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.\ud 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.\ud 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

Can Contraries Prompt Intuition in Insight Problem Solving?

“…Our results from the explicit guidance condition add to the previous literature based on implicit guidance which we mentioned in the introduction (e.g., Gale and Ball, 2012; Branchini et al, 2015a). The participants in our study were exposed to a brief training session in which it was suggested that they approach the task by systematically transforming the spatial features of a problem into their contraries.…”

“…It would also be interesting to explore new ways of stimulating both implicit processing (e.g., using dynamic visual tasks) and explicit processing (e.g., using different types of training). In terms of the current state of the art situation, only a provisional comparison can be made between the improvement due to prompting participants to use contraries in implicit and explicit guidance conditions based on the findings from the present study and that carried out by Branchini et al (2015a). There are obvious limits when one compares two experiments which do not perfectly coincide in terms of their experimental design.…”

“…As stated in the introduction, the study presented in this paper represents a conceptual development of a previous study in which contraries were used as an unaware, implicit strategy (Branchini et al, 2015a). A comparison between the effects of providing contraries as an implicit versus explicit guidance might tell us something more about how this heuristic impacts on the solution process.…”

“…The study presented in this paper represents a conceptual development of a previous study (Branchini et al, 2015a). In that study participants working in small groups were given implicit guidance during the search phase in order to help them to analyze the spatial properties of the problems they had been presented with in terms of contraries.…”

“…A brief training program was developed which demonstrated that the systematic manipulation of the features relating to a problem (in this case transforming them into their contraries) might facilitate the search for a solution. We focused on problem solving in a group setting (with groups of three people) since a previous study which demonstrated the positive effects of providing implicit guidance to use opposites in problem solving (Branchini et al, 2015a) was conducted with groups. It is also well known from previous literature that problem solving in groups does not necessarily follow the same path as individual problem solving (for a review, see for example Laughlin et al, 2006).…”