## Section A.1 Research Synthesis

Here I review two ways in which mathematics instructors promote equality of opportunity through their teaching work: promoting the academic success of underrepresented students and encouraging students to critically analyze their sociopolitical environment with an eye toward social change. Of course, the definition of “equality of opportunity” is not agreed upon, but in this review it will mean a state in which that no systemic or structural bias prevents groups such as students of color, women, LGBTQ+ students, or poorer students from accessing mathematics and the jobs for which it is a gatekeeper.

There are many reasons that an equity framework is useful for teaching mathematics. There is still substantial inequality within schools, as financially under-resourced schools have fewer highly-qualified teachers, and 83% of teachers are White. Many teacher training programs provide limited education about social justice or culturally relevant pedagogy, though researchers have confirmed that culturally relevant teaching practices contribute to educational equity (McGee 2014). Preservice teachers often view student diversity as a problem rather than a resource, and many teachers hold a view that “all students should be treated equally in the classroom”, even when this leads to disproportionately negative outcomes for students of color (Rousseau & Tate, 2003). This “one-size-fits-all” mentality is a common, serious obstacle to true teacher reflection and equity. Further, the “color-blind” mentality, in which a teacher claims “not to see color”, leads to ignoring students’ cultural backgrounds in the classroom, thus leading to decreased student engagement, as well as a refusal to combat historical and actual racist practices (Rousseau & Tate, 2003). In classroom observations, Rousseau & Tate (2003) report several instances of students being “allowed to fail” through their teacher’s neglect; such students were disproportionately Black, specifically Black men.

In addition, the way mathematics is taught around the world is often indicative of a colonial, Eurocentric narrative in which Europe is a “civilizing” force and the significant contributions of mathematicians from non-European backgrounds are downplayed. Such mathematical leaps as written mathematical records, a place value number system, the technique of measurement, our base 10 number system, the “Pythagorean Theorem”, and algebra all originated outside of Europe and were then used by Europeans to advance their own mathematics (Joseph, 1987). The marginalization of these contributions contributes to the perception of mathematics as independent of economics, politics, and culture; frames mathematical pursuits as confined to a select few (usually white, cisgender, heterosexual men); and enshrines deductive axiomatic logic (i.e. “formal” mathematical proof) as the “only” method of mathematical discovery (Joseph, 1987).

Teaching mathematics with an equity frame doesn’t just help fight these trends of inequity; using an equity frame that emphasizes the role of mathematics in democracy and addressing inequality results in student learning and achievement (Gutstein, 2003; Moses & Cobb, 2001; Winter, 2007). The National Survey of Student Engagement, 2004, has found that undergraduate students are often passionate about social and political issues; bringing such issues into the mathematics classroom can increase student engagement and performance (Winter, 2007).

One major way that teachers can promote equity and justice is by focusing on reaching students who are traditionally marginalized in schools. Black students are one of the largest underrepresented groups in US education, and several studies have been done to examine what pedagogical techniques promote Black students’ classroom success. Across all the studies reviewed by Johnson and Wilson (2012), it seems that providing African-American students with a common experience that grounds mathematical ideas, as well as explicitly encouraging and supporting African-American students to do more sophisticated mathematics, are important.

Another way teachers can increase their orientation toward equity issues in the classroom is through reflection. The

*Professional Standards for Teaching Mathematics*(NCTM, 1991) recommend that teacher reflection should focus on how students’ linguistic, ethnic, racial, socioeconomic, and cultural backgrounds influence their learning of mathematics. Generally, student-centered educational models backed by research can provide insights about how to teach mathematics better to all students, including underrepresented groups.Two such models were discussed in the proceedings of the Teaching Undergraduates Mathematics workshop at the Mathematical Sciences Research Institute (2009): Action-Process-Object-Schema (APOS) theory and covariation. APOS theory defines an “action” as a step-by-step transformation of a set of mathematical objects into another mathematical object; for instance, evaluating a composition of functions at the point

*x*. In contrast, the “process stage” of understanding takes place when students “internalize the action into a process” and can then think about the process without performing it. The process stage entails a greater level of abstraction, e.g. finding a general formula for a composition of functions given data for each function in table or graph form.*Covariational reasoning*is defined as “the cognitive activities involved in coordinating two varying quantities while attending to the ways in which they change in relation to each other”; for instance, attending to parametric equations. Observations of students suggest that covariational processing involves five kinds of mental action; questioning strategies to promote each action in students are suggested (Lai, 2009).A common problem with implementing student-centered pedagogical styles is a lack of time and institutional support. Research has indicated that a first-level teaching move to engage more with students often involves increasing

*pressing*, or trying to help learners articulate and hence deepen their thinking; perhaps this would be a good, low-overhead way to bring more learner-centered instruction into public schools (Brodie, 2008).The second reviewed question involved educating all students in a manner that promoted equity, justice, and a critical analysis of their sociopolitical contexts. In this direction, guidelines include: (1) working with a textbook with a strong mathematical framework and scaffolding, (2) talk to students to decide on equity/justice issues to cover, (3) set up units around “Essential Questions”, (4) introduce the equity/justice issue first, (5) then begin the mathematics, devoting as much time as necessary to the concepts and scaffolding both math and equity/justice along the way, (6) end with a great project. Some specific unit ideas: for exponents, studying compound interest and population growth; for probability, exploring the possibility that a traffic stop should be (and is) a person of color (Osler, 2007; Gutstein, 2008).

Winter (2007) provides a model of equity- and social justice-oriented pedagogy in STEM courses which introduces sociocultural phenomena through readings, videos, and activities, then assigns a problem and a structured worksheet to help students apply mathematics to the problem. Finally, students interpret their mathematical solution in the context of the original issue, often leading to discussion about the broader implications of their solution. This model has been applied to precalculus classes, teaching functions, graphing, and statistics through examining political corruption and economic development worldwide, climate change in Zimbabwe and its impact on agriculture, and water security and native peoples’ rights in Botswana, to name a few (Winter, 2007). Winter derives several principles for justice-focused education from Marilyn Frankenstein (1990), including using real situations and real information; emphasizing situations that students might have learned about through news or other media; and using controversial materials to help students increase their curiosity, understand other perspectives more accurately, solve problems more effectively, and generate creative ideas (Johnson & Johnson, 1979). Students taught using the justice approach performed statistically significantly better than a control group; they performed better on a mathematical assessment (exceeding the control group’s scores by 11.9%) and had fewer students with a grade of D or lower in the class (15.4% in the justice pedagogy condition, as opposed to 22.9% in the control group) (Winter, 2007).

There is a dearth of studies that investigate specific teaching practices which benefit underrepresented students, including teacher-student interaction and its effects. Although trying to specify “general” practices across a group as diverse as, for example, African-Americans in the US, may lead to essentialization and/or a deficit framing, a variety of historical conditions in the US have meant that many students of color have been told that they are inferior academically. Therefore, such studies would benefit many groups which are systemically marginalized in US mathematics education, including women and Latin@/e students (Jackson and Wilson, 2012). Further, although there are several collections of “mathematics for social justice” projects, units, and lessons targeted mostly at K-12 educators, Gutstein (2008) claims that no cogent and cohesive curriculum exists and identifies the need for one. Thankfully, Karaali and Khadjavi (2019) have provided a book of resources for postsecondary educators looking to teach math for social justice, and another volume is forthcoming (expected 2021). Further research is needed into the pedagogy and impacts of such an approach, and that such research is deeply essential, since equity-focused mathematics is good for students, underrepresented and otherwise, and good for the society in which we live.