Adaptive interpretation:

Abstract

We discuss opportunities to build better continuity between students' experiences in arithmetic and in algebra by examining ways that external representations can be used to solve problems. We use examples from our research on algebra learning to illustrate often overlooked complexities that arise when using a single representation to analyze relationships and patterns of change between two covarying quantities. We use the termadaptive interpretation to describe ways in which, in the course of solving problems about situations that contain covarying quantities, students must shift their perspective on a representations as they shift their thinking about the stituation. One set of examples demonstrates students' difficulties shifting their perspective on a equations when shifting their attention from a varying quantity in a situation to a specific unknown value of that quantity. A second demonstrates students's difficulties shifting their perspective on tables and graphs when shifting their attention from initial quantities in a situation to changes in those quantities. Finally, we describe possible antecedent experiences with adaptive interpretation in arithmetic problem solving that could better prepare students for solving problems about situations containing covarying quantities.