UC Berkeley

What does it mean to be “good at math”? Traditionally, schools have valued getting the right answer quickly—a perspective that excludes important aspects of mathematics, as well as many students. This multi-site case study investigates how teachers work together to redefine mathematics and mathematical competence. The study involved more than a year of ethnographic observations and interviews at two diverse urban high schools on the West Coast of the United States, where teachers expressed strong commitments to serving all students, especially students from non-dominant backgrounds.

The dissertation tells a complex story of teacher learning, as viewed through the lenses of classroom instruction (Chapter 2), collegial conversation (Chapter 3), and the organization of teachers’ professional support networks (Chapter 4). Drawing on scholarship that takes learning as a negotiation of meaning through engagement in social practices (Vygotsky, 1986; Wenger, 1998; Saxe, 2012), the dissertation examines the relationships between extra-local systems of meaning and moment-to-moment interactions. Extending beyond prior work, the dissertation elucidates the negotiation of intensely conflicting meanings—namely, culturally dominant definitions of mathematics as a discipline, students as learners, and teachers as professionals, and non-dominant definitions that attempt to expand both teachers’ and students’ opportunities to engage with rich, challenging, and rewarding learning experiences.

In each of the contexts studied, navigating tensions between dominant, restrictive meanings and non-dominant, expansive meanings was a challenge for all of the teachers. Dominant discourses frame mathematical activity as consisting primarily of computation and memorization; mathematical ability as innate, fixed, and distributed along a bell-shaped curve; and the work of teaching as private, autonomous, and grounded in personal style and preference. In contrast, equity- and reform-oriented discourses frame mathematical activity as inclusive of a wide variety of skills and practices; position all students as capable learners; and position teachers as learners who benefit from ongoing collaboration and support. Dominant discourses are restrictive: they limit students’ opportunities to learn rich mathematics and teachers’ opportunities to negotiate equity- and reform-oriented shifts in their practice. But as teachers engage with non-dominant meanings that potentially expand learning opportunities, commonsense meanings do not simply disappear. Rather, they interact with non-dominant meanings in messy and complex ways that require careful study in order to understand how and what teachers learn.

The theme of negotiating meaning is laid out in Chapter 1, with a discussion of the dissertation’s underlying theoretical perspective. Research sites are introduced; the dissertation’s structure is presented; and major findings and contributions are highlighted.

Chapter 2, “(Re)Framing Mathematical Competence in Everyday Instruction: Struggles and Successes of Equity-Oriented Teachers,” examines tensions and contradictions in teachers’ classroom practice. It shows that despite the best intentions of the teachers in this study, many of their efforts to support all students position some students as capable of engaging with challenging mathematics and others as just the opposite. Conversely, teacher moves that are counterintuitive within dominant frames of teaching, employed by two of the teachers in the study, are shown to expand students’ opportunities to develop positive mathematical identities. The chapter thus contributes to conversations about what equitable mathematics instruction looks like, while illuminating obstacles—cultural as well as technical—that teachers face as they attempt to enact classroom practices that support all students.

Chapter 3, “Tensions in Equity- and Reform-Oriented Learning in Teachers’ Collaborative Conversations,” examines how collaborative conversations open up and close down opportunities for teachers to navigate the tensions between restrictive and expansive discourses of mathematical competence, through close analysis of a 9½-minute segment of a routine meeting of mathematics teachers. Although the group appeared to be an ideal professional learning community in many ways, and the focal interaction and others like it were generative in a number of respects, teacher talk enacted both restrictive and expansive discourses. The existence of tensions between these discourses presented opportunities for the teachers to negotiate non-dominant meanings for themselves, i.e., to learn; but the ways that teachers framed their own collaborative work interfered with these opportunities. By highlighting conversational norms that impede collaborative learning, the chapter contributes to the field’s understanding of the challenges of equity- and reform-oriented learning in teachers’ professional communities.

Ways of supporting teachers to negotiate expansive meanings are examined in Chapter 4, “Supporting Teachers’ Equity-Oriented Learning and Identities: A Resource-Centered Perspective.” The chapter investigates two cases of ongoing teacher engagement with non-dominant practice and two cases of relative disengagement, illustrating how various resources come together to support teachers’ learning and identity development (or not). Four types of resources are found to be critical, and learning and identity processes are shown to intertwine in mutually informing ways as teachers interact with these different resources.

In elucidating both challenges and supports associated with making sense of non-dominant meanings, this dissertation contributes to the field’s understanding of equity- and reform-oriented teacher learning and why it is so difficult. It also points to ways that the contexts in which teachers work might be constructed to support their engagement with non-dominant, expansive meanings, so that they can support all of their students to engage with rich, challenging mathematics and to develop identities as powerful learners and doers of mathematics.