Contraries as an effective strategy in geometrical problem solving

Abstract

A focused review of the literature on reasoning suggests that mechanisms based upon contraries are of fundamental importance in various abilities. At the same time, the importance of contraries in the human perceptual experience of space has been recently demonstrated in experimental studies. Solving geometry problems represents an interesting case as both reasoning abilities and the manipulation of perceptual–figural aspects are involved.In this study we focus on perceptual changes in geometrical problem solving processes in order to understand whether a mental manipulation in terms of opposites might help. Four conditions were studied, two of which concerned the search for contraries as an implicit or explicit strategy.Results demonstrated that contraries, when used explicitly in solution processes, constitute an effective heuristic: The number of correct solutions increased, less time was needed to find a solution and participants were oriented towards the use of perception-based solutions—not only were perceptual solutions more frequent, but also, more specifically, the number of correct perceptual solutions increased. These last results concerning perception-based solutions were found both when participants were advised about the usefulness of the strategy and when they were not advised. Differences concerning which aspects of a problem were focused on during the solution process also emerged.