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Balance the Equation - Suggested Reading

Key Research Papers Supporting Priority Students

Why Am I Always Being Researched? “Chicago Beyond created this guidebook to help shift the power dynamic and the way community organizations, researchers, and funders uncover knowledge together. It is an equity-based approach to research that offers one way in which we can restore communities as authors and owners. It is based on the steps and missteps of Chicago Beyond’s own experience funding community organizations and research, and the courageous and patient efforts of our partners, the youth they serve, and others with whom we have learned.” (Chicago Beyond, 2019)

Race, Culture, and Researcher Positionality: Working Through Dangers Seen, Unseen, and Unforeseen. “This author introduces a framework to guide researchers into a process of racial and cultural awareness, consciousness, and positionality as they conduct education research. The premise of the argument is that dangers seen, unseen, and unforeseen can emerge for researchers when they do not pay careful attention to their own and others’ racialized and cultural systems of coming to know, knowing, and experiencing the world. Education research is used as an analytic site for discussion throughout this article, but the framework may be transferable to other academic disciplines. After a review of literature on race and culture in education and an outline of central tenets of critical race theory, a nonlinear framework is introduced that focuses on several interrelated qualities: researching the self, researching the self in relation to others, engaged reflection and representation, and shifting from the self to system.” (Milner IV, 2007)

Expanding Visions of Success in Mathematics for Marginalized Students: Building More Equitable and Inclusive Mathematics Environments. “Research revealed a set of deeply interconnected factors that, while non-exhaustive, are key to building more inclusive mathematics environments.” A one-page summary of these factors surrounding sociohistorical context, family and community involvement, curriculum, educator leadership, instruction, school policies, assessment, and interpersonal interactions can be found here. (Mindset Scholars Network, 2020)

Fostering an inclusively relevant mathematics environment: The case for combining social-justice and utility-value approaches. “Despite a common belief that mathematics is neutral and apolitical, a critical analysis reveals a legacy of mathematics education that has catered to the dominant (white, middle-class) culture, and served to stratify students along the lines of race, gender, socioeconomic status, and other dimensions of identity and difference. However, there is increasing awareness that mathematics education should be reformed to make it more relevant to all students’ lived experiences.” (Priniski & Thoman, 2020).

The Opportunity Myth. Students spend most of their time in school without access to four key resources: grade appropriate assignments, strong instruction, deep engagement, and teachers with strong expectations. (TNTP, 2018)

Reviewing the research on marginalization in mathematics education. Findings from this review highlight the normality of marginalization in mathematics education, the material and ideological means of marginalization, and the interlacing of individual and structural sources of marginalization. (Chen & Horn, 2020)

Black Students and Mathematics

Access to Upper-Level Mathematics: The Stories of Successful African American Middle School Boys. “This article is about 8 African American middle school boys who have experienced success in mathematics. Working within a phenomenological methodological framework, the researcher investigated the limitations these students encounter and the compensating factors they experience. Critical race theory was the theoretical framework for this study; counter-storytelling was utilized to capture the boys' experiences, which is in stark contrast to the dominant literature concerning African American males and mathematics. Five themes emerged from the data: (a) early educational experiences, (b) recognition of abilities and how it was achieved, (c) support systems, (d) positive mathematical and academic identity, and (e) alternative identities.” (Berry, 2008)

Clean Corners and Algebra: A Critical Examination of the Constructed Invisibility of Black Girls and Women in Mathematics. “This article takes a critical approach to unsettling the apathy around Black girls’ and women’s mathematics achievement and participation.” Gholson discusses “how prevailing narratives about White girls and women, as well as Black boys and men, make the existence of coherent narratives of Black girls and women in mathematics essentially impossible.” Gholson argues that “Black girls and women serve as a referent group providing a quiet, invisible, and menial labor of sanitizing theoretical and empirical spaces for other demographic groups.” Gholson calls “for the creation, occupation, and sharing of positive, socio-epistemic spaces that allow for the visibility of Black girls and women in mathematics.” (Gholson, 2016)

Counter Narratives: Examining the Mathematics and Racial Identities of Black Boys who are Successful with School Mathematics. "Four factors positively contributed to mathematics identity: (a) the development of computational fluency by third grade, (b) extrinsic recognitions, (c) relational connections, and (d) engagement with the unique qualities of mathematics. For these boys, racial identity in school is connected to perceptions of others’ school engagement; this sense of “otherness” leads to a redefinition of their own mathematics and racial identities." (Berry, Thunder & McClain, 2011)

How are Black learners positioned in mathematics classrooms? What do we know and what do we need to know?Findings suggest that Black learners are positioned in both productive and unproductive ways by their peers and teachers. Additionally, these positions are connected to the multiple identities of students and teachers, and how they intersect with issues of power, intersectionality. Implications of this synthesis include considerations for how teachers position students implicitly and explicitly, development of policy that requires professional development around intersectionality and training for teachers to improve their practice.” The authors recommend that future research: “use intersectionality theory to uncover inequities that occur during mathematics instruction across grade levels, but particularly in middle school grades.” (Wilkes & Ball, 2020).

Latino Students and Mathematics

The Counter Narrative: Reframing Success of High Achieving Black and Latino males in Los Angeles County. “While there are a number of troubling issues affecting Black and Latino males, there remains a pressing need to tell a more complete story.” This report takes a deeper look into the rich assets these young men bring to school, family, and their communities. (UCLA Black Male Institute, 2017)

Examining the Academic Success of Latino Students in Science Technology Engineering and Mathematics (STEM) Majors. “Using a longitudinal sample of 146 Latino students’ in science, technology, engineering, and mathematics majors, the purpose of the study was to examine factors that affect their academic performance. The main premise supporting this study suggested that Latino students perform better academically when they have cultural congruity within their chosen academic major. Although this premise was supported, college experience variables like studying with other students and attending diversity functions were negatively correlated with performance. Such experiences may reveal insight into the cultural incongruity that exists for students in these majors and their peers outside of the majors.” (Cole & Espinoza, 2008)

Guidance of Latino High School Students in Mathematics and Career Identity Development. “This study examines two models of guidance—the assisted performance model, derived from sociocultural theory, and the individuation model—in relation to students’ math achievement and career identity development. One hundred fifteen Latino high school students completed a questionnaire assessing their experiences with assisted performance, individuation, mathematics, and career identity development. As predicted, higher assisted performance was related to higher math grades for those in the college-prep track, but contrary to predictions, assisted performance was related to lower math grades for students in the remedial track. Also as predicted, higher individuation was related to higher identity achievement. Overall, although students’ experiences of assisted performance were positively related to their experiences of individuation, assisted performance only predicted mathematics and individuation only predicted career identity. This study has implications for students, families, teachers, and programs designed to enhance educational and career opportunities for ethnic minority youth.” (Lopez, 2001)

Teaching for Equity and Excellence in Mathematics. “For this TEEM special issue on mathematics education through the lens of social justice, we sought manuscripts from classroom teachers, teacher educators, and other interested scholars whose work involves mathematics teaching and learning from a social justice perspective. By social justice perspective, we mean work that has explicitly disrupted institutional structures, policies and practices to advocate for and advance children, historically underrepresented in STEM fields, in learning rich, rigorous and relevant mathematics. Transforming mathematics from a tool of systemic oppression to one of liberation that engages all of us: students, families, and educators in experiencing mathematics in a more just and humanizingway. Each article in this special issue provides ideas, strategies and resources for this challenging work. Each author highlights the promises, tensions, and struggles of engaging themselves and others, whether it is PreK-12 students or pre service and veteran teachers, in fundamentally changing the experience of learning and teaching mathematics. And each article affirms the importance of mathematics in our lives.”  (Todos: Mathematics for All, Aguirre & Civil, 2016)

Understanding the Needs of Latino Students in Reform-Oriented Mathematics Classrooms. Changing the Faces of Mathematics: Perspectives on Latinos. “Curriculum guidelines and research in mathematics education have outlined the characteristics of reform-oriented mathematics classrooms (National Council of Teachers of Mathematics (NCTM) 1989). These characteristics include an increased emphasis on communication and collaborative work. It is important in designing classroom instruction for Latino students to consider how these two new emphases—a focus on mathematical discourse and new forms of student participation—might intersect with the needs of Latino students and affect their experiences in the mathematics classroom.” (Moschkovich, 1999)

English Learner (ELs) and Mathematics

English Learner’s Participation in Mathematical Discussion: Shifting Positioning and Dynamic Identities. “In our view, conducting equitable mathematical discussions in linguistically diverse contexts depends on understanding how to facilitate ELs’ agentive participation and how to help other students come to see ELs as important contributors. In addition, our study highlights an important dimension of positioning—that teachers model strategic positioning moves (e.g., positioning an EL as a powerful mathematical thinker) and, over time, those moves may be appropriated by students. Contained in this dimension of positioning is our view of students as key agents for creating and sustaining transformations of the asymmetrical relations of power in schools. We contend that the dynamic interactive positioning that occurred during our after-school program constitutes emerging evidence that students were learning to relate to each other in ways that remind us of the concept of relational equity (Boaler, 2007), where students develop a sense of responsibility and respect for their peers’ learning.” (Turner, Dominguez, Maldonado & Empson, 2013)

Guidelines for Improving Math Materials for English Learners. These guidelines “were developed to provide specific guidance to developers of mathematics content on key areas of English language development that must be embedded across a curricula, in units, and in lessons so that English learner students (ELs) can access and engage in grade-level content.” (English Learners Success Forum

Principles and Guidelines for Equitable Mathematics Teaching Practices and Materials for English Language Learners. "Mathematics instruction for ELLs should address more than vocabulary and support ELLs’ participation in mathematical discussions as they learn English. Instruction should draw on multiple resources available in classrooms (objects, drawings, graphs, and gestures) as well as home languages and experiences outside of school." (Moschkovich, 2013)

Principles for the Design of Mathematics Curricula: Promoting Language and Content Development. “The framework is intended to help teachers address the specialized academic language demands in math when planning and delivering lessons, including the demands of reading, writing, speaking, listening, conversing, and representing in math (Aguirre & Bunch, 2012). Therefore, while the framework can and should be used to support all students learning mathematics, it is particularly well-suited to meet the needs of linguistically and culturally diverse students who are simultaneously learning mathematics while acquiring English.” (Understanding Language, 2017)

Supporting English Learners in STEM Subjects. “English Learners in STEM Subjects: Transforming Classrooms, Schools, and Lives recognizes that ELs comprise a diverse and multi-talented pool of learners, yet these students continue to be underrepresented and lack access to rigorous STEM learning opportunities. The report showcases the interconnectedness of language and content area learning and identifies factors that affect ELs' opportunities to engage in rigorous, grade-appropriate STEM learning. The report recommends steps that policy makers, district and school leaders, and educators can take to increase this access and to support ELs' engagement and success in these subjects.” (The National Academies of Sciences, Engineering, and Medicine, 2018)

Students Experiencing Poverty and Mathematics

Checking In: Are Math Assignments Measuring Up? “Although roughly three-fourths of all assignments at least partially aligned to the grade- or course-appropriate math content, they also tended to: have low cognitive demand, over-emphasize procedural skills and fluency, and provide little opportunity for students to communicate their mathematical thinking. And this tendency was often worse in higher poverty schools.” (Education Trust, 2018)

Closing the Mathematics Achievement Gap in High Poverty Middle Schools: Enablers and Constraints. “The mathematics achievement levels of U.S. students fall far behind those of other developed nations; within the United States itself, the students who are falling behind come predominantly from high-poverty and high-minority areas. This article reports on a series of analyses that followed 4 cohorts of students from 3 such schools through the 5th to 8th grades, where studies have found the mathematics achievement gap to develop most rapidly. The cohorts followed in these analyses attended schools implementing whole-school reform models that incorporated research-based, proven curricula, subject-specific teacher training and professional development, multiple layers of teacher and classroom support, and school climate reforms. The research found that students at schools implementing the whole-school reform (WSR) models made greater progress in closing the mathematics achievement gap than at the other 23 high-poverty, high-minority schools in their district. Using the results from a Binary Logistic Regression model, we show which factors were key in enabling or constraining a student's ability to close the achievement gap during the middle school years. We conclude that various student-, classroom-, and school-level factors are all key in helping students to close the gap. WSR models, while often time- and cost-intensive, address issues at all of these levels and may be more able to affect the achievement gap than other, more simply implemented reforms.” (Balfanz & Byrnes, 2002 and updated 2006)

Understanding the Relationships between Poverty, School Factors and Student Achievement. “The purpose of this quantitative descriptive study was to explore the relationship between poverty, school factors, and student achievement. Drawing on previous literature regarding student and school factors that influence student achievement gains, this work explores whether these factors explain variation in student achievement gains across schools in MCPS [Montgomery County Public Schools].” (Jackson & Addison, 2018)

 All Priority Students, Including a Gender Lens

We encourage potential applicants to think through how our priority students have multiple identities and how math with a gender equity lens is also an important consideration.

Am I a “Math Person”? How Classroom Cultures Shape Math Identity Among Black and Latinx Students. “Mathematics instruction therefore cannot focus merely on teaching the mechanics of the subject (e.g., order of operations), but instead must be more holistic; it must consider how the structures, cultures, norms and stereotypes, and practices surrounding the topic of mathematics affect students’ experiences when they enter mathematics classrooms.” The paper further states: “positioning students as mathematical doers and providing opportunities for them to engage with mathematics must go beyond rote memorization. Unfortunately, in schools with high proportions of Black and Latinx students, students tend to be exposed to more rote memorization, with fewer opportunities for engaging activities that lead to conceptual knowledge.” Furthermore, “classroom culture and the historically racialized nature of mathematics may be preemptively alienating Black and Latinx students before their mathematics identity has a chance to take form in a positive way that will promote their continued engagement in mathematics. Black and Latinx students may be motivated to participate in mathematics and see themselves as mathematicians in contexts where they are offered opportunities to participate, engage in activities where they can see the links between what they are learning and their communities, and have their thinking affirmed.” (Miller-Coto & Lewis, 2020)

Creating More Inclusive Learning Environments in Mathematics. “In the context of mathematics education, the knowledge, contributions, language, and practices associated with white, Western, and male-dominated societies are considered uniquely credible and worthy, which marginalizes Black, Latinx, and Native American students, students from families facing economic disadvantage, students who are multilingual learners, and girls.” (Mindset Scholars Network Powerpoint, 2020)

A Framework for Understanding Whiteness in Mathematics Education. Another may be society’s belief that math ability is innate. While this belief is harmful for student learning and math identity overall, research suggests it is particularly harmful to Black, Latino/a, and female students as it influences the interactions among students and between students and teachers in math classes. (Leyva, 2016)

"She's Always Been the Smart One. I've Always Been the Dumb One”: Identities in the Mathematics Classroom and Smart Girls, Black Girls, Mean Girls, and Bullies: At the Intersection of Identities and the Mediating Role of Young Girls' Social Network in Mathematical Communities of Practice. The social dynamics and social networks in the classroom, including those found in the discourse between students and between students and teachers, affects students’ math identities. (Bishop, 2012; Gohlson & Martin, 2014)

Teacher’s Bias Against the Mathematical Ability of Female, Black and Hispanic Students. A recent study of teachers analyses of student work found no detectable bias in assessing correctness of the work but, when asked to assess students’ mathematical ability teachers assessments were biased against Black, Hispanic, and female students, with biases largest against Black and Hispanic girls. (Copur-Gencturk, et al., 2019)

Unpacking the Male Superiority Myth and Masculinization of Mathematics at the Intersections: A Review of Research on Gender in Mathematics Education. In his review of gender research in math education, Leyva argues complementing situated analyses of gender with intersectionality theory allows for more nuanced insights on students’ experiences at multiple intersections of gender and other socially constructed identities, including race or ethnicity, culture, class, and sexuality. Leyva found that race or ethnicity and sexuality were largely absent in achievement and participation studies’ sex- and gender-based analyses of assessment performance and experiences in mathematics. Future research should focus on the intersection of gender with multiple intersections of other socially constructed identities. (Leyva, 2017)

Beyond Algebra 1: What Comes Next?

Branching Out. Just Equations makes the case for different math pathways after completing Algebra 1. While Algebra 2 and beyond is outside the scope of this Grand Challenge, we encourage you to read, for what might be next in high school math and beyond. (Just Equations, 2019)

Additional Resources

Books and Papers

Access and Equity Book Series: Middle School and High School (NCTM, 2018)

The Impact of Identity in K-8 Mathematics: Rethinking Equity-Based Practices (NCTM, 2013)

Mathematics for Human Flourishing (Su, 2020)

Mathematics Success and Failure Among African-American Youth (Martin, 2000)

Negotiating Opportunities: How the Middle Class Secures Advantages in School (Calarco, 2018)

Racialized Identities: Race and Achievement Among African American Youth (Nasir, 2011)

Radical Equations: Civil Rights from Mississippi to the Algebra Project (Moses, 2002)



Rochelle Gutiérrez: Rehumanizing Mathematics, A Vision for the Future (2018)

Center for Equity for English Learners (Loyola Marymount University)

NAEP Results: 8th Grade Mathematics (2019)

A Pathway to Equitable Math Instruction (Equitable Math)

Supporting ELLs in Math (Understanding Language, Stanford University)

Targeted Universalism: Policy and Practices (Haas Institute, 2019)

Teacher Education Reinvented: Supporting Excellence in Teacher Education (NYU Steinhardt)

Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students (What Works Clearinghouse, 2018)

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