Investigating Opportunities to Develop the Practice of Responding to Students’ Contributions to Mathematical Discourse in Embedded Rehearsal.

Abstract

Proponents of practice-based teacher education are calling for new pedagogies to prepare beginners capable of doing ambitious teaching (Ball & Forzani, 2009; Grossman, Hammerness, and McDonald, 2009; Lampert, et al., 2010; National Council for the Accreditation of Teacher Education, 2010). Rehearsal is one such pedagogy designed to provide beginners with opportunities to learn to tailor their responses to students’ contributions through instructional simulation and analysis. This dissertation investigates (1) the kinds of opportunities to learn to do the improvisational, interactive work of ambitious teaching made available in rehearsals when beginners work on the core practice of responding to students’ contributions to mathematical discourse, and (2) how the broader organizational design in which rehearsal is embedded of daily repeated Cycles of Enactment and Investigation with instructional activities contributes to those opportunities to learn over the span of four weeks in the context of one integrated math content and methods course. I begin by developing a conceptual framework for understanding what is entailed in the focal practice of responding to students’ contributions to mathematical discourse. To do this, I integrate Sawyer’s (2004) framing of teaching as disciplined improvisation with Schon’s (1983) conception of reflection-in-action as a transactional process and identify three categories of structuring resources that discipline this transactional process. This framework sub-divides the practice of responding to students into its constituent phases to enable a more nuanced understanding of what novices need to learn to do and for what purposes structuring resources may be employed in the process. Then I apply this framework as a lens to develop a set of three sequential, narrative case studies to provide elaborated images of how the components of the design can synergistically support work on the practice of responding to students’ contributions to mathematical discourse inside the rehearsal activity setting, and to characterize how it changes and to what that change might be attributed. To develop these cases, I analyze video records of rehearsal and draw on course documents, materials, and knowledge drawn from my own experience as one of the teacher educators.