Past research in cognitive science reveals that prototypical configurations of domain objects, called perceptual chunks, underlie the abilities of experts to solve problems efficiently. Little research, however, has been carried out on the mechanism used for learning perceptual chunks from solving problems. The present paper addresses this issue in the domain of geometry proof problem-solving. We have developed a computational model that chunks, from problem diagrams, configuration of the elements which are visually grouped together, based on perceptual chunking criterion. This criterion, called recognition rules, reflects how people see problem diagrams and thus works effectively to determine which portion of problem diagrams are more likely to be grouped as a chunk. This distinguishes the proposed method from the goal- oriented chunking techniques used in machine-learning community. Experiments on solving geometry problems show that our technique can detect essential diagram configurations common to many problems. Additionally, implications of the recognition rules are discussed from a cognitive point of view.

This paper reports on an exploratory study of diagrammatic reasoning. Concurrent think-aloud protocols and gestures of subjects solving a set of device behavior hypothesis problems presented as labeled diagrams were collected. In addition to analyzing verbal protocols, the gestures and marks made by the subjects were examined and used to annotate encoded verbal data. A model of diagrammatic reasoiung in this task is proposed and compared with results of analyzing the protocols. Besides lending support to results of previous experimental studies, this study also revealed some interesting aspects of diagrammatic reasoning that merit further investigation.

Diagram-based problem solving is an activity in which subjects solve problems that are specified in the form of diagrams. Since the diagram contains critical information necessary for problem solving, this is an activity that clearly requires reasoning with the diagram. Recent research on diagrammatic reasoning has uncovered many interesting aspects of this process. One such aspect that the authors have been exploring, by means of a set of verbal and gestural protocol analysis experiments, is the role of the diagram in guiding the reasoning process. The trajectory of reasoning is revealed both by the intermediate hypotheses gen?erated, and by the shifts of focus induced from problem solving protocols. In this paper w e focus on the protocols collected for a particularly interesting problem, one whose solution is ar?rived at through a pair of contradictory inferences. W e derived the reasoning trajectories of subjects by extracting the temporal order and spatial distribution of their intermediate hypotheses leading toward the final solution. These trajectories indicate that the spatio-temporal order of hypotheses depend on more than the device structure depicted in the diagram and inferred causation of events from the diagram. W e propose that subjects employ impUcit search strategies which together with their in?ternal goals to verify hypotheses and the need to replenish short term memory influence their reasoning trajectories