UC Berkeley

The construction of equitable, ambitious mathematics classrooms in which students learn together hinges on teachers representing students’ mathematical struggle as supported and constrained by interactions they have with peers and teachers. However, commonsense narratives about “perseverance” locate the responsibility for struggling productively in the individual, diminishing or ignoring the role that interpersonal interactions play in students’ perseverance. Individualist orientations diminish teachers’ agency by placing responsibility for productive mathematical struggle with students. In contrast, group-oriented perspectives towards perseverance have the potential to broaden how teachers conceive of productive student thinking and empower teachers to work towards ambitious mathematics teaching practices. However, supporting teachers to locate perseverance in the collective is complex work. It is complicated by challenges professional developers face in organizing teachers for collaborative inquiry and by how entrenched individualist ideologies are in education—both traditional and reform—and society at large.

This dissertation follows four high school mathematics teachers over a semester as they navigated tensions between commonsense individualist narratives of perseverance and ambitious visions of mathematics instruction. It explores how features of the professional development (PD) environment in which the teachers worked supported or constrained their collaborative inquiry. Interactions among the teachers and PD facilitator were observed and videoed. As summarized below, close examination of the work of these PD participants yields findings with implications for the research and practice of practice-based PD for mathematics teachers.

Analysis examines how the teachers represented perseverance as they engaged in PD activities. How the teachers represented perseverance is situated in two broad but distinct discourses of mathematics teaching and learning, “traditional” and “ambitious.” Those discourses have ties to broader discourses and ideologies used in society at large, which tend to privilege individualist narratives. Focusing on representations of perseverance illuminates the explicit or tacit systems of categorization that the teachers used to organize people, phenomena, and ideas, which the teachers in turn used to make teaching decisions.The teachers were found to use both individualist and group-oriented representations of perseverance throughout the PD, with group-oriented representations gaining in explanatory power and prevalence as the PD progressed. Over time, the teachers increasingly used group representations of perseverance to explain successful perseverance and inquired into how they could support perseverance by encouraging students to build on each other’s mathematical thinking. Nonetheless, individualist representations of perseverance continued to hold significant explanatory power for the teachers, especially as first resort and to explain failed perseverance. Facilitation that problematized individualist representations of perseverance, frameworks that drew teachers’ attention to specific ways in which collaboration can support productive mathematical struggle, and iterative, collaborative classroom-video watching followed by collaborative planning were found to support inquiry that broadened the teachers’ horizons of observation around perseverance to include more group-oriented perspective. These findings strongly suggest that PD should be grounded in explicit theoretical frameworks, demand reasoning grounded in examples rather than justified by vague principles, and be guided by facilitation that explicitly problematizes individualist reasoning about students.