Reframing learning: How small shifts in teacher talk can support new patterns of mathematical engagement by nondominant students

This dissertation documents and analyzes the successful efforts of four experienced Black teachers in a high poverty urban school to develop and sustain ambitious teaching practices. These four focal teachers were part of a larger department learning community that also included three new teachers and a full-time instructional coach, of various ethnic backgrounds, and a White researcher in a participant observer role (myself). The work of these focal teachers was consistent with, and can in turn inform and enrich, research on culturally and mathematically responsive classroom discourse./nThe first contribution of the dissertation is to propose and illustrate an integrated model of culturally and mathematically responsive classroom pedagogy. Mathematically responsive pedagogy is conceptualized in terms of the shift from a knowledge transmission (KT) frame, consistent with traditional and typical mathematics instruction in the U.S., toward a productive disciplinary engagement (PDE) frame. This shift is conceptualized and analyzed in terms of three aspects of framing: (1) mathematics content, (2) classroom discourse moves, and (3) teacher and student roles. Culturally and mathematically responsive pedagogy is conceptualized in terms of explicit attention to the negotiation of equitable power relationships that (1) recognize the funds of knowledge of nondominant communities, (2) welcome the discourse practices of nondominant communities, and (3) position nondominant students in positions of mathematical authority. Illustrative cases are provided in which the focal teachers leverage Black cultural practices to support nondominant students’ co-development of racial and mathematical identities, as the teacher and students engage together in new types of classroom activity that center these students’ mathematical ideas./nThe second contribution of the dissertation is to conceptualize and describe changes in classroom discourse from a continuity perspective (Russ, Sherin & Sherin, 2016). A continuity perspective holds that learning is rarely a “gestalt shift,” and instead looks for ways that prior knowledge and practices are adapted and repurposed to create new knowledge and practice. Two examples are analyzed in detail. The first example concerns Initiation-Response-Evaluation (IRE) sequences (Mehan, 1979), which are typically associated in the literature with a KT frame. My analysis illustrates how IRE sequences can serve important functions in responsive classrooms. Specifically, when combined with more open forms of talk such as student presentations, IRE sequences can help elaborate and refine student ideas while ascribing ownership for mathematical ideas to students. The second example concerns student presentations, which are often associated in the literature with a PDE frame. I analyze the learning trajectory of one teacher who implemented and adapted a new student presentation practice over the course of the school year. Initially, the practice was implemented in a way that was consistent with a KT frame, but over the course of the year it shifted substantially and became increasingly consistent with a PDE frame. My analysis details these shifts and their affordances. Both examples provide evidence that points of continuity between the KT and PDE frames can be identified and leveraged to understand and support teacher learning.

Advisor: diSessa, Andrea
Schoenfeld, Alan