Giving Reason and Giving Purpose

Abstract

Skillful teaching involves seeing mathematics in ways that are coherent and making decisions during planning and teaching. In particular, teaching requires making decisions about what connections to make, when to make them, and how students might make them. We posit that it is important for teachers and teacher educators to understand the pedagogical work of making connections, as this pedagogical work positions students to access ideas later in the curriculum. We analyzed the teaching and planning sessions of a first grade teacher to examine the question: What are the characteristics of planning that make it possible for students to connect mathematics in ways that are productive in the short and long term? We frame this work in terms of connections that “give reason” (Duckworth, The having of wonderful ideas and other essays on teaching and learning. New York: Teachers College Press, 1996) and “give purpose” – making sense of mathematical representations and arguments and increasing students’ access to content and practices valued by the discipline. We provide a concrete decomposition of the pedagogical work of planning for connections that give reason and give purpose. To illustrate the components we identify, we use the example of a first grade lesson whose goal was to help students transition from counting one by one when adding or subtracting to using the base ten system more intentionally. We close by describing possible future work in two arenas: designing opportunities to learn teaching that makes connections well and identifying learning opportunities made possible by such teaching.