On Transitions Between Representations: The Role of Contextual Reasoning in Calculus Problem Solving

This article argues for a shift in how researchers discuss and examine students' uses and understandings of multiple representations within a calculus context. An extension of Zazkis, Dubinsky, and Dautermann's (1996) visualization/analysis framework to include contextual reasoning is proposed. Several examples that detail transitions between modes of reasoning and how these transitions inform students' reasoning in a calculus context are discussed. These examples are used to provide evidence for the usefulness of the model for unpacking student reasoning.