Anti-Deficit Narratives: Engaging the Politics of Research on Mathematical Sense Making

Abstract

This article identifies a self-sustaining system of deficit narratives about students of color as an entry point for studies of cognition to engage with the sociopolitical context of mathematical learning. Principles from sociopolitical perspectives and Critical Race Theory, and historical analyses of deficit thinking in education research, support the investigation into the system. Using existing research about students' understanding of a limit in calculus as context, this article proposes a definition of a deficit perspective on sense making and unpacks some of its tenets. The data illustration in this article focuses on the mathematical sense making of a Chicana undergraduate student. The analysis uses an anti-deficit perspective to construct a sensemaking counter-story by a woman of color. The counter-story challenges existing deficit master-narratives about the mathematical ability of women of color. The article closes with a proposal for an anti-deficit method for studying the sense making of students of color.

Students’ metarepresentational competence with matrix notation and Dirac notation in quantum mechanics

“…Our findings for Buzz and Milan are consistent with Smith's [39] characterization of student "observable expertise" as rich, highly adaptable to problem specifics, and composed of a wide variety of strategies. Instead of focusing on the identification of students' difficulties with notation, we highlight what students attend to when using (or choosing to use) a particular notation and how this seems to impact their decision when using a particular notation; this is consistent with recent calls for research from antideficit perspectives with respect to investigating student learning [40]. In turn, educators might examine how they can build upon the metarepresentational competence students already have to help deepen and strengthen their understanding of quantum mechanical and mathematical representations.…”

Cognition, Interdisciplinarity, and Equity

“…The discussion continues with Morton (2014) who focused on the problemsolving practices of African American female middle school students and their understanding of proportionality and ratios. Adiredja (2019) and Adiredja and Zandieh (2017, in press) extended the discussion about equity and cognition into undergraduate mathematics, investigating the construction of conceptual metaphors about basis in linear algebra by a group of female undergraduate students of color. Lewis (2014) and Lewis and Lynn (2018a, b) focused on the mathematical engagements of students with Mathematical Learning Disabilities (MLD) at different academic levels, ranging from middle school to university.…”

“…Adiredja (2019) explored the connections between cognitive research with academic mathematics and equity research in the context of undergraduate mathematics. Adiredja (2019) argued that the result of an anti-deficit analysis of mathematical sense making can disrupt deficit narratives about students (and women) of color in society. Adiredja and Zandieh (2017) followed a framework, which was later presented in Adiredja (2019), and invited eight female undergraduate students of color (African American, Asian, and Latinx) to study how they made sense of the concept of basis from linear algebra.…”

“…The review in this chapter highlights the contributions of these studies and, in turn, explores potential models for future cognitive research to positively contribute to "making learning inclusive and equitable" (Goos 2018, p. 13). This review joins the ongoing efforts in the field to better understand the intersections and connections between equity-focused research and research on mathematical cognition (Adiredja 2019;McKinney de Royston and Sengupta-Irving 2019).…”

Stages of a Mathematical Model Developing of the Educational Trajectory

“…Working from a constructivist point of view, Simon (1995) answers a specific question about how a teacher can provide tools to help students move from their prior ideas to more complex thinking about the target concept. At the same time, he proposes a "hypothetical learning trajectory" (HLT), which includes "the purpose of learning, learning actions, as well as thinking and learning, in which students participate" [13,[20][21][22]. Based on this, significant research efforts have been made in this area to quantify students 'long-term teaching pathways as a model of the evolution of students' thinking as part of their slow approach to targeted ideas.…”