Contraries as an effective strategy in geometrical problem solving

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