ms. Martinez was an active participant in her students’ construction of
knowledge through questioning techniques and strategies for guidance. Ms. Martinez’s own
mathematical talk allowed her students to develop the language and discourse for mathematics.
Ms. Martinez demonstrated the importance of developing a sociocultural discourse that
encourages the development of interest and persistence in mathematics (Khisty & Chval, 2002).
The inability for many African American males to develop a sociocultural discourse that allows
them to build a strong mathematical identity is due in part, to inadequate or faulty mathematics
teaching in primary grades (Khisty & Chval, 2002).
Mathematics Identity Development
Middle school students, including African American males, develop mathematical
identities at the same time they develop racial and ethnic identities (Berry, 2003 & 2008). A
combination of students’ cultural models of understanding, social realities, and learning
strategies constitute their identities (Sfard & Prusak, 2005). Mathematics literacy can be linked
to a construction of identities based on the intersection of ethnic and mathematical identity
development (Martin, 2007).
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 60
Positive Math Identity
The development of a positive mathematics identity is essential towards students’
sustaining an interest in mathematics and developing persistence with mathematics. African
American males’ mathematics identities, as with those of other racial and ethnic groups, are
shaped by culture, community, and experiences with mathematics (Berry, 2003 & 2008). When
the context for identity development among African American males is one in which they are
depicted by society and schools as unintelligible, uneducable, and dangerous (Jackson & Moore,
2006) these depictions have an impact on their cultural and racial identities as well as on their
mathematics identity.
Also, during the time when African Americans are expected to develop their mathematics
identities, they are influenced by the sociopolitical and sociocultural context of schools. In this
context, they often encounter a dilemma whereby they may have to choose between dominant
culture in which they are viewed mathematically incapable and a mathematically competent
identity that veers outside of socially constructed norms (Nasir & Saxe, 2003; Oyserman et al.,
1995). Fordham and Ogbu (1986) found that some African American students and communities
looked unfavorably on African American students who perform well academically, perceiving
them as yielding to a Eurocentric culture. African American males themselves miss opportunities
to learn math because they subscribe to the values and beliefs that dictate a cool pose culture
(Majors & Billson, 1993). African American males may dismiss expending effort towards
mathematics achievement in exchange for receiving perceived greater social and psychosocial
awards from family and peers including other male youth both African American and White
(Jackson & Moore, 2008). These rewards encourage behaviors that devalue academic
achievement and depress educational aspirations, while condoning activities that contradict
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 61
traditional standards of success in academics, in particular, mathematics (Jackson & Moore,
2008).
Math Self-Concept
Academic self-concept and friends can enhance or diminish African American males’
academic functioning (Jones et al., 2012). Socially comparing one’s academic performance to
other students can increase or decrease one’s academic self-concept (Marsh, 1986). Students
with academically successful friends may have greater self-concepts if they believe their abilities
are comparable to those of their friends (Altermatt & Pomerantz, 2005). Thus, a negative
conception of friends’ mathematical ability can attribute to a negative mathematical self-concept
for African American males.
Jones et al. (2012) conducted a study to examine the relationship of math self-concept to
African American students’ math performance; they sought to answer research questions as to
the extent to which academic perceptions of friends and academic self-concept pertain to the
math achievement of African American adolescents and as to how the relationship between
academic perceptions of friends and academic self-concept differentially support math
performance by students in rural, suburban, and urban settings. Jones et al. confirmed the notion
that academic perceptions of friends are related to math self-concept, which in turn, is related to
math performance and may have an effect on the development of a positive mathematics identity.
Mathematics Experiences and Mathematics Identity
Berry et al. (2011) studied the mathematics and racial identities of African American
males in grades five through seven and found that four factors positively contributed to their
mathematics identity: the development of computational fluency by third grade, extrinsic
recognitions, relational connections, and engagement with the unique qualities of mathematics.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 62
The absence of a consistent realization of the four factors that contribute to a positive
mathematics identity constitutes a negative mathematics identity, which can in turn, lead to a
path of poor outcomes in mathematics achievement. However, addressing these factors requires
teachers with mathematics content and mathematics pedagogical knowledge that is culturally
relevant and responsive.
The degree to which African American males’ families are involved in their education
can influence their academic achievement and school behavior (Ford & Moore, 2013). Barton
and Cooley (2009) assert that urban African American families tend to participate less in their
children’s education than do families of other ethnic groups. Barton (2003) notes that 44% of
urban parents report feeling unwelcome in schools. It is reasonable to assume that
disenfranchisement of African American parents and the discounting of historically marginalized
groups by school personnel contributes to their low participation rates. Low participation rates of
African American parents may also be attributed to projections of a deficit-minded perception of
African American parents based on a belief that their parents do not care or lack the desire for
their children’s mathematics achievement (Ford & Moore, 2013). Further, it is difficult for
African American parents to participate meaningfully if they too had a weak school experience.
They do not know what is expected from the school for their children. Many African American
parents do not know how to participate in their children’s education in a meaningful way (Barton,
2003).
Berry (2008) studied eight successful African American boys and found that their parents
contributed to African American boys’ mathematics success. Seven of the boys’ parents
emphasized the importance of pre-school experiences and exposure to educational materials
early, as a way of ensuring that their initial mathematics experiences were positive. The parents
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 63
understood that mathematical success in pre-school could contribute to mathematics success in
primary and secondary grades. Berry discussed academic readiness in order to proactively solve
potential problems that parents perceived African American males could encounter early in
school. Seven of the boys reported feeling successful in elementary grades because they knew
their multiplication tables before their peers, were grouped with the smart kids for mathematics,
and were challenged during their pre-fourth grade years with assignments that were above their
grade level. The early development of a positive mathematics identity was instrumental in the
students’ navigation through an educational system that often fails to meet the cultural needs of
African American boys in mathematics.
The literature on African American male students in mathematics shows that African
American males often view racism as central to their mathematics learning experiences (Berry,
2008). One way in which racism plays out in mathematics education is through tracking, as
African American male students have reported being overlooked for gifted and talented
programs and disproportionately identified as ADHD and enrolled in special education (Berry,
2008). The presence of these phenomena in mathematics education reflects the issues facing
African American males in school and in society more generally.
Stinson (2006) argues that African American males continue to be stigmatized by a
deficit view of African American culture that is rife with the notions of moral and economic
poverty, and the notion that African American males tend to reject schooling. Successful African
American males were those who were able to navigate through a negative narration of African
American culture and attitudes towards schooling, in particular mathematics, in spite of
racialized obstacles that spread through their schooling experiences (Nasir & Shah, 2011).
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 64
Self-Efficacy
African American males, who are depicted as unable and unwilling to persist in
mathematics, tend to have math teachers who lack cultural competence and maintain a deficit
mindset. Disproportionate numbers of African American males who underachieve
mathematically could stem from cultural conflicts within the mathematics classroom (Siwatu &
Starker, 2010). In many underserved schools where African American males attend, cultural
conflicts arise when their culture differs from the teacher’s and/or school’s culture (Siwatu &
Starker, 2010). As a result, these students often suffer from low self-efficacy, which in turn,
leads to cycles of mathematics underachievement. Teachers who do not recognize the
relationship between culture and classroom behavior may not implement culturally responsive
teaching strategies that could enhance these students’ educational experiences and increase their
self-efficacy in the mathematics classroom (Gay, 2000; Siwatu & Starker, 2010)
Teachers and Self-Efficacy
Self-efficacy can determine the self-regulatory practices in which individuals engage as
they attempt to monitor their progression through specific task and goals, and consider whether
or not to persist (Pajares, 2006). A teachers’ failure to acknowledge cultural differences may
result in miscommunication between the student and his or her teacher, student withdrawal, low
academic achievement, and disruption of the learning environment (Bondy et al., 2007).
Teachers’ self-efficacy beliefs are related to teachers’ strategies for working with students whom
the teacher considers to be disruptive, which lead to unnecessary disciplinary decisions for
behaviors that may actually be appropriate (Siwatu & Starker, 2010). In the case of African
American males, removal from math classes for unnecessary reasons may result in further loss in
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 65
mathematics instruction, which may decrease African American males’ self-efficacy regarding
mathematics learning.
Math Self-Efficacy for African American Males
Students tend to try harder, persist, and perform better (Pintrich & Schunk, 2002) in
mathematics when they expect to do well. Thus, the African American male narrative that
portrays African American males as skilled in athletics and other areas of entertainment, but
lacking the intellectual aptitude to succeed in mathematics can influence their self-efficacy,
which, in turn, may limit their mathematical achievement. A common belief is that the only
option for these students to be considered moderately successful is through athletics and sports
(Noble, 2011).
Sports participation has been an avenue for high self-esteem, prestige, personal
affirmation, and a connectedness to school for African American males (Rowley et al., 2014).
However, African American males are often stereotypically perceived as naturally athletic but
naturally unintelligent (Rowley et al., 2014). The high level of athletic self-efficacy among
African American males can be a detriment to their academic self-efficacy, particularly in
mathematics. Thus, the possible positive contribution of sports to African Americans males’
academic identity and connectedness to school is reduced by the reinforcement of athleticism to
the narrative that presents African American males as mathematically unintelligent (Rowley et
al., 2014). In order to increase mathematics self-efficacy and rebuild African American males’
mathematical identity, it is necessary to reverse the mathematically incompetent narrative of
African American males and replace this narrative with the counter-narrative that suggests they
are mathematically thriving, competent, and high achievers (Noguera, 2012; Rowley et al., 2014).
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 66
Prior mathematics success can increase African American males’ self-efficacy for
mathematics, while prior failure can decrease African American males’ self-efficacy for
mathematics (Noble, 2011). Davis et al., (2002) found that increased self-efficacy can lead to
high achievement in academics, particularly mathematics. Thus, it is crucial to African American
males’ positive mathematical identity development for teachers’ mathematics pedagogy to be
implemented in a manner that leads to these students’ increased self-efficacy as early as in the
primary grades (Jonson-Reid et al., (2005). The increase in self-efficacy during primary grades
may help to improve their mathematics achievement prior to middle school, which could, in turn,
lead to a positive mathematics identity and improved mathematics outcomes during middle
school.
Noble (2011) used qualitative methods of research to study six mathematically successful
African American male students who attended a historically Black college and sought to answer
the question, “What is the influence of self-efficacy on the motivation of African American
males and how does this influence affect their academic achievement in mathematics at the
collegiate level?” (p.193). Noble found that the six African American male participants shared
the goal of achieving success in mathematics because they knew they were capable.
The participants in Noble’s (2011) study used vicarious experiences to judge their beliefs
in their mathematical abilities. Noble’s participants asserted that teachers, family members, and
peers’ examples of positive mathematical outcomes was instrumental in their increasing
mathematical self-efficacy. In addition, the participants in Noble’s study developed mechanisms
to continuously assess their efficacy judgments, and were able to rely on those attributes
throughout their academic career. The findings from Noble’s study are consistent with Berry’s
(2008) assertion that African American males must navigate through an educational system with
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 67
deeply embedded racist undertones, in order to successfully access the necessary resources and
institutional agents for favorable outcomes in mathematics. Clearly, this journey is less
problematic if African American males experience teachers who are adequately prepared with
content knowledge, content pedagogy, and the cultural competency to create classrooms in
which African American students can develop the mathematics identities and self- efficacy
regarding their ability to learn mathematics, particularly Algebra 1.
Summary
Throughout United States history, African American males have struggled to achieve
mathematics, and particularly in Algebra 1. Underlying causes of this Algebra 1
underachievement include racialized narratives and stereotypes that socially construct them as
unable to achieve in mathematics, systematic and institutional racism that fail to provide them
with the necessary resources to develop positive mathematics identities, and teacher education
programs that do not provide teachers with the necessary content, cultural, and pedagogical
knowledge for teaching math.
Critical race theorists assert that mathematically successful African American males have
been able to navigate through an inherently racist system of education to thrive mathematically,
by refocusing racialized narratives and developing positive mathematical identities. If the system
of education were reformed such that there was no need for African American males to exert
energy in navigating through racism, there would be more examples of positive mathematical
outcomes.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 68
CHAPTER THREE: METHODOLOGY
African American males continue to lag behind their White peers in academic
achievement. Chapter One stated the problem of their underachievement in mathematics,
particularly Algebra 1. It also presented the purpose of the study and the significance of the
study, along with research questions that enabled the researcher to clarify and shed further light
on this problem.
Chapter Two reviewed literature on the history of African American males’
underachievement in Algebra 1 and the underlying causes of these unfavorable outcomes. The
literature includes a critical race perspective about the contribution of traditional educational
structures to this populations’ unfavorable outcomes in Algebra 1. Critical race theorists assert
that racism, discrimination, and prejudice is so entrenched in the mindset of U.S. educators that
they often subconsciously carried out acts of discrimination and micro-aggressions through
policy, curriculum, and teacher pedagogy (Howard, 2014; Ladson-Billings, 1997; Noguera,
2008).
Purpose
In order to improve African American males’ Algebra 1 achievement, it is necessary to
closely examine the classroom experiences of African American males who experienced success
in algebra. Mathematically successful African American males can provide examples of how
others can be successful although the structure of California schools and teacher pedagogy may
inexplicitly coexist to produce unfavorable outcomes (Stinson, 2008). Yet, it is important to
identify teachers who can create equitable opportunities to learn mathematics. Through the lens
of CRT, this study sought to determine how teacher pedagogy may contribute to African
American males’ Algebra 1 success and favorable mathematical outcomes.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 69
Researchers often focused their studies on African American males who underachieved
in mathematics in an attempt to determine causes for their underperformance and lack of
favorable outcomes. Studies that focus on underachievement can inadvertently add to negative
perceptions of African American males as underperforming and unable to achieve and
experience favorable outcomes in mathematics. These studies may support deficit views which
blame these students for their own underachievement. Deficit views may, in turn, fail to identify
institutional causes for African American males’ underachievement in mathematics, particularly
Algebra 1.
By focusing on successful African American males through the lens of CRT, it was the
hope that this study would uncover ways in which they navigate California classrooms despite
institutional racism embedded in the policies, systems, and structures of U.S. and California or
how their navigation is facilitated by teachers who are culturally competent and who have the
appropriate pedagogy and mathematics content knowledge. This study sought to identify teacher
pedagogy that assists African American males as they attempt to achieve success in Algebra 1.
The study aimed to identify the practices of teachers who facilitate these students’ achievement
in Algebra 1, although they are operating in a system of mathematics education that is not
structured to promote a positive African American male mathematical identity. Two research
questions guided. the study.
1. What pedagogical content knowledge do secondary math teachers believe is necessary
for teaching Algebra 1 to African American males?
2. How can Algebra 1 teachers’ pedagogy support African American males in developing a
positive mathematics identity?
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 70
Research Design
A qualitative research method was used for this study. Qualitative research focuses on
how people view and interpret their experiences (Merriam, 2009). In order to collect data for a
qualitative study, the researcher can observe, interview, and/or analyze documents. These data
are generally collected in the participants’ setting, and the process of analyzing data is inductive.
The researcher uses the data to build concepts, hypotheses, or theories (Merriam, 2009). The goal
of qualitative researchers is to gather rich, descriptive information, in order to understand the
meaning that individuals or groups ascribe to a social phenomenon (Creswell, 2014).
The process of qualitative research is inductive, whereby researchers gather data to build
concepts, hypotheses, and/or theories. Thus, the sampling and population is smaller in
comparison to quantitative research where large amounts of data are collected and hypotheses
are tested for the purpose of generalization and replication of findings (Creswell, 2014; Merriam,
2009). A case study was used for this study. The purpose was to determine the methods by which
six African American males navigated the system of education that some critical race theorists
have described as inherently racist and Eurocentric in nature to achieve mathematical success.
Further, this study aimed to determine how teachers’ content knowledge and pedagogy may
enable African American males to access Algebra 1 curriculum and develop positive math
identities.
Sampling and Population
Purposeful and snowball sampling were used to select six high school African American
male students in grades 9 through 12, who successfully completed algebra as 8
th
graders and are
currently taking a mathematics class preferably beyond Algebra 1. In some cases, the students
may have passed Algebra 1 with a “C” or higher, but at the time of the study, may be repeating
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 71
Algebra 1, based on the school’s requirement that all entering 9
th
graders must repeat Algebra 1
at that school regardless of a previous grade. Additionally, two Algebra 1 teachers were selected
based on input from the student interviews. Pullman Catholic High School and South East Los
Angles High School (SELA) were chosen as the high schools from which the participants were
selected. Pullman Catholic High School is an all-male high school in which African Americans
represent 30% of the enrollment. South East Los Angeles High School is a coeducation high
school in which African Americans represent 8% of enrollment. The two schools demonstrate a
contrast in the percentage of African American students enrolled. These schools were chosen
based on their histories of producing mathematically successful students as well as high rates of
African Americans, particularly males, who were accepted to colleges and universities.
In addition, Pullman was chosen, in part, due to its close proximity to the researcher’s
school of employment and place of residence. Pullman was also selected because 70% to 100%
of their high school graduates were consistently accepted to college. The selection of the six
African American male students who participated in this study was based on grades of at least a
“C” in Algebra 1 courses, grades of “B” or higher in mathematics beyond Algebra 1, and
enrollment in 9th grade Algebra 1, or 10th, 11th, or 12th-grade enrollment in some class in the
math sequence above Algebra. These criteria served as evidence of African American male
participants’ mathematical success.
The teacher participants were chosen based on input from student interviews and/or
principal/administrator recommendations. The criteria for teacher recommendation was that they
taught one of the student participants selected or they have a record, compared to other teachers
in their school for the past 3 years, of producing a higher percentage of African American
students who meet the criteria set in this study for high mathematics achievement. Convenience
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 72
to the researcher and availability of the participants was a factor in determining the selection of
the teacher participants.
Participants’ identity remained confidential, as the researcher used pseudonyms to
represent them. All voice and audio recordings, observations notes, and interview data were only
used for the purpose of the study; the recordings, observation notes, and interview data were
discarded after the study was complete. Participants received gift cards in the amount of $20 for
participation in the study. The researcher offered to conduct professional development that is
related to the study and its findings to the staffs of the participating schools.
Data Collection
The researcher secured written permission from parents to interview the student
participants. The six students were interviewed to determine how they believe teachers’
pedagogy contributed to their learning in mathematics, particularly Algebra 1. Each of the
students was interviewed once for a period of 45 minutes to an hour at a pre-arranged time. The
students and researcher discussed the best available times for interviews with members of their
school’s administration and the students’ parents. The purpose of the student interviews was to
determine students’ perceptions of teacher behaviors that the students believe supported them in
their successful completion of Algebra 1.
The selected teachers were observed in their classrooms to identify the pedagogical
content knowledge, the subject matter content knowledge, and the culturally responsive and
relevant pedagogy they demonstrate in teaching Algebra 1. The researcher asked about and
observed other teacher behaviors that engage African American male students in active learning.
The interview and observation protocols were adapted from existing interview and observation
protocols for the purpose of answering the research questions from the study.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 73
Two of the four teacher participants were observed on two different occasions within a
period of one week. The observations took place during the class periods in which the teachers
had at least 6.16% African American male students assigned. The observations lasted for the
entire period. In addition to observations, the teachers’ classrooms were photographed with the
permission of the teachers, for evidence of whether the classroom setting, room environment,
and student work samples reflected teaching and learning the literature asserts fosters
mathematics learning.
Each of the four teachers was interviewed once in their classroom for a period of 50
minutes to one hour. The purpose of the interviews was to determine the extent to which the
teachers were able to articulate the pedagogy, pedagogical content knowledge, content
knowledge, and classroom environment that they employ in their teaching. Further, the
interviews were used to triangulate the data from the observations.
Parents of African American male participants were contacted, notified of the study, and
they gave permission to interview the student participants. Parents were notified that the students
would be interviewed once for a period of 45 minutes to one hour. Consent forms were given to
the parents and students. Principals were also contacted and notified of the study, and the length
of time for the interviews.
Principals gave permission to interview and observe teachers in the teachers’ classrooms.
In addition, teachers were also granted permission to be observed and interviewed in their
classrooms. An information sheet was provided to the teachers that explained the overview and
purpose of the study.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 74
Instrumentation
The researcher conducted semi-structured interviews to the student and teacher
participants based on the research questions. The semi-structured interview questions were
adapted from pre-existing interview and observation protocols used in similar previous studies.
The interview and observation protocols were used in Kirkwood (2012) study on successful
African American males in a suburban middle school. The protocols are included in the
appendices of this study. The researcher used an audio recording device with the permission of
the participants, along with notes taken during interviews, to capture the interviews. Interview
questions were semi-structured to allow probing for deeper and detailed answers.
Table 3
Methods
Research Questions Observations Interviews
1) What pedagogical content
knowledge do secondary math
teachers believe is necessary
for teaching Algebra 1 to
African American males?
Teachers

Teachers
2) How can Algebra 1
teachers’ pedagogy support
African American males in
developing a positive
mathematics identity?
Teachers’
classrooms

Photographs
Teachers
Students

The student interview protocol consisted of 26 questions that were modifications of the
Kirkwood (2012) study to reflect the intent of the research questions, for the purpose of
gathering rich, descriptive data. The teacher interview protocol consisted of 27 questions that
were also modifications of the Kirkwood (2012) study to reflect the research questions and the
intent of the study. In addition, the observation protocol consisted of a pre-existing classroom
observation form that allowed for scripting of what the researcher saw and heard while observing
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 75
the classroom. The scripting content was later analyzed using a checklist. The interview and
observation protocols were placed in the appendices. Observations were quietly recorded in a
scripting form that captured the discourses and activities taking place on the part of the teacher
and the teachers’ interactions with students. The scripting form was used for the purpose of
analyzing the observational data by connecting teacher actions to a checklist that was used to
identify specific teacher pedagogy that coincides with student beliefs on teacher pedagogy that
fosters mathematical success.
Data Analysis
According to Creswell (2014), there are six steps for analyzing data in qualitative
research: organize and prepare data for analysis by transcribing interviews and re-writing notes,
look at all data and begin to find consistency, code the data into chunks for discernment, use
coding to develop categories and themes for analysis, address how description and themes will
be represented in a qualitative narrative, and use the narrative to discuss your findings and make
interpretations.
Data from the interviews were transcribed, coded, and analyzed in relationship to the
research questions. Notes taken during the interviews to capture elements that are unable to be
recorded via recording device such as gestures and facial expressions were rewritten and noted.
Field notes taken during classroom observations were typed and surveys were summarized. The
scripted observations were analyzed by comparing the scripting details to a research-based
instrument that identifies elements of effective mathematics teaching.
After the interviews were transcribed and observations were typed, themes were noted
and coded in relation to each research question. Further, findings were examined in connection
with prior research on mathematically successful African American males and used to make
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 76
recommendations for improving their mathematics achievement in Algebra 1. Recommendations
were made for further research on improving their mathematics achievement.
Credibility and Trustworthiness
Merriam (2009) describes internal validity as the extent to which the findings from the
research is congruent with reality. Maxwell (2013) states that methods and procedures are
essential to the process of ruling out validity threats and increasing the credibility of conclusions.
The researcher will incorporate the following strategies suggested by Creswell (2014) to increase
the level of reliability and validity: triangulation of the data, the use of rich, thick descriptions,
clarification of biases, and presentation of negative or discrepant information.
Clarification of Biases
The researcher stated the researcher’s personal identifications with the participants in
order to clarify potential biases that may affect the validity and reliability of the study. The
researcher’s participants were secondary school math teachers and mathematically successful
African American males. The researcher can be considered a mathematically successful African
American male since the researcher’s academic records may be on par with those of the
participants. In addition, the researcher was a middle school math teacher and has had both
mathematically successful and unsuccessful African American male students. It is possible that
the researcher’s data was analyzed and/or interpreted based on influences from past experiences.
Consistent self-reflection throughout data collection and data analysis helped to offset possible
influences due to personal biases.
Presentation of Negative or Discrepant Information
The researcher attempted to include information that may be oppositional to expected
results or information from the literature. Creswell (2014) asserted that real life is composed of
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 77
different perspectives and discussing contrary information adds to the credibility of an account.
The researcher sought to include information from participants that may or may not contradict
theories that were used to guide the research.
Ethical Considerations
Merriam (2009) states that the protection of subjects from harm, right to privacy, the
notion of informed consent, and the issue of deception all need to be considered ahead of time.
These issues were considered during the selection of the participants. Participants were informed
of all expected means for collecting data. In addition, the participants interviewed were notified
of the equipment that was used for interviews, the purpose of the interviews, and how the
interview data was analyzed. Parents of all student participants signed consent forms and were
notified that their names were not used, and the data was only used for the purpose of completing
the study.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 78
CHAPTER FOUR: FINDINGS
The purpose of this study was to determine how teacher pedagogical content knowledge
can support African American males in their development of positive mathematics identities with
a focus on teaching and learning in Algebra 1. The study was guided by the following research
questions:
1. What pedagogical content knowledge do secondary math teachers believe is necessary
for teaching Algebra 1 to African American males?
2. How can Algebra 1 teachers’ pedagogy support African American males in developing a
positive mathematics identity?
Data were collected on the campuses of SELA and Pullman Catholic High School, both
in the Los Angeles area. SELA is a public high school that includes grades 9 through 12. It is
87% Hispanic, 8% African American, 1% White, and less than 1% Asian. Many of the
mathematically successful African American students complete Algebra1 in middle school and
are enrolled in Geometry at SELA upon entering the 9th grade.
Fifty-six percent of the 9th graders at SELA scored proficient or higher on the CST for
Geometry in 2013. On that same test, 54% of the African American 9th graders at SELA scored
proficient or higher. Statewide, 45% of 9th graders scored proficient or higher, but only 25% of
African American 9th graders did so. These data show that SELA’s African Americans were on
par with their entire school’s 9th grade geometry scores on the 2013 CST, but exceeded the
scores of the African American 9th graders in California by 9%.
Pullman High School of Los Angeles is an all-male Catholic High School located in the
Los Angeles area. Pullman High School is 67% Hispanic and 28% African American, and 78%
of the graduating class of 2015 were accepted to a 4-year college. Pullman High School has
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 79
been a member of the Cristo Rey Network of schools since 2002. The Cristo Rey Network
consists of 30 Catholic college preparatory schools that focus on the education of
underrepresented urban youth.
Participants
Table 4
Student Participants
Student
Participant
High School
Attended
High School
Classification
Grade
Received
in Algebra
1
Math Course Enrolled in
During the Study
Corey SELA Junior B Geometry
Drew SELA Senior A Pre-Calculus
Quentin SELA Senior B Pre-Calculus
DeAnthony SELA Junior B Algebra 2
Emmitt Pullman Catholic
High
Freshman C Algebra 1
Mike Pullman Catholic
High
Sophomore B Geometry

The participants for this research were two Algebra 1 teachers and four African American
male students from SELA as well as two Algebra 1 teachers and two African American male
students from Pullman Catholic High School. The Algebra 1 teachers from SELA were Mrs.
Pedrosa, who was in her 9th year of teaching and Mrs. Reyes, who was in her 21st year of
teaching. Mrs. Pedrosa had taught mostly Algebra 1 and Algebra 2, while Mrs. Reyes has taught
math at the 6
th
, 7
th
, and 8
th
grade level as well as Algebra 1 and Algebra 2. The students from
SELA High were Corey, a junior enrolled in geometry who received a “B” in Algebra 1; Drew, a
senior who had taken pre-calculus during the previous year, and received an “A” in Algebra 1;
Quentin, a senior who was enrolled in pre-Calculus and received an B in Algebra 1; and
DeAnthony, a junior enrolled in Algebra 2 and received a “B” in Algebra 1.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 80
The Pullman High School teacher participants were Mrs. Rivers, who was in her 5th year
of teaching Algebra 1 and Mr. Zody who was in his 1st year of teaching Algebra 1. The student
participants were Emmitt, a freshman enrolled in Mrs. River’s Algebra 1 course who received a
“C” on the first semester report card for Algebra 1, and Mike, a sophomore who was enrolled in
Mr. Zody’s Geometry course who received a “B” in Algebra 1.
Table 5
Teacher Participants
Teacher
Participant
High School Years of
Experience
Subjects
taught
Student
Participants
enrolled in
course
Participated in
classroom
observations
Mrs. Reyes SELA 21 Algebra 1 and
Algebra 2
None No (Math
Coach)
Mrs. Pedrosa SELA 9 Algebra 1 and
Algebra 2
None No (declined)
Mrs. Rivers Pullman
Catholic High
5 Algebra 1 Emmitt Yes
Mr. Zody Pullman
Catholic High
1 Algebra 1 and
Geometry
Mike Yes

Each of the participants was interviewed. However, only Mrs. Rivers and Mr. Zody of
Pullman High School agreed to allow classroom observations. They also agreed to allow the
research to take photographs of their classroom. In addition, Mrs. Rivers, who was also the math
department chair, agreed to allow the researcher to have a copy of the study guide for the end of
the year assessment that the students were preparing to take in both Mrs. Rivers and Mr. Zody’s
Algebra 1 courses. Mrs. Pedrosa of SELA declined participation in classroom observations,
stating that there was a lot going on due to the school year being close to ending. Mrs. Reyes did
not participate in observations because Mrs. Reyes was a math coach and did not teach any
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 81
classes during the time. Mrs. Reyes stated that she participated in demonstration lessons as a
math coach.
Equations and Functions
The California Common Core state standards curriculum for Algebra 1 consists of four
conceptual categories: Number and Quantity, Algebra, Functions, and Statistics and Probability.
The conceptual category of Algebra consists of two domains: “creating equations” and
“reasoning with equations and inequalities.” Standards related to the analysis and interpretation
of graphs and functions are embedded within the four domains, particularly algebra and
functions. Embedded within these domains are standards related to analyzing and interpreting the
graphs of equations and functions (California Department of Education, 2013). The teacher
participants’ focus was on analyzing and interpreting the graphs of equations and functions.
Throughout the interviews and observations, the teacher participants mentioned equations,
graphs, and functions, as concepts they deemed vital for success in Algebra 1 and preparation for
higher levels of mathematics.
Themes for Research Question 1
The following themes were evident in relationship to the pedagogical content knowledge
that the teacher participants considered necessary to effectively teach Algebra 1 content to
African American males: math content knowledge beyond Algebra 2; developing a growth
mindset as opposed to a fixed mindset for students; and creating an interactive environment that
is culturally responsive for African American males. Math content knowledge beyond Algebra 2
is needed for the effective teaching of Algebra 1 content; particularly graphing equations, and
interpreting/analyzing the graphs of equations and functions. It is necessary for Algebra 1
teachers to determine whether or not their students, particularly African American males, have a
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 82
growth mindset upon entering their Algebra 1 course. If it is evident that students’ enter an
Algebra 1 course with fixed mindsets, Algebra 1 teachers should be able to develop growth
mindsets through their pedagogy. In addition to having math content knowledge beyond Algebra
2, and possessing the pedagogical skill to develop growth mindsets, Algebra 1 teachers should be
able to create an interactive environment where African American males’ culture is viewed as an
asset to learning mathematics.
Conceptual understanding. The teacher participants assert that teachers’ conceptual
understanding of the graphs of equations and functions should be well beyond that of the
students. They stated that teachers should have a deeply embedded knowledge and understanding
of subject matter and pedagogy in order to present lessons to students in a manner in which
students will understand. In addition, teachers must address students’ mathematical errors and
misconceptions. Further, teachers need to know the best pedagogical means for assisting
students in learning Algebra 1 content. Interview and observational data confirmed that the
teacher participants considered the analysis and interpretation of the graphs of equations and
functions to be crucial to students’ preparation for higher levels of mathematics such as geometry,
algebra 2, trigonometry, and calculus.
Teachers should be able to assist their students in converting their mindsets from a fixed
mindset to a growth mindset. Students with a growth mindset are more likely to persevere
through challenges, and to view algebra 1, particularly interpreting/analyzing the graphs of
equations and functions, as mathematics that can be learned by all who exert energy and effort.
In addition, students with a growth mindset, who understand the ways in which they can become
empowered to learn and participate in mathematics, are more likely to study and complete tasks
outside of school hours, and view mistakes as opportunities for further growth. Interviews and
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 83
observations of teacher participants supported the notion that they believe teachers should be
able to support their students in developing a growth mindset for learning algebra content.
Teachers also showed agreement that teachers of all students, particularly African
American students should have the pedagogical knowledge to create a classroom environment
that is interactive and culturally responsive to African American males learning Algebra1. In
creating an interactive environment, teachers should be able to connect Algebra 1 to their
students’ culture, particularly African American males, and make Algebra1 content relevant as
teachers view African American males’ culture as an asset for learning Algebra 1 content.
Content Knowledge Beyond Algebra 2
The teacher participants assert that teachers should know some calculus, and, minimally,
have conceptual understanding of Algebra 2 in order to effectively teach Algebra 1 to students in
an urban school setting, particularly African American males. Teachers must be able to
manipulate the mathematics in a manner that best fit the level of conceptual understanding of
students who are in their first year of algebra, particularly African American males. Since
African American males have a history of underperformance in Algebra 1, it is crucial to their
mathematics success beyond Algebra 1 that teachers are able to address common mathematical
misconceptions, and effectively implement lessons for conceptual understanding of Algebra 1
content. Conditions under which math is taught in urban schools where large numbers of African
American students attend include high teacher turnover rates, a disproportionate number of
teachers with less than five years’ experience, high administrative turnover, and elementary and
middle school teachers without strong mathematics backgrounds. Therefore, they are more likely
to have developed misconceptions about mathematics or gaps in their mathematics knowledge
(Barton & Coley, 2009; Flores, 2007; Hill, 2007; Moore & Lewis, 2012). They need teachers
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 84
who can close these gaps and address misconceptions as they learn new math concepts. Teachers
made specific comments around these themes.
Mrs. Rivers. Mrs. River’s earned an undergraduate degree in secondary education, math
and German. She states that she has taken “lots of math pedagogy courses.” In addition, Mrs.
Rivers stated that she has had extensive professional development through a university whose
education program is connected to Pullman High School. Mrs. Rivers asserted that teachers
should have the minimum of an undergraduate degree in mathematics to effectively teach
Algebra 1 content. Mrs. Rivers responded to the question of how she would rate the depth and
quality of her Algebra 1 content knowledge on a scale of 1 to 5, 1 being minimally
knowledgeable and 5 representing highly knowledgeable by stating the following:
I would say 4. I’d say it because if I had a graduate degree in math…My graduate degree
is in German, but I think my undergrad degree in math is really giving me what I need
especially to teach Algebra 1 and to have a good understanding of how to present that
content to my students.
Mrs. Rivers asserted that teachers need to have deep content knowledge in order to teach
topics related to solving equations and functions in a manner that will yield deep conceptual
understanding for their students. Teachers should be able to correct mistakes and address
misconceptions that students may have maintained from elementary and middle school
mathematics. Teachers’ mathematical knowledge is positively correlated to student achievement
(Hill et al., 2005; Robichaux & Guarino, 2013). Nearly 30% of teachers who teach in schools
with large populations of African American students do not have a major or minor in the subject
area in which they teach (Ford & Moore, 2013). More than 50% of California’s high school math
teachers lack a major or minor in mathematics (Powers, 2004); and 8th grade students whose
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 85
teachers were certified in secondary mathematics scored 14 points higher on the NAEP
mathematics assessment than those students whose teachers did not have secondary mathematics
certification. Mrs. River’s responded to the question regarding what she thinks are some of the
reasons there has historically been a performance gap mathematically between African American
males and other ethnic groups and genders by stating,
I think that some of those performance gaps are really based on the foundational skills
that they’re getting in elementary and middle school. I think a lot of the times, by the
time they come to high school, they’ve been in schools or school districts where they’re
not getting the highest level of content knowledge that maybe they should be getting.
Maybe they have math teachers, especially at the elementary level where math wasn’t
their thing, right.
They don’t feel comfortable teaching it to that deep understanding. By the time
they get to high school, I think, because of a lot of the districts that they sometimes come
from, there’s already a gap there and then you’re spending your high school years trying
to bridge that gap. You’re mostly doing extra work as a high school teacher trying to get
them where they need to be in terms of your high school curriculum. Also, trying to
address those gaps that may exist already from the elementary and middle school level.
Since Algebra 1 content consists of manipulating, analyzing, and interpreting equations
and functions, Mrs. Rivers further discusses the foundational skills that African American males
may lack due, in part, to inept and inadequate teaching from previous grades. Mrs. Rivers states,
I think that the biggest thing for me is really the standards for mathematical practices. If I
have a student that comes in and understands how to persevere in problem-solving,
understands how to analyze and critique the reasoning of someone else. They’re probably
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 86
going to do well in my classroom. In terms of math foundational skills, I would really say
the big thing for me is just number sense. It’s not even like they can solve an equation or
they can do this. It’s really that basic number sense. They understand what numbers mean.
For my students, a gap that we deal with is the understanding of negative numbers.
Understanding what a negative number is, comparing quantities of negative numbers like,
“What’s greater, -10 or -5?” They really struggle with that. Fractions, decimals, really
feeling like they have the confidence to deal with those but also to understand how they
work. Then, to understand inverse operations. It’s something that a lot of my students
struggle with and the ones who do understand inverse operations tend to do really well in
class. Because then they can do things like solve equations, they can manipulate
equations, they tend to be more successful.
Mrs. Rivers alluded to elementary and middle school teachers’ ill preparing students for
high school math, particularly Algebra 1, and she stated that students often lack the conceptual
understanding of number sense that is necessary to solve and graph equations. Mrs. Rivers also
stated that students do not understand negative numbers, fractions, and decimal. Due, in part, to
the lack of preparation for Algebra 1 by elementary and middle school teachers, Mrs. Rivers
asserted that some students, including African American males, do not enter her Algebra 1
course with the necessary foundational skills for Algebra 1 success. Harbison & Hanushek
(1992) asserted that teachers’ mathematical knowledge plays a role in partially explaining some
of the perceived achievement gap, as mathematically knowledgeable teachers produce more
mathematically knowledgeable students.
Equations, graphs, and functions. Mrs. Rivers showed that her focus was on analyzing
and interpreting the graphs of equations and functions. She stated that she would like to have the
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 87
students enter with the foundational skills such as operations with fractions and decimals, and a
strong number sense, which includes the conceptual understanding of integers, to be able to solve
equations. It is necessary for elementary and middle school teachers to have the conceptual
understanding of the mathematics necessary for preparing students to solve and graph equations.
Mrs. Rivers stated that the foundational skills that students should have upon entering Algebra 1
includes those skills that are necessary for solving and graphing equations, such as number sense,
which includes the conceptual understanding of fractions, decimals, and integers. The pictures
below show her students’ work on solving equations and analyzing and interpreting the graphs of
equations and functions. It was necessary for Mrs. Rivers’ to have sufficient content knowledge
on solving and graphing equations in order to provide the instruction that students needed for the
conceptual understanding of solving and graphing equations.

Figure 1. Graphical Models

ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 88

Figure 2. Mind Map

ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 89

Figure 3. Final Exam Topics
Figures 1 and 2 are examples of student work comparing graphical models of three types
of functions: linear, exponential, and quadratic. Mrs. Rivers states that teachers need the
pedagogical content knowledge of equations in order to adequately teach and assess students’
degree of conceptual understanding of the mathematics involved with presenting and analyzing
graphical models of functions. Figure 3 shows the topics that were covered on the final
examination for Algebra 1. Functions, graph models, and solving/graphing linear equations
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 90
represent focal points of Mrs. River’s Algebra 1 course as well as heavy representation from the
California Common Core content standards.
Mr. Zody. Mr. Zody has an undergraduate degree in economics and is in his first year of
teaching Algebra 1. At the time of this study, he was enrolled in a credentialing program for
math education. When asked to rate his perception of the depth and quality of his math content
knowledge on a scale of 1 to 5, Mr. Zody rated the depth and quality of his math content
knowledge at 4 or 5. He stated,
I’ve gone through the calculus sequence and statistics and upper division class and
statistics. At the high school level, I feel I would consider myself a 4 or 5 in terms of
knowing it all and understanding where the math goes in order to prepare the students for
college.
Mr. Zody asserted that he feels prepared and has adequate content knowledge for
teaching Algebra 1 content to African American males. Mr. Zody credited his high school
preparation for his algebra content knowledge. Mr. Zody further stated that he did not receive
much mathematics preparation during college since he majored in economics, and his current
math-education credentialing program focused on both general and content pedagogy. Mr. Zody
stated the following regarding the math-education credentialing program:
One, the biggest thing with Common Core is collaborative learning, which I don’t agree
with in most cases, especially in Algebra. In a lot of cases, there is one way to do it.
There are different ways to approach it, but there’s only one way to do that. I really
dislike the idea of collaborative learning. I’m teaching students something new or
especially in this area, they are coming in below grade level. Why am I going to have
them work together if they don’t even have the foundation? They’re going to spend 5, 10,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 91
15 minutes trying to see if they get it, and, more times than not, they don’t because it’s a
new concept. It’s abstract. The credentialing program really emphasizes collaborative
learning, and that’s why I give it a 1. Maybe I’m just not paying attention to all the
pedagogy and strategies, but, yeah. The credentialing program I feel like it doesn’t really
focus on, in terms of mathematics, the need for mathematics.
Mr. Zody gave the credentialing program a 1 on a scale of 1 to 5 in terms of preparing
prospective teachers to teach math content in urban schools, specifically to African American
males. Mr. Zody did not display much confidence in credentialing programs. He stated that he
had learned much of his pedagogy through educational experiences such as tutoring, experience
as a para-educator, and summer youth camp experiences.
Milner et al., (2013) assert that teacher education programs do not properly prepare
teachers to meet the mathematics needs of secondary students, including African American
males. There has been little progress in recent years of teacher education programs to effectively
prepare prospective teachers to teach secondary school mathematics to students of color,
particularly African American males. These data support Mr. Zody’s notion that credentialing
programs do not properly prepare prospective teachers to teach math content in urban schools,
especially to African American males. Hill (2004) asserted that the content knowledge that
teachers need for teaching mathematics consists of more than general knowledge of mathematics,
but a deep conceptual knowledge in great depths in order to teach students, particularly those in
an urban school. Math teachers should be able to communicate to their students why a particular
math statement is true, how to represent mathematical ideas in multiple ways, how to identify the
math that is involved in conceptualizing and making meaning of definitions and terms or
concepts, and methods for evaluating or appraising mathematical methods.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 92
Mr. Zody did not discuss means in which he incorporated students’ prior knowledge into
his mathematical instruction as he stated that there is only one way to teach Algebra 1. When
students, particularly African American males, can connect mathematics to accurate and relevant
prior knowledge, students retain and learn more (Ambrose et al., 2010). Therefore, informal
mathematical problem solving associated with tasks such as sports analysis, cooking, shopping,
and dieting, should be embedded within Algebra 1 instruction. When the link between informal
math and formal math is missing, individuals’ prior learning can act as a barrier to new learning
due to students’ development of inaccurate preconceptions.
Further, Algebra 1 teachers are more effective when they encourage students to explain
and justify their thinking in Algebra 1, and share their reasoning while listening to their peers
share their thinking (Steel, 2001). It is through a sociocultural context that an algebraic culture
for learning in the classroom is created, as students, particularly African American males who
are often denied the opportunity to learn Algebra 1 in a sociocultural context, can internalize the
algebraic language and openly function as algebraic thinkers (Steele, 2001). In addition, teachers
are able to develop an understanding of African American language which enables them to
connect the culture of African Americans, including their language, into a discourse for Algebra
1.
Mr. Zody asserted that some knowledge of calculus should be a minimum requirement
for secondary school teachers to effectively teach Algebra 1. Algebra 1 teachers will have many
questions from their students regarding algebra and the teacher will need a deep conceptual
understanding of algebra in order to answer algebra-related questions in a manner that will help
their students develop their own conceptual understanding. Mr. Zody expanded on his thoughts
by stating the following:
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 93
I feel like you definitely need the calc sequence. Algebra is the basis, the foundation of
mathematics. You have the different theories, but the theory goes into an equation, which
is combining like terms like we see here, combining like terms, creating the equations for
different functions. I feel like you definitely need the calc sequence in order to be the
most effective, in order to make sure that the Algebra is clear. Some teachers, when they
did have restrictive requirements, they just taught it because that’s what the textbook says.
When the students ask a question, they can’t answer that. I feel like it’s the intrigue and
the ability for them to wonder and be able to answer that, and which pushes them even
further. I think that’s the most important thing. I feel calc sequence is a basic, in my
opinion, skill in order for you to be the most effective.
Hill’s (2007) study supports Mr. Zody’s notion that teachers need a minimum of calculus
in order to effectively teach Algebra 1. Hill (2007) found that math teachers with a subject-
specific certification tend to be more prepared for teaching Algebra1 content, as they possess
higher levels of mathematical content knowledge for teaching. Further, teachers’ mathematical
knowledge is positively correlated to students’ mathematical achievement (Hill et al., 2005;
Robichaux & Guarino, 2013). Harbison & Hanushek (1992) assert that teachers who are
mathematically knowledgeable are more likely to produce mathematically knowledgeable
students.
In a fashion similar to Mrs. Rivers, Mr. Zody focused on analyzing and interpreting the
graphs of equations and functions. During classroom observations, Mr. Zody consistently
circulated through the classroom to check on the understanding of his students. The students
were completing error analysis activities from a portion of their final exam. The algebraic
concepts that the students were analyzing consisted of equations, graphs, and functions.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 94
During classroom observations, Mr. Zody fluctuated between whole group and
cooperative learning strategies. Although Mr. Zody stated during the interview that he preferred
to teach whole group instruction and had little confidence in cooperative learning, Mr. Zody’s
students were placed in a setting where students could collaborate as a group, in pairs, or
complete assignments individually.
Mr. Zody demonstrated that he had adequate content knowledge for the topics that he
covered included functions, solving equations, and graphing equations. During whole group
discussions, however, the students were quiet, but the degree to which they were listening and
following Mr. Zody’s algorithms as he explained his methods for arriving to correct answers was
not clear. Mr. Zody rarely questioned students individually during whole group, as the majority
of the classed were quiet and seemed to be focused on the topic. However, during the latter part
of the instructional day, the final class period, the students seemed to be more focused on the
assignments when they worked in cooperative learning groups. This supports the notion that
students learn more and are able to speak with an Algebra 1 discourse, when they have the
opportunity to share thoughts and ideas with their peers, although there was not much evidence
of an Algebra 1 discourse. There was one instance where Mr. Zody attempted to explain the
meaning of exponents. Figures 4, 5, and 6 are examples of the problems that Mr. Zody explained
during the class session. Mr Zody stated:
If we add or subtract, does that affect our exponents? What are exponents? It means
multiplication- X*X*X*X, that’s X to the fourth. You are adding X times X times X
times X. Same exponent makes it like terms. If it does not have the same exponent, you
cannot combine it. Same variable and exponent. When you simplify, you make it simpler,
you do not change it, you should be able to plug a value and get the same thing.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 95
This class session was a review in preparation for the final exam, and Mr. Zody used
Algebra 1 language such as variable, exponent, like terms, simplify, and plug. If an Algebra 1
discourse was developed with the students, the students would have responded by using those
same terms. There was no evidence that the students had developed a discourse for algebra as the
students rarely responded by using algebraic terms. Further, Mr. Zody used the word “plug” as
opposed to the word “substitute.” Mr. Zody asked if students knew what exponents are, and,
later, if they knew what like terms are. He followed both questions by responding with the
definitions that he wanted the students to know. These examples support Mr. Zody’s notion that
there is one way to teach Algebra 1 which is to show the students the methods in which he would
like for them to use. This type of pedagogy is similar to Freire’s (1993) idea of a banking system
where the teacher’s pedagogy is to deposit information to the students rather than supporting
students in developing their own views and ideologies.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 96

Figure 4. Mr. Zody’s Board 1
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Figure 5. Mr. Zody’s Board 2

Figure 6. Mr. Zody’s Board 3
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The pictures above are examples of Mr. Zody’s efforts in assisting his students with
equations and functions. Some of the students looked on while other students seemed to be
confused and inattentive. One student placed his hands on his head in a manner that suggested
that it was difficult to remain engaged as Mr. Zody explained answers. Mr. Zody stated that the
slope was the change in our y’s over the change in our x’s. After Mr. Zody completed the
explanation of a series of problems, Mr. Zody stated, Yay, math. Are we good?” A few students
clapped, but most did not yield a response. After discussing linear, quadratic, and exponential
functions, Mr. Zody asked the students, “Are we chillin on that?” This was an attempt by Mr.
Zody to relate to students by the use of the slang word “chillin.”
Mrs. Pedroza. Mrs. Pedroza has an undergraduate degree in Liberal studies with a
minor in math. She responded to the question asking how, on a scale of 1 to 5, she would rate her
perceptions of the depth and quality of her math content knowledge by rating herself at 4. She
credited a mathematics software program with helping her with the content as she stated:
“Because of the program that I am using, compared to the textbook teaching. Lets consider my
perception of the depth and quality of my math content knowledge a 4.” Mrs. Pedroza stated that
teachers should have content knowledge at Calculus 2 or 3 in order to effectively teach Algebra 1.
Mrs. Pedroza stated, “Many people begin to understand math once they teach it. As a student,
you see it, you can do the process, but you don’t see the full picture until you teach it. ” Although
Mrs. Pedroza acknowledged that Algebra 1 teachers should have some calculus content
knowledge in order to effectively teach Algebra 1, she did assert that teachers could develop a
deep knowledge of Algebra 1 from teaching experience.
Mrs. Reyes. Mrs. Reyes has a bachelor’s degree in mathematics. While Mrs. Reyes
participated in many professional development sessions during the course of her teaching career,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 99
she stated that the majority of professional development was tied to the district’s initiatives and
math. Mrs. Reyes asserted that she has not participated in any specific professional development
on math content. Mrs. Reyes rated her perception of the depth and quality of her content
knowledge at a 3 on a scale of 1 to 5. Mrs. Reyes elaborated by stating,
Up until this point where I had moved over here, I had not seen any higher level math
classes. Algebra 2, pre-cal, what not. I try and get the kids to link as far as that, but as far
as experiences, I’ve never actually taught Algebra 2. Based on my limitation of what I
actually taught, not necessarily what I can do, I believe that I would be at a 3.
Mrs. Reyes stated that she did not rate above 3 due to the minimal amount of exposure to
higher levels of mathematics during her teaching career. Since she had over 20 years of
experience, and she spent the majority of her career teaching Algebra 1, she did not consider
herself to be highly knowledgeable, or as knowledgeable as she was at the beginning of her
career on math content beyond Algebra1. However, Mrs. Reyes stated that teachers’ level of
math content knowledge for effective teaching of Algebra 1 should minimally be at Algebra 2.
Theme 1 Summary. Mrs. Rivers, Mr. Zody, and Mrs. Pedroza all stated that teachers
should have content knowledge at the calculus level in order to effectively teach Algebra 1
content. Mrs. Reyes stated that Algebra 2 should be the minimum math content level for
effective teaching of Algebra 1. She further stated that the Common Core state standards elevate
the level of teacher expectations and knowledge in an effort to ensure that all students are
prepared for college level math as well as employment in STEM-related fields (Banks & Lafors,
2015). California Common Core content standards that the teacher participants focused on were
largely found in the algebra and functions domains. These domains contain standards that are
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 100
repeated at an increased level for Algebra 2, as well as developmental standards for calculus
content (California Department of Education, 2013).
Therefore, it would be ideal if Algebra 1 teachers’ content knowledge was beyond the
Algebra 2 level with some knowledge of calculus content in order to prepare students,
particularly African American males, for mathematics beyond Algebra 1. Teachers’ should know
mathematics at a much higher depth than the general mathematics knowledge held by most
adults (Hill et al., 2004). Math teachers should be able to explain abstract mathematical concepts,
represent mathematical ideas in multiple ways, identify various mathematical algorithms and
how they should be applied to a particular problem, and be able to appraise students’
mathematical methods (Hill et al., 2004).
Algebra 1 teachers’ content knowledge should be deep enough to connect to the manner
in which students think about, know, or learn mathematics (Hill et al., 2008). There were
instances throughout observations where both Mr. Zody and Mrs. Rivers assisted students with
their math. They asked the students probing questions to encourage the students to think about
their work towards solutions. For example, while students worked on error analysis in Mr.
Zody’s class session, Mr. Zody circulated and asked questions such as, “Where did you make
your mistakes, Did you get the same answer after retrying the problem, How many ab’s do we
have in the problem?”
This demonstrates that Mr. Zody’s knowledge of math content for Algebra 1 was deep
enough for him to address mistakes and misconceptions at whatever point students experienced
them. Similarly, Mrs. Rivers asked questions such as, “What would this be if you needed both
equations to cancel?” The problem that the students were working on was 3z-2y = 3 and 6z + Ky
= 4. The students’ task was to determine the value of “K” so that the system had no solution. Mrs.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 101
Rivers responded to another student by stating, “I agree that something has to equal zero. You
are on the right track.” This discourse between the teachers and students demonstrates that Mrs.
River’s content knowledge is beyond that which is necessary to be able to determine the value of
“K” so that the system had no solution. It was clear that both teachers were using their
knowledge of mathematical concepts and content to engage students’ problem-solving thinking
to scaffold students into constructing knowledge. The teachers seemed to be using an inquiry-
based pedagogy. Also, they are tapping into students’ zones of proximal development to scaffold
them into knowledge that they are co-constructing with students.
Fixed Versus Growth Mindset Pedagogy
The teacher participants assert that Algebra 1 students, particularly African American
males, may enter their courses with a fixed mindset regarding Algebra 1. Students with a fixed
mindset believe that they are not capable of learning Algebra1. The teachers assert that there are
different factors that lead to the development of a fixed mindset, and that Algebra 1 teachers
must know the language and attitude of a fixed mindset and be able to convert fixed mindsets
into growth mindsets. Students with growth mindsets are more likely to persevere through the
challenges of learning Algebra 1 and many of its abstract mathematical components. Interviews
and observations support the notion that the teacher participants believe that it is necessary for
Algebra 1 teachers to develop a growth mindset within their students, particularly African
American males, in order for their students to be successful in Algebra 1, and believe that they
are capable learners of mathematics.
Mrs. Rivers. Mrs. Rivers began the classroom session that I observed with a short two-
minute video that discussed the benefits of maintaining a growth mindset. After the video, Mrs.
Rivers posted a question that asked, “What does the video tell you?” Mrs. Rivers began by
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 102
stating, “You can learn anything.” The teacher asked, “Why do we watch this particular video?”
A student responded by stating, “A problem that you have in class maybe you can feel you can
learn.” A second student responded by stating, “Growth mindset?” The students’ responses
demonstrated previous discussions regarding the teacher’s belief of the importance of students’
developing and maintaining a growth mindset. Mrs. Rivers elaborated on her views of mindsets
during the interview:
What I’ve really learned throughout my 5 years here is that one of the most important
things that I can do for my students is to teach them that they can learn math. For me,
that’s different than teaching them math. I’ve done a lot of focus this year on fixed versus
growth mindset. I really want my students to understand that they can learn anything,
including mathematics. Teaching them that they don’t have a math brain or not have a
math brain, right? Everybody has a brain. Everybody’s brain can be trained to do new
things. The first couple of years were frustrating because I had a lot of students who
would come in and just say, “Well, I’m not good at math. I’ve never been good at math.
My mom is not good at math. I’m never going to be good at math.”
Really being able to teach them about fixed versus growth mindset has really
changed that dialogue to my students saying, “Hey, this is the mistake I made, right?
How do I move past it? How do I get further? I don’t understand this yet or what can I do
to improve?” It’s really changed the whole dialogue that I’ve had with them and it’s also
helped my students I think in terms of their math proficiency. Because now they’re
coming at this from a place of, I can do this. It’s really changed the dialogue into the
learning versus them self-labeling themselves as being good or not good at math.
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Figure 7. Mrs. Rivers’ Board 1
Mrs. Rivers stated that she focused on the development of a growth mindset within her
students. Students who attend urban schools, particularly African American males, may attribute
past negative experiences with math to a natural inability to learn math. The belief in a natural
inability to achieve in math constitutes a fixed mindset regarding math. Mrs. Rivers’ pedagogy
for teaching mathematics includes an acknowledgement of fixed mindsets and a focus on
reversing the trend of students’ fixed mindsets by allowing students to work in cooperative
groups, encouraging students to be patient with mistakes and view mistakes as opportunities for
growth, and create plans for improving on areas of mathematical weaknesses. Figure 7 is a photo
taken during classroom observations that shows the importance that Mrs. Rivers placed on the
development of a growth mindset.
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Figure 8. Mrs. Rivers’ Board 2
Mrs. Rivers discourse for a growth mindset is evident in the display board shown in the
figure 8. Statements such as “This (math) is too hard, I’m bad at math, and I give up” exemplify
a fixed mindset. Statements such as, “I can do this!,” “Mistakes help me learn!,” and “Is this
really my best work?” exemplify a growth mindset. Secondary Algebra 1 teachers, especially
teachers of African American males, who have had numerous experiences in learning
mathematics, due largely to inequitable opportunities to learn, should know the language of a
fixed mindset and be able to transform that language and culture into that of a growth mindset.
Mr Zody. Mr. Zody acknowledged that some students entered his course with negative
views of mathematics. He stated that students had voiced their frustrations with mathematics in
the past. Students would voice opinions regarding math such as “I hate math.” Mr. Zody
asserted that he had been successful in changing the views of students, particularly African
American males, towards mathematics. Observations confirmed that Mr. Zody attempted to
create an environment that encouraged collaboration, participation, and growth by embracing
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 105
and correcting mathematical errors, although students were not consistently engaged and Mr.
Zody would often revert back to direct teaching. Further, Mr. Zody stated that he encourages
students to practice algebra problems and study for tests. During interviews, Mr. Zody stated that
his students acknowledged how their studying and practicing lead to improved math achievement,
which, in turn, improves students’ confidence and encourages a growth mindset for Algebra 1.
The greatest things that I hear the students telling me that I’ve made an impact. I’ve
changed their minds about the subject itself, and how they view themselves. My biggest
kind of belief and it’s always been this way is I want to teach the students to look at
challenges as an opportunity for growth, and accept that there are going to be challenges.
It doesn’t matter how you can get through. That’s going to determine their character and
their ultimate success. Seeing students kind of make that turn around it, which has
happened this semester of, “I hate math.” My Algebra students have been coming in and,
oh, I did all the studying, and seeing the better grades and seeing the smiles and having
the students thank me. That’s what I love.
The words “practice,” “patience,” and “perseverance” were written on the board in Mr.
Zody’s class. These words embody the idea of growth mindset in that students with a growth
mindset tend to realize how practice, patience, and perseverance can lead to Algebra 1 success
(Dweck, 2006).
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Figure 9. Mr. Zody’s Board 4
There was more evidence during the observations that Mr. Zody’s pedagogy encouraged
the development of a growth mindset. Mr. Zody’s students worked on completing error analysis
activities, which called for students to find and correct mathematical errors and mistakes.
During one observation, Mr. Zody worked with groups of students on combining like
terms. The teacher reminded the class on several instances that their focus was on error analysis.
One particular group of students were adding -3ab + ba. The group did not consider ba and -3ab
to be like terms. The students’ answers reflected this misconception. Mr. Zody asked the
students: “Is ba the same as ab?” The students were not able to answer. Mr. Zody said to them:
“Letters are numbers put together. It means to multiply it doesn’t matter if there is a
multiplication symbol. When you look at the “ab’s.” How many “ab’s” do you have?” The
students answered, “Two.” Mr. Zody stated, “Your only error was with combining the like
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terms.” When Mr. Zody left, the students continued working and showed satisfaction by
increasing their intensity for working.
This interaction between Mr. Zody and his students seemed to have illustrated how he
attempts to instill a growth mindset in his students. Although the students in the group were
confused about combining like terms such as -3ab and ba, Mr. Zody focused on the analysis of
mathematical errors in their computations. The students seemed to be relatively comfortable in
their mathematical errors and viewed errors as a part of the learning process for mathematics.
However, Mr. Zody’s pedagogy consisted mostly of direct teaching and a focus on
reproducing the correct algorithms. This method of direct teaching may not address the
conceptual understanding that is necessary for students to learn Algebra 1. Factual knowledge as
well as conceptual knowledge should be intertwined for effective mathematics instruction
(Donovan & Bransford, 2005). Further, inaccurate preconceptions can act as barriers to learning
if they are not addressed.
Preconceptions such as math is about learning to compute, math is about following rules
to guarantee correct answers, and some people have the ability to do math while others don’t
should be addressed through teacher pedagogy (Donovan & Bransford, 2005). Mr. Zody’s focus
on error analysis addresses the preconception that some people have the ability to do math while
others don’t; which is a widespread mathematical preconception in the United States and plagues
African American males in their attempt to positively identify with mathematics (Donovan &
Bransford, 2005). However, Mr. Zody’s pedagogy does not address the preconceptions that math
is about learning to compute and math is about following rules to guarantee correct answers; as
the interactions between Mr. Zody and his Algebra 1 students seemed to focus on his students’
ability to memorize the correct algebraic algorithms for combining like terms.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 108
Mrs. Pedroza. Mrs. Pedroza stated that students tend to lack the necessary drive to
achieve in Algebra 1. Mrs. Pedroza states: “If students are trying and put forth an honest effort,
then I will help them. I like my students to try and put in an honest effort” This statement
suggests that students must put forth the effort in order to receive assistance from the teacher.
Mrs. Pedroza says “Algebra 1 is so challenging, students may create a barrier which makes it
difficult for students to learn. Students begin to remove the barrier during the course of a school
year, and may begin to grasp the algebra.”
The barrier that Mrs. Pedroza speaks of may be the lack of motivation that students,
particularly African American males, display when they are uncomfortable with mathematics.
The mathematics barrier that Mrs. Pedroza mentions may be related to Mrs. Rivers and Mr.
Zody’s idea of a fixed mindset, which suggests that students are less likely to put forth an effort
in learning algebra if they believe that they are not mathematically competent. When students put
forth the effort, the results are more favorable which suggests that students can learn if they are
willing to complete assignments, study, and seek tutoring when necessary.
Mrs. Reyes. Mrs. Reyes responds to the question about some of the challenges,
frustrations, and disappointments as an Algebra 1 teacher by stating,
The frustrating part of this is that, when students allow themselves to get into a hole and
they realize that there are things and steps they need to take in order to improve the grade
or their skills, but they refuse to do it. I don’t know why. Maybe it’s just easier to just say,
I’m not going to try, but they don’t take advantage of the interventions that are there. I
just hope that everyone just sees the beauty of it. Like, “okay, I can do this.” Although
that doesn’t make any sense, I can go from point A to point B and I can say to myself,
“Oh, okay.”
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 109
Mrs. Reyes asserted that there is some reason beyond her understanding that students are
not motivated to complete the necessary task to achieve mathematically. She states that she
would like to have students, particularly African American males, see the beauty in mathematics
and gain the confidence that is necessary for African American males to persist mathematically
although challenges are presented. This does not necessarily suggest that Mrs. Reyes believes
that students need to develop a growth mindset. However, Mrs. Reyes discussed characteristics
that are aligned to Mrs. Rivers and Mr. Zody’s idea of pedagogy that focuses on how the
development of a growth mindset can be central to the Algebra 1 achievement and favorable
mathematics outcomes for African American males. Mrs. Reyes did not demonstrate in her
comments the knowledge of the kind of pedagogy required to develop a math growth mindset
among her students. Further, she did not indicate her role in helping students develop this
mindset.
Theme 2 Summary. Mrs. Rivers and Mr. Zody both have identified fixed and growth
mindsets as important factors in African American students’ mathematical identities, and thus
their engagement in learning algebra. There was evidence that both teachers considered the idea
of fixed and growth mindsets as they planned lessons and created their classroom environments.
Mrs. River’s focus on fixed and growth mindsets is much more extensive than that of Mr. Zody.
Mrs. River’s embedded the idea of a growth mindset within her lesson. Throughout the course of
the lesson that was observed, Mrs. Rivers asked questions that solicited a growth mindset. For
example, Mrs. Rivers had the students create action plans that included individual goals for the
class period. The action plan included questions such as, “How can you best use your time
wisely? How will you know if you are proficient?” These questions encourage thinking that
supports students in developing beliefs in their ability to learn algebra.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 110
Mr. Zody circulated the classroom as students worked on error analysis. Error analysis is
an assignment where students are given the task of determining mistakes in particular problems.
Mr. Zody stated that error analysis may help students develop a growth mindset by allowing
students to view errors as opportunities for mathematical growth.
The notion of developing a fixed mindset is consistent with Donovan and Bransford’s
(2005) assertion that it is necessary for mathematics teachers to address students’ mathematics
preconception that some people have the ability to do math and some do not, in order to foster
success in mathematics. However, neither Mrs. Rivers nor Mr. Zody’s fixed mindset pedagogy
addressed preconceptions that math is about learning to compute and math is about following
rules to guarantee correct answers, as both Mrs. Rivers and Mr. Zody focused on students’
reproduction of the correct mathematical algorithms for arriving at solutions to problems.
In addition to the use of fixed mindset pedagogy, Algebra 1 preconceptions could be
addressed by linking informal mathematics such as the math that individuals use in everyday life
such as shopping, analyzing sports, cooking, and dieting, with the formal math that is taught
through directed teaching (Donovan & Bransford (2005). Students learn and retain more Algebra
1 when students can connect the algebra to accurate and relevant prior knowledge (Ambrose et
al., 2010). It is significant for African American males, who are presented with overcoming
challenges associated with racial prejudice, micro-aggressions, and teacher pedagogy that lack
cultural relevance, to be able to transfer their informal mathematics knowledge to the formal
context of the Algebra 1 classroom.
Although there was no evidence that Mrs. Pedroza and Mrs. Reyes were aware of the
concepts of fixed and growth mindsets, they both showed an understanding of the need for
Algebra 1 teachers to address issues of students’ belief that they are not capable of math
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 111
achievement. Both teachers stated that students perform better when they try. When students put
forth effort, students achieve at higher levels. Mrs. Pedroza did not seem to understand that the
motivation to try is fueled by a belief that effort leads to growth. Teachers with deep content
knowledge and content pedagogy are able to construct learning opportunities that allow students
to experience the relationship between their efforts and their growth (Flores, 2007). Students
initially do not perform well in algebra, but, when they continue to persevere, the results tend to
become favorable. Students are more likely to persevere if they have a growth mindset and
believe that through studying and hard work, they are capable of achieving mathematically. Mrs.
Reyes stated that Algebra 1 students sometimes allow themselves to get in a hole. They know
that there are measures that they could take but they refuse to seek help, study, or complete
assignments. She does not demonstrate an understanding of how students learn and the role of
motivation. Mrs. Reyes states that she constantly gives students positive feedback and
encourages students to know that they are capable of Algebra 1 achievement. She expresses little
understanding of her role in the development of a growth mindset in the context of learning math
(Dweck, 2006). Telling students they are capable is not the same as giving them the opportunity
to experience their capability through meaningful engagement.
While the teacher participants assert that development of a growth mindset can support
students’ learning, the interpretation of this ideology may be related to a deficit cognitive frame.
Bensimon, (2005) states that educators may know that there are diverse students in urban schools,
and that there are disparities in educational outcomes. However, educators may attribute the
problem of unequal outcomes to the students and fail to consider their roles in creating
inequitable educational environments and how these inequities contribute to unequal outcomes.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 112
African American males are often presumed to be lazy and unwilling to put forth the
effort to learn. The teacher participants may view the unwillingness to put forth effort as lazy, or
the teacher participants may attribute the unwillingness to put forth effort to a fixed mindset.
Regardless, there is little evidence that the teacher participants considered African American
males’ culture as an asset to learning Algebra 1 or considered this asset as they developed
lessons and presented instruction (Bensimon, 2005). They do not seem to understand that their
pedagogy could be a factor. Their pedagogy lacked engagement in academic discourses related
to math, the modeling of a mathematics language, and the fostering of student collaborative
efforts to construct Algebra 1 knowledge in relationship to prior mathematical knowledge and
conceptual understanding.
Interactive Environments
The teacher participants assert that it is necessary for Algebra 1 teachers of African
American males to create an educational environment that encourages student participation and
cooperative learning, and to bridge cultural differences. Teachers must have knowledge of the
content pedagogical skills needed for Algebra 1 achievement for all students. The teacher
participants stated that it is necessary to create environments where students feel empowered to
challenge each other’s thinking, encouraged to work together as the teacher support and assist
them, and view their culture as an asset to their learning Algebra 1.
Mrs. Rivers. Mrs. Rivers stated that much of her Algebra 1 pedagogy was learned
through professional development. She stated that instructional strategies such as group-based
learning, investigations, leveling, students’ self-assessment, and error analysis was learned in
professional development, and she continues to implement these strategies in the classroom. Mrs.
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Rivers explained how error analysis can be used to create an environment where Algebra 1
students, particularly African American males, are empowered to learn Algebra 1:
Any time that my students take any form of assessment be it formal or informal, what
they get back is their assessment and they get back what I call a questions’ key. They
don’t get an answer key but they get a series of questions that should push them towards
understanding the questions. What they do is they then, using the roadwork that we use,
they self-assess their own proficiency. I don’t tell them their proficiency, right? They
look at it and say, Okay, based on what I did hear, this is the level of proficiency I think
I’m at right now. Then they use the questions’ key, they use their notes, they use help
from their partner, they use help from me. To try to bring themselves up to a level 4,
which is our highest level. At the end of their process of working with the questions’ key,
trying to fix their mistakes, trying to verbalize what their mistakes were, and they create
notes saying in essence, “Hey, this is what I learned, this what I figured out.”
During observations, Mrs. Rivers used the first five minutes of the class period to help
her students understand the importance of maintaining a growth mindset, before allowing
students to work in groups and/or pairs to complete error analysis and other activities. She made
several comments during the first five minutes of the class period that were associated with the
development of growth mindsets, and encouraged students to work together, sharing ideas,
thoughts, and procedures. The use of error analysis, self-assessments, and action plan activities
were completed in groups, pairs, and at times individually. Students felt empowered as they were
given the freedom to determine if they needed to work in groups, work in pairs, or work
individually to complete assignments.
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Mrs. Rivers’ error analysis activities allowed students to pinpoint specific mistakes that
lead to incorrect answers, and attribute those mistakes to a lack of preparation, and/or
mathematical preconceptions. Throughout the allotted time that the students were given to work
on various activities, Mrs. Rivers continuously circulated through the classroom and assisted
students. During interviews, Mrs. Rivers stated,
Sometimes they’re writing down questions they still have for me. At the end of that
process they then self-assess again and say, Hey, I think I was at a 2. I don’t think I’m a 4
yet but I think I’m at 2.5 or I think I’m at a 3. Then they are able to say, “Hey, how far
have I gotten?” Then they create an individualized action plan. This is my goal. This is
how I’m going to get from where I am now to that goal that I have for myself, in addition
to the self-assessment and error analysis strategies,
The significance of the self-assessment activity was to allow the students to determine
their areas of strengths and weaknesses, reflect on their approaches to solving algebraic problems,
analyze what has led to algebraic misconceptions, and create a plan for addressing their
shortcomings in Algebra 1. Mrs. Rivers stated that it is important for teachers to have the
pedagogical knowledge to create an atmosphere where African American males can relate to
mathematics:
I think that what I really try to do in terms of keeping the math relevant is look at data
together. We really try to look at data that are relevant to them. When we are analyzing
data, we’ve done things like looked at data that talks about the percentage of African
American males, Hispanic males, females, White males, White females that get into
college and get through college. Right? It involves really having a conversation about
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something that affects them and really using it and then saying, “Well this is the math;
this is what it’s showing us.”
Mrs. Rivers asserted that African American males are willing to put forth more effort into
their Algebra 1 learning when they feel comfortable, empowered to seek help, and when the
math is relevant to their culture. However, the teacher must set a tone where an algebraic
discourse is created, and lessons should revolve around this discourse prior to summative
assessments. Further, the discourse for Algebra 1 should be connected to formative assessments.
Mr. Zody. Mr. Zody acknowledged that he uses cooperative learning as a tool for
enhancing learning. In this regard, he seems to have conflicting ideas about students learning in
groups. He uses small-group learning, but he seems to lack the skills and understanding of how
to make maximal use of groups. Mr. Zody stated, “Cooperative learning is one that I kind of use,
and then direct instruction is kind of my main one. That’s kind of my belief especially for
algebra. There are not too many ways to do it.” Although Mr. Zody does implement some
cooperative learning strategies, he stated that teacher lecture is best used for algebra lessons.
Mr. Zody stated that he focuses on direct instruction and that teacher lecture is best used
for algebra lessons, but, research has supported the acquisition of mathematics within a
sociocultural context (Lerman, 2000). Algebra 1 teachers who encourage students to explain and
justify their thinking and listen to their peers share algebraic reasoning, create an algebraic
culture for learning in the classroom (Steele, 2001). In a sociocultural context, African American
males can internalize the algebraic language and function as algebraic thinkers (Steel, 2001).
The teacher’s role is to actively participate in students’ mathematical experiences in a manner
that models and facilitates the use of algebraic language and algebraic thinking.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 116
During classroom observations, Mr. Zody implemented both direct instruction and
cooperative learning strategies. Some students were placed in groups of four, while others
worked in pairs. The classroom seating structure allowed students to easily transition from
groups of four to working in pairs and back into a whole group setting. Mr. Zody often
monitored the groups, instructed the students in whole groups by modeling methods for arriving
to the correct solutions and interpretations of graphs, functions, and equations, and encouraged
students to discuss the mathematics with their partners.
In addition to cooperative learning and direct instruction, Mr. Zody attempted to create a
culturally responsive environment. In response to the question about some aspects of his teaching
that he considers to be culturally responsive, Mr. Zody stated,
The kids will come in, play some of their music, and I know all the artists that they know.
I’m not really big with the sports, but, as soon as they see the artists that I know and the
artists that I play, it’s like all right, all right. It makes it more relatable. They come from
certain environments like gangs and stuff like that. I know I’m not supposed to really talk
to them about that or discourage that, but I want to know about those things. Because, as I
progress through my career, I want to know the challenges that come with those students
because I need to know their background in order for me to kind of reach them. I need to
identify their challenges, and that’s how I’m going to help them get around them. I can’t
think of some statistics I cited off the top of my head, but I do use some of the math-
related statistics to get them to see how big the problem is, and how important it is for
them to try and change that. Or how they think the odds are stacked against them, but
really using the statistics, there’s not that much. You are close. You are part of something
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 117
that is a bubble you can get out of it. In terms of in front of class, the main thing is
relating to music or sports, mainly basketball or football. That’s what I usually do.
Mr. Zody attempts to connect with what he considers to be African American male
culture. He discussed his knowledge of hip-hop, gangs, and sports, and asserts that these are
methods of creating a culturally responsive environment. Mr. Zody’s statement, “how they think
the odds are stacked against them,” demonstrates a deficit mindset where marginalized groups
are blamed for their own oppression. This view is consistent with Ford and Moore’s (2013)
notion that African American males’ underachievement in mathematics is due, in part, to deficit
thinking, low teacher expectations, cultural incompetence among educators, and few or no
resources.
During observations, Mr. Zody explained how the he considered his room environment to
be culturally responsive. Mr. Zody placed sports banners around the classroom and stated that
the sports banners were used to create an athletic atmosphere that relates to his students. He
mentioned that he used baseball and hockey banners in addition to football banners because he
wanted students to be open to sports outside of the typical sports that are connected to African
American male culture such as baseball and football. Figures 10, 11, and 12 show the banners
displayed in the front of Mr. Zody’s classroom.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 118

Figure 10. Mr. Zody’s Room 1

Figure 11. Mr. Zody’s Room 2
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 119

Figure 12. Mr. Zody’s Room 3
Mr. Zody did not seem to connect Algebra 1 content to African American culture or vice
versa. He does not go beyond an attempt to relate to African American culture through sharing
his own affinities to aspects of African American culture such as hip-hop and sports. Mr. Zody
did state that he uses statistics to describe issues that affect African American males such as gang
violence and underrepresentation in colleges and universities, but he did not state that he
incorporates aspects of his students’ interests and culture into learning mathematics.
True culturally responsive pedagogy occurs within the context of academic content (Gay,
2010). According to the most recent knowledge about how to help students learn mathematics,
Mr. Zody seems to lack deep mathematics content pedagogy. He demonstrates the ability to
connect with students by creating a positive social environment in which students can construct
positive racial and gender identities, but not necessarily positive mathematics identities. There is
a gap however, between these. Further, he limits African American culture to current pop culture
without exploring the deeper roots of African American culture. For instance, he does not
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 120
address language differences that may play a role in how African American students
conceptualize mathematic concepts.
There are word order, word meaning, and grammatical structures that differ from the way
math is presented in most mathematics textbooks. He does not express that he uses some of the
ways African American family members interact with one another as a way to structure group
learning. He does not consider creating math problems that reflect the richness of African
American culture such as jazz and Black visual art, as well as how African Americans confront
the challenges of African Americans learning to survive in America.
Mrs. Pedroza. Mrs. Pedroza did not seem confident about the teaching and learning
environment in her class as she declined to participate in classroom observations. Mrs. Pedroza
stated that since we were in the last month of school, there would be some chaos and unruly
students. When asked the question about aspects of her teaching she considers to be culturally
responsive, she responded by stating that she tries to help all students who struggle. She uses a
program that creates word problems that are culturally diverse, and she will help students that put
in an honest effort. She did not elaborate or provide examples of the culturally diverse word
problems she used nor how she used them to teach mathematics concepts. Further, Mrs. Pedroza
stated that all males are focused on pop culture, social media, fitting in, and being cool. Mrs.
Pedroza did not explain how she connects algebra with students’ culture and embeds aspects of
their culture such as hip-hop, pop, social media, and the propensity to be cool into her Algebra 1
curriculum.
Mrs. Reyes. Mrs. Reyes stated that she has taken cross-cultural language and academic
development training. She stated that she received the training “a long time ago,” and that she
did not recall much of the pedagogical content that was taught during the training. Mrs. Reyes
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 121
answered the question about aspects of her teaching she considers to be culturally responsive by
stating,
I don’t know if there’s anything that I particularly do for one group or the other. I provide
them a very structured...There’s a tendency to be repetitive. At the same time, when I
make comments on a student, it’s always about the work. Not necessarily their behavior
that led to the work. Every comment I have is, “Okay, how did you do this problem?” Or,
“Good job.” What I try and always do is provide positive feedback and always address
the concepts, whether they are African American or not, but it’s always consistently that.
I don’t know if there’s anything else I do other than I try and make sure that I pronounce
it correctly and properly. They know that I’m constantly beating myself up. Like, “How
do I say your name? Give me a chance.” Again, I try and respect that. I had one student
in particular. He told me his name is Devon and I would call him Mr. Bush. He would
say, “Mrs. Reyes, don’t call me by that name.” I’m like, “Why?” He goes, “Well, I
respect my grandmother. That’s why I’m going to keep my name, but at the same time,
my ancestors to slavery.” This is what he was saying. “This is the name of the group of
people who enslaved my family. Because of that, I don’t want you saying my last name.”
I said, “Okay, Devon.” I’m like, “I got it.” Him telling me that, I’m like, “I need to
respect this young’s man view, but I should not call him by his last name.” I said, “Okay,
I understand.”
Teachers utilize culturally relevant pedagogy when they acknowledge students’ culture
and allow students to develop intellectually by using aspects of students’ culture in their
instruction (Ladson-Billings, 2009). Mrs. Reyes acknowledged Devon’s cultural history by
listening to Devon’s explanation of the history of his last name and adhering to Devon’s request
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 122
to refer to Devon by his first name. However, Mrs. Reyes did not state in the interview examples
of culturally relevant instruction, and whether or not she viewed African American culture as
assets that could be used to guide and complement algebraic instruction.
Mrs. Reyes stated that she creates an environment that is welcoming for all of her
students. She is very nurturing and attempts to treat all of her students in the same manner that
she treats her own children. When asked what she believed were some of the reasons for the
performance gap between African American males and their peers of other ethnic groups
regarding Algebra 1, she stated,
That is a very good question. Again, I’m thinking maybe it’s because of the
representation. There aren’t that many that they can relate to within classrooms when
they’re the only one, but at the same time, I’m guessing that maybe they don’t see the
importance of this, the purpose of knowing what the math is because when you get to the
Algebra 1 level, there tends to be more abstract at that point as opposed to concrete. That
lack of connection between why do I have to do this, what’s the point? It’s not enough for
them. There has to be something more tangible.
Mrs. Reyes acknowledged the need for teachers to be able to connect the algebra to
students’ culture and create lessons that are relevant. In addition, she stated that it is necessary
for teachers to be able to create instructional environments where students are able to learn
through cooperative groupings. She stated that students have to be able to work individually, in
pairs, as well as in groups. It is the responsibility of the teacher to be able to create the
environment and determine which is the best method for a particular lesson, topic, or concept.
Mrs. Reyes seemed to be aware of the need for teachers to connect algebra to students’
culture, but she did not seem to know how to connect algebra to students’ learning. Teachers
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should build on students’ cultural assets, engage students in critical reflection about their own
lives and societies, and reveal oppression systems through their instruction (Arronson &
Laughter, 2015). Mrs. Reyes interaction with Devon confirms her knowledge of these aspects of
culturally relevant pedagogy, yet she lacks particular knowledge about Devon’s culture;
therefore she demonstrates a kind of tentativeness about how to approach him. She seems unable
to create bridges that connect student’ culture and utilize their assets in developing Algebra 1
lessons and presenting Algebra 1 instruction.
Theme 3 Summary. The teacher participants demonstrated knowledge that it is
necessary to create an interactive environment and connect to African American male culture.
However, the teacher participants did not demonstrate evidence of culturally relevant content
pedagogy. Mr. Zody stated that he listens to hip-hop music and is familiar with sports. Mrs.
Pedroza stated that she uses a program that creates culturally relevant problems for students to
solve. Mrs. Reyes asserted that she is nurturing and treats all students in the same manner in
which she treats her own children.
While these strategies are examples of ways in which teachers could consider the
students’ culture as they create environments that are interactive and culturally responsive, these
strategies are not what Gay (2010) considers to be culturally relevant mathematics. Culturally
relevant mathematics teachers utilize cultural sites and sources such as cooking, art, music, and
games for teaching mathematical knowledge, concepts, and skills (Gay, 2010). The teacher
participants attempted to create an interactive context for learning, in part, through the
implementation of cooperative learning strategies; however, the teacher participants did not show
evidence of using the mathematics curriculum to present lessons that are culturally relevant. Mrs.
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Rivers stated that she presents lessons where students analyze data that is related to their
everyday lives such as college entrance data.
This may have been Mrs. Rivers attempt at relevancy, albeit inherently superficial.
However, this is an example of culturally relevant and responsive math, as the focus is on a topic
of concern for African American males, but not necessarily connected to African American
males as cultural and social beings. There are minimal examples of deep, consistent use of
culturally relevant and responsive mathematics to create interactive environments that are
conducive to African American males’ assets and African American males’ Algebra1 learning.
One aspect of culturally relevant and responsive pedagogy in the context of math is allowing
students to talk, rather than use teacher directed only instruction. The students were reviewing
their assessment results collaboratively, which allowed students to discuss common mistakes and
find solutions as well as correct mistakes that were unique to their peers individually.
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Themes for Research Question 2
Interview data from teacher and student participants were collected to answer research
question #2, “How can Algebra 1 teachers’ pedagogy support African American males in
developing a positive mathematics identity ”?
Middle school students develop mathematical identities as they develop racial and ethnic
identities (Berry, 2003 & 2008). In order to assist African American males in developing a
positive mathematics identity, which may, in turn, lead to mathematics success, it is crucial that
Algebra 1 teachers’ instruction incorporates their culture, community, and experiences with
mathematics (Berry, 2003; 2008). In addition to the need for cultural relevance, Berry et al.
(2011) found four factors that contribute to the development of positive mathematics identity.
They are: the development of computational fluency by third grade, extrinsic recognitions,
relational connections, and engagement with the unique qualities of mathematics. The following
themes were evident in relationship to the participants’ data on how Algebra 1 teachers’
pedagogy can support African American males in developing a positive mathematics identity:
relevancy, repetition, and relationships. Interviews with African American students provided
insights about their identities in relation to mathematics.
Theme 1: Relevancy
The student participants assert that some of their elementary, middle school, and high
school math teachers presented mathematics instruction that was relevant to African American
male culture, which, in turn, helped the student participants positively identify with Algebra 1.
In addition, some of the teacher participants stated that they have attempted to create lessons that
were relevant to their culture. Lessons and activities such as analyzing data on African American
male college and university enrollment, creating songs to help memorize formulas, and
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 126
mathematics games are all examples of instructional activities that the teacher participants have
implemented to increase the relevancy of the math content to their culture, which is instrumental
in their development of a positive math identity.
Emmitt. Emmitt did not state that his elementary and middle school teachers created
math lessons that were relevant to African American male culture; however, he does
acknowledge that his high school teachers implemented instruction that he considered to be
relevant to his learning math, thus assisting him in his development of a positive math identity.
Emmitt responded to the question regarding how his elementary schooling prepared him for
learning math and demonstrated that he can learn math by stating, “They just taught me stuff like
multiplication or whatever.” They said, “Oh you are going to need this when you get older so
you got to learn it now.”
Emmitt did speak of a project regarding the creation of a map in eighth grade Algebra 1.
He responded to the question about how his teacher treated him as an African American male
learning math by stating,
There was one project that had to do with slope intercept and all that. You had to make…
I wouldn’t say some map, but a layout of the mall and where this bathroom or whatever is.
You got to tell where the restroom is according to the plots that it was on, or something
like that.
This project does seem to be an attempt by Emmitt’s middle school Algebra 1 teacher to develop
Algebra 1 lessons that involved aspects of everyday life such as going to malls, the use of
restrooms, and using maps to assist with traveling. The lesson was not necessarily centered
around African American culture, but it did involve aspects of Emmitt’s everyday life. Emmitt
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 127
was not able to recall other examples of teacher math instruction that were relevant to his
everyday life as an African American male.
Emmitt stated that his high school Algebra 1 teacher, Mrs. Rivers, “is a good teacher.”
He responded to the question regarding what he remembers about his teacher that helped him
believe he could be a high achiever in Algebra 1 by stating,
Mrs. Rivers is a good teacher. We do this thing called error analysis where you check all
your mistakes to see what you did wrong on a test and how you can do better. We have
action plans where we make a graph or a little calendar saying what we’re going to do to
prepare for our next test or quiz or whatever.
Emmitt earned a “C” during the first semester of Mrs. Rivers’ Algebra 1 course.
During the interview, Emmitt stated that he did not feel comfortable with math until
entering Mrs. Rivers Algebra 1 class. Prior to that course, Emmitt’s math teachers taught with a
traditional approach. He mentioned that he did not like math prior to Algebra 1 and that Mrs.
Rivers was very interactive and that the action plans and error analysis were helpful. Emmitt
responded to the question about some instructional strategies implemented by his Algebra 1
teacher that he considered to have been helpful for his learning Algebra 1:
The error analysis, action plans and the totaling problems. You get a list of problems and
you start from beginning and then it goes all the way up to advanced and teams or
whatever. It’s like a total pool of problems that you do. It just lets you know where
you’re at because on this other side like beginning or efficient. Error analysis lets you
know what you did wrong so you can correct it. The next time you take the test you do
better on it and not make the same mistake. Action plans; it just helps you prepare, like
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 128
study or something like that. An action plan is a plan that you make…is when you plan
out activities or things that you’re going to do to get ready for a test or a quiz.
According to Emmitt, relevance had more to do with the practical activities related to
mathematics and his own personal development more than cultural relevance as defined by
Ladson-Billings (1998) and Gay (2010). In this personal planning experience, Mrs. Rivers
helped students claim responsibility for their own learning. This is a move toward becoming
autonomous learners in relation to mathematics, which is essential for developing mathematics
identities (Berry et al., 2011).
Mrs. Rivers’ understanding of relevance had to do with helping African American males
see the relationship between mathematics and their future. She stated that she used data that
described African American males’ underrepresentation in colleges and universities as material
for analyzing and interpreting graphs and functions. This idea does comply with Aronson and
Laughter’s (2015) four components to culturally relevant education. Aronson and Laughter
(2015) argued that culturally relevant education consists of (1) use of constructivist methods to
create bridges that connect students’ cultural references to academic skills and concepts,
particularly mathematics, (2) building on the mathematical knowledge and cultural assets all
students bring into the classroom, (3) engaging students in critical reflection about their own
lives and societies, (4) explicitly unmasking and unmaking oppressive systems through the
critical discourses of power (p. 5). Mrs. Rivers’ use of data on African American males’
underrepresentation in colleges and universities in her Algebra 1 instruction addressed their
marginalization through limited access to colleges and universities.
In addition, Mrs. Rivers used constructivist methods to create bridges between students’
cultural references to the Algebra 1 standards that are related to the analysis and interpretation of
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 129
graphs and functions, since actual data from African American males’ underrepresentation in
colleges and universities were used for graphs and equations. Mrs. Rivers engaged students in a
critical reflection of their lives and society as they discussed the significance of college and
career access. Further, Mrs. Rivers helped to unmask the oppressive system of education that
critical race theorists assert is inherently racist and shuts African American males out of college
and career opportunities, as she acknowledged their lack of college and careers access through
her lesson.
Mike. Mike asserted that he became efficient in math during elementary school. He
stated that his elementary school teachers made math practical, fun, and interesting. This early
interest in math set the stage for Mike’s continued mathematical success during elementary,
middle school, and high school. In response to the question about how his elementary school
prepared him for learning math, he stated,
They sort of taught me, helped me learn the different ways of how math could be applied
to different things. A fun topic we learned about was proportions. We did a lot of
different things in class. I thought it was really interesting because it was hard at one
point, but it was also easy at the same time. It taught you that little mistakes can really
change the result you going to get. So it was pretty interesting…well, the fact that a lot of
practical uses of a lot of math things can be used in proportions, in a sense. It was really
fun because we could do it with a whole bunch of different random things like an actual
real life instead of just a random problem.
Mike stated that the math was simultaneously difficult and easy and that creating lessons
that are relevant and practical, help him to see the relevance of math to everyday life. Thus,
helping Mike to positively identify with the mathematics. Further, mathematics became fun and
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 130
interesting for Mike during elementary school. Creating problems that were connected to real life
as opposed to “random problems” was significant in shaping Mike’s early views of math and
himself as a math learner. However, Mike was not able to recall specific problems and activities
that he considered to be relevant to his culture.
Mike asserted that his current geometry teacher, Mr. Zody was “empowering” but he did
not provide examples of relevant instruction from Mr. Zody. Mr. Zody stated that he attempted
to incorporate class activities that were relevant to the day-to-day lives and culture of his
students. Mr. Zody responded to the question of whether he had coursework in culturally
relevant instruction by stating,
I’ve just had one multicultural class in my education, credentialing courses, but, beyond
that, it was just multicultural. There wasn’t anything specific. I’ve kind of had experience
with diverse students. I find the education program that I’m in, it hasn’t really offered any
new material. I’ve been around that environment for such a long time, and I have my own
style, and it’s been working. Some of the classes kind of complement that; they are
already teaching me the same things I already do.
Mr. Zody appeared to have mathematics content knowledge adequate for the lesson he
was teaching on the day of the observation; however, he did not seem to have the pedagogical
content knowledge necessary to integrate the students’ cultural knowledge as a means of
promoting their conceptual understanding. The talk about music, sports, and gangs appeared to
be separate from enabling students to construct conceptual understanding. The whole lesson
seemed to be based on transmitting factual knowledge through direct instruction. Unlike the
error analysis activity in Mrs. Rivers’ class where students were working together to construct
conceptual understanding, in Mr. Zody’s class, he was the main source of the corrections through
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 131
direct instruction. Students were mainly quiet while he taught. Some seemed to have puzzled
looks, but they did not stop him to ask questions. Mr. Zody seemed to lack the content
pedagogical knowledge necessary to promote students’ active thinking while learning math.
Mr. Zody asserted that he was knowledgeable of African American male popular culture,
and he associates this knowledge with culturally relevant mathematics. He as able to engage
students in discussions regarding their culture, but he did not give many examples of how
culturally relevant mathematics is implemented through instruction. He stated,
Hip-pop is the music that I listen to. It’s been since I was 12. The kids will come in, play
some of their music, and I know all the artists that they know. I’m not really big with the
sports, but, as soon as they see the artist that I know and the artist that I play, it’s like all
right, all right. It makes it more relatable. They come from certain environments like
gangs and stuff like that. I want to know the challenges that come with those students,
because I need to know their background in order for me to kind of reach them. I need to
identify their challenges, and that’s how I’m going to help them get around it. You are
close. You are part of something that is a bubble. You can get out of it. In terms of in
front of class, the main thing is relating to music or sports, mainly basketball or football.
That’s what I usually do.
Mr. Zody again discussed what he considered to be important aspects of African
American males’ culture and how his identification and/or awareness of these cultural aspects
qualifies as relevant instruction. He stated that he has used statistics to help students understand
challenges that African American males encounter such as gang violence.
Mr. Zody’s comments suggest a deficit perspective about African American students’
culture. He said he used the knowledge of their day-to-day lives to reach them, but he did not say
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 132
he used this knowledge to teach them. Reaching them and teaching them seemed to be separate
in his mind. He was building connections at a personal level, but not at a teaching and learning
level. His repeated reference to gang violence rather than positive aspects of his students’ culture
suggests a deficit view. He did not seem to acknowledge any features of their culture as useful
in learning math; therefore, he kept discussions involving their culture separate from learning
math.
Mr. Zody suggested that sports could be a means for African American males to
experience success. However, sports can be a detriment to the African Americans males’
mathematics success when educators perpetuate the narrative that they are skilled in athletics and
areas of entertainment, but are lacking in the intellectual aptitude to succeed in math (Noble,
2011).
Corey. Corey did not discuss methods in which his elementary teachers attempted to
make math relevant to African American culture. Corey responded to the question about his
earliest memories of studying mathematics in elementary, by stating,
My earliest would probably be 3rd grade because that’s when we would be starting off
with long division. I was just struggling with long division because it was just so weird
for me. It was like you had to go from 225, and, during that age, you’re just like, “Oh,
this is a lot of numbers,” and just like, “Can I even do this?” It would be the point where I
would just be like, “Okay, I’m going to figure something else,” so I would ask the teacher,
I would ask the smartest kid in the class at the point like, “Okay, how do you do it? Do
you have an easier way of figuring it out?” Then it was to the point where I finally was
able to figure it out after like a good week after the first lesson of it and was just like,
Okay. It’s easier than what I thought it was.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 133
Based on Corey’s response to the interview question, his 3rd grade elementary teacher’s
method of instruction was focused on the development of factual or procedural knowledge and
lacked cultural relevancy. Further, Corey’s elementary teachers implemented direct teaching in a
teacher-centered environment. This environment forces the teacher’s mathematical strategies and
problem-solving approach on their students (Freiri, 1993). Corey states that he struggled with
long division, so he had to “figure something out” He gave the example that he would ask the
smartest kid for help. Corey mentioned that he would persevere, and eventually learn how to
complete the mathematical algorithm.
Although there was no evidence of culturally relevant mathematics instruction from
Corey’s elementary teachers, Corey demonstrated evidence of his negotiating through Stinson’s
(2008) notion of discourses of deficiency and rejection while reconfiguring the White male-
math-myth and persevering through his initial struggles in 3rd grade mathematics. Corey
mentioned that he struggled with long division but he had to “figure something out.” In
attempting to process the necessary methods for his learning long division while in the 3rd grade,
Corey stated that he asked the teacher, in addition to asking the “smartest kid.” This is
significant as Berry et al. (2011) assert that the development of computational fluency by 3rd
grade was one of four factors that positively contributed to the development of mathematics
identity. Corey’s description of his elementary school experience does not demonstrate culturally
relevant teaching from his teacher. He had to rely on his own perseverance and the assistance of
another student to get the math. In this case, his own initiative enabled him to learn the math, not
the teacher’s effectiveness.
Corey had a different kind of experience with one of his middle school teachers. He
stated that his middle school 8th grade Algebra 1 teacher, Mrs. Morgan, used a song that he
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 134
considered to have helped him memorize the quadratic equation. Corey described Mrs. Morgan’s
Algebra 1 class and the use of a song to memorize the quadratic formula in his response to the
question regarding strategies his 8th grade math teacher implemented that helped him to learn
mathematics, he stated,
It would probably be the quadratic formula because it was so important that everyone
learned this, even had us doing a song for it, but, yeah, she really helped us in terms of
figuring it out. I guess it was stupid catchy because you understood…She used the beat,
“Dunt-dunt-ta-duh-duh,” so you’re just like, Yeah. It was like, “X equals opposite B plus
or minus square root, B squared minus 4AC all over 2A,” and then there you go.
Although Cory described the quadratic equation song as “catchy” and credited the song
with helping him learn the formula for the quadratic equation, which is an example of factual
knowledge, factual and conceptual knowledge are both necessary for deep mathematical
understanding (Donovan & Bransford, 2005). Cory did not discuss other examples of culturally
relevant mathematics instruction from his middle school teachers to help him acquire conceptual
knowledge, as Cory’s interview responses consisted mostly of examples of teachers’ use of
Freire’s (1993) notion of a banking system for learning where mathematical knowledge is
deposited to students as opposed to supporting students as they construct mathematical
knowledge. Even the song, though catchy, mainly promoted factual learning, but Corey saw it as
a power tool that enabled him to navigate aspects of learning math.
Drew. Like Corey, Drew was also an 8th grade student in Mrs. Morgan’s Algebra 1
class. Students’ descriptions of her teaching suggest that she implemented some aspects of
culturally responsive teaching and enabled students to acquire conceptual understanding of
mathematics. In describing Mrs. Morgan’s 8th grade Algebra 1 course, Drew stated,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 135
Mrs. Morgan’s class was fun. I loved it. She made learning fun. She wasn’t just like do
your book-work, do these problems out the book and then turn it in and that’s class. She
would actually get involved with the students. We had projects. She would somehow
incorporate art into some of our projects. She would do a lot of things to make class more
enjoyable, make kids actually want to go to her class. So when the bell would ring,
because I had her after lunch, it wouldn’t be like, “Aww now I’ve got Mrs. Morgan.” It
would be like, “Oh, okay, I’ve got Mrs. Morgan now. Let’s go have some fun.”
Drew further described his experience with Mrs. Morgan by stating,
We had this thing; it was more on the artsy side, but it was to help us get used to graphs
and stuff. There was a little miniature size of a picture with a graph and it was broken up
into a graph and we had a big poster version, so we had to draw the graph on there and
then copy on the picture. It was more artsy, but it was to help us get used to using graphs
and stuff like that. If we didn’t understand a problem, she would put it in terms that we
more relate to. Like if a kid liked cars or something like that, if he wasn’t understanding
the way the problem was written in the book, she would change the example to where
that student could understand it, could more relate to it.
Drew considered Mrs. Morgan’s methods of teaching to be relevant to his culture, and he
was able to give examples of specific lessons that he considered to have made mathematics
interesting and fun. Drew was able to identify with Algebra 1 in Mrs. Morgan’s class, and went
on to successfully complete mathematics coursework beyond Algebra 1.
Quentin. Quentin stated that a few teachers had contributed to his success in elementary,
although he did state that his earliest memory of mathematics success was 3rd grade when he
received his first “A.” Quentin stated that his 3rd grade teacher did a great job of teaching:
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 136
She really helped me understand math a lot, because I used to struggle with math a lot
actually, until I met her. She helped me get along with math better. She had good
teaching techniques, and she would reward you if you got an answer right. I guess that
motivated kids to probably do better in her class.
Quentin stated that he attended a private school prior to attending SELA. He discussed
experiences with his math teachers in private school: “Well actually prior to coming here, I went
to a private school. I used to really love math. The teachers, they made it fun and interesting and
involving.” Quentin’s description of his experience with his 3rd grade teacher provides an
example of the value of extrinsic rewards as described by Berry et al. (2011). The fact that
Quentin remembers it and associates it with his developing a math identity is significant.
DeAnthony. DeAnthony asserted that his elementary teachers related mathematics to
money, and that helped DeAnthony to become interested in mathematics. He stated, “You have
to add money and be sure it is the right amount.” He credited his ongoing success in math to his
elementary teachers. He stated that his earliest memories of success in mathematics took place in
the 3rd grade. He remembers focusing on profits and discounts in the 4th grade. The
mathematics related to profits and discounts were of interest to DeAnthony as these topics
related to money. DeAnthony provided and example of how his 4
th
grade teacher was able to
connect mathematics learning to the everyday experience of using money. The relevance is not
necessarily cultural, but relevant to his everyday life. The examples provided by Quentin and
DeAnthony are consistent with one of Berry’s four factors contributing to African American
boys’ learning mathematics and adopting math identities. They both were learning
computational fluency through relevance to day-to-day activities.
Theme 1 Summary
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 137
The African American male participants seemed to have identified more strongly with
mathematics when their teachers created lessons and presented instruction that the participants
considered to be relevant to real life. They provided few examples of instruction tied to African
American culture specifically. However, most of these experiences occurred during elementary
school rather than middle school or high school except with Mrs. Rivers and Mrs. Morgan.
Although the participants discussed the importance of Algebra 1 relevancy, they provided
few examples of culturally relevant mathematics such as the examples discussed by Gay (2010).
Gay (2010) stated that lessons that engaged students in trips, hair braiding, shopping, star
navigating, making pattern designs, making or listening to music, creating art, cooking, and
games could all be used to increase the relevancy of mathematics to students’ culture,
particularly African American males.
Based on the teacher and student interviews, it appears there were instances of
engagement that students recalled as relevant to their desire or ability to learn mathematics.
Experiences like collaboratively analyzing their own test results facilitated by their teacher
provided relevance and helped them take ownership of their own learning and develop a growth
mindset. Analyzing statistics regarding African American students’ admission to and completion
of college also helped them discover ways in which learning math was relevant to their lives.
Also, teachers stated they constructed word problems that were relevant to the lives of their
students. Creating an atmosphere in which African American males’ interests in sports and rap
music was socially relevant made them comfortable being themselves in relation to their math
teacher. This kind of experience may not have been directly related to mathematics, but it had the
potential to reduce barriers to the teaching-learning relationship. Teachers mentioned the practice
they utilized to make students more comfortable in the math classroom; however, no students
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 138
referred to it as one of the ways they directly developed a positive perception of themselves as
mathematics learners.
Theme 2: Repetition
The student participants asserted that repetition and practice with math problems has been
instrumental in their learning mathematics. Their statements are consistent with research that
asserts students are able to memorize algorithms and learn new concepts when teachers provide
adequate opportunity for the students to repeatedly practice algorithms and their relationship to
new concepts. The students were able to memorize and learn the algorithms. Often, the student
participants stated that their teachers would make themselves available for tutoring when they
needed extra help. In the tutoring setting, teachers and students had the opportunity to repeat
information and learning experiences that had occurred in class. In addition, the student
participants stated that their teachers provided opportunities for the students to practice with
partners and/or cooperative groups, which the student participants considered to be instrumental
in their learning mathematics and in their mindset that they were capable of learning math.
Pullman Catholic High School required all students to take Algebra 1 in ninth grade, even if they
took it in middle school. This policy provided opportunities for repeating information and
concepts.
Emmitt. Emmitt responded to the question regarding what study habits (if any) that
pertain to math did he begin to formulate in elementary by stating that he would just practice
going through problems over and over. He stated that 4th grade was when he began to really
understand math. He stated, “I was already pretty good with the multiplication and stuff, which
came in handy.” Emmitt also stated that his 8th grade Algebra 1 teacher repeatedly told him that
he would need to try problems over and over again and attend tutoring if he wanted to become
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 139
efficient. Emmitt concurs with his Algebra 1 teacher, stating: “With math, it’s like you got to
practice it a lot to get good in my opinion.” However, Emmitt also stated that, although he
personally practiced problems repeatedly, many of the students in his 8th grade Algebra 1 class
did not have many opportunities to practice math problems. “The class was unruly and the
teacher was unable to enforce policies such as completing assignments and taking notes.” This
student’s comment points out the importance of generalized pedagogy that engages students in
learning. This kind of pedagogy does involve creating an environment of mutual respect for
students’ differences. Effective pedagogy includes classroom management routines, accountable
talk, and rules that give all students equitable opportunities to learn. Emmitt asserted that his 9th
grade Algebra 1 teacher provided plenty of opportunities for practice. When asked what he
remembers most about his teacher that helped him believe he could be a high achiever in Algebra
1, he stated,
I’d actually pay attention and do everything the teacher asked me to do. When the test came,
it was easy and I did pretty good on it. She does a lot of tutoring after school and I’ll go to
that. We do a lot of practice and when we’re done with our tests we do this thing called error
analysis where you check all your mistakes to see what you did wrong on a test and how you
can do better. We have action plans where we make a graph or a little calendar saying what
we’re going to do to prepare for our next test or quiz or whatever. We’re covering all the
stuff that we did so I don’t forget it, I remember that too. Because with my 8th grade Algebra
1 teacher, it was like we’d just go through all the lesson plans and then right at the end we
could just have a short note review of everything that we learned and that’s it. With Mrs.
Rivers it keeps on coming back to the surface so you don’t really forget it.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 140
According to Emmitt, Mrs. Rivers’ pedagogy involves multiple opportunities for students to
repeat and practice what they have learned. In this respect, Emmitt valued the opportunities for
extra practice that was provided by Mrs. Rivers in comparison to his Algebra 1 teacher in the 8th
grade.
During observations, it was noted that Mrs. Rivers provided time for students to practice
problems individually, in pairs, and in groups. Mrs. Rivers had a timer and would allot a period
of time during the day to complete specified tasks. During the first five minutes of the class, Mrs.
Rivers gave a warm-up activity in which students discussed growth versus fixed mindsets. Next,
students had 30 minutes to work in pairs, groups, and/or individually to complete error analysis.
Error analysis was an assignment where students were given a graded test and took on the
task of determining and correcting errors that were made on incorrect problems. Mrs. Rivers kept
a timer and the timer was set to ring after the time allotted for a specific task ended. This kind of
activity provided additional opportunities for students to repeat and rehearse information and
concepts. By working in groups, students could learn from one another as they presented
information and concepts in ways that might be more culturally relevant. Mrs. Rivers gave
copies of a reference sheet to the students with examples of the correct procedures for
completing all problems. Students used the reference sheet as a tool to help with their error
analysis. All students were deeply engaged in the error analysis activity.
Mike. Mike stated that elementary teachers taught him that “repetition was the best way
for learning, and the only way to learn things is to keep trying and keep practicing until you
understand it.” In addition, Mike responded to the question about what study habits (if any) that
pertain to math he began to formulate in elementary by stating,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 141
Making up practice problems. Instead of finding real ones from a textbook, making them
up yourself. A really good habit. Not for word problems, but for quadratic equations that
I did. Make up hard ones. Doing specific quadratic equations. I guess (x+43)
2
. Making
that into a quadratic then putting it back as a regular quadratic equation, expanding it.
Mike stated that he would create specific problems and practice completing those problems.
Mike considers Mr. Zody to be a “pretty good” teacher stating that Mr. Zody “allowed a lot of
time doing a lot of repetition of things.”
Not only does this pedagogical practice on the part of the teacher provide opportunities
for practice and repetition, it is also culturally relevant. When students make up their own
problems they demonstrate conceptual understanding in contexts that are familiar to them.
Corey. Corey stated that he was challenged in learning the quadratic formula and solving
quadratic equations. He mentioned that one of his teachers, Mrs. Morgan, would allow time for
students to practice in addition to using a song to help students remember the quadratic formula.
Corey stated, “I would always write out the steps when practicing problems on my own.” I
would ask myself: “What did I do from this step to get to this step”? This process is a
demonstration of Vygotsky’s concept of the role of language in apprenticing students to acquire
language that they later turn into inner speech as they attempt to complete tasks. It is critical to
the metacognition students need to develop an identity as a mathematics learner. Corey
acknowledged that many questions on tests would say, “Suzie did this for the question and made
a mistake. What was Suzie’s mistake.” Corey stated that the practice and analysis of his methods
for arriving to solutions has helped to prepare him for success on tests in which the question asks
to identify mistakes. It is noteworthy here that Corey did not refer to explicit instruction from a
teacher that he learned practice strategies. It appeared to be a technique he learned on his own. In
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 142
using this technique, he was developing factual knowledge, but not conceptual knowledge which
may require a teacher to guide the process
Drew. Drew provides an example of repetition within a group setting in which students
also developed conceptual understanding. Drew stated that his 4th grade elementary teacher
would place students in groups and allow the students to practice problems together. “The
teacher would give us problems and allow us to solve the problems together. Then we would
quiz each other on the problems.” Drew stated that his 8th grade Algebra 1 teacher would assign
individual work and students would work on the problems until they figured out the solutions.
“She would have us think as hard as we could until we just couldn’t get what we needed. It was
basically try to help yourself until you absolutely needed help.” This practice cited in the 2011
Trends in International Mathematics and Science Study Report (Mullis et al., 2012), was
reported to be a practice employed in nations like Japan. It requires students to be metacognitive
about what they have learned in a social setting and thus develop math identities. Drew
responded to the question as to the study habits and/or problem-solving strategies he developed
on his own to which he attributed his ability to learn mathematics by stating,
For me it would be like thinking outside the box. Not thinking like everybody thinks.
Like if there’s a problem, and there’s multiple ways to solve it, I probably would solve it
in a more unusual way than everybody else. So, basically, thinking outside the box and
doing things unusually.
Drew attributed his identity as a learner of mathematics to these study habits and practices
cultivated by his teachers. These pedagogical practices on the part of the teacher require deep
math content knowledge as well a math content pedagogy.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 143
Quentin. Quentin asserted that teachers have also helped him by allowing him to have
time to practice problems, stating that a few of his elementary teachers would stay after class to
help him with mathematics. In addition, Quentin stated that his mom was a teacher and would
require him to write notes and study for a minimum of two hours each night. Quentin attributed
the development of his math learning habits to his mother’s influence.
Quentin responded to the question regarding what strategies his Algebra 1 teacher
implement that have helped him to learn mathematics by stating,
I would say reinforcement, just reinforcing ideas so everyone got it. That helps. It helped
me understand the subject better. Well there was a lot of group projects we did, so that
always made it easier. Tests. That’s a big one. Probably just those two. For her, it was
reinforcement. Just drilling until it was installed in your memory forever.
Quentin explains that his Algebra 1 teacher helped him to be successful by reinforcing
concepts. Quentin responded to the question as to what study habits and/or problem-solving
strategies he developed on his own to which he attributed his ability to learn mathematics by
stating, “Well, now I just do practice problems. If the teacher gives 1 through 10 out of 40
problems, I’ll do 10 extra problems to make sure I understand those 10 problems for the test or
quiz or whatever.” Quentin credited the extra practice, in part, to his Algebra 1 success, and,
ultimately, his continued mathematical success.
DeAnthony. DeAnthony stated that his elementary school teachers allowed time for him
to practice decimal and fractions. He remembered that decimals were challenging, and it was
necessary to practice problems involving decimals in order for him to understand them. He
recalled being given scratch paper by his fourth grade teacher, and calculating discounts and
profits. DeAnthony stated that these problems often involved operations with decimals.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 144
DeAnthony credited his 8th grade Algebra 1 teacher with giving him time to study and allowing
him to come to after-school tutoring for extra practice.
In addition, DeAnthony would practice completing homework problems after his graded
homework was corrected and returned. He would often attempt to reproduce the correct
algorithms and solutions without looking at his graded homework paper. DeAnthony credited “a
lot of practicing” on math problems, reading and re-reading math questions, and practicing the
use of formulas for his success in mathematics.
These students’ willingness to practice over and over suggests high levels of motivation.
They seemed to attribute this willingness to teachers who showed them strategies and contexts in
which to engage in practice, rather than just telling them to do it. From these experiences, they
saw results that motivated them to continue. This pedagogical practice seems to reflect
Resnick’s (1995) notion of effort vs. ability, which gives more weight to the value of effort than
perceived ability in students (Resnick, 1995).
Theme 2 Summary
The student participants credited some of the teachers for allotting time to practice
problems as being instrumental to their learning mathematical factual knowledge, and in some
cases, such as Mrs. Rivers, to their mathematics conceptual knowledge. The students stated that
some teachers, like Mrs. Rivers, allowed them to work in pairs; others allowed them to work
individually. In some cases, the teachers did not allow any time to practice individually or in
groups; however, a few of the students took it upon themselves to practice their algorithms or
factual knowledge, and in some cases, mathematics problems that contributed to their conceptual
understanding, and developing a positive math identity. It is not clear from these students what
motivated them to take on this personal responsibility.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 145
Theme 3: Relationships
The student participants asserted that, when their teachers create classroom environments
where they are comfortable working with one another, seeking assistance from the teacher and/or
their peers, and being involved in classroom discussions, they feel empowered to learn math, and
positively identify with math. The student participants described how some of their teachers
would approach them to make sure they understood the math, allow them to work with groups, in
pairs, or individually, and make themselves available for tutoring or extra help outside of class
time. The manner in which teachers build positive relationships with their students, and facilitate
positive relationships between students and their peers, has, in part, played a role in the African
American male student participants’ Algebra 1 success.
Emmitt. Emmitt asserted that his elementary teachers treated him “well around math”
and made him feel that he was special. Emmitt stated, it was like they were treating me like I was
special but not bad, like I had a lot of potential as to…they’d help me after school, they came in
the class to help me out. In addition, Emmitt stated that his middle school teachers encouraged
him and he felt good about praise such as, “See, I knew you could do it.”
Emmitt’s middle school teacher encouraged him to attend tutoring when necessary,
although he admitted that he could not attend, or chose not to attend tutoring because he
participated in sports and often attended practice after school.
Emmitt did not discuss relationships with his 8th grade Algebra 1 teacher. He stated
that he received a poor grade in his 8th grade Algebra class, no one worked or took notes, and
students constantly talked while the teacher talked. Emmitt stated, “They just played around and
stuff.” According to Emmitt, this particular teacher did not successfully develop a strong
teacher-student learning relationship with him, nor create an instructional environment that
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encouraged students to work together, and/or approach the teacher for assistance. However, he
described his 8th grade Algebra teacher as fair in disciplining the students. He responded to the
question regarding how his teacher treated him as an African American male learning math by
stating, “Well, I would get in trouble and it was with somebody else or something. A group of us
did something, so it’d get them into trouble too.” Emmitt considered himself to be “bad” in his
8th grade Algebra 1 course, but he took responsibility for his behavior in did not state that the
teacher punished him excessively or disproportionately in relationship to other students.
The description of this class may lend weight to the concept that without effective
pedagogy that engages students, even the students with potential get caught up in oppositional
behavior or in behavior that runs counter to learning academic content. It also lends merit to Mr.
Zody who said he allowed the students to discuss sports and rapping. Although he had not
succeeded in integrating this particular relevance to content pedagogy, the students did have a
social context for learning and for developing positive identities, which may or may not have
contributed to their math identities. His approach may have encouraged students to come to class
and develop positive learning relationships within the class, and with the teacher.
Emmitt explained how his ninth grade Algebra 1 teacher was more interactive than his
eighth grade Algebra 1 teacher. Emmitt stated, “She does a lot of tutoring after school and I’ll
go to that. Mrs. Rivers is just more interactive in general. She works with the board a lot more.
At first, I thought she was lazy but she really isn’t. She works hard and, yeah, she has helped the
kids more. She made these working groups and she has the tutoring as I said before and after and
the error analysis help too.” It appears that Mrs. Rivers has the content pedagogy to organize
groups into in a manner that fosters effective learning.
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Emmitt seemed to have developed a rapport with Mrs. Rivers. During observations, Mrs.
Rivers frequently circulated the classroom and checked on him and other students to see if they
understood the mathematical concepts. Mrs. Rivers would often go to different groups to check
on their level of understanding. During one instance, Mrs. Rivers reported to Emmitt’s group
stating, “Are you doing okay on the assignment, Emmitt”? Emmitt nodded. Mrs. Rivers stated,
“Think about what this would be if you need both equations to cancel. I want you to determine
what is linear and what is not linear.” Mrs. Rivers’ level of questioning invited analysis and
evaluation, which are the highest dimensions of cognitive engagement according to Bloom’s
Taxonomy. These questions invited the students to be metacognitive about mathematics.
Metacognition is an important element in developing a positive mathematical identity (Ambrose
et al., 2010), because students are engaged in high levels of thinking that enable them to
construct knowledge and key concepts.
Mrs. Rivers used various instructional techniques to build positive relationships with her
students. Emmitt was one of her more challenging students, yet she had strategies to keep him on
task. On several occasions, Emmitt would lose focus and play games or start conversations that
were off the topic while working in his group. Mrs. Rivers never confronted him nor any of the
other students when they were off task. Mrs. Rivers constantly circulated the class to help
students. Instead of confronting individual students who were off task, she stopped when she
noticed the majority of the students were off task. She said,
Okay, by showing me your thumbs, tell me how productive you have been so far.
Thumbs up mean 75% or higher productivity, thumbs in the middle means somewhere between
50% to 75% productivity, and thumbs down means less than 50% or you have spent less than
half the time on task.
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When students held up their thumbs, Mrs. Rivers got an idea of who considered themselves to be
on task and who admitted to being off task over half the time period. Next Mrs. Rivers stated,
“Okay, for the next 15 minutes, I want everyone to shoot for 100% productivity.” In addition to
her in-class strategies, Mrs. Rivers also made herself available for tutoring before and after
school. Mrs. Rivers seemed to have a positive teaching-learning relationship with her students,
including students like Emmitt, who was prone to getting off task. Emmitt spoke of Mrs. Rivers
with respect and gratitude for her teaching.
Mike. Mike did not mention ways in which his elementary teachers built positive
mathematical relationships with students. However, he did discuss his 8th grade Algebra 1
teacher and how she helped him learn Algebra 1:
One thing that she really did was she made us students help each other in a sense. So, it
helped you when you were trying to help someone else with a problem. It was sort of that
you knew how to do it, but they didn’t know it and vice versa a lot of times. If they can
do it and they can teach me, then I can, obviously, do it, too. Mike stated that his Algebra
1 teacher would have lecture days at times, and at other times cooperative learning days
He also asserted that his Algebra 1 teacher created a relaxed learning environment. His
description of this teacher indicates the teacher had strong content pedagogy for teaching
mathematics.
Although Mr. Zody was selected to participate in the study because he taught a section of
Algebra 1, Mike, who was a student participant in the study, was a student in Mr. Zody’s
geometry class. Therefore, Mike’s description of his teaching in the geometry class was
included in the findings to indicate the kind of relationship Mike had with his math teacher at the
time of this study.
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Mike stated that Mr. Zody, was “empowering,” and would constantly remind him of his
potential. He appreciated Mr. Zody telling him that “you could learn mathematics faster than
most people.” During classroom observations, it was noted that Mr. Zody’s students worked
individually as well as in groups. Mr. Zody played classical music during the class. While
students were in groups, Mr. Zody circulated the classroom constantly, helping students with
math problems.
During the observation, a few students were off task during the group work. Mr. Zody
never confronted students who were off task. Instead, he focused on helping individual students
and groups, as he circulated the classroom. In order to refocus the students and groups, Mr. Zody
gave one warning to the class as a whole. He stated, “If you do not use your time wisely, your
final test may suffer.” The students regained their focus after Mr. Zody’s comment regarding the
final test. Several students also stated that they would report to Mr. Zody’s class after school for
tutoring. Mr. Zody told the students that he was unavailable on that particular day due to our
scheduled interview.
It was noted that Mr. Zody used warnings and reminders of the final test in order to
refocus students. The frequency with which Mr. Zody had to remind students to stay on task may
have indicated that his instructions to groups were inadequate. It is not clear whether their
response to his warning was because of their relationship with him or because they did not want
to get a bad grade on the test. Several students reported to Mr. Zody’s class during the interview,
seeking math tutoring from him. On several occasions, Mr. Zody turned the students away due
to our scheduled interview. Mr. Zody asserted in the interview that he had built a strong rapport
with his students, and they were eager to learn math.
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Several students reported to Mr. Zody after school for tutoring. Mr. Zody’s students may
have sought extra help and tutoring outside class time in order to perform well on the final test. It
is evident the students felt comfortable coming to him after class. In that sense, they had a
positive relationship with him, but the need for large numbers to come for tutoring may have
indicated that they did not have a strong teacher-student relationship with him that enabled them
to learn math in the context of the day-to-day instruction in a way that led to math student
identities. His relationship with them did not seem to foster effective first teaching and learning.
They may have been over-reliant on after-school tutoring. Therefore, it is likely that Mr. Zody
lacked the necessary pedagogical skills to develop relationships with his students that lead to
confident math identities. Yet, the influence of his relationship with students is significant.
Corey. Corey asserted that his elementary teachers were great in the kinds of
relationships they developed with students. He stated that his first teacher, Mrs. Sims (he did not
recall the grade), taught him to never give up on his math. Corey struggled with math, but Mrs.
Sims always gave Corey hope and helped him learn to persevere through challenges with
mathematics. Corey stated that he pushed to develop strong relationships with his mathematics
teachers. Corey responded to the question regarding what study habits and/or problem-solving
strategies he developed on his own to which he attributed his ability to learn mathematics by
stating,
I would like to ask. I did a lot of asking questions. I would be like, “Okay, how did you
go from 25 to 5? How did you divide that? What is multiplication? How did you go from
a fraction to that?” Then I would also ask...sometimes, I would go back to the class at
recess, talk to the teacher, have a one-on-one session because I felt like teachers are better
in terms of talking to you solo than doing a group because they’re more focused on you.”
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Corey stated that he went to a predominantly African American school and he had African
American teachers. Corey discussed interactions with his 2nd grade teacher, Mrs. Conroy:
She would always tell me, “Corey, you’re very smart. You should definitely be going
wherever you’re going.” She always gave me tips on what to do. She would tell me,
“Okay, assess the problem. Read the question. Don’t just rush into it! Sometimes I would
just look at just the numbers and then one of the numbers didn’t even go with the
question. She always taught me, “Make sure you read the question. Assess the problem.
Which formula is going to be used in terms of are you going to be adding, multiplying,
dividing?” That always stuck with me. “Make sure you read the question, be able to
break it down from, okay, you take the biggest number, subtract it, then go to this, and
then there.”
Corey asserted that he asked questions as early as 2nd grade when he did not understand the
math”
I know for sure they rather let me have an A than [get an] F…Some people would just be
like, “Oh man, what? What? What?” How did they go from this then there?” They won’t
ask a question even when they don’t understand. That’s why I’d be like, “I need to ask
this question because I can’t be worrying about that.”
During middle school, Corey continued to be assertive as a student and asked questions
when he did not understand. He stated that his 8th grade Algebra 1 teacher, Mrs. Morgan,
encouraged the students to work together and help one another with the math. Corey stated the
following regarding Mrs. Morgan’s Algebra 1 class: “She had us in groups, so we would have to
figure out how to solve problems together. She would just give us a random question and then
your group would have to figure out.”
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In addition, Corey asserted that Mrs. Morgan’s “quadratic equation song” helped him to
memorize the quadratic formula. Corey responded to the question about what an observer would
see if one were to go into Mrs. Morgan’s class for classroom observations by stating,
She makes the students involved. She tries to help them out constantly. She would always
help someone out in terms of a lesson. She was very clear in her work. She always tells
you how to do it, and so, yeah, that’s one thing I would say you’ll probably see. Yeah,
she helped me a lot. She always...because I remember one day, she did find out that I did
copy off of a friend, and she was like, “Come on now, you know you shouldn’t be doing
that.” I told her I needed help with the stuff, and then she really helped me out. She even
made me go to tutoring, which I did even though I was angry because I had to come after
school and do this, but it was for the better because it really did help me with that
studying. Then I ended up getting an A on that test and I was like, “Hard work pays off.”
Regarding relationships, Corey added how he believes teachers often had biased attitudes
towards African American students and the effects that those biases had towards African
American students:
I think teachers do come with a bias towards the African American kids because they feel
like they’re going to most likely be loud, they’re going to be talking to their friends a lot;
so, I really tried to go against that stigma. I would make sure I was going to be...I think
that really drove me, too, because I was surrounded by other races. I was like, I need to
show them that I can do what they really wouldn’t think I could do. They feel like
African Americans are going to be loud, they’re disrespectful, they’re full of attitudes,
usually the girls, and they feel like the boys just talk too much. They always interrupt the
class. They always got to be making jokes. I’d just be like, “Yeah, sometimes, most of
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the time, but it just depends on the student. Sometimes, they just don’t care. Sometimes
they do actually care. It’s just that they feel like the teacher isn’t helping them enough. I
always felt like I always did the work, I always went through the things, and just showed
them that not every African American student is…You shouldn’t follow that bias.
Throughout the interview, Corey discussed ways in which he was able to build positive
school relationships with teachers. He credits these relationships with helping him to develop a
positive mathematics identity. Corey experienced mathematical success in elementary, middle
school, and high school, although Corey’s assertion that teacher biases are consistent with the
narrative of the mathematical incapable African American male (Taylor, 1999; Howard, 2010).
Racial stereotypes and biases are so deeply embedded in the psyche of many educators that they
are often unnoticed, unintentional, and/or misunderstood as acts of encouragement (Steele &
Aronson, 1995; Sue et al., 2007). Corey used teacher biases as motivation to develop a math
student identity that exceeded some teachers’ expectations of African American males.
African American males are often portrayed as lazy, lacking mathematical ability, and/or
uninterested (Sue et al., 2007). Corey recognized these biases and was determined to create a
counter-narrative that identified him as mathematically capable, focused, and cooperative. In a
fashion similar to that of the African American males in Stinson’s (2008) study, Corey
negotiated the White-male-math-myth as well as discourses of deficiency and rejection to
positively identify with mathematics and experience favorable mathematics outcomes in
elementary school, middle school, and high school.
Drew. Drew explained how his elementary teachers helped him by teaching tricks that
he found interesting. He stated that his 4th grade teacher, Mr. Walker, would always give tricks
that made math easier: “Mr. Walker focused on math a lot during elementary school. We did a
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 154
lot of math in his class.” Drew responded to the question about what study habits (if any) that
pertain to math he began to formulate in elementary by stating, “It was studying in groups
because me, as a person, I don’t like to do things alone. I always like to have somebody doing
something with me.” This statement from Drew is indicative of African American culture, so
teachers who provide opportunities for interactive group learning are providing culturally
responsive pedagogy (Gay, 2010). Drew also stated: “Studying with groups makes it more
enjoyable for me. I actually retain information more. Yeah, when there was a test coming up or
something, he would have us get…we sat in table groups and we would all study, like quiz each
other and everything, on what we had just learned.”
Drew explained how his elementary teacher helped him by allowing him to build a
mathematical relationship with his peers through cooperative group learning Drew stated that
Mrs. Morgan was always available to give extra help when he felt that he needed tutoring. In
addition, he felt comfortable enough in Mrs. Morgan’s Algebra 1 class to ask questions when he
felt the need to ask questions about the mathematics.
Through cooperative learning, tutoring, extra help, and individual tasks, Drew considered
Mrs. Morgan to have been instrumental in his development of a positive math identity. Drew
responded to the question regarding what strategies his 8th grade math teacher implement that
helped him learn mathematics by stating that Mrs. Morgan was very supportive and helped him
when he did not understand the mathematics. He stated that Mrs. Morgan cared and wanted to
help ensure that he developed a deep understanding of Algebra 1 concepts. which in turn,
supported the development of a positive math identity.
Quentin. Quentin asserted that his elementary teachers were helpful in that they
supported him by allowing him to struggle with mathematics and encouraged him to put forth
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 155
effort on tests. In particular, Quentin stated that his 3rd grade teacher was very supportive and
helped him to understand math. He stated that she would reward students when they were able to
give correct answers. Students’ relational connections with mathematics and their mathematics
teacher, engagement in the uniqueness of mathematics and various forms of extrinsic recognition,
must all be a part of mathematics instruction (Berry et al., 2011). This is what constitutes
pedagogy that elicits the development of a positive mathematics identity for African American
males.
Although Quentin mentioned he had some really good teachers, he also stated that he had
“bad” teachers who were not supportive. Although he had some “bad” teachers who were not
supportive, and did not make themselves available for tutoring and extra help, he was able to
persevere through early struggles with mathematics. Quentin stated that his Algebra 1 teacher
was very welcoming. She was energetic and eager to assist students mathematically whenever
she could. However, Quentin stated that his high school teachers did not always make
themselves available for extra help and tutoring. In comparing the teachers at SELA to the
teachers at his previous private school, Quentin stated,
I would say the difference is availability. Because I know most of the teachers here, they
leave like, what? Twenty minutes after the bell rings? There, they would stay as late as
probably 6:00. Just availability and just being there to help students. That showed some
extra effort.
Although Quentin did not feel that his SELA teachers worked to develop strong
mathematical relationships with the students, he was, nonetheless, able to excel mathematically
and receive high marks in math. Perhaps his positive experiences in elementary school enabled
him to succeed with his high school teachers.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 156
DeAnthony. DeAnthony asserted that he found fractions and decimals to be challenging
throughout elementary, and his elementary teachers did an excellent job of helping him through
his early mathematical struggles. In describing his 8th grade Algebra 1 teacher, he stated,
She tutored after school step by step. I wasn’t getting Algebra at the beginning, but the
practice from after-school tutoring help me get better at it. People who weren’t really
getting it practiced after school, and corrected each other’s work. In addition to the after-
school tutoring.
DeAnthony’s Algebra 1 teacher provided regular feedback on homework assignments.
DeAnthony stated that his teacher was extremely fair, and he felt very comfortable as an African
American student in her class.
Theme 3 Summary
The participants showed that positive relationships with mathematics teachers play an
important role in their development of mathematical identities, which contributed to their ability
to learn Algebra 1. Further, when mathematics teachers are adept at facilitating positive
mathematical relationships between students and their peers, African American males feel
comfortable and become more interested in the math, which in turn, motivates them to put forth
more effort and persevere through challenges. These positive relationships are developed through
cooperative groups, extra help/tutoring, mathematical songs and games, class discussions,
teacher feedback, checking for understanding, equitable disciplinary procedures, and one-on-one
tutoring with their own teacher.
Often, the teacher participants would focus so much on instruction and assisting students
during individual or group work, that behaviors that lead to teacher chastisement and disciplinary
measures went without teachers addressing it on an individual level during the class time. Instead,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 157
the teacher used various strategies and instructional techniques to eliminate these behaviors
including placing the onus on students for completing assignments, listening to instruction, and
thinking and talking mathematically. Siwatu and Starker (2010) asserted that the disproportionate
numbers of African American males who underachieve mathematically could be due, in part, to
inequitable disciplinary procedures. Cultural differences between teachers and African American
males could lead to cultural conflicts where African American males are removed from
mathematics classes (Siwatu & Starker, 2010).
The African American males in this study were successful due, in part, to the
development of positive relationships with teachers. According to interview and observational
data, the Algebra 1 teachers understood African American males’ behaviors and did not remove
the students from classes or fail to make themselves available when African American male
participants needed extra tutoring or help. Instead, the African American male participants stated
that their math teachers were fair, interactive, and used various instructional techniques to help
them maintain their positive self-efficacy, which, in turn, led to the development of positive
mathematical identities.
Although the African American males in this study developed a positive mathematical
identity, the pedagogy of some of their teachers, particularly those who often provided tutoring,
was not consistent with the literature. It is evident in the need for tutoring that the student
participants sought extra help outside of the allotted classroom time to improve their skills and
increase their level of conceptual understanding. The teacher participants implemented strategies
supported by the literature, such as cooperative groups, awareness of cultural assets and norms,
and creating lessons, that embed aspects of African American culture into the instruction. When
the student participants experienced teachers who implemented this suggested pedagogy, and the
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 158
teacher participants utilized this suggested pedagogy, African American males tended to
experience success without the need for extra help and tutoring outside the allotted class times.
Chapter Four Summary
Math Content Beyond Algebra 2
Three of the four teacher participants agree that Algebra 1 teachers should have math
content knowledge at the calculus level while one of the teachers asserted that the minimal level
of math content knowledge for Algebra 1 teachers should be at the Algebra 2 level. These
findings are consistent with Hill et al.’s (2004) assertion that teachers’ math content knowledge
should be higher than the general math knowledge held by most adults. Algebra 1 teachers
should be knowledgeable of mathematics beyond Algebra 2, since Algebra 1 teachers must
assess and evaluate Algebra 1 student work, progress, and level of comprehension (Hill et al.,
2004).
All of the teachers in the study emphasized the need for deep mathematics content
knowledge. Three of the four rated the depth and quality of their math content knowledge for
Algebra 1 at 4 based on a scale of one to five with one being minimally knowledgeable and five
being highly knowledgeable. The lone teacher to rate herself below a 4 on content knowledge
stated that she did not believe that she maintained the depth and knowledge of Algebra 1 at a
level that was necessary to effectively teach it over the course of her 20 years of teaching math
due, in part, to the lack of exposure to mathematics beyond Algebra 1. There was not much
discussion from student participants related to teachers’ deep math content knowledge.
Fixed Versus Growth
Mrs. Rivers facilitated her students’ creation of action plans and error analysis activities
to develop a growth mindset, as she consistently circulated the classroom asking probing
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 159
questions and seeking responses that were indicative of a growth mindset. Mr. Zody also
circulated his classroom, and facilitated error analysis activities, although there was no evidence
of student-created action plans. Error analysis activities, facilitated by teachers who had strong
content knowledge, appears to be a powerful tool for helping students adopt a growth mindset.
Although neither of the teacher participants from SELA High School incorporated growth
mindset pedagogy into their lessons, they both asserted that it is important for students to be
motivated to put forth effort towards learning mathematics.
Both teacher participants from SELA understood that students who believed they are
capable math students were more likely to persist and persevere when they did not perform well
initially, which is consistent with a positive belief about one’s ability and consistent with a
growth mindset. However, neither of the teacher participants from SELA understood the role of
the teacher in developing a growth mindset for their students, particularly African American
males. Growth mindset pedagogy is important although teachers did not implement this
pedagogy in the same manner. Some teachers used error analysis, and fostered metacognition
with interactive lessons, while others relied on rote memorization.
Interactive Environments
Mr. Zody was the most adamant of the four teacher participants regarding the need for
direct instruction in Algebra 1. Although his teacher preparation program promoted the use of
cooperative learning, he expressed the belief that direct instruction is the best method for
Algebra 1 instruction. During the observations, Mr. Zody did implement cooperative learning
strategies, but often reverted to direct teaching, which encouraged rote memorization of algebraic
facts and algorithmic procedures (Flores, 2007; Gutierrez, 2008a; Martin, 2007). Among others,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 160
much emphasis was placed on rote learning and teacher directed learning. Only one teacher gave
evidence tied to standards in designing tasks that were related to standards.
Relevancy
Two of the student participants reflected on their learning the quadratic formula and
attributed their learning of the quadratic formula to a song that their teacher created to help them
memorize it. One of the student participants, Quentin, stated that he lost interest in math after
leaving private school, where they made math fun, interesting and relevant. Finally, another
student participant, DeAnthony identified with mathematics during elementary when his teachers
focused on profits and discounts and how relevant finances were to mathematics.
There was not much evidence of deeply embedded culturally relevant pedagogy at any
grade level. Teachers’ pedagogy was more relevant to kids’ day-to-day activities. The teachers
did express a need to develop lessons that are culturally relevant, but did not seem to have the
knowledge and or conceptual understanding of what entails deeply embedd culturally relevant
instruction.
Relationships
Students treasured teacher-student learning relationships more during primary grades. In
high school, there was more metacognition through error analysis and some attention to higher
levels of thinking. Among others, much emphasis was placed on rote learning and teacher-
directed learning. There was a lot of remedial work particular to teachers who did not foster good
first teaching. When day-to-day first teaching was inadequate, many students returned for
tutoring and extra help or practice.
Building teacher-student learning relationships allowed some participants to provide an
environment that encouraged and invited students’ requests for tutoring or extra help and
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 161
practice. However, the teacher-student learning relationships that are inviting of tutoring and
extra practice outside of the classroom structure does not replace strong content knowledge,
strong content pedagogy, and mathematics relevancy.

ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 162
CHAPTER FIVE: DISCUSSION
Chapter One presented the problem of African American males’ history of low
achievement in Algebra1. The purpose of the study is to contribute to the research that focuses
on how teacher pedagogy can contribute to African American males’ Algebra 1 success. Chapter
Two is a review of literature that pertains to the problem of low Algebra 1 achievement from the
perspective of CRT. Chapter Three described the method for this study, which was qualitative.
Chapter Four presented the findings, and Chapter Five summarizes the findings, discusses their
implication, and follows with recommendations for fostering African American males’ Algebra 1
success.
Research Questions
This study was guided by the following research questions: (1) What pedagogical content
knowledge do secondary math teachers believe is necessary for teaching Algebra 1 to African
American males? (2) How can Algebra 1 teachers’ pedagogy support African American males’
in developing a positive mathematics identity?
Summary of Findings
The data collected from observations and interviews presented the following themes in
response to research question one: math content knowledge beyond Algebra 2, fostering a
growth versus fixed mindset for students, and creating an interactive environment that is
culturally relevant. These findings indicate teachers’ beliefs about what is needed to support
African American males in successfully completing Algebra 1 and in developing math identities.
These are the actions that may be able to counter the experiences that critical race theorists
describe as typical for African American males.
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Math Content Knowledge Beyond Algebra 2
Teachers need high levels of content knowledge to be able to respond to the varied levels
of understanding among students and to help them rethink misconceptions they have developed
about mathematics from their learning experiences prior to taking Algebra 1. In-service
professional development rarely addressed the issue of teachers’ lack of content knowledge or
maintenance of content knowledge due to the perceived importance of focusing on mandated
district initiatives. Most teachers in this study displayed adequate content knowledge, but some
struggled with implementing content pedagogy.
Fixed Versus Growth Mindset Pedagogy
The development of a growth mindset was an essential part of the teacher participants’
Algebra 1 pedagogy, particularly the two participants from Pullman Catholic High School. They
both incorporated pedagogy aimed at transforming students’ mindset, particularly that of African
American males’, from fixed or believing that math is an ability that some people have while
others do not, to growth wherein students believe that math is attainable through effort (Donovan
& Bransford, 2005; Dweck, 2006).
Although the teacher participants showed minimal evidence that they viewed African
American male culture as an asset to be incorporated directly into activities for learning
mathematics, popular culture was used by some to build a relationship with students.
Discussions on topics related to popular culture, such as hip-hop and sports, as well as
discussions on topics related to social justice and injustice like gang violence, prison, and
African American males’ underrepresentation in colleges and universities are examples of
culturally responsive teaching, although these examples were not deeply embedded within their
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 164
Algebra 1 instruction. These examples show that the teacher participants were aware of issues
that positively and negatively affect African American males.
Interactive Environment Pedagogy
The teacher participants agreed on the importance of pedagogy that supports an
interactive classroom environment for African American males. African American males can
share problem-solving strategies, explain solutions to various algebraic problems, and justify
answers in a sociocultural context (Lerman, 2000; Steele, 2001). Further, teachers created an
algebraic culture for learning and this culture supports African American males as they
internalize the algebraic language and function as algebraic thinkers (Steele, 2001).
Math Identities. The data collected through interviews and observations of teacher and
student participants presented the following themes in response to research question two:
relevancy, repetition, and relationships. The participants all agreed that students, particularly
African American males, can strongly identify with Algebra 1 when they are allowed to develop
student-teacher mathematical relationships, and mathematical relationships with their peers.
Relevancy. Although the teachers did not demonstrate or express deep understanding of
African American culture, nor ways to incorporate that culture in their math lessons, the teachers
did understand the importance of tying math learning to social issues that affect African
American males such as disparities in African American students’ access to college admission
and employment. Some teachers (mainly elementary school teachers) tied math learning to
students’ everyday experiences. They also used pop culture to connect to their students at a
personal level. Teachers also used music as a way to help students memorize formulas. One of
the student participants, Quentin, lost interest in math at one point and DeAnthony identified
more with mathematics during elementary school.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 165
The study pointed out the importance of elementary school experiences in students’
development of math learner identities. The pedagogies employed by elementary school
teachers provided learning strategies and knowledge that students continued to use in middle
school and high school. Positive learning experiences in elementary school remained strong and
students valued those memories through high school.
Teacher participants spoke of the need to increase the relevancy of algebra to their
students, particularly African American males. However, the teacher participants mentioned few
examples of lessons that show the relevancy of Algebra 1 to African American males’ culture as
well as African American males as individuals.
Repetition. The student participants asserted that the repetition of mathematical
algorithms led, in part, to their mathematical success, particularly in Algebra 1. Student
participants gave examples such as practicing during class and after school, and taking notes as
means by which they were allotted time to repeat and practice completing Algebra 1 problems.
Although the student participants assert that repetition and practice are essential for
understanding mathematics, repetition and practice can lead to rote memorization (Flores, 2007;
Gutierrez, 2008; Martin, 2007). Teachers need to build upon this knowledge to help students
build math concepts.
Relationships. The student and teacher participants asserted that it is important for
teachers and students to develop positive mathematics relationships. The student and teacher
participants asserted that students are more likely to positively identify with Algebra 1 if their
teachers create an environment that encourages cooperative learning, seeking assistance from
peers and/or the teacher, and participating in class discussions. Cooperative learning groups,
after-school help or tutoring, teacher feedback, and mathematical song and games are some of
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 166
the ways teachers can build positive mathematical relationships with their students and
encourage students to interact with their peers.
African American males are more likely to positively identify with Algebra 1 if the
teacher can build positive mathematical relationships (Steele, 2001). It is important for African
American males to develop positive Algebra 1 relationships with teachers and peers, as they are
often viewed as mathematically incapable of positively identifying with Algebra 1 (Oyserman et
al., 1995; Nasir & Saxe, 2003). Since African American males are often socialized out of a
positive identification with mathematics due, in part, to socially constructed norms (Oyserman et
al., 1995; Nasir & Saxe, 2003), the facilitation of positive relationships between them and
Algebra 1 teachers is crucial to their development as well as their maintenance of a positive
Algebra 1 identity, as they continue to construct their personal identities.
In some cases, students’ perceptions of teacher bias, led them to construct counter
narratives about who they are as a math student. They adopted math learner identities that they
believed were acceptable to teachers to prove to teachers they are the exception to stereotypes
about African American students.
Implications for Practice
The findings from this study indicate that there is a need for Algebra 1 teachers to
maintain their content knowledge at or beyond the level of Algebra 2 as well as increase their
pedagogical knowledge for teaching Algebra 2. Increasing and/or maintaining teachers’ level of
content and pedagogical knowledge is related to findings on content knowledge, growth mindset,
and repetition. Deep content knowledge enables teachers to provide instruction in a variety of
ways suitable to different students’ ways of learning. Further, it may be necessary for teacher
education programs to monitor teachers well into their teaching careers and keep Algebra 1
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 167
teachers updated on the latest advances in teacher education research, as well as push for Algebra
1 teachers to maintain their content knowledge beyond Algebra 2.
In addition to strengthening content and pedagogical knowledge for Algebra 1, social and
cultural perspectives of Algebra 1 should be taught in teacher preparation programs and
reinforced as part of ongoing teacher development as teachers work together to create Algebra 1
lessons. The focus on social and cultural perspectives of Algebra 1 is a key factor in the findings
regarding making Algebra 1 relevant, interactive environment pedagogy, and repetition.
Several of the student participants, although relatively successful mathematically,
discussed the need for tutoring in order to maintain a level of competence in Algebra 1.
Considering relatively large class sizes in most schools, schools may need to build small-group
tutoring into African American students’ school day. Students seem to benefit from the close
relationships they build with their teachers in these small settings. However, the
disproportionately high volume of African American males seeking tutoring in comparison to
other ethnic groups, suggests that African American males’ cultural and social assets may not be
considered when teachers create and plan Algebra 1 lessons.
Recommendations
Recommendation 1: Continuously Support Algebra 1 Teachers in Developing and
Maintaining Deep Content Knowledge of Algebra 2 and Beyond
Findings from the study reveal that teachers are more effective and have increased self-
efficacy when their content knowledge is strong. The teacher participants acknowledged the
importance of developing and maintaining content knowledge for teaching math. Since African
American males have consistently underperformed in mathematics, they should have access to
teachers who have the mathematical content knowledge to present math in a meaningful,
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 168
descriptive way (Flores, 2007; Vygotsky, 1978). Teacher education programs should equip
teachers with the necessary means for developing and maintaining the content knowledge and
pedagogical content knowledge for teaching math (Ball et al., 2008). Professional development
is needed to place more emphasis on ensuring teachers have strong mathematics content in order
to strengthen content pedagogy. Schools, to the extent possible, need to require the teachers they
hire, including elementary school teachers, to demonstrate a minimal level of mathematics
knowledge, including algebra. Students’ math conceptualization and the math identities that
prepare them for Algebra 1 start with their elementary school experiences.
Recommendation 2: Develop Lessons That Are Relevant to The Social Lives and Culture of
African American Males
The student participants stated that math was much more interesting and fun when
teachers made math relevant to their culture and daily lives. The teacher participants asserted that
they are more successful and students respond better when the math is relevant. Although the
examples presented, such as the use of song, error analysis projects, test reviews, and action
plans, may demonstrate teachers’ effort and awareness of the need to create interactive lessons
that are related to students’ culture, students’ culture should be considered an asset to learning
and thus embedded into teachers’ lessons. Further, African American males’ culture should be a
focal point of Algebra 1 instruction. Moses (2001) stated that teachers should not be lecturers
who attempt to pour knowledge into students’ intellect. Students should be encouraged to
experience mathematics by sharing their mathematical experiences and cultivating an algebraic
discourse for learning (Steele, 2003). Teachers need a deeper understanding of African
American students’ culture expressed through their language patterns in order to tap into how
they express their conceptual understanding. Teachers need to understand African American
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 169
students’ social engagement patterns that are linked to their culture. It will help teachers
organize group-learning activities that allow students to bring their cultural capital to the learning
process.
Recommendation 3: Algebra 1 Teachers Should Consistently Reflect on Algebra 1
Pedagogy for Biases and Culturally Insensitive Practices
Since racism is deeply embedded in the psyche of many mathematics teachers, it is
necessary for Algebra 1 teachers to consistently reflect on their pedagogy. Rodgers (2002)
asserted that a reflective cycle can play a crucial role in shifting teachers’ thinking from a focus
on their teaching to a focus on student learning. One of the goals of the reflective cycle, which
could reveal teacher biases, prejudices, and/or micro-aggressions, is to think critically about
student learning through reflection, and consider what student learning reveals about their
teaching, the subject matter, and how student learning, teachers’ teaching, and the subject matter
interrelate (Rodgers, 2002).
Recommendation 4: Consider Purposeful Repetition, especially in the Early Grades, As A
Way to Promote the Background Knowledge Students Need to Construct Mathematical
Concepts
Just as teachers promote automaticity in decoding to enable students to focus on making
meaning from text, students need a level of automaticity with algorithms so they can focus on
more complex math concepts.
Recommendation 5: Recruit African American Math Teachers
Colleges need to be intentional about recruiting potential African American mathematics
teachers. The recruitment can begin as early as high school, or even middle school, by creating a
pipeline to college for students who demonstrate an interest and proficiency in mathematics with
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 170
intention of creating more African American math teachers. Teacher preparation programs
should also recruit teacher candidates from historically Black colleges and build partnerships
with civic organizations in the African American community to provide scholarship to these
promising candidates.
Recommendation 6: Future Research
Based on these findings and implications, the following research questions could be addressed
for future reference:
1. How does a sociocultural-based mathematics curriculum have an impact on the self-
efficacy of African American males?
2. What is the role of the administrator in increasing Algebra 1 teachers’ pedagogical
content knowledge?
3. What is the role of teacher education programs in developing secondary math teachers’
self-efficacy in urban schools?
Conclusion
African American males have a history of underperformance in mathematics, particularly
Algebra 1. There are not enough stories of their mathematics success, which could help break the
continuous cycle of underachieving and underperforming (Howard, 2010). The narrative of the
underachievement and underperformance must be shifted to determine how schools’ culture can
foster their mathematical success (Howard, 2010).
The researcher presented findings that included teacher content knowledge, fixed versus
growth mindset, interactive environments, making math relevant, math repetition, and building
relationships. These findings uncover ways in which teachers’ pedagogy may foster Algebra 1
success for African American males. These findings also suggest that Algebra 1 teachers play a
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 171
major role in African American males’ math identity development. Since these students have a
history of underperformance and a lack of college access (Ladson-Billings, 1998), it is crucial to
present the counter-narrative to the underperforming, unmotivated, African American male.
African American males can be mathematically successful and gain access to higher education,
which, in turn, may lead to careers in STEM-related fields. This study uncovered some of the
practices that enable African American males to experience favorable outcomes in mathematics.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 172
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ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 196
Appendix A
Student Interview Protocol
A Teacher Pedagogy for Mathematically Successful African American Males.
INTERVIEW QUESTIONS (ALGEBRA 1/Math Student)
SEMI-STRUCTURED ALGEBRA 1 STUDENT INTERVIEW PROTOCOL
The following questions allow the participants to share their experiences as
Algebra 1/math students:.
Identifiers:
A) What is your current grade level?
B) How old are you?
C) What middle school did you attend?
D) What year did you first take Algebra 1?
We are going to begin with you telling me about your math experiences you remember
from elementary school.
1). How has your elementary schooling prepared you for success in math?
2). What study habits (if any) did you begin to formulate in elementary?
3) What are some of your earliest memories of studying mathematics in elementary school?
Now let ’s talk about your experiences in learning mathematics in middle school.
4) What strategies did your 8
th
grade math teacher implement that have helped you to maintain
success in mathematic?
5) What study habits and/or problem-solving strategies did you develop on your own to which
you attribute your ability to learn in mathematics?
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 197
6) Describe yourself in a few sentences as a mathematics student. What descriptors apply to you
as a mathematics student?
7) How do you think your Algebra 1 teacher would describe you as a mathematics student?
What words would that teacher use to describe you as a math learner?
8) What did it feel like to be a student in your Algebra 1 class? Who did most of the talking in
class: the teacher, students in small groups, teacher and students together?
9) How did your teacher treat you as an African American male learning math?
In what ways was did your race and gender matter in the way the classroom?
10) What do you remember about your teacher that helped you believe you could be a high
achiever in Algebra 1?
11) In which areas of mathematics are most confident: a) solving equations; b) word problems;
c) explaining how you solved a problem; d) using math formulas? e) computations f) others
12) What mathematical strategies did your middle school teacher implement that you attribute to
your becoming a proficient in Algebra 1?
13) What particular lessons do you recall in middle to which you attribute your successful
completion of Algebra 1?
14) What experiences in middle school, if any, shaped your perception of mathematics?
These next few questions are about your experiences as a math student in high school.
15) Describe for me your experiences as a math student so far in high school. What are some of
the positive experiences that stand out in your mind?
16) In what ways did your middle school teachers, particularly your Algebra 1 teacher, prepare
you for continuing to progress in learning mathematics in high school?
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 198
17) What challenges if any are you presently experiencing in your learning mathematics in high
school?
18) What mathematical knowledge do you think a middle school math teacher should have in
order to teach Algebra 1 and related math effectively?
19) In what ways (if any) do you feel and act differently in the context of your math class in
comparison to your other classes?
20) In what ways (if any) do you feel and act differently in the context of your math class
compared to when you are socializing with friends?
21) How have parents (if at all) assisted or influenced you in becoming a confident and proficient
mathematics learner?
22) Is there anything else you would like to add to the interview?

ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 199
Appendix B
Interview Questions (Algebra 1 Teacher)
SEMI-STRUCTURED ALGEBRA 1 TEACHER INTERVIEW PROTOCOL A Study of
Mathematically Successful African American Males.
The following questions allow the participants to share their beliefs, practices, and experiences
as Algebra 1math teachers.
1. What math classes do you currently teach?
2. What math classes have you taught in the past?
3. Do you have an undergraduate or graduate degree in mathematics?
4. Have you had classes in mathematics pedagogy?
5. Have you had classes in culturally relevant and responsive pedagogy?
6. How many years have you taught middle school math?
7. How many years have you taught Algebra 1?
8. How long have you taught Algebra 1 in middle school?
Share with me for a few minutes what being a middle school mathematics teacher is like for you.
Share some of your most rewarding experiences. Share some of your challenges, frustrations,
and disappointments as a teacher.
9. Describe some of your own experiences as a mathematics student that you recall,
especially around learning algebra in in middle school, high school, and/or college
10. What experiences as a student can you remember shaped your perception of yourself as a
math learner?
11. Describe aspects of your teaching that you consider to be culturally responsive,
particularly for African American males? Give examples.
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 200
13. How do the African American males in your classes respond to your culturally responsive
pedagogy?
14. On a scale of 1 to 5 (with 1 representing minimally responsive and 5 representing highly
knowledgeable) rate the depth and quality of your math content knowledge?)
15. What mathematical content knowledge should a middle school math teacher have in order to
teach effectively?
16. What challenges, if any, have you experienced in teaching African American males?
17. What do you believe are some of the reasons for the performance gap between African
American males and other subgroups’ levels of achievement in Algebra 1?
18. What are the most important foundational skills, if any, an 8
th
grade student needs to have
upon entering your classroom to be able to achieve proficiency in Algebra 1?
19. Describe the level and type of engagement of African American males who complete your
Algebra 1 class with a grade of “B” or higher and/or test as proficient?
20. What kind of learning environment do you believe all students need to be successful learners
of mathematics?
21. On a scale of 1 to 5 (with 1 representing least and 5 representing most) rate how well your
college coursework prepared you for teaching math content?
22. On a scale of 1 to 5 (with 1 representing least and 5 representing most) how well did your
college coursework prepare you for implementing math content pedagogy?
23. On a scale of 1 to 5 (with 1 representing least and 5 representing most) how well did your
teacher education program prepare you for teaching African American males?
24. What do you wish your teacher education program had included to better prepare you for
teaching math to African American male student?
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 201
25. In your years of experience, what differences in readiness for Algebra 1have you noticed
between African American males and members of other ethnic and gender groups?
26. What learning theories learned in your teacher preparation program guide your thinking as
you plan instruction?
27. Is there anything else you would like to add to the interview?
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 202
Appendix C
Teacher Observation Protocols
Classroom Observation Instrument

Teacher _______________________ Level/Class ______ Number of Students _____

Lesson Title __________________________________________________________

1. Physical Setting/Classroom Environment (Mark all that apply.)
A. Classroom Facility
 Classroom adequate size for student number
 Adequate storage for resources/materials/equipment
 Furnishings allow for inquiry-based instruction
 Student Seating ____ rows ____ pairs _____ small groups ____ other
______________
 Room size will accommodate activities
 Flat top surfaces are sufficient for investigations, projects, displays, etc.

B. Classroom Environment
 Math manipulatives/tools evident
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 203
 Math displays/posters promote learning
 Core curriculum materials evident
 Math student work displayed
 Adequate resources available for hands-on lesson (as appropriate)

C. 21
st
Century Tools
 Class set of calculators available - type ________________________
 Interactive Whiteboard
 Number of computers available to students ____ teacher ____
 Projection system
 Document camera

2. Lesson Effectiveness (Mark all that apply.)

A. Major Instructional Resources Used
 Textbook  Manipulatives  Computer to access
Internet
 Other print materials  Calculators  Computer to
collect/analyze data
 Overhead  Overhead Calculator  Computer to practice a
skill
 CD/DVD 21st Century Tools Math tools (rulers,
compass, protractor, etc.)
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 204
 Document Camera  TI-Navigator  Palms
 GPS Software like Sketchpad, Tinkperplots, or Fathom

B. Content Focus
 Number/computation
 Algebra/pre-calculus/calculus
 Geometry
 Measurement
 Data/Probability

C. Content Delivery
 Instructional resources used appropriately and effectively
 Content presented is accurate
 Use of real-world context
 Focus on problem solving
 Students solved one or more non-routine, or open-ended problems

D. Inquiry-Based Lesson Design
 Launch
 Investigation
 Summary/Closure

E. Grouping Arrangement(s) Used
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 205
 Whole Group
 Small groups working on same task
 Small groups working on different tasks
 Individuals working on same task
 Individuals working on different tasks
 Grouping arrangements were appropriate for the instructional goal and activity

F. Teacher and Student Behaviors Observed
Teacher Behaviors
 Setting up and guiding students through meaningful real-world problems
 Moving around the room monitoring/questioning
 Encouraging students to consider multiple ways to solve problems/test solutions
 Guiding students in the use of manipulatives/technology
 Promoting student use of inquiry/creativity through questioning/collaboration
 Facilitating discussions about problem-solving processes/ efficiency/effectiveness
 Leading students through discussions/journaling of their understanding
Student Behaviors
 Interacting with others
 Working alone
 Working in groups to test solutions
 Working in teams to challenge and defend solutions
 Applying math to real-world problems
21
st
Century Information and Communication Skills
ALGEBRA 1 SUCCESS FOR AFRICAN AMERICAN MALES 206
 Sharing solution processes and listening to others share their thinking
 Defending solution processes’ efficiency and usefulness
 Communicating math ideas: demonstrations, models, drawings, and arguments
 Helping to clarify each other’s learning through discussion/modeling
G. Instructional Strategies
 Connection to prior knowledge
 Provides differentiated instruction
 Teacher modeling
 Collaborative grouping
 Opportunities for students to justify solutions
 Incorporate varied assessments

3. Questioning Strategies (Mark all that apply.)
 Wait Time I  Wait Time II  No/limited wait time
 Questions were higher-order and stimulated broad student responses
 Questions were lower-cognitive and stimulated narrow student responses
No questions were asked by the teacher or posed through the activity being conducted

Abstract (if available)

Abstract This study examines the experiences of mathematically successful African American males in secondary Algebra 1 courses through the lens of critical race theory (CRT). The purpose of this study was to contribute to the knowledge of how to promote their success in mathematics, particularly Algebra1, when there are structures in place that impede their mathematics success. Further, this study aims to determine how teachers’ pedagogy may or may not have contributed to African American males’ Algebra 1 success. Qualitative methods were used to collect data from the interviews and classroom observations of 10 participants. The 10 participants include six African American males and four high school Algebra 1 teachers. The data was then transcribed and coded for analyzing in relationship to the following research questions: (1) What pedagogical content knowledge do secondary math teachers believe is necessary for teaching Algebra 1 to African American males? (2) How can Algebra 1 teachers’ pedagogy support African American males in developing a positive mathematics identity? ❧ Findings from this study suggest that teachers’ math content knowledge for teaching Algebra 1 be beyond that of Algebra 2 with some knowledge of calculus. In addition, Algebra 1 teachers should be able to foster a growth mindset for African American males who have not developed a positive mathematics identity, and they should be able to create an interactive classroom environment for teaching and learning Algebra 1. Further, Algebra 1 teachers should be able to provide Algebra 1 instruction that is relevant to African American males’ daily lives and culture, provide opportunities for students to practice skills and develop strong factual knowledge, and create a classroom environment that is inviting of student-teacher interaction as well as student interaction with their peers. ❧ The implications of this study is that teacher education programs as well as in-service professional development should prepare teachers for teaching math by equipping them with the proper content knowledge and monitoring them to ensure that they maintain the level of content knowledge. In addition, teacher education programs as well as in-service professional development should teach cultural and social perspectives of math, including Algebra 1, and reinforce this knowledge as part of an ongoing teacher development process. Finally, schools should implement small-group settings or Algebra 1 support courses into the school curriculum to supplement Algebra 1 content learning and help negate African American males’ reliance on tutoring in order to benefit from their Algebra 1 instruction.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Frelix, Darius (author)

Core Title The role of secondary mathematics teachers in fostering the Algebra 1 success of African American males

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Degree Conferral Date 2016-12

Publication Date 09/29/2016

Defense Date 09/07/2016

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

Tag African American,males,mathematics,OAI-PMH Harvest,Success

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Rousseau, Sylvia (committee chair), Carbone, Paula (committee member), Hasan, Angela (committee member)

Creator Email dfree2009@hotmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC11214590

Unique identifier UC11214590

Identifier etd-FrelixDari-4856.pdf (filename)

Legacy Identifier etd-FrelixDari-4856

Dmrecord 311637

Document Type Dissertation

Format theses (aat)

Rights Frelix, Darius

Internet Media Type application/pdf

Type texts

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

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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

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