The Development of Pedagogical Reasoning in Mathematics Teachers’ Collaborative Conversations

• In Event: Understanding the Development of High-Leverage Mathematical Teaching Practices

Abstract

The Adaptive Professional Development project was a six-year design experiment aimed at increasing access to and rigor in secondary mathematics through intensive professional development (PD) in urban high schools toward a form of collaborative learning called “complex instruction” (Cohen, 1994). In conjunction with formal PD, the project supports building-level teacher collaboration. Through active participation, we have collected hundreds of hours of fieldnotes of PD activities, yearly interviews with teachers, videotape recordings of classrooms, student achievement data, and recordings of teacher collaboration meetings.

This paper focuses on 14 videotaped collaborative teacher meetings from the 2008-2009 academic year. Three groups of mathematics teachers had regularly scheduled collaborative planning periods during the school day and were at different stages of pedagogical accomplishment, which we categorized as Beginning, Emergent, and Sophisticated. To sample teacher collaboration over time, we taped each group of teachers working together over the course of the school year to examine how accomplishment in teaching changes conceptualizations of teaching problems.

To investigate how teachers’ collective thinking develops, we parsed the videotapes using a unit of analysis called episodes of pedagogical reasoning (EPRs, [Horn, 2005]). That is, we looked for units of teacher talk where the teachers revealed their reasoning about pedagogical issues. Usually these begin with questions or assertions about practice that are accompanied by a statement of reason, explanation, or justification. EPRs can be single-turns of talk or more elaborate, multiparty co-constructions.

By looking cross-sectionally at teacher workgroups, this analysis hones in on both the development of group processes that support professional learning as well as the changes in conceptualizations of mathematics teaching. We found shifts in teachers’ pedagogical reasoning along several dimensions. A notable process shift was the increased attention teachers devoted to any problem of practice. Along with that, we see broader time frames invoked for weighing teaching decisions. Earlier on teachers tend toward the presentism (Lortie, 1975), primarily concerned about what they are doing now. As groups increased in sophistication, teachers consider long- and short-term past experiences (last year vs. yesterday), invoking both immediate futures (what students do next) and long-term futures (what students should develop through the course).

Shifts in conceptualizations of mathematics teaching are tied to process shifts. The Beginning and Emergent groups, for example, primarily focused their reasoning on themselves as teachers, while the Sophisticated group focused more on students’ mathematical understanding; the increased complexity in the problem conceptualization necessitated more time. Overall, as teachers’ competence in ambitious practice evolved, they more closely attended to relationships between goals for student learning and their teaching moves; incorporate feedback from student performance; and reconsider teaching choices in light of these. Bringing together the process and content development, we offer a model of how teachers’ collective reasoning develops alongside accomplishment in practice.

Authors

• Ilana S. Horn, Vanderbilt University

• Britnie Delinger Kane, Vanderbilt University