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Culturally relevant pedagogy in Khan Academy’s Algebra 1 course

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Culturally relevant pedagogy in Khan Academy’s Algebra 1 course

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Content Running Head: CRP in Khan Academy’s Algebra 1

Culturally Relevant Pedagogy in Khan Academy’s Algebra 1 Course

by

Tara-Marie Desruisseaux
Doctoral Candidate

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(URBAN EDUCATION POLICY)

May 2023

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ACKNOWLEDGEMENTS

I am so grateful for all the people in my life who have been instrumental in this journey. Thank
you to my friends, family, committee members, research assistant, and colleagues, I would not
be here without you.

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TABLE OF CONTENTS
ACKNOWLEDGEMENTS ......................................................................................................... II
LIST OF TABLES ........................................................................................................................ V
ABSTRACT ................................................................................................................................. VI
CHAPTER 1: BACKGROUND, PURPOSE, AND OVERVIEW OF STUDY ...................... 1
STATEMENT OF PROBLEM ............................................................................................................ 3
PURPOSE OF THE STUDY ............................................................................................................... 5
SIGNIFICANCE OF THE STUDY ...................................................................................................... 6
KEY CONCEPTS AND DEFINITIONS ............................................................................................... 8
ORGANIZATION OF THE DISSERTATION ...................................................................................... 10
CHAPTER 2: THEORETICAL FRAMEWORK AND LITERATURE REVIEW ............ 11
CRITICAL RACE THEORY ........................................................................................................... 11
Tenets of CRT ....................................................................................................................... 12
CRT as a Lens for Math Education ....................................................................................... 17
CULTURALLY RELEVANT PEDAGOGY ........................................................................................ 18
Academic Success ................................................................................................................. 20
Cultural Competence ............................................................................................................ 21
Socio-Political Critical Consciousness ................................................................................. 23
Culturally Responsive Teaching ........................................................................................... 24
Culturally Sustaining Pedagogy ............................................................................................ 25
Cultural Relevant Pedagogy for Black Students ................................................................... 26
Culturally Relevant Mathematics Pedagogy ......................................................................... 33
Cultural Relevance in Online Learning Spaces .................................................................... 37
BLACK STUDENTS AND MATHEMATICS ..................................................................................... 42
How Culturally Relevant Math Pedagogy Impacts Black Students’ Experiences ............... 45
CHAPTER 3: METHODOLOGY AND METHODS ............................................................. 47
THE RATIONALE FOR THE USE OF MIXED-METHODS ................................................................. 47
Quantitative Inquiry .............................................................................................................. 48
Qualitative Inquiry ................................................................................................................ 48
METHODOLOGICAL APPROACH: MIXED-METHODS CASE STUDY .............................................. 49
SETTING AND CONTEXT ............................................................................................................. 50
DATA COLLECTION PROCEDURES .............................................................................................. 51
CASE SELECTION ....................................................................................................................... 51
DATA ANALYSIS PROCEDURES .................................................................................................. 51
Quantitative Analysis ............................................................................................................ 51
Qualitative Analysis .............................................................................................................. 56
Convergence ......................................................................................................................... 58
TRUSTWORTHINESS .................................................................................................................... 58
Role of the Researcher .......................................................................................................... 58
Research Team ...................................................................................................................... 60
Limitations ............................................................................................................................ 60
CHAPTER 4: RESULTS AND FINDINGS ............................................................................. 61
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RQ 1: HOW DO KHAN ACADEMY’S ALGEBRA 1 VIDEOS SCORE ON THE ONLINE CURRICULAR
RESPONSIVENESS AND RELEVANCE PROTOCOL ......................................................................... 62
RQ 2: HOW, IF AT ALL, DOES KHAN ACADEMY’S ALGEBRA I COURSE UTILIZE CULTURALLY
RELEVANT PEDAGOGY? .............................................................................................................. 63
Theme 1 ................................................................................................................................ 64
Theme 2 ................................................................................................................................ 65
Theme 3 ................................................................................................................................ 69
Theme 4 ................................................................................................................................ 71
RQ 3: HOW, IF AT ALL, DOES KHAN ACADEMY’S ALGEBRA 1 COURSE INCORPORATE BLACK
CULTURE? .................................................................................................................................. 72
Quantitative Analysis ............................................................................................................ 72
Qualitative Analysis .............................................................................................................. 72
Summary ............................................................................................................................... 73
RQ 4: HOW FREQUENTLY DOES EACH UNIT EMPLOY CULTURALLY RELEVANT PEDAGOGY?....... 73
RQ 5: ARE THERE DIFFERENCES IN THE USE OF CULTURALLY RELEVANT PEDAGOGICAL
PRACTICES ACROSS UNITS OR CATEGORIES OF VIDEOS?.............................................................. 79
CHAPTER 5: DISCUSSION/CONCLUSION ......................................................................... 82
SUMMARY OF THE STUDY .......................................................................................................... 82
SUMMARY AND ANALYSIS OF FINDINGS .................................................................................... 83
RQ 1: How do Khan Academy’s Algebra 1 videos score on the Online Curricular
Responsiveness and Relevance Protocol? ............................................................................ 83
RQ 2: How, if at all, does Khan Academy’s Algebra I course utilize culturally relevant
pedagogy? ............................................................................................................................. 86
RQ 3: How, if at all, does Khan Academy’s Algebra 1 course incorporate Black culture? . 88
RQ 4: How frequently does each unit employ culturally relevant pedagogy? ..................... 90
RQ 5: Are there differences in the use of culturally relevant pedagogical practices across
units or categories of videos? ................................................................................................ 90
Implications for Practice ....................................................................................................... 91
Implications for Future Research .......................................................................................... 96
CONCLUSIONS ............................................................................................................................ 98
REFERENCES .......................................................................................................................... 100
APPENDIX A ............................................................................................................................ 111
APPENDIX B ............................................................................................................................ 113

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LIST OF TABLES

Table 1: Instances of Rubric Items in Khan Academy Algebra 1……………………………….61
Table 2: Gender Representations in Khan Academy Algebra I…………………...…………….67
Table 3: Rubric Item Video Scores by Unit………………………………………………….….74
Table 4: Highest Scoring Units by Rubric Item………………………………..…………….….78
Table 5: ANOVA for Video Score and Unit…………………………………...…………….….80
Table 6: ANOVA for Video Score and Type of Vide……………………………….……….….68

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ABSTRACT

While only 21% of K-12 public school students in the United States took even one entirely
online course before the 2019-20 school year, nearly every school district was forced to move
instruction entirely online due to the COVID-19 pandemic. Considering the growth and impact
of online learning, there is a need to understand its integration of culturally relevant pedagogy
(CRP). Researchers have investigated the importance of CRP practices for students of color in
traditional classroom. However, there is a lack of literature on CRP in online learning. Given the
prominence of Khan Academy in online learning, I submit, in this dissertation, a study to
investigate how, if at all, culturally relevant practices are integrated into its platform. I use a
mixed-methods case study approach to analyze the 328 instructional videos that comprise Khan
Academy’s Algebra 1 curriculum. Analyses are done using a rubric that stems from Darling-
Aduana, Good, and Geraghty’s (2020) Online Course Curricular Relevance and Responsivity
Protocol. My analytical and conceptual framework uses critical race theory and culturally
relevant pedagogy as I examine how CRP practices are implemented in math online learning
spaces. I also utilize critical platform studies and culturally responsive computing in examining
the technological components. This study will contribute to the scholarly literature by providing
a framework to assess and understand how online learning can be conducted in a culturally
relevant way. Findings indicate that Khan Academy’s Algebra 1 course addresses some, but not
all, aspects of CRP. The curriculum performs best on rubric items pertaining to requiring
students to apply their learning to issues beyond school (79 instances) and using examples from a
diverse representation of life (68 instances). However, there is a need for improvement in many
other aspects of CRP, most notably regarding the integration of Black culture. Furthermore, I
found differences in how units and categories of videos performed on the rubric.
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CHAPTER 1: BACKGROUND, PURPOSE, AND OVERVIEW OF STUDY

In March 2020, the COVID-19 pandemic prompted a shutdown of schools nationwide.
School leaders and politicians alike were unclear on how to proceed as there was no end date in
sight and they were unaware if the closures would last weeks, months, or the rest of the school
year. In most cases, the pandemic kept students out of their traditional classroom settings for
months, with many school districts not reopening until well into the following school year
(Ferren, 2021). Prior to the shutdown, in the 2017-18 school year, only 21% of K-12 public
schools offered even a single course entirely online (Taie & Goldring, 2020). However, as
schools shut down for public safety purposes, online learning became omnipresent in American
K-12 schools. In fact, almost 100% of school districts had moved instruction online in response
to the pandemic (Goldstein, Popescu & Hannah-Jones, 2020).
The COVID-19 pandemic also generated more interest in the possibilities within online
learning platforms. As students began to fall behind for numerous reasons, online resources that
allowed them to learn at their own pace became necessary. For the online learning-based
nonprofit Khan Academy, usage of the platform skyrocketed from 30 million minutes of learning
a day to a peak of 92 million daily learning minutes, with an average of 75 million minutes
(Anderson, 2020). Student and teacher use of the program increased five to six times the pre-
pandemic amount, far less than the 10 to 20 times increase in parent registration (Anderson,
2020). There was also a doubling in engagement for low-income students (Anderson, 2020). In
response to the increase in usage and, in many cases, reliance on the platform, Khan Academy
created detailed daily schedules for students of all ages to help parents, teachers, and schools
with student learning. As a free and established platform, Khan Academy was well equipped to
supplement learning while schools worked to determine how best to educate their students. Khan
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Academy was lauded for its efforts to bridge learning loss gaps during the pandemic. Amid
COVID-19, Khan Academy was awarded millions of dollars, including funds targeting learning
and educational equity (Amgen, 2020). As engagement soared, students from all over the world
began using the platform more. With this in mind, there is a need to consider the intended
audience that Khan Academy had in mind when developing the curriculum.
Despite a growing number of racially minoritized students in schools, Eurocentric
education has dominated the American education system (Bell, 2019; Bonner, 2009). This is
especially true in mathematics, which has been taught through a lens that centers whiteness
(Battey & Leyva, 2016). Whiteness is an ideology that maintains white supremacy and values
white people over other racial groups (Leonardo, 2004). This results in privilege for white people
and the devaluing and oppression of different racial groups, and serves as a basis for racism.
Thus, it is critical to study how cultural relevancy for racially minoritized populations was
considered in Khan Academy’s math curriculum design. It is essential that the curriculum is
designed with racially minoritized students in mind and that steps are explicitly taken to integrate
their cultures and traditions into the curriculum. This is imperative in traditional in-person
classrooms and should also be carried out in online learning spaces.
Specifically, Black students have been marginalized in most educational spaces, and their
particular needs are often ignored in curriculum development. Little is known about how Black
students’ needs were considered in the development of Khan Academy’s curriculum. However,
what is known about the importance of culturally relevant pedagogy suggests that it should be
present in all learning spaces, regardless of the medium (Schmeichel, 2012). Students from every
racial/ethnic background should see themselves and their lives reflected in learning materials,
and their experiences should be drawn on as they work to learn new material. Black students
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should experience lessons that depict content related to their everyday lives, including their
culture and values, in the design of materials and instruction.
Thus, this dissertation considers how culturally relevant pedagogy is employed in Khan
Academy’s Algebra 1 curriculum. Additionally, I consider how, if at all, culturally relevant
pedagogical practices that center Black students’ cultures and experiences are present in Khan
Academy’s Algebra 1 curriculum. I mainly focus on math because in addition to being one of
Khan Academy’s most prolonged offered courses, it is often viewed as an objective and culture-
devoid subject matter. Furthermore, I highlight Khan Academy’s Algebra 1 curriculum because
algebra is often regarded as a gatekeeper to higher-level mathematics (Muchoko et al., 2019). I
include a statement of the problem addressed in my dissertation, the purpose and significance of
this study, and the definition of critical terms elemental to the study. Lastly, I conclude this
chapter with an overview of the organization of my dissertation.
Statement of Problem
This dissertation focusses on understanding how, if at all, Khan Academy’s Algebra 1
online course incorporates the culture of students from historically marginalized backgrounds.
The study addresses problems at the intersection of online learning, culturally relevant pedagogy,
and Black students’ experiences with mathematics. The issue addressed in this study is that there
is a need to investigate how online learning spaces integrate the culture of Black and other
racially minoritized students.
Current literature on related topics is limited to Black students’ achievement in traditional
math classrooms and often centers the opportunity gap. The opportunity gap is typically
discussed in the context of one group of students, usually grouped by a social marker such as
race/ethnicity, income level, or gender, having different opportunities than another group,
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leading to a statistically significant difference in average scores on a standardized assessment.
Research has demonstrated a considerable opportunity gap between Black and white students in
mathematics wherein Black students have performed at lower levels than white students on
standardized tests. With the discrepancies in many standardized achievement measures, we can
deduce that the current approach used in math classrooms is inadequate for Black students.
While the performance gaps can be thought about as achievement gaps, it is essential to view
them as gaps in opportunity (Flores, 2007) regarding how schooling has been insufficient in
increasing Black students’ performance on standardized tests.
Since 1990, the National Assessment of Education progress (NAEP) has been used to
assess student performance in math and reading in grades 4, 8, and 12 in public and private
schools across the nation. Black-white gaps in math and reading achievement have appeared in
every grade studied. For example, in grade 4, the 2019 average reading scores for white students
were 26 points higher than their Black peers, less than the 28-point gap between Black and white
students in 8
th
grade and the 32-point gap in 12
th
grade (NCES, 2019). In mathematics, in grade
4, the 2017 average math scores for white students were 25 points higher than their Black peers,
33 points higher in grade 8, and 30 points higher in grade 12 (NCES, 2019). Given these
persistent gaps, more research is needed regarding what is occurring in math educational spaces
and what can be done to combat Black students’ diminished experiences. Furthermore, while few
studies exist on Black students’ experiences in math classrooms (Rogers Jr., 2020), the scope has
been limited to traditional classroom settings.
There is a need to expand upon the current literature on the topic and to explore what
Black students’ experiences are like outside of the traditional classroom setting. This is
particularly important given the growth of online learning and the possibility of using it as a tool
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to work toward educational equity. Furthermore, while scholars have considered culturally
relevant pedagogy in traditional classroom settings, most literature has focused on language arts
and social studies. There is a gap in literature pertaining to exploring culturally relevant
pedagogy as it relates to mathematics, particularly because research has suggested that many
view mathematics as an objective subject with little room for implementing culture (Bishop,
1994; Goodman, 1979; Gutiérrez, 2017). There has also been little development on how these
practices can be enacted in online learning spaces.
Purpose of the Study
The current study expands the understanding of the implications of relying upon online
learning platforms such as Khan Academy to disperse education content, particularly regarding
Black students. The COVID-19 pandemic turned a spotlight on the gaps in resources and
educational opportunities that Black students experience daily. It is crucial to understand how
this extends into online learning spaces. The findings of this study establish the extent to which
Khan Academy’s Algebra 1 course can create an environment wherein the cultures of Black
students and other students of color are celebrated and embraced.
Using an in-depth analysis to examine how content is presented in this fully online
instructional platform, I can identify how Black students’ cultures and experiences are integrated,
validated, and celebrated as critical components of the curriculum. Through my research, I build
upon the literature on how culturally relevant pedagogy can be integrated into online learning
spaces to understand its potential to be present and prevalent in all learning spaces.
The primary research questions guiding this study are: RQ 1: How do Khan Academy’s
Algebra 1 videos score on the Online Curricular Responsiveness and Relevance Protocol? RQ 2:
How, if at all, does Khan Academy’s Algebra I course utilize culturally relevant pedagogy? RQ
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3: How, if at all, does Khan Academy’s Algebra 1 course incorporate Black culture? RQ 3b:
How does Khan Academy’s Algebra 1 curriculum perform on the amended rubric items
pertaining to Black culture? RQ 4: How frequently does each unit employ culturally relevant
pedagogy? RQ 5: Are there differences in the use of culturally relevant pedagogical practices
across units or categories of videos?
Significance of the Study
Online learning has been growing rapidly since the turn of the century. Between 2000
and 2010, the number of K-12 U.S. students enrolled in online courses grew from 45,000 to over
1.5 million (Horn & Staker, 2011; Queen & Lewis, 2011). As of 2011, data from the National
Center for Education Statistics indicated that 45% of public schools had students enrolled in
distance education, and 74% of those districts planned to expand distance learning opportunities
(Queen & Lewis, 2011). Furthermore, 30 states offer fully remote learning options for their K-12
students (Watson, Pape, Murin, Gemin & Vashaw, 2014). A 2015 report by the National
Education Policy Center (NEPC) on virtual schooling in the U.S. found that full-time virtual
schools are also increasing in availability and popularity (Huerta, Shafer, Barbour, Miron, &
Gulosino, 2015). Despite the growth of online learning in K-12 schools, little is known about
what constitutes good online pedagogical practices and how culturally relevant pedagogical
practices can be implemented in online learning. Nevertheless, how online courses are taught is
vital because it has the potential to impact the learning of millions of students.
Those who encourage online learning in K-12 spaces have often claimed that it can
provide more equitable learning opportunities by offering access to courses that might not
otherwise be available to specific students and providing personalized learning experiences
(Lawrence, 2017). However, a meta-analysis prepared for the U.S. Department of Education
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found that students who participated in online learning performed only slightly better than
students in traditional in-person courses (Means et al., 2010). Thus, it is essential to consider
which students are more successful with online learning. Generally, the student who succeeds in
online learning is highly motivated and self-directed (Lawrence, 2017). However, as online
education becomes more relied upon to meet educational needs because of global crises and
credit recovery efforts, it is crucial to think about how online learning can be done to maximize
the potential for all students to be successful.
While learning loss has been rightfully criticized for its lack of accuracy and the ability to
come to drastically different conclusions depending on methodology (Reed, Aloe, Park &
Reeger, 2021), there is merit in understanding changes in learning during the shift to online
learning. Using assessment data from Fall 2021, Dorn and colleagues (2020b) found that, on
average, in reading, many students started school just a month and a half behind historical
averages. In mathematics, however, students began school about three months behind where we
would expect them to be. Furthermore, the authors found that students of color were about three
to five months behind in learning, whereas white students were only about one to three months
behind. Even as students began to attend school in-person, Black and Latinx students were more
likely to remain remote and less likely to have devices, internet access, and live contact with
teachers (Dorn et al., 2020b). As we work to close opportunity gaps and provide every student a
chance to excel in schools, understanding how all curricula can be dispersed in a more culturally
appropriate way will be instrumental to reaching that end. It is also imperative to note that while
students may be underperforming on standard academic progress metrics, many learned essential
life skills during this adjustment period.
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A study by Darling-Aduana, Good, and Geraghty (2020) discussed culturally relevant
pedagogy in online spaces. The authors note it is the first study to examine culturally relevant
pedagogy within an asynchronous online learning context. Outside of this study, others that have
investigated the impact of online learning in a general sense overwhelmingly focus on teacher-
directed or facilitated online instruction. Khan Academy’s platform is unique in this aspect
because it is not teacher-directed or facilitated. There is, in fact, no real interaction between the
course instructor and those taking the course. This study is committed to filling these critical
gaps.
Key Concepts and Definitions
The following is a list of key concepts and definitions of terms critical to this dissertation.
Black: I use the term “Black” to refer to individuals of African descent living in the
United States. This term includes Caribbean-Americans.
Culturally relevant pedagogy: I use this term to encapsulate pedagogical practices that
build off students’ knowledge and experiences and integrate content knowledge with students’
development of cultural competence and a socio-politically critical lens. This term was coined by
Ladson- Billings in 1995.
Culturally relevant math pedagogy: This term refers to pedagogy that empowers students
by helping them to develop a deep understanding of math through personal connections with
their experiences and communities.
Culturally responsive teaching: This term, first introduced by Geneva Gay, refers to
teaching in which students’ cultural knowledge, prior experiences, and performance styles are
connected to their academics in a way that legitimizes what they already know.
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Culturally sustaining pedagogy: Introduced by Django Paris in 2012, this term pushes for
teaching and learning to be relevant and responsive to the languages, literacies, and cultural
practices of students in a way that maintains the languages and cultures of racially/ethnically
marginalized groups.
Educational Space: I use the term “educational space” to refer to any setting that serves
as a student’s learning environment. This includes any place where teaching and learning occur.
In the context of online learning, this can consist of online platforms.
Educator: I use this term to refer to anyone who provides instruction or education to a
student. This can include teachers and those who offer content knowledge via online platforms.
Eurocentric: I use the term “Eurocentric” when referring to matters that interpret the
world around European and Anglo-American ideals, values, and experiences (Catarci, 2014).
Online Learning: Online learning refers to delivering instruction and content over the
Internet.
Marginalized: The term “marginalized” refers to “groups excluded due to race, religion,
political or cultural group, age, gender, or financial status” (Cook, 2008).
Remote learning: I use “remote learning” to refer to education whereby the learner and
instructor are not physically present in a traditional classroom environment.
Racism: This term refers to the prejudice, discrimination, marginalization, and oppression
faced by racially minoritized people based on the socially constructed racial hierarchy that
privileges white people.
Sociopolitical consciousness: I use this term to refer to a person’s ability to critically
assess the political, economic, and social forces impacting society and understand their role
(Ladson-Billings, 1995).
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Organization of the Dissertation
Chapter two of this dissertation contains an overview of the literature related to critical
race theory, culturally relevant math pedagogy, and the historical experiences that Black students
have had in math educational spaces. Additionally, chapter two identifies gaps in the literature as
it relates to the experiences of Black students in online math educational spaces. Chapter three of
this dissertation describes the methodology used in this dissertation. An overview of the data
collection and analysis will also be provided. In chapter four, I provide an overview of the
findings that emerged from my data analyses. Lastly, in chapter five, I summarize the study,
present a discussion of the findings, and offer future directions for policy and research.

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CHAPTER 2: THEORETICAL FRAMEWORK AND LITERATURE REVIEW
In this chapter, I provide a synthesis of the literature related to the racialized experiences
of Black students in math classrooms, culturally relevant math pedagogy, and how they should
be considered in online learning spaces. First, I provide an overview of critical race theory
(CRT) and its relevance to understanding the history of racism as it relates to Black students’
experiences in math educational spaces. Second, I discuss culturally relevant pedagogy and how
it has been studied and understood in various areas. More specifically, I present a case for why it
is vital to investigate the culturally relevant nature of Khan Academy’s Algebra 1 curriculum as
it relates to the incorporation of Black culture and the cultures of other historically marginalized
groups. Lastly, I discuss the potential for culturally relevant math pedagogy to improve Black
students’ experiences in math spaces in this online space.
Critical Race Theory
When considering Black students’ experiences in educational spaces, there is a need to
apply a lens that takes into account the role that racism plays in schooling. Ladson-Billings &
Tate (1995) first introduced CRT to the field of education by connecting race and property rights
to analyze educational inequities. They argue for a critical, race-centering theoretical perspective
in education that acknowledges three primary assumptions: 1) race continues to be significant in
the United States, 2) American society is based on property rights rather than human rights, 3)
the intersection of race and property creates an analytical tool for understanding inequity. Some
may refute claims of racial inequities in school by citing that low-income students, regardless of
race, do not do as well as their more affluent counterparts and blame poverty for extant
inequities. However, Ladson-Billings and Tate (1995) contend that institutional and structural
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racism cause the poverty associated with the subjugated condition of many racially minoritized
students’ schools and schooling.
Tenets of CRT
As critical race theory has developed, numerous tenets have emerged to help scholars
understand its primary assertions. DeCruir and Dixson (2004) modified the original theory and
outlined five central tenets of CRT: (a) counter-storytelling, (b) the permanence of racism, (c)
Whiteness as property, (d) interest convergence, and (e) the critique of liberalism.
Counter-storytelling. This tenet of critical race theory recognizes and values the
experiential knowledge of people of color. Counter-storytelling is a method of telling a story to
challenge the validity of accepted premises or myths held by the majority (Delgado & Stefanic,
2001). Dominant groups have often obscured the voices of marginalized people and telling
counter-stories allows the experiences of marginalized groups to be legitimatized and brought to
light. Furthermore, by critiquing notions that may have been normalized, counter-stories can
expose racist false truths that have been passed down. Counter-stories can also counter deficit
storytelling (Solorzano & Yosso, 2002). Amplifying the voices of Black students, for example,
can cultivate a greater understanding and appreciation for their school experiences. An
overwhelming majority of studies that address student experiences in math classrooms do not
consider race's role in learning experiences. Therefore, in my decision to focus specifically on
Black students’ culture in math education spaces, a counter-story is being told that highlights
their unique experiences. Focusing on understanding culturally relevant mathematics pedagogy
as it relates to Black students is an essential step in working toward combatting the factors that
hinder them from gaining an interest in mathematics. The opportunity gap that Black students
experience in math cannot be addressed until it is understood.
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The Permanence of Racism. One of the founders of critical race theory, Derrick Bell,
has argued that racism is a deeply engrained and interminable component of American society
(1992). Thus, in America, white people continue to be privileged over people of color in most
arenas, including education. Critical race theory seeks to make sense of the ties between race and
the allocation of resources (social, political, and economic). Without the ability to deeply
investigate and consider the pervasiveness of racism, the impacts of white supremacy cannot be
thoroughly understood. To work toward an equitable education system with racial justice, it is
crucial to understand that racism is inextricably woven throughout the education system and
permeates into online learning.
Furthermore, Black students must be provided with the tools to navigate and combat a
culture dominated by white supremacy through the development of a sociopolitical
consciousness. This includes understanding systemic racism and the culture of anti-Blackness in
American society. In learning about these critical elements, students can work against the
societal norms that produce inequities (Milner, 2011). Education is inherently political, and
students can challenge disparities when they are provided with the skills to recognize and remedy
societal injustices (Milner, 2011). This is a critical component of culturally relevant pedagogy
and is evaluated throughout my study because education and educators should play a
fundamental role in creating a just and democratic society.
Whiteness as Property. Critical race theory acknowledges that American society is
based on property rights and that America’s history has seen continuous tensions and struggles
over property (Ladson-Billings & Tate, 1995). In education, the importance of property can be
seen in how school systems are funded from a tax base that is partly funded based on property
values, and thus, those who can afford more expensive homes will get access to better schools.
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Harris (1995) contends that the origins of property rights in the United States are rooted in racial
domination and that whiteness falls under the historical definition of property in that it includes
nearly everything to which a person can attach value. For example, she presents the case that
identifying as white has “conferred tangible and economically valuable benefits” and “was
jealously guarded as a valued possession, allowed only to those who met a strict standard of
proof” (1995, p. 280). Harris (1995) sees the right of disposition, the right to use and enjoy, and
the absolute right to exclude as the property functions of whiteness.
This notion has permeated into schooling, and Irvine and Armento (2000) posit that
American schools have disseminated culturally responsive teaching for white students
throughout history, mainly because the values, culture, and practices in schools are heavily
rooted in a Eurocentric worldview and ideology. Thus, the experiences, history, contributions,
and culture of people of color are ignored. The authors argue that the dominant school
curriculum has met the needs of U.S.-born, middle-class, English-speaking white students, which
is why they have historically outperformed other student groups. The performance of Black
students in math that is often discussed in research is partly due to a lack of sustaining
engagement with the curriculum (Howard & Terry, 2011). If math education were a space
wherein Black students felt welcomed and valued, they would likely experience better outcomes.
In working toward culturally relevant mathematics pedagogy, Black students must see aspects of
their culture and everyday lives in the material and instruction. While it may seem apparent, it is
essential to note that whiteness as property is an asset that only white people can possess. Black
students will never be able to possess whiteness and will not be afforded the privileges that
whiteness entails. Thus, Black students in math classrooms experience mathematics differently
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than those who benefit from white privilege, and steps must be taken to integrate Black cultural
aspects into the math curriculum.
Moore (2008) presents an argument for elite law schools serving as white institutional
spaces and offers a robust framework for understanding the necessary components. The four
elements that encompass a white institutional area include the racist exclusion of people of color,
the development of a white frame that organizes the logic of the intuition, the historical
construction of a curricular model based on the thinking of white elites, and the assertion of the
subject as neutral and impartial. Martin (2008) argues that the same principles can be applied to
math and thus designated math as white institutional space. Like the elite law schools discussed
by Moore (2008), math as a field has experienced the racial exclusion of colored people,
promotion of a white framework that organizes math education logic and normalizes white racial
superiority. It includes constructing a curricular model based on the thinking of white elites and
the assertion that mathematics education is politically neutral. For example, Martin considers
how white people have disproportionately been given space to speak on issues related to math
teaching, learning, curriculum, and assessment and how they have dominated positions of power
in research and policy contexts. As a result, mathematics is taught through a lens that centers on
whiteness and the contributions of white people, and achievement is measured based on
Eurocentric ways of knowing and learning. In math classrooms, “Black students learn that White
men created mathematics, and the purpose for learning mathematics is to get a high-paying job in
White institutions” (Davis, 2018, p. 69). There is a need for a shift in mathematics education
wherein Black students learn math in a way that highlights the contributions of Black people and
measures achievement and knowledge in a more inclusive way.
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Martin (2008) also discusses how race has been minimized in math education,
particularly given the “Mathematics for All rhetoric” (p. 393). Within math education and policy
contexts, race is typically only discussed as a categorical variable to disaggregate data and to
rank students in a racial hierarchy of ability, without enough focus on the role and impact of
racism. Moreover, math education policies have been viewed as neutral in producing racial
disparities (Martin, 2008), even though math education is not politically neutral (Gutiérrez,
2009). Many of the racial gaps in mathematics achievement result from policies that failed to
consider the needs of Black students. With math’s positioning as a white institutional space and
given the historical exclusion of people of color from the field, Black students may not see
themselves represented in math spaces. In moving toward a culturally relevant math pedagogy,
the math curriculum should intentionally highlight the contributions and strengths of Black
people, particularly in the math realm. Furthermore, the influences of Black people and the
African Diaspora should be highlighted when providing content about significant contributors to
mathematics.
Interest Convergence. The tenet of interest convergence is informed by the notion that
white people will support racial justice and progress only to the extent that it benefits them (Bell,
1980). For example, although much of the legislation during the civil rights era was presented as
being beneficial for Black people, white people have been the primary beneficiaries. Societal
progress for Black people will only be achieved when the goals of Black people are consistent
with the needs of white people. Hence, it is essential to consider how white people might support
implementing culturally relevant pedagogy to the extent that they believe it benefits them. This
might promote the integration of Black culture and values in the math curriculum if it results in
better overall math performance of students. However, the integration of Black culture is not
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enough. Culturally relevant educators should ensure that the curriculum explicitly addresses
white supremacy and antiblackness.
The Critique of Liberalism. The last central tenet of critical race theory, as per DeCuir and
Dixson (2004), is the critique of liberalism. Liberalism tends to support meritocratic ideals and a
belief that access and achievement are based on one’s worthiness. However, attempting to
understand the performance of Black students in mathematics through an ahistorical and race-
neutral lens would allow for a deficit lens that misplaces the responsibility onto Black students
themselves. It is vital to take systemic racism and structures that disproportionality impact Black
people into account (Bonilla-Silva, 2006).
Furthermore, liberalism, while often well-intentioned, can lead to policies that are race-
evasive and the belief that law and policies are race-neutral. When people can pretend that race
and racism don’t exist, it will enable them to ignore racist policies that perpetuate social inequity.
It also supports the continued existence of systems that reproduce privilege and power for white
people. The consequences of a race-evasive perspective can be seen through the math curriculum
and how it has not considered the needs and culture of Black students. In this study, I work
against this notion by specifically assessing Khan Academy’s consideration of the needs and
culture of Black students. Culturally relevant pedagogy cannot exist without acknowledging
cultural and racial differences. Instead, these differences should be highlighted and leveraged to
provide instruction that helps students make sense of new information.
CRT as a Lens for Math Education
In addition to likely facing racism in their lives, Black students are impacted by racism in
schooling. According to Kivel (2011), “Racism is based on the concept of whiteness…
Whiteness is a constantly shifting boundary separating those entitled to have certain privileges
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from those whose exploitation and vulnerability to violence is justified by their not being white”
(p. 17). Whiteness has been so engrained and normalized in a society that it can be difficult to
discern. Math has been considered a white institutional space (Martin, 2010, 2013) because it
disregards the needs and perspectives of the people who do not align with white ideologies or
ways of knowing and doing math. For example, math content knowledge and certain pedagogical
practices operate similarly to whiteness and can be considered “property” in mathematics (Frank,
2019). When considering racial differences in access to math instruction and coursework, it
becomes clear that access to mathematical knowledge can be viewed as access to intellectual
property. Similarly, math being a white institutional space creates an environment wherein one
racial group is deemed superior, and other racial groups are devalued and subsequently
oppressed (Battey & Leyva, 2016). This can operate as a tool of oppression in math classrooms.
CRT provides a vital lens for understanding many factors that lead to Black students
experiencing difficulty feeling welcomed in math spaces. CRT also informs the methods used in
this study because, as Tate argues, a CRT-informed methodology “should explore the lives,
successes, marginalization, and oppression of people of color both within and outside of the
academy” (1999, p. 268). However, CRT does not fully inform what can be done to combat
Black students' difficulties. Understanding culturally relevant mathematics pedagogy is also
necessary for understanding the shifts needed in math education to garner a more welcoming and
supportive environment for Black students.
Culturally Relevant Pedagogy
Ladson-Billings (1995) coined the term “culturally relevant pedagogy” to refer to a
teaching practice that draws on students’ knowledge, resources, and experiences and helps their
lived experiences become a catalyst for learning. Central to this approach is also assisting the
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students to be academically successful, increasing or maintaining their cultural competence, and
supporting the development of a socio-politically critical lens.
The theory of culturally relevant pedagogy (Ladson-Billings, 1995) came about via a
study of the pedagogical practices of eight exemplary teachers of Black students. The educators
in the study believed that all their students were capable of academic success, saw their
pedagogy as a constantly evolving process, thought teaching was a way to give back to the
community, and saw themselves as community members. Students in the eight classrooms
observed as a part of Ladson-Billings’ (1995) study performed at higher levels than their district
counterparts, and more students in these classrooms were at or above grade level on standardized
achievement tests. Studies have continued to find that teachers who incorporate culturally
relevant pedagogy see positive outcomes with their students. For example, Lee’s (2007) study
found that high school teachers who included cultural references to help Black students identify
and use literary devices to understand their texts improved their English course outcomes.
However, it is essential to note that test scores are not the only important learning outcome to
assess when looking at culturally relevant pedagogy. Some critical results include student
empowerment, knowledge and maintenance of their culture, and understanding of the
sociopolitical nature of society (Milner, 2011).
Culturally relevant pedagogy aims to help students accept and affirm their cultural
identities and challenge the inequities perpetuated in schools. Utilizing CRP is essential because
it helps us understand how teaching can better match the home and community cultures of
students of color and, for this study, Black students. CRP is necessary for students of color
because they are often not part of the white, middle-class mainstream that dominates education,
particularly math. For many Black students, schools are a hostile place where they can feel
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alienated (Hollins, 1994; King, 1994). It is also important that culturally relevant teachers form
caring relationships with their students and know their students’ interests and the information
they relate to. This facet is difficult to accomplish given the framing of Khan Academy’s online
platform.
When employing culturally relevant pedagogy, an educator must achieve three goals
which will be expanded upon below: help students to be academically successful, develop and
maintain cultural competence, and create a socio-politically critical lens. Culturally relevant
pedagogy builds on the premise that learning differs across cultures. Teachers can enhance
students’ success by gaining knowledge of their cultural backgrounds and implementing this
knowledge into their pedagogical practices (Irvine, 2010). In moving toward CRP, educators
must be pushed beyond ideas of diversity and multiculturalism; they must be encouraged to
question the curriculum and the pedagogy (Irvine, 2010).
It is also important to note that employing CRP is not a practice limited to Black teachers
or teachers of color. For example, a white science teacher used culturally relevant pedagogy in
his classroom by building cultural competence in his racially diverse, urban school and
deepening his knowledge and understanding of himself and his practices (Milner, 2011). Like
this science teacher, those who may not identify with a racially minoritized background can still
embody the principles necessary to achieve a culturally relevant classroom once they see
students’ cultures as an asset and not a hindrance to their academic success.
Academic Success
Culturally relevant pedagogy maintains that students must be provided with the necessary
tools to achieve academic proficiency. Ladson-Billings (1995) emphasizes that educators who
employ CRP must believe that all students are capable of academic success and maintain high
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expectations. In working toward the goal of expanding students’ abilities and having them be
participants in society, they must develop their academic skills. Thus, Ladson-Billings (1995)
clarifies that educators should not simply make their students feel good but must attend to their
students’ educational needs and create opportunities for them to experience and showcase
academic success. This is not limited to performance on standardized assessments but includes
students’ abilities to read, write, speak, solve complex problems, engage in peer review of
problem solutions, and more. . In 2006, expanding upon what was meant by the term “academic
success,” Ladson-Billings writes “Rather, what I envisioned is more accurately described as
‘student learning,’ what it is that students actually know and are able to do as a result of the
pedagogical interactions with skilled teachers” (p. 168). This is a great pedagogical practice for
all educators and is of particular importance for marginalized students as research has shown that
factors such as culture, language, background experiences, and country of origin impact learning
styles (Msengi, 2021).
Cultural Competence
Ladson-Billings (2006) defines cultural competence as, “helping students to recognize
and honor their own cultural beliefs and practices while acquiring access to the wider culture,
where they are likely to have a chance of improving their socioeconomic status and making
informed decisions about their lives they wish to lead’’ (p.36). Culturally relevant pedagogy calls
for learning environments where students can preserve their cultural integrity. Employing CRP
requires educators to draw on students’ knowledge, resources, and experiences (Ladson-Billings,
1995). They must use students’ experiences to connect knowledge to their home lives and
communities. Thus, students’ cultures become a catalyst for learning. This can help to bridge
gaps between what students are familiar with and the unknown content. In doing so, students can
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make sense of new concepts and ideas because they can hear their voices and see their
experiences in the curriculum. This often leads to better student experiences and outcomes
(Byrd, 2016).
The underpinnings for a curriculum that centers and affirms the identities of Black
students were first introduced by Woodson (1933), who argued that schooling had caused Black
students to be educated away from their culture and traditions and instead prepared them to begin
the life of a white man:
“When a Negro has finished his education in our schools, then he has been equipped to
begin the life of an Americanized or Europeanized white man, but before he steps from
the threshold of his alma mater he is told by his teachers that he must go back to his own
people from whom he has been estranged by a vision of ideals which in his
disillusionment he will realize that he cannot attain” (p. 5-6).

In response, scholars began looking for alternative schooling methods, including
centering students’ cultures and experiences. Culturally relevant pedagogy builds on this
thinking and works against the discontinuity between students’ home experiences and their
interactions in school. Au and Jordan (1981) discussed the importance of understanding school
learning versus informal learning. They noted that “the context of school learning is often
different from that of informal learning and often unrelated to the child’s culture. Bringing the
relevance of the text to the child’s experience helps the child make sense of the world” (p. 149-
150). Irvine (1990) found that cultural misunderstandings and asynchronization between Black
students and Eurocentric schooling placed Black students at risk of discrimination. Irvine
suggested a need for Afrocentric education and more effective teaching of Black students. The
current schooling system was not working for Black students, and a more culturally relevant
approach was necessary. This can be done through teaching students about the contributions of
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Black people and using content examples from the African Diaspora, both of which are
evaluated in my study.
For one teacher in Ladson-Billings’ (1995) study, cultural competence entailed
connecting their love of poetry with the student's passion for rap music and discussing literal and
figurative meanings. Developing cultural competence can also be done by involving students’
family members in the classroom and using them as resources to provide students with an
opportunity to learn about familiar topics or skills on which the teacher may not have sufficient
knowledge. This stands in contrast to the traditional way of doing schooling. For example, Stiff
and Harvey (1988) found that Black students who attempted to center their experiences and lives
in math learning spaces risked being disregarded by teachers for focusing on extraneous matters.
This can result in students believing that they are not the ideal math learner. Other authors have
also found that Black students have been penalized for integrating their culture and home
experiences to solve math problems instead of using more traditional and Eurocentric methods
(Glaser & Silver, 1994; Tate, 1994).
Socio-Political Critical Consciousness
Educators must encourage cultural competence when employing CRP while helping their
students recognize, understand, and critique current social inequities. Educators should be able to
identify social injustices and their causes. Culturally relevant teachers must also support students
in reforming our society. This lens builds on a notion that Giroux (1983) discussed, who argued
that education should play a fundamental role in creating a just and democratic society. By
proposing the use of an emancipatory pedagogy, students and teachers are invited to critically
analyze political and social issues and the consequences of social inequity. In practice, this can
manifest as educators offering criticism of the knowledge represented in textbooks or curricula
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or criticizing the historical exclusion of diverse perspectives in the ways other topics have been
taught. This can be coupled with teachers introducing supplementary materials that provide
counter-stories.
Teaching through a socio-politically conscious lens requires an understanding that
education is inherently political and offers educators and students the ability to become agents of
change in identifying and remedying societal injustices and inequalities. Culturally relevant
teaching also builds upon the idea of teaching as freedom (Freire, 1998; hooks, 1994). Using this
framework, education is a part of a project of freedom and is eminently political. Teachers
should instruct students on how to think critically and transgress against social inequalities to
achieve the gift of freedom. To realize this, teachers must be aware of themselves as practitioners
and human beings if they wish to teach in a non-threatening and anti-discriminatory way.
Furthermore, this notion insists that educators think critically about the culture of power and are
able to critique the societal norms and values that produce and maintain social inequities. To this
end, Aronson and Laughter (2016) state that critical consciousness “begins with teachers
recognizing sociopolitical issues of race, class, and gender in themselves and understanding the
causes.” This is of particular importance in STEM, as per Johnson and Elliott (2020), because
STEM educators tend to be white men.
Culturally Responsive Teaching
Many scholars have continued to build upon Ladson-Billing’s theory of culturally
relevant pedagogy. Gay (2000) wrote about culturally responsive teaching, when students’
cultural knowledge, prior experiences, and performance styles are connected to their academics
in a way that legitimizes what they already know. It makes the role of culture in teaching and
learning more explicit and calls for teachers to connect with the academic content by building
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from students’ prior knowledge. This is particularly useful for students from marginalized
backgrounds because it engages their different ways of knowing and understanding the
curriculum. It also allows students to connect more with their academic content, which yields
higher interest and enables the material to be learned more easily. The students' histories and
current sociocultural realities are considered when using culturally responsive teaching. Teachers
must have a deep knowledge of the cultural practices and particularities of the various ethnic
groups in their classrooms. These cultural aspects should be incorporated into the school to
reflect the students' communities.
Educators using culturally responsive teaching must consider their biases and develop
new thinking patterns. In their curriculum, they should tackle controversial issues head-on. It is
also essential to become aware of their inaccurate knowledge about different ethnic groups by
acquiring more knowledge. Some of the critical features of culturally responsive teaching
include communicating high expectations, engaging students in learning, and understanding the
assets and lives of students. It also involves sharing control of the classroom as you facilitate
learning, visiting students’ families and communities, and exploring personal and family
histories. While culturally responsive teaching has many affordances, given the scope of this
research project and what is accessible using an online learning platform, it is not a primary
component in developing my theoretical framework.
Culturally Sustaining Pedagogy
Ladson-Billings has also argued for a “remix” of her original theory of culturally relevant
pedagogy into a culturally sustaining approach that allows for a fluid understanding of culture
and explicitly engages with notions of equity and justice (2014). Paris (2012) presented a
theoretical framework that considers the current realities and necessities in education and coined
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the term culturally sustaining pedagogy. One of Paris’ (2012) main reasons for wanting to move
beyond culturally relevant pedagogy is because culturally sustaining pedagogy better embodies
the value of society’s multiethnic and multilingual present and future. Culturally sustaining
pedagogy considers what it means to make “teaching and learning relevant and responsive to the
languages, literacies, and cultural practices of students across categories of difference and
(in)equality” (p. 93). For example, Paris (2012) challenges the idea that culturally relevant
pedagogy in and of itself would ensure the maintenance of the languages and cultures of
racially/ethnically marginalized groups. This shift in thinking to culturally sustaining pedagogy
challenges the deficit approaches that formerly deemed the different languages, literacies, and
cultural ways of knowing that students brought to the classroom as barriers to overcome.
Instead, the linguistic and cultural practices that these students bring with them from their homes
are viewed as culturally rich assets.
Culturally sustaining pedagogy requires that educators engage with a pedagogical
approach that goes further than being relevant or responsive. It pushes educators to consider how
they can support students in “sustaining the cultural and linguistic competence of their
communities while simultaneously offering access to dominant cultural competence” (p. 95).
Supporting multilingualism and multiculturalism is an explicit goal of culturally sustaining
pedagogy and imperative in schooling is challenging to employ and assess through an online
platform.
Cultural Relevant Pedagogy for Black Students
When Ladson-Billings (1995) introduced the theory of culturally relevant pedagogy, she
centered on the pedagogical practices of teachers who worked with Black students. Although the
theory has been expanded and adapted to consider the needs of various racial and ethnic groups,
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it is essential to consider what culturally relevant pedagogy looks like for Black students. Even
though students might holistically benefit from a curriculum inclusive of numerous racial/ethnic
backgrounds, different students would benefit differently. What is essential, however, is that the
curriculum encourages students to view their racial/ethnic group positively.
When scholars have written about culturally relevant teaching, they have considered the
integration of multiple cultural backgrounds and emphasized contributions from minoritized
groups on a general level. However, there is a need to delve more deeply into what it means to be
a culturally relevant teacher of Black students. Howard (2001) examined the impact of culturally
relevant pedagogy amongst elementary school teachers who worked with Black students, and
three pedagogical themes emerged. These included (a) holistic instructional strategies, in which
teachers were not exclusively concerned with students’ academic development but also their
social, emotional, and moral growth, (b) culturally consistent communicative competencies,
which required the understanding or use of discourse patterns and vocabulary that was consistent
with modes of communication in students’ home lives, and (c) skill-building strategies to
promote academic success which entailed helping students understand the what, when, how and
why of academic tasks and believing that all students are capable of learning. With a caring
attitude and classroom environments that reflected students’ home lives and engaged them in
their learning, students' levels of engagement and achievement improved. Educators who wish to
use culturally relevant pedagogy to better the educational experiences of Black students should
be familiar with Black cultural values and norms and allow this to influence their practice.
In addition to having a profound conception of Black culture, culturally relevant
pedagogy for Black students must include discussions about systemic racism and anti-blackness
and how they impact students’ lives. By virtue of living in America, Black students have been
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imbued with the beliefs and values of white culture. This can lead to Black students developing
internalized negative Black stereotypes. Black culture should also be included in the design of
materials and instruction. Students should be exposed to the contributions and strengths of Black
people and the various cultures that encompass the African Diaspora.
Making Systemic Racism Explicit. A key component of culturally relevant practices is
that students should develop a sociopolitical consciousness that enables them to critique societal
norms that produce social inequities. Included is understanding the centrality of race and
systemic racism in American history. Systemic racism refers to how racial oppression is
embedded across all major institutions in the United States, primarily rooted in the fact that it is
the only major Western country explicitly founded on racial oppression (Feagin, 2013). Feagin
(2013) argues that today, as it has been historically, systemic racism is made up of a range of
white-racist dimensions that include: the racist ideology, attitudes, emotions, habits, actions, and
institutions of white people in this society. Learning about systemic racism is crucial because it
paves the way for students to seek out opportunities to explore aspects of their history and
culture to become anchored in a positive sense of racial identity eventually.
Brown, Brown, and Ward (2017) argue that educators who wish to use culturally relevant
pedagogy must engage the structures and systems that enabled specific dominant U.S. histories.
Thus, it becomes essential to teach students about racism, anti-blackness, and the culture of
power, all of which are evaluated in this study. Black students must be aware of the culture of
anti-Blackness permeating American culture. Anti-blackness refers to racism directed at Black
people to strip Blackness of value and marginalize Black people (Ossom-Williamson et al.,
2021). This is important to highlight because historically marginalized groups have distinct lived
experiences, and students must be aware of anti-Black racism.
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Furthermore, teaching Black students about the impact of anti-Black racism can lead
them to seek opportunities to explore aspects of their history and culture. This often allows them
to become anchored in a positive sense of racial identity (Cross, 1971). It is also important to
note that while some might consider the potential for stereotype-threat to be activated through
discussions on systemic racism and anti-blackness, Dee and Penner (2017) suggest that
forewarning about stereotypes, values affirmation and an external attribution for experiencing
challenges can serve as stereotype threat buffers, and closely parallel the essential elements of
CRP.
In a traditional classroom setting, making systemic racism explicit can be carried out by
teaching students about the experiences of groups that have been historically marginalized in
society. Students can also learn about how non-Eurocentric mathematical knowledge has been
suppressed. This could be incorporated into Khan Academy’s Algebra 1 course when the
overview and history of algebra are presented. This principle could also be implemented by
being intentional about the example problems used. For example, when teaching students about
linear equations that start at different points (y-intercept) or increase at differing rates (slope),
real-world examples that depict racial inequality and systemic racism can be used.
Including Black Culture in the Curriculum. Incorporating Black culture into a
curriculum requires understanding Black culture and traditions and the knowledge that Black
culture is not monolithic but consists of many subcultures. Tillman (2002) defines culture as “a
group’s individual and collective ways of thinking, believing, and knowing, which includes their
shared experiences, consciousness, skills, values, forms of expression, social intuitions, and
behaviors” (p.4). In addition to being a culture, Black is also a race. While culture is not only
about race, “race is a central dimension of culture, and for some racial and ethnic groups, race is
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the most salient feature of their cultural identity” (Milner, 2017, p. 5). Thus, it is crucial to
understand how culture encompasses racial/ethnic identity and can influence how we behave and
think. It is also imperative to comprehend that while race is socially constructed, cultural aspects
of racial difference are essential to acknowledge. In taking on a cultural constructionist view of
race, participation in distinctive ways of life is a unifying force for Black people (Jeffers, 2019).
As argued by Jeffers, there is a need to consider how cultural differences between students
impact how they experience and interact with the curriculum. Black students come from a racial
group that is comprised of a diversity of ethnic backgrounds and traditions. However, what
unites Black people in America is a shared history of slavery and other systems of
discrimination, oppression, and racism that has led to resilience.
To teach Black students in a culturally appropriate way, educators must have an in-depth
understanding of Black students’ cultural backgrounds in terms of their shared histories and
within-race cultural variation. Boykin (1994) offers nine dimensions of Black culture that
represent the cultural strengths educators should seek to employ when teaching Black students.
These dimensions comprise spirituality, harmony, movement, verve, affect, communalism,
expressive individualism, oral tradition, and social perspective. Spirituality is “an approach to
life as being essentially vitalistic rather than mechanistic, with the conviction that nonmaterial
forces influence people’s everyday lives” (Swindler Boutte & Hill, 2006). Thus, a belief that
forces greater than humans exist in the world and allows for the development of faith and hope.
Harmony builds on the idea that one is linked to their surroundings. It also refers to an ability to
read an environment and nonverbal behaviors well. Thus, students who feel unwelcome in their
classes may become less interested in learning. Movement refers to many Black students being
tactile and kinesthetic learners who prefer learning experiences incorporating movement, rhythm,
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percussion, music, and dance. Verve deals with an inclination for high levels of stimulation and
classroom activities that are energetic and lively. Affect refers to emphasizing emotions, being
emotionally expressive, and being sensitive toward emotional cues. Communalism refers to how
people are interrelated and committed to social connectedness. Black students may value
learning in groups, particularly with students who share their culture, as opposed to being in
classrooms that emphasize individualism and competition. Moore (2005) argues that
communalism and harmony may explain why many eligible Black students choose not to be in
gifted programs because they recognize that such programs are primarily comprised of white
students and express fear and concerns about alienation and isolation. Expressive individualism
stems from the idea that Black people have a propensity for a spontaneous expression of self that
is less about being correct or efficient and more rooted in personal style. Oral tradition is based
on a preference for oral modes of communication. Lastly, social time perspective represents an
orientation in which time is viewed in terms of significant events to be engaged in as opposed to
being based on clocks or appointments.
In a traditional classroom setting, incorporating these dimensions can be accomplished by
integrating high levels of stimulation through energetic classroom activities. While this is not
easily accomplished in online learning, primarily through a self-guided platform such as Khan
Academy, other aspects such as incorporating rhythm, percussion, and music into instructional
videos are much more feasible. This can present in myriad ways, including using fractional
music note beat measures or using music in helping to commit mathematical concepts to memory
Highlighting the Contributions and Strengths of Black People. One of the core
principles of culturally relevant pedagogy is that it helps students to recognize and honor their
own cultural beliefs and practices. As educators build on students’ lived experiences and use
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their cultures as catalysts for learning, the contributions and strengths of Black people should be
highlighted. This should include referencing famous Black mathematicians and their
contributions. . For example, when teaching about time, students can be introduced to Benjamin
Banneker, a Black man who created the first American clock.
Additionally, word problems can cite feats that Black people have accomplished.
Students must be aware of the person’s race either because they are well-known or stated. As an
example: In 1965, Wendell Scott, the first Black driver in NASCAR, earned $20,000. This was
approximately six times more than what he made in 1961. Write an equation to calculate how
much money he earned in 1961. Ladson-Billings (1992) argues that this representation is vital
for Black students because of the “constant and repeated denigration of both African and African
Americans … both in and outside of the classroom (p. 387). In highlighting the contributions and
strengths of Black people, Black students will have readily available examples that counter the
negative portrayals of Black people they may see in society.
Using Examples from the African Diaspora. As students learn to recognize and honor
their own cultural beliefs and practices and how they are relevant to their learning spaces, it is
also vital that examples incorporate the multiple cultural backgrounds that encompass the
African Diaspora. The African Diaspora refers to the multitude of communities to which people
of African descent have been dispersed due to voluntary and involuntary movement. This group
includes, but is not limited to, African-American, Caribbean, Afro-Latinx, and African people. In
honoring the knowledge that has emerged from the African Diaspora, students will be able to
counter the Eurocentric lens that has permeated the curriculum of American schools and
understand the impact and innovation that has been present in Black culture. As with
highlighting the contributions of Black people, these counternarratives are necessary to counter
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the dominant ideology regarding the intellectual ability of Black people (Perry, Steele, &
Hilliard, 2003). Boutte (2002) argues that the lack of Black perspectives and stories in school
literature allows students to hold onto misconceptions, stereotypes, and discrimination,
undermining the importance of Black views. In English courses, teachers can incorporate this by
selecting texts written about or through the lens of Black people from various ethnic
backgrounds. In math, this can manifest as students studying the mathematical patterns of
African art to understand symmetry or geometry.
Culturally Relevant Mathematics Pedagogy
A culturally relevant pedagogical approach is vital in mathematics education because its
present structure is based on pillars that have a foundation in Eurocentrism (Anderson, 1990).
These include the belief that mathematical results must conform to the style devised by Greek
people over 2,000 years ago and the acceptance that mathematical discoveries only take place
after a rigorous application of deductive logic, also rooted in Greek traditions (Anderson, 1900;
Powell & Frankenstein, 1997). Many scholars have contributed to conceptualizing what
culturally relevant mathematics pedagogy could and should be. While Stanic (1991) did not use
the language of culturally relevant mathematics, they argued that we must question the very
epistemological foundations of mathematics if we want to move toward equity. The framework
presented in their work explored the relationship between inequality and the school mathematics
curriculum. Furthermore, they believed mathematics education should prepare citizens to engage
in social action. Tate (1995) built on Stanic’s work and argued that Black students “should be
encouraged to use mathematics as an agent to change their out-of-school realities” (p. 169).
Tate (1995) introduces the idea of culturally relevant math pedagogy as an approach that
contrasts with the typical mathematics pedagogy wherein teachers describe a technique to solve a
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problem, and students are expected to listen to the lecture and work alone on textbook problems.
Using a culturally relevant approach, math teachers who work with Black students must
understand the relationship that Black students have historically had with mathematics and use
that to shape how they navigate teaching. By understanding their students’ backgrounds and
mathematical needs, they can foster an environment that allows for a positive relationship
between mathematics and Black students to develop in a way that affirms their identities.
Furthermore, Tate (1995) suggests that culturally relevant math pedagogy helps Black students
become prepared to use math as a tool to rectify the democratic complexities of the United
States. This builds off on Tate’s (1994) notion that math teachers should provide pedagogy that
“builds and expands on the thinking and experiences of African American students and that
focuses on preparing these students to function within our democracy” (p. 477). Tate argues that
connecting math to the lives and experiences of Black students enables them to take part in our
democracy, which is imperative because of the significant role that mathematics literacy plays
within the “democratic system of governance” (p. 482).
Tate (1994) also argues that failing to provide Black students with math curriculum,
instruction, and assessments centered around their experiences and cultures is a significant
obstacle to achieving equitable math education. He gives an example of Black students
“incorrectly” answering a district-wide test question that asked them; if it was more beneficial
for someone going to work to buy a weekly bus pass for $16 or pay per ride if each ride costs
$1.50 because the test makers failed to consider that students may not all have a notion of people
working five days a week, that an employee would only have one job, or that only one family
member could use the weekly pass. Because these were not assumptions consistent with the daily
lives and realities of these Black students, they essentially answered that it would be a better
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option to buy a weekly pass. With a culturally relevant pedagogical approach, the perspectives
and experiences of Black students would have been considered, and district test makers would
have been forced to consider their assumptions. For educators of Black students, culturally
relevant math pedagogy allows for Black students to be placed in the center of the curriculum.
Educators who want to use culturally relevant math pedagogy must be aware of Black children's
problems in education and society.
Using existent theories and research on culturally relevant and responsive practices,
Townsend (2016) proposes five elements of culturally relevant mathematics pedagogy that can
be used in math classrooms to work toward equity for historically marginalized students. These
include: “using students’ culture within the pedagogy, using instructional decisions based on
socio-constructivism, developing caring relationships with students and between students,
developing personal responsibility for both teacher and student, and taking a critical or social
justice perspective” (p. 39). The social constructivist approach ensures that students’ knowledge
is constructed through dialogue and active engagement so that the mathematical knowledge
grows out of the community. Moreover, under this framework, students’ cultural backgrounds
and experiences should be the foundational building blocks for academic content. This allows
students to develop positive attitudes, increase motivation, gain a sense of competence in their
abilities, and achieve self-efficacy. For example, Civil and Khan (2001) investigated teachers
who achieved success when they became aware of students’ home experiences with planting
gardens and built from that knowledge to develop essential math concepts in the classroom, such
as measuring and area.
Townsend (2016) also delves into how educators can work against normative frames and
instead use a culturally relevant mathematics pedagogical approach by teaching in a way that
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resonates with students based on their cultural backgrounds. For example, rather than choosing a
word problem about the incline of a ski slope when working with students who may not have had
the lived experience of skiing, word problems can be constructed around students’ experiences
and things they have experienced. Involving examples and real-world situations that are relevant
and familiar to students and connecting math concepts to their own lives and experiences is a
pivotal component of culturally relevant math pedagogy. This could be done by using real data
from local or familiar businesses to help student understand certain mathematical concepts such
as statistics, percentages, and budgeting. In analyzing a high school math department that was
able to get Black students to pursue high levels of math, Gutiérrez (2000) found that the
department was successful because it provided students with opportunities to bring their culture
into the classroom.
Culturally relevant math pedagogy is an approach that aims to bridge the cultural gap that
is present in math education spaces by incorporating the cultural backgrounds, experiences, and
perspectives of students into the curriculum. This approach acknowledges that students bring
their cultures, experiences, and identities to the classroom and seeks to make connections
between their lived experiences and the math concepts being taught. For example, when teaching
students about concepts related to money or finances, teachers might ask their students to solve a
problem related to how they would budget their allowance. In doing so, students would be able
to see the practical applications of math in their daily lives. culturally relevant math pedagogy
makes math more accessible, meaningful, and engaging for all students, with a particular impact
on those from historically marginalized backgrounds.
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Cultural Relevance in Online Learning Spaces
A 2015 National Educational Policy Center report on educational equity asserted that
policymakers must promote culturally relevant curriculum and allow students to experience
“culturally responsive teaching to have equal opportunity” (Rice, 2015, p. 5). The opportunity to
experience culturally relevant teaching should be available for all students, including those who
elect to online learning opportunities. Research on culturally relevant instruction in online spaces
has found that it is rooted in frequent and ongoing dialogue and communication between students
and teachers (Lawrence, 2020). In a study of full-time online high school teachers who practiced
culturally responsive online pedagogy, Lawrence (2020) found that the teachers used multiple
strategies to get to know their students, their students’ cultures, and their learning needs and
preferences. However, culturally relevant pedagogy typically necessitates using instructional
practices and strategies that are difficult to implement in asynchronous online courses, such as
building relationships and having students feel cared for. Because employing culturally relevant
pedagogy in asynchronous online spaces presents challenges, it must be done intentionally. This
is particularly important for online courses that enroll students from historically marginalized
groups because research suggests that the declines in learning that occur in high school students
enrolled in asynchronous learning environments are disproportionately experienced by students
from historically marginalized groups (Ahn & McEachin, 2017).
There is also a need to evaluate online learning platforms through a critical lens,
particularly as we seek to understand how they are embedded within a society that is not exterior
to the platform itself. Decuypere and Landri (2021) argue that platforms need to be researched
and assessed for the ways that they perform and “substantiate a specific sort of world for the
ones who make use of the platform” (p. 4). They note that platforms perform specific
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operations, convey particular messages, decide what to draw in or out, and make choices about
what can appear and how the material is organized. With this in mind, many have used a critical
platform gaze to analyze digital platforms. According to Decuypere, Grimaldi, and Landri
(2021), this gaze is an analytical stance that rejects the notion that platforms are neutral but
instead views them as tools that are “constitutive of, as well as constituted by, active socio-
technical assemblages that are in the process of significantly transforming the educational sector”
(p. 2). A critical platform lens is essential when studying the role of race and culture in digital
platforms. As the reach of online learning expands, it is vital to consider how online learning
platforms can be leveraged as an opportunity to better the educational experience and outcomes
of all students, particularly those from historically marginalized backgrounds. Furthermore, it is
imperative to critique platforms that exclude the cultures of historically marginalized people.
Online learning platforms can and should be leveraged as a tool for educational equity to benefit
students who have not thrived in traditional classroom settings
There are few studies on the instructional and pedagogical strategies that can promote
students’ success in online education, particularly for Black students. Finkelstein et al. (2013)
found that students had tremendous success using web-based technology that used a culturally
relevant dialect, suggesting that incorporating culturally relevant practices can lead to more
significant achievement for more students. To reach this goal, however, course instructors and
developers must be culturally competent themselves and be able to teach in a culturally
appropriate way. This is particularly important for Black students because research demonstrates
that they excel when materials are taught in a culturally appropriate way (McKinley, 2010;
Howard & Terry Sr., 2011). Implementing culturally relevant pedagogy in the classroom is
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essential in combatting the opportunity gap between Black and white students. This gap is a
byproduct of deficiencies in our society, including our current educational system.
Very little research has been conducted on culturally relevant online learning. However,
given the changing demographics of online learning spaces, we must evaluate online platforms
and understand how they differ in their ability to facilitate good pedagogical practices, including
culturally relevant teaching. Darling-Aduana, Good, and Geraghty (2020) conducted the first
study of its kind that examined culturally relevant pedagogy within an asynchronous online
learning context in an urban emergent school district in the Midwest. The authors aimed to
establish the extent to which their sampled online courses perpetuated privilege by reinforcing
the culture of power. They consider the culture of power to include ideas, attitudes, and activities
that are regarded as conventional and are most often aligned with the practice of social groups in
power. They examine two research questions: 1. What is the nature of cultural responsiveness
and relevance in online courses, and precisely the extent to which they perpetuate, acknowledge,
and disrupt the culture of power? 2. Where are the places where cultural responsiveness and
relevance are and could be better integrated into asynchronous online courses?
Using mixed-methods, the authors analyzed four widely used online high school courses
and assessed the degree to which they were culturally relevant and responsive. Considering a
lack of existing research tools to evaluate online courses for cultural relevance, the authors
developed the Online Curricular Responsiveness and Relevance Protocol based on previous
rubrics to evaluate culturally relevant pedagogy. While developing their rubric, they were sure to
exclude elements of culturally relevant pedagogy that an online course could never facilitate.
Their rubric was divided into three categories: curricular content, instructional tasks, and
assessment strategies. Evaluating the curricular content included items like; what was taught,
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such as assessing the presence of content examples from multiple cultural backgrounds, using
examples taken from a diverse representation of everyday life, making the culture of power
explicit, countering dominant narratives of white, male authority, and power. When evaluating
instructional tasks, the authors looked at: how content was taught, whether the module used a
variety of teaching methods, integrated students’ interests to make the learning process meaning
for them, prioritized depth over breadth, and if the module incorporated tasks that required
students to apply their learning to an issue, context, or problem beyond school. Lastly, analyzing
the assessment strategies entailed: looking at how students demonstrated understanding-- if
student learning was assessed using various types of assessments, if students’ readiness,
strengths, weaknesses, and developmental needs were assessed if linguistically and culturally
diverse content was integrated, and if assessments adapted to students’ level of understanding.
This protocol encompasses many integral aspects of culturally relevant pedagogy and is a
foundational tool in my evaluation of culturally relevant pedagogy in Khan Academy’s Algebra
1 course.
The findings of the study suggest that there are barriers to culturally relevant pedagogy
embedded into the very structure of standardized, asynchronous online learning platforms such
as Khan Academy and the platform analyzed in their study. After evaluating the online high
school courses, the authors found that normative values, perspectives, and visual representations
were identified in many courses at varying degrees for each subject matter. Using a definition
inspired by Apple (2018), Darling-Aduana and colleagues (2021) define normative as “ideas,
attitudes and activities that appear conventual due to their alignment with cultural norms” (p. 9).
These values were present in 49 percent of citizenship lessons, 35 percent of Algebra 1 lessons,
21 percent of ELA 9 lessons, and 17 percent of physical science lessons. Furthermore, the most
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prevalent theme that emerged was a failure to challenge dominant cultural narratives in course
content, including ignoring the experiences of individuals other than white men. The authors also
found that the online lessons reflected a culture of power, perpetuated neoliberal ideologies, and
emphasized normative cultural narratives. For example, when discussing budget deficits,
economic crises, wars, and random events were addressed without acknowledging human or
corporate culpability.
Gender and the Culture of Power in Online Learning. Hanson (2002) proposes that
there is a need to investigate the gendered and racialized nature of online learning because most
technologists and technology developers are white males. Culturally responsive computing
(Scott et al., 2015) offers a lens to help understand the relationship between technology and
historically marginalized groups (racially minoritized people and women). Specifically, the goals
of the theory are framed in relation to understanding the persistent gap in historically
marginalized groups’ opportunities to enter disciplines that involve technology. Drawing from
the theory of culturally responsive teaching, the authors argue that “digital technology and
technology education can reflect, and encourage reflection on, learners’ complex and
intersectional” culture (p. 3). Similar to critical race theory, there are five central tenets to
culturally responsive computing: 1. All students are capable of digital innovation. 2. The learning
context supports transformational use of technology. 3. Learning about one’s self along various
intersecting sociocultural lines allows for technical innovation. 4. Technology should be a
vehicle by which students reflect and demonstrate understanding of their intersectional identities.
5. Barometers for technological success should consider who creates, for whom, and to what
ends rather than who endures socially and culturally irrelevant curriculum. The lens offered by
culturally relevant computing insists that technology-based learning environments to be
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constructed in a way that nurtures participants’ identities. This is an imperative perspective when
assessing Khan Academy’s Algebra 1 course for the extent to which it incorporates and
celebrates the experiences of people from historically marginalized backgrounds. Furthermore,
culturally relevant computing calls for discourse about students’ identities and a consideration of
intersectionality to comprehend different students’ experiences in digital spaces.
Black Students and Mathematics
Mathematical literacy has served as a gatekeeper to educational and economic
opportunities. Mathematics is considered a high-status field of knowledge, and mathematical
proficiency has been politicized and is typically instrumentalized in ways that convert its high
status into a privileged indicator (Larnell, 2019). The racial hierarchy of mathematics
achievement (Martin, 2009) positions those who identify as Black, Latinx, and Native American
at the bottom, with systems of white privilege helping to maintain this hierarchy. Math has been
used to sort, stratify, and judge students along racial/ethnic lines more so than any school subject
(Martin, 2012). With this in mind, teaching mathematics is not politically neutral (Gutiérrez,
2009) and needs further investigation.
Many researchers have empirically explored the opportunity gap for Black students in
mathematics (Flores, 2007; Johnson-Ahorlu, 2012; Kotok, 2017). Given the disparities between
Black students and their white and Asian counterparts, it is essential to consider what factors
may contribute to these findings and what can be done to counteract the gap. Doing so has
important implications for the economic mobility and other future outcomes of Black students.
Moses and Cobb (2002) argue that mathematics became a civil rights battleground because
financial access and full citizenship in today’s society depend crucially on math literacy,
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As it currently stands, mathematics learning encompasses cultural ways of participating
in mathematical activities that privilege Eurocentric ways of knowing and being in math
classrooms (Nasir, Hand & Taylor, 2008). Martin (2006) proposes that being both Black and a
doer of math requires resistance for many. Making sense of the relationship Black students have
with math should not be based on the correlation between achievement in the subject and their
attitudes towards it (Di Martino & Zan, 2010; Rech, 1994; Thompson & Davis, 2013). Instead,
steps should be taken to improve the experiences that Black students have while in their learning
environments.
The dominant narrative about Black students in mathematics is that they perform at low
levels in class and on standardized tests. Martin (2012) notes that mathematics education policy
reports dating back 25 years explicitly labeled Black children as mathematically illiterate.
Narratives such as these may suggest that Black students are to blame for their low performance.
However, more consideration should be given to the fact that race is a significant factor in
determining inequity in math settings, schools, and society for Black students (Ladson-Billings
& Tate, 1995). While constructing their math identities, Black students in math classrooms must
negotiate historically rooted narratives about mathematics related to a constriction of
opportunities to learn math because of racism and racial stratification (Nasir et al., 2008). In an
attempt to acquire mathematical literacy, Black students’ identities can influence their
mathematics learning. Martin (2006) argues that the same life experience of Black people
“makes it difficult to maintain a positive identity in the pursuit of mathematics knowledge” (p.
157). With this in mind, it is essential to remember that schools, teachers, and educational spaces
can transmit and reproduce social and racial hierarchies within classrooms and schools
(Condron, 2007; Hallinan, 2001).
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When considering the performance of Black students in mathematics, researchers have
suggested that it is partly a result of a contrast in cultural norms and beliefs between Black
students and their primarily white female teachers (Porter, 1997; Corey & Bower, 2005). Stiff
and Harvey (1988) present evidence that Black students who were as successful in mathematics
as their white classmates in kindergarten are not as successful by age nine, citing a failure in
formal mathematics instruction. Bonner (2009) suggests that Black students have performed
below their potential in math because of cultural dichotomies in American classrooms and
schools that mirror Eurocentric norms. This includes inconsistencies in schools versus home
culture and can be seen in how learning is assessed and how information is acquired. Bonner
(2009) notes that these inconsistencies can be overcome by educators having vast funds of
knowledge about their pedagogical content, their students’ lives, cultures, and interests,
employing familiar patterns of interaction, and building relationships that allow for the
development of trust. Furthermore, Bonner offers strategies including referring to metaphors and
family ties when presenting material, using chants and call-response techniques, integrating
rhythms, dance, and music, and employing warm demander pedagogy (Ware, 2006). When an
educator employs warm demander pedagogy they are able to establish a caring relationship with
their students, and communicate warmth while simultaneously holding them to a high
performance standard
Corey and Bower (2005) consider how social and cultural divides occur in online
learning through web-based environments. Their case study compared the learning experience of
a Black male Algebra 1 student within an online learning environment and in a traditional
mathematics classroom. Their findings revealed that the online classroom gave the student
access to information that facilitated his understanding of algebra at a pace and in an
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environment more supportive of his learning style. This study suggests that online learning has
the potential to be an effective solution to bettering the math learning experiences for Black
students.
How Culturally Relevant Math Pedagogy Impacts Black Students’ Experiences
Since the cultures of racially minoritized children are often misunderstood, ignored,
denigrated, or discounted in schools, Black people are likely to experience cultural alienation and
discontinuity in schools, even as teachers. This lack of belonging is particularly prevalent in
mathematics since, throughout American history, mathematics education has been designed,
developed, and delivered within a Eurocentric philosophy. According to Anderson (1990),
today's dominant mathematics curriculum has been set upon Western Eurocentric ideals and does
not engage or promote relevance for Black students. Proper mathematical knowledge can only
flourish if educators break away from the Eurocentric perspective and the current ineffective
pedagogical and curricular traditions. For example, some have looked to ethnomathematics,
which aims to highlight non-Western cultures' contributions to the field of mathematics
(Gutiérrez & Irving, 2012). By embracing this philosophy, one can understand that the world has
diverse mathematical practices and that one way of doing math should not be prioritized simply
because it has Eurocentric roots.
The importance of representation and visibility can also be found in subjects outside of
math. Researchers have discussed the need for Black students to see themselves in literature
(Cai, 2002; Sciurba, 2014). Gray (2009) examined fifth-grade students’ responses to the
literature that their teachers selected and found that students wanted literature that had realistic
plots and book covers and that included characters that were similar to themselves and their
families. Brooks (2006) also studied Black students’ responses to literary depictions of
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themselves. He noted a need to consider cultural complexity in understanding that even within
the same racial group, what was relevant for one student may not be suitable for another.
In part, culturally relevant mathematics pedagogy is vital because of its ability to help
Black students feel a sense of belonging in a space they have historically felt excluded.
Simultaneously, critical race theory (CRT) is necessary for understanding how racism prevails in
learning spaces and how schooling can maintain and support the racial hierarchy. This theoretical
lens can help us understand why Black students may find it particularly difficult to feel
welcomed in math spaces due to racism and racial bias.

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CHAPTER 3: METHODOLOGY AND METHODS
In the previous chapters, I discuss how critical race theory and culturally relevant
pedagogy are helpful tools in analyzing the content of Khan Academy’s Algebra 1 course. This
chapter provides details of the research methods used for data collection and analysis to examine
the culturally relevant nature of Khan Academy’s Algebra 1 course. In this chapter, I first
provide a rationale for using mixed methods. Next, I describe my methodological approach.
Then, I offer my procedure for data collection and analysis. Lastly, I conclude by discussing the
researcher's limitations and role.
The Rationale for the Use of Mixed-Methods
Mixed-methods research can be described as: “research in which the investigator collects
and analyzes data, integrates the findings, and draws inferences using both qualitative and
quantitative approaches or methods in a single study or program of inquiry” (Tashakkori &
Creswell, 2007, p. 4). A mixed-methods approach allows for an in-depth understanding of how
culturally relevant pedagogy is used in Khan Academy’s Algebra 1 curriculum to develop an
overall picture of how it is used across lessons. Using solely quantitative or qualitative methods
would not create a complete idea of what is occurring throughout the course, as it would not
allow me to understand patterns and trends across units.
There are myriad study designs that one can employ when conducting mixed-methods
research. I use a triangulation mixed-methods design in which my qualitative and quantitative
data and results inform my interpretation. This allowed me to gather complementary data on the
same topic to understand the research problem at hand fully. With the triangulation design, I
utilized a convergence model. In this model, I collect and analyze quantitative and qualitative
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data separately and then converge the specific results into one set of findings (Creswell, Piano
Clark, Gutmann & Hanson, 2003).
Quantitative Inquiry
Quantitative inquiry is an approach that seeks to numerically represent observations to
describe and explain the phenomena that those observations reflect (Sukamolson, 2007).
Quantitative methods generally establish relationships among variables that can be measured and
analyzed using statistical procedures. In this study, quantitative analyses use descriptive statistics
to calculate which of the units and types of videos often integrated culturally relevant
pedagogical practices. Quantitative methods address the following research questions:
RQ 1: How do Khan Academy’s Algebra 1 videos score on the Online Curricular
Responsiveness and Relevance Protocol?
RQ 3b. How does Khan Academy’s Algebra 1 curriculum perform on the amended
rubric items pertaining to Black culture?
RQ 4: How frequently does each unit employ culturally relevant pedagogy?
RQ 5: Are there differences in the use of culturally relevant pedagogical practices across
units or categories of videos?
Qualitative Inquiry
Using qualitative methods allows researchers to delve deeply into the complexities of the
subject matter at hand and discover nuances that may be overlooked only by quantitative
analysis. This helps achieve my goal of examining the culturally relevant nature of Khan
Academy’s Algebra 1 course because qualitative methods allow me to explore aspects of Khan
Academy’s Algebra 1 curriculum that quantitative approaches cannot articulate. Furthermore,
given the qualitative nature of the videos being used as data, qualitative research equips me to
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capture meaningful insights into what pedagogical tools are enacted. One of the values of
qualitative research lies in the description and themes developed in the context of a specific site
(Creswell, 2009). Thus, rather than generalizability, qualitative research is based on
particularities.
Qualitative inquiry is well-suited for answering “how” and “what” questions (Creswell,
2007). Qualitative methods are instrumental in addressing the following research questions:
RQ 2. How, if at all, does Khan Academy’s Algebra 1 course utilize culturally relevant
pedagogy?
RQ 3. How, if at all, does Khan Academy’s Algebra 1 course incorporate Black culture?
Methodological Approach: Mixed-Methods Case Study
In this study, I use a mixed-methods case study approach. A case study seeks to
understand a phenomenon within its context and is particularly useful in eliciting phenomena in
specific situations. Further, case studies are designed to fit the needs of the case and research
questions. According to Stake (1995), case study research draws on “naturalistic, holistic,
ethnographic, phenomenological, and biographic research methods” and provides a level of
flexibility that is not offered by other qualitative approaches such as grounded theory or
phenomenology. A mixed-methods case study design is one in which quantitative and qualitative
data are collected, and the results are integrated and used to provide evidence for a case or
develop cases for comparative analysis (Creswell & Clark, 2018).
A case study is defined by the interest in a case rather than the method of inquiry used.
Case study research can be conducted as an analysis of a single case or collective cases. This
study uses Khan Academy’s Algebra 1 course as a single case. Case study methodologists strive
to highlight a particular phenomenon by learning as much as possible about the particulars of
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their case, and cases are carefully selected for how they are likely to reveal the phenomenon of
interest (Stake, 2005). One of the most critical components of a case study is bounding, meaning
there needs to be cohesive, explicit connections between each part of the case study. In this
study, the pedagogical practices I am assessing are bound by being made available on the Khan
Academy platform. It is also bounded by the unit of study, the Algebra 1 curriculum.
Setting and Context
Khan Academy was founded in 2007 as a non-profit organization that aims to provide
free, world-class education anywhere. Khan Academy is a free online program with thousands of
instructional videos, exercises, and quizzes covering numerous subjects. It began with videos on
math, science, and economics and now has expanded to offer courses in the arts and humanities,
reading, language arts, computing, and test prep. One of the aspects that makes Khan Academy
unique is that students can learn at their own pace without any actual correspondence with an
instructor.
The Khan Academy instructional videos began with Salman Khan posting them on
YouTube to help his cousins with their math homework. His cousins found success and ease
because they could pause and rewind the videos until they fully understood the concepts. The
videos were available publicly, and soon, Khan’s audience grew. Due to the nature of how the
videos began, the voice of Salman Khan narrates each one. When watching a video, students see
a blackboard as Khan works through different problems. On average, the videos are about 10
minutes long (Khan & Slavitt, 2013).
Each math course is broken down into units, and each unit has a sub-unit that has a subset
of videos. After each sub-unit, students can take a quiz made up of practice problems. At the end
of the unit, there is a unit assessment. It is important to note that students can take the course at
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their own pace, which includes skipping through videos, watching videos out of order, and
progressing through the course without passing any assessments. The Algebra 1 curriculum has
328 videos across 15 different units. This study analyzed all Algebra 1 course videos published
before October 2021.
Data Collection Procedures
The first data collection phase required downloading the Khan Academy Algebra 1
videos. This required using Loom, a video and screen recording software. Once the videos were
recorded and downloaded, they were imported into Nvivo for analysis. Additionally, the
transcripts for each video were uploaded to Nvivo for coding.
Case Selection
Algebra is often considered one of the most fundamental math courses for students.
Kaput (1999) argues that: “algebraic reasoning in its many forms, and the use of algebraic
representations … are among the most powerful intellectual tools that our civilization has
developed. Without symbolic algebra, there could be no higher mathematics and no quantitative
science; hence no technology and modern life as we know them” (p. 134). The fundamental
principles of algebra run throughout all of mathematics, making it a foundational course for
higher levels of mathematics. Thus, Khan Academy’s Algebra 1 course serves as a great
representation of its math curriculum as a whole.
Data Analysis Procedures
Quantitative Analysis
The primary tool used for this study's quantitative components is a protocol (Appendix
A) adopted from the Online Course Curricular Relevance and Responsivity Protocol developed
by Darling-Aduana, Good, and Geraghty (2020). The usage of this protocol complements the
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qualitative data collected to add further the understanding that answers the research questions
proposed. The protocol assesses cultural relevance and responsiveness in online or digital
courses. When using the protocol, observers are asked to rate the frequency at which they
observe crucial elements within a module. It is important to note that the protocol does not
differentiate gradated performance levels, but rather, provides a checklist for items that coders
count for instances of in each video. I used this protocol to address the following quantitative
research questions:
RQ 1: How do Khan Academy’s Algebra 1 videos score on the Online Curricular
Responsiveness and Relevance Protocol?
RQ 3b: How does Khan Academy’s Algebra 1 curriculum perform on the amended
rubric items pertaining to Black culture?
RQ 4: How frequently does each unit employ culturally relevant pedagogy?
RQ 5: Are there differences in the use of culturally relevant pedagogical practices across
units or categories of videos?
The original protocol is divided into three components: Curricular Content, Instructional
Tasks, and Assessment Strategies. Although it exists explicitly only to include elements that
could be facilitated by the structure of an online course, the portion of the protocol dedicated to
Assessment Strategies was excluded because of the standardized nature of Khan Academy
assessments. This element of the protocol assesses if modules assess student learning using
elements such as self-assessment and if the assessments are adapted for students’ levels of
understanding. Because all students who complete a unit receive the same assessment, there is no
differentiation in assessments and no opportunity for self-assessment. Furthermore, an
Instructional Tasks item was excluded because it merely measured good pedagogy as opposed to
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culturally relevant pedagogy. This item reads: The module uses a variety of teaching methods
(i.e., visual and auditory elements of a lecture, guided practice, student-directed investigation) to
help meet the needs of all students.
Due to a lack of existing research tools designed to assess online courses for cultural
relevance for Black students, supplemental codes are used that center on Black culture. Rooted in
the literature on culturally relevant pedagogy, these include codes relating to whether systematic
racism is made explicit; whether the module consists of elements of Boykin’s nine dimensions of
Black culture in the design of materials and instruction; whether the contributions and strengths
of Black people are highlighted, and lastly if the module uses content examples from the cultures
that comprise the African Diaspora. Again, this methodological technique was employed to
highlight the role of my theoretical framework in this research project.
An extensive literature search was conducted to determine what rubric items should be
added to evaluate culturally relevant pedagogy as it relates to Black culture. Culturally relevant
pedagogy is rooted in three goals: helping students to be academically successful, developing
and maintaining cultural competence, and creating a socio-politically critical lens. Researchers
have argued that culturally relevant pedagogy should include a critical analysis of race and
racism (Brown-Jeffy & Cooper, 2011). In an effort to recognize the lived experiences of Black
students, and to prepare them to challenge the social injustices that impact them, they must be
able to recognize, understand, and critique these societal issues. Thus, the first rubric item in the
amended rubric pertains to whether systemic racism is made explicit. This item targets the goal
of creating a socio-politically critical lens wherein students are given the tools to challenge the
inequities perpetuated in society.
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When evaluating the extent to which Khan Academy’s Algebra 1 course centers Black
culture, it was important to incorporate a well-established framework regarding the topic. Boykin
(1994) offers nine dimensions of Black culture that represent the cultural strengths educators
should seek to incorporate when teaching Black students. In evaluating modules for their
inclusion of elements of Boykin’s nine dimensions of Black culture, Khan Academy’s Algebra 1
course is evaluated for the extent to which it creates a learning environment that allows Black
students to preserve their cultural integrity. Also at the core of culturally relevant pedagogy is a
need for students to accept and affirm their cultural identities. This builds off of the notion of
cultural competence, wherein students are encouraged to recognize and celebrate their cultures. It
is critical that Khan Academy’s Algebra 1 videos are evaluated for their incorporation of Black
culture. To this end, two different rubric items were added: one to assess if the module
highlighted the contributions and strengths of Black people, and the other to evaluate if the
module used content examples from the cultures that encompass the African Diaspora.
I appended the four aforementioned items because they target critical elements of
culturally relevant pedagogy related to Black students within the context of Khan Academy’s
Algebra 1 course. As students develop sociopolitical consciousness that enables them to critique
societal norms that produce social inequities, they must understand the history and impact of
systemic racism. Furthermore, another core principle of culturally relevant pedagogy is that it
equips them to recognize and honor their own cultural beliefs and practices, which will have
long-lasting effects on how they live their lives. To reach that end, it is imperative that their
culture is appropriately incorporated into the curriculum and done in a way that celebrates and
highlights the influence and impact of Black people and Black culture.
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Data analysis was conducted with the help of a research assistant. Using the rubric, each
video was evaluated twice, once by me and once by a research assistant. To ensure consistency
between members of the researcher team, we established coding guidelines through training
sessions that involved talking through each item on the rubric in depth and going over a coding
manual (Appendix B). After the training session, we coded one video together and discussed any
discrepancies in depth, identifying how these could be resolved. We then coded the remaining
videos in Unit 1 and went through each discrepancy until there was a consensus. Before sorting
through discrepancies and settling on the final scores, there was >80% agreement with ratings.
For Unit 2, we individually coded each video with > 90% agreement and rectified any
discrepancies so that there was 100% agreement. The research team continued to evaluate every
video for each unit on their own, with weekly meetings to discuss any ambiguities and determine
a video’s final score. Each week, agreement among the research team was >90% before
reviewing discrepancies. After all discrepancies were sorted by referring back to the manual and
establishing whether the proposed example met the criterion, we established a count for how
often each item occurs in each video. We used an Excel document to keep track of quantitative
coding.
After each video's analysis was completed, we calculated a count for the number of
instances per rubric item. We also established a unit score for the total number of rubric points
per unit. Using the number of videos per unit, the unit video score was divided by the number of
videos to determine the average score for each video in the unit. I also performed two Analysis
of Variance Analysis (ANOVA) tests. The first one was to evaluate if there were differences
between the video scores of each unit. With this test, the unit number is viewed as a categorical
variable, wherein I evaluated differences between units without regard for the unit sequence. The
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second ANOVA test was run to see if there were differences between the video scores of the
three categories of videos: History of Algebra, Example Problem, and Instructional Videos.
Lastly, given the small number of videos in the History of Algebra category, and the higher than
average scores for these videos, a t-test was conducted to establish if there were differences in
the video scores of Example Problems and Instructional Videos.
Qualitative Analysis
To conduct the qualitative analyses for this study, 328 video transcripts corresponding to
the 328 videos in Khan Academy’s Algebra I curriculum were uploaded to NVivo. The codes
that emerged from the qualitative analysis process were used to answer the following research
questions:
RQ 2. How, if at all, does Khan Academy’s Algebra 1 course utilize culturally relevant
pedagogy?
RQ 3. How, if at all, does Khan Academy’s Algebra 1 course incorporate Black culture?
In step one of the data analysis stage, I watched each video alongside its corresponding
transcript to ensure accuracy. I took notes about what was occurring in each video, particularly
for elements that may not be apparent through the transcripts such as the gender of the guest
speakers. I also noted elements that I should continue to watch for and make a note of in future
videos and began to generate a coding scheme that would be used for the coding of the video
transcripts. Some of the codes that were developed at this stage included “mention of
mathematician,” “mention of country,” “history of algebra,” and “real-world example.”
However, a vast majority of the coding for the transcripts was done inductively, allowing
theories to emerge from the data itself.
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For each transcript, descriptive codes, which use a word or short phrase to summarize the
topic of a passage of qualitative data (Saldaña, 2013), were used. These codes served as the
foundation of my qualitative inquiry and assisted me in understanding the observations in each
video. Thematic codes were also used to identify what a data unit represents or means. DeSantis
and Ugarriza (2000) state that a theme is “an abstract entity that brings meaning and identity to a
recurrent experience and its variant manifestations. A theme captures and unifies the nature or
basis of the experience into a meaningful whole” (p. 362). In the last watch of the video, I
conducted a second cycle of coding to “develop a sense of categorical, thematic, conceptual, and
theoretical organization” using the constructed descriptive and thematic codes.
As codes emerged, I kept them in a codebook with content descriptions and brief data
examples for reference. Attribute coding (Saldaña, 2013) was also used for logging essential
information about each video, including basic descriptive information. This includes coding
whether videos were purely instructional or contained an example problem, the video's length,
and the video's unit. Additionally, I created analytic memos by documenting my thought process
and lessons learned during the analysis of each video. Memos are an analytical tool that can be
used through the coding process to assist with the formation of codes and categories. According
to Saldaña (2013), these memos allow one to reflect on their coding processes, code choices, and
emergent patterns, categories, and themes. My analytic memos allowed me to reflect critically on
the analyzed data and informed further stages of the analysis by highlighting the process taken.
Furthermore, these analytic memos contained data regarding strategies that either perpetuated,
addressed, or countered antiblackness, reinforcing and aligning with my theoretical framing of
critical race theory. They were used in conjunction with my codes to understand how, if at all,
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the course is using culturally relevant pedagogy, with specific attention paid to the incorporation
of Black culture.
Convergence
Together, the quantitative and qualitative analyses helped form a complete picture of
what was happening in Khan Academy’s Algebra 1 course regarding cultural relevance. The
qualitative data provided holistic information on the entire course as it relates to culturally
relevant pedagogy and the incorporation of Black culture. The quantitative data helped establish
if specific units better meet these needs than others and provided insight into whether certain
types of videos better integrate culturally relevant pedagogical practices.
Trustworthiness
The trustworthiness of this project’s methods is asserted in many ways. First, combining
both qualitative and quantitative analysis reinforces these findings, as using only one type of
analysis may have overlooked essential findings. Further, within each methodology utilized,
techniques were employed to ensure the highest quality of research. For example, qualitative
techniques such as watching and coding each video multiple times acted as a way to ensure data
collected from videos was done so in the proper ways. For the quantitative analysis, we used a
protocol that had been established through previous research.. Furthermore, the use of a research
assistant to double code each video contributed to the trustworthiness by reducing rater error.
Together, these methodological approaches support an intensive, rigorous process that produces
trusthworthy results.
Role of the Researcher
Studies suffer when researchers do not investigate their role or assumptions about the conduct of
research and how knowledge is developed (Kezar, 2004). Researchers must understand their views and
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beliefs concerning the research process because paying attention to positionality is vital to undertake
ethical research (Sultana, 2007). Researchers cannot detach and distance themselves from the research
process completely. As researchers exist on the planet, they develop views and identities that influence
how they understand the world. Researchers cannot be value-free because one’s values always impact
the research process. My lived experiences as a Black woman and former math teacher are integral to
my research study. My background impacts the research questions I ask, how I go about conducting
research, and what I choose to pay attention to. My identities and experiences also influence my
understanding of culturally relevant pedagogy, particularly regarding Black culture.
In my research, I take a pragmatic approach, which does not require one to adhere to a single
philosophical position about the nature and reality of knowledge. Instead, it calls for researchers to take
a realistic view when attempting to problem solve and link theory and practice through the research
process (Savin-Baden & Major, 2013). I believe that the best way to conduct research is to be well-
versed in the topic and the methods that researchers have used to study it in the past and then identify the
best approach based on the individual research project’s circumstances. Pragmatic research allows for a
combination of techniques best determined by what the researcher concludes is most appropriate. This
can call for a mixed-methods approach where theory can be used deductively, as in quantitative research
or inductively, as found in qualitative research (Creswell, 2009). Pragmatists also reject the positivist
notion that researchers can access the ‘truth’ about the world by virtue of a single scientific method but
also disagree with the constructivist/interpretivist belief that it is possible to determine social reality as
constructed (Kirunja & Kiyii, 2017). Reality is constantly being renegotiated, debated, and interpreted
in different ways, causing the best available approaches to research to be different depending on the
time, place, and space. Likewise, what one considers truth depends on the social and temporal context,
and it is impossible to always access ‘truth’ under a single method.
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In my research, it is crucial to consider the social, historical and political contexts of a research
problem and the methods researchers have used to address it in the past. As a pragmatic researcher, I am
invested in using approaches that best meet my needs and purposes. The choices made in this study are
based on my experiences; thus, what I choose as the best and most appropriate approach may not be the
same as what someone else would find most suitable. For this reason, there is no objective truth. A valid
answer will depend on the question and how it is being asked.
Research Team
A two-person team has conducted the research in this study. The other research team member
was a 2
nd
year Ph.D. student in Urban Education Policy and a former math teacher.
Limitations
This study only examined one online course focused on one subject matter hosted on one online
learning platform, which limits its generalizability to other online courses, subjects, and platforms.
Although Khan Academy is well known and widely used, additional research is needed to document the
curriculum and instruction provided by their other online courses as well as courses provided by other
platforms in different subjects. Furthermore, because the study only samples Algebra 1, the findings do
not preclude the possibility of more culturally relevant Khan Academy math courses.
Additionally, while I attempted to interrogate my role as a researcher, the process and findings
that came from such a process were influenced by my lived experiences and perspectives, which may
have led to different approaches than other researchers would have embraced.

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CHAPTER 4: RESULTS AND FINDINGS
This chapter discusses the results and findings of the present study in detail. These results
were obtained via the mixed-methods approach described in the previous chapter. This study was
designed to investigate how online learning spaces incorporate culturally relevant pedagogy and
integrate Black culture, as this represents a significant gap in the present literature. While
substantial research has focused on the opportunity gap affecting Black students, there has been
little attention paid to how this manifests in the context of an online education setting. The
specific purpose of the current study was to better understand the implications of relying upon
online learning platforms such as Khan Academy to disperse education content.
Quantitative methods were used to address the following research questions:
RQ 1: How do Khan Academy’s Algebra 1 videos score on the Online Curricular
Responsiveness and Relevance Protocol?
RQ 3b: How does Khan Academy’s Algebra 1 curriculum perform on the amended
rubric items pertaining to Black culture?
RQ 4: How frequently does each unit employ culturally relevant pedagogy?
RQ 5: Are there differences in the use of culturally relevant pedagogical practices across
units or categories of videos?
Qualitative methods were used to address the following research questions:
RQ 2. How, if at all, does Khan Academy’s Algebra 1 course utilize culturally relevant
pedagogy?
RQ 3. How, if at all, does Khan Academy’s Algebra 1 course incorporate Black culture?
This chapter will be structured concerning these research questions, and the findings will
be presented accordingly.
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RQ 1: How do Khan Academy’s Algebra 1 videos score on the Online Curricular
Responsiveness and Relevance Protocol
While there are many methods to assess culturally relevant pedagogy, a previously
established 12-point rubric for culturally relevant pedagogy was chosen as a framework for the
study (Darling-Aduana et al., 2020). As a first determination of how Khan Academy’s Algebra I
course utilizes culturally relevant pedagogy, each of the 328 videos in the Khan Academy
Algebra I curriculum was evaluated for each instance in which a video used one of the 12 rubric
points. Each occurrence of a rubric point was given a score of 1. There was no limit to how many
times a video could score for a single rubric point. The video scores for each rubric point were
then tallied (Table 1).
Table 1
Instances of Rubric items in Khan Academy Algebra 1.

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For example, Rubric Item 11: The module incorporates tasks that require students to
apply their learning to an issue, context, or problem beyond school, had a score of 79, which
means that across the 328 videos in the curriculum, this rubric item came up 79 times.. Videos
that were scored for this item included lessons that integrated real-world problems such as Video
06.36 which states: “As a birthday gift, Zoey gave her niece an electronic piggy bank that
displays the total amount of money in the bank as well as the total number of coins. After
depositing some number of nickels and quarters only, the display reads: Money: $2.00 Number
of coins: 16. How many nickels and quarters did Zoey put in the bank?
Other rubric points did not fare as well, as some categories had scores of zero. These
categories were: Rubric Item 5: The module provides students with the academic knowledge and
skills needed to function in the culture of power, Rubric Item 6: The culture of power is made
explicit, Rubric Item 8: The module acknowledges current socio-political realities versus
essentializing a culture or group of people, and Rubric Item 9: The module uses the interests of
students to make the learning process meaningful for them.
RQ 2: How, if at all, does Khan Academy’s Algebra I course utilize culturally relevant
pedagogy?
To address this research question, 328 video transcripts corresponding to the 328 videos
in Khan Academy’s Algebra I curriculum were uploaded to NVivo. The transcripts were then
coded for aspects of culturally relevant pedagogy related to race, the culture of power, cultural
identities, and drawing from students’ lived experiences. This provided a detailed description of
the addition of culture to the Algebra I curriculum. The findings are presented through four
significant themes: (1) the presentation of a version of algebra’s history based solely on
European and Middle Eastern contributions (2) the centering of white men as great minds (3) a
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need to make more use of real-world examples that incorporate students’ cultures and
experiences, and (4) missed opportunities to make the culture of power explicit and counter the
dominant narrative of white, male authority and power.
Theme 1
The first significant finding of this research question is that Khan Academy’s Algebra 1
course presents a version of algebra’s history based solely on European and Middle Eastern
contributions. In Unit 1, when teaching about the origins of algebra, Khan is able to use his use
his knowledge of Urdu and Hindi to help translate the title of a book that translates to:
Compendious Book on Calculation by Completion and Balancing. The book was written by al-
Khwarizmi, a Persian mathematician living in Baghdad in 820 AD. According to Khan, the book
is “the first time that algebra … took on many of its modern ideas” including “ideas of balancing
an equation” (Video 01:01). He also states that the word algebra comes from the Arabic term al-
gabr, which means restoration or completion and discusses the Arabic language and its influence
on algebra (Video 01:01).
In addition to the influence of Persians and Arabic on algebra, Khan continues to provide
a more in-depth history of the subject, where he discounts the contributions of mathematicians
from other regions who may have shown evidence of algebra use. According to Khan,
“So the first traces, and I’m skipping out, and really, it’s just what we can find. I’m sure
if we were able to dig more, we might be able to find other evidence of different
civilizations and different people stumbling on many of the ideas in Algebra; but our first
records of people really exploring the ideas that are hit upon in Algebra come from
ancient Babylon around 2000 years before the common era, before Christ” (Video 01:01).
He discusses the tablets that were found “where it looks like people were exploring some of the
fundamental ideas of algebra.” Khan further discusses the Babylonian region and the influence it
had on algebra by stating,
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“And that was, once again, in this part of the world. Babylon was right about there. And
Babylon, it’s kind of kept the tradition of Sumeria. The whole region was called
Mesopotamia, Greek for between two rivers. But that’s the first traces of people that we
know of that were starting to do what we would call real, real algebra.”
In this overview provided by Khan, it is very clear that he views the Mesopotamia region as
being very important in the history of algebra. In addition to neglecting to mention countries in
other regions that may have had “traces of people” who were conducting algebra, he also
devalues the algebra being performed by people in other parts of the world by insinuating it was
not “real algebra.”
Khan also contributes to presenting a history of algebra based solely on European and
Middle Eastern contributions by crediting mathematicians and philosophers from those regions
with being founders of algebra. For instance, in considering who the “father of algebra” is, Khan
references the Greek scholar called Diophantus and Persian mathematician al-Khwarizmi. He
states: “Diophanus, and he is sometimes credited with being the father of algebra, and it’s
debatable, whether it’s Diophantus or al-Khwarizmi.” (Video 01:01). He provides a brief
overview of both of their contributions to algebra and reminds viewers that while they both “did
contribute in their own way,” “both of them were kind of beat to the punch by the Babylonians.”
In summary, Khan Academy’s Algebra 1 course provides viewers with a skewed
understanding of the history of algebra. In Video 01:01, which provides an overview of the
origins of algebra, Khan presents the history in a way that highlights the contributions of
European and Middle Eastern mathematicians. Additionally, he neglects and devalues the
contributions made by mathematicians from other regions.
Theme 2
The second significant theme pertains to the centering of white men as great minds.
Throughout the curriculum, white men are continually referred to as ‘great minds.’ Early on in
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Video 01:01, Khan credits Diophantus (Greek) and al-Khwarizmi (Persian) with being the
fathers of Algebra. Later in the course, Video 01:03 begins with a quote by Galileo Galilei,
whom Khan refers to as “one of the greatest minds in human history,” as he displays a picture of
Galilei. In Video 01:04, Khan begins by showing a picture of Rene Descartes and introduces him
as “one of the great minds in both math and philosophy.” He then states that viewers should
begin to see “a little bit of a trend here, that the great philosophers were also great
mathematicians and vice versa” (Video 01:04). Khan then discusses the vast contributions
Galileo and Descartes were able to have in their short lives and cements their importance in
viewers minds by stating, “it makes you realize that these great minds, these pillars of
philosophy and mathematics, at the end of the day, they really were just human beings” (Video
01:04). Khan proceeds and refers to Descartes as being responsible for the strong connection
between geometry and algebra. At this point, it is important to note that every contributor
introduced by Khan was non-Black, and the greatest minds and contributors were white. This is
particularly important because in a later video, Video 01:18, students are told to try to “think of
yourself as some type of ancient philosopher/mathematician.” With most of the examples of the
great mathematicians and philosophers being white men, namely, Diophantus, al-Khwarizmi,
Galilei, and Descartes, and a brief mention of Brahmagupta, there is little room for non-white
and non-men to be able to really see themselves as an ancient mathematician or philosopher.
Furthermore, given the emphasis on white men in the curriculum, and the consideration
for intersectionality as per the culturally relevant computing framework, coding was done to
examine the presence of different genders throughout the curriculum. To this end, the video
transcripts were coded for any mention of gender and categorized into five classes:
mathematician (men), mathematician (women), men, women, and gender-neutral. Gender was
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assessed through the presence of the pronouns he/his and she/her for men and women genders,
respectively. Names mentioned in the videos that were overtly belonging to a man or woman
were coded as such. However, some names could have been classified as either belonging to a
man or a woman and were coded as gender neutral. Gender neutral was also coded when a type
of person, such as a banker, was referenced without mentioning a particular gender. Table 2
shows the results of this gender analysis.
Table 2
Gender Representations in Khan Academy Algebra I

The Khan Academy transcripts were assessed for whether there were contributions of
both men and women mathematicians mentioned in the course. The results indicate that six men
mathematicians and zero women mathematicians were mentioned. These results negate the
notion that the curriculum counters the dominant narrative of white, male authority and power
because no contributions of women to the field of mathematics were discussed in any of the 328
videos. Moreover, of the six mathematicians mentioned, five were white men, including
Diophantus (Video 01.01), al-Khwarizmi (Persia, Video 01.01), Galileo Galilei (Videos 01.03
and 01.04), Rene Descartes (01.04), and Euclid (Video 01.04). The other mathematician
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mentioned was Brahmagupta (India, Video 01.01). These data suggest that, concerning its
treatment of the history of mathematics, the module does not counter the dominant narrative of
white male authority and power. Rather, these data indicate that the Algebra I curriculum focuses
heavily on men mathematicians.
One way to counter the dominant narrative of white male authority and power is to
ensure that women and gender-neutral individuals are included in the curriculum. As shown in
Table 2, the curriculum mentions men 47 times, women 31 times, and gender-neutral individuals
15 times. These data suggest that men are featured more explicitly than women or gender-neutral
individuals. Representative examples of the 47 mentions of men include, “Mr. Theisen is honing
his deadly three-point precision on the basketball court” (Video 08:32) and “We’re told that
Adam flew his remote-controlled drone off a platform.” Representative examples of the 31
mentions of women include, “We’re told Lauren uses a blend of dark roast beans and light roast
beans to make coffee at her cafe” (Video 06.07), “Jada is ordering Mother’s Day gifts online
(Video 08.26) and “Seo-Yun hosted a party. She had 50 party favors to give away” (Video
09.16). Finally, there were examples of gender-neutral names and types of people that could not
be assigned either gender category. This included some instances of professions, including a
nurse (Video 03.09), a doctor (Video 03.09), factory workers (Video 06.32), and general mention
of adults (Videos 06.11) and children (Videos 06.11 and 06.14). One name, Taylor (Video
14.41), was included as gender-neutral.
In summary, the Khan Academy Algebra I curriculum does not appear to favor all
genders equally, as it is primarily male dominant. In particular, there were six men
mathematicians discussed and zero women mathematicians. Similarly, in examples, there were
47 mentions of men, but only 31 mentions of women and 15 mentions of gender-neutral
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individuals. In conjunction with the results from the examination of culture, these data conclude
that the curriculum focuses on a white male culture of authority and power.
Theme 3
A third significant finding was that there is a need to use real-world examples that
incorporate students’ cultures and experiences. There are numerous opportunities in the videos
where Khan Academy could choose to use more real-world examples incorporating students’
cultures and lived experiences. An example of this is when Khan is introducing the concept of
combining like terms. In this video, Video 01:11, Khan combines two Chuck Norris photos with
three Chuck Norris photos to show that it equates to five Chuck Norris photos. Khan had the
world at his disposal in terms of possibilities for introducing the concept of how to combine like
terms and he chose to use an image of a white man. Using Chuck Norris is arguably outdated
considering the target audience of Khan Academy and the average age for students taking
Algebra 1. Thus, one could argue that Chuck Norris is not culturally relevant. It is also important
to note that while it is not necessarily common knowledge to everyone, Chuck Norris was quoted
making comments that many deemed racist when he warned of “1,000 years of darkness” if
former President Barack Obama got re-elected. In the subsequent video, Khan mentions that he
had “gotten feedback that all the Chuck Norris imagery in the last video might have been a little
bit too overwhelming” and that he will “include something a little bit more soothing” (Video
01:12). In this instance, he had an opportunity to choose a more culturally relevant public figure,
or to find another way to incorporate cultural relevancy, however, he resorted to using images of
polar bears.
Another example is in Video 03:04, which teaches about how to calculate volume using
the example of a backyard wading pool. Although Khan does define what a wading pool is, this
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is not something that will be familiar or relevant to many students. There are numerous other 3-
dimensional objects that students are familiar with that could have served as a basis for learning
how to calculate volume. In the same unit, Video 03:07 provides an example problem that takes
place in a toy factory that sells toys at $10, makes 25 toys and has 40 workers. This is another
missed opportunity where Khan could have chosen a concept more familiar and relevant to
students lives.
In addition to problems that rely upon concepts that many students cannot relate to or are
unfamiliar with, Khan also misses opportunities to build upon students’ prior knowledge. For
example, Video 04:11 teaches students about the slope of a horizontal line. There is a missed
opportunity to lean on students’ knowledge of horizontal lines and allow them to draw
connections to their lived experiences. For example, Khan could have discussed how looking at
the sunrise over the horizon is an example of a horizontal line. This could have help students
retain the concept or gain a better understanding of the topic.
Notably, there are some instances where Khan uses appropriate examples incorporating
students’ cultures and lived experiences. For instance, Khan uses an example of himself working
at a restaurant and earning $10/hour to introduce the concept of a variable (Video 01:06). This
example captures the real-life experiences of students because many students can relate to the
concept of working and making $10 per hour. Other instances of great usage of real-world
examples are Video 01:03, where Khan introduces the formula for the price of any object with a
discount while using the example of a 30% off sale on a $20 pair of pants and Video 02:16
which discusses the total fare of riding a subway.
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In summary, while there are some real-world examples used throughout the curriculum,
there are many missed opportunities where Khan could have incorporated the cultures and lived
experiences of students to make material more relatable.
Theme 4
The last significant theme was missed opportunities to make the culture of power explicit
and counter the dominant narrative of white male authority and power. Salman Khan should
have extensively researched the contributions to algebra made by non-white and non-male
mathematicians, including individuals from all ethnicities. Research shows that great female
mathematicians have made remarkable contributions to algebra, including Hypatia (Egyptian),
Sophie Germain (White - French), Ada Lovelace (White - English), Sofia Kovalevskaya (White -
Russian), Emmy Noether (White - German), Dorothy Vaugh (African-American), Katherine
Johnson (African-American), Julia Robinson (White - American), Valerie Thomas (African-
American), and Maryam Mirzakhani (White - Iranian). Furthermore, even if Khan’s version of
algebra’s history only contains white men as being important figures, there should be a
discussion and critique of why this might be and what factors may have contributed to this.
Khan’s Algebra 1 lessons are also presented from a perspective that encourages the idea
of white male dominance. Khan makes minimal effort to exhibit cultural and gender equity in his
practice examples. Furthermore, while the nature of the videos does not call for instruction to be
directed by anyone but Khan, there are two examples where guest speakers are invited (Video
01:05 and Video 08:09) and Khan chose to bring on men who present as white. While Khan
could have leveraged these as opportunities to counter the dominant narrative of STEM being
dominated by white males, he continued to perpetuate this narrative through his choices.
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RQ 3: How, if at all, does Khan Academy’s Algebra 1 course incorporate Black culture?
To address this research question, two sub-research questions were established, one about
quantitative analysis and the other about qualitative analysis. To address this question
quantitatively, the following question was asked: How does Khan Academy’s Algebra 1
curriculum perform on the amended rubric items pertaining to Black culture? The next research
question was asked to address the qualitative aspects of the question: How, if at all, does Khan
Academy’s Algebra 1 course incorporate Black culture?
Quantitative Analysis
To address how Khan Academy’s Algebra I course incorporates Black culture, four
rubric points were added to the previously established 12-point rubric. These four rubric points
were: (1) Systemic racism is made explicit, (2) The module includes elements of Boykin’s nine
dimensions of Black culture in the design of materials and instruction (spirituality, harmony,
movement, verve, affect, communalism, expressive individualism, oral tradition, and social time
perspective), (3) The module highlights the contributions and strengths of Black people, and (4)
The module uses content examples from the various culture that encompass the African Diaspora
(including, but not limited to, African-American, Caribbean, Afro-Latinx, and African histories).
In quantitative analysis of the videos, each of these rubric points had a total score of zero,
meaning that none of the 328 videos in the curriculum scored in any of these four categories.
Thus, by quantitative analysis, Khan Academy’s Algebra I curriculum does not incorporate
Black culture.
Qualitative Analysis
Qualitative analysis was also applied to the video transcripts to determine if there were
any instances of Black culture that were not captured by the rubric. To this end, codes for
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cultures encompassing the African Diaspora were created. In addition to codes for African and
African-American cultures, codes for Central American and South American cultures were
included under the umbrella of Afro-Latinx. The only mention of African culture was using a
location in Africa in a word problem. Video 08:36 says, “Let T(t) denote the temperature in
Windhoek, Namibia.”
Similarly, the only mention of Central American culture was using Mexican money in a
word problem. Video 12:03 says, “Your uncle bought a car for 130,000 Mexican pesos. Each
year, the value of the car decreases by 10,000 pesos.” There were no instances of African-
American culture mentioned, and South American culture was added to the curriculum like
African culture - by mentioning a place in South America. To this end, Video 08:12 says, “Let
P(t) denote the number of people, P, at the Copacabana beach in Rio de Janeiro, t hours past
midnight on a specific day.” These were the only references to Black culture mentioned in the
curriculum.
Summary
In summary, Khan Academy’s Algebra I course is mainly devoid of Black culture. While
there were cultural references identified by qualitative analysis, they were all very surface level
references to places or currency, without a true discussion of culture. As in RQ 1, there were
many missed opportunities across the units where the contributions of Black mathematicians to
Algebra could have been highlighted, and Black cultural activities could have been mentioned or
used as examples.
RQ 4: How frequently does each unit employ culturally relevant pedagogy?
To assess the frequency with which each unit employed culturally relevant pedagogy, the
Khan Academy Algebra I video curriculum was analyzed as it was for RQ 1, except that the
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amended 16-point rubric was utilized. At the end of this analysis, all 328 videos had a score
ranging from 0-11. Even though no upper limit was placed on video score, the highest scoring
video only had a score of 11. Next, the video scores were summed for each unit to create a unit
video sum divided by the number of videos in each unit. This resulted in an average video score
for each unit. Finding the average video score for each unit was necessary because the units had
very different numbers of videos. For example, Unit 15 consisted of 11 videos, whereas Unit 14
had 46 videos. The data used in this analysis are summarized in Table 3.
Table 3
Rubric Item Video Scores by Unit

The units with the lowest average video scores were those with a score of 0 and include
Unit 10, Unit 13, and Unit 15. To put these scores in perspective, in each of these units, no
rubric items were present among all any of the videos. For Unit 11, which had the fourth lowest
average score of 0.1, this indicates that on average, each video had 0.01 of a rubric point. For
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Units 13, 15, and 11 it is perhaps not surprising that these units had such low scores concerning
culturally relevant pedagogy, as these units are the ones that introduce the mathematical concepts
that most require additional examples and repetition. Unit 13 addresses the multiplying and
factoring of quadratics, Unit 15 provides an overview of irrational numbers and Unit 11 reviews
exponent properties and teachers students how to simplify square roots. These topics are also not
prone to word problems, which is one way a mathematics curriculum can incorporate culturally
relevant pedagogy.
The qualitative analysis facilitated identifying representative examples from problems in
these units to illustrate this point. For Unit 13, Quadratics – Multiplying and Factoring,
representative examples include: “Multiply (3x+2) by (5x-7)” (Video 13.05), “Start with an
expression like 4x+18 and see if we can rewrite this as the product of two expressions” (Video
13.11), and “Factor 25x
2
– 30x + 9” (Video 13.26). Unit 13 contains similar problems, which do
not lend well to the addition of word problems or the addition of culture. For Unit 11,
representative examples include: “Let’s calculate to see if we can calculate the fifth root of 32”
(Video 11.07), and “Let's see if we can simplify 5 times the square root of 117” (Video 11.08).
Likewise, Unit 15, Irrational Numbers, is another concept that is taught in a purely mathematical
way, with worked examples used to understand what a rational number is, how once can add and
multiply rational and irrational numbers, and various proofs regarding irrational numbers. Unit
10: Absolute Value & Piecewise Functions , is also a very technical mathematical unit that
discusses how to graph, shift, and scale absolute value and piecewise functions. However, there
were missed opportunities to discuss real-world examples of piecewise functions in the course
of this unit.
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Unit 2, Solving Equations and Inequalities, is another low scoring unit. While using
equations in real-world problems would be a way to integrate culturally relevant pedagogy, Unit
2 merely focuses on solving for x in equations and inequalities. Representative problems in this
unit are “We have the equation 20-7x = 6x-6, and we want to solve for x” (Video 02.03) and
“We are asked to solve for x, and we have this compound inequality here: -16 ≤ 3x + 5 ≤ 20”
(Video 02.20). Therefore, the topics covered within Units 2, 10, 11, and 15 and the types of
problems these topics encompass can explain the lack of culturally relevant pedagogy in these
units.
Other units had relatively high average video scores compared to the low-scoring units.
Units with the four highest average video scores were Unit 3 (Score = 1.556, Working with
Units), Unit 12 (Score 1.261, Exponential Growth & Decay), Unit 7 (Score = 1.067, Inequalities
(systems and graphs)), and Unit 1 (Score = 1.056, “Algebra Foundations”).
The fact that Unit 3 and Unit 1 scored high on the rubric is not surprising. Unit 3,
“Working with Units,” describes real-world situations where dimensional analysis allows for
solving complex problems. Such real-world situations allow for the addition of culture. While
quantitative coding of Unit 3 did not reveal overt mentions of cultural backgrounds, qualitative
coding of video transcripts supports the notion that some mentions of culture are hidden in Unit
3. For example, a reference to Asia is found in Video 03.06 with an example problem involving
climbing Mount Everest. Similarly, Middle Eastern culture is also found in video 03.06, with an
example problem involving climbing the K2 mountain that spans Pakistan and China. Unit 1 has
a high average video score because this unit covers the history of algebra, which would be
largely incomplete without mentioning culture in the founding of mathematics. This idea is
further supported by qualitative analysis of the video data. The following cultures are named in
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Unit 1: European (Videos 01.01, 01.03, and 01.04), Indian (Video 01.01), Middle Eastern (Video
01.01), and white American (Videos 01.02, 01.11, 01.12, and 01.16). The European references
in Unit 1 included Greece, Alexandria, the Roman Empire, Galileo Galilei, and Rene
Descartes. The Indian reference involved a discussion of the Urdu and Hindi languages and the
Indian mathematician, Brahmagupta. Middle Eastern culture was mentioned in the discussion of
the Persian mathematician al-Khwarizmi. In addition to these cultural influences, white
American culture was highlighted by examples involving the artist Jackson Pollock, the actor
Chuck Norris, and the comedian Steven Wright.
Unlike Units 3 and 1, Units 7 and 12 did not make many overt mentions of culture when
examined qualitatively. Thus, there was a need for further investigation of how Units 12 and 7
resulted in high scores for culturally relevant pedagogy.
Table 4
Highest Scoring Units by Rubric Item

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To determine how these units utilize culturally relevant pedagogy, I examined the raw
data to determine which rubric points were well-represented (Table 4). Examination by rubric
point demonstrates that while Unit 1 did not have the highest overall score, it had the most
diversity and breadth in its use of culturally relevant pedagogy, as it covered six of the 11 rubric
items, including Rubric Item 1: The module uses content examples from multiple cultural
backgrounds, Rubric Item 2: The module teaches students about contributions by individuals or
societies that belong to minoritized groups, and Rubric Item 7: The module counters the
dominant narrative of white, male authority and power. In this way, Unit 1 appears to exhibit
more of the cultural components of culturally relevant pedagogy than the other units, even
though they scored higher. In comparison, Units 7 and 12 only received scores for the same two
rubric items Rubric Item 3: The module explains new concepts using examples that are taken
from a diverse representation of everyday life and Rubric Item 11: The module incorporates
tasks that require students to apply their learning to an issue, context, or problem beyond school.
Unit 3 received scores for three rubric items, which include Rubric Items 3 and 11, and Rubric
Item 4: The module provides opportunities for students to use prior knowledge. This suggests
that these units incorporated culturally relevant pedagogy by connecting mathematic instructions
to the everyday real-world experiences that students have. Interestingly, while units 3, 7, and 12
all had a high percentage of their rubric points received from Rubric Item 11, Unit 1 received no
points in this category. This occurred because Unit 1 focused much more on the history and
foundations of algebra, and did not emphasize real-world examples of word problems.
In sum, research question 4 examined the frequency that each unit employs culturally
relevant pedagogy using the chosen rubric to measure culturally relevant pedagogy. The rubric
for culturally relevant pedagogy contains 11 items, some of which pertain to culture and some
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solely to instructional strategies. Using this rubric, high-scoring units were Units 3, 12, 7, and 1.
These units scored high for different reasons; Unit 1 had genuine mentions of culture. Units 3, 7,
12 had high rubric scores because they integrated the students’ lives and experiences into the
curriculum.
RQ 5: Are there differences in the use of culturally relevant pedagogical practices across
units or categories of videos?
The previous section looked at the frequency with which each unit of Khan Academy’s
Algebra I course employed the use of culturally relevant pedagogy. This was judged
quantitatively using the rubric items. This research question expands upon this idea by looking at
the differences in the use of culturally relevant pedagogy across units and categories of videos.
To determine if there were differences in the use of culturally relevant pedagogical practices
across units, an ANOVA test was utilized to analyze whether there was a difference between the
mean number of rubric points between units. The analysis revealed that there was a statistically
significant difference in unit score between the units F(14, 327) = 3.56, p < 0.001 (Table 5). This
leads to the conclusion that culturally relevant pedagogy is not taught equally between units.
Table 5
ANOVA for Video Score and Unit
Partial sum
of squares
df Mean
square
F Sig.
Model 58.53 14 4.18 3.56 .000
unit 58.53 14 4.18 3.56 .000
Residual 367.17 313 1.17
Total 425.7 327 1.3

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I also sought to determine if there was a significant difference in culturally relevant
pedagogy deployed in the three different types of videos in the curriculum: History of Algebra,
Instructional Videos, and Example Problems. To this end, I ran another ANOVA test. The results
of the analysis (Table 6) suggest a statistically significant difference in the group means, F (2,
327) = 29.48, p < 0.001. This is likely explained by the History of Algebra group having two
videos with significantly higher means than the Instructional Videos and Example Problems.
Moreover, because the variances of the three groups are not roughly equal and the History of
Algebra group only has 2 videos, I next evaluated if there was a significant difference between
the video scores for the Instructional Videos and the Example Problem Videos. I performed a t-
test for the difference between the two means. The results of the t-test are that there was a
significant difference between the culturally relevant pedagogy in the Instructional Videos (M =
0.27 SD = 0.08) and Example Problem Videos (M = 0.57 SD = 0.07), t(324) = -2.18, p = 0.03.
Table 6
ANOVA for Video Score and Type of Video

Partial sum
of squares
df Mean
square
F Sig.
Model 65.36 2 29.48 29.48 .000
Type of Video 65.36 2 29.48 29.48 .000
Residual 360.33 325 1.11
Total 425.7 327 1.3

In summary, there does appear to be a significant difference in the use of culturally
relevant pedagogy in the different units of Khan Academy’s Algebra I curriculum. An ANOVA
test was performed to compare the video score between the 15 units, where I found a significant
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difference between the means. Importantly, I can conclude that there is a difference, but not what
the difference is between the units. Secondly, I examined if the use of culturally relevant
pedagogy differs between the three types of Videos: History of Algebra, Instructional Videos,
and Example Problem Videos. When an ANOVA was conducted using three types of videos,
there was a significant difference between the means. However, there is a need to exercise
caution when interpreting these results, as there were only two videos in the History of Algebra
category. When the History of Algebra videos were excluded, and a t-test was done comparing
the mean video scores of the Instructional Videos and Example Problem Videos, and the means
were still statistically significantly different. This leads to the conclusion that the Example
Problem Videos utilize elements of culturally relevant pedagogy differently than the
Instructional Videos. This difference is likely because the Example Problem Videos allow for
greater use of word problems that can integrate the cultures and lived experiences of students.

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CHAPTER 5: DISCUSSION/CONCLUSION
Summary of the Study
The purpose of the current study was to expand the understanding of the implications of
relying upon online learning platforms such as Khan Academy to disperse education content,
particularly as it relates to these platforms ability to incorporate culturally relevant pedagogy.
The study aimed to answer the following primary research questions:
RQ 1: How do Khan Academy’s Algebra 1 videos score on the Online Curricular
Responsiveness and Relevance Protocol?
RQ 2: How, if at all, does Khan Academy’s Algebra 1 course utilize culturally relevant
pedagogy?
RQ 3: How, if at all, does Khan Academy’s Algebra 1 course incorporate Black culture?
RQ 3b: How does Khan Academy’s Algebra 1 curriculum perform on the amended rubric
items pertaining to Black culture?
RQ 4: How frequently does each unit employ culturally relevant pedagogy?
RQ 5: Are there differences in the use of culturally relevant pedagogical practices across
units or categories of videos?
The conceptual framework that guided my study relied upon critical race theory and
culturally relevant pedagogy as I examined how culturally relevant pedagogical practices are
implemented in math online learning spaces. This study will contribute to the scholarly literature
by providing a framework to assess and understand how online learning can be conducted in a
culturally relevant way. Furthermore, it contributes to our understandings of endemic racism
within math curricula and pedagogy. A mixed-method research design allowed me to collect and
analyze data, integrate the findings, and draw inferences using qualitative and quantitative
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approaches. A mixed-methods approach also allowed for an in-depth understanding of how
culturally relevant pedagogy is used in Khan Academy’s Algebra 1 curriculum.
Summary and Analysis of Findings
RQ 1: How do Khan Academy’s Algebra 1 videos score on the Online Curricular
Responsiveness and Relevance Protocol?
The findings show that the module performs relatively well in terms of relying on a
variety of teaching methods, explaining new concepts using examples that are taken from a
diverse representation of everyday life, and requiring students to apply their learning to an issue,
context, or problem beyond school, but does not do well at addressing most of the other
elements. An inspection of the quantitative tallies for each rubric item demonstrates disparities in
rubric points. Some rubric items had high scores, some did not fare well, and others scored zero.
There were several rubric items pertaining to the socio-political critical consciousness aspect of
culturally relevant pedagogy, which is grounded in the belief that students should be given the
tools to be able to identify, analyze, and solve real-world problems that pertain to social
inequities (Ladson-Billings, 2014). These rubric items were Rubric Item 5: The module provides
students with the academic knowledge and skills needed to function in the culture of power,
Rubric Item 6: The culture of power is made explicit, Rubric Item 7: The module counters the
dominant narrative of White, male authority and power, and Rubric Item 8: The module
acknowledges current sociopolitical realities versus essentializing a culture of group of people,
and Rubric Item 11: The module incorporates tasks that require students to apply their learning
to an issue, context, or problem beyond school. The module performed relatively well on Rubric
Item 11, which received a score of 79. This reflects the module performing well at incorporating
tasks that require students to leverage math to tackle real-world problems, however, these real-
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world problems did not work to address the culture of power or social inequities. The rubric
items that addressed this aspect of sociopolitical consciousness did not perform well. Rubric
Items 5, 6, and 8 receive scores of zero, and Rubric Item 7 received a score of one. With regard
to these items, it is clear that this aspect of culturally relevant pedagogy is not integrated into the
curriculum. While math is often thought of as an objective subject (Goodman, 1979), education
is inherently political, and educators have an obligation to their students to incorporation
sociopolitical consciousness. It is important that the ideals of sociopolitical consciousness are
embedded into curriculum as we work towards emancipatory pedagogy (Giroux, 1983).
Education has an obligation to prepare students to challenge the current social inequities and
work towards a more equitable society, which is not possible to do without acknowledging and
addressing the racism that exists within education, and specifically, math education.
There were also several rubric items that pertained to the cultural competence aspect of
culturally relevant pedagogy, which is the idea that students should learn about their culture and
other cultures in a way that contributes to them being able to recognize and honor these cultures.
These rubric items were Rubric Item 1: The module uses content examples from multiple
cultural backgrounds, and Rubric Item 2: The module teaches students about contributions by
individuals or societies that belong to minoritized groups. While these had scores of seven and
three, respectively, an overwhelming majority of these rubric points were earned in one video,
Video 01:01 Origins of Algebra. Specifically, this video had a score of four for Rubric Item 1
and a score of three for Rubric Item 2. With the exclusion of this video, there are only three
instances where the Khan Academy 1 curriculum incorporated examples from multiple cultures
and no instances where students learn about any contributions from people or societies that
belong to minoritized groups. This latter point includes both people from racially minoritized
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backgrounds and women. Mathematics, and algebra in particular, has such a rich history with
contributions from countless minoritized groups, and Khan Academy does students a true
disservice by failing to introduce them to these individuals and societies. Students who complete
this curriculum receive messaging that suggests algebra is a subject that solely stems from the
ideas and contributions of white men from European counties and the Middle East. This could
have a particularly negative impact on students of color and women who fail to see themselves
represented in any of the 328 videos that are a part of this curriculum.
The rubric items that Khan Academy’s curriculum performed best on fall under the
category of academic success, which is centered on the notion that educators should employ the
pedagogical tools necessary to help their students achieve academically (Ladson-Billings, 1995).
The items that fall under this category are Rubric Item 4: The module provides opportunities for
students to use prior knowledge (14 instances), Rubric Item 9: The module uses the interest of
students to make the learning process meaningful for them (0 instances), and Rubric Item 10:
The module prioritizes depth over breadth, by engaging students in increasingly complex
activities around a particular topic or learning goal (1 instance). While there is certainly a need
for improvement, the category of academic success is where Khan Academy’s curriculum
performs best. Strong pedagogical techniques to address the learning needs of a diverse student
body are present.
Rubric Item 3: The module explains new concepts using examples that are taken from a
diverse representation of everyday life (i.e., financial, political, and social) does not neatly fall
under any of the three aforementioned categories, as there is as intersection of socio-political
consciousness, cultural competence, and academic success. This rubric item achieved moderate
success in the curriculum, with 68 instances. Overall, there is room for improvement across all
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rubric items. There is a particular need to integrate the concept of sociopolitical consciousness by
addressing societal inequities as well as the culture of power present in math and in society at-
large. Khan Academy could leverage many of its word problems to introduce students to these
concepts. Furthermore, for an organization with a mission to provide education to anyone,
anywhere in the world, Khan Academy’s Algebra 1 curriculum does an inadequate job at
incorporating cultures from all over the world. By incorporating the contributions of women and
racially minoritized people and cultures, the curriculum would provide students with a more
dynamic understanding of algebra and do a better job at addressing this aspect of culturally
relevant pedagogy.
RQ 2: How, if at all, does Khan Academy’s Algebra I course utilize culturally relevant
pedagogy?
Analysis results indicate four important themes pertaining to how Khan Academy’s
Algebra I course utilizes culturally relevant pedagogy. The first theme is that the curriculum
presents a version of Algebra’s history based solely on European and Middle Eastern
contributions, with no regard for contributions from other countries or regions. Khan cites
several mathematicians from the European and Middle Eastern region and credits them with
being the founders of algebra. Khan also cites those in the Mesopotamia region as being the first
to do “real algebra.” In doing so, Khan disregards the contributions from other societies and
regions and also dubs the algebra that they were doing as fake algebra. This is messaging that
can be harmful to students, particularly those who may be aware of instances wherein their
cultures made important contributions to algebra. In working to achieve Ladson-Billings’ (2006)
notion of cultural competence, it is important that students learn “to recognize and honor their
own cultural beliefs and practices while acquiring access to the wider culture’’ (p. 36). This is an
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aspect that the curriculum really struggles with, which mirrors the lack of cultural competence
found through the quantitative analysis from RQ 1.
Secondly, throughout the course, white men are considered “great minds.” Khan credits
the development of algebra to “great minds” like Diophantus, al-Khwarizmi, Galilei, and
Descartes. By centering white men as great minds, the curriculum contributes to the notion of
math being a white institutional space (Martin, 2010). In addition to failing to mention the
contributions of people from racially minoritized backgrounds, there is also no incorporation of
women as being contributors to mathematics. There are so many women who have made
important contributions to mathematics and should be incorporated into the curriculum. In failing
to do so, the curriculum not only fails to counter the narrative of white male authority and power,
but actually supports it. Furthermore, one way to counter this culture of power that is present in
math would be to ensure that women are represented in the curriculum at least as often as men.
However, the curriculum mentions men more often than women or gender-neutral individuals,
with men mentioned 47 times, women 31 times, and gender-neutral individuals 15 times. Even if
the mentions of women and gender-neutral individuals were combined, men would still be
mentioned more.
Thirdly, there is a need for better use of real-world examples that incorporate students’
cultures and experiences. While there are instances where the module incorporates real-world
examples, depicted through qualitative analysis and the quantitative analysis scores on Rubric
Items 3 and 12, there are so many missed opportunities to incorporate students’ cultures and
experiences. Many of the examples discussed involve events or occurrences that contemporary
Algebra I learners likely do not relate to. There is a need for a greater understanding of who is
consuming the material of Khan Academy’s Algebra 1course and what their day-to-day lives
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look like. For instance, Khan could have used more culturally relevant examples involving social
media platforms such as TikTok and Instagram. Furthermore, given how fast the world is
changing, what examples are relevant to students’ lives and experiences may be different over
time. With this in mind, the curriculum should be consistently updated to reflect societal
changes, which is not currently the case.
Lastly, there are numerous missed opportunities to make the culture of power explicit
and counter the dominant narrative of white, male authority and power. The “culture of power
includes the ideas, attitudes, and activities that are regarded as normal or conventional and are
often aligned with (and advantage) the cultural norms and practices of the social groups in
power” (Darling-Aduana et al., 2020). Throughout the curriculum, rather than countering this
narrative, the module contributed to it. Critical race theory calls for counter-stories (Delgado &
Stefanic, 2001) wherein challenges to dominant perspectives are made to allow the experiences
of marginalized groups to be highlighted. Counter-stories are missing from Khan Academy’s
Algebra 1 curriculum, and they should have been used to counter the deficit-based narrative that
has been told about women and racially minoritized people in STEM. There is no mention of the
racialized nature of mathematics and no criticism of the sexist and racist policies that may have
contributed to mathematics being the way that it is. While challenging the culture of power is an
element that should be present in the teaching of all subjects, countering the narrative of white,
male authority and power is particularly important in STEM. The curriculum makes no effort to
address this notion that so many know is present in mathematics.
RQ 3: How, if at all, does Khan Academy’s Algebra 1 course incorporate Black culture?
The results show that Khan Academy Algebra I course does not incorporate Black
culture, and in fact, the course is mainly devoid of Black culture. While there are references to
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Black culture that emerged from qualitative analysis, these are not true incorporations of Black
culture. Instead, these are merely examples and references to places and currency without a
discussion of how Black culture has contributed to the development of algebra. As in RQ 1, there
were many missed opportunities across the units where the contributions of Black
mathematicians to algebra could have been highlighted, and Black cultural activities could have
been acknowledged. Rather than including Black historical figures in the curriculum, Khan
Academy’s Algebra 1 course perpetuates the idea of white superiority.
Quantitative analysis of the videos reveals that each rubric classification pertaining to
Black culture had a total score of zero, meaning that none of the 328 videos in the curriculum
scored in either of the four rubric items. Qualitative analysis results indicate that the only
mention of Africa was the use of a location in Africa in a word problem. Similarly, the only
mention of Central America was using Mexican money in a word problem. Furthermore, there
were no instances of African-American culture mentioned, and South America was only
reference in the curriculum, like Africa, by mentioning a place in South America. These surface
level references were the only times that Black culture was mentioned in the curriculum.
The scope of this study does not allow for conclusions to be drawn about how the lack of
culturally relevant pedagogy, particularly as it pertains to Black culture, may impact Black
students. However, CRT provides a lens for understanding how math being a white institutional
space that disregards the needs and perspectives of people who do not associate with white
ideologies and ways of doing math (Martin, 2010) can serve as a tool of oppression and isolation
for Black students. The CRT framework can help us to understand how Black students may not
feel welcomed in the educational space provided by Khan Academy’s Algebra 1 course.
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RQ 4: How frequently does each unit employ culturally relevant pedagogy?
The findings show differences in how frequently each algebra unit employs culturally
relevant pedagogy. Algebra units with the highest mean scores were Units 3 (1.556), 12 (1.261),
7 (1.067), and 1 (1.056). These units scored high for differing reasons. Units 1 scored well in the
rubric items pertaining to cultural competence. Units 3, 7 and 12 had high rubric scores because
incorporated tasks that required students to apply their learning to an issue, context, or problem
beyond school, and explained new concepts using examples that related to students everyday
lives. Units 10, 13, and 15 the lowest mean scores concerning culturally relevant pedagogy, each
having a score of zero. This finding is attributed to the introductory nature of the topics since
they introduce mathematical concepts to learners, involve minimal word problems, and require
numerous examples. This leads to the conclusion that culturally relevant pedagogy is not taught
equally between units.
RQ 5: Are there differences in the use of culturally relevant pedagogical practices across
units or categories of videos?
Results of the ANOVA test show statistically significant differences in the use of
culturally relevant pedagogy across the units in Khan Academy’s Algebra I curriculum. ANOVA
results indicate statistically significant differences in the mean scores of the 15 units. This leads
to the conclusion that culturally relevant pedagogy is not taught equally between units, however,
not many conclusions were able to be drawn about why this occurs. Analyses were also done to
evaluate the extent to which culturally relevant pedagogy was the same when videos were
grouped by category: History of Algebra, Instructional Videos, and Example Problem Videos.
The analysis indicated that there was a statistically significant difference between the means of
the three groups. Furthermore, after excluding the history of Algebra category and running a t-
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test comparing the mean video scores of the Instructional Videos and Example Problem Videos,
there is a statistically significant difference in the mean scores of the two groups. This indicates
that the different categories of videos have a significant difference in the extent to which
culturally relevant pedagogy is integrated. The fact that the History of Algebra videos have a
significantly different level of integration of culturally relevant pedagogy than the other two
categories is not surprising. These videos overwhelmingly account for the presence of the rubric
items pertaining to culture. While the average video had a score of 1.006, these videos had an
average score of 7.5. While this is impressive for this category of videos, the history of algebra
should be better integrated across all lessons. There is no need to limit conversations about the
history of algebra and its important contributors to a couple of videos at the beginning of the first
unit. Discussing the history and evolution of algebra over time throughout the curriculum would
better allow for the integration of culturally relevant pedagogy. Furthermore, Example Problem
Videos having a statistically significantly higher average score than Instructional Videos is
sensible given the increased opportunities to incorporate culture and students’ lives into word
problems examples.
Implications for Practice
This research finds that there is significant room for growth and improvement regarding
the ways in which Khan Academy’s Algebra 1 course incorporates culturally relevant pedagogy.
However, many of these findings are not limited to Khan Academy’s Algebra 1 course and can
be found in math education spaces as well as online learning spaces. Scholars have called on
educators to deconstruct the racial hierarchy of mathematics that places white and Asian students
at the top and Black, Latinx, and Native American students at the bottom (Cintron et al., 2021;
Gutiérrez, 2017; Martin, 2009). In fact, Martin (2009) argues that as it currently stands,
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mathematics education plays a role in producing and maintaining racial inequity in the United
States. One way to combat this is to increase the presence of culturally relevant pedagogy,
particularly as it pertains to the inclusion of historically marginalized cultures and the celebration
of people of color. The historical exclusion of people of color in mathematics that has led to
math being a white institution space been well documented (Martin, 2008). Furthermore, it
perpetuates the idea of mathematics centering whiteness (Battey & Leyva, 2016) and the white
supremacist ideal that values white people over other racial groups (Leonardo, 2004).
As we move toward a more digital world and increase reliance on online learning
platforms, it is also imperative that we assess them critically. Weaknesses in courses like the
ones identified in the Khan Academy’s Algebra I course can adversely affect student learning,
cultural competence, and critical consciousness. Online learning platforms should investigate the
extent to which they perpetuate normative values and perspectives regarding the culture of power
and the notion of white male authority and power. They should use a critical platform gaze
(Decuypere et al., 2021) to first accept that their platforms are not neutral spaces, and interrogate
what values and cultures are perpetuated through their curriculum. Moreover, these courses
should consider gathering data on their student body so that they are able to incorporate the lived
experiences and cultures of their students into the curriculum. There are inherent limitations in
the ability to incorporate culturally relevant pedagogy in standardized and/or asynchronous
online learning environments. Online learning platforms adopting this model should work to
incorporate opportunities for learners to interact with each other and/or learn from each other.
This can include the presence of discussion boards or the ability to send messages or comments
to other learners.
Recommendations for Khan Academy
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It is critical that Khan Academy’s curriculum and learning materials incorporate the
diverse cultural backgrounds of all the students they serve. Thus, those who seek to engage in
math education need to understand whiteness and the role that it plays in mathematics education
(Battey & Leyva, 2016) so that intentional steps can be taken to combat this issue. In an effort to
be a tool that provides “a free, world-class education to anyone, anywhere” as Khan Academy’s
mission states, there is a need to incorporate the cultures of students who live all over the globe.
Given the lack of culturally relevant pedagogy in Khan Academy’s Algebra 1 course, it can be
assumed that CRP is not prioritized in the writing and designing of the Algebra 1 curriculum. As
Khan Academy aims to expand its reach and impact, there should be a greater prioritization of
culturally relevant pedagogy. Every curriculum writer should receive training on culturally
relevant pedagogy. This should include a deeper understanding of the theories surrounding
culturally relevant pedagogy. Each of Khan Academy’s videos should be evaluated for the
presence of CRP and intentional efforts should be made to increase the incorporation of the
culture of historically marginalized groups into the curriculum. Furthermore, Khan Academy
should work to gather information on the learning needs, cultural backgrounds, and lives of their
students to determine what real-world examples make sense given their target audience.
The lack of incorporation of non-white and non-male mathematicians in Khan
Academy’s Algebra 1 curriculum indicates that Khan Academy should conduct extensive
research on the contributions by non-white and non-male mathematicians on algebra and
highlight those contributions throughout their curriculum. Khan Academy should leverage
counter-storytelling (Delgado & Stefanic, 2001) to present the experiences of marginalized
groups in a way that legitimatizes their stories and brings their contributions to light. There is
also a need to revise the curriculum’s current rhetoric around devaluing the algebra being
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performed by people in other parts of the world and the designation of this not being “real
algebra.” This deficit-based lens and continued exclusion of contributions by people of color
further contributes to the notion of math being seen as a white institution space (Martin, 2008).
In order to tackle this pervasive concept, for each unit, curriculum writers should specifically
investigate women who have contributed to the concepts being discussed, contributions from
non-European and non-Middle Eastern cultures, and incorporate the cultures of historically
marginalized groups. For example, in Unit 1, Videos 01.01-01.05 present a history of Algebra
that is primarily based on European contributions (Diophantus, Galileo Galilei, Rene Descartes
and Euclid), with the exception of a discussion of al-Khwarizmi, a Persian mathematician and
Brahmagupta, an Indian mathematician. In reality, the history of Algebra began long before it
became documented as “algebra” by Greek philosophers and mathematicians. Before 2000 BCE,
many communities and civilizations along the rivers of Africa, Asia and North America used
mathematics in a practical, scientific fashion to facilitate tax collection and to manage their local
government administrations (Kelley, 2000). Such examples could serve as a culturally relevant
introduction to the study of algebra. In addition, Unit 1 could have discussed Hypatia, an
Egyptian who is thought of as being the first woman to have a profound impact on the survival of
early mathematical thought (Kelley, 2000; Osen, 1974). Descartes, a prominent figure in Unit 1,
expanded on Hypatia’s work in the field of algebra (Deakin, 1994). There are also numerous
other missed opportunities to integrate an array of cultures including discussing how
mathematics is evident in the art of many cultures including weaving, beadwork, and pottery of
Native American and African cultures.
Regarding the lack of integration of Black culture in the curriculum and the zero rubric
points scored on these items by any of Khan Academy’s Algebra 1 videos, there is a clear need
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to repair the curriculum. Black students have been marginalized in many educational spaces, and
their needs are often overlooked in curriculum development. Black students should experience
lessons that depict content related to their everyday lives, including their culture and values, in
the design of materials and instruction. Khan Academy’s Algebra 1 course is mainly devoid of
Black culture and the platform should work to meaningfully incorporate Black culture
throughout their curriculum. It is essential that this is done intentionally and meaningfully in a
way that demonstrates that curriculum writers have an understanding of Black culture and can
center the knowledge and experiences of Black people. This includes the integration of Black
language, music, film, dance, and mathematicians. In their paper, Sharp and Stevens (2007),
present a mathematical model using simple, linear piecewise-defined function to describe the
rhythms of two drums, the tumbao and the bembe ostinato, used by the African Burundi people
in their Mwami ceremony, the purpose of which was to the honor the king and his ancestors.
Since the rhythms of the two drums are different, this allows for the generation of ordered pairs,
which leads to the generation of a piecewise-defined function. This presentation not only
highlights the role of mathematics in music, but also allows for a rich discussion of African
culture that includes traditional African music and dance. Another example is in Unit 4, which
focusses on linear equations and graphs, presents a great opportunity to introduce the work of
African-American surveyor and mathematician, Benjamin Banneker. Benjamin was born the son
of a freed American slave and President Thomas Jefferson recommended him to serve as the
surveyor for the new American capitol, Washington, DC, in 1791 (Wiest, 2001). In addition to
an important conversation about race and the history of racism in the United States, this
discussion could also lend an introduction to the importance of linear equations. Moreover, it
could serve as a lead into the discussion of linear graphs, beginning with an overlay of linear
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equations with different slopes. Furthermore, in an effort to adopt a socio-politically critically
conscious lens, there is a need to discuss systemic racism and to make the racialized nature of
mathematics apparent.
Following my data collection process, Khan Academy began incorporating short, non-
instructional, Creativity Break videos into the Algebra 1 curriculum with topics that range from
Why is Creativity Important in Algebra and How are Math and Creativity Changing the World.
While the addition of these videos allows for new perspectives and highlights women guest
speakers, there is a need to expand beyond the relationship between algebra and creativity.
Additional videos should be incorporated to discuss how various mathematical concepts can be
leveraged in students’ lives and to solve real-world problems, particularly problems pertaining to
developing social-political critical consciousness.
Lastly, the nature of Khan Academy’s Algebra 1 curriculum, and many other videos on
the platform, is one wherein Salman Khan narrates each instructional video. The decision to have
the instruction led by a single person should be interrogated. Receiving instruction from different
voices could be beneficial to students, particularly if they are able to see themselves in the
instructor. By providing instruction from women and people from various racial/ethnic
backgrounds, students would be able to see that mathematicians can look and sound like them.
Implications for Future Research
Researchers are encouraged to conduct studies are encouraged to provide additional
insight into this research topic by overcoming the limitations of this study. While the findings of
this study suggest that there are differences in the presence of culturally relevant pedagogy
across units, further investigation should be done to understand these differences and why they
might be occurring. While conducting the analyses for this study, I found that in general,
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culturally relevant pedagogy decreased as the course progressed. Although unit number and
placement in the course could not be used as a proxy for subject matter difficulty, further
research should examine how, if at all, the difficulty of the subject matter being discussed in each
module relates to the use of culturally relevant pedagogy. This is particularly noteworthy because
having more culturally relevant instruction and examples could be helpful to students as the
difficulty of math concepts increases.
This study only focused on Khan Academy Algebra I curriculum. There is a need for
researchers to examine numerous other courses, subjects, and learning platforms to understand
the extent to which the findings from this study can be extrapolated onto other courses and
subjects. It is also important to understand how these results might compare to an Algebra I
course on a different platform. Studies should also explore the degree to which asynchronous
online learning environments compare to synchronous learning environments regarding the
ability to incorporate culturally relevant pedagogy.
While the goal of incorporating culturally relevant pedagogy is often to improve learning
experiences for students, this study did not incorporate students’ perspectives and thus, is unable
to draw conclusions about how these findings impact students’ experiences. Researchers should
delve into students’ experiences with online learning as it relates to culturally relevant pedagogy.
Specifically, they should explore how, if at all, students of various racial/ethnic identities
respond differentially to the content based on the degree of cultural relevance and how it impacts
their mastery of the subject matter. This should also include an understanding of how having a
lack of culturally relevant pedagogical practices in online learning impacts the learning
experiences of racially minoritized students. Particularly, researchers should seek to look at
school districts that have adopted Khan Academy or similar platforms as part of their full-time
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curriculum and examine how outcomes differ from students who come from different
backgrounds.
Lastly, while I attempted to interrogate my role as a researcher, the process and findings
that came from such a process were influenced by my lived experiences and perspectives, which
may have led to different approaches than other researchers would have embraced. Therefore,
future studies should ensure that a high degree of objectivity is maintained throughout the
research.
Conclusions
The findings of this research paper highlight the need to tell counter-stories and amplify
the culture and lived experiences of Black students. In addition, the results demonstrate that
Khan Academy’s Algebra I course does not effectively meet the objectives of culturally relevant
pedagogy. The module performs well in terms of relying on various teaching methods,
explaining new concepts using examples taken from a diverse representation of everyday life,
and requiring students to apply their learning to an issue, context, or problem beyond school.
However, it fails to address critical elements such as the need for race and gender equity in the
education system.
The findings of this study can assist stakeholders of education systems in ensuring that
courses are evaluated and redesigned (if necessary) to ensure that the objectives of culturally
relevant pedagogy are met to enhance teaching and learning processes. Stakeholders include
donors, state and federal governments, communities, students and parents, faculty and staff,
administrative leaders, and policymakers. Facilitation of dialogue and active participation will
promote students’ moral development and intellectual growth, encourage them to appreciate
cultural diversity, and assist them in solving real-life problems caused by societal inequities.
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Furthermore, in addition to a need for racial equity in digital learning, there is a need to integrate
anti-racist teaching as well.

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APPENDIX A

CURRICULAR CONTENT Count
The module uses content examples from multiple cultural
backgrounds (i.e., literature, history, images).

The module teaches students about contributions by individuals or
societies that belong to minoritized groups.

The module explains new concepts using examples that are taken
from a diverse representation of everyday life (i.e., financial,
political, social).

The module provides opportunities for students to use prior
knowledge to help them make sense of new information (i.e., by
scaffolding new content on prior experiences).

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The module provides students with the academic knowledge and
skills needed to function in the culture of power.

The culture of power is made explicit
The module counters the dominant narrative of White, male
authority and power (e.g., shows women or minoritized populations
in positions of power).

The module acknowledges current sociopolitical realities (of
minoritized and/or dominant groups) versus essentializing a culture
or group of people.

INSTRUCTIONAL TASKS Count
The module uses the interests of students to make the learning
process meaningful for them (i.e., choice involved in generating an
open-ended response).

The module prioritizes depth over breadth, by engaging students in
increasingly complex activities around a particular topic or learning
goal (i.e., requires analysis, synthesis, or application).

The module incorporates tasks that require students to apply their
learning to an issue, context or problem beyond school.

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CENTERING BLACK CULTURE Count
Systemic racism is made explicit.
The module includes elements of Boykin’s nine dimensions of
Black culture in the design of materials and instruction (spirituality,
harmony, movement, verve, affect, communalism, expressive
individualism, oral tradition, and social time perspective).

The module highlights the contributions and strengths of Black
people

The module uses content examples from the various culture that
encompass the African Diaspora (including, but not limited to,
African-American, Caribbean, Afro-Latinx, and African histories).

APPENDIX B

CURRICULAR CONTENT Explanation Example
The module uses content examples from multiple cultural
backgrounds (i.e., literature, history, images).

Possible Examples:
Make references to other cultures outside of American
culture
Non-Eurocentric activities
Using references to cultural foods

The module highlights
contributions such as images,
literature and history from
multiple cultural backgrounds.
Examples that are relevant
include references to soursop
(fruit native to South American
countries) or the history of
Benjamin Banneker. An
example that does not count is
reference to a cultural names
such as Jamal or Carlos.

Unit 8 Video 12
The problem in the
video references
Copacabana- a
famous beach in
Brazil.
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The module teaches students about contributions by
individuals or societies that belong to minoritized groups.

Possible Examples:
Racially minoritized people’s contributions to math
Women’s contributions to math
Historical math figures that were non-white
Providing context of a non-white person that helped with
the advancement of a formula
If talking about an invention that was invented by a non-
white person, references who they were and their race
The module mentions the
inventions, books and/or
products that minoritized groups
have produced.

Unit 1 Video 1
This video discusses
that the word Algebra
comes from Persian
author and
mathematician that
lived in Bagdad.
The module explains new concepts using examples that are
taken from a diverse representation of everyday life (i.e.,
financial, political, social).

Possible Examples:
Incorporates real-world issues
Incorporates political or social issues
Brings up current events
Problems that reference modes of transportation to get to
school
This module teaches students
new concepts that include facets
of everyday life experiences
such as watering plants, playing
chess and buying fruit.

Unit 7 Lesson 11
This video solves a
problem related to
using a gift card
online.
The module provides opportunities for students to use prior
knowledge to help them make sense of new information
(i.e., by scaffolding new content on prior experiences).

Possible Examples:
Using student’s past experiences
Scaffolds off of experiences students are likely to have had
The module presents material
that allows students to use their
prior experiences such as fueling
a car, taking the subway or using
discounts in a store. An example
that is not included is using
student prior math knowledge
alone and/or using content that is
not based on student experiential
knowledge.

Unit 2 Video 1
This video uses
students prior
knowledge of weight
on a scale to describe
steps in solving
equations.
The module provides students with the academic
knowledge and skills needed to function in the culture of
power.

Possible Examples:
Providing students with the ability to think critically about
the numbers and math problems they are exposed to
This module employs content
that presents students with
opportunities to think critically
about the math that they are
working with.

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115
This problem require
students to critically
think about how
poverty affects life
expectancy.
The culture of power is made explicit

Possible Examples:
Teaches students about ideas, attitudes, activities that are
regarded as conventional and being taught to challenges
cultural norms
Teaching students about social hierarchies
The module centers the culture
of power by teaching about
social hierarchies like classism,
wealth and education.

This content teaches
students about
multiple social
hierarchies like
wealth and education.
The module counters the dominant narrative of White,
male authority and power (e.g., shows women or
minoritized populations in positions of power).
Possible Examples:
Shows women or minoritized people in positions of power
or in dominant positions
The module shows minoritized
populations in spaces of success
and power. Examples include
highlighting Black
mathematicians and their
contributions to the field.

This content
describes Katherine
Johnson and her
contributions to
mathematics and
physics. It can be
used to reference her
contributions and
then include a math
problem related to
Apollo 11.
The module acknowledges current sociopolitical realities
(of minoritized and/or dominant groups) versus
essentializing a culture or group of people.

Possible Examples:
Discusses sociopolitical realities of people of color
Addresses issues faced by low-income people or
undocumented people
Uses real world example that builds from experiences that
everyone would have had (ex. Not skiing)
The module centers
sociopolitical realities. Examples
that are included are problems
that build from experiences like
voting rights, health care or
hunger. Examples that would
not be included are problems
that build from experiences such
as skiing or yachting.

This graphic depicts
poverty rates with
and without Covid
relief. Analyzing this
graphic could allow
students to critically
think about the
numbers and issues
CRP in Khan Academy’s Algebra 1

116
faced by low-income
people.

INSTRUCTIONAL TASKS Explanation Example
The module uses the interests of students to make the
learning process meaningful for them (i.e., choice involved
in generating an open-ended response).

Possible Examples:
Asking open-response questions where there are multiple
correct answers
Answer questions as you go through questions
Giving students multiple options for how to solve problems
The module incorporates
student interest to make the
learning process meaningful for
them. Examples include
soliciting student feedback,
asking open-ended questions and
letting students choose which
method to solve the problem.
An example problem
that meets the module
criteria would be a
problem that allows
students to pick the
method of solving the
problem whether that
be arithmetic, models
or line numbers.
The module prioritizes depth over breadth, by engaging
students in increasingly complex activities around a
particular topic or learning goal (i.e., requires analysis,
synthesis, or application).

Possible Examples:
Questions require students to use analysis
Scaffolding in a video and beginning with more trivial tasks
and working toward more complex ones
The module scaffolds material
by explaining content in
increasingly complex activities.

An example problem
could start by
introducing students to
Pythagorean Theorem.
Then allow students to
use a digital ruler to
measure and find the
missing side of a
triangle. Finally, the
problem would require
students to apply their
knowledge to to find
out how tall an average
football goal post is
based on a given
image.
The module incorporates tasks that require students to apply
their learning to an issue, context or problem beyond school.

Possible Examples:
Integrates real world problems
Bringing up current events
The module includes practice
that requires students to apply
their to an real-world issue or
problem beyond the school
setting. Examples include the
comparing subway ticket pricing
and calculating miles on a road
trip.

Unit 3 Video 3
This problem requires
students to apply their
learning about rates to
determine which
website is more
productive.

CENTERING BLACK STUDENTS Explanation Example
CRP in Khan Academy’s Algebra 1

117
Systemic racism is made explicit.
Possible Examples:
Acknowledging the role that racism plays in society
Math problems that get at inequities and systematic racism
A problem about compounded interest and home loans and
how people of color get higher interest rates
The module makes systemic
racism explicit. Examples
include math problems
centered on examining the
racial wealth gap and racial
pay gap that exists today.
An example of a
problem that centers
systemic racism is
examining the long term
effects of redlining on
home values from the
1930s to present day.
After examining home
values, students can
describe the gap in
housing prices in
affected neighborhoods
today.
The module includes elements of Boykin’s nine dimensions
of Black culture in the design of materials and instruction
(spirituality, harmony, movement, verve, affect,
communalism, expressive individualism, oral tradition, and
social time perspective).
Possible Examples:
Incorporating rhythm, percussion and/or music into
instructional videos are much more feasible.
Ex. using fractional music note beat measures
Using music in helping to commit mathematical concepts to
memory
Using language that is engaging and colorful
The module includes elements
of Boykin’s nine dimensions
of Black culture in the design
of materials and instruction.
Examples include encouraging
movement and music with
learning.
An example problem
could include a creating
a song to help students
commit mathematical
concepts to memory.
The module highlights the contributions and strengths of
Black people
Possible Examples:
Highlight the contributions and strengths of Black people
Acknowledges that the person’s race
Word problems cite feats that have been accomplished by
Black people
The module illuminates the
contributions of Black people.
Examples include highlighting
Black inventors,
mathematicians and artists.

An example problem
would include
background information
on the Black inventor
who created the Super
Soaker- Lonnie Johnson.
The module uses content examples from the various
cultures that encompass the African Diaspora (including,
but not limited to, African-American, Caribbean, Afro-
Latinx, and African histories).

Possible Examples:
Using examples from or about Carnaval (Caribbean)
For word problems using travelling: incorporate
historically Black countries or cities
The module uses content from
the cultures of descendants of
the African Diaspora.
Examples include using
examples about the
geographical features of Haiti,
the cost of production of
Carnaval or geometric patterns
evident in hair braiding.
An example problem
could look at the past
enrollment of a
Historically Black
College or University
(HBCU) and encourage
students to predict the
following year’s
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118
Using geographical features (mountains) from Haiti as
opposed to Switzerland
Mathematical patterns of African art to understand
symmetry or geometry
enrollment based on rate
of change.

Abstract (if available)

Abstract While only 21% of K-12 public school students in the United States took even one entirely online course before the 2019-20 school year, nearly every school district was forced to move instruction entirely online due to the COVID-19 pandemic. Considering the growth and impact of online learning, there is a need to understand its integration of culturally relevant pedagogy (CRP). Researchers have investigated the importance of CRP practices for students of color in traditional classroom. However, there is a lack of literature on CRP in online learning. Given the prominence of Khan Academy in online learning, I submit, in this dissertation, a study to investigate how, if at all, culturally relevant practices are integrated into its platform. I use a mixed-methods case study approach to analyze the 328 instructional videos that comprise Khan Academy’s Algebra 1 curriculum. Analyses are done using a rubric that stems from Darling-Aduana, Good, and Geraghty’s (2020) Online Course Curricular Relevance and Responsivity Protocol. My analytical and conceptual framework uses critical race theory and culturally relevant pedagogy as I examine how CRP practices are implemented in math online learning spaces. I also utilize critical platform studies and culturally responsive computing in examining the technological components. This study will contribute to the scholarly literature by providing a framework to assess and understand how online learning can be conducted in a culturally relevant way. Findings indicate that Khan Academy’s Algebra 1 course addresses some, but not all, aspects of CRP. The curriculum performs best on rubric items pertaining to requiring students to apply their learning to issues beyond school (79 instances) and using examples from a diverse representation of life (68 instances). However, there is a need for improvement in many other aspects of CRP, most notably regarding the integration of Black culture. Furthermore, I found differences in how units and categories of videos performed on the rubric.

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Asset Metadata

Creator Desruisseaux, Tara Marie Kirsten (author)

Core Title Culturally relevant pedagogy in Khan Academy’s Algebra 1 course

School Rossier School of Education

Degree Doctor of Philosophy

Degree Program Urban Education Policy

Degree Conferral Date 2023-05

Publication Date 03/20/2023

Defense Date 03/17/2023

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

Tag critical race theory,culturally relevant pedagogy,Khan Academy,math education,OAI-PMH Harvest,online learning

Format theses (aat)

Language English

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Advisor Quinn, Dave (committee chair), Tynes, Brendesha (committee chair), Copur-Gencturk, Yasemin (committee member), Kaplan, Elaine Bell (committee member)

Creator Email Desruiss@usc.edu,Taramkd@gmail.com

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