Possibilities and Pressure Points in Leveraging Student Thinking in Mathematics

• In Event: Learning Ambitious Teaching: Cases From Across the Disciplines

Abstract

Recent scholarship on mathematics pedagogy offers a distinctive conception of the relationships among learners, teachers, and mathematics. On this view, teachers engage learners in making mathematical sense of and solving problems, communicating and justifying their reasoning, and reflecting on their reasoning in relationship to that of others in the classroom community (Lampert, 2001; Stein et al., 2008). Supporting the learning of mathematics in this way has a characteristic trajectory: from using generative problems to elicit student thinking, to attending to what is mathematically productive in that thinking and interpreting it within a developmental framework, to hypothesizing next steps for learners’ development, to facilitating forms of discussion that capitalize on the diversity of students’ ideas and offer a bridge to more sophisticated understandings and skills (Jacobs et al., 2010; Smith & Stein, 2011; Schifter, 2011). In other words, teachers engaged in “ambitious pedagogy” (Lampert, Boerst, & Graziani, 2011) position students’ thinking and solution strategies as central means to drive learning forward. Our research team has come to call this constellation of practices “leveraging student thinking.”

Although much of this research focuses on experienced teachers, a handful of studies support the claim that prospective and beginning teachers can attend to and engage student reasoning in varying degrees (Levin, Hammer, and Coffey, 2009; Monte-Sano, 2011; Thompson, Windschitl & Braaten, 2013). This paper takes a step further to investigate why and how.

The paper is based on data collected over two years in the classrooms of nine novice elementary teachers, all graduates of a program in which attention to student thinking was central. We visited each teacher 3-4 times, videotaping two or more consecutive days of mathematics and science lessons, and audiotaping structured pre- and post-observation interviews for each lesson. Observations focused on teachers’ use of tasks, talk, representations and other tools to position student thinking as a resource for learning. Interviews surfaced participants’ goals and instructional plans and “readings” of their students’ understandings in relation to instructional goals and decisions. Context-focused interviews with each participant, her administrator, and several colleagues provided insight into the conceptions of high quality teaching and institutional factors shaping participants’ practice.

Data show that while participants easily learned routines for eliciting student thinking, knowing what to do with that thinking required a particular vision of the nature of mathematics and how it might be learned. Where our participants’ understandings conflicted with such a vision, they struggled to leverage. Using our data analysis, we zero in on four “pressure points” that shape and constrain participants’ understandings, and so can support or short-circuit novices’ attempts to leverage. These pressure points are epistemic, what it means to know mathematics; academic, the nature of mathematical activity and agency in school; developmental, how mathematics learning might proceed from less to more sophisticated patterns of thought and action; and managerial, how one manages the multiplicity of voices and ideas in an environment that values order. The paper illustrates these pressure points in participants’ practice, and explores implications for pre-service and early career support.

Authors

• Marcy Singer-Gabella, Vanderbilt University

• Barbara S. Stengel, Vanderbilt University