ABSTRACT
This special issue of Mathematical Thinking and Learning describes models and modeling perspectives toward mathematics problem solving, learning, and teaching (Lesh & Doerr, 2003). The term “models” here refers to purposeful mathematical descriptions of situations, embedded within particular systems of practice that feature an epistemology of model fit and revision. That is, “modeling” is a process of developing representational descriptions for specific purposes in specific situations. It usually involves a series iterative testing and revision cycles in which competing interpretations are gradually sorted out or integrated or both—and in which promising trial descriptions and explanations are gradually revised, refined, or rejected. The latter emphasis on the “fitness” of models is critical because it suggests that models are inherently provisional, and it emphasizes that they are developed for specific purposes in specific situations—even though they may endure for longer periods of time, and even though they generally are intended to be sharable and reuseable in a variety of structurally similar situations.
