Abstract Planning and Perceptual Chunks: Elements of Expertise in Geometry

Planning and Perceptual Chunks: Elements of Expertise in Geometry KENNETH R. KOEDINGER AND JOHN R. ANDERSON Carnegie-Mellon UniversiIy We present o new model of skilled performance in geometry proof problem solvtrig called the Diagram Configuration model (DC). While previous models plan proofs in o step.by-step fashion we observed that experts plan at o more abstract 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 plonnmg. We compore DC with other models of geometry expertise ond 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 towords o unified explanation of (1) experts’ superior problem-solving effectlveness, (2) experts’ superior problem-state memory, and (3) experts’ ability, in certain domains. to solve relatively simple problems by pure forward inferencing. We also argue thot the porticulor and efficient knowledge organization of DC challenges current theories of skill acquisition as it presents on end-state of learning thot is difficult to explain within such theories. Finally. we discuss the Implications of DC for geometry instruction. Detailed study of successful performance in difficult task domains can provide a strong basis for understanding the processes of problem solving and the nature of thought in general. To become an expert in a difficult field This research was supported by grant 86-17083 from the NatIonal Science Foundation and by a United Stares Air Force Graduate Fellowship 10 the firsr author. Thanks 10 Jill Larkin. Kurt Vanlehn. and Herbert Simon for insightful counsel. Thanks also IO Christina Allen. Stephen Casner. Lael Schooler. editor Jim Green0 and the reviewers: Jeremy Kilpatrick. Robert Lindsay, and an anonymous cognitive psychologist for their helpful comments and advice. Portions of this work were reported at the 1989 meeting of rhe American Educational Research Association in San Francisco, CA and at the 1989 meeting of the Cognitive Science Society in Ann Arbor, MI. Correspondence and requests for reprints should be sent 10 Ken Koedinger, Psychology Department. Carnegie-Mellon University. Pittsburgh. PA, 15213.