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Best practices to improve mathematics achievement of middle school Latina/o students

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Best practices to improve mathematics achievement of middle school Latina/o students

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Best Practices to Improve Mathematics Achievement of Middle School Latina/o Students
by
Aida Boulatian

Rossier School of Education
University of Southern California
A dissertation submitted to the faculty
in partial fulfillment of the requirements for the degree of
Doctor of Education

May 2021

© Copyright by Aida Boulatian 2021
All Rights Reserved

The Committee for Aida Boulatian certifies the approval of this Dissertation

Rudy Castruita
John Roach
David Cash, Committee Chair

Rossier School of Education
University of Southern California
2021

iv

Abstract
The low academic achievement rates of Latina/o students within mathematics are a complex and
multi-faceted issue that needs addressing. With a growing number of Latina/o students within
California, teachers need to adapt to the diverse needs of students within their classrooms.
Understanding the different challenges that Latina/o students face within the school, and
approaching these challenges, is essential and can provide more equitable outcomes for these
students. The purpose of this study is to identify the best practices that can be implemented
within middle school mathematics classrooms to ensure increases in the achievement levels of
Latina/o students. This study uses a mixed-methods approach of both quantitative and qualitative
data. The study conducts surveys and interviews with middle school mathematics teachers in Los
Angeles county to discover instructional methods that best support Latina/o students. The study
provides strategies for other middle school mathematics teachers to facilitate classroom
instruction that evokes interest and critical thinking.
Keywords: middle school mathematics, Latina/o students, best practices in mathematics
instruction, technology integration, Critical Race Theory, Culturally Responsive Teaching.

v

Dedication
To my husband, parents, and brother, I could not have achieved this without your love and
support.

vi

Acknowledgements
For a very long time, I have dreamt of the moment when I complete this dissertation.
Without the support of my dissertation committee, parents, brother, and husband, I would not be
able to achieve this goal.
I would like to thank my dissertation chairs, Dr. Cash and Dr. Castruita. Dr. Cash, I
cannot thank you enough for all the support you have provided during this process. You have
been so patient and kind with all my questions. Without your guidance, I am not sure how I
could have gotten this far. Dr. Castruita, thank you for constantly keeping me encouraged and
motivated to reach the end of such a beautiful journey. Most importantly, thank you both for
teaching us all how to be better leaders of tomorrow. Finally, thank you Dr. Roach for taking
your time in joining our committee and providing such great feedback. I am honored to have had
such incredible support from you all.
I would like to thank my dad, mom, and brother for cheering me on right from the
moment I got accepted into the program. Thank you for having faith in me and always reminding
me that I can accomplish anything I set my heart to.
And a very special thank you to my husband, Artur. Thank you for the countless
moments of motivating me to complete my work. Thank you for believing in me and always
being equally excited as I was about completing this milestone. Thank you for keeping a smile
on my face even at the most stressful times. Thank you for your constant love and support-it
means the world to me.

vii

Table of Contents
Abstract .......................................................................................................................................... iv
Dedication ....................................................................................................................................... v
Acknowledgements ........................................................................................................................ vi
List of Figures ................................................................................................................................ ix
Chapter One: Overview of the Study .............................................................................................. 1
Background of the Problem ................................................................................................ 1
Statement of the Problem .................................................................................................... 3
Purpose of the Study ........................................................................................................... 4
Research Questions ............................................................................................................. 4
Significance of the Study .................................................................................................... 5
Limitation and Delimitations .............................................................................................. 6
Definition of Terms ............................................................................................................. 6
Organization of the Study ................................................................................................... 8
Chapter Two: Review of the Literature .......................................................................................... 9
Historical Perspective ......................................................................................................... 9
Latino Students and the Achievement Gap ....................................................................... 11
Impact of Classroom Instruction and Quality on Math Education ................................... 12
Best Practices Highlighted in Research ............................................................................ 14
Theoretical Framework ..................................................................................................... 19
Chapter Three: Methodology ........................................................................................................ 22
Purpose of the Study ......................................................................................................... 22
Selection of the Population ............................................................................................... 23
Design Summary ............................................................................................................... 24

viii

Instrumentation and Protocols .......................................................................................... 25
Data Collection ................................................................................................................. 26
Data Analysis .................................................................................................................... 27
Validity and Reliability ..................................................................................................... 27
Summary ........................................................................................................................... 28
Chapter Four: Results or Findings ................................................................................................ 29
Research Questions ........................................................................................................... 30
Purpose of the Study ......................................................................................................... 31
Coding of Data .................................................................................................................. 31
Findings ............................................................................................................................ 32
Research Question One ..................................................................................................... 32
Research Question Two .................................................................................................... 45
Research Question Three .................................................................................................. 56
Summary ........................................................................................................................... 70
Chapter Five: Discussion .............................................................................................................. 71
Findings ............................................................................................................................ 72
Limitations and Delimitations ........................................................................................... 79
Implications for Practice ................................................................................................... 79
Future Research ................................................................................................................ 80
Conclusion ........................................................................................................................ 81
References ..................................................................................................................................... 82

ix

List of Figures
Figure 1: Survey Participants’ Perspectives on Student-Teacher Relationships. .......................... 34
Figure 2: Survey Participants’ Perspectives on Heterogenous Grouping. .................................... 38
Figure 3: Survey Participants’ Perspectives on Heterogenous Grouping and Academics. ........... 39
Figure 4: Survey Participants’ Perspectives on Culture and Relevance of Content. .................... 42
Figure 5: Survey Participants’ Perspectives on Using Student Work and Assessments
for Self-Evaluation. ........................................................................................................... 46

Figure 6: Survey Participants’ Perspectives on Meeting with Colleagues for
Self-Evaluation. ................................................................................................................ 49

Figure 7: Survey Participants’ Perspectives for Reflecting on Strategies Used Within
the Classroom. ................................................................................................................... 50

Figure 8: Survey Participants’ Perspectives on Professional Development. ................................ 54
Figure 9: Survey Participants’ Perspectives on Use of Technology for Latina/o
Students to Learn at their own Pace. ................................................................................. 58

Figure 10: Survey Participants’ Perspectives on Technology and Individualized Learning. ........ 59
Figure 11: Survey Participants’ Perspectives on Technology and Higher Achievement
Levels of Latina/o Students. ............................................................................................. 60

Figure 12: Survey Participants’ Perspectives on Culture and Relevance of Content. .................. 68

1

Chapter One: Overview of the Study
While the number of Latina/o students continues to increase in California’s public
education system, teachers continue to face challenges with adequately serving the needs of
culturally different students. The academic achievement gap across races is one of the main
issues that continues to exist and increase regarding educational inequities (Mitchell, 2018). One
of the main subjects with a noticeably large achievement gap among Latina/o students and their
white counterparts is in mathematics. Achieving grade level proficiency in mathematics is an
essential need for students to pass through the education system successfully.
Furthermore, all students deserve an equal opportunity to succeed academically and enter
the workforce being prepared with the right skills to conduct the work required of them. The
California Department of Education, under its equity framework, states that it is the teachers’ and
school leaders’ responsibility to ensure equity by attending to the diverse challenges of the
students they serve (California Department of Education, 2019). In October 2019, state
superintendent Tony Thurmond announced that only 39.73% of all students met or exceeded the
California Assessment of Student Performance and Progress (CAASPP) summative assessment
for mathematics (California Department of Education, 2019). Teachers must use the best
practices to provide effective instruction for all students. Furthermore, teachers should continue
to evaluate the strategies used within classrooms to ensure the effectiveness of instruction.
Background of the Problem
Throughout the past, Latina/o students have continued to perform at lower levels
compared to their white counterparts (Flores, 2007). Even though there have been minimal
improvements in the Latina/o mathematics levels, these levels are insignificant compared to the
achievement of White students (Madrid, 2011). Per the CAASPP mathematics scores, there are
little to no changes in the levels of middle school Latina/o students who met or exceeded the
2

state standards from 2015 to 2018 (California Department of Education, 2019). The percent of
sixth-grade students in the Los Angeles county who met or exceeded the mathematics standards
in 2015 was 21%, while in 2018, it was 27% (California Department of Education, 2019). The
percent of seventh grade Latina/o students who met or exceeded the state standards in 2015 was
21%, while in 2018, it was 26% (California Department of Education, 2019). Finally, the percent
of eighth grade Latina/o students who met or exceeded the state standards in 2015 was 21%,
while in 2018, it was 25%. (California Department of Education, 2019).
Data also shows that the performance of White students throughout the same years was
consistently higher than Latina/o students (California Department of Education, 2019). The
percent of sixth-grade White students in the Los Angeles county who met or exceeded the
mathematics standards in 2015 was 51%, while in 2018, it was 58% (California Department of
Education, 2019). The percent of seventh grade White students in the Los Angeles county who
met or exceeded the mathematics standards in 2015 was 51%, while in 2018, it was 57%
(California Department of Education, 2019). Finally, the percent of eighth grade White students
in the Los Angeles county who met or exceeded the mathematics standards in 2015 was 50%,
while in 2018, it was 53% (California Department of Education, 2019).
These achievement gaps have continued to exist throughout the past because of the
different economic circumstances of Latina/o students. Economic inequities have caused
Latina/o students to live in high poverty areas with fewer educational opportunities and resources
available to them (Flores, 2007). Research shows that there is a direct correlation with the level
of quality of education received and income received. The low-quality education received at
schools for low-income students, in this case, Latina/o students has contributed to the
achievement gap in subjects such as mathematics (Erickson & Highsmith, 2018). According to
Flores (2007), Latina/o students have been less likely to have access to qualified and experienced
3

teachers, have faced low expectations, and have been less likely to receive equitable per-student
funding.
Policies such as the No Child Left Behind Act of 2001 and Every Student Succeeds Act
(ESSA) of 2015 were enacted to aid with the existing academic disparities. The No Child Left
Behind Act of 2001was established to create high academic standards for all students and to
diminish the current achievement gaps among students of all racial and ethnic backgrounds. The
act also required teachers to be highly qualified, or in other words, fully certified with a
bachelor’s degree, and have expertise in the subject they are teaching (Lee, 2006). The ESSA
replaced the NCLB and included provisions that were expected to help ensure success for all
students. The policy was expected to advance equity by maintaining protections for America's
disadvantaged and high-need students (California Department of Education, 2019). All students
in America were also expected to be taught to high academic standards that would prepare them
to succeed in the future (California Department of Education, 2019). However, even though
these two different policies were enacted with multiple revisions to ensure the success of
students of other races, such as Latina/o students, we have seen little to no changes in
achievement levels throughout the years.
Statement of the Problem
Latina/o students continue to face academic disparities in their mathematics achievement
levels. Having proper knowledge of mathematics is essential to prepare students to succeed in
college. The achievement levels of Latina/o students within the area of mathematics is a large
area of concern. It is important that all students are taught in ways that help build their
conceptual knowledge and help them make real-world connections with the mathematical
information they learn. Mistakenly, mathematics has been viewed as a universal language for all
and as “culturally-neutral,” which has caused teachers to place little attention on the additional
4

needs of Latina/o students (Ukpokodu, 2011). Because of standardized curriculums and the
pressure to increase student scores, teachers have generally been known to teach to the test
instead of focusing on content and student understanding (Ukpokodu, 2011). This study will
focus on the best practices that teachers and principals can implement within their organizations
to ensure the increase in mathematics achievement levels of Latina/o students.
Purpose of the Study
The purpose of this study was to identify best practices that can be implemented within
middle school mathematics classrooms to ensure increases in the achievement levels of Latina/o
students. This study focused on middle school classrooms within Los Angeles county. It
addressed the academic barriers and disparities that Latina/o students continue to face within
their mathematics classrooms. The study was conducted using personal interviews with teachers.
The purpose of these interviews will be to learn about the most effective strategies teachers have
used within their classrooms that have shown improved results in the mathematics section of the
CAASSP assessments for Latina/o students. The interviews also focused on teachers’ methods of
evaluation used to measure the effectiveness of the practices they have used within their
classrooms. Finally, teachers were asked about the different ways they incorporate technology
into their classes to provide effective instruction for Latina/o students.
Research Questions
The following research questions were used to guide this study:
1. What practices do middle school mathematics teachers use to provide effective
instruction for Latina/o students in Los Angeles county?
2. How do middle school mathematics teachers evaluate the effectiveness of the
practices used in classrooms for Latina/o students in Los Angeles county?
5

3. How do middle school mathematics teachers in Los Angeles county use
technology in their classrooms to provide effective instruction for Latina/o
students?
This study explored the successful practices used by middle school teachers to improve
the mathematics achievement levels of Latina/o students. The research also focused on the
evaluation methods used by organizations to ensure the effectiveness of the strategies
implemented in classrooms. With the latest technology improvements, the study also examined
the use of technological advances to increase middle school Latina/o student achievement in
mathematics. This study was examined through a social constructivist worldview. Since I
interviewed teachers’ experiences and beliefs about the practices that they found most effective
for Latina/o students in their mathematics classrooms, they all had subjective meanings of their
experiences. Like social constructivists, I looked for the complexity of the views instead of
narrowing meanings into ideas (Creswell, 2008). The study used open ended questions for
participants to be able to share their opinions.
Significance of the Study
The poor academic achievement of Latino students has been a complex, multi-layered
problem that must be addressed. Within the California education system, the Latino student
population has continued to grow and increase. However, their poor achievement, especially in
the subject of mathematics, has significant consequences for Latina/o students’ ability to succeed
in the future, for California’s public educational system, and the state’s and nation’s social,
political, and economic future (Madrid, 2011). Mathematics is the critical process of thinking
that engages students in problem posing and problem-solving. With proper mathematics
teaching, students can build strong learning abilities. Every student deserves the opportunity to
receive a quality education that will positively impact their futures. Mathematics scores in
6

assessments such as the CAASSPP can predict student college eligibility, and every student must
be given the equal opportunity to develop these required skills. Latina/o students within
California have been recognized as having one of the most significant achievement gaps in
mathematics and as being the greatest students in need. This study may provide teachers with
insight into the best practices that they can implement into their classrooms to ensure the success
of their Latina/o students. These practices may help teachers provide equitable instruction and
the quality education that all students deserve.
Limitation and Delimitations
This study was limited to middle school mathematics teachers in Los Angeles County in
California and their individual experiences and beliefs on the effective instructional strategies
used within their classrooms. Interview questions were related to the effective strategies used,
how teachers evaluated the effectiveness of these strategies, and the use of technology in their
classrooms. The data received was limited to the personal and individual experiences of the
participants’ in the study.
The delimitations of this study were limited to the geographic region of California and
the number of middle school mathematics teachers interviewed.
Definition of Terms
• Achievement Gap is an expression used to describe the significant difference within
academic performance among students of color and their White counterparts (Mitchell,
2018).
• Educational equity is the attempt to provide different treatments to suit different students’
needs in a fair manner (Catapano, 2013).
• Effective Teachers refers to competent instructors and experts in the subject they are
teaching. These teachers can facilitate new knowledge among students and provide
7

instruction that is interesting, promotes critical thinking, and allows them to learn in
meaningful ways (Sogunro, 2017).
• Equal opportunity means “providing the same resources, opportunity, treatment for each
student” (Bitters, 1997, p. 7).
• Ethnic Background is “a sense of togetherness shared by members of a group linked
through cultural tradition, ancestry, national origin, history, or religion” (Bitters, 1997, p.
7).
• Quality education is providing education effectively engages students in the learning
process; quality education is dynamic, motivating, and uses different delivery styles;
quality education provides best teaching and learning practices to students (Sogunro,
2017).
• “Culturally neutral” refers to content that is designed in a way that incorporates all
students’ cultural experiences to help them learn.
• Race as defined by Bitters (1997) is:
1) biological definition = a concept used by physical anthropologists to
differentiate between various human subgroups based on their physical
characteristics;
2) social definition = a group of people who others believe are biologically
distinct and whom they treat accordingly; a concept used to isolate, separate, and
stigmatize groups, which results in differential treatment of people of different
skin colors. (p. 14)
• Social Constructivism refers to those who hold assumptions that people want to
understand the world that they live and work in (Creswell, 2008).
8

Organization of the Study
A Study of Successful Practices to Improve the Mathematics Achievement Levels of
Middle School Latina/o Students is organized into five chapters. Chapter 1 provides an overview
of the study. This chapter also introduces background information on the disparities experienced
by Latina/o students within their mathematics classrooms and includes definitions of terms that
are important to this study. Chapter 2 presents a literature review that describes effective
instructional strategies within mathematics classrooms, strategies of evaluating effectiveness of
instructional methods, and the use of technology within classrooms. Chapter 3 will include the
methodology of the study and strategies used during research, such as sampling, instrumentation,
data collection, and data analysis. Chapter 4 will include the findings geared for the research
question. Chapter 5 will state the summary of the findings and implications for future practice.
References and appendices will be included at the end of the study.

9

Chapter Two: Review of the Literature
Latina/o students have continuously performed drastically lower than their White
counterparts in mathematics content areas. Having access to quality mathematics education is
important for students to build critical thinking and problem-solving skills that will prepare them
for college. This section will provide a review of the existing literature that relates to the best
practices focused on increasing the mathematics achievement levels of Latina/o students. The
review will begin by discussing policies that were implemented to ensure that schools provide
quality education that meets the needs of all students. The researcher will then look at data
relating to Latina/o students and their relation to the achievement gap. Additionally, various
pedagogical practices found in literature will be reviewed to discover what strategies have helped
improve mathematics achievement levels of Latina/o students. Finally, the theories that frame
this study will be discussed.
Historical Perspective
No Child Left Behind Act of 2002
Throughout the years, many strategies have been implemented using education policies to
increase achievement and attainment levels of Latina/o students (Chudowsky et al., 2007). These
actions have been taken through federal, state, and local levels. One strategy to help eliminate the
achievement gap was known as the No Child Left Behind Act of 2002, which was enacted by
George W. Bush (Chudowsky et al., 2007). Under the NCLB Act, schools were supposed to
strengthen their standards-based reforms and measure achievement levels in grades three to eight
through mathematics and English assessments (Chudowsky et al., 2007). Additionally, NCLB
required schools to show significant increases in subgroup achievement levels, particularly those
at the lower end of the gaps (Chudowsky et al., 2007). NCLB gave state and local districts more
flexibility on how to establish their testing and accountability requirements and with deciding
10

how to use federal funds (Chudowsky et al., 2007). The act was supposed to help assist in
eliminating barriers Latina/o students faced within the education system such as inequitable
funding in high poverty schools, low access to challenging curricula, unqualified teachers, and
unsuccessful parent involvement strategies. The act also required schools and districts to collect
separate data and test results for all major racial-ethnic groups, low-income students, English
language learners, and students with disabilities (Chudowsky et al., 2007).
Every Student succeeds Act of 2015
While the NCLB was designed to address many disparities that exist within the system, it
also created its own barriers (Haller et al., 2016). Some of these barriers included the reduction
of the quality and quantity of instruction due to all the time allocated towards testing (Haller et
al., 2016). In 2015, President Barack Obama passed Every Students Succeeds Act (ESSA) to
address the barriers and challenges that were found in NCLB (Dynarski, 2015). The ESSA holds
information based on nine topics geared towards improving schools and districts.
The first section of the ESSA focuses on refining and improving the programs adopted by
state and local educational organizations (Hope, 2017). It includes detailed information about the
allocation of funds to districts and schools, accountability plans, and education programs for
students of different subgroups (Hope, 2017). The second section focuses on the preparation and
hiring processes of high-quality teachers, principals, and administrators (Hope, 2017). This
requires having enough federal funds that will be allocated towards student achievement, the
effectiveness of teachers, and equitable access to quality education (Hope, 2017). The third
section modifies the allocation of funds needed to improve language instruction for the growing
number of English Learners within the nation (Hope, 2017). The fourth topic revolves around
creating 21
st
-Century schools that include student supports, community learning centers, family
engagement, and student safety programs (Hope, 2017). The fifth section gives states control on
11

how to distribute federal funding across programs (Hope, 2017). The sixth section focuses on the
unique needs of Indian, Native Hawaiian, and Alaska native students to improve their
educational opportunities (Hope, 2017). The seventh section focuses on the impact aid, which is
the funding of schools and districts located on tax-exempt properties. The eighth section focuses
on general provisions such as health services, transportation, and state plans. Finally, the last
segment focuses on the education of homeless students (Hope, 2017).
Latino Students and the Achievement Gap
The number of Latino students has significantly grown not only within our nation but
within California public schools as well (Madrid, 2011). Madrid (2011) stated that Latino
students will soon comprise the majority of the population of schools within California. Data
from the California Department of Education shows that in the 2018-2019 academic school year,
Hispanic and Latino students comprised 54.6% of the population in public schools. Yet, data
from CAASPP mathematics scores shows that changes in the levels of middle school Latina/o
students who met or exceeded the standards from 2015 to 2018 are insignificant (California
Department of Education, 2020). The percent of middle school Latina/o students in Los Angeles
County who met or exceeded the mathematics standards in 2015 was on average 21% while in
2018 it was on average 27% (California Department of Education, 2020). However, the percent
of middle school White students in Los Angeles County who met or exceeded the mathematics
standards in 2015 was on average 50.6% while in 2018 it was on average 56% (California
Department of Education, 2020). This data shows that Latina/o students were performing 29.6%
lower in 2015 and continued to perform 29% lower in 2018.
The achievement of Latino students is affected by many different elements including
quality of instruction (Madrid, 2011). Latino students have been less likely to have access to
high-quality teachers that provide quality mathematics instruction within their classrooms
12

(Flores, 2007). Flores (2007) described that teachers with a lot of experience and qualifications
have been inequitably distributed within educational organizations and districts. Schools that
were populated by mostly Latino and African American students were twice as likely to be
taught by teachers less experienced compared to those at schools with predominantly White
students (Flores, 2007). In his research, Flores (2007) found that the least prepared teacher
recruits were largely populated in schools with the least resources that served the majority of
low-income and minority students. While these students were more likely in need of highly
qualified teachers, they were the least likely to have access to them (Flores, 2007).
Gloria Ladson-Billings (2006) identified many different factors that have contributed to
the existence of the achievement gap. In her research, Ladson-Billings (2006) found that since
the 1960s, there have been multiple cultural deficit theories that suggest children of subgroups
are victims of lifestyles that are restricted from receiving an education that is beneficial to them.
This idea did not just mean having students restricted from only material resources. Instead,
Ladson-Billings (2006) pointed out that research has stated factors such as students’ sense of
control of their surroundings, skilled teachers, and even family backgrounds influence student
achievement levels.
Impact of Classroom Instruction and Quality on Math Education
Research and data have consistently proven the direct link between high-quality
instruction and student achievement (Goe & Sticker, 2008). Researchers have, therefore, always
tried to identify the characteristics that make some teachers more effective than others (Goe &
Stickler, 2008). For example, they have found that asking questions in a timely manner or
facilitating discussions that invoke high-level, content-focused conversations are critical
characteristics of effective teachers (Goe & Stickler, 2008). While there are fundamental
13

characteristics all teachers should have to be effective, there are specific characteristics that are
particularly important in mathematics teachers (Goe & Stickler, 2008).
In his research, Charles (2005) found that a crucial part of quality mathematics teaching
involves teachers understanding the “big ideas” of mathematics and being able to show students
that mathematics is a coherent and interconnected process. These “big ideas” are described as the
topics that are essential to the learning of mathematics (Charles, 2005). Having these topics
broken down will give teachers an easy way to link all essential parts of the content together.
Charles (2005) explained that big ideas in mathematics are the foundation for both a teacher’s
and student’s understanding of the subject. Breaking down the big ideas will allow teachers to
see how each topic is interrelated and to make other real-world connections with the content
(Charles, 2005). Determining the real-world connections will enable teachers to facilitate
discussions that will promote student learning, understanding, and critical thinking (Charles,
2005). Through discussions, students will be able to stay motivated and engaged throughout the
lesson and will quickly grasp concepts without relying on memorization (Charles, 2005).
Establishing classrooms that offer good, quality mathematics instruction will lead
students toward both academic and life-long success (Gutierrez & Irving, 2012). While students
must have a grasp on basic and fundamental concepts of mathematics, they must also be able to
apply the concepts to real-world circumstances (Gutierrez & Irving, 2012). Quality instruction
will demonstrate to students how to transfer the information received from classrooms to other
contexts (Gutierrez & Irving, 2012). This means that when students are presented with real-
world issues, they must be able to accurately diagnose the problem, choose the strategy that best
fits the circumstances, and test the chosen strategy (Gutierrez & Irving, 2012). Receiving quality
mathematics instruction will provide students with the proper skills and tools to critically analyze
and respond to existing issues (Gutierrez & Irving, 2012).
14

Best Practices Highlighted in Research
Integrating Technology
Educators and teachers all have the common goal of improving their students’
proficiency in all subjects, including mathematics. To achieve this, they must create learning
experiences that are personalized to each student’s different needs, particularly in today’s diverse
classrooms (Fazal & Bryant, 2019). Having students at all different levels creates challenges for
teachers to meet the needs of all their students. One method of differentiating instruction in
today’s classrooms is through recent advances in technology (Fazal & Bryant, 2019). Integrating
both technology and traditional teaching methods is known as blended learning (Fazal & Bryant,
2019). Blended classrooms are usually divided into two parts, where the first half is led by their
teacher, and the second half is instructed through online content (Fazal & Bryant, 2019).
Combining both methods of learning gives students more individualized experiences and
opportunities to succeed and gain more content acquisition (Fazal & Bryant, 2019). Using
technology allows for content to be customized at the different paces of students. It also allows
the content to be modified automatically based on frequent responses of students and constant
formative assessments (Fazal & Bryant, 2019). The idea of pacing content individually for each
student gives teachers the opportunity to differentiate instruction within their classrooms (Fazal
& Bryant, 2019).
While having the ability to cater to the different needs of diverse students within a
classroom is captivating, data from blended classrooms still provides inconsistent results in terms
of ensuring the academic growth of students (Fazal & Bryant, 2019). Mackey (2015) found that
students in blended classrooms outperformed students from traditional classes on MAP
assessments. On the other hand, Fazal and Bryant (2019) found that the results of STAAR
assessments were a lot higher for students in traditional classrooms versus students from blended
15

classrooms. Fazal and Bryant (2019) explained that the differences in these results may be from
the different natures of both assessments. While the STAAR assessment measures student
performance based on content standards in regards to specific grade levels, MAP provides a
measure of student achievement over time.
Ozel et al. (2010) also agreed that integrating technology within mathematics classrooms
will result in higher achievement and growth among students. They explained that effective
implementation of technology within classrooms is student-centered and provides diversified
instruction methods. Technology also should not replace traditional methods of mathematics
instruction. Instead, it should be used as additional support to ensure student comprehension of
different standards (Ozel et al., 2010). Technology in mathematics classrooms can create
experiences for students that are active, engaging, applicable, and reflective (Ozel et al., 2010).
However, organizations and teachers will not be able to notice the benefits of technology without
a successful implementation of technology (Ozel et al., 2010). Teachers will require access to
training and professional development in the use of technology within their classrooms that are
appropriate to their grade-levels (Ozel et al., 2010). Minshew and Anderson (2015) explained
that the key to helping teachers recognize the power of technology will be through specific
professional developments that highlight the strategies that these tools can be used to enhance
their pedagogical skills.
Student-Teacher Relationships and Teacher Expectations
Over the years, there has been much research about the significance of caring teachers
having positive impacts on levels of student engagement and growth in students’ academic
knowledge (Jansen & Bartell, 2013). This research is particularly important for students of
subgroups, which are students who share similar racial and ethnic identifications. Students of
different subgroups who perceive that their teachers care for them have continued to outperform
16

those who do not feel the same way about their teachers. Jansen and Bartell (2013) stated that
teachers who care about the success of their students also take time to build relationships with
them. By establishing these relationships, teachers know their students well enough to determine
which methods of support align with each student (Jansen & Bartell, 2013). This will help
teachers better scaffold and deliver content to their students. In this study, Jansen and Bartell
(2013) also found that students are immediately aware when a teacher cares about them and that
these caring environments make students feel welcomed, supported, and engaged in their school
communities. These factors later led to increased performance outcomes for students of different
subgroups (Jansen & Bartell, 2013).
Similarly, Lewis et al. (2012) found that caring teachers can help increase their students’
self-efficacy and confidence in mathematics. When teachers care about their students, they
consistently challenge them and hold them to high expectations. This, in turn, increases students’
perceptions of their abilities in mathematics (Lewis et al., 2012). Lewis et al. (2012) explained
that increased self-efficacy in mathematics has also shown drastic increases in students’
academic achievement. On the other hand, teachers who do not care about their students
generally feel helpless, hold low expectations of their students, and create negative classroom
environments (Flores, 2007). Teachers with such mindsets hinder the learning process of their
students and prevent them from having the opportunity to succeed (Flores, 2007).
Research has also shown that collective teacher efficacy improves school culture and also
increases academic achievement (Donohoo et al., 2018). Collective efficacy is defined as "a
group's shared belief in its conjoint capability to organize and execute the courses of action
required to produce given levels of attainment" (Bandura, 1977, p. 477). Having shared
collective efficacy among faculty and staff within organizations helps to create a shared culture
that focuses on student learning and achievement (Donohoo et al., 2018). Through this model,
17

teachers see themselves as change agents and continuously evaluate their practices through
student achievement (Donohoo et al., 2018). Rather than blaming students for low performance,
teachers focus on changing their pedagogical practices to meet the needs of their students
(Donohoo et al., 2018). These teachers place a great deal of value in collectively solving
problems they come across. Having collective teacher efficacy allows teachers to take
accountability of their own teaching, continuously challenge their students, and produce
improved achievement levels (Donohoo et al., 2018).
Cooperative Learning
Cooperative learning is another strategy that has consistently been used by mathematics
teachers to ensure that they can successfully deliver content that meets the needs of diverse
groups of students (Jao, 2012). Vaughan (2002) has defined cooperative learning as a strategy
where teachers create small, heterogeneous groups of students who will work with one another to
maximize their academic skills. Jao (2012) explained that cooperative learning supports both
academic and social development. When incorporating cooperative learning within mathematics
classrooms, teachers facilitate class sessions that allow students to communicate their
mathematical thinking to others (Jao, 2012). Cooperative learning within mathematics
classrooms will create an environment where students can freely hold discussions and reflect on
their work (Jao, 2012). Research shows group discussions among students helped to lower the
difficulty of the questions and make it less confusing on the students (Morisano et al., 2010).
Reflections also helped students because it allowed them to understand what they did and did not
understand based on feedback provided (Muhammad & Jaafar, 2015).
Additionally, this strategy allows for all students to stay on task and complete their work
by receiving help from their classmates (Jao, 2012). Having cooperative learning will also enable
the students to share different methods of solving mathematical problems (Jao, 2012). It will also
18

give them the opportunity to discuss each issue through the lenses of their diverse cultural
backgrounds (Jao, 2012). This will increase students mathematical understanding, make content
more relative and applicable, and also help students socialize and learn about each other (Jao,
2012).
Jao’s (2012) findings are also supported through a study conducted by Carlan et al.
(2016). The focus of this study was to analyze the impact of cooperative learning on fifth grade
Latina/o students. The results of this study showed that cooperative learning not only improves
Latina/o mathematics achievement levels but also helps improve their language skills. Latina/o
students who participate in cooperative learning consistently worked together to ensure that all
students within their group understood the material by translating material to one another. By
working together, they were able to develop language skills in both languages while also making
sense of mathematical problems. Carlan et al. (2016) realized that students often understood
mathematical concepts, but were unable to communicate or express their answers verbally.
Cooperative learning groups taught them how to express themselves over time through the help
of their peers (Carlan et al., 2016). The study showed that cooperative learning creates engaging
mathematical classrooms where students continuously share ideas and participate in the learning
process (Carlan et al., 2016).
Integrating Culture
The latest research has shown that achievement gaps within mathematics continue to
exist because schools and teachers fail to integrate different cultural aspects that will make
content applicable to their students. Ukpokodu (2011) stated that urban schools fail to recognize
the rich culture students can bring to the learning process that will make education more relevant
and exciting for them. For years, many students have not been able to see the connection to the
mathematics concepts they learn in school with their experiences outside of school (Wager,
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2011). It is essential to understand how students culturally engage in mathematics outside of
school to make content more meaningful (Wager, 2011). Helping students build these
connections will strengthen their thinking skills and improve their academic achievement levels
(Wager, 2011). Understanding the different cultures of students within the classroom will also
help teachers understand the strengths, weaknesses, and needs of diverse learners (Ukpokodu,
2011).
Integrating culture within mathematics classrooms will also allow students to learn
mathematics in ways that are meaningful. When content is meaningful to students interests, it
helps them develop a positive “mathematics identity” (Leonard et al., 2010, p. 261). A
mathematics identity is developed when students’ have the right confidence, motivation, and
persistence needed to succeed in the subject (Leonard et al., 2010). Building these identities are
important for students of subgroups because it helps them break away from racial structures that
have conditioned them to believe they cannot succeed in the subject (Leonard et al., 2010).
Teachers help develop their students mathematical identities by including culturally relevant
examples related to student experiences in their lessons and discussions (Leonard et al., 2010).
Theoretical Framework
Critical Race Theory
One theory important for examining the mathematics achievement levels and gaps among
Latina/o students and their White counterparts is the Critical Race Theory. The Critical Race
Theory (CRT) is a theoretical framework that intends to expose the relationships among race,
power, and societal structures (Larnell et al., 2016). Ladson Billings and Tate (1995) had
introduced CRT to education as an analytical tool to understand the inequalities and inequities
that exist within school structures.
20

Based on Ladson Billings and Tate’s (1995) approach to CRT, it is clear that specific
social structures have created challenging environments for students of different subgroups to
succeed. For years Latina/o students have been deprived of an education that is equitable to that
received by their White counterparts. Through the lens of CRT, we can analyze the continuing
disparities that Latina/o students face within educational organizations because of their race and
culture. CRT also helped this study by bringing awareness to educational inequities.
Understanding these inequities will allow us to find solutions that will lead educational
organizations to greater justice in the future.
Culturally Responsive Pedagogy
Culturally responsive pedagogy is the method of instruction that incorporates students’
cultural references to facilitate their learning process (Ukpokodu, 2011). The use of culturally
responsive pedagogy allows teachers to see the different cultures of the students in their
classrooms as a resource to learning rather than a barrier (Santamaria, 2009). Failing to focus on
the diverse cultural needs of students in the subject of mathematics contributes to their low
achievement levels (Ukpokodu, 2011). To provide students with an exceptional learning
experience, teachers need to provide instruction that is relative to their unique experiences and
cultures (Santamaria, 2009). All students have different approaches to learning, and teachers
must be able to meet their various needs (Santamaria, 2009). Therefore, it is essential that
teachers use varying strategies within their classrooms to meet the diverse needs of all students
(Ukpokodu, 2011). Strategies such as cooperative learning and instructional scaffolding are
directly linked with culturally responsive pedagogy and have shown to be successful for
multicultural classroom environments (Ukpokodu, 2011).
Gutierrez (2000) found that culturally responsive mathematics teachers also know
students well enough to align their interests with challenging mathematical concepts. Teachers
21

take the time to build personal relationships with each individual student in order to relate the
content with their different interests. Santamaria (2009) explained that it is important for teachers
to take accountability for learning about their students’ communities and use their cultures as the
base for learning. Teachers who establish relationships with their students will be able to
understand the individual needs of their students better. Creating these relationships will allow
teachers to help their students reach maximum growth potentials in mathematics context areas
(Gutierrez, 2000). Teachers must also believe that all students have the capability of learning
challenging mathematical concepts (Ladson-Billings, 1997). Teachers must set high expectations
for all students and hold themselves accountable if students are not reaching high levels of
achievement (Ukpokodu, 2011).
Culturally relevant pedagogy is another theory that was used as a lens to interpret the
findings of this study. This theory shows that students have been continuously disconnected from
the subject of mathematics because of organizations’ and teachers’ failing to make content
relevant and meaningful to students. CRP reveals that organizations and teachers have seen
diverse cultures of students as a barrier rather than a resource.

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Chapter Three: Methodology
While having proper mathematics knowledge is essential for preparing students to
succeed in college, Latina/o students continue to face disparities within their classrooms
compared to their White counterparts. The consistent low performance of Latina/o students’
achievement in mathematics courses is a complex and multifaceted issue that must be addressed
(Madrid, 2011). Understanding the different barriers faced by Latina/o students and how teachers
can approach these barriers within classrooms is essential and can provide more equitable
outcomes for these students (Madrid, 2011). It is crucial to uncover mathematics teaching
strategies that are more culturally relevant to meet the needs of Latina/o students.
Purpose of the Study
The purpose of this study was to distinguish the best practices that can be used within
middle school mathematics classrooms to increase achievement levels of Latina/o students. The
study addressed the academic barriers and disparities that Latina/o students have consistently
encountered within their mathematics classrooms. Hearing the different strategies used by
middle school mathematics teachers can provide others with new and effective pedagogical
approaches that could support Latina/o students and their mathematics learning.
Research Questions
The following research questions were used to guide the study:
1. What practices do middle school mathematics teachers use to provide effective
instruction for Latina/o students in Los Angeles county?
2. How do middle school mathematics teachers evaluate the effectiveness of the
practices used in classrooms for Latina/o students in Los Angeles county?
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3. How do middle school mathematics teachers in Los Angeles county use
technology in their classrooms to provide effective instruction for Latina/o
students?
Selection of the Population
The researcher of this study interviewed and surveyed middle school mathematics
teachers in the Los Angeles county to discover instructional methods that best support Latina/o
students. The study may provide strategies for other middle school mathematics teachers that
may help them facilitate classroom instruction that is equitable to the needs of Latina/o students.
The participants included 30 middle school mathematics instructors serving in public
schools within the Los Angeles County during the 2020–2021 school year. Five middle school
mathematics teachers were selected to be interviewed from the Los Angeles County area.
Participants were chosen from local middle schools from the California Department of Education
website. The selected participants for surveys and interviews were teachers with at least three
years of experience teaching middle school mathematics to Latino students.
There were two sampling strategies used by the researcher to conduct the interviews and
surveys for this study. The first strategy was purposeful selection. Purposeful selection is a
sampling strategy based on choosing people, environments, or activities specifically relevant to
the researcher’s questions and goals (Maxwell, 2013). Participants were purposefully chosen in
this study since the researcher had to sample teachers who have had at least three years of
experience teaching middle school mathematics to Latino/a students. These teachers were also
expected to have technology integration within their classrooms. The second strategy used for
this study was convenience sampling, a sampling strategy used to sample based on time, money,
location, or other reasons (Merriam & Tisdell, 2016). The convenience sampling in this specific
24

study was based on location because the researcher picked districts and schools close to where
the researcher lived.
Design Summary
In this study, it was important to conduct both qualitative and quantitative research. The
qualitative aspect allowed the researcher to interact with participants and hear their direct
experiences as teachers within their classrooms. The researcher also used qualitative research to
learn in-depth information about the participants’ knowledge and reasoning about the practices
used to teach mathematics to middle school Latina/o students (Johnson & Christensen, 2014).
The quantitative aspect allowed the researcher to analyze trends through the opinions of those
who participated in the study. Using the mixed-methods approach, the researcher had access to
multiple forms of data to draw conclusions that supported the study (Creswell, 2014).
This study used Maxwell’s (2013), and Creswell’s (2014) recommended steps to
conducting a research study. The study was centered on the research problem and purpose of the
study stated in chapter one. A review of the literature was also provided in chapter two. In
chapter three, the researcher discusses how data was collected. Chapters four and five will focus
on analyzing the findings and stating implications for future practice.
Methodology
The methodology used in this study includes data from both qualitative and quantitative
research methods. The qualitative data comes from interview responses of middle school
mathematics teachers in Los Angeles County. The quantitative data comes from the participants’
responses from the survey questionnaire. For the interview protocol, the researcher used the
interview guide strategy advised by Patton (2002), which is also known as the semi-structured
interview. This strategy allowed the researcher to cover important topics with each person being
interviewed (Patton, 2002). Semi-structured interviews also allowed the researcher to build more
25

in-depth conversations through probing based on the participants’ responses (Patton, 2002). The
researcher also found it important to collect data from both interviews and surveys to discover
what instructional methods supported mathematics learning, reasoning, and problem-solving for
middle school Latina/o students. The interview and survey questions also focused on how middle
school mathematics teachers in Los Angeles County used evaluations and technology to provide
effective instruction for Latina/o students.
Mixed Method
The instrumentation used in this study were specifically chosen to guarantee internal
validity throughout the research process. Using a mixed-methods approach allows for
triangulation, which is the process of collecting information from diverse groups of individuals
and settings using different methods (Maxwell, 2013). The process of triangulation was used by
conducting a literature review, interviews, and surveys. The various methods of data collection
allowed the researcher to ensure coherency throughout the study. The findings were then
connected with the broader theories of Critical Race Theory (CRT) and Culturally Responsive
Pedagogy (CRP).
Instrumentation and Protocols
Qualitative Instrument
To collect qualitative data for this study, the researcher conducted interviews with five
middle school mathematics teachers within Los Angeles County. To ensure each interview was
aligned with the study, an interview guide was created to help answer each research question
(Patton, 2002). The interview protocol begins with a brief introduction of the researcher and the
study and follows with ten open-ended questions that participants should answer. Questions three
and nine from the guide included probes in order to receive more in-depth responses from the
26

participants (Patton, 2002). Each interview was conducted through a web-based platform, known
as Zoom, and were recorded with each participant’s consent.
Quantitative Instrument
To collect quantitative data for this study, the researcher conducted surveys with 30
middle school mathematics teachers within Los Angeles County. Each aspect of the survey was
connected with the research questions. To conduct the surveys, the researcher used
SurveyMonkey as a platform to easily receive responses and had a total of 13 questions. The
survey was made in a Likert-type Scale format (Fink, 2013). The scale ranged from five points:
strongly disagree, disagree, neither agree nor disagree, agree, or strongly agree (Fink, 2013). The
first five questions of the survey focused on the first research question. The following questions,
numbers six through nine, focused on the second research question. The final four questions
focused on the third research question.
Data Collection
There were several steps taken by the researcher to collect both qualitative and
quantitative data. In order to collect quantitative data, interviews needed to be conducted with
five different middle school mathematics teachers. The teachers who participated in this study
were purposefully chosen based on location and experience. Before starting interviews, the
researcher sent each participant an informed consent form. The consent form included a
background of the researcher, the research questions, and the purpose of the study. The form also
stated that all information would be confidential. Participants were also notified that all
interviews would be recorded, and the researcher would also take notes. Each interview took
about 50 minutes, and participants were contacted again if the researcher had any questions
about their responses. Once all data from interviews were collected, they were transcribed and
analyzed.
27

For quantitative research, the researcher conducted surveys with 30 middle school
mathematics teachers in Los Angeles County. With the survey link, there was a letter attached,
which also informed the participants of their confidentiality and the purpose of the study. The
surveys were conducted using SurveyMonkey.
Data Analysis
Since the researcher used a mixed-methods approach for data collection, data came from
both surveys and interviews that were designed to answer the research questions. To start
analyzing the data, the researcher began from the qualitative data of interviews. The recordings
and notes taken by the interviewer were all first transcribed. The transcriptions were then used
for coding, as recommended by Merriam and Tisdell (2016). Once all interviews were
interpreted and coded by the researcher, the codes were categorized into common themes
relevant to the study and research questions (Merriam & Tisdell, 2016).
When analyzing the quantitative data of surveys, similar steps were taken. The researcher
first transcribed and coded the data, looking for common trends and responses among the
surveys (Pazzaglia et al., 2016). Response rates were calculated by dividing the number of
responses by the total number of members who took the survey as recommended by Pazzaglia et
al. (2016). Responses from both interviews and surveys were also connected with the theoretical
frameworks, Critical Race Theory (CRT) and Culturally Responsive Pedagogy (CRP), which
informed the study.
Validity and Reliability
The researcher used many strategies to ensure that there were validity and reliability from
the data collected throughout the study. One primary strategy used for validity was triangulation,
where data was collected through multiple outlets of surveys, interviews, and literature reviews
(Creswell & Creswell, 2018). Other strategies for validity include using member checks to
28

determine the reality of interpretations and also peer examinations (Creswell & Creswell, 2018).
In terms of reliability, the researcher described the focus of the study, context for the data, and
foundation for the selection process (Creswell & Creswell, 2018). Triangulation also helped
reinforce reliability within the study (Creswell & Creswell, 2018).
Summary
The researcher used a mixed-methods approach to conduct this study, which included
both qualitative and quantitative data collection methods. For qualitative data, interviews were
conducted, and for quantitative data survey questionnaires were distributed. The data gained
from these methods focused on discovering effective practices used by middle school
mathematics teachers that support Latina/o students in Los Angeles County. The data also
focused on how teachers evaluated the effectiveness of the practices they used and how they
implemented technology in their classrooms for effective instruction. The research findings are
discussed in chapter four, and future implications are discussed in chapter five.

29

Chapter Four: Results or Findings
This chapter analyzes the data collected to distinguish the best practices that middle
school mathematics teachers can implement within their classrooms to provide effective
instruction for Latina/o students. Within the United States, there is a significantly large Latina/o
population, and they are one of the fastest-growing student populations (Musu-Gillette et al.,
2016). Yet certain classroom practices have created a gap in Latina/o mathematics learning
(Morales & DiNapoli, 2018). Recent research conducted by Garcia et al. (2017) shows that
quality mathematics education begins with teachers’ knowledge of their students’ strengths,
which are influenced by their cultural backgrounds. Other research conducted by Miller-Cotto
and Lewis Jr. (2020) also adds that quality instruction allows students to identify and build a
connection with the content taught because it helps them process the information presented.
The results and findings of this study will examine the effective practices that are said to
have shown positive results among Latina/o students within middle school mathematics
classrooms. These findings can also support middle school mathematics teachers when planning
and choosing strategies to deliver content to their students.
The researcher connected the findings of this study with the Critical Race Theory (CRT).
This theory exposes relationships among race, power, and societal structures (Larnell et al.,
2016). The Critical Race Theory also allows us to understand the additional inequities within
organizations based on student populations. This study also addresses the different inequities that
Latina/o students face every day within their middle school mathematics classrooms. Teachers
who participated in this study expressed the variety of barriers Latina/o students face in
mathematics classrooms compared to their White counterparts.
The researcher also connected the findings of this study with ideas from Culturally
Responsive Pedagogy (CRP). The use of CRP allows teachers to incorporate cultural references
30

within mathematical content to facilitating student learning and engagement (Ukpokodu, 2011).
This study distinguishes the various ways teachers can make mathematics content relevant to
their diverse groups of students. Teachers share their knowledge of the best practices that allow
students to be actively engaged and make real-life connections with the content.
The quantitative data of this study was collected by conducting surveys through a web-
based platform known as SurveyMonkey. The survey consisted of 14 questions based on a
Likert-type Scale format (Fink, 2013) and had three sections that matched the research questions
respectfully. The final question on the survey asked participants for their willingness to
participate in an interview. It asked participants to include an email address of their preference to
be contacted to schedule the interview. The survey was completed by 30 middle school
mathematics teachers within Los Angeles County who had at least three years of teaching
experience.
This study’s qualitative data was collected by conducting one-on-one interviews with five
middle school mathematics teachers within Los Angeles County with at least one year of
teaching experience. The interviews were conducted and recorded through a web-based platform
known as Zoom. The interviews were conducted in a semi-structured format, which allowed the
researcher to probe and ask additional questions that may have been beneficial to the study
(Merriam & Tisdell, 2016). The researcher had an interview protocol that consisted of ten
questions intended to answer the research questions. The interview protocol also consisted of
three sections, and each section is directly linked with the research questions.

Research Questions
The following research questions were used to guide the study:
31

1. What practices do middle school mathematics teachers use to provide effective
instruction for Latina/o students in Los Angeles county?
2. How do middle school mathematics teachers evaluate the effectiveness of the
practices used in classrooms for Latina/o students in Los Angeles county?
3. How do middle school mathematics teachers in Los Angeles county use
technology in their classrooms to provide effective instruction for Latina/o
students?
Purpose of the Study
The purpose of this study was to uncover the best practices that teachers can implement
in their mathematics classrooms to increase the achievement levels of Latina/o students. This
study was also conducted to help teachers better understand how they can evaluate the
effectiveness of various pedagogical techniques, which they use within their classrooms. The
research may also distinguish how the use of technology within mathematics classrooms can
help provide effective instruction for Latina/o students. This chapter presents the results and
findings of this study. These results provide vital details that focus on effective instruction,
evaluation of instruction, and the use of technology during instruction.
Coding of Data
To conduct data analysis, the researcher used a process of coding (Merriam & Tisdell,
2016). For the qualitative data, the researcher first transcribed the interviews and notes, then
coded relevant and familiar findings into categories and themes (Merriam & Tisdell, 2016). For
the quantitative data, the responses were also coded based on common trends (Pazzaglia et al.,
2016). Response rates were also taken into consideration and were calculated by dividing the
number of responses by the total number of members who took the survey as recommended
32

(Pazzaglia et al., 2016). Responses from interviews and surveys were also connected with the
literature reviews and the theoretical frameworks of CRT and CRP.
Findings
The findings of this research study are presented through common themes and categories
for each research question that was established during data analysis (Merriam & Tisdell, 2016).
The data analysis presented below was based on discovering the practices that middle school
mathematics teachers used to provide effective instruction for Latina/o students in Los Angeles
county, how they evaluated their practices, and how technology integration was useful within
their classrooms.
Research Question One
Research Question 1 aimed to learn more about the practices middle school mathematics
teachers used to provide effective instruction for Latina/o students in Los Angeles County.
Relationships and Expectations (Caring)
Prior research studies have shown that the relationships teachers build with their students,
and the expectations they hold for them can play a significant role in student achievement
(Jansen & Bartell, 2013). Teachers who build relationships with their students can understand the
necessary and individualized supports their students will need to succeed (Jansen & Bartell,
2013). Students’ self-efficacy, motivation, and engagement also increase when they recognize
that their teachers care about their success. These are all essential factors that are tied to student
achievement (Lewis et al., 2012).
The quantitative section of this research study included a survey conducted with 30
participants. The survey questions were related to the research questions, respectively. The first
section of the survey focused on the practices middle school mathematics teachers used to
provide effective instruction for Latina/o students. The questions in this section focused on the
33

delivery of content, instruction, student-relationships, and grouping. All teachers who
participated in these surveys had experience with teaching large populations of Latina/o students.
Figure 1 examines survey participants’ perspectives on student-teacher relationships. The
question was to observe teachers’ views of whether or not students succeed in environments
where teachers care about them and hold them to high expectations. Based on the results, 83.33%
of the participants strongly agreed that students succeed in classrooms where teachers challenge
them, have high expectations, and care for them. The remaining 16.67% of participants agreed
with this as well.

34

Figure 1
Survey Participants’ Perspectives on Student-Teacher Relationships

The qualitative section of this study included semi-structured interviews conducted with
five middle school mathematics teachers in Los Angeles County.
Teacher A has been a teacher for 23 years. Of these 23 years, 13 of them have been spent
teaching mathematics. She has been a mathematics teacher within three different districts.
Teacher A shared her experiences as a middle school mathematics teacher. Her perspective on
student-teacher relationships and expectations were as follows:
It’s about making mistakes that happen is okay, and in my class, students know math
stands for mistakes are allowed to happen. When they make a mistake, I let them
know. . . . That hey that’s a good mistake to make I made a similar mistake. . . . I
35

especially like it when they’re asking questions in the class, the one thing is we really
make it a big thing to applaud when there’s questions . . . say oh thank you so much for
your question, and I look for different ways and different examples to explain it and set it
up for them, and I think if students are comfortable enough to ask questions its good
because we’ll catch their needs more often. . . . I will have an opportunity to explain the
concept again, make sure they understood it, and know how to work it out. I need to
make sure every student understands the concept, because if one student asked a question
there might be at least 5 other students who will have the same question at one point. . . .
And I think these are the factors that help them.
Teacher A shows her students she cares by teaching them that mistakes are acceptable,
inevitable, and an essential part of the learning process. She emphasizes that teachers need to be
open and allow students to make mistakes or ask questions for them to learn.
Teacher B has been a mathematics teacher for 18 years. He spends the majority of his
time learning and reading about the adolescent brain and its development processes. Through his
teaching experiences and readings, he shared the following thoughts on the importance of
building relationships with students and showing students that their teachers care about them:
I think it’s a way of caring more than anything else because when you care about
somebody and the kids feel that you care about them, then the academics will follow, the
way you instruct it. You would not get impatient and say you should already know this, I
hate when teachers say you should know this, regardless if students are in my advanced
class, I do not say things like that, I always say let’s take a look backwards and see why
you do not remember. . . . I want my students at the end of class to feel that I am always
successful in math and this is my philosophy for middle school because we want them to
grow and their egos are so big but so fragile at the same time that if you break that you
36

can lose them forever. . . . It takes me a long time to build that relationship, a comfortable
relationship, and then from there I can move onto teaching mathematics, and once I have
an idea of where my students are in my classroom that’s when I start scaffolding so I
know I hit all the levels so I can hit the topic. You have to be in tune with the kids in your
classroom . . . and in a classroom with a person to person contact you have a better idea
of students focus and if you are really in tune then you can find out why some students
are struggling and then you can adjust your grading, you have to have a compassionate
form of grading . . . you have to have that compassion and empathy . . . it’s not that they
cannot learn, it’s that they have different challenges that at this point might be stifling
their learning so how you as a teacher help them overcome that barrier.
Teacher B emphasizes that caring about students’ successes and building relationships
with them will help students perform better academically. Teacher B highlights that the
relationships built will allow teachers to have a better idea of how to deliver content that is
suitable to each student’s needs.
Teacher C has been a mathematics teacher for 18 years. His first assignment as a teacher
was in South Los Angeles, where he worked for eight years. He states that the demographics at
this site were majority African American and Latina/o. He emphasizes the following information
about teacher-student relationships and how he supports his students:
When it comes to my students and even students who are behind in math, I encourage
them, I try to meet them half way, find out what their needs are, makes sure that they see
the opportunity to do better . . . I make sure to push them . . . I know that sometimes
students don’t like it, but it’s so important to encourage and push students to live up to
that potential. I have given opportunities and chances to make up assignments . . . I make
sure kids actually do the work, I communicate with their parents, with the student
37

themselves . . . and it can be about assignments or tests or making sure they understand
that math is just like any subject, it takes practice it takes work, and sometimes some
students will think oh yea I am not smart in math and I say you should not be saying that,
just because you don’t have a high grade and just because you didn’t do well or if you are
behind it does not mean you are not smart it just means you need to work a little harder to
catch up and I make sure they can get that encouragement I make sure they practice and
make sure they do their work to do better
Teacher C notes that it is important to show students that they are cared for by giving
them the time to absorb the material, encouraging them, and giving them chances to make up the
work to learn from their mistakes. Teacher C also highlights the importance of building
relationships with families to monitor student progress.
Cooperative Learning/ Heterogenous Grouping
Cooperative learning, or heterogenous grouping, is another strategy that other researchers
have found that can help increase student achievement (Jao, 2012). This strategy supports
students with their academic and social development (Jao, 2012). Heterogenous grouping allows
students to communicate their mathematical thinking with their peers. (Morisano et al., 2010).
Research shows that students might feel more comfortable discussing content with their peers
and will help decrease the confusion or difficulty of the questions (Morisano et al., 2010).
Cooperative learning allows teachers to create engaging mathematical classrooms where students
can share their ideas, share different ways of solving problems, and participate in the learning
process (Carlan et al., 2016).
In the quantitative portion of this research study, middle school mathematics teachers
were asked if they believed that group work allowed for students to learn different ways of
38

problem-solving and critical thinking. The results of their beliefs and perspectives are
demonstrated in Figure 2 and Figure 3.

Figure 2

Survey Participants’ Perspectives on Heterogenous Grouping

39

Based on the results, 53.33% of participants strongly agreed that group work can help
students learn different methods of problem-solving and critical thinking. From the remaining
participants, 40% also agreed that grouping could help support students. However, 3.33% of
participants neither agreed nor disagreed, and another 3.33% disagreed.
In this section, teachers were also asked if they believed that grouping would allow for
students to maximize their social skills and academic skills.

Figure 3

Survey Participants’ Perspectives on Heterogenous Grouping and Academics

40

Looking at the participants’ responses, 46.7% strongly agreed that grouping would allow
students to increase their social and academic skills. Another 36.67% of participants also agreed
with this strategy. The remaining 13.33% of participants neither agreed nor disagreed, and 3.33%
disagreed with this strategy.
Teacher D has been a mathematics teacher for 20 years. She has been serving classrooms
of students who are 80% Latina/o and 20% African American. Teacher D discussed her
perspectives with heterogeneous grouping with her students. Her perspectives are as follows:
I really like pairing them up with other kids and grouping them up so that other kids can
explain it to them if my explanation did not make sense. . . . This way if they did not
understand they were at least in a heterogenous enough group where some person can
help them understand because heterogenous grouping is where kids are allowed able to
explain and discuss with their peers and where we can let them talk about the math.
Teacher D highlights the key benefits that can come with heterogenous grouping during
classwork. These benefits include discussions that allow students to learn from one another.
Teacher D explains that students’ communication with one another can help them better grasp a
concept in ways that perhaps were not conveyed by the teacher.
Teacher B also uses heterogeneous grouping within his classroom to help students better
understand concepts. After demonstrating concepts within the classroom, Teacher B uses
grouping to allow students to practice amongst themselves. Teacher B states his perspectives on
heterogenous grouping:
You know . . . sometimes the students are more comfortable asking their friend for help
so your ears have to be open as you move around, so when they are doing stuff in their
little groups and you’re walking around and listening if a kid does not understand you
have to be compassionate enough to ask and sit there and help them out, some kids just
41

want you to help them and its identifying and taking the time to answer the question, and
the first thing you cannot be doing is upsetting the kid, because if you upset one kid you
upset the whole classroom, and some kids want to get the help from their friend because
they feel more comfortable, which is where grouping helps.
Teacher B states that students, at times, feel more comfortable approaching their friends
with questions. This allows teachers to have the opportunity to walk around and listen to their
questions and carefully approach them. Teacher B highlights that some students are not as vocal,
and grouping will allow them to voice their questions with their peers.
Culture and Relevance
Research has shown that making mathematics content relevant to students’ interests and
cultures is also connected with student achievement. When content is relevant, students can
make real-world connections to problems, gain a better understanding, and enhance their
achievement rates (Wager, 2011). Understanding students’ cultures will also allow students to
understand the backgrounds of diverse students along with their strengths, weaknesses, and
various needs (Ukpokodu, 2011). Incorporating students’ cultures and interests can also help
students build a more positive attitude toward mathematics, which can build their confidence and
motivation (Leonard et al., 2010). Having the right level of confidence and motivation are also
key factors that can increase student achievement levels (Leonard et al., 2010).
In the quantitative portion of this study, the middle school mathematics teachers were
asked about their thoughts on the importance of culture within a classroom and the relevance of
content. Their responses are recorded in Figure 4.

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Figure 4

Survey Participants’ Perspectives on Culture and Relevance of Content

Based on the participants’ responses, 56.67% of participants strongly agreed that making
mathematics content relevant to students’ interests and cultures can increase achievement levels.
Another 33.33% of participants also agreed, and 10% of participants neither agreed nor
disagreed.
In the qualitative portion of this study, participants were asked to share their experiences
and beliefs on the importance of incorporating culture into their instruction and making it
relevant to students’ experiences.
Teacher D shared her perspectives and experiences with students’ achievement results
when making content more relevant to them and their cultures. She expressed that she mainly
found seventh-grade mathematics to be of most relevant to real-world scenarios. She shared the
following based on this matter:
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Math is so fun! You can always make it relevant! Especially seventh grade math . . . like
for example when you think about certain topics such as direct variation and proportional
reasoning, it is really the teacher’s chance to make it realistic so that the kids can really
understand. I think the more realistic and concrete you can make it the better . . . like
bringing in concrete strategies, spelling things out more basically making mathematics
more accessible to everyone and helping students see that mathematics is not an abstract
subject, make it a concrete subject.
Teacher D emphasizes that when the subject is relevant to students’ experiences, the
content will be more concrete and realistic, making it easier for them to understand. As Teacher
D shares, mathematics can seem abstract without adding real-world examples. However, when
students can make these connections, the content can be more accessible and tailored to meet
each student’s needs.
Teacher B also shared his perspectives about incorporating students’ interests and values
within mathematics content and instruction. Teacher B takes a lot of time to learn about
adolescents by reading about brain development and teaching strategies. He had the following
perspectives about incorporating culture within the classroom:
We can make always make mathematics relevant. It’s not easy but mathematics is life.
We can put it into testing, such as finding averages. . . . There is always context. Context
in things in the country like politics, sports, business . . . like something that is dealing
with graphs, if a graph is going up or down, we can discuss what this means . . . even
culturally I can even make it relevant. If parents have a type of business, we can see are
they making money? Well let’s put it on a graph. You can always find context. What I
have difficulty with as a teacher is that my 8
th
grade students in particular want it to be
fun and it is difficult to make math fun, but the way I can make it fun is the way that I
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behave, like me uh making a joke, making things light, making it interesting to them . . .
we can always find a context in math with everything we do, and make it reachable to
students. . . . I’m always reading books about adolescent brain development and
strategies for teaching and every single one of these books talks about having to make it
personable, emotional. We know these kids, young people, react on emotion more than
anything and so thinking about making that connection I think uhm and being happy at
the same time and enjoying teaching at the same time. The math theory can be boring, but
what is not boring is the teacher, if we make it fun and make a few jokes here and there
and we care, I think that enhances the instruction.
Teacher B stresses that mathematics is easy to make relevant to students and their
interests because mathematics is everywhere. He highlights that making it relevant and exciting
is important because content should be personable and emotional for students’ to be able to
connect with it. Making mathematics reachable and accessible to students needs can enhance
instruction, as Teacher B explains, and also student achievement levels.
Working with a large group of Latina/o students for the majority of his career, Teacher C
also had his thoughts on the role of students’ culture and values in mathematics classrooms.
Teacher C shared that he can relate and understand students’ challenges since he also came from
a diverse background. Teacher C had the following perspectives:
I think it is important to make the subject relevant, inspire the students, make the subject
matter to them and their lives, adjust and modify and accommodate to the students’
needs, these are the strategies that I have been using for years now. It is important to
make it relevant to students and make it correspond to their daily lives and what they are
aspiring to do. Need to be good at math to go into STEAM, Sciences, need to make it
relevant use some strategies and problems and projects that correspond with real life
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situations, need to students to buy into the subject, show them the reason they need it so
they can excel in it.
Teacher C emphasizes the importance of making content relevant to students, particularly
because when bringing a subject to life, students can see why it matters and why it is important.
Teacher C also notes the importance of teaching content in ways where it corresponds with
students’ lives for them to succeed.
Research Question Two
Research Question 2 aimed to learn more about how middle school mathematics teachers
evaluate the effectiveness of the practices used in their classrooms for Latina/o students in Los
Angeles County.
Formative Assessments
Previous researchers had discovered that there were large gains among low achievers
when teachers incorporated formative assessments within their classrooms (Hudesman et al.,
2013). Formative assessments are assessments where teachers respond to students through proper
feedback that will be beneficial and help them improve (Hudesman et al., 2013). For formative
assessments to be practical, researchers state that teachers must provide quality feedback and not
just praise or punishment (Hudesman et al., 2013). Instead, feedback should focus on how
students can complete a task more effectively. When students receive feedback, it allows them to
establish learning goals and develop the right skills to achieve them (Heritage, 2010). It also
allows teachers to adjust their instructional strategies or activities to promote student learning
(Heritage, 2010).
In the quantitative portion of this study, teachers were asked whether they regularly check
on student work or assessments to understand if they are meeting performance expectations. The
results are displayed in Figure 5.
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Figure 5
Survey Participants’ Perspectives on Using Student Work and Assessments for Self-Evaluation

47

Based on Figure 5, 20% of participants strongly agreed that they regularly check on
student work and assessments to understand how they perform, and 53.33% agreed. Of the
remaining participants, 16.67% neither agreed nor disagreed, and 10% disagreed.
In the qualitative portion of this study, the participants shared their perspectives on how
they use assessments and student work to evaluate their instruction.
With his many years of experience as a middle school mathematics teacher, Teacher B
finds formative assessments to be an effective strategy to help benefit his students’ achievement.
Teacher B shares the following about implementing formative assessments:
I like most of all formative assessments; I’m active in my classroom when I’m in person I
can see what the kid is doing, I demonstrate something for 10 min, make sure I have all
the tools, what I need has to be in place for when they come into the class, and now once
I show them something I can move around and I can see what they are producing, if they
are not producing anything then that’s an indicator that I have to ask questions and say
did you understand what I was doing or did you not understand, which part did you not
understand. And then I have this protocol which is “You do not tell me I do not know
anything I don’t understand anything.” We have steps in this class, and you can tell me I
did not understand step one or the question and then we can move forward from there,
this on its own is another type of formative assessment for me, I never give a test that’s
uhm trying to trick my students, I do not believe in that. Everything that I test will be in a
way that they can and will be successful. But we also do formative assessments on paper
and if for some reason they do not perform well, I must provide feedback and modify my
teaching. I want my students at the end of class to feel that I am always successful in
math and this is my philosophy for middle school because we want them to grow and
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their egos are so big but so fragile at the same time that if you break that you can lose
them forever.
Teacher B stresses that he usually likes to give oral or regular formative assessments
because it allows him to recognize the students’ level of understanding. Teacher B uses this
information to modify his instruction and provide direct feedback to his students. Teacher B also
stresses the importance of allowing students to feel successful at the end of each class.
Teacher C has used technology to do formative assessments within his class since
technology became easily accessible to classrooms. Teacher C shares the following information
about formative assessments:
I always end my class with a quiz that is usually taken online. It usually has 4 to 5
problems that take about five to ten minutes to take and these are actually formative
assessments. Now these assessments are really helpful to me and my instruction because
this is where I see that on which topics the student did well on and did not do well on,
and I start to understand that oh I have to go over this once again, think of different ways
to teach it, I notice trends in the questions like what majority of the class understood or
did not understand and I re-evaluate my instruction and what I can do better to help them.
Teacher C emphasizes that formative assessments really help him understand the areas
and topics that his students did not grasp and uses them to transform his instruction. Teacher C
stresses that formative assessments help him notice whole-class trends for areas of concern,
helping him understand how he can assist his students.
Reflection and Evaluation
Research has shown that teachers who continuously evaluate their classroom practices
usually have higher student achievement levels (Donohoo et al., 2018). When teachers reflect on
their techniques and instructional strategies, they can change their pedagogical practices to meet
49

their students' immediate needs (Donohoo et al., 2018). Teachers can also self-reflect through the
professional learning communities established within their schools to solve problems they come
across collectively. These teams help teachers build collective teacher efficacy, allowing teachers
to take accountability for their teaching and their students' success (Donohoo et al., 2018).
In the quantitative portion of this study, participants were first asked if meeting with their
colleagues consistently helped reflect on their instruction's effectiveness. The results are shown
in Figure 6.

Figure 6
Survey Participants’ Perspectives on Meeting with Colleagues for Self-Evaluation

50

The figure shows that 26.67% of participants strongly agreed that meeting with their
colleagues is beneficial for their reflection and self-evaluation, and 60% of participants agreed.
The remaining 13.33% of participants neither agreed nor disagreed.
The quantitative portion of the study also asked participants if regularly reflecting on
strategies used within their classrooms helped to understand which were most appropriate for
their students’ needs. The participants’ responses were recorded in Figure 7.

Figure 7

Survey Participants’ Perspectives for Reflecting on Strategies Used Within the Classroom

51

Based on the participants’ responses, 53.33% of participants strongly agreed that
reflecting on the different instruction methods used within their classroom helps them discover
which is most suitable for their diverse students. Another 43.33% of participants also agreed.
The remaining 3.33% of participants disagreed.
In the qualitative portion of the study, teachers discussed their experiences reflecting on
their strategies and evaluating the practices they use in the classroom.
Regardless of the many years of experience Teacher B has, he still evaluates and reflects
on the strategies he uses within his classroom. After reviewing formative assessments and
analyzing students’ reactions during classwork, Teacher B re-evaluates the next steps necessary
to help his students succeed. He shares the following:
If they do not get something I am constantly thinking of new strategies, if they do not
understand something I step back, and I check what I did, and my brain is always going
in that direction: what can I do next based on what’s happening right now? And that’s the
hardest part about teaching because thinking about what is happening right now is an
individual thing because when you go to student a, the question they will ask might be
super advanced and you want to know how to answer it then you go to a different student,
student b, and this student is struggling with something differently and you have to
identify all of this in those 45-50 minutes. And so, when we are planning, I am constantly
thinking about the possible questions that might come up and how I would answer those
questions.
Teacher B shares that he is always thinking about improving his instruction, especially
whenever he notices that students do not understand the concept. He states that he is constantly
reflecting and looking back to understand what he can do to meet his students’ needs. Even when
lesson planning, Teacher B reflects on the possible questions, his students might ask him to plan
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his instruction accordingly. This way, he can ensure that his students understand the lesson and
succeed in his class.
Teacher E has been a mathematics teacher for three years. He has been teaching
classrooms that are majority Latina/o and African American students. Teacher E uses different
forms of reflection on his teaching that he believes helps his instruction. Teacher E shared the
following perspectives:
One of the things that I love is reflecting on my teaching. The main thing I use the Stulls
objectives which basically helps me reflect on my current and future goals and what I am
going to accomplish within this year, and I get to also review this with my boss, who can
be a little bit of a micromanager, which I like a lot because I need it, and she will help me
with it give me advice like what about changing this or also trying this and she picks my
brain a lot, helps me evaluate the techniques I use, and helps me grow and helps for . . .
further reflection on the ways that I am teaching which will also be better for my
students.
Teacher E highlights that reflection is important for him because it helps him create and
target certain classroom goals. He also emphasizes that reviewing these goals with his superiors
allows him to challenge himself as a teacher and re-evaluate his strategies, which benefits his
students and their achievement levels.
Teacher A explained that she takes time to reflect on her progress as a teacher through
professional learning communities they have established in the district. Teacher A shared the
following perspectives on reflection and evaluation:
Well as a team within our professional learning communities, we have developed
something known as a common assessment . . . and these common assessments are very
beneficial for me and others to know how we are performing across the board. We stay
53

consistent with one another in our professional learning communities and whenever I
look and reflect on my common assessments and see where my students have gaps and
compare it to other teachers, and understand that okay I have to go through this one more
time because my kids maybe need more time to process or a different way or strategy
needs to be used for them to understand it, and taking the time to evaluate these common
assessments is so important because that’s how I see where my students need the most
help.
Teacher A notes that taking time to reflect using the common assessments allows her to
see how her class performs across the board. She also stresses that reflecting is essential to
understand which areas can be taught differently in the classroom to understand the content
better.
Professional Development
Many research studies conducted in the past have shown that participating in professional
development can enhance teachers’ pedagogical abilities (Fischer et al., 2018). The purpose of
professional development opportunities is to guide teachers toward better instruction strategies
that will enhance student learning (Fischer et al., 2018). Research shows that useful professional
developments are content-focused, provide teachers with learning experiences, model
instruction, and allows for engagement and participation (Fischer et al., 2018). Professional
development opportunities with these factors enable the teachers to incorporate effective
strategies within their classroom and learn new ways of modeling and delivering instruction
(Fischer et al., 2018).
In the quantitative portion of this study, participants were asked whether they participated
in professional development opportunities to advance their instructional skills further. The
participants' perspectives are recorded in Figure 8.
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Figure 8
Survey Participants’ Perspectives on Professional Development

55

The figure shows that 30% of participants strongly agreed that they participate in
professional development opportunities to advance their skills, while another 63.33% agreed. Of
the remaining participants, 3.33% neither agreed nor disagreed, and another 3.33% disagreed.
Even though Teacher A has been a teacher for 23 years, she shared that she is still
learning something new as a teacher every day. Teacher A still takes time out of her schedule to
attend professional development opportunities that will benefit her and her students. She shared
the following perspectives:
I think that there is always room for improvement no matter the field you are working in.
I mean I have been a teacher for 23 years and we always learn new things during
professional development, or even from different classes and different colleagues. What
is most important though is that you need to be willing to learn from others and take
advantage of the professional development opportunities given to you. Don’t claim that
you have all the answers and don’t just depend on yourself to know it all, you don’t even
need to be the best at what you do, instead us teachers need to be open to learn and to
look to others for help, and be willing to do something different that will bring better
results for our students, especially if you see that something can actually work and has
shown to be effective, learn about it and bring it into your classroom.
Teacher A highlights that professional development opportunities are important and can
provide teachers with strategies that deliver results. She states that teachers must be open-minded
to using new methods, especially if they are effective. Teacher A emphasizes that teachers
cannot claim to know it all and instead need to learn from those around them.
Teacher E is relatively new to teaching but agrees with Teacher A that professional
development opportunities are necessary and effective. Teacher E shares the following beliefs
about professional development:
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There are certain factors that are key in teaching, and one of those, at least in my opinion,
is participating in professional development . . . because times are changing, kids are
changing, their ways of thinking and learning are always changing, and we need to adapt
to these changes as teachers. Participating in professional development opportunities
keeps us up-to-date with the needs of today’s classrooms and students. These
development opportunities give teachers key insights on how to give better instruction
and delivery which will help their students’ achievement.
Teacher E highlights that generations are continually changing, and teachers need to
adapt to newer generations and students' diverse needs. Teacher E emphasizes that one way to
understand how to reach students is to bring innovative teaching strategies that can be received
from participating in professional development. He states that professional development can
keep us informed on how to teach the children of today’s society.
Research Question Three
Research Question 3 aimed to learn more about how middle school mathematics teachers
in Los Angeles county use technology in their classrooms to provide effective instruction for
Latina/o students.
Individualized and Differentiated Instruction
In recent years, technology integration within mathematics classrooms has become very
popular and has shown to be effective (Fazal & Bryant, 2019). Technology integration within
classrooms can occur in many ways. The most common way is having direct instruction led by
the teacher within the classroom during the first half of the class and allowing the second half
conducted through online content (Fazal & Bryant, 2019). Research has shown that combining
both instruction methods gives students more personalized and individualized experiences within
the classroom (Fazal & Bryant, 2019). The use of specific programs through technology allows
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teachers to customize content based on the areas of need per student (Fazal & Bryant, 2019). It
also allows students to move and learn content at their own pace or even review previous content
that may not have been fully understood (Fazal & Bryant, 2019). Ozel et al. (2010) also agreed
that integrating technology within classrooms can be effective, especially since content can be
student-centered and allow for differentiated instruction.
In the quantitative portion of this study, teachers were asked about technology
integration. The first question they were asked was if they believed that using technology within
mathematics classrooms allows Latina/o students to learn at their own pace. The participants’
responses are recorded in Figure 9.

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Figure 9
Survey Participants’ Perspectives on Use of Technology for Latina/o Students to Learn at their
own Pace

After analyzing the table results, 40% of participants strongly agreed that technology can
allow Latina/o students to learn at their own pace and further develop their schools, while
another 40% also agreed. From the remaining participants, 16.67% neither agreed nor disagreed,
and 3.33% disagreed.
Furthermore, participants were asked whether they believe that technology can help
individualize and personalize a student’s mathematics learning experience. The participants’
responses are presented in Figure 10.

59

Figure 10
Survey Participants’ Perspectives on Technology and Individualized Learning

Based on the participants’ responses, 33.33% strongly agreed that instruction can be more
individualized and personalized through technology, and another 63.33% also agreed. Looking at
the rest of the participants, 3.33% neither agreed nor disagreed.
Finally, participants were also asked if they believed that technology integration could
bring higher achievement levels for Latina/o students within the classroom. The participants’
perceptions are recorded in Figure 11.

60

Figure 11
Survey Participants’ Perspectives on Technology and Higher Achievement Levels of Latina/o
Students

Looking at the chart, 30% of participants strongly agreed that technology integration has
helped Latina/o students reach higher achievement levels. Another 40% of participants also
agreed with this statement. The remaining 26.67% of participants neither agreed nor disagreed.
In the qualitative portion of this study, participants were asked to share the different types
of software that they have incorporated into their mathematics classrooms and how it helped
their instruction.
Teacher D has been using technology within her classroom for quite some time now and
shared that she has noticed how it can change her student’s reaction toward mathematics.
Teacher D shared the following:
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One thing that our district uses is iReady, especially for intervention. Now, iReady is a
purchased platform and how it works is that kids first take a diagnostic test, and based on
the results of this test, the program creates a path for where each individual kid falls in.
This is amazing because it totally helps with differentiating instruction because it allows
kids to learn at exactly the right place and pace that they belong in. This makes the
instruction very personalized. I also like Khan Academy because I can track students’
progress through Khan Academy, and also because it has a mastery-based approach
which also allows students to move at their own pace and time, and master concepts that
they did not earlier, or even move forward to master new topics. Khan Academy has
something for all the kids. . . . Another one of my favorite technology to integrate inside
my classroom is Desmos. Wow. Desmos is just so powerful, it truly takes the pain of
graphing out of graphing, and kids can automatically see and understand what is
happening on a graph, where the intercept is, what the graph depicts. It makes the subject
concrete to them again because now they have a visual to go off of. Students can also see
what happens to the graph instantly when you change one aspect or element of the graph
and allows them to understand how to interpret it.
Teacher D emphasizes that certain programs, such as iReady, allow students to move at
their level, especially since it assigns them work based on a diagnostic test. She notes that this
allows for teachers to differentiate instruction because now students are learning at the right level
that they fall within. Teacher D also highlights that programs such as Khan Academy can also
allow students to relearn old topics and even master new ones. Teachers can also monitor the
students’ progress. Teacher D shares that tools such as Desmos are also powerful since it makes
concepts such as graphing less abstract and more relatable and understandable.
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Teacher C started implementing technology within his classroom right when it first
started becoming accessible in society. He claims that he knew it was the future and that it would
be helpful to his students. Teacher C shares the following:
Technology is essential, especially right now and it can do so much for us as teachers,
even the students, for example . . . today in my class we were working at absolute values
and they did not know what it was, and they were just sitting and waiting for me to tell
them what it is and I was like guess what . . . you have a computer in front of you just
click on a new tab and look it up and they were like, “Wait what we can do that?” and I
said, “Absolutely go online find out and raise your hand a participate” and it was just
amazing cause now everyone’s hands were up in class, everyone is engaged, and now
they realize oh yea this computer is not just for YouTube and or other applications it’s
actually a good source of information and a good tool for learning, and that is what I am
fighting for right now as a teacher. A lot of our students get a laptop and a Chromebook
they’re just used to playing on it, that it’s just used for fun you know? But now it’s
actually making them see you can and should do school work on this and the transition is
hard. You have to make them see how it can benefit them. . . . And even for my ELA
students, technology is so beneficial because they can do the work basically at their own
pace and you know I can help them with it, they can do it at a later time if needed or in
class or afterschool, so technology is very powerful and helpful when it comes down to
that. . . . And I use Kahn Academy, which is a really good supplement to enforce and
reinforce when teaching a concept. The best part of it is that students can go ahead and
work on their own. I do make sure that everyone is at least at a certain level, they do
certain assignments and work on certain skills but anyone who would like to go on I
encourage my students to do so and it’s amazing how some of my students get so into it
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and its mostly the ELA students. Because it can come in different languages and they can
do it in their own language, the problems are short, they are fun and they can do it, and it
also gives them a chance to redo the assignment if they want, and if a student needs to
review older lessons that they did not understand, they can.
Teacher C notes that technology allows all students to learn, have answers, and engage
with the mathematics content. Teacher C stresses that it is especially beneficial for ELA students
because it will enable students to learn and complete assignments at their own pace. Finally,
Teacher C highlights that programs such as Khan Academy make it easier for students to learn
because it comes in many different languages and either move ahead to newer topics or review
other issues.
Teacher A stated that she has been using technology in her classroom for quite some
time, particularly for review days. Teacher A shared the following:
One application I also really like using is Nearpod. Now Nearpod already has premade
lessons in there but you can also develop your own of that’s what you prefer. What I like
about Nearpod is that it gives them slides with problems to solve, but it also gives them
individual white boards to solve on and you, as a teacher, can see all of their virtual
white-boards to see what they are all doing. This helps because you can pick out white-
boards individually and see what they did correct or what they did incorrect and provide
personal feedback on the spot while they are working, so students correct their
misunderstandings right there during the direct instruction.
Teacher A emphasizes that tools such as Nearpod allow teachers to catch students’
mistakes right on the spot and correct them for them not to be repeated in the future. She also
highlights that teachers can also give direct and individualized feedback to the student
automatically.
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Critical Race Theory
The Critical Race Theory (CRT) exposes the relationships among race, power, and
societal structures (Larnell et al., 2016). CRT helps to analyze and understand the inequalities
and inequities that exist within school structures. Based on Ladson Billings and Tate’s (1995)
approach to CRT, certain social structures that have shaped difficult environments for students of
different subgroups to succeed can be uncovered. Latina/o students have been disadvantaged by
the educational system and have not received an education that is justifiable compared to those
received by their White counterparts.
In the qualitative portion of this study, teachers were asked if they believe that Latina/o
students face challenges within their mathematics classrooms that their White counterparts do
not. The majority of the teachers who participated in the study agreed that certain societal factors
had put Latina/o students at a disadvantage compared to White students. The teachers’
perspectives on this topic are as follows:
Teacher C has been working at schools with large Latina/o student populations for most
of his teaching career. When asked if Latina/o students’ face more challenges compared to their
White counterparts, Teacher C had the following perspectives:
Yes, it’s true especially if they are from economically disadvantaged areas and if there’s a
language barrier as well. And I can understand this first-hand, especially the language
barrier, because it can truly hinder and discourage students from excelling in math. These
students do not just face one challenge, but they have a few . . . like language, economic
disadvantages, cultural issues. There are so many challenges that these subgroups are
facing, and society can take the blame for not easing the situations and circumstances for
them. It even becomes difficult for parents to support their kids because they are busy
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trying to make enough money to survive and place food on the table and can hardly have
time to spend time with their kids.
Teacher C emphasizes that there are definite challenges that Latina/o students face
compared to their White counterparts. Teacher C stresses that those challenges come from
socioeconomic issues and even language barriers. Teacher C notes that because there are
socioeconomic challenges at home, they lack the support factor. Teacher C also notes that the
language barrier Latina/o students have can hinder and discourage their learning and motivation.
Similarly, Teacher B has also been teaching at schools with large populations of Latina/o
students. Teacher B also had similar perspectives on the topic and shared the following:
Yes, I do, you know what, and this is where instruction needs to change. When we say
white counterparts, I assume a student who comes from a high socio-economic
background, so where the kids have a place to sit and study quietly, where kids have
access to really good computers, where kids have access to food, where kids have access
to parents being home. . . . A lot of my kids who are majority Latina/o do not have this,
alright. Unfortunately, they have those challenges . . . and those challenges we have to
take it into context, well especially me, when I am instructing.
Teacher B also stresses that there is a socioeconomic disadvantage that Latina/o students
face compared to their White counterparts. Teacher B notes that those socioeconomic
disadvantages cause them to have less accessibility to support factors such as tutors, study areas,
technology, and additional resources to help student achievement.
While teacher D has served large populations of Latina/o student populations, she states
that she did not have too many White students to compare the challenges. Teacher D shared her
own experiences and challenges that she recognized:
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They may. It is hard for me to say because I did not have any white kids in the classroom
to compare the circumstances with. I had very little experience teaching populations of
White students. But I do think that there is more of a socioeconomic and support
challenge that Latina/o students face compared to White students. Thinking about it now,
White students have more resources and more accessibility, especially in certain areas, to
additional supports like tutors and so on. They also have more pressure and the ability to
get support from their parents to do better and to do well. Some parents in Latina/o
communities want to be available for their students, but the truth is that they are so busy
working so many jobs that it became hard for them to be involved and know everything
about their child’s studies or be able to support them.
Teacher D also emphasizes that there are socioeconomic challenges that Latina/o students
come across in their learning experiences. Teacher D also notes that Latina/o students have less
accessibility to support systems such as tutors. Teacher D reports that Latina/o students can also
lack support from their parents because most of them have to work multiple jobs.
Teacher A has also been serving schools with large Latina/o populations and has had 23
years of teaching experience. Teacher A had the following to share:
There are definitely challenges. For example, socioeconomic challenges. Like take for
example schools that are located in rich White neighborhoods. The children can easily get
access to a tutor, it is so easy for them to get access to that extra support, and for other
communities such as possibly Latina/o communities, it is not very easy for them to be
able to do the same for their children, it is not as accessible. This is where teachers and
school organizations need to be willing to provide those extra supports.
Teacher A also stresses that there are socioeconomic challenges in Latina/o communities.
Similar to the other participants, Teacher A emphasizes the easy access to support systems for
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Latina/o students. Teacher A also notes that teachers and organizations need to be willing to
provide the additional supports that these students cannot access.
Culturally Responsive Pedagogy
Culturally responsive pedagogy is the method of instruction that allows teachers to
implement students’ cultures into mathematics content to facilitate their learning process
(Ukpokodu, 2011). This strategy encourages teachers to see their students’ cultures as a resource
to learning rather than a barrier (Santamaria, 2009). Research has shown that exceptional
learning environments provide relative and realistic instruction to the students’ unique
experiences and cultural backgrounds (Santamaria, 2009).
In the quantitative portion of this study, participants were asked if they believed that
culture played a large role in mathematics classrooms. To analyze participants’ perspectives, the
researcher looked back at Figure 12.

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Figure 12
Survey Participants’ Perspectives on Culture and Relevance of Content

Looking at the figure once again, 56.67% of participants strongly agreed that
incorporating students’ different backgrounds and cultures can increase achievement levels. The
remaining 33.33% of participants also agreed, and 10% of participants neither agreed nor
disagreed.
In the qualitative portion of the study, participants were asked to share what they believed
was important when delivering instruction, and many of the participants constantly mentioned
culture.
Teacher C uses cultural references within his classroom to connect his students with the
subject and to also understand them on a more personal level. Teacher C shared the following
information about the role of culture:
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Culture absolutely plays a role in a mathematics classroom. These can include making
problems more relevant to my students’ cultures, including their names in the problems,
helping them identify with the subject. There are even different dynamics that we can see
in different cultures that show within classrooms because for example some communities
are used to working together and as a group, while some communities who prefer
working on their own and do not accept the co-working part . . . this all flows into the
classroom, students will either prefer group work or will prefer to work on their own.
Culture is everywhere and we as teachers can learn from the diverse cultures to benefit
our students, not place them at a disadvantage for being different from one another.
Teacher C places emphasizes that culture allows teachers to make the content more
relevant to his students. However, Teacher C also notes that culture helps to understand
important characteristics of his students’ personalities, such as enjoying group work or not.
Teacher C highlights that culture is everywhere and that it is important for teachers to take the
time to learn about their students’ cultural backgrounds and use them to their advantage.
Teacher B’s perspectives on culture also align with Teacher C’s. Teacher B had the
following information to share on the role of culture within mathematics classrooms.
When I learn about my students, I take the time to learn about their culture, what their
backgrounds are, where they come from, their beliefs, I try to understand their values and
basically build a relationship with them. And once I am familiar with them, it makes it so
much easier for me to be able to guide them, because now all of a sudden I know how to
make content more interesting for them, or I know what I need to do differently to meet
their needs, or I know what cultural aspects influence their behaviors and this is all so
important.
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Teacher B notes that taking the time to learn about his students’ cultures helps him build
a relationship. Teacher B stresses that this is important because he learns how to scaffold content
focused on his students' needs and interests.
Summary
In this chapter, the researcher reported the findings of 30 survey respondents and the 5
interview respondents who are currently serving as middle school mathematics teachers within
Los Angeles County. This chapter analyzed the different experiences of middle school
mathematics teachers as they shared their thoughts on the best practices in mathematics
classrooms, their evaluation methodologies, and their use of technology in the classroom. The
results of this study indicated that certain factors such as student-teacher relationships, culture,
high expectations, and grouping are some of the best practices that can increase student
achievement, which all align with the culturally responsive pedagogy framework. The results
also indicated that certain strategies such as formative assessments, professional development
opportunities, and individual reflections can help teachers evaluate their pedagogical strategies.
Finally, the results indicated that technology integration can enhance instruction by making it
more catered and individualized to fit each student’s needs. The teachers’ experiences also align
with the Critical Race Theory because they agree that certain societal factors, such as
socioeconomic challenges, have hindered Latina/o communities from receiving an equitable
education.
Chapter five will present a summary of the research findings, implications for practice,
and recommendations for future research.

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Chapter Five: Discussion
This chapter will summarize all the findings related to implications for middle school
mathematics teachers' practice. The research findings discussed within the chapter are intended
to inform middle school mathematics teachers of the best strategies to implement within their
classroom to help increase Latina/o student achievement. The chapter will also include
recommendations for future research that can be conducted within this study's scope.
This study focused on problems associated with middle school Latina/o students’
achievement levels in mathematics classrooms. Research has shown that teachers continue to
struggle with adequately serving the needs of Latina/o students. The academic achievement gap
among Latina/o students and their White counterparts is one of the main issues that continue to
exist within educational organizations (Mitchell, 2018). Lacking proper knowledge of
mathematics content will make it difficult for students to succeed in college and plan for a future
(Mitchell, 2018). It is also crucial that the education system establishes equitable and accessible
resources to increase students’ achievement levels (Erickson & Highsmith, 2018). Latina/o
students should be taught in ways that help build their conceptual knowledge and help them
make real-world connections with the mathematical content taught in classrooms (Erickson &
Highsmith, 2018). The purpose of this study is to discover the best practices that teachers can
implement into their mathematics classrooms to increase the achievement levels of Latina/o
students. The following research questions were used to guide the study:
1. What practices do middle school mathematics teachers use to provide effective
instruction for Latina/o students in Los Angeles county?
2. How do middle school mathematics teachers evaluate the effectiveness of the
practices used in classrooms for Latina/o students in Los Angeles county?
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3. How do middle school mathematics teachers in Los Angeles county use
technology in their classrooms to provide effective instruction for Latina/o
students?
This study used a mixed-methods research design, and the data collected comes from
interviews and survey responses of middle school mathematics teachers in Los Angeles County
(Creswell, 2014). Using this research design allowed the researcher to have various data
collection methods and to establish coherency throughout the study (Creswell, 2014). This
study's qualitative portion included interviews with five middle school mathematics teachers
practicing in Los Angeles County. In this study's quantitative part, 30 middle school mathematics
teachers answered survey questions directly linked with the research questions. The analysis of
both the qualitative and quantitative data was conducted in relation to one another.
Findings
Study findings determined that there are various strategies middle school mathematics
teachers can use to provide effective instruction for Latina/o students in Los Angeles County.
The most effective strategies found in this study include building student-teacher relationships,
heterogenous grouping, and connecting content with student cultures and interests. Findings also
suggested that there are various ways teachers can evaluate the effectiveness of practices used
within their classroom. Strategies that originated from this study included formative assessments,
teacher reflections, and attending professional development opportunities. Finally, this study's
findings also determined that technology integration is powerful if used effectively and allows
for personalized learning experiences catered to each student’s needs. This section presents a
summary and discussion of the findings related to the study in relation to the literature.

73

Research Question One
Research Question One inquired, What practices do middle school mathematics teachers
use to provide effective instruction for Latina/o students in Los Angeles county? The quantitative
and qualitative data related to Research Question One produced several findings. The first
finding showed that it is essential for mathematics teachers to build supportive relationships with
their students, care about their success, and hold them to high expectations. This finding is
consistent with the work of Jansen and Bartell (2013), who stated that when teachers build
relationships with their students and have high expectations of them, it can significantly increase
student achievement. Teachers who have relationships with their students understand the
necessary supports to provide to their students to succeed. (Jansen & Bartell, 2013). Having
relationships with teachers can increase students' self-efficacy and motivation toward
mathematics and increase achievement (Lewis et al., 2012).
In the quantitative portion of this study, all 30 participants, 100%, agreed that students
succeed in settings where teachers show they care about them and hold them to high
expectations. Findings from the qualitative portion of the study also directly correlated with
those found in the survey. During interviews, all three participants stated that it is important to
make students feel comfortable and build relationships with them. The teachers discussed that
they must help students understand that making mistakes is part of the learning and growing
process. The teachers share that after taking time to build relationships with their students, they
can help their students perform better because they know how to deliver the content in ways that
are suitable to each student’s individual needs. Having these relationships with students also
allows teachers to communicate with the parents, monitor their progress, and continuously
establish new learning goals.
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The second finding that surfaced in relation to Research Question One established that
cooperative learning, or heterogenous grouping, benefits students by allowing them to discuss
problems and learn different problem-solving methods and critical thinking. Research has shown
that grouping students into pairs or groups help support academic and social development (Jao,
2012). Students are given the ability to discuss mathematical content with their peers and build
connections that are more applicable to their daily experiences (Peterson et al., 2010). Having
peers to discuss content with is also important because it will reduce the misunderstandings they
may have (Morisano et al., 2010). Heterogenous grouping allows students to have more engaging
learning experiences (Carlan et al., 2016).
Looking at this study’s quantitative findings, the majority of participants, about 93.33%,
confirmed that heterogenous grouping could benefit students’ progress in middle school
mathematics classrooms. Approximately 83.36% also agreed that heterogeneous grouping helps
students maximize their social and academic skills. Interview responses from participants also
found that heterogenous grouping allows students to hold discussions with their peers and learn
from one another. Students have ways of communicating concepts to one another that perhaps
were not conveyed by the teacher. Responses also indicated that students feel more comfortable
approaching their peers with questions than their teacher, and grouping allows those questions to
be revealed. Teachers also noted that grouping would enable students to discuss the math and
understand the topics more conceptually.
The final finding related to Research Question One was that making mathematics content
more relative to students’ interests and culture can increase Latina/o student achievement.
Research has shown that it is crucial for teachers to use the different cultural experiences of
students as a resource to make the delivery of content more powerful and effective (Wager,
75

2011). When content is relative to students’ interests and cultures, students develop positive
attitudes toward the subject and build self-confidence (Leonard et al., 2010).
Based on participants’ survey responses, 90% of participants agreed that delivering
mathematics content by connecting it to students’ interests and cultures can help increase
achievement rates. Interview responses also confirmed that the reason mathematics is so exciting
and fun is because math is everywhere, and we can always make it relevant to student’s everyday
lives and experiences. The teachers shared that there is still context for understanding
mathematics questions, no matter the field, and bringing these connections into the classroom
makes math more accessible to students. Similarly, teachers emphasized that bringing in the
students’ cultures and other references that they are familiar with makes it more personable for
them. Finally, interview responses confirmed that bringing in real-world examples helps students
see why the subject is important and why it matters, which gives the students a purpose and
reason to learn.
Research Question Two
Research Question Two inquired, how do middle school mathematics teachers evaluate
the effectiveness of the practices used in classrooms for Latina/o students in Los Angeles county?
The quantitative and qualitative data related to Research Question Two produced three findings.
The first finding related to Research Question Two is that middles school mathematics teachers
can use formative assessments to evaluate the effectiveness of the practices used within their
classrooms. Prior research has stated that there are large gains among low achievers
when teachers incorporate formative assessments into their instruction (Hudesman et al., 2013).
Through formative assessments, teachers can respond to students’ mistakes with suitable
feedback (Heritage, 2010). Students should use teachers’ feedback to establish learning goals and
advance their skills (Heritage, 2010).
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Data from the quantitative portion of this study shows that 73.33% of teachers regularly
check their students’ work and assessments to understand and evaluate how they perform
pedagogically. In their interview responses, teachers shared that after teaching, they give
students formative assessments to understand how they can modify their instruction. According
to the teachers, based on students’ responses on their assessments, they know the topics students
have fully grasped and the topics they need to spend extra time on. The teachers stated that the
formative assessments could help them understand trends in the classroom and transform their
instruction to better meet the needs of their students. Finally, teachers also agreed that formative
assessments allow them to give their students direct and prompt feedback on their responses,
allowing them to learn from their mistakes and correct them.
The second finding in relation to Research Question Two established that teachers should
constantly reflect on their teaching practices and evaluate them to maintain high student
achievement levels. Research states that teachers who reflect on their instructional methods can
regularly change their instructional practices to meet their students’ diverse needs (Donohoo et
al., 2018). Self-reflecting through professional learning communities also helps teachers to
evaluate their instruction collectively and take accountability for their instruction (Donohoo et
al., 2018).
Data from the quantitative portion of this study depicts that 86.67% of participants agree
that evaluating their practices and meeting with other colleagues to reflect on their instruction
helps assess their teaching effectiveness. During interviews, participants shared that they spend
the majority of their time reflecting on their instruction because it helps them understand what
they can do differently to meet their students’ needs. Teachers also stress that implementing self-
reflection into their daily routine allows them to establish and meet classroom goals. The
interview responses confirmed that teachers prefer discussing their practices in their professional
77

learning communities because they get the opportunity to learn different ways of delivering
content. Other teachers even shared that they appreciate reflecting on their work with their
superiors to receive direct feedback on how they can communicate content more effectively to
their students.
The final finding in relation to Research Question Two established that teachers evaluate
their instruction by participating in professional development opportunities to learn strategies
that will better suit their students’ needs. Data from the quantitative portion of this study revealed
that 93.33% of participants value professional development opportunities because it allows them
to advance their pedagogical skills. Professional development opportunities educate teachers on
better pedagogical strategies to enhance student learning and achievement (Fischer et al., 2018).
Research has consistently shown that effective professional development opportunities provide
teachers with successful strategies to promote more engagement and student achievement in
classrooms (Fischer et al., 2018).
Data from the quantitative portion of this study conveys that 93.33% of participants agree
with participating in professional development opportunities to improve their instructional skills
further. Interview responses also showed that teachers find professional development
opportunities resourceful because they provide strategies that deliver results. Teachers shared
that it is crucial to be open-minded to learn various instruction methods, especially if the research
has shown them to be effective. Participants also stressed that professional development allows
teachers to stay up-to-date with the mindsets of newer generations and helps them learn how to
educate the children of today.
Research Question Three
Research Question Three inquired, how do middle school mathematics teachers in Los
Angeles county use technology in their classrooms to provide effective instruction for Latina/o
78

students? The quantitative and qualitative data related to Research Question Three produced one
main finding. The finding related to Research Question Three is that, if used effectively,
technology integration allows for students to have individualized and differentiated learning
experiences. Research has shown that more and more classrooms have started using technology-
based platforms to enhance their students’ learning experiences (Fazal & Bryant, 2019).
Teachers usually use technology during the second half of the class after direct instruction by the
teacher (Fazal & Bryant, 2019). Using both instruction methods gives students more
personalized and individualized learning experiences within the classroom (Fazal & Bryant,
2019). Teachers can customize content that is individually catered toward each student’s needs.
Students can learn at their own pace and review previous materials if they feel it is necessary
(Ozel et al., 2010). Technology integration allows instruction to be student-centered and
differentiated (Ozel et al., 2010).
Data collected from the quantitative portion of this study showed that 80% of teachers
believed that using technology within mathematics classrooms allows Latina/o students to learn
at their own pace. It also showed that 96.33% of participants agreed that technology integration
promotes individualized and personalized learning opportunities for Latina/o students. Interview
responses from participants indicated that specific web-based platforms, such as iReady, are
useful because they create content for each student based on diagnostic test results. Teachers also
agreed that platforms such as Kahn Academy benefit students because it helps eliminate learning
gaps from unmastered topics. Teachers also shared that platforms such as Kahn Academy are
also effective because other students have the opportunity to be adequately challenged by being
allowed to move onto new topics. Teachers stress that these technology platforms simplify
learning experiences, especially for students with language barriers, since they come with
different language options. Participants noted that students could feel more engaged with
79

mathematics content and make abstract concepts more concrete. Interview responses also
determined that teachers could benefit from technology integration because monitoring their
students’ progress is more easily accessible.
Limitations and Delimitations
The study's limitations include that the research is restricted to middle school
mathematics teachers in Los Angeles County in California. The data collected from this study is
limited to the personal and individual experiences of the teachers who participated in the study.
The delimitations include California's geographic location and the small sample of middle school
mathematics teachers interviewed and surveyed. The self-reported data of surveys and interviews
can also produce respondent validity. However, triangulation between data was used to minimize
potential threats.
Implications for Practice
This study examined the best practices that middle school mathematics teachers can use
within their classrooms to increase Latina/o student achievement. The findings of this study
provide valuable and effective practices that middle school teachers can implement within their
classrooms. After analyzing the common trends and themes, the study established implications
for teachers and the techniques used in their classrooms.
The first implication for practice was that teachers should focus on building relationships
with their students, caring about their future success, making content more interesting, and
allowing them to discuss content with their peers. Triangular findings from the study also
supported the importance of establishing relationships, holding high expectations of students,
and making the content more exciting. Study findings suggest that when teachers build
relationships with their students, they better recognize the individual needs and provide
individualized and effective learning experiences. Teachers will also know what their students’
80

interests are to incorporate them within the content and have their active participation and
engagement.
The second implication for practice focuses on the ability of teachers to self-reflect on
their instruction based on student work, such as formative assessments. The study determined
that teachers who reflect on their work either on their own, with colleagues, or with superiors,
can modify their pedagogical strategies based on the needs of their classroom. The study also
determined that teachers could learn beneficial information from professional development
opportunities to improve their instructional skills.
The third implication for practice is that teachers should correctly implement technology-
based platforms within their classrooms to customize and differentiate student learning
experiences. Teachers emphasized that effective platforms are beneficial because they allow
students to learn at their own pace and level. Teachers stress that technology provides for fast
modification and also tracking of student progress.
Future Research
This study focused on the best practices that teachers can implement within their
classrooms that have shown to be successful for increasing achievement levels of Latina/o
students. While the study did discover these best practices, there is still further research that can
be conducted in the context of middle school mathematics classrooms. Further research is
suggested to address one main area associated with this study.
The recommendation for future research is to provide further definition on what
appropriate implementation of technology within mathematics classrooms looks like. Study
findings revealed that teachers emphasized the importance of knowing which technology
platforms teachers should bring into their classrooms and how many they should bring in. Future
research studies can help determine what strategies teachers can use to understand what platform
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best fits the needs of students within their classrooms. Further examination of how teachers and
school sites determine the platforms they use within their classrooms could be a good addition to
the effective practices middle school mathematics teachers use.
Conclusion
This study established that there are many strategies middle school mathematics teachers
can implement within their classrooms to benefit Latina/o student achievement. Even though
there are many different challenges Latina/o students face, this study confirms that certain
practices can eliminate achievement gaps within mathematics classrooms. Study findings suggest
that some of the best practices include building relationships with students, allowing them to
discuss content with their peers, and making content relevant to students’ experiences. Teachers
can further assess their instructional skills by analyzing results from formative assessments,
reflecting on their practices, and attending professional developments. Lastly, findings confirmed
that teachers should use technology to individualize student learning experiences, target areas of
concern, and monitor student progress. This study offers educational leaders an understanding of
the implications that specific classroom practices have on Latina/o student achievement levels.
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References
Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change.
Psychological Review, 84(2), 191–215.
Bitters, B. (1997). Useful definitions for exploring educational equity. Equity Mission Team
Wisconsin Department of Public Instruction
California Department of Education. (2019). English arts, literacy, and mathematics, smarter
balanced summative assessments. California Department of Education.
California Department of Education. (2020). English arts, literacy, and mathematics, smarter
balanced summative assessments. California Department of Education.
Carlan V. G., Rubin R., & Morgan B. M. (2005). Cooperative learning, mathematical problem
solving, and Latinos. CveI Department, School of Education.
Catapano, J. (2013). TeachHUB education blog. http://teachhub.blogspot.com/2016/04/the-
challenges-of-equity-in-public.html?q=equity
Charles, R. I. (2005). Big ideas and understandings as the foundation for elementary and middle
school mathematics. Journal of Mathematics Education Leadership, 7(3), 9–22.
Chudowsky, N., Chudowsky, V., & Kober, N. (2007). Answering the question that matters most:
Has student achievement increased since No Child Left Behind? Center on Education
Policy.
Creswell, J. W., & Creswell, J. D. (2018). Research design: Qualitative, quantitative, and mixed
methods approaches (5th ed.). SAGE.
Creswell. (2008). https://www.sagepub.com/sites/default/files/upm-
binaries/27395_Pages5_11.pdf
Donohoo, J., Hattie, J., & Eells, R. (2018). The power of collective efficacy. Educational
Leadership, 75(6), 40–44.
83

Dynarski, M. (2015). Using research to improve education under the Every Student Succeeds
Act. The Brookings Institution.
Erickson, A. T., & Highsmith, A. R. (2018). The neighborhood unit: Schools, segregation, and
the shaping of the modern metropolitan landscape. Teachers College Record, 120.
https://www.tc.columbia.edu/faculty/ate11/facultyprofile/files/38_22078-(1).pdf
Fazal, M., & Bryant, M. (2019). Blended learning in middle school math: The question of
effectiveness. Journal of Online Learning Research, 5(1), 49–64.
Fink, A. (2013). How to conduct surveys: A step-by-step guide. SAGE.
Fischer, C., Fishman, B., Dede, C., Eisenkraft, E., Foster, B., Frumin, K., Lawrenz, F., Levy, A.,
& McCoy, A. (2018). Investigating relationships between school context, teacher
professional development, teaching practices, and student achievement in response to a
nationwide science reform. Teaching and Teacher Education, 72, 107–121.
https://doi.org/10.1016/j.tate.2018.02.011
Flores, A. (2007). Examining disparities in mathematics education: Achievement gap or
opportunity gap? The High School Journal, 91(1), 29–42.
Garcia, O., Johnson, S. I., & Seltzer, K. (2017). The translanguaging classroom: Leveraging
student bilingualism for learning. Caslon.
Goe, L., & Stickler, L. M., (2008). Teacher quality and student achievement: Making the most of
recent research. National Comprehensive Center for Teacher Quality.
Gutierrez, R. (2000). Advancing African-American urban youth in mathematics: Unpacking the
success of one math department. American Journal of Education, 109, 64–111.
Gutierrez, R., & Irving, S. E. (2012). Latino/a and Black students and mathematics: The students
at the center series 2012. Jobs for the Future.
84

Haller, A., Hunt, E., Pacha, J., & Fazekas, A. (2016). Lessons for states: The “Every Student
Succeeds Act” (ESSA) increases focus on and investment in supporting principal
preparation and development. Center for the Study of Education Policy.
Heritage, M. (2010). Formative assessment and next-generation assessment systems: Are we
losing an opportunity? The Council of Chief State School Officers
Hope, S. (2017). The Every Student Succeeds Act: A research brief. VCU MERC Publications
https://files.eric.ed.gov/fulltext/ED520769.pdf
Hudesman, J., Crosby, S., Flugman, B., Issac, S., Everson, H., & Clay, D. B. (2015). Using
formative assessment and metacognition to improve student achievement. Journal of
Developmental Education, 37(1), 2–13.
Jansen, A., & Bartel, T. (2013). Caring mathematics instruction: Middle school students’ and
teachers’ perspectives. Middle Grades Research Journal, 8(1), 33–49.
Jao, L. (2012). The multicultural mathematics classroom. Multicultural Education.
https://files.eric.ed.gov./fulltext/EJ1001529.pdf
Johnson, R. B., & Christensen, L. (2014). Educational research: Quantitative, qualitative, and
mixed approaches (5th ed.). SAGE.
Ladson-Billings, G. (1997). Crafting a culturally relevant social studies approach. In E. W. Ross
(Ed.), The social studies curriculum: Purposes, problems, and possibilities (pp. 121–
136). State University of New York Press.
Ladson-Billings, G. (2000). Fighting for our lives: Preparing teachers to teach African American
students. Journal of Teacher Education, 51, 206–2014.
Ladson-Billings, G., & Tate, W. (1995). Toward a critical race theory in education. Teachers
College Record, 97(1), 47–68.
85

Larnell, G. V., Bullock, E. C., & Jett, C. C. (2016). Rethinking teaching and learning
mathematics for social justice from a critical race perspective. Journal of Education,
196(1), 19–27.
Lee, J. (2006). Tracking achievement gaps and assessing the impact of NCLB on the gaps: An in-
depth look into national and state reading and math outcome trends. The Civil Rights
Project at Harvard University.
Leonard, J., Brooks, W., Barnes-Johnson, J., Berry, R. (2010). The nuances and complexities of
teaching for mathematics for cultural relevance and social justice. Journal of Teacher
Education, 61(3), 261–270.
Lewis, J., Ream, R., Bocian, T.M., Cardullo, R., Hammond, K. & Fast, L. (2012). Con carino:
Teacher caring, math self-efficacy, and math achievement among Hispanic English
learners. Teachers College Record, 114, 1–42.
Mackey, K. (2015, September 19). Proof points: Blended learning success in school districts.
Christensen Institute. https://www.christensen- institute.org/publications/proof-points/.
Madrid, E. M. (2011). The Latino achievement gap. Multicultural Education, 19(3), 7–12.
Maxwell, J. A. (2013). Qualitative research design: An interactive approach (3rd ed.). SAGE.
Merriam, S. B., & Tisdell, E. J. (2016). Qualitative research: A guide to design and
implementation (4th ed.). Jossey Bass.
Miller-Cotto, D., & Lewis, N. A., Jr. (2020). Am I a “math person”? How classroom cultures
shape math identity among Black and Latinx students.
https://doi.org/10.31219/osf.io/hcqst
Minshew, L., & Anderson, J. (2015). Teacher self-efficacy in 1:1 iPad integration in middle
school science and math classrooms. Contemporary Issues in Technology and Teacher
Education, 15(3), 334–367.
86

Mitchell, M. (2018). Organizational change plan for closing the Black and white achievement
gap. National Louis University.
https://digitalcommons.nl.edu/cgi/viewcontent.cgi?article=1320&context=diss
Morales Jr, H., & DiNapoli, J. (2018). Latinx bilingual students’ perseverance on a mathematical
task: A rehumanizing perspective. REDIMAT – Journal of Research in Mathematics
Education, 7(3), 226–250. https://doi.org/10.4471/redimat.2018.3274
Morisano, D., Hirsh, J. B., Peterson, J. B, Pihl, R. O., & Shore, B. M. (2010). Setting,
elaborating, and reflecting on personal goals improves academic performance. Journal of
Applied Psychology, 95(2), 255–264. https://doi.org/10.1037/a0018478
Muhammad, S. N. H., & Jaafar, S. N. (2015). TVET teacher professionalism in leadership
personality formation. Journal of Education and Practice, 6(1), 143–147.
Musu-Gillette, L., Robinson, J., McFarland, J., Kewal Ramani, A., Zhang, A., & Wilkinson-
Flicker, S. (2016). Status and trends in the education of racial and ethnic groups 2016
(NCES 2016-007). U.S. Department of Education, National Center for Education
Statistics. http://nces.ed.gov/pubsearch.
Ozel, S., Yetkiner, Z. E, & Capraro, R. M. (2010). Technology in K-12 mathematics classrooms.
School Science and Mathematics, 108(2), 80–85.
Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). SAGE.

Pazzaglia, A. M., Stafford, E. T., & Rodriguez, S. M. (2016). Survey methods for educators:
Selecting samples and administering surveys (part 2 of 3) (REL 2016–160). U.S.
Department of Education, Institute of Education Sciences, National Center for Education
Evaluation and Regional Assistance, Regional Educational Laboratory Northeast &
Islands. http://ies.ed.gov/ncee/edlabs.
87

Santamaria, L. J. (2009). Culturally responsive differentiated instruction: Narrowing gaps
between best pedagogical practices benefiting all learners. Teachers College Record,
111(1), 214–247.
Songunro, O. A. (2017). Quality instruction as a motivating factor in higher education.
International Journal of Higher Education, 6(4), 17–184.
Ukpokodu, O. N. (2011). How do I teach mathematics in a culturally responsive way?
Identifying empowering teaching practices. Multicultural Education, 47–56.
https://files.eric.ed.gov/fulltext/EJ955945.pdf
Vaughan, W. (2002). Effects of cooperative learning on achievement and attitude among
students of color. The Journal of Educational Research, 95(6), 359–364.
Wager, A. A. (2012). Incorporating out-of-school mathematics: From cultural context to
embedded practice. Math Teacher Education, 15, 9–23. https://doi.org/10.1007/s10857-
011-9199-3

Abstract (if available)

Abstract The low academic achievement rates of Latina/o students within mathematics are a complex and multi-faceted issue that needs addressing. With a growing number of Latina/o students within California, teachers need to adapt to the diverse needs of students within their classrooms. Understanding the different challenges that Latina/o students face within the school, and approaching these challenges, is essential and can provide more equitable outcomes for these students. The purpose of this study is to identify the best practices that can be implemented within middle school mathematics classrooms to ensure increases in the achievement levels of Latina/o students. This study uses a mixed-methods approach of both quantitative and qualitative data. The study conducts surveys and interviews with middle school mathematics teachers in Los Angeles county to discover instructional methods that best support Latina/o students. The study provides strategies for other middle school mathematics teachers to facilitate classroom instruction that evokes interest and critical thinking.

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Asset Metadata

Creator Boulatian, Aida (author)

Core Title Best practices to improve mathematics achievement of middle school Latina/o students

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 04/28/2021

Defense Date 03/19/2021

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

Tag best practices in mathematics instruction,critical race theory,culturally responsive teaching,Latina/o students,middle school mathematics,OAI-PMH Harvest,technology integration

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Cash, David (committee chair), Castruita, Rudy (committee member), Roach, John (committee member)

Creator Email aboulatian@gmail.com,boulatia@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-454762

Unique identifier UC11668787

Identifier etd-BoulatianA-9569.pdf (filename),usctheses-c89-454762 (legacy record id)

Legacy Identifier etd-BoulatianA-9569.pdf

Dmrecord 454762

Document Type Dissertation

Rights Boulatian, Aida

Type texts

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

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

Repository Name University of Southern California Digital Library

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