Abstract planning and perceptual chunks: elements of expertise in geometry

Abstract

We present o new model of skilled performance in geometry proof problem solving called the Diagram Configuration model (DC). While previous models plan level. They focus on the key steps and skip the less Important ones. DC models this abstract planning behavior by parsing geometry problem diagrams into perceptual chunks, called diagram configurations. which cue relevant schematic knowledge. We provide verbal protocol evidence that DC’s schemas correspond with the step-skipping inferences experts make in their initial planning. We compare DC with other models of geometry expertise and then, in the final section, we discuss more general implications of our research. DC’s reasoning hos important similarities with Lorkin’s (1988) display-based reasoning approach and Johnson-Loird’s (1983) mental model approach. DC’s perceptually hosed schemas ore o step towards a unified explanation of (1) experts’ superior problem-solving effectiveness, (2) experts’ superior problem-state memory, and (3) experts’ ability, in certain domains. to solve relatively simple problems by pure forward inferencing