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A document analysis of the math curriculum on teachers pay teachers

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A Document Analysis of the Math Curriculum on Teachers Pay Teachers

by
Reham Ahmed

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

August 2022

© Copyright by Reham Ahmed 2022
All Rights Reserved

The Committee for Reham Ahmed certifies the approval of this Dissertation

Marsha Riggio
John Roach
Morgan Polikoff, Committee Chair

Rossier School of Education
University of Southern California
2022

iv
Abstract
In this dissertation, I conduct a thorough document analysis of the mathematics curriculum on
Teachers Pay Teachers. I developed a grading rubric that is guided by my education expertise,
research, and literature review that I conducted. It is important for teachers to have a rubric as a
tool to assess the rigor and relevance of the supplemental mathematics curriculum that they plan
to use with students in the classroom to address their academic, cultural, and social needs.

v
Acknowledgements
I would like to thank my family, my committee members and committee chair and my
peers at USC who have formally helped me reach this point in my academic career.
As an educator and a mother my passion is to ensure the best education for our children. I
was able to use the input from my school, my experience and research to feed my research. I
intend for this research to be an asset to the education community and for the future of education
in the United States.

vi
Table of Contents
Abstract ……………………………………………………………..……………………………iv
Acknowledgements……………………………………………………………………………….v
List of Tables…….……………………………………………………………………………….ix
List of Figures……………………..………………………………………………………………x
Chapter One: OVERVIEW OF THE STUDY……………………...………………………..……1
Background of the Problem……………………………………………………………….2
Document Analysis ………………………………………………...…………………..…3
Purpose of the Study………………………………………………………………..……..3
Research Questions…………………………………………………………………..……4
Significance of the Research Study………………………………………………...…..…4
Definition of Terms…………………………………………………………….…………5
Organization of the Study……………………………………………………………..…10
Chapter Two: LITERATURE REVIEW…………………………………………...……………11
Historical Background………………………………………………………………...…11
Other Policy Efforts to Narrow Gaps……………………………………………………14
Multicultural Education……………………………………………………...…………..15
Culturally Relevant Pedagogy………………………………………………………...…16
Teacher-Student Relationship……………………………………………………………18
Culturally Responsive Teachers…………………………………………...…………….20
Teachers’ Role in Culturally Relevant Curriculum……………………………………...22
Gaps in Mathematics Achievement……………………………………………………...24
Connecting Culturally Relevant Education to Student Outcomes……………………….26
The Importance of Curriculum Materials……………………………………………..…29

vii
Supplemental Curriculum………………………………………………………….…….31
Teachers Pay Teachers…………………………………………………………..……….32
Conceptual Framework…………………………………………………………..………33
Chapter Three: METHODOLOGY……………………………………………………...………44
Rationale for Qualitative Research……………………………………………....………44
Central Research Questions………………………………………………….…..………45
Role of Researcher…………………………………………………………………….…45
Case Study Approach…………………………………………………………………….47
Research Site……………………………………………………………………………..47
Data Collection and Analysis Procedures…………………………………………….….48
Document Analysis Criteria………………………………………………………..…….48
Alignment with TEKs/Common Core Standards Criteria………………………….……49
Mathematical Discourse…………………………………………………………….……50
Real World Application and Social Justice Support……………………………..………51
Analysis Plan…………………………………………………………………….………52
Advantages and Limitations of Document Analysis ………………................................55
Potential Flaws…………………………………………………………………………...57
Trustworthiness and Credibility………………………………………………………….58
Chapter Four: FINDINGS……………………………………………………………………….60
Introduction ……………………………………………………………………...………60
Discussion of the Findings……………………………………………………………….60
Research Question One…………………………………………………………………..60
Alignment with TEKs/Common Core Standards………………………………………..61

viii
Research Question Two………………………………………………………………….71
Mathematical Discourse and Communication………………..………………………….71
Research Question Three………………………………………………………….……..79
Real World Application and Social Justice Support………………………………….….79
Chapter FIVE: DISCUSSION and CONCLUSION…………………………………………….85
Do Teachers Pay Teachers Lessons Target Grade Level standards?.................................85
Are Math Standards on TPT Lessons Connected Well to the Content of the Lesson?.....86
Do TPT Math Lessons Satisfy a Balance of Mathematical Procedures and a Deep
Conceptual Understanding of Mathematical Operations?................................................86
Do TPT Lessons Encourage Students to Use Multiple Solutions or Strategies to Solve
Problems?...........................................................................................................................88
Do TPT Lessons Require or Allow Students to Explain and Present Ideas and Reasoning
to Each Other or to the Whole Class?................................................................................90
Do TPT Lessons Encourage Students to Use Accurate Mathematical and Academic
Language?..........................................................................................................................90
Do Teachers Pay Teachers Lessons Use Math to Help the Students Understand Issues
that are Relevant to Them or Enable Them to Make Informative Decisions as
Independent Individuals?...................................................................................................91
Policy Implications…………………………………………………………………..…..92
Limitations………………………………………………………………...……………..93
Conclusion…………………………………………………………………………...…..93
References…………………………………………………………………………...…...……....96

ix

List of Tables
Table 1: Teachers Pay Teachers Rubric Page 53

x

List of Figures
Diagram 1: Conceptual Framework……………………………………………….………….… 43
Figure 1: Integer Operations Maze1………………………………………..……………………63
Figure 2: Mathematics Maze…………………………………………………………………….64
Figure 3: Integer Operations Maze2…………………………………………………..…………64
Figure 4: Comparing Functions………………………………………………………………….65
Figure 5: Description………………………………………………………………..…………...66
Figure 6: Common Core Standards and Description……………………………………..……...67
Figure 7: Stem-ersion…………………………………………………………………………….68
Figure 8: Algebra I End of Year Project: Functional Designs…………………………...………70
Figure 9: First Category: Alignment with TEKs/Common Core Standards…………….…….…70
Figure 10: Second Category: Mathematical Discourse and Communication…………………....71
Figure 11: Representing Linear Equations………………………………………...…….……....73
Figure 12: Comparing Functions………………………………………………………………...73
Figure 13: Variable Description…………………...………………………….………………….75
Figure 14: Hang the Man- Key…………………………………………………………...……...76
Figure 15: Tic-Tac-Toe………………………………………………………...….………..……77
Figure 16: Simple Interest Word Problem……………………………………………........…….78
Figure 17: Third Category: Real World Application and Social Justice Support……...………...79
Figure 18: Starbucks Coffee………………………………………………………………...…...81
Figure 19: Pi Day Pie Problems………………………………………………………………….81
Figure 20: Financing Options……………………………………………………………………83

xi
Figure 21: Road Trip Plan………………………………………………………………….…….84
1

Chapter One: Overview of the Study
Education for our students of color in the United States continues to be a controversial
topic. Historically, many diverse learners were being denied the right to an education, which led
to the filing and winning of fundamental Supreme Court cases such as Brown v. Board of
Education in 1954 and Lau v. Nichols in 1974.
When the Supreme Court determined that “separate but equal” was inherently unequal in
Brown v. Board of Education (1954), it set the journey for African American children to fight for
their right for a free and appropriate education. In Lau v. Nichols (1974), the court decided that
students who speak a foreign language as their first language have the right to receive support
with their acquisition of the English Language. While these court cases were fundamental
milestones in the history of education in the US, diverse learners continue to fall behind in their
education (Delpit, 2006; Howard, 2010; Rothstein, 2004; Villegas & Lucas, 2002, b).
Education and race have been linked in the US for many generations (Cross, 1998;
DuBois, 1994; Howard, 2010; Ladson-Billings, 2006; Marable, 2000, 2002). In American
history, the systemic denial of appropriate education, housing, and employment has caused
diverse children to fall behind while reinforcing the privilege of culturally dominant children
(Bell, 1973; Bowles & Gintis, 1976; Marable, 2002; Wise, 2013). This drives the study of the
achievement gap phenomenon. The achievement gap is the term being used to refer to the
disparity in academic achievement between students who differ in race, socioeconomic status,
gender, language proficiency, and learning ability. There is an overwhelming body of literature
that targets the achievement gap and relates it to social inequalities, and the dependence on state
testing alone to determine student achievement (Howard, 2010; Kozol, 2005).
2

The current education system has continued to fail numerous diverse students. Traditional
schools in the US were founded on White Eurocentric ideologies that have been embedded in the
culture of schools across the nation (Buras & Apple, 2008; Rizvi & Lingard, 2010). The culture
of our schools is largely that of middle-class, European, Christian values (Boykin, 1994; Nieto &
Bode, 2012). This has caused the diverse cultural and linguistic makeup of our students to be
ignored. With the rising number of English Learners (Collins & Samson, 2012) and the increase
in the number of culturally and linguistically diverse students, it is necessary to investigate
policies and practices that can bring about greater educational equity. Darling-Hammond (2010a)
suggests that the way diverse students are being educated now “will determine our future.” She
examines the teachers’ lessons and urges for needed changes to improve the educational
experience for diverse learners.
Background of the Problem
Research on improving education for diverse learners has drawn the attention of many in
the education community. One method to improve classroom instruction is to carefully choose a
curriculum that is academically informative and culturally nourishing for our students. Education
survey data has shown that teachers frequently supplement their curriculum with supplemental
materials that they create or download from the internet (Opfer et al., 2016; Blazar et al., 2019 as
cited in Polikoff & Silver, 2021). Polikoff and Dean (2019) assert that over two-thirds of U.S.
educators supplement their curriculum by online supplements to enhance the academic
experience of the students they support. However, supplemental material should be relevant to
the students’ cultures, languages and lived experiences of the students (Banks, 2004; Gay, 2010,
2013; Ladson-Billings, 2009).

3

While supplemental curriculum is available for all content areas, as a mathematics
educator, I intend to focus on the quality of mathematics supplemental curriculum and its
relevance to our students in classrooms today. Previous research on the context of supplemental
material suggests that poor, inaccurate, and sometimes a lack of representation of diversity and
linguistic elements is often noted (Gay, 2010). Teachers must consciously make connections to
student cultures, languages, and home experiences to allow students to experience academic
achievement while preserving their cultural and linguistic identities (Klingner et al., 2005, p. 23).
Therefore, the problem at hand is the absence of a high-quality mathematics supplemental
curriculum that is rigorous and relevant to the students’ lives and culture.
Document Analysis
Virtually all teachers supplement to some degree (Polikoff & Dean, 2019). Polikoff and
Dean (2019) find that many supplemental resources lack quality along multiple dimensions;
however, a lot of work is required to determine what is good. Teachers pay Teachers is one of
the most popular websites that teachers use to supplement their curriculum. According to a 2017
federal survey of teachers, more than half of teachers supplement their curriculum from Teachers
Pay Teachers every week (Barshay, 2021). Teachers pay Teachers contains more than four
million items according to the for-profit company. This document analysis seeks to investigate
the degree of cultural relevance of some of the most popular supplemental mathematics materials
on Teachers Pay Teachers.
Purpose of the Study
The purpose of this study is to explore the degree of cultural relevance in supplemental
mathematics curriculum. There is limited information available on this topic in current literature;
this literature is reviewed in the next chapter. Culturally relevant curriculum incorporates an
4

exploration of beliefs, cultural funds of knowledge that could be of use in the classroom. The
study investigates the cultural relevance based on criteria developed based on intensive research
and educational experience. My aspiration is that this journey will inform educators,
administrators, and parents about methods to investigate the degree of cultural relevance in
supplemental mathematics curriculum.
Research Questions
1. How does supplemental curriculum support a rigorous academic curriculum that adheres
to state standards?
2. How does supplemental curriculum incorporate opportunities for students to express their
individualized ideas using appropriate academic language?
3. How are supplemental materials including support for all learners, elements of cultural
pluralism and social justice?
Significance of the Research Study
Research and statistics show that students who continue to underachieve are more likely
to drop out of school, be incarcerated, experience health problems and become a burden on our
society (Alexander, 2010; Barton, 2003; McKinsey & Company Report, 2009; McKown &
Weinstein, 2008; Wise, 2013). When students study a curriculum that is not related to their lives
and does not challenge their intuition, they lose interest (Oakes, 2005; Orfield, 2004; Rubal-
Lopez, 2004; Steele, 2009).
Curriculum is a powerful component of the educational experience for our students.
Accessing a high quality and relevant curriculum can create opportunities for all learners to gain
equal access to academic and life-long success (Gay, 2002, 2010a). Therefore, this document
analysis allows us to investigate ways to provide a better learning experience to our students by
5

providing them with an empowered curriculum that can fulfill legal, and moral responsibilities
(Ladson-Billings, 2006b).
Definition of Terms
For the purposes of this study, the terms below have been defined and are used
throughout this study on using culturally relevant pedagogy in the classroom. However, as
literature is being analyzed, the term that was used in original literature will also be used
throughout this literature review.
Achievement gap. Documented and researched differences in academic achievement
based on socioeconomic factors such as race/ethnicity, gender, social status, or economic
standard variables in standardized K-12 tests. (Hanushek, 2010)
Care. Looking after and providing for the needs of another individual. Showing concern
and interest to the other individual. Noddings (1992) mentions that there are three key
components to care: relatedness, receptivity, and responsiveness.
Critical pedagogy. Giroux (2003) discusses critical pedagogy, which connects between
conception and practice by honoring students’ experiences and connecting them to academia. He
urges educators to stand against curriculum and classroom practices that avoid controversial
topics such as gender, class, race, and sexual orientation, which should be areas of learning and
strength for the students. Critical pedagogy allows teachers and students to be critical about the
world around them, which allows a major transformation in student thinking, discussions, and a
movement against inequities in school and community.
Culture. A particular group’s program for survival and adaptation to its environment.
Culture is the knowledge, values and concepts that are shared by members of the group by
communication (Madhlangobe, 2009; Saifer et al., 2011, p. 218). Lederach (1995) defines
6

culture as the “shared knowledge and schemes created by a set of people for perceiving,
interpreting, expressing and responding to the social realities around them” (p. 9).
Critical race theory (CRT). Ladson Billings and Tate (1995) identified the critical race
theory in education to study the social inequity present in racist practices in academic institutions
(Brown-Jeffy & Cooper, 2011).
Culturally relevant pedagogy (CRP). A term coined by Gloria Ladson-Billings (1995) to
describe pedagogical and theoretical frameworks that are designed to empower racially and
ethnically diverse students socially, emotionally, politically, and intellectually by using cultural
references. The purpose of culturally relevant pedagogy is to foster academic achievement,
cultural competence, and a sociopolitical consciousness in students. (Ladson-Billings, 1994)
Ladson-Billings describes culturally relevant pedagogy as a tool that has three pillars: a)
academic success b) cultural competence c) “critical consciousness through which they challenge
the status quo of the current social order” (p. 160).
Culturally relevant teaching. Gay (2002) defines it as “using the cultural characteristics,
experiences, and perspectives of ethnically diverse students as conduits for teaching them more
effectively” (p. 106). Sustaining a culturally relevant teaching allows teachers to use tools to
support young people in achieving cultural competence and maintaining the culture and
linguistics of the community.
Culturally responsive teachers. Described by Howard (2003) as educators who are aware
of the important role of race and significance in the way the students learn. These teachers are
aware that an important factor to successful instruction is by linking students’ knowledge and life
experiences to what they are learning inside the classroom (Marks, 2005). Effective teaching
7

results in higher engagement and learning levels that will not occur without connecting with
students’ needs, experiences, and interests (Darling-Hammond, 1997).
Ladson-Billings (1994), Nieto (1999), Bailey and Paisley (2004), Banks (2004) and Gay
(2000) define culturally responsive teachers as educators that have the following characteristics.
1. They acknowledge and appreciate students’ differences and similarities.
2. They make their students aware of diversity by educating them about the existence of
diversity around them.
3. They embrace their students’ cultural identity within their classroom and by
implementing components within their instructional material.
4. They create an environment of equity and respect with and among students.
5. They use assessments as tools to make judgements about students’ academic achievement
and encourage positive student interrelationships.
6. Culturally responsive teachers challenge students to reach their potential and help their
students develop a sense of political, cultural, and social consciousness.
Villegas and Lucas (2002) further describe the six distinguishing characteristics of
culturally responsive teachers.
1. They are socially aware of different cultures and that there is more than one lens that
students view education and reality through and that these lenses are shaped according to
their culture and home environment.
2. They are affirmative of the diversity of their students and view diversity as a resource to
learning.
3. Culturally responsive teachers must hold themselves accountable as changing agents in
their schools.
8

4. They need to have a thorough understanding of how students construct knowledge.
5. Culturally responsive teachers need to be familiar with their students’ communities and
backgrounds.
6. They need to incorporate their knowledge into their curriculum, instruction, and the
learning environment they create (as cited in Sullivan, 2009).
In addition, culturally responsive teachers need to formulate lessons to students that have a
personal meaning to them, meet high expectations and hold respect and value to the students and
their communities (Villegas & Lucas, 2002). In conclusion, culturally responsive teachers are
described by Ladson-Billings (1995b) as educators who encourage their students to reach their
full academic potentials, culturally competent thinkers who challenge current beliefs and
practices about socio-political status.
Culturally responsive teaching is formulated to provide all students an equal opportunity
to succeed academically (Irvine, 1990; Nieto, 2002; Weinstein, Curran & Tomlinson-Clarke,
2003). Culturally responsive teaching is designed to help train teachers to fill in the gaps that
emerge when students “attempt to make sense of the curriculum” (Ladson-Billings, 2006, p. 32).
Culturally sustaining pedagogy (CSP) Recently in 2012, Django Paris coined the term
“culturally sustaining pedagogy” (CSP), which is an extension of the terms culturally responsive
pedagogy and culturally relevant pedagogy. Paris asserts that culturally sustaining requires that
our “pedagogies be more than responsive of or relevant to the cultural experiences and practices
of young people-it requires that they support young people in sustaining the cultural and
linguistic competence of their communities while simultaneously offering access to dominant
cultural competence” (Paris, 2012, p. 95). CSP would support other aspects such as multilingual
students and multicultural students as they “sustain linguistic, literature, and cultural pluralism as
9

part of the democratic project of schooling” (Paris, 2012, p. 95). Ladson-Billings (2013)
suggested that she adds Paris’ (2012) idea of culturally sustaining pedagogy. She acknowledges
the fact that scholarship is dynamic and is subject to change and take new forms. She asserts that
though culturally relevant pedagogy is well-known by many scholars, it should not be a static
idea (Ladson-Billings, 2014, p. 77). She argues that the idea of culturally relevant pedagogy has
“rarely pushed students to consider critical perspectives on policies and practices that may have
direct impact on their lives and communities…there was no discussion of issues such as school
choice, school closing, rising incarceration rates, gun laws” (Ladson-Billings, 2014, p. 78).
Instead, culturally relevant pedagogy currently means “adding some books about people of color
having a classroom Kwanzaa celebration or posting ‘diverse’ images “(Ladson-Billings, 2014, p.
82). Ladson-Billings believes that CSP incorporates the “multiplicities of identities and
cultures” along with culturally relevant pedagogy.
Racial identity theory Individuals who can develop their specific racial identity and
awareness by learning, accepting, acknowledging, and resisting existing oppression amongst
individuals from diverse groups (Helms, 1990).
Students of color Non-White students and students who identify as non-White.
When students walk into the classroom, they bring their own knowledge and understanding of
the world around them. Each student’s culture, experience and unique upbringing produces a
different lens that he or she sees the world through. To assist teachers in understanding the world
from the students’ lens, culturally relevant pedagogy has been developed to guide teachers about
being non-judgmental of student cultures and inclusive of culture to be a more effective learning
facilitator in the classroom. The idea of culturally relevant pedagogy started previously as a
phenomenon in multiple ways including culturally appropriate, culturally congruent, among
10

others. Lastly, it has been identified as culturally relevant pedagogy to reflect the needs of
students from various cultures (Brown-Jeffy & Cooper, 2011).
Organization of the Study
This study is organized into five chapters. Chapter One introduces the problem, outlines
the purpose of the study and its importance in the education community. The background of the
achievement gap and culturally relevant teaching in the US are also discussed.
Chapter Two summarizes the known literature on culturally relevant teaching, the history
behind it and what constitutes it. It also discusses studies that have implemented culturally
relevant teaching and investigates the effects of it on students. Teachers Pay Teachers is also
discussed as a popular source of supplemental curriculum for many teachers in the mathematics
classroom.
Chapter Three presents the research methods employed in this study analysis. It describes
the research design, the site of the study, the criteria that will be used to rate supplemental
curriculum on Teachers Pay Teachers and the rubric that will be used to score the mathematics
lessons. The procedure for grading supplemental mathematical lessons is outlined and justified in
detail.
Chapter Four lays out the findings from my study analysis. Lastly, Chapter Five is a
discussion of the overall study analysis including the summary of the ratings, implications for
practice and future recommendations based on study analysis.

11

Chapter Two: Literature Review
This chapter discusses the literature that is available in the academic community on the
history of the quality of education students of color have had access to. Before I start my
document analysis on supplemental math curriculum, I would like to account for the literature
that is already available on the history of the access to education in the US, causes of present-day
achievement gaps and researchers’ approach toward a better educational future.
Historical Background
An educational gap has challenged our schools ever since students of color have had the
ability to participate in the public education system. This educational gap is particularly clustered
in urban schools and urban school districts across the US whose student demographics consist of
diverse ethnic and socio-economic groups. Historically, in the 1800s when this gap first appeared
it was referred to as the “literacy gap” (Anderson, 2007). The reason behind this educational gap
was the fact that 90% of White children were able to read and write, while 90% of African
American children were not able to read. Slavery was the major reason behind this gap because it
was simply against the law for any enslaved individual to be taught to read. In the 20
th
century
the literacy gap started to narrow when the Emancipation Proclamation in 1863 took place and
the Civil War ended in 1865 (Anderson, 2007). It was only at this time that enslaved individuals,
who participated in the Civil War, were freed. This enlightened the path for underrepresented
children to complete their education.
The educational gap widened when African American children did not have schools they
were allowed to attend. Schools were primarily intended for White students. However, there
were small efforts to teach African Americans to bridge the educational gap between African
American and White children Anderson, 2007). In 1863, after the Emancipation Proclamation,
12

African Americans constituted the largest percentage of uneducated individuals in the US. Racial
differences were obvious even in the quality and quantity of education African American
students were accessing. An education reform was established in the South, which stated that
public education is a right of citizenship (Anderson, 2007).
While African Americans were freed, they were still unable to attend schools as they
were not accepted in White schools with White students. The Freedom Bureau Schools were
opened to educate African Americans who served in the Civil War where they were taught by
other African Americans who could read. 200,000 individuals were educated, which brought
down the illiteracy rate to 61% (Margo, 1990). This helped narrow the gap between African
American students and White students. Unfortunately, as of 1990, only 20% of school aged
African American children were able to attend school (Margo, 1990) At the time, illiterate
parents had low income and they would rather send their children to work instead of attending
school and getting an education. Only parents who were well-off could afford to send their
children to school if it was available. However, once African American children were no longer
required to work on farms, more of them started attending school, which slightly narrowed the
literacy gap. (Margo, 1990)
Court case rulings such as Plessy v. Ferguson and Jim Crow laws allowed the ‘separate
but equal,’ which established a national and legal agreement for institutionalized racism
(Douglas, 2007). African Americans and White Americans were legally licensed to be separated
in schools, and public areas, including schools. However, in Brown v. Board of Education,
Plessy v. Ferguson separate but equal was ruled unconstitutional, which led to a series of
fundamental changes throughout the US. (Reardon, 2014) The intention of this court case was to
create an education system that was equal for all students from all races. Schools in the 1950s,
13

60s and 70s started desegregating and creating unified school systems. The civil rights
movement also introduced education equity of bilingual education, and special education (Sleeter
& Grant, 1987).
Many believed that the Brown decision would narrow the achievement gap. Therefore,
school districts desegregated bussing and schools. Unfortunately, evidence suggests that the
achievement of African American students in desegregated schools was worse than their
achievement in their segregated schools (McNeal, 2009). The courts remained silent on the issue
of segregation for the first decade after the ruling; therefore, little progress was made toward
integrating schools. The courts had a limited role in the actual desegregation process. Actual
school desegregation happened after the enactment of the 1964 Civil Rights Act under the
Johnson administration by using effective enforcement tools such as denial of federal funds, and
the pursuit of lawsuits against segregated school districts (Orfield & Lee, 2007). Therefore, real
efforts toward desegregation of public schools were made between 1964 and 1988.
The genuine role of desegregation was to ensure that all children receive high-quality
education. Unfortunately, Brown’s decision seems to have made a symbolic impact on education
rather than a substantive impact (Orfield & Lee, 2005, 2007). A symbolic function means that
the goal behind passing this law was to simply reaffirm society’s values rather than acting on it
in a substantial way. Many U.S. schools failed to fully desegregate, and some schools were
quickly re-segregating (Orfield & Lee, 2005, 2007). The reality is that more than 250 school
districts still operate dual school systems, which are separate and unequal. There are also still
schools that have high-poverty, high-minority student populations who have low graduation
rates, poor teacher quality and low standard academic achievement outcomes (Berliner, 2006;
Hollins, 2006; Love & Kruger, 2005; Orfield & Lee, 2007; Yates & Collins, 2006)
14

In the 1990s, major Supreme Court cases significantly shaped resegregation by relaxing
desegregation standards. In Board of Education of Oklahoma City v. Dowell (1991), the Court
ruled that if districts act in good faith to eliminate segregation, but re-segregation is still
occurring due to private choices, then desegregated busing mandates could be eliminated. This
eliminated accountability measures on schools to fully desegregate to a large extent (McNeal,
2016). Other court cases including Freeman (1992) and Missouri (1995) also established that
when a school district has demonstrated attempts to comply with desegregation orders, then it is
lawful for the school district to end desegregation orders. (Orfield & Thronson, 1993) As a
result, the era of mandatory school desegregation ended. Lastly, in Parents Involved in
Community Schools v. Seattle School District No. 1 (2007), the Supreme Court ruled that schools
may employ race-conscious policies that do not account for student’s individual race such as site
selection of new schools, resource allocation, student and faculty recruitment, and neighborhood
demographics (McNeal, 2016).
In the 1950s and the 1960s, the civil rights movement was initiated to integrate the school
system in the US. Unfortunately, segregation continues as communities are segregated by zip
code patterns (Orfield, 2013). The quality of schooling is directly related to differences in
neighborhood income, school financial resources and quality of human capital. Nationally, as of
2016-2017, some $269 billion, or 82 percent of local revenues for public school districts were
derived from local property (NCES, 2020). In the San Antonio Independent School District v.
Rodriguez, the Supreme Court ruled that the financial resources of a school are dependent on the
community’s property values. This essentially means that there is currently housing segregation
that is taking place placing a barrier to many diverse students (Orfield, 2013).
Other Policy Efforts to Narrow Gaps
15

Since the 1960s, the federal government has enacted programs to improve the academic
achievements of students. The Elementary and Secondary Education Act of 1965 (ESEA) was
passed to expand the learning opportunity for low-income students of color. The goal of this act
was to further implement the Brown vs. Board of Education (Hewitt, 2011). Subsequently, Title I
programs were enacted where funds are provided to schools that have a high number of low-
income students. Afterwards, under ESEA, the No Child Left Behind (NCLB) act was passed to
ensure that all students meet academic standards, which are tested for on standardized
assessments (Allington, 2006, p. 3). The Common Core State Standards (CCSC, 2012) was also
introduced to ensure equity of all student curriculum across the US.
Multicultural Education
De facto segregation is still evident after the attempted integration of schools following
Brown. v. Board of Education. Segregation, marginalization, and inequity remain in our school
system (Banks, 2008). Underrepresented students, poor children and minority students’
achievement is below grade level compared to European American students (Nieto, 2004) The
study of this inequity has led researchers to investigate the phenomenon of multicultural
education. Multicultural education is transforming education from a single culture system to a
multicultural school system (Bennett, 2007). Bennett asserts that multicultural education’s
foundation is respect, appreciation and understanding of diversity. Multicultural education has
been the focus of extensive research by multiple significant researchers.
In today’s schools there has been an increased understanding of multicultural education.
Using students’ cultural experience to teach and enhance the classroom environment are
important traits of a modern effective educator. Nawang (1998) asserts that the academic
achievements of students will increase tremendously if schools and teachers are able to ensure
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that their academic instruction is responsive to students’ home culture. This type of effective
instruction is known under different terms in different research literature such as culturally
responsive (Erickson, 1997), culturally compatible (Jordan 1997), culturally relevant (Ladson-
Billings, 1990) or culturally congruent (Au & Kawakami, 1994).
Culturally Relevant Pedagogy
Culturally relevant pedagogy is the method of meeting the academic and social needs of
culturally diverse students Gay, 2000; Howard, 2001; Ladson-Billings, 1994; Shade, Kelly &
Oberg, 1997). Culturally diverse students have specific academic and social needs that need to be
addressed by teachers in the classroom to help them reach their full potential. Gay (2000) defines
culturally relevant pedagogy as the method of “using the cultural knowledge, prior experiences,
frames of reference, and performance styles of ethnically diverse students to make learning more
relevant to and effective for them; it teaches to and through strengths of these students” (pp. 28-
29). In other words, using the students’ cultural strengths enhances students’ learning experience.
When lessons are relevant and connect to the students’ cultural background, learning becomes
powerful enough to help students reach their full learning potential. Gay adds on the definition of
culturally relevant pedagogy by describing it as “culturally validating, comprehensive,
multidimensional, empowering, transformative and emancipatory” (p. 29). When students are
learning through their cultural knowledge and are connecting to their lessons on a personal and
cultural level, this is liberating to them as they do not have to divorce their culture and home life
when they step into school campus. Validating and affirming students’ culture, learning styles
and funds of knowledge is transformative to the student’s academic, cognitive, and social
development.
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In the classroom, the phenomenon of teaching by implementing culturally relevant
pedagogy has been characterized by Gay (2000) as culturally responsive teaching, which is
specifically about the acknowledgement that the authenticity of student cultures as students
approaches to learning will be different. Culturally responsive teaching is described in research
as having specific characteristics such as supporting a relationship between home and school as
well as strengthening the relationship between academia and sociocultural awareness. The third
characteristic of culturally responsive teaching is the usage of numerous instructional strategies
to appeal to different learning styles. Fourth, students should be trained to be aware of and praise
their cultural background and each other’s cultural heritage. Fifth characteristic is that
multicultural resources and materials should be incorporated across subjects and content areas
that are routinely taught in schools (p. 29).
Culturally relevant pedagogy and culturally responsive teaching connect to the pedagogy
of multicultural education, which is centered around promoting equity for students. (Banks,
2008; Bennet, 2007, Ladson-Billings, 1995, and Nieto, 2004) Other authors have used similar
terms to describe the same phenomenon including culturally appropriate pedagogy (West-
Olatunji, Behar-Horenstien, Rant, & Cohen-Phillips, 2008), culturally responsive teaching (Gay,
2013), culturally sustaining pedagogy (Paris & Alim, 2014) and cultural competence (Colombo,
2007). Throughout existing literature, it is observed that different authors use different terms to
describe similar phenomena. The existence of multiple terms used can sometimes cause
confusion; therefore, a consistent term to describe the pedagogy used to establish equity in the
learning environment is crucial. Some consistent terms that will be used throughout this paper
include cultural competence, culturally relevant pedagogy, and culturally responsive teaching, all
of which have been defined above.
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Teacher-Student Relationship
Effective instruction starts in the classroom environment, and it involves a defined
design, lesson delivery and dedication to the curriculum along with evaluation and assessment of
student learning, which can help guide future instruction. The heart of instruction lies in the
relationship the teacher creates with the students. This relationship should involve trust, respect,
care, and cultural appreciation to help the students feel safe and welcome in their learning
environment. Establishing this relationship with the students is as effective as lesson delivery,
curriculum standards and assessments. This literature review is focused on deep research that
investigates how the interaction between students and teachers has impacted student
achievement.
In the twenty-first century, some of the major policy efforts to drive instruction include
common core standards, standardized tests, and accountability policies. Teachers often use core
standards, assessment, evaluation, and district curriculum as the blueprint for instruction (CCSC,
2012). Unfortunately, the social student-teacher relationship is a factor that is neglected by many
educators in many schools (CCSC, 2012). A strong teacher-student relationship creates a rapport
with students, which allows the teacher to nourish trust in the relationship with students, hold
high academic expectations, promote better student behavior, motivation, and dedication.
The urgency to establish an effective teacher-student bond is well documented in research
(CCSC, 2012). Positive rapport allows students to feel cared for and loved. Students often look
up to their teachers as role models in their attitude; therefore, teachers should consistently
demonstrate a positive attitude, and high academic expectations that the students can attain
according to their grade level. Students’ perspective on their relationship with their teachers has
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a direct effect on student engagement in class, achievement on assessments and expectations of
themselves (Davila, 2003).
Research reflects the contextual meaning of an effective teacher-student relationship.
Riddle (as cited in Gonzales, 2016) asserts that there are four components at the heart of a good
relationship between students and teachers. These four components include discipline, respect,
communication, and trust. Teacher-child relationships are crucial for the cognitive and social-
emotional development of students, which are just as essential as academic learning. If the
children’s developmental needs are not met at a young age in their classroom, they do not value
academic work and their motivation to perform well in school diminishes (Deci, Vallerand,
Pelletier, & Ryan, 1991). Children greatly benefit from a positive rapport with the teachers.
Students must feel that they are cared for by their teachers and that their teachers want them to
succeed.
As children develop into independent individuals, their sense of interest in learning the
value of education needs to develop as well. Children need to develop confidence in their own
abilities, which is described under the self-determination theory (Deci et al., 1991). The self-
determination theory suggests that when students’ psychological needs are met as far as feeling
competent, and establishing a connection to the teacher, then they are more likely to seek new
challenges. A positive connection with adults by constructing authentic social interactions builds
an intrinsic strength in the students, which is an integral component of success. The quality of
these social interactions directly influences the students’ motivation and engagement level,
which shapes a student's academic success (Patrick et al., 2008).
This connection has been the focus of a great deal of research. Henderson & Milstein
(2003) even asserted that a healthy social bonding and constructive interactions with others
20

boosts the level of positive relationships between students, peers, and other surrounding adults.
These social skills act like building blocks for students' overall social schema, which nurtures
their path toward a healthy academic career. When students build their social schema, they are
developing the foundation of their social and emotional health, which directly determines their
ability to succeed academically (Pianta & Stuhlman, 2004).
Culturally Responsive Teachers
Culturally responsive teachers should have a “high degree of sociocultural consciousness,
holding affirming views of students of diverse backgrounds, see themselves as agents of change,
understand and embrace constructivist views of learning and teaching and know the students in
their classes” (p. 28). For example, Ladson-Billings (2006) observes that teachers who are
successful with African American students are mostly knowledgeable of the African American
culture and role in society and how that shapes the reactions and expectations of students.
Students who experience behavior problems in their early years but have teachers who
are sensitive to their needs and provide them positive feedback have less of a possibility of
having problems later in their school career (Hamre & Pianta, 2001). This calls for a sensitive
teaching practice. Jacobson (2000) asserts that an insensitive teaching practice can decrease the
motivation of students, which hurts students especially when they are already academically low.
Jacobson suggests that some comments such as “We will do the best we can for these people, but
we don’t expect them to go very far,” and “We all know what those developmental students are
like – they are just a joke in the English department” place students under lower expectations and
labels these students as low achieving “losers” before serious efforts are exerted to explore and
reach their potential for development and academic success. This is where culturally responsive
teachers are needed to “employ differentiated instruction and integrate various learning materials
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which help to make learning more relevant, thereby increasing student success” for all students
(Irvine & Armento, 2001, p. 4).
Teacher-student rapport is one of the major keystones that contributes to the success of
students. The teacher should acknowledge and provide positive feedback to the student and also
positively affects the teacher-student relationship and enhances the learning experience. The
importance of genuine relationships between students and teachers is demonstrated by the self-
determination theory (Patrick et al., YEAR as cited in Patrick, 2008). Self-determination theory
states that positive relationships with the teacher are a major foundation for student motivation.
This positive relationship comes from the teacher’s influence on the students in the classroom
and from the collective learning atmosphere.
To create a positive learning atmosphere, culturally responsive teachers should clearly
teach, model, and reinforce appropriate social behaviors for the student with one another and
with teachers. When teachers are constantly modeling and explicitly teaching appropriate
behaviors, the students feel the consistency and stability of their learning environment, which
boosts the quality of the teacher-student relationship (Murray, 2002).
Villegas and Lucas (2002) discuss culturally responsive teaching and they mention that it
is not an easy task “it is not simply a matter of applying instructional techniques, nor is it
primarily a matter of tailoring instruction to incorporate assumed traits or customs of particular
cultural groups …culturally responsive teachers have a high degree of sociocultural
consciousness, holding affirming views of students of diverse backgrounds, see themselves as
agents of change, understand and embrace constructivist views of learning and teaching, and
know the students in their classes. It is the combination of all these dispositions, knowledge, and
skills that enables them to design instruction that facilitates student learning. (p. 27).
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Teachers’ Role in Culturally Relevant Curriculum
Gay (2002) asserts that culturally diverse students have been ‘divorcing’ their cultures
and learning in school according to the cultural norms of European American standards. This
adds a burden on the students to function under cultural conditions that are not natural to them. A
teacher may not even be aware or reflective of the differences in power or the White cultural
dominance that is occurring in the classroom, leading to the egalitarian ideal of meritocracy.
Many teachers were raised to believe that schools should only equalize students based on talent,
effort, and hard work (Sleeter, 2008). Sleeter (2008) mentions that many White teachers are
fearful and resistant of change to their beliefs. It has been believed by many
White teachers that programs that are designed to “remedy racial discrimination” are themselves
discriminatory against Whites (p. 95). However, if this is the core belief of educators, what
would explain the “school failure of students of color?” (Howard, 2010, p. 99). Howard (2010)
asserts that educators need to realize that it is not a coincidence that students of color are failing
in schools at high rates. Howard (2010) and Nieto and Bode (2011) mention that less than 50%
of Black male students graduate high school, while Latino and Black male students are the
majority of individuals who end up incarcerated. This has drawn scholars to “investigate the
prevalence of a school-to-prison pipeline in the name of zero-tolerance policies” (Howard, 2010,
p. 149). Villegas and Lucas (2002) stress the importance of encouraging and supporting a
culturally diverse learning environment. Teachers’ attitudes in the classroom significantly mold
the expectations they have for their students, how they treat their students and how students learn
(p. 37). Educators may perceive, by default, the underachievement of underrepresented students
because of their race, disability, or socioeconomic status. This negative expectancy also
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undermines student performance (Achinstein et al., 2012; Bell, 2003; P.L. Carter, 2003; Gay,
2013; Goldenberg, 2014).
Nieto (2012) explains that 85-90% of American teachers are White and only speak one
language. She asserts that immigrant students who speak multiple languages and are encouraged
by their learning environment to hold on to their ethnic identity at school have a healthier mental
health and higher academic records. Moreover, Villegas and Lucas (2002) urge schools of
education to educate prospective teachers on the operation of racism in schools and society to
enable them to be aware and conscious of the learning environment they create. Teachers who
have gained an awareness and appreciation of cultural diversity are able to activate students’
prior knowledge and experience to set up a platform for learning (Dewey, 1938; Gay, 2013).
These educators would be able to build a cultural capital in their underrepresented students by
giving them special attention, holding them to high expectations, and bridging the barriers that
they may face (Goldenberg, 2014). They will not view underrepresented students as inferior to
other students or that they do not have the appropriate toolbox to gain and navigate knowledge
(Bigelow, n.d.) This type of learning community was implemented and compared to a normal
learning environment where teachers did not give much attention to the diverse needs of their
students and were not able to build strong relationships with their students (Darling-Hammond et
al., 2002; Legster et al., 2013). Peasant reports that the mean scores on the state Biology I test for
Black students within these learning communities were greater than the mean scores in
traditional learning environments (2006). The state traditional dropout rate was 12.5% compared
to 6.6% for the implemented learning community (Cook et al., 2008).
McAllister and Irvine (2002) studied teachers who received multicultural training on
culturally responsive teaching in the classroom. The study was on fifty-one teachers and
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demonstrated that teachers who have undergone training in culturally responsive techniques with
students from diverse populations were able to create a supportive and more supportive student-
centered learning environment (McAllister & Irvine, 2002). The program started with teacher
self-reflection about their own positionality and cultural identities. The second phase was a
simulation in which teachers were in a simulation to experience a new culture as an outsider. The
third phase was for teachers to be trained on knowledge they need to know to implement a
culturally responsive classroom (McAllister & Irvine, 2002). As a part of the training, teachers
were taught characteristics that teachers need to have to create a culturally responsive classroom
such as sensitivity, patience, tolerance, acceptance, understanding and openness (McAllister &
Irvine, 2002)
Gaps in Mathematics Achievement
According to the U.S. Department of Education, the achievement gap is the difference in
academic performance between students from different ethnic groups. This gap is the significant
difference between students of color and White students in standardized-test scores, grades,
course choices, college graduation and drop-out rate.
Before children become of school age, developmental aspects of children reflect
deficiencies in language, social skills, personal and mathematical thinking skills (Hassan &
Mahmoud, 2011). The achievement gap is highly determined by the degree to which the learning
community including students, teachers, and parents and the community believe it is important
and should be addressed (Hassan & Mahmoud, 2011).
There are multiple causes for the achievement gap, which are quite complex. According
to researchers, the causes fall under four main categories related to socioeconomic status,
cultural environment, family background and the students’ schools (Barton, 2003; Bennett et al.,
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2004; Campbell & Levin, 2009; Carey, 2002; Duncan, Featherman, & Duncan, 1972; Evans,
2004; Fan & Chen, 1998; Griffith, 1996; Lee & Bowen, 2006; Smith, 2006). Among numerous
studies, 9% of research asserted that teacher education is the one of the most important
classroom resources, while 14% asserted that student-teacher ratio is an important factor for
student achievement. Among the rest of the research studies, it is argued that teacher quality is a
key factor in promoting student achievement in the US (Harris & Sass, 2009).
The specific reason behind the achievement gap in mathematics is not known. Empirical
research suggests that mathematics instruction that fits the instructional guidance set by the
National Council Teachers of Mathematics is not available for many minority students (Johnson
& Kritsonis, 2006). However, the reason seems to be a complex relationship between teacher
quality, socioeconomic status, student demographics, and school characteristics.
High quality mathematics education is a requirement for many colleges and
postsecondary education programs (Achieve, 2005; ACT, 2006; National Science Board, 2008;
Achieve, 2005). Many students are not receiving a quality mathematics education and are subject
to low expectations for mathematics achievement. They are often not exposed to higher level
mathematics and tasks that require high cognitive demand (Boaler, Wiliam, & Brown, 2000;
Schmidt, Cogan, Houang, & McKnight, 2011; Stiff, Johnson, & Akos, 2011; Tate & Rousseau,
2002).
Mathematics education can highly benefit from culturally relevant pedagogy. By
applying these frameworks, students can realize that there are multiple important purposes for
learning mathematics, that math is important for daily life and that they can succeed in math.
Students need to develop their self-efficacy in performing mathematical operations and they need
to experience math as a problem-solving technique that can be used to understand the world
26

around them (Thomas & Berry, 2019). Incorporating culturally responsive pedagogy into math
lessons could take the form of allowing students to solve mathematical problems that relate to
their lives and communities (Ensign, 2003; Razfar, 2012). Students may also participate in real-
life application of math in construction work (Civil, 2002). Students can use mathematical
operations to analyze inequalities today such as racial profiling during traffic stops (Gutstein,
2003). By applying mathematics to real life scenarios as the ones mentioned, students can
socially use mathematical skills to change the world around them.
Connecting Culturally Relevant Education to Student Outcomes
Sleeter (2012) asserted that it is crucial to find evidence that connects a culturally
relevant education to student outcomes. Student outcomes should not only include standardized
test scores, but rather, overall student achievement. The outcomes for policy makers may solely
be test scores; however, for educators, it could mean life skills that students acquire. While the
focus on preparing students for a test or teaching to the test might yield higher test scores; this
does not prepare them for life-long independent learning (Amrein & Berliner, 2002).
While research exists that uses higher test scores as student outcome, there are other
research studies that include other domains, which include student motivation (Civil & Khan,
2001), higher interest in content (Choi, 2013), higher student ability in content area (Civil &
Khan, 2001), higher levels of student self-efficacy (Robbins, 2001) and boost of confidence
(Hubert, 2013).
Civil and Khan (2001) used a gardening project to help students connect math to their
previous experiences and home knowledge. Civil and Khan (2001) asserted that culturally
relevant instruction is the type of instruction that bridges between home and school by building
upon students’ home experiences. They define culturally relevant instruction as one that “links
27

home and school by building on experiences shared by most students in the class” (p. 400). Civil
and Khan used a qualitative study in an Arizona school district whose demographics was majorly
low income, Latino, and ELLs to incorporate a culturally responsive instruction with
mathematical concepts of area and perimeter. Teachers used the theme of a garden, which the
students were familiar with due to their work with their parents in the gardens. The class
consisted of 38 fourth and fifth graders. The garden theme was used to connect their background
knowledge about gardening to incorporate perimeter and area. Students and parents planted
seeds in pots and soil. The students kept a five-month log of observations and growth
measurements. The students took proper care of their plants, and shared material from home with
their classmates. As the students worked on growing their gardens, they were also able to
increase their knowledge about mathematical concepts. The students learned about keeping logs,
and drawing observations, which were major parts of the assignment as well.
Civil and Khan asserted that relevant instruction occurred by having students incorporate
their home experience into their math class. Through this lesson framework, students were able
to relate the mathematical concepts to their home experiences. It also increases student
motivation and academic engagement. It is suggested by Newman (1981) that academic
engagement is an integral role to keep student engagement. When students feel disengaged to
their learning, they stop caring about their academics, termed as disidentification (Aronson,
2002). As time progresses, students lose faith in the education system and develop the
“perception that they do not have the same chances at success as White students” (Smith, 2011,
p. 76).
Walker (2009) studied the full impact of culturally relevant teaching practice in a
mathematics class during a six-week enrichment program that has 55 third to fifth grade students
28

across Memphis, Tennessee that are labeled as “at-risk” due to low mathematics performance on
state-wide assessment. Ninety three percent of the students were African American and 7% were
Hispanic. Walker (2009) assigned participants randomly into either experimental group in
ethnocentric pedagogy or control group with traditional pedagogy. Ethnocentric group was
exposed to a culturally relevant classroom by using mathematics in daily lives and they discussed
the beginnings of math in African American and indigenous Hispanic cultures where they also
learned about the accomplishments of famous Hispanics and African Americans in mathematics.
They also used hands-on math skills, life skill training, games, and online tutorial. Class
assignments and homework were designed to fit their interests. On the other hand, the traditional
group received individualized learning and their motivation was basically driven by competition.
The class discussed famous European mathematicians and homework and assignments followed
traditional methods to reinforce mathematical concepts. Students were allowed to celebrate their
achievement and work independently (Walker, 2009).
At the end of the activity, students took an assessment online called ALKS (Assessment
Learning in Knowledge Spaces) to assess their knowledge and identify what they still need to
learn (Johnson, 2006). Results confirmed that students who participated in the experiment as part
of the ethnocentric group returned their homework at higher rates compared to their counterparts.
These results conclude that there is a significant difference in students’ behavioral engagement
with the curriculum because of the inclusion of culturally relevant materials.
The Importance of Curriculum Materials
Research suggests that curriculum shapes teachers’ instruction (Holland & Mongillo,
2016; Parsons et al., 2011; Siuty, Leko et al., 2016; Stodolsky, 1999; Valencia et. al., 2006;
Woodward et. al., 2017). Susan Stodolsky (1999) asserts that teachers teach a curriculum based
29

on their own perspectives and materials they use, the school they teach in, the students in their
class, subject matter, and grade level.
Valencia, Place, Martin, and Grossman (2006) conducted a study to learn how teachers
understood and used curriculum materials for reading. The four teachers in the study worked by
reading scripted reading programs and using supplemental materials without teaching guides.
The two teachers with more restrictive materials and weak content knowledge were less able to
shape instruction to meet their students’ needs. The two teachers that had stronger content
knowledge, access to multiple materials and support were able to adapt instruction most
effectively to fit the needs of their students (Grossman et al., 2006). The study concludes that
curriculum materials are highly significant to teaching practices and student learning.
Engaging students in solving meaningful real-life problems will allow them to engage in
higher level thinking, which will increase their motivation to learn and solve issues in their daily
lives. Teachers must also create opportunities for students to challenge injustice or inequality in
their lives or communities (Ladson-Billings, 2001). Therefore, teachers may gather and critique
additional sources to supplement textbook curriculum so the lessons they deliver to students
would better reflect their students’ cultural and linguistic backgrounds. This approach challenges
de facto community inequities and divides and steers the students towards making a meaningful
change. For example, Tate (1995) mentions that one teacher engaged her students in
investigation zoning laws using math and reading skills to reduce the number of alcohol stores
along with associated problems including drug trafficking, prostitution, and public intoxication
around school site. As a result, the students lobbied their state senate and made a presentation to
the city council, resulting in multiple citations being issued to liquor stores and the closure of
two liquor stores near the school site (Tate, 1995).
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Unfortunately, many students of color receive an easy version of the curriculum due to
the low expectations that are usually set for them (Ladson-Billings, 2006; Milner, 2009; Murrell,
2007). Students from diverse cultural, racial, and ethnic backgrounds are not usually represented
in the curriculum, materials, and assessments in public education school settings. Instead, the
values and beliefs in literature are mostly dominated by Eurocentric perspective, which is
centered around White, middle-class individuals and completely discounts the culture of diverse
students.
Billings (2016) describes the current curriculum as a White supremacist master script
meant to keep racism in the classroom. Watkins (2001) supports this by stating that the current
education system has been designed to prepare ‘former slaves’ to become a part of society within
limited roles that resemble slavery; however, without being physically bonded by engraining
Black inferiority and White superiority into the social setting. For example, in Teaching for
Black Lives (2018), slavery, the Civil Rights Movement and reconstruction has been narrated in a
way to glorify White contribution to society while minimalizing the role African American had
to liberate themselves. Gay (2002) also mentions that the formal curriculum tends to avoid
topics such as racism, hegemony and historical atrocities that may be controversial to students,
which entice students to think, criticize and challenge the status quo on racism.
Ladson-Billings (2009) says that “the negative effects [of the dominant culture] are
brought about, for example, by not seeing one’s history, culture or background represented in the
textbook or curriculum” (p. 17). Milner (2011) also adds that
This idea of seeing oneself in the curriculum and through instruction helps students
understand the important way in which their culture has contributed to various genres of
curriculum content and to the fabric of U.S. society (p. 69).
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In other words, the solution to end the White supremacist curriculum is for students to read about
their own culture and the perspectives that come with their own cultural background. This proves
the importance of multiculturalism, which is crucial for students to think critically as they are
exposed to texts of different cultures that represent different perspectives.
Therefore, teachers are encouraged to integrate research-developed and selected materials
that incorporate students’ cultural, linguistic, and racial background by supplementing as
necessary to provide these resources to the students (Banks, 2004; Gay, 2010, 2013; Ladson-
Billings, 2009). Supplementary materials mostly come from online resources to offer “a bridge
between state academic standards and the enacted curriculum students experience in the
classroom” (Polikoff & Dean, 2019).
Learning that is based on meeting standards is based on the understanding of the
relationships between and among mathematical concepts, principles, and the procedures of
performing mathematical operations (Hibert & Wearne, 1993). As students learn mathematics,
they should be focusing on improving their ability to generalize, justify, communicate, and apply
what they are learning about mathematics (Schoenfeld, 1992).
Supplemental Curriculum
Education surveys show that about two-thirds of teachers supplement their curriculum for
so many reasons such as to save time to prepare materials or two employ different activities into
their instruction (Polikoff & Silver, 2021). Supplementation of curriculum is defined by the
Teacher Curriculum Supplemental Framework (TCSF) as an intentional change made by the
teacher to curriculum materials, which is often meant to help students learn the curriculum or to
save time and add different activities to the lesson (Polikoff & Silver, 2021). While teachers use
supplementary materials to help their students, supplemental materials need to be carefully
32

chosen by teachers. Unfortunately, research along with my experience as an educator shows that
teachers have little to no support in growing their skills around choosing high quality
supplemental materials. Therefore, teachers need to be provided guidelines and rubrics during
professional development opportunities to choose the appropriate supplemental curriculum for
their students.
Teachers Pay Teachers
Intensive and informative research is not yet available on the overall quality of online
math supplemental materials. The most relevant literature found was on the evaluation of cultural
relevance of online English Language Arts supplemental material by Polikoff and Dean (2019).
Recently, there has been an explosion of online sources for instructional materials that are
teacher-produced such as Teachers Pay Teachers. This is the focus of my dissertation. More
specifically, I analyzed supplemental materials on the website Teachers Pay Teachers.
Teachers Pay Teachers is a website where teachers can create and upload supplementary
material, which other educators can use for free or after paying a small price. About 55 percent
of teachers in 2018 used supplementary materials from Teachers Pay Teachers at least once a
week (Kaufman, et al., n.d.) Teachers Pay Teachers attracts teachers because it is created by
other teachers and are reviewed by teachers with supporting comments. There is not a single
criterion that guarantees the usefulness and effectiveness of supplemental curriculum Therefore,
in my dissertation, I develop specific criteria to analyze the relevance and rigor of the
supplementary math material on Teachers Pay Teachers.
Polikoff and Dean (2019) studied the effectiveness of supplemental curriculum. They
evaluated the content of supplemental curriculum by examining 328 materials for cultural
diversity by including multiple authors from diverse backgrounds or topics that are from diverse
33

cultural backgrounds. The curriculum is observed for support provided for diverse learners, high
or low-performing students, students with disabilities and English language learners (Polikoff &
Dean, 2019).
Teachers Pay Teachers material is investigated by Polikoff and Dean (2019) on potential
to keep students interested and that the material represents “diverse authors or even texts about
culturally diverse topics.” Only 53% of materials on Teachers Pay Teachers were rated as
materials with adequate interest or engagement, while about two-thirds of materials were voted
as ones that “do not include diverse authors or cover culturally diverse topics” (Polikoff & Dean,
2019, p. 17).
Conceptual Framework
A major foundation of developing the conceptual framework of Culturally Responsive
Teaching is the critical analysis of race and racism that was described by Ladson-Billings. She
states that:
The history of the U.S. has informed us that race is very central to how people perceive
and relate to the world. While CRT provides a framework and for some a tool of analysis
for examining educational practices and structures that continue to subordinate groups of
people, culturally relevant pedagogy offers a model of theory to practice and examples of
how such instruction can be delivered. When CRT is related to CRP, the centrality of race
to American culture is acknowledged (p. 71).
The first pillar of culturally responsive teaching is Racial Identity Theory in the
conceptual framework. Racial Identity Theory entails that race, perceived racial beliefs and racial
attitudes mold an individual’s relationships, interactions, actions, choices, and thoughts (Helms,
1990). Being aware of one’s self-identity, others’ identities, and the dynamic nature of socio-
34

cultural power in society is a process that develops over time. Culturally responsive teaching
implements the racial identity theory with the way a teacher reacts to his or her students on a
pedagogical level. Implementing culturally responsive teaching in the classroom calls on
teachers to have sufficient awareness of their own positionality and racial identity. This
awareness and understanding will enable educators to implement culturally responsive pedagogy
in the classroom based on their perception of racial differences, similarities, and their
significance to society.
The pillar of Racial Identity Theory considers the identity of the students and the teachers
as well (Brown-Jeffy & Cooper, 2011). The teacher’s responsibility entails a realization of the
cultural construct of her or his classroom and that students’ perceptions of themselves and the
world around them will be different (Brown-Jeffy & Cooper, 2011). Gay (2002) urges teachers
to educate themselves on culture preferences of different ethnic groups (p. 107). Nieto (1999)
further supports this in urging teachers to be aware of their own positionality and identity by
“reconnecting with their own background, and with the sufferings as well as the triumphs of their
own families, teachers can lay the groundwork for students to reclaim their histories and voices”
(Nieto, 1999, p.3; as cited in Brown-Jeffy & Cooper, 2011). Cultural awareness does not mean
colorblindness or being race-neutral (Brown-Jeffy & Cooper, 2011). Brown Jeffy and Cooper
(2011) mention that when teachers are aware of the nature of the system as being ‘racist’ they
can help eliminate social actions that reproduce more racism, and they can reevaluate the system,
recognize racist actions in it or change them if possible, and affirm, appreciate, and value all
cultures around them (p. 73).
The next pillar is equal access to a rigorous and relevant curriculum. Being color blind and
avoiding sensitive racial topics in the classroom “is not an equitable approach to teaching and
35

learning” (Brown-Jeffy & Cooper, 2011, p. 74). Incorporating multicultural content into the
curriculum and instruction is crucial because students may not always see themselves in the
traditional curriculum presented in schools and do not feel a connection to it (Brown-Jeffy &
Cooper, 2011; Gay, 2001).
Critical race theory suggests that “equity and excellence clearly focus on realizing that
race is a significant factory in inequality” (Brown-Jeffy & Cooper, 2011, p. 75). This is mainly
due to the storytelling and narrative technique in mainstream narratives in today’s curriculum.
Cultural inclusions should not only be implemented during a specific time of the year, such as
Black History Month; however, this should be a practice interwoven into the curriculum
throughout “the entire academic process” (p. 75). This practice acknowledges that equity and
academic excellence should include all students including students of color.
Not only should students of color be included in academic excellence and equity;
however, their knowledge and culture that they bring into the school with them should be utilized
and acknowledged (Brown-Jeffy & Cooper, 2011). In addition to using students’ funds of
knowledge, teachers should also acknowledge the knowledge the student knows and where they
need to be with “innovative teaching methods and assessments” (p. 76). Brown-Jeffy and Cooper
(2011) mention that:
Critical race theory forces teachers to critique liberalism and challenge the dominant
ideology. This includes the development and use of diverse assessment opportunities
which begins with high standards and expectations for all. CRP teachers have to advocate
for and perform a paradigm shift in assessment (p. 76).
36

In other words, the curriculum should be implemented by the teacher to meet the needs of
students cognitively, socially, emotionally, psychologically, and academically as they engage in
the learning process.
The third pillar of culturally responsive teaching is student-teacher relationships. Students
and teacher relationships are critical in promoting student achievement and maintaining a
culturally relevant learning environment. Students need to know and feel that their teachers care
about them and their success (Brown-Jeffy & Cooper, 2011). They also need to feel respected by
their teachers for who they are and as members of a particular cultural group (p.77). Noddings
(1998, 2013) explains that if students feel a certain way about the teachers, the perception
becomes a reality. When students feel disliked by the teacher, it becomes a reality in the mind of
the student. Therefore, culturally responsive teachers should value their students’ culture, lived
experiences and perspectives and they should also be aware of elements of social racism that
continues to divide students in the classroom and the effect on this on student perspective and
view of the world (Brown-Jeffy & Cooper, 2011, p. 79). However, at the same time, this should
not cause the teacher to lower the academic standards and expectations of her or his students. On
the contrary, teachers are still urged to maintain high expectations of all students regardless of
any other factors.
Another component of the student-teacher relationship is that educators should show care
to their students. A form of care according to Valenzuela (1999) is for a teacher to adhere to high
expectations of students, clearly define objectives, learning goals and academic state standards.
Noddings (1992) defines care by saying that there are two stages of care, caring for and caring
about someone. Caring for someone is physical; while caring about someone is emotional where
37

the other individual can “see it, feel it and experience it” (Noddings, 1992). Teachers must
combine types of care when they deal with students.
The fourth pillar is the presence of an effective learning environment. A learning
environment includes the physical surroundings, psychological or emotional conditions and
social or cultural influences affect the growth or development of the students. An effective
learning environment starts with the classroom environment, which is composed of the
arrangement of the room, the student diversity, the posters on the wall, daily routines, academic
language rich environment and clear academic goals.
As children spend most of their day in a classroom, there are four considerable factors
that are key to an effective environment for students, especially Els and culturally diverse
students (De Bruin-Parecki, 2008; Greenberg & Rodriguez, 2007). First, the classroom
environment must be engaging to the students while providing them with ample opportunities to
learn and interact with other students in a way that reflects the students’ diversity, culture, and
needs. A second factor is to value and accept the diversity of students. A third factor is a daily
consistent routine for activities throughout the day. The last factor is creating a classroom
environment that is culturally and linguistically rich.
The arrangement of the classroom should be appealing to promote learning and effective
interactions between children and adults (DeBruin-Parecki, 2008; Feeney, Christensen &
Moravcik, 2006; Greenberg & Rodriguez, 2007; Wellhousen & Crowther, 2004). The classroom
environment must be set up in a fashion that allows learning while interacting with peers, little to
no distractions, and a set schedule for students’ opportunities to play (Greenberg & Rodriguez).
Materials including textbooks, toys, and learning tools should be accessible to all students
regardless of language, dialects, and disability. Books should reflect various cultures and
38

backgrounds, and the environment should reflect posters of people from different cultures and
backgrounds and learning areas should reflect the true diversity of the children in the classroom.
Expression of value and acceptance toward students helps students feel motivated and
involved in classroom activities (Gersten & Jimenez, 1998). Students’ work may be displayed
around the classroom to reflect the teachers’ value of the students and their work. Gersten and
Jimenez suggest that the classroom environment reflects an understanding of the cultural
backgrounds and makeup of the children by having books in multiple languages about popular
events and figures in various cultures and locations all over the world.
Pedro Noguera (2003) argues that “high performing students of color are more likely to
be successful if they attend schools that support and affirm their racial and cultural identities”
(Noguera, 2003, p. 57). Students need to be in a learning environment where educators are
setting high expectations of them, challenging them academically, modeling, scaffolding,
clarifying, using their strengths as instructional foundation, investing into their students’ progress
and being accountable for their progress, creating a nurturing, safe environment and maintaining
high behavioral expectations (Morrison et al., 2008). Culturally responsive educators should also
implement a multicultural curriculum by reshaping the prescribed curriculum, building on
students’ funds of knowledge, and bridging between school and home (Morrison et al., 2008).
Creating a warm and safe environment is crucial for students of diverse backgrounds
especially when instruction is monolingual. As a former EL student, I know that ELLs have
diverse English accents, cultural and educational backgrounds. English classes set an ideal where
an American accent, and American culture should be the norm without connecting to the culture
of ELLs (Ionescu, 2014). Furthermore, students start to perceive “native English speakers [are]
seen as the only appropriate conveyors” of the American cultural values (Auerbah, 1993, p. 26).
39

This monolingual teaching technique does not complement the multicultural learning
environment outlined by culturally responsive teaching.
This lack of connection with students’ diverse background, prior academic and social
experience makes it difficult for ELs to learn English and to adapt to the American education
system. In addition to that, EL students will also feel stereotyped and judged negatively because
of their native background, culture, language, accent, or dialect. This can be emotionally and
mentally damaging to students. Delpit (1995) affirms this by saying that:
First, they [teachers] should recognize that the linguistic form a student brings to school
is intimately connected with loved ones, community, and personal identity. To suggest
that something is ‘wrong’ or even worse, ignorant, is to suggest that something is wrong
with the student and his or her family. On the other hand, it is equally important to
understand that students who do not have access to the politically popular dialect form in
this country, that is Standard English, are less likely to succeed economically than their
peers who do (p. 53).
In other words, students will start to feel inferior to their peers due to their culture or
accent, which is going to negatively affect them as they develop. Studies show that students who
feel proud of their home language, and safe in their classroom environment feel the freedom to
learn, practice and apply new language skills in the classroom environment (Artiles et al., 2004;
Au, 1993; Banks, 1979, 1997a, 1997b, 2002; Delpit, 1992, 1995; Garcia, 2004; Gay, 1995; Grant
& Tate, 1995; Hernandez, 1989; Ladson-Billings, 1994, 2004; Nieto, 1996, 1999; Padrón et al.,
2002; Sleeter & Grant, 1987; Smith-Maddox, 1998). Language is not just words and accents.
Language is the culture, behavior, social interaction, and perceptions about the world.
Mainstream confusion about other cultures, languages and dialects are remedied when they are
40

exposed to others who speak other languages or dialects (Artiles et al., 2004; Au, 1993; Banks &
Banks, 2004; Delpit, 1992, 2006; Garcia, 2004; Gay, 1995; Majors, 1998; Nieto, 2004; Padrón et
al., 2002; Suarez-Orozco & Suarez-Orozco, 2001; Tatum, 1997; Wills et al., 2004). This is the
core of multicultural education and the goal behind implementing it in the classroom
consistently.
There are many effective strategies discussed in literature that support a culturally
responsive learning environment especially for EL students. Restrepo and Gray (2007) suggest
that providing opportunities for students who speak the same first language to interact with one
another is one effective way to express value for the student’s first language, which will convey
acceptance and value of the student’s home language and culture. Another method to provide a
culturally responsive learning environment is to establish a routine that permits EL students to
blend in with the classroom schedule and environment without feeling alienated or having to
directly interact with teachers and peers (Tabors, 2008). This will also allow students to focus
majorly on the language being used in the classroom rather than trying to figure out what is
happening around them (De Alites & Allexsaht-Snider, 2002). Overall, teachers and adults
should be role models to acceptance, and respect for diversity, multiculturalism, and differences
in the classroom. The goal is for EL children to reach their full potential by strengthening their
language skills. Ludwig Wittenstein says, “The limits of my language mean the limits of my
world” (as cited by Wardhough, 2006, p. 219).
Maslow’s theory (1943) mentions that all human basic needs must be met before they are
able to achieve advanced goals. According to hierarchy of needs, Maslow argued that an
individual must feel love and belongingness before they can progress onto mastery and
achievement levels. School belonging is a psychological framework that is highlighted by
41

“valuing, connection, and caring” (Goodenow, 1993; Osterman, 2000). The outcome of this
conceptual framework is that students become independent, critical individuals who can
contribute positively to society. Banks (1997a) states that “an important goal of the schools in a
democratic society is to help students acquire the knowledge, values, and skills needed to
participate effectively in public communities (p.1).” Therefore, carefully structured scaffolding is
crucial for students from diverse cultural and linguistic backgrounds where high academic and
behavioral expectations must be set and maintained regardless of culture, language, race, gender,
dialect, accent, religion, social status, sexual orientation, economic level, physical ability, mental
ability, or any other classification that may be used in society to place students in different
hierarchal positions. Banks (1997a) advocates in Educating Citizens in a Multicultural Society
that students who are in classrooms now will grow up to become citizens. It is also through
“transforming and restructuring institutions and institutionalizing new goals and ideals within
them” (p. 11) can educators teach students from diverse backgrounds the skills they need to
participate in society as responsible and contributory individuals.
Critically responsive teaching is targeted for the students to develop their critical
consciousness, which is critical for building the minds of active citizens of the future who will
challenge the existing status quo and social inequities. Banks (2006) states that:
It is not sufficient to help students learn to read, write, and compute within the dominant
canon without learning also to question its assumptions, paradigms, and hegemonic
characteristics. Helping students become reflective and active citizens of a democratic
society is at the essence of our conception of equity pedagogy…An education for equity
enables students not only to acquire basic skills but to use those skills to become effective
agents for social change (p. 152).
42

Education is meant to cultivate physically, psychologically, and cognitively healthy citizens who
are highly trained and educated and care about society and the world around them while being
aware of their own values and of the impact they can make in society. Therefore, as educators,
we need to ensure that the supplemental curriculum being used in the classroom is powerful
enough to educate students and to prepare them to challenge the current status quo in society.
This is the heart of my document analysis. I hope that I can use this document analysis to inform
educators and policy makers of a thorough technique to identify and analyze the degree of
cultural relevance of current day mathematics supplemental curriculum. Mathematics
supplemental curriculum needs to hit home for our students by challenging, motivating, and
empowering them.

43

Diagram 1: Conceptual Framework

Culturally
Responsive
Teaching
Pillar 1
Identity Race and
Achievement
Pillar 2
Equal Access to a
Rigorous and Relevant
Curriculum
Outcome
Students who are
independent, critical
mathematicians and
individuals.
Pillar 3
Student-Teacher
Relationship
Pillar 4
Effective Learning
Environment
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Chapter Three: Methodology
This chapter includes a discussion on the qualitative research design, its characteristics,
and why this approach is the most appropriate for the current study. Moreover, this chapter is
going to include the researcher’s role; a discussion on strategy of document analysis; selection of
material, data collection, data analysis, and the scoring rubric that will be used as the foundation
of the document analysis.
Rationale for Qualitative Research
This research topic requires a social constructivist worldview approach. This perspective
is a major part of qualitative research. Creswell (2013) asserts that social constructivists view
individuals as seekers of a full understanding of the world around them and that their subjectivity
from their past experiences influences their interaction with the world.
The social constructivist approach of this research will help fill our knowledge gap by
investigating the perceptions of culturally responsive teaching in a K-12 school when using
supplemental math curriculum. As the number of underrepresented students in the education
system increases, research has urged the importance of culturally relevant teaching (Ladson-
Billings, 2009 and Gay, 2000).
In studying culturally relevant teaching qualitative research was used. Qualitative
Research is a method of inquiry where the inquirer is exploring a main phenomenon such as
culturally responsive teaching, capturing their perspectives accurately, analyzing the data
collected and interpreting the meaning of the information and themes in a final report that
includes possible biases and positionality (Creswell, 2013, p.4).
The researcher should use an instrument of collecting data that captures the “words or
pictures, analyzes them inductively, focuses on the meaning of the participants, and describes a
45

process that is expressive and persuasive in language” (Creswell, 2013, p. 197). In other words,
qualitative methodology is used to capture the words and pictures of stakeholders as accurately
as possible to answer the core research question driven by the inquiry about culturally responsive
teaching.
Central Research Questions
In assessing the quality of teachers pay teachers top twenty-five math lesson, my central
research questions are:
4. How does supplemental curriculum support a rigorous academic curriculum that adheres
to state standards?
5. How does supplemental curriculum incorporate opportunities for students to express their
individualized ideas using appropriate academic language?
6. How are supplemental materials including support for all learners, elements of cultural
pluralism and social justice?
Role of Researcher
The role of a researcher depends primarily on the context and nature of the research study
and the researcher’s positionality and values (Glesne, 1999). The goal of a research study is to
capture a glimpse of reality as experienced by stakeholders and participants involved. The role of
a researcher is to capture this as objectively and bias-free as possible. While the researcher’s
positionality, epistemology, personal biases, and values will still add dimension to this captured
reality during analysis, it is important for the researcher to be aware of these factors that can
shape the findings of a research study (Collins, 1992, 1998; Roni, 2013).
When conducting qualitative studies, we need to ensure that the findings are not merely
stories for the readers, but valuable information that is trustworthy enough to be used for further
46

research and/or as a resource for other research studies. Therefore, it is important to establish
trustworthiness and credibility of the researcher by being aware of his or her own positionality
and biases as to eliminate and diminish the possibility of influencing the research findings or the
research process (Patton, 2003).
It is important for me as a researcher to be aware of my own positionality as an educator,
a researcher, and a former Middle Eastern English Language Learner who longed for a sense of
belonging to my Elementary school classroom. Milner (2007) discusses a framework that is
designed to make the researcher aware of his or her own positionality and culture through
“researching the self” questions designed to engage the researcher in critical race and cultural
self-reflection (Milner, 2007, p. 395). Applying Milner’s framework, I had to research within
myself to identify my cultural and race values, my values as an educator and how these factors
affect culturally responsive teaching. I realized that by researching culturally relevant teaching, I
can place myself in the place of English Learning students and underrepresented students as I
construct my research pieces. I can fully understand how an uncaring and unsafe classroom may
lead students into feeling disoriented and alienated from the entire classroom learning experience
and I can also see areas where the educator can promote a sense of a caring and safe
environment. As Milner (2007) suggests when the researcher investigates “the self in relation to
others,” he or she acknowledges and becomes aware of the roles of the positions, and identities
of the research and research participants in the research process (p. 395). This leads the path
towards power dynamics at the elementary school where I currently work as a seventh and eighth
grade math teacher. As an educator, my position of power is over my classroom environment,
my students, and my lesson plans, which must abide by the department of education standards. I
work in cooperation with my fellow educators and under the supervision of my administrator.
47

Therefore, being in this position may shape the way I analyze and interpret my documents for
elements of culturally relevant teaching.
Case Study Approach
One investigates a case study because he or she is interested in it for “uniqueness and
commonality” (Stake, 1995). Therefore, I have chosen a topic that I believe is common in
today’s schools and unique in nature as it pertains to the education of our underrepresented
students across the nation. The approach to this document analysis is an investigation of
supplemental curriculum materials on Teachers Pay Teachers to investigate the quality of the
lessons and their relevance to the students. Teachers Pay Teachers is a privately owned website
where teachers, whether they are former or current, create, upload, and use instructional
materials for their students. Some materials are free, and some are for sale for a few dollars.
National Surveys report that in 2017, 55 percent of teachers used material from Teachers Pay
Teachers once or more than once per week. Teachers Pay Teachers reports that more than two
thirds of all U.S. teachers have used the site to access supplemental material (Polikoff et. al.,
2019).
Research Site
Teachers Pay Teachers (TPT) is my research site. As previously stated, this is a website
where former and current educators create and upload lessons to be used in classrooms across the
US. Teachers Pay Teachers is a company that launched in 2006 from New York and has been
supporting teachers in selling lesson plans and supplemental curriculum to other teachers
(Griffith, 2013). According to founder Paul Edelman, it has become the “iTunes for digitally
delivered educational content.”
48

My research is designed around selecting Math curriculum on Teachers Pay Teachers and
analyzing it for elements of culturally relevant teaching such as using cultural names in word
problems, culturally themed Math Units, connection with the real world, and giving students
opportunities to collaborate (Kagan, 2010). In Table 1, I describe the full rubric that I used to
evaluate Teachers Pay Teachers math supplemental material.
Data Collection and Analysis Procedures
Documents were collected from Teachers Pay Teachers. I logged in from my educator
account, selecting the grade level (7
th
and 8
th
grade), selecting math topics, and organizing my
search based on the ratings and popularity of supplemental activities. These documents were
studied and rated according to the rubric in Table 1 for meeting the designated criteria under
each mentioned category. Table 1 has been designed to include the criteria that constitute a
culturally relevant lesson, according to my literature review in chapter 2. I scored the documents
according to the presence of the criteria in a table and all evidence of presence or absence of any
criteria included in my document analysis.
All categories listed in table 1 were scored based on meeting the specific criteria listed. A
score was assigned to each document according to the number of criteria met. Two categories
include three criteria, while one included two criteria. If the document contains none of the
required criteria, it scored a 0. If it contains evidence of one of the criteria, it scored a 1. If it
contains evidence of two criteria, it scored a 2. If it contains evidence of three criteria, it scored a
3/3. Evidence of the criteria found within the lesson is in chapter 4 presented in the figures and
explained.
Document Analysis Criteria
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The following rating categories were used to analyze and score the highest rated lessons
on Teachers Pay Teachers in mathematics grades 7 and 8. Table 1 has been carefully developed
using literature and research to also include specific criteria that constitute each rating category.
Alignment with TEKs/Common Core Standards Criteria
To be culturally responsive, students need to be exposed to lessons that are challenging
and complex that are facilitated by their teachers. Teachers need to provide lessons that provide
rigorous work that is not “watered down”. Instead, the tasks and lessons should be engaging on a
conceptual and procedural level by providing “real-life problems by using estimation skills and
collaborating with their peers” (Garcia, 2021). Therefore, targeting common core math standards
or TEKS math standards is an important dimension of evaluation of mathematics lesson plans on
Teachers Pay Teachers.
Typically, on Teachers Pay Teachers, the standards are included. The documents that
were analyzed in this study include the math learning standards, according to grade levels. I
intended on using the math lessons and activities on Teachers Pay Teachers to select 7
th
and 8
th

grade Math documents that correlate to Math standards set in Common Core or Texas Essential
Knowledge and Skills (TEKs).
The presence of math standards in the lesson material ensures equity of the quality of
education. Even though underrepresented students “are vulnerable to negative stereotypes about
their intelligence, academic ability and behavior,” all students should have access to a rigorous
core curriculum. This helps students develop high academic expectations for themselves (Muniz,
2020, p. 6).
High academic expectations element is crucial to culturally relevant teaching. An
educator’s lesson plan must ensure that the curriculum supports equity for all students. Equity is
50

defined as “development that improves the learning of all students [which] prepares educators to
understand and appreciate all students, create safe, orderly and supportive environments; and
hold high expectations for their academic achievement” (Learning Forward).
Mathematical Discourse
The second dimension of analysis is mathematical discourse. I analyzed whether the
student has an opportunity to express his or her viewpoint, such as the method of solving a
problem and reasoning behind it. Students must be given the opportunity to communicate in
“culturally and linguistically sensitive ways” with their teachers, and their peers (Muniz, 2020).
Students must be allowed to use their natural ways to communicate effectively in the classroom.
The students’ individual culture, and language must be honored and respected. This “discourse
of power” from teacher to student level enables the student to acquire knowledge by engaging in
conversations and using language forms that are appropriate for the math context (Powell,
Cantrell, & Rightmyer, 2013).
Instructional conversations allow high levels of participation in extended discussions
amongst themselves with the teacher acting as the facilitator. Each student’s statement should
either build upon the previous one, extend or challenge it (Powell, Cantrell, & Rightmyer, 2013).
The purpose of these conversations is to enrich student comprehension, academic language, and
the development of their “socio-political consciousness”. Sociopolitical consciousness is an
integral component of developing critical thinkers, and independent individuals who are aware of
the differences that exist around them. Realizing this empowers the students to be more
cognizant of their own positionality, race, class, gender, and biases and pushes toward the social
equity movement Powell, Cantrell, & Rightmyer, 2013).
51

Any element in the supplemental material where the student can have space for
expression was considered. The student must not feel as though the lesson is planned with no
room for voice, opinion, or an opportunity to explain his or her thought process. This dimension
of instructional conversations was analyzed and assigned to a simple rubric with two to three
criteria. The criteria that are satisfied received a check mark in the relevant criteria. Any
opportunities for students to explain their work, present their work or come up with a different
method were considered elements of student voice and opinion.
Real World Application and Social Justice Support
Students need to feel that math exists all around them. For example, the arrangement of
rows and columns in a rose garden in connection to the algebraic formulas used to construct
homes. This type of connection helps bridge the gap between math and the real world by
presenting math in a culturally responsive manner (Jenkins, 2021). When math is connected to
real world scenarios, it brings ‘reality’ to the “abstractions of mathematics” (Hindawi, 2019).
The student’s interest in learning should “be proportional to individual experience” (Hindawi,
2019) to address the question “so what?” by students as they attempt to connect what they are
learning in the classroom to their everyday lives. Often in mathematics class, many students ask:
“what does this material have to do with [our] lives?” “Does this knowledge connect to an issue
[I] care about?” and “How can [I] use this information to take action?” (Muniz, 2020). Therefore,
lesson plans need to address the connection between student lives and the curriculum they are
learning to help “build their sense of civic responsibility and learn to see themselves as agents of
change” (Muniz, 2020).
When students “see themselves as agents of change,” this becomes crucial in challenging
the current inequities of school and society. Problems presented to students in mathematics must
52

be authentic for the students. Mathematics lessons need to be explicitly based on known student
experiences that most students find ‘genuinely problematic’ (Aguirre & Zavala, 2013). Aguirre
and Zavala (2013) assert that mathematics must be used as a tool to educate students on “power
relationships and structures of social, economic and civic issues” within the national and global
context. At the school level, some examples may be budget problems using multiplication,
measurement, addition, and data analysis involved in challenging a district against “closing a
neighborhood school” (Aguirre, J. & Zavala, M., 2013). Another example is data analysis to
address race and racism in schools or measurement concepts involved to challenge society views
on the ideal body image (Kitchen & Lear, 2000; Tenorio, 2004; Varley-Gutierrez, 2011 as cited
by Aguirre, J. & Zavala, M., 2013).
Lessons need to be tailored to guide the students’ mathematical investigation as they
understand, analyze and challenge social issues around them. Research suggests that powerful
mathematics teaching is founded upon students’ funds of knowledge being used in collaboration
with mathematics concepts to interpret and understand social issues in the world. Therefore,
lessons and activities on Teachers Pay Teachers were analyzed for the presence of powerful
supplemental mathematics teaching which helps the students to interpret the world around them
and act on social issues that are relevant to their lives.
Analysis Plan
On Teachers Pay Teachers, I selected 7
th
and 8
th
math material as they pertain to the
Texas Department of Education math standards that I am familiar with as an educator (TEKS) or
common core standards. I selected the twenty-five highest-rated math supplemental materials to
view as they would be more likely to be used by educators. Next, according to the rating
categories mentioned in table 1, I graded each document. The criteria mentioned have been
53

developed to detect the existence or absence of the culturally relevant elements that are believed
to contribute to a coherent culturally relevant lesson according to literature reviews and research
(Hammersley & Atkinson, 2007).
Creswell (2012) suggests a model to help analyze data in the following steps:
1. Organize and prepare data
2. Read all data
3. Code your findings
4. Generate categories for analysis
5. Use a narrative to write about findings of analysis
6. Interpret findings
All documents collected from Teachers Pay Teachers were organized and prepared for
analysis. The authors and titles of each lesson were recorded. I read all of them and organized
them on a table. Rating categories were used to score each lesson according to the number of
criteria aligning to the content. Evidence is provided about the exact location of the content
matching the criteria in chapter 4. Moreover, a thorough analysis and reasoning is also included
on the evidence collected and the score given.
Lastly, I interpreted and discussed my findings across all curricula collected and used
from Teachers Pay Teachers as we investigate the culturally relevant quality of the supplemental
curriculum being used frequently by many teachers across the nation in the math classroom.
Table 1
Teachers Pay Teachers Rubric
Rating Category 0 1 2 3
54

1. Alignment with
TEKs/Common
Core standards
Criteria
● Targets grade level
standards.
● Math standards are
well connected to
the content of the
lesson
● Balance of
mathematical
procedures and a
deep conceptual
understanding of
mathematical
operations.
Meets 0 of the
criteria.
0/3
Meets 1 criteria.
1/3
Meets 2
criteria.
2/3
Meets all
criteria.
3/3
2. Mathematical
Discourse and
Communication
● Students are
explaining and
presenting ideas
Does not meet the
criteria in
dimension.
0/3
Meets 1 criteria.
1/3
Meets 2
criteria. 2/3

Meets all
criteria.
3/3
55

and reasoning to
each other or the
whole class.
● Students are
encouraged to use
accurate
mathematics and
academic
language.
● Multiple
solutions/strategies
are encouraged.
3. Real world
application and
Social Justice
Support
● Content uses math
to help the students
understand issues
that are relevant to
them.
● Content uses math
to enable the
Does not meet the
criteria in
dimension.
0/2
Meets 1 criteria.
1/2
Meets 2
criteria. 2/2

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students to make
informative
decisions as future
independent
individuals.
Advantages and Limitations of Document Analysis
In comparison to other methods of qualitative research, document analysis has many
advantages and potential flaws. One of the most important advantages is that it is a highly
efficient method (Bowen, 2009). It is less time-consuming and requires selection of data rather
than collection of data (Merriam, 1988). Especially after many schools have switched to virtual
education due to the COVID-19 pandemic, it is much more time-efficient to collect documents
rather than data from educators and stakeholders.
Document analysis is also advantageous due to the availability of the documents on the
internet. Documents readily available on Teachers Pay Teachers are available to be analyzed by
research and are also available to be used by thousands of teachers nationwide with their students
(Merriam, 1988). This enables my research analysis results to target lessons that are being used
by educators in the classrooms daily.
Analyzing supplemental curriculum on Teachers Pay Teachers is a cost-effective method
in collecting curriculum that is free or considerably less expensive to the average teacher
compared to pricey textbooks and material. This means that more teachers will be using these
cost-effective methods to teach their students as well, which adds more practical value to the
results of this document analysis.
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Lack of reactivity is a crucial advantage to using document analysis methods in this
research. Documents are ‘non-reactive’ as they are not subject to an interaction from researchers.
When interviews are conducted with teachers and stakeholders, there is a human interaction that
always gives a chance for them to feel intimidated or judged by the interviewer; whereas, when a
document is being analyzed, there is less room for reactivity and biased data.
Another limitation is the correct estimation of the rigor of the curriculum on Teachers
Pay Teachers as an educator and not a curriculum evaluator. As an educator, I evaluated the rigor
of the math curriculum based on my knowledge and experience in the classroom. I intended to
use definitions of depth of knowledge levels one through four to evaluate the rigor of math
curriculum on Teachers Pay Teachers as they would apply in my classroom. However, all
reviewers may not agree with my ratings of the supplemental materials.
Potential Flaws
Despite the advantages mentioned to the document analysis approach, there is also an
opportunity of biased selectivity. This document analysis only analyzes supplemental
mathematics curriculum not the core curriculum that may be used in classrooms. It is impossible
to analyze all the documents on Teachers Pay Teachers that are being used by educators. Since I
will be the only individual responsible for document analysis, it will not be possible to select all
the documents to analyze and score using the rubric. Therefore, an incomplete collection of
documents could occur (Yin, 1994, p. 80). However, to minimize the chance of biased
selectivity, I intend to choose the documents that are already rated highly by other educators.
This will result in data that is most relevant to the documents that are practically used by most
teachers in the nation.
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Another disadvantage to document analysis is insufficient detail due to documents not
being communicative or not providing enough details to answer my research question. They may
not also give adequate information about the purpose of the creator or author. Sometimes content
analyzed by the rubric may be not fully understood in written form without explanation from the
author. Therefore, it may be challenging to rate material according to criteria using solely written
content without human contact or interaction.
Trustworthiness and Credibility
Credibility and rigor of the qualitative study is what makes the case study feel “right” to
the researcher and reader (Corbin & Strauss, 2008). The validity and dependability of a research
study relies on the credibility of the researcher (Patton, 2003). The research must be skilled,
competent, and rigorous throughout the research process (p.14). Dependability is an indicator of
“trustworthiness through methodological protocols that are designed and developed in a manner
that is consistent, logical, systematic, well documented, and designed to account for research
subjectivities” (O’ Leary, 2005, p. 60).
Trustworthiness is “how can an inquirer persuade his or her audiences that the research
findings of an inquiry are worth paying attention to and are the findings applicable to other
studies?” (Guba, 1985, p. 290). Qualitative researchers primarily consider trustworthiness rather
than validity, reliability, applicability, and objectivity (Creswell, 2013; Denzin & Lincoln, 2003,
2011; Lincoln & Guba, 1985; Padgett, 1998).
Being explicit and transparent about the framework of the qualitative data analysis and
the coding rubric enhances the credibility of the study by establishing a coherence between the
researcher’s positionality, purpose of the research study, the nature of the collected document
and their analysis (Sebar et. al., 2020).
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To further enhance credibility and trust, I seek the advice and direction from my
dissertation chair, Dr. Morgan Polikoff, who has written and published highly valuable work in
the education community, including “The Supplemental Curriculum Bazaar: Is What’s Online
Any Good?” In this report, Dr. Polikoff and his team developed a rubric that captures “the
dimensions of quality” such as “rigor and usability” in the more than three hundred of the most
downloaded ELA curriculum materials on three of the most popular supplemental websites:
Teachers Pay Teachers, ReadWriteThink, and Share My Lesson. As I progressed through my
dissertation, I continued to consult Dr. Polikoff on my rubric and my coding structure.

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Chapter Four: Findings
Introduction
As stated in Chapter 1, the purpose of this study is to (1) examine the cultural relevance
of the mathematics supplemental curriculum on Teachers Pay Teachers, (2) rating the twenty-
five seventh and eighth grade mathematics lessons with the highest ratings on Teachers Pay
Teachers according to the rubric developed, (3) exploring how these ratings can help teachers,
administrators, and stakeholders as they develop culturally relevant mathematics lessons to
students. This chapter is organized around the research questions developed in Chapter 1. I
explored twenty-five mathematics lessons that are highly rated and downloaded according to
Teachers Pay Teachers. Each lesson is broken down and rated according to the rubric developed.
Findings from this case study are collected and presented to reflect the overall cultural relevance
of the mathematics supplemental curriculum on the popular platform; Teachers Pay Teachers.
Discussion of the Findings
My research questions were formulated through the application of the theoretical
frameworks of practice and culturally responsive teaching.
1. How does supplemental curriculum support a rigorous academic curriculum that adheres
to state standards?
2. How does supplemental curriculum incorporate opportunities for students to express their
individualized ideas using appropriate academic language?
3. How are supplemental materials including support for all learners, elements of cultural
pluralism and social justice?
Research Question One
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1. How does supplemental curriculum on TPT support a rigorous academic curriculum that
adheres to state standards?
The first question looked at the ways that supplemental curriculum on TPT supports the
mathematics standards provided by the state. A supplemental curriculum should be used to fill in
academic gaps, provide differentiated instruction and provide demanding academic work that
adheres to the academic standards. The highly rated content on TPT was evaluated in the way
they build students’ understanding of the topic and the level of cognitive demand that is required
for students to understand the material. The twenty-five selected lessons were evaluated on the
alignment with TEKs standards for Mathematics. All of the evaluated lessons satisfied a rigorous
academic curriculum adhering to state TEKs standards. All twenty-five lessons included TEKS
standards in the description box of each individual lesson. The TEKS standards were listed by
number along with the description of what the standard is. Upon review of the lessons, I found
that the TEKS standards included the lesson aligned to the content of the lesson.
The content of the top twenty-five lessons did not only align to the standard described but
it also included mathematical problems that require a deep understanding of the mathematical
concepts by the students to complete the questions successfully. Therefore, all twenty-five top
rated lessons were rated highly with a three out of three on all categories of the rubric for the first
category of TEKS alignment.
Alignment With TEKs/Common Core Standards
My three criteria in the first rating category are (1) target grade level standards (2) Math
standards are well connected to the content of the lesson (3) Balance of mathematical procedures
and a deep conceptual understanding of mathematical operations. I used a 0-3 scale that ranged
from (0) meets no criteria to (3) meets all criteria. The average alignment rating is 3.0. All
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lessons aligned strongly with the TEKs standards they were listed to offer or with the math topic
that was labeled on the lesson.
Content was evaluated according to Webb’s (1997) depth of knowledge (DOK)- this is
the cognitive demand from students as they complete an academic task. All twenty-five lessons
contained DOK level one questions in which the students were being asked to recall and
reproduce mathematical concepts by working out problems using basic calculations. All twenty-
five lessons also contained DOK level two questions that include an engagement of deeper
mental processes such as explaining the answer, showing the work they had to do to get answers
to problems, and doing more complex calculations such as multi-step problems. DOK level three
questions require analysis, evaluation, creation of a representation, and higher order thinking
skills to solve problems (Webb’s 1997).
As an example, in Figure 1, DOK level one questions are used where students are stating
basic facts such as 14+(-30) and -15+59 as a part of integers practice. These sorts of integer
problems are basic ones that require students to recall and reproduce mathematical operations
using basic calculations. DOK level two questions are also present in the twenty-five lessons
analyzed, as an example from the same lesson, the problems become multi-step problems that are
a bit more complex such as 18-(-43), which requires the students to apply the distributive
property as well as the distribute the negative sign into the -43 that is inside the parenthesis. The
next step will be to realize that a negative sign multiplied by a negative sign result in a positive
sign. The last step is to add 18+43 to get the final answer. This fits the definition of second order
depth of knowledge. In this lesson, each problem is provided with more than one possible answer
that the students must evaluate and choose the right answer from to complete the appropriate
path of the maze. This also requires the students to draw observations, show their work by using
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more demanding mathematical reasoning to solve the problems and choosing the correct
answers. This satisfies the depth of knowledge level three of strategic thinking and complex
reasoning. Moreover, this maze path requires the students to strategically answer only nine
problems to which the answers are going to form the correct maze pattern from start to finish.
This complex reasoning and planning of the appropriate maze pattern relate this mathematics
topic of solving integers to a real-word application such as solving a maze and identifying
solution paths, which fits depth of knowledge level four of extended thinking (figure 3).
Figure 1
Integer Operations Maze 1

Figure 2
Mathematics Maze
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Figure 3
Integer Operations Maze2

Target Grade Level Standards
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Grade level mathematics and algebra standards are listed along with each selected lesson
on Teachers Pay Teachers. As an example, one of the lessons named Comparing Functions listed
the Algebra standard: 8.F2: “compare properties of two functions each represented in a different
way (algebraically, graphically, numerically in tables, or by verbal descriptions) in figure 4” The
lesson included the TEKs from grade level appropriate standards to meet grade level
achievement. All mathematics and algebra standards are appropriate for the grade level (7th/8th)
grade and are listed along with the lesson on the website. This ensures that the supplemental
lesson provided adheres to state math standards that are going to be assessed on the state
assessment at the end of the school year. This lesson on comparing functions and it lists the
TEKS standard, which compares two functions algebraically, graphically, numerically, or
verbally. The lesson distinctly lists the different functions and the questions from the first
situation includes different functions that represent the baby pandas’ weight and growth
compared to their age. These questions and function representations help the students determine
how the same data could be represented using different functions, which aligns well to the TEKS
standard provided in the top section of the lesson.
Figure 4
Comparing Functions
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Another example of a strong lesson is a lesson on the topic of Combining Like Terms,
covering TEKS A.10A: Student Expectation: Add and subtract polynomials of degree one and
degree two. This algebra standard is one that students need to master in Algebra so they can pass
their state test. Therefore, this is the major standard listed on the description page of this lesson
on Teachers Pay Teachers. The same standard aligns to Common Core State Standard 7.EE.A.1,
which also covers combining like terms.
Figure 5
Description
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Math Standards Are Well Connected to the Content of the Lesson
Not only are the standards listed next to the lesson on Teachers Pay Teachers aligned to
typical state standards in math and algebra, but the contents of the standards are well connected
to the content of the lesson. This is typically assessed by looking for the content of the actual
lesson to recognize keywords that are a part of the standard and are found within the content of
the lesson.
A positive example is on Teachers Pay Teachers in a lesson titled “STEMersion- Systems
of Equations with Substitution- Accountant” with Common Core Standards as follows:
CCSS8.EE.C.8CCSS8.EE.C.8aCCSS8.EE.C.8bCCSS8.EE.C.8cCCSSHSA-REI.C.6.
Figure 6
Common Core Standards and Description
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The algebra standards in figure 6 align to the content of this lesson on solving systems of
equations with substitution. The keywords used in the word problem such as linear models,
revenue, expense, cost, and profit make the content of this lesson align nicely with the standards
that are mentioned in the Teachers Pay Teachers description section of the lesson.
Figure 7
Stem-ersion
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Balance of Mathematical Procedures and a Deep Conceptual Understanding of
Mathematical Operations
The top twenty-five lessons analyzed balanced mathematical procedure application along
with a deep conceptual understanding. For example, one material focused on algebraic functions
and their corresponding graphs. In this example, not only are students required to understand
algebraic functions, which is an Algebra standard, but they are also expected to create and use
representations to organize and communicate their ideas. Students are provided with an
interactive software that allows them to come up with different algebraic functions, graph them
and create a visual image of an object. The students are encouraged to create their own visual
image using algebraic functions. They are also required to use different types of functions to
compose their final image. This allows the students to develop a deep conceptual understanding
of algebraic functions using linear, quadratic, and exponential models. This also allows them to
manipulate functions by setting the domain, the range and make predictions about the overall
shape and visual of the algebraic function.
Figure 8
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Algebra I End of Year Project: Functional Designs

Figure 9
First Category: Alignment with TEKs/Common Core Standards

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In conclusion, all twenty-five lessons assessed received a 3 out of 3 in the Alignment with
TEKs/Common Core Standards Category. The scale score of 3 out of 3 corresponds to the fact
that all twenty-five lessons assessed contain math standards that are well connected to the
content of the lesson and require an understanding of mathematical operations, a balance of
mathematical procedures and a deep conceptual understanding of mathematical operations and
target grade level standards.
Research Question Two
2. How does supplemental curriculum incorporate opportunities for students to express their
individualized ideas using appropriate academic language?
Figure 10
Second Category: Mathematical Discourse and Communication

Mathematical Discourse and Communication
The next category is mathematical discourse and communication. The evaluation of the
twenty-five top rated lessons revealed that 48% of the lessons evaluated encouraged the use of
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multiple strategies or solutions to solve mathematical problems, while the rest of the lessons only
gave the students one method to solve the problems and expected the students to keep using the
same methods to solve all the problems. Only 20% of the lessons evaluated had the students
explain and present ideas and reasoning to each other or to the whole class, which is a major
foundation for mathematical discourse. Students are encouraged to use accurate academic
mathematical vocabulary in 52% of lessons evaluated, while the rest did not include the required
mathematical vocabulary for the covered math content.
Multiple Solutions/Strategies Encouraged
48% of the lessons assessed encourage multiple solutions or strategies to solve
mathematical problems. A positive example of this is in a lesson that covers representing linear
functions (figure 11). Linear functions can be represented in an equation form, table form, graph
form or in intercept form using coordinate sets. Multiple ways of representing linear equations
provides the students more opportunities to envision the problems in multiple ways and to use
different strategies to understand the linear equations.
Figure 11
Representing Linear Equations
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Another positive example is a lesson on Comparing Functions, which “compare(s)
properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). Each situation provided in the lesson for
practice should be solved by the students by using any of the representations (algebraically,
graphically, numerically, or verbally). The students may use any of these representations to
analyze and compare linear functions.
Figure 12
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Comparing Functions
A negative example of this is shown in a lesson on solving one step equations based on
word problems. The lesson lists distinctive steps on how to solve for x. The student is expected
to show work involved in solving for x by following the specific steps that are distinctively
sequenced. The steps are as follows “Let x represent the number of packs of stickers bought (x-
35=70). Let x represent the numbers of points scored in the first game (x-4=12). Let x represent
the number of stickers brought to school (x+35=70). Let x represent the amount of money that
needs to be saved (4x=12). Let x represent the amount of money in the savings account
(x/4=12).” In this lesson, in other words, students are only expected to use a single solution
strategy of defining the variable(x), writing an equation that includes the variable, and solving
for x to find the solution for the problem. This is a cookie-cutter method of solving for x that
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does not provide the students much opportunity to come up with other possible solutions or
strategies to solve the problem.
Figure 13
Variable Description

Students Are Explaining and Presenting Ideas and Reasoning to Each Other or to the
Whole Class
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In some of the lessons studied (5 lessons out of 25 assessed, 20%), the students are
encouraged to partner up and present their ideas and reasoning to each other or the whole class.
A positive example of this is in a lesson about combining like terms, where students are
encouraged to solve the problems in pairs and discuss their solutions. The students are given the
option to choose a game from a list of games including Tic-Tac-Toe, Square-Up!, or Hang the
Man. The students have the choice to pick the game they prefer. Each game contains problems
that belong to the TEKS standard of the lesson. The students are encouraged to answer the
questions and explain the answers to each other, as a part of the game. The students compete
against each other to win the game; however, they are still working on solving the problems and
explaining the solutions to one another.
Figure 14
Hang the Man- Key

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Figure 15
Tic-Tac-Toe

Students Are Encouraged To Use Accurate Mathematical and Academic Language
52% of the lessons assessed encouraged students to use accurate mathematical and
academic vocabulary. A positive example of this is in a lesson focused on solving systems of
equations using the substitution method. In this lesson, the students are given a word problem
involving an accountant that works in a firm and must secure expense and revenue reports. The
students are required to use accurate mathematical terms such as “revenue” and “expense”. They
are also required to use academic language in presenting the evidence they need from the word
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problem to use a specific strategy to solve the problem. Students are also required to provide an
analysis of the evidence they find in the word problem using mathematical terms.
Another great example is a lesson on Simple Interest Word Problems that asks the
students to answer questions based on word problems about interest. Mathematical terms such as
deposits, withdrawal, balance, interest rate, and account are used throughout the problems.
Students are also expected to learn and use these mathematical words within their answers and
while showing their work as seen in figure 16.
Figure 16
Simple Interest Word Problems

Only 20% of the twenty-five lessons assessed received a 3/3 on all three criteria while
48% received a ⅔ and 52% received ⅓. Therefore, it is fair to conclude that a small percentage
of the top-rated lessons allow students to communicate and express their ideas in the
mathematics classroom using appropriate academic terminology.
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Research Question Three
3. How are supplemental materials including support for learners, elements of cultural
pluralism and social justice?
Figure 17
Third Category: Real World Application and Social Justice Support

Real World Application and Social Justice Support
13% of the lessons enable the students to make decisions to inform action towards a more
socially just world. This was determined by the type of word problems and mathematical
operations the students had to solve. The answers to math word problems were only informative
to the students’ decision-making process daily in only 13% of the lessons evaluated on Teachers
Pay Teachers. Only two lessons, which make up 8% of the lesson evaluated, satisfy the two
criteria of the social justice category including using math to help the students understand issues
that are relevant to the students and using math to enable the students to make informative
decisions as future independent individuals. 80% of the lessons evaluated on Teachers Pay
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Teachers met none of the criteria and scored 0 out of 2 on the rating scale as they did not satisfy
any of the criteria that satisfy the social justice category.
Content Uses Math To Help the Students Understand Issues That Are Relevant to Them
Only 8% of the lessons evaluated exhibited content that used math to help the students
make sense of authentic real-life issues or to understand issues that matter to the students. This
was exhibited in the use of word problems or solving mathematical operations that revolved
around real-life situations that the students find important and engaging.
One positive example of this is a lesson that has students use unit rates to determine the
largest size coffee at Starbucks that is the best deal. Almost all students are familiar with
Starbucks and when they can use mathematical functions to determine the cheapest Starbucks
coffee deal, this enables them to apply what they have learned to a real-life situation that is
relevant to their daily lives.
Figure 18
Starbucks Coffee

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Another positive example of this is a lesson that covers the value of Pi. There are
multiple problems that ask the students to use a pumpkin pie or a pie dish to calculate the cost
per square inch, ribbon needed to fit around the dish, and the area of the remaining portion of a
pie after someone eats a portion of it. These kinds of questions are centered around issues that
students in middle school age can relate to.
Figure 19
Pi Day Pie Problems
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Content Uses Math to Enable the Students to Make Informative Decisions As Future
Independent Individuals
Only 13% of the twenty-five lessons evaluated satisfied this criterion by using math to
help students make informative decisions in the adult world. A positive example of this involves
simple and compound interest presenting a car and its price and offers four financing options.
Students are required to calculate the total amount to be repaid for each finance option. Students
get to answer questions and compare compound and simple interest and understand how the
length of taking a loan affects credit. This topic is socially critical for these students to become
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independent adults in the future as they make important decisions that may affect their financial
future and therefore, the financial future of our community as well.
Figure 20
Financing Options

Another positive example is a lesson titled Road Trip Plan, which is centered around a
road trip around the US. Students need to calculate which car to use that is going to provide the
most mileage per gas tank. The car types are listed in a table along with the gas mileage and size
of the gas tank. This is an incredibly important topic for adults and for students to consider
thinking of to make informative decisions in the future about car efficiency and gas mileage.

Figure 21
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Road Trip Plan

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Chapter Five: Discussion and Conclusion
Online curriculum supplemental materials are highly used by teachers in the classroom
daily. Therefore, it is important to study the quality and relevance of these materials to the
students. The quality of these supplemental materials corresponds to the TEKS standards
covered and the alignment of the TEKS standards. The relevance of these materials relates to the
cultural relatedness of the curriculum to the students’ culture and everyday lives and how these
supplemental materials train the students to be more responsible individuals in the future.
Twenty-five lessons from Teachers Pay Teachers were analyzed and graded using the
rubric provided in chapter three. The highest rated lessons in mathematics for seventh and eighth
grade were used. Most lessons were visually appealing, had no significant mathematical or
algebraic errors and had good reviews on Teachers Pay Teachers from educators.
Do Teachers Pay Teachers Lessons Target Grade Level Standards?
The quality of the academic rigor was assessed first to cover the Alignment with
TEKs/Common Core Standards, which was broken down into three criteria (1) target grade level
standards (2) Math standards are well connected to the content of the lesson (3) Balance of
mathematical procedures and a deep conceptual understanding of mathematical operations. The
grade level standards for seventh and eighth grade mathematics and algebra were listed in the top
rated twenty-five lessons evaluated. The grade level standards were appropriate to the grade
levels under TEKS or Common Core State Standards. All twenty-five lessons covered grade
level mathematics standards.
The grade level standards were listed on the lesson’s description page or within the lesson
itself. They are listed in numerical form and word form from the TEKS resource system and/or
the Common Core State Standards system. It is easy to search for lessons that cover a certain
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standard or topic by simply typing into the search box the full standard or the keywords from the
standard. Some lessons list the mathematics/algebra standards according to Common Core while
others list the standards in TEKS, and others contain both.
Are Math Standards on TPT Lessons Connected Well to the Content of the Lesson?
The content of the twenty-five lessons succeeded in covering the mathematics and
algebra standards that were listed in the lesson. To investigate this criterion further, Webb’s
(1997) depth of knowledge was used. All twenty-five lessons include elements that cover all four
DOK levels that form the foundation for strong grade-level lessons. All twenty-five lessons
included elements such as basic recall and reproduction of mathematical concepts DOK 1, an
engagement of deeper mental processes in multi-step problems DOK 2, analysis, evaluation, and
requirement of higher order thinking skills (DOK 3) and extended thinking (DOK 4). To ensure
equity, it is important for mathematics and algebra lessons to cover all DOK levels to ensure that
all students are held to high academic standards that are appropriate for their cognitive and
mental capabilities.
The content of the lessons evaluated were found to contain keywords from the
mathematics standards within the questions and problems in the lessons evaluated. Using those
keywords within the problems ensures a high-quality lesson that satisfies mathematics and
algebra state standards and rigorous, cognitively demanding tasks for the students. Mathematical
terminology should not be watered down or substituted for simpler words for the students. On
the contrary, students should be exposed to mathematical terminology and should be encouraged
to use them with peers and during solving mathematical problems.
Do TPT Math Lessons Satisfy a Balance of Mathematical Procedures and a Deep
Conceptual Understanding of Mathematical Operations?
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A deep conceptual understanding of mathematical operations is integral to the learning
experience of students. The presence of DOK level 3 and 4 elements in the math lesson ensures
the deep understanding of mathematical operations and the application of mathematical functions
to cognitively demanding and challenging tasks.
All students deserve an intellectually stimulating curriculum that enriches and nourishes
their learning experience. All lessons evaluated on Teachers Pay Teachers contain opportunities
for the student to develop and apply a deeper understanding of algebraic functions by making
predictions about unknown situations or higher-level mathematical scenarios.
While a deep conceptual understanding of mathematical operation is necessary to trigger
and stimulate students’ minds, it is important to also have a meaningful balance between basic
mathematical functions and deeper conceptual problems to challenge students without
discouraging them. It is apparent in all twenty-five math lessons evaluated that there is a
meaningful balance between basic (DOK 1 and 2) and higher-level math problems (DOK 3 and
DOK 4), which is also appreciated by educators who reviewed the lessons on Teachers Pay
Teachers by leaving comments and giving the lessons high ratings to place it them in the top-
rated lessons.
Overall, it is evident that supplemental curriculum from Teachers Pay Teachers that is
rated highest does indeed support a rigorous curriculum that adheres to state academic
mathematics standards. The key words in the TEKS standards in every lesson plan match to the
content of the lesson. The standards in all twenty-five lesson plans are 7th and 8th grade
standards that are included in the TEKS resource system. All mathematical problems in the
lessons dig deep in the students’ deep conceptual understanding of mathematical concepts and
operations. Most of the lessons analyzed start off with the topic, then there are basic questions
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about the topic and the questions start to become more challenging for the students by asking
them to solve word problems or higher-level questions in the lessons. It seems that the ratings
provided by educators to place the twenty-five lessons assessed amongst the top-rated lessons is
the academic rigor and alignments to TEKS and Common Core standards contained in those
lessons.
Even though the top twenty-five lessons on Teachers Pay Teachers seem to be
academically coherent and strong, this study goes deeper into the analysis of the quality of
mathematical discourse and communication. While it is important for students to be held to high
academic expectations and to be cognitively stimulated and challenged to think critically and
deeply about the mathematical concepts they learn and apply in the classroom, it is also
important for students to learn how to ‘speak’ and communicate in mathematical terms, which is
important for mathematical discourse.
Do TPT Lessons Encourage Students to Use Multiple Solutions or Strategies to Solve
Problems?
In mathematics, there are usually multiple strategies to solve problems. There are also
multiple ways to present numbers and equations for example, in picture form, equation form,
graph form or table form. It is important for students to be exposed to multiple strategies of
solving problems and to also be given the opportunity to use or create strategies to solve
problems that are logical to them and to their cognitive abilities and imaginative thinking. All
students think differently; therefore, using a cookie-cutter method to solve problems may not be
the most effective way to teach students to solve math problems. Students should realize that
solving math problems can take many forms and ways.
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Only 48% of the lessons assessed from Teachers Pay Teachers encourage students to use
multiple solutions or strategies to solve math problems. Some of them encouraged students to
use different ways to represent functions or equations. Students can envision the problems in
multiple ways that make sense to them and align with their learning style when they are provided
the freedom and opportunity of choice. Giving students a choice to represent their answers or
solve problems allows them to be creative thinkers who can add their own personal touches or
techniques to a topic they are learning.
Overall, it seems that the top-rated lessons on Teachers Pay Teachers excel in covering
content that aligns with state standards. Teachers Pay Teachers is also user friendly as it allows
teachers to type into the search box the key words of the standard or topic they are looking for
and the top-rated lessons come up for free or for a few dollars. Most of the reviews on the top
twenty-five lessons praise the problems that are within the lessons, the colorful, student-friendly
design, easily downloadable and the ‘no-prep’ feature that accompanies these lessons. The top
twenty-five lessons also include answer keys for the teachers to easily check the students’
answers.
Frankly, all the mentioned features make Teachers Pay Teachers lessons highly appealing
to teachers including myself. Teachers can easily spend ten minutes finding those lessons and
making copies for their students to practice mathematical concepts. From an educator
perspective, I enjoyed assessing, reading, and using these lessons with my students. They save
more time and energy that is required to create a lesson that includes key mathematical words,
align with standards and strong content that satisfies all four levels of the depth of knowledge.
Therefore, the reason those lessons assessed in this case students appeared within the top twenty-
five most highly rated lessons is incredibly clear from an educator’s perspective.
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However, perhaps this perspective is not a complete reflection of the true quality of these
lessons. There is a blind spot of ‘other’ factors that make these lessons high quality lessons that
are worthy of supplementing the curriculum that we provide to our students every day across the
nation in every classroom. This blind spot includes factors that are beyond the academic
application of mathematical operations. These factors include communicating using appropriate
math terms in mathematical discourse and allowing the students to choose or devise strategies
that help them solve problems and understand topics in their own tailored, individualized
method.
Do TPT Lessons Require or Allow Students to Explain and Present Ideas and Reasoning to
Each Other or to the Whole Class?
Mathematical discourse and communication allow students to express their mathematical
ideas about mathematical concepts using appropriate academic language while discussing with
each other or with peers. Only 20% of the twenty-five top lessons on Teachers Pay Teachers
encouraged or required students to explain and present ideas and reasoning to one another or as a
whole class. Some lessons encouraged students to explain the answers to each other in a game
format such as Tic-Tac-Toe, Square-Up! or Hang the Man. Unfortunately, the rest of the lesson
evaluated required students to solve problems by writing the solutions and working out the
problems without discussing the possible solutions or strategies. This is mostly considered
‘silent’ work, where the students quietly work on assignments much like adults who quietly work
in cubicles.
Do TPT Lessons Encourage Students to Use Accurate Mathematical and Academic
Language?
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52% of the lessons assessed encourage students to use mathematical language. It is
important for students to practice using appropriate grade level academic and mathematical
language. As a math teacher, I often see students in second grade refer to subtraction as ‘take
away’ problems. It is not typically till third grade that students start to use the correct term
‘subtraction’ when they conversate with peers and teachers.
Students must be encouraged within their math lessons to use mathematical language that
comes from the TEKS, or Common Core Standards listed as they process the math problems and
as they discuss math with their peers. This helps the students understand mathematical concepts
better and apply them within their vocabulary. The educator or the math lesson should help guide
the students to use mathematical terminology accurately and in a meaningful way.
Do Teachers Pay Teachers Lessons Use Math to Help the Students Understand Issues That
Are Relevant to Them or Enable Them to Make Informative Decisions As Independent
Individuals?
During the assessment of the twenty-five top rated math lessons on Teachers Pay
Teachers, only 8% of the lessons used math to help students understand issues that are relevant
to them and their lives. One lesson used Starbucks to help students understand unit rates and
identify the best deal on Starbucks drinks. The rest of the lessons included basic math problems
that do not relate to the students and are not relevant to their daily lives.
Students need to apply mathematical concepts to more than plain numerical problems. As
an educator, I see students in the classroom everyday wondering ‘why do I need to know this?’ ‘I
do not need math in my life.’ Students need to realize that the mathematical concepts they learn
in school can help them in their daily lives. Mathematical problems must be relevant to the
students as they apply what they learn in math to relevant real-world situations.
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Not only do students need to solve math problems that are relevant to their daily lives,
but they also need to be exposed to problems that are going to help them make better decisions in
the adult world. For example, when students are given a simple and compound interest word
problem that asks them to make the best decision about a finance option, this enables them to
make better decisions as adults. When our students today grow up to be independent,
knowledgeable, and informed decisions, they can contribute to our community and our society.
These positive contributions to our society by our students’ intelligent financial decisions will
help improve our economy and the overall future of our nation and quality of life. The more
students learn today about making intelligent decisions using mathematical operations, the less
of a financial burden we will have in our society.
Policy Implications
Based on the findings, there are a few important takeaways for policymakers and
educators. First, supplemental math materials on TPT are highly rated only based on academic
basis. They may fill the academic gaps by attributing to depth of knowledge
(DOK1-4); however, they fall short in academic discourse and in relating to students’ daily lives
and elements of social justice.
Second, the supplemental math materials market on TPT should be reviewed and
assessed by curriculum developers who place guidelines for a coherent, high-quality curriculum
that is relevant to students and helps them make informed decisions in the real world. Third,
schools, district leaders and learning communities need to provide students with a high-quality
curriculum that is strong academically and relevant to their students’ daily lives.
While teachers are on the hunt to find the perfect supplemental curriculum that covers
math standards, asks deeper DOK 3 and 4 questions, it is also important to inform educators that
93

a well-rounded, high-quality curriculum should include more than just common core or TEKS
math standards. These pieces should be included in the criteria educators and administrators use
to rate curriculum that is used by teachers to improve the quality of teaching and learning in our
classrooms and the lives of students even after they graduate from school in their practical lives.
Limitations
This study only focused on the top twenty-five rated math lessons on Teachers Pay
Teachers and not the core curriculum that may be used by teachers. Therefore, there is an
opportunity of biased selectivity as the lessons selected may not represent all supplemental
material or all the math material on Teachers Pay Teachers. There is also a limitation of not
accurately rating the lessons correctly in terms of rigor or levels of depth of knowledge as I rated
the lessons based on my experience as an educator and the rubric that I developed according to
research and classroom experience.
Conclusion
Online supplementary materials on Teachers Pay Teachers are incredibly popular;
however, the quality of these materials is still under scrutiny. The quality of these materials
remains subject to educators’ opinions, reviews, and recommendations. The real question is
around what truly defines the quality of such supplementary materials. According to the reviews
on Teachers Pay Teachers and my experience as an educator, high-quality supplementary
material corresponds to a coherent, standard-aligned supplementary material that can be used in
the mathematics classroom to provide students with more practice.
The top-rated twenty-five mathematics lessons contained lessons that were aligned to the
TEKS or Common Core standards and had math problems at all four depth of knowledge levels
to expose students to high mathematics standards. The lessons were error free, easy to use,
94

colorful, aesthetically pleasing, and many of them included the answer key to help teachers grade
their students’ work.
However, as educators, are we only teaching our students mathematics? Is the only
requirement for a high-quality supplemental math curriculum the alignment to standards? In the
previous chapters, it has been presented that there is more to the quality of curriculum than the
adherence to high quality academic standards. Supplemental materials should also provide
appropriate support for learners in relating to their lives and nurturing their learning experience
and development towards becoming independent individuals.
In the previous chapters, the support for learners has been outlined to include the
importance of mathematical discourse where students communicate with peers and adults using
mathematical terminology to represent their ideas and reasoning. Learners need to be encouraged
to solve mathematical problems using multiple solutions or strategies that are meaningful to the
students. Unfortunately, the most popular lessons on TPT seem to be disappointing in this
category, which does not provide complete high quality mathematics lessons to students. Most
lessons found seem to only offer students a cookie-cutter approach to solving math problems and
circling the final answer to be graded by the teacher. There is little to no room for the students to
discuss new strategies or techniques to solve problems amongst each other or their teachers. In
fact, some of the most highly rated lessons provide the students with a set of steps that should be
followed by the students to find the final solution. Providing opportunities for mathematical
discourse allows students to make connections to the concepts and curriculum they are learning,
especially as they discuss and share ideas with peers and adults while using accurate and
meaningful terminology.
In addition to meaningful, purposeful academic discourse, it is also essential for
95

supplemental curriculum to present math lessons in a way that is relevant to the students’ lives
and can help them become independent, informed, and knowledgeable adults who can make
intelligent financial and life decisions. These future life decisions contribute to our community
and to overall social justice. Providing the students with mathematics lessons that they can
identify with will help them realize the importance of what they are learning in school and that if
these concepts are applied to their lives as they grow up, they will live better and more
comfortable lives.

96

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Abstract (if available)

Abstract In this dissertation, I conduct a thorough document analysis of the mathematics curriculum on Teachers Pay Teachers. I developed a grading rubric that is guided by my education expertise, research, and literature review that I conducted. It is important for teachers to have a rubric as a tool to assess the rigor and relevance of the supplemental mathematics curriculum that they plan to use with students in the classroom to address their academic, cultural, and social needs.

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Asset Metadata

Creator Ahmed, Reham (author)

Core Title A document analysis of the math curriculum on teachers pay teachers

School Rossier School of Education

Degree Doctor of Education

Degree Program Educational Leadership (On Line)

Degree Conferral Date 2022-08

Publication Date 08/03/2022

Defense Date 07/15/2022

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

Tag analysis,cultural,cultural relevance,culture,curriculum,diversity,document,Education,Good,high quality,high-quality,lesson plans,lessons,Math,mathematics,OAI-PMH Harvest,relevance,relevant,rubric,Students,supplemental,Teachers,Teachers Pay Teachers,TPT,work sheets,worksheets

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Polikoff, Morgan (committee chair), Riggio, Marsha (committee member), Roach, John (committee member)

Creator Email rehamahmed_2008@yahoo.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC111376112

Unique identifier UC111376112

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Format application/pdf (imt)

Rights Ahmed, Reham

Type texts

Source 20220804-usctheses-batch-969 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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