Teaching to "The Good Ones"? Examining the Relationship Between Inequity and the Practice of and Preparation for Postsecondary Mathematics Instruction.

Abstract

This dissertation focused on inequity in calculus instruction through a two-part study that built on the findings from an earlier exploratory study. The exploratory study, conducted in the same department, revealed connections between personal theories of mathematics intelligence that doctoral student instructors (DSIs) held for themselves and those that they held for their students. The first component of the dissertation project was a design intervention study that examined a practice-based approach to preparing DSIs to give students equitable feedback, a core instructional practice, in their postsecondary calculus instruction. The second component was a comparative investigation of teacher/student interactions across identity difference in postsecondary calculus instruction. Four of the instructors from the intervention study were observed and interviewed throughout their first semester of teaching to examine their interactions with their undergraduate students across identity difference. The three articles in this dissertation focus on the findings from this second study.

The findings suggested that the DSIs, who were members of overrepresented groups (i.e., majoritized students identifying as men and Asian or White), held some common understandings about what in meant to do mathematics well, which they used as lenses for gauging their own and others’ potential to successfully navigate mathematics as a discipline. Moreover, evidence from this study indicated that when the DSIs viewed students through these lenses that they noticed different characteristics for minoritized and majoritized students, even when they exhibited similar behaviors. These impressions formed the DSIs’ opinions about the potential of their students, which systematically disadvantaged women, especially those identifying as Latina and Black. Finally, the findings suggested that the DSIs acted on their ideas about intelligence through their teaching practices, creating differentiated access to learning opportunities and marginalizing minoritized students. The resulting inequitable approaches to instructional practices may reduce domain identification and motivation, create lower expectations, and depress performance for minoritized students in mathematics classrooms as explored in the pre-calculus case presented in the third article. These findings support the need for the design of equitable approaches to mathematics instructional practices and the explicit preparation of postsecondary instructors to engage in them.