Eye Movements during Geometrical Problem Solving

Abstract

Diagrams are used extensively in posing and solving geometry problems. It is likely that strategies that good problem-solvers have developed for looking at diagrams reflect their reasoning about each problem. This suggested that the eye-movement patterns of geometry experts, observed while they solve problems posed with diagrams, are likely to contain new information about their reasoning. Eye-movement data, collected while subjects solved geometry problems posed as diagrams, were examined. Three subjects participated. Two of the subjects (‘experts’) were skilled at solving geometry problems. The third subject (‘non-expert’) had last solved such problems over 50 years prior to the experiment, and did not know how to proceed on most of the problems. The eye-movement pattern reflected cognitive operations used to solve each problem. Fixation durations depended, to some extent, on cognitive or perceptual processing of features at each gaze location. For example, fixations were longer when gaze was on the angle in question, than when gaze was on other angles or line-segments. Likewise, saccades were made to features that were being considered, as indicated by verbal protocols. Expert subjects combined simple features into more complex, imaginary structures, as was required to solve the problem. They scanned the areas of the diagram that fell within the imagined contours of these structures. The non-expert did not construct such structures. He only scanned visible features of the diagram. Variability in durations of fixations and landing positions of saccades was not due solely to the probabilistic nature of the oculomotor processes. Such processes, however, clearly play an important role in determining the eye-movement pattern in this task, as they do in other visually-guided tasks.