Dynamic mental models in learning science: The importance of constructing derivational linkages among models

Abstract

We present a theory of learning in science based on students deriving conceptual linkages among multiple models which represent physical phenomena at different levels of abstraction. The models vary in the primitive objects and interactions they incorporate and in the reasoning processes that are used in running them. Students derive linkages among models by running a model (embodied in an interactive computer simulation) and reflecting on its emergent behaviors. The emergent properties they identify in turn become the primitive elements of the more abstract, derived model. We describe and illustrate derivational links among three models for basic electricity: a particle model, an aggregate model, and an algebraic model. We then present results of an instructional experiment in which we compared high school students who were exposed to these model derivations with those who were not. In all other respects, both groups of students received identical instruction. The results demonstrate the importance of enabling students to construct derivational linkages among models, both with respect to their understanding of circuit theory and their ability to solve qualitative and quantitative circuit problems. © 1999 John Wiley & Sons, Inc. J Res Sci Teach 36: 806-836, 1999 This article is concerned with how students come to understand abstract scientific models and use them in explaining physical phenomena and solving problems. In a series of studies, we have been evaluating a theory of the development of such understanding which focuses on the linkages among models at different levels in an abstraction hierarchy (Frederiksen & White, 1992; White, 1993a;White & Frederiksen, 1990;White, Frederiksen, & Spoehr, 1993). Lowerlevel models typically are based on a finer grain of analysis, they focus on more concrete phenomena involving objects and their interactions, and they employ causal reasoning about object interactions (cf. White, 1993a). An example is an electrostatic model of the interaction of charged particles. Higher-level models focus on more abstract representations of variables and JOURNAL

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