Diverge Then Converge: A Strategy for Deepening Understanding Through Analyzing and Reconciling Contrasting Patterns of Reasoning

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  • 1 Western Michigan University

One of the challenges of teaching content courses for prospective elementary teachers (PTs) is engaging PTs in deepening their conceptual understanding of mathematics they feel they already know (Thanheiser, Philipp, Fasteen, Strand, & Mills, 2013). We introduce the Diverge then Converge strategy for orchestrating mathematical discussions that we claim (1) engenders sustained engagement with a central conceptual issue and (2) supports a deeper understanding of the issue by engaging PTs in considering both correct and incorrect reasoning. We describe a recent implementation of the strategy and present an analysis of students’ written responses that are coordinated with the phases of the discussion. We close by considering conditions under which the strategy appears particularly relevant, factors that appear to influence its effectiveness, and questions for future research.

Contributor Notes

Theresa J. Grant, Department of Mathematics, Western Michigan University, 4427 Everett Tower, Kalamazoo, Michigan 49008-5152; terry.grant@wmich.edu

Mariana Levin, Department of Mathematics, Western Michigan University, 4421 Everett Tower, Kalamazoo, Michigan 49008-5152; mariana.levin@wmich.edu

(Corresponding author is Grant terry.grant@wmich.edu)(Corresponding author is Levin mariana.levin@wmich.edu)
Mathematics Teacher Educator
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