Learning to Lead Mathematical Discussions

• In Event: Core Practices in Teacher Education: Preparing Teachers to Facilitate Whole-Class Discussion

Abstract

Our goal is to analyze the learning process that the mathematics methods team engaged in as we worked to specify and prepare novices to lead mathematical discussions. We view learning to teach as participation in a community of practice where people who have similar aims, use common tools, and share common interpretations of problems (Lave & Wenger, 1991) can develop the visions, understandings, practices, and dispositions for what counts as high quality teaching (Bryk, Sebring, Allensworth, Luppescu, & Easton, 2010). Learning in the company of other teachers who value and investigate student thinking, take time to develop meaningful relationships with students, and adapt teaching to learning has resulted in teachers being able to maintain high expecta¬tions of all students, attend to students’ socioemotional learning needs, and enact practices that accomplish high-level academic learning goals (Gutiérrez, 1996).
Records of mathematics methods courses across two universities were collected for analysis: video records, fieldnotes, artifacts documenting class sessions where preservice teachers were learning how to lead discussions. Qualitative methods of analysis were used to develop a coding system that corresponded to the way the research team defined and decomposed discussions for purposes of learning. Research meetings were recorded to provide records of the tensions and dilemmas the team wrestled with.
Mathematical discussion is not a single or set practice that can be defined by a checklist or a single representation. Mathematical discussion by nature, and based on our view of learning, involves the interaction of people, constructing mathematical ideas together in relation to a set of tools, within a particular social context shaped by the economic, political, and social world outside of school. This means that defining discussion for the purpose of teacher learning raises a number of tensions we are working to address:
a. what components of leading a discussion to specify and at what grain size to support teacher learning
b. how to bound the work on leading discussions and whether or not to include instructional work that might be preparatory and necessary
c. how to evaluate class sessions or pedagogies in which the practice of the preservice teacher fell short of a mathematically productive discussion but there were early attempts at interacting with children’s mathematical ideas
d. how to account for preservice teacher learning at an individual versus group or class level
These tensions become even more salient when we consider prepare teachers in ways that attend to (a) the classroom and school structures that shape discussion, (b) the experiences and histories of the students, and (c) ways mathematical discussion can challenge the status quo.
The quality of teaching in disenfranchised communities is both full of possibility (Rose,1999; Ladson-Billings, 1997; Martin, 2009) and injustice (Delpit, 2013; Martin, 2009). The imperative we face as teacher educators to prepare teachers for a democracy is a moral one. We must be cautious in our efforts to specify core practices at the same time that we do our best to investigate, make public, and discuss what constitutes high quality teaching and teacher education.

Authors

• Deborah Loewenberg Ball, University of Michigan - Ann Arbor

• Megan L. Franke, University of California - Los Angeles

• Hala N. Ghousseini, University of Wisconsin - Madison

• Elizabeth Hartmann, University of Washington

• Elham Kazemi, University of Washington

• Emily Shahan, Stanford University

• Meghan M. Shaughnessy, University of Michigan