Dissertation Defense Announcement Ph.D. in Education Program: Megumi Asada “Teaching Logic for Social Justice: Connecting Advanced Mathematics and Logic to an Abolitionist Perspective”

Mathematics education, like all forms of education, can replicate or resist social inequities.
This replication is present in the very content students learn. In particular, students learn
mathematics in ways that promote the disciplinary values of decontextualization and objectivity,
which can permit mathematicians to draw harmful conclusions while receiving little scrutiny. For
example, the belief that mathematics is objective lends an automatic legitimacy to the subjective
choices made by statisticians. These disciplinary values are especially relevant within proof and
abstract mathematics, in which context is deliberately discarded. However, just as mathematics can
be used to reinforce injustice, mathematics can also be used to fight them. Prior work in
Teaching Math for Social Justice (TMSJ) describes possibilities to teach students to analyze,
critique, and change societal injustices using mathematics. Nevertheless, this scholarship
predominantly relies on statistics and computation, drawing connections between math and social
justice that are not generalizable to more abstract areas of mathematics, such as proof. This is
notable as proof plays a critical role throughout K-16 mathematics. I propose, however, that proof
can be modified to honor the goals of teaching math for social justice and subvert the
disciplinary values of objectivity and decontextualization.

This dissertation examines three lines of inquiry from a design-based research study aimed at
developing a learning trajectory for how undergraduates can engage in reasoning that is both
faithful to mathematical practice and supports their reasoning about social justice issues. The
study involved two cycles of constructivist teaching experiments, each with a pair of
undergraduate mathematics students. I designed activities aimed at having students engage the two
disciplinary contexts via the same strategies. Students engaged reasoning about axioms and
definitions in a geometric setting and similarly engaged definitions and pro-prison assumptions
via an abolitionist lens. Chapter Two analyzes parallels in how students can engage with
definitions across mathematics and a social justice context. Chapter Three details mechanisms by
which students can draw from their lived experience across the two disciplines. Finally, Chapter
Four theorizes parallel mechanisms by which students can engage tensions between competing
mathematical and sociopolitical assumptions. Collectively, these three lines of analysis introduce
novel opportunities for using proof in service of social justice by unifying mathematical and
critical pedagogical goals around parallel activity. This study provides a framework for how
advanced undergraduate mathematics can be used to enable students to question assumptions that
replicate injustice.