Insight and Search in Katona’s Five-Square Problem

Abstract

Insights are often productive outcomes of human thinking. We provide a cognitive model that explains insight problem solving by the interplay of problem space search and representational change, whereby the problem space is constrained or relaxed based on the problem representation. By introducing different experimental conditions that either constrained the initial search space or helped solvers to initiate a representational change, we investigated the interplay of problem space search and representational change in Katona’s five-square problem. Testing 168 participants, we demonstrated that independent hints relating to the initial search space and to representational change had little effect on solution rates. However, providing both hints caused a significant increase in solution rates. Our results show the interplay between problem space search and representational change in insight problem solving: The initial problem space can be so large that people fail to encounter impasse, but even when representational change is achieved the resulting problem space can still provide a major obstacle to finding the solution.

Moving arms: the effects of sensorimotor information on the problem-solving process

“…Our results are in contrast with an earlier report showing no effect of an initial hint on the solution ( € Ollinger et al, 2014). € Ollinger and colleagues cued participants by highlighting either the matchstick that has to be moved to decompose the chunk of the central square in Katona's (1940) five-square problem or highlighting the position where this matchstick has to be placed for a successful solution.…”

“…We predicted (a) an initial shift of participants' gaze to the left jar across arm movement conditions (e.g., Kazandjian et al, 2010); (b) that the left jar would be used more often for the initial problem representation and subsequently for producing problem solutions (Werner & Raab, 2013; (c) a small effect of the sensori-motor information on solution preferences ; and (d) a combined effect of jar arrangement and sensori-motor information on solution preferences (cf. € Ollinger, Jones, & Knoblich, 2014).…”

Can Contraries Prompt Intuition in Insight Problem Solving?

“…We acknowledge the limits of an analysis conducted on only one of the seven problems. However, analyses of a single problem are not uncommon in insight-problem solving studies (e.g., Grant and Spivey, 2003; Kershaw et al, 2013; Öllinger et al, 2013, 2014). Moreover, the results which emerged from this analysis were not meant to be conclusive, our intention was merely to offer some further indications on how training might have modified the direction which the participants' search took.…”

“…The training we exposed participants to was not specific to a given problem (as in, for example, Chronicle et al, 2001, Experiment 3; Weisberg and Alba, 1981; Grant and Spivey, 2003; Kershaw and Ohlsson, 2004; Kershaw et al, 2013; Öllinger et al, 2013, 2014) but rather provided advice on how to search for a solution to a set of (spatial) problems and in this sense it resembles meta-cognitive training. However, it differs from other types of domain-specific meta-cognitive training investigated in previous literature (some of which is domain specific, e.g., Walinga et al, 2011; Patrick and Ahmed, 2014; Patrick et al, 2015) in that the participants in the present study were asked to use the “oppositional reasoning” strategy they had been told about in their exploration of the spatial domain.…”

“…The aim of the experiment was to investigate the effects of specific hints or training on insight problem solving. The impact of general meta-cognitive training on performance has been addressed in previous literature (e.g., Walinga et al, 2011; Patrick and Ahmed, 2014; Patrick et al, 2015), as has the impact of more specific hints which have been customized to the contents of a specific problem (e.g., Chronicle et al, 2001, Experiment 3; Weisberg and Alba, 1981; Grant and Spivey, 2003; Kershaw and Ohlsson, 2004; Kershaw et al, 2013; Öllinger et al, 2013, 2014). What we aimed to focus on here, and to further test based on the results of the experiment, was the hypothesis that thinking in contraries might support transformations in the mental representation of a problem, as required by insight problem solving.…”