The Flexible Use of Multiple Mental Domain Representations

In this paper we present a framework which describes learning in physics domains as a succession of multiple levels of mental domain representations ordered along the dimension qualitative/quantitative. The emphasis is on the mental representation of functional relationships between physics variables. We exemplify our approach in the domain of elastic impacts, a subtopic of classical mechanics. In order to analyze the feasability of our framework an empirical study as well as three cognitive models are presented. MULEDS, a computerized multi-level diagnosis system, is capable of diagnosing correct, incorrect, and incomplete elements of students’ knowledge. It incorporates mechanisms for tailored testing as well as for active adaptation of instruction to diagnosed misconceptions. KAGE is a cognitive model of how students acquire knowledge about functional relationships between physics variables. It accounts for the question which knowledge states have to be expected when specified analysis-based learning mechanisms are applied to given instructional information. The Sepia model shows which and how qualitative physics knowledge facilitates quantitative physics problem solving. Sepia is also discussed with respect to its potential for supporting the design of physics instructions.