Individual differences in problem solving via insight

The purpose of the present work was to identify general problem solving skills that underlie the production of insight. One hundred and eighteen participants completed insight problems, analogies, series-completion problems and the Remote Associates Test. Scores on all measures were related to performance on the insight problems (Pearson r's ranged from .31 to .47, p < .008). These findings are consistent with the notion that the abilities to apprehend relations and fluency of thought are involved in insightful problem solving.     

Interactive insight problem solving

Insight problem solving was investigated with the matchstick algebra problems developed by Knoblich, Ohlsson, Haider, and Rhenius (1999 Knoblich, G., Ohlsson, S., Haider, H. and Rhenius, D. 1999. Constraint relaxation and chunk decomposition in insight problem solving. Journal of Experimental Psychology: Learning, Memory and Cognition, 25: 1534–1555. [Crossref], [Web of Science ®] , [Google Scholar]). These problems are false equations expressed with Roman numerals that can be made true bymoving one matchstick. In a first group participants examined a static two-dimensional representation of the false algebraic expression and told the experimenter which matchstick should be moved. In a second group, participants interacted with a three-dimensional representation of the false equation. Success rates in the static group for different problem types replicated the pattern of data reported in Knoblich et al. (1999 Knoblich, G., Ohlsson, S., Haider, H. and Rhenius, D. 1999. Constraint relaxation and chunk decomposition in insight problem solving. Journal of Experimental Psychology: Learning, Memory and Cognition, 25: 1534–1555. [Crossref], [Web of Science ®] , [Google Scholar]). However, participants in the interactive group were significantly more likely to achieve insight. Problem-solving success in the static group was best predicted by performance on a test of numeracy, whereas in the interactive group it was best predicted by performance on a test of visuo-spatial reasoning. Implications for process models of problem solving are discussed.     

Dynamics and constraints in insight problem solving

This article reports 2 experiments that investigated performance on a novel insight problem, the 8-coin problem. The authors hypothesized that participants would make certain initial moves (strategic moves) that seemed to make progress according to the problem instructions but that nonetheless would guarantee failure to solve the problem. Experiment 1 manipulated the starting state of the problem and showed that overall solution rates were lower when such strategic moves were available. Experiment 2 showed that failure to capitalize on visual hints about the correct first move was also associated with the availability of strategic moves. The results are interpreted in terms of an information-processing framework previously applied to the 9-dot problem. The authors argue that in addition to the operation of inappropriate constraints, a full account of insight problem solving must incorporate a dynamic that steers solution-seeking activity toward the constraints.     

Intuition in insight and noninsight problem solving

People’s metacognitions, both before and during problem solving, may be of importance in motivating and guiding problem-solving behavior. These metacognitions could also be diagnostic for distinguishing among different classes of problems, each perhaps controlled by different cognitive processes. In the present experiments, intuitions on classic insight problems were compared with those on noninsight and algebra problems. The findings were as follows: (1) subjective feeling of knowing predicted performance on algebra problems but not on insight problems; (2) subjects’ expectations of performance greatly exceeded their actual performance, especially on insight problems; (3) normative predictions provided a better estimate of individual performance than did subjects’ own predictions, especially on the insight problems; and, most importantly, (4) the patterns-of-warmth ratings, which reflect subjects’ feelings of approaching solution, differed for insight and noninsight problems. Algebra problems and noninsight problems showed a more incremental pattern over the course of solving than did insight problems. In general, then, the data indicated that noninsight problems were open to accurate predictions of performance, whereas insight problems were opaque to such predictions. Also, the phenomenology of insight-problem solution was characterized by a sudden, unforeseen flash of illumination. We propose that the difference in phenomenology accompanying insight and noninsight problem solving, as empirically demonstrated here, be used to define insight.     

Working memory demands in insight versus analytic problem solving

Working memory is one of the cognitive processes thought to differentiate insight and analytic forms of problem solving. The present research examined memory involvement in the solution of insight versus analytic problems. Participants completed verbal and spatial working memory and short-term memory measures and a series of analytic and insight problems. Results demonstrated a relationship between working-memory capacity and the solution of analytic problems and between verbal short-term memory capacity and the solution of insight problems. This distinction was generally though not universally supported when memory was examined in relation to individual problems. Memory involvement in insight problem solving was further examined to clarify whether restructuring in insight is the end result of active memory search or spontaneous processes. The present research supports the theory that differences exist in the cognitive processes underlying insight versus analytic problem solving, and provides support for the spontaneous theory of restructuring in insight.     

Effects of subliminal hints on insight problem solving

Two experiments tested a total of 509 participants on insight problems (the radiation problem and the nine-dot problem). Half of the participants were first exposed to a 1-min movie that included a subliminal hint. The hint raised the solution rate of people who did not recognize it. In addition, the way they solved the problem was affected by the hint. In Experiment 3, a novel technique was introduced to address some methodological concerns raised by Experiments 1 and 2. A total of 80 participants solved the 10-coin problem, and half of them were exposed to a subliminal hint. The hint facilitated solving the problem, and it shortened the solution time. Some implications of subliminal priming for research on and theorizing about insight problem solving are discussed.     

An eye movement study of insight problem solving

The representational change theory of insight claims that insight problems cause impasses because they mislead problem solvers into constructing inappropriate initial representations. Insight is attained when the initial representation is changed. In the present study (N = 24), we tested three specific implications of these hypotheses against eye movements recorded while participants solved matchstick arithmetic problems. The results were consistent with the predictions, providing converging evidence with prior findings using solution rates and solution times. Alternative theories of insight can explain individual findings, but only the representational change theory accounts for both the performance data and the eye movement data. The present study also suggests that eye movement recordings provide an important new window into processes of insight problem solving.     

Improving insight and non‐insight problem solving with brief interventions

Developing brief training interventions that benefit different forms of problem solving is challenging. In earlier research, Chrysikou (2006) showed that engaging in a task requiring generation of alternative uses of common objects improved subsequent insight problem solving. These benefits were attributed to a form of implicit transfer of processing involving enhanced construction of impromptu, on‐the‐spot or ‘ad hoc’ goal‐directed categorizations of the problem elements. Following this, it is predicted that the alternative uses exercise should benefit abilities that govern goal‐directed behaviour, such as fluid intelligence and executive functions. Similarly, an indirect intervention – self‐affirmation (SA) – that has been shown to enhance cognitive and executive performance after self‐regulation challenge and when under stereotype threat, may also increase adaptive goal‐directed thinking and likewise should bolster problem‐solving performance. In Experiment 1, brief single‐session interventions, involving either alternative uses generation or SA, significantly enhanced both subsequent insight and visual–spatial fluid reasoning problem solving. In Experiment 2, we replicated the finding of benefits of both alternative uses generation and SA on subsequent insight problem‐solving performance, and demonstrated that the underlying mechanism likely involves improved executive functioning. Even brief cognitive– and social–psychological interventions may substantially bolster different types of problem solving and may exert largely similar facilitatory effects on goal‐directed behaviours.     

Gender differences in advanced mathematical problem solving

Strategy flexibility in mathematical problem solving was investigated. In Studies 1 and 2, high school juniors and seniors solved Scholastic Assessment Test-Mathematics (SAT-M) problems classified as conventional or unconventional. Algorithmic solution strategies were students' default choice for both types of problems across conditions that manipulated item format and solution time. Use of intuitive strategies on unconventional problems was evident only for high-ability students. Male students were more likely than female students to successfully match strategies to problem characteristics. In Study 3, a revised taxonomy of problems based on cognitive solution demands was predictive of gender differences on Graduate Record Examination-Quantitative (GRE-Q) items. Men outperformed women overall, but the difference was greater on items requiring spatial skills, shortcuts, or multiple solution paths than on problems requiring verbal skills or mastery of classroom-based content. Results suggest that strategy flexibility is a source of gender differences in mathematical ability assessed by SAT-M and GRE-Q problem solving.     

Priming insight in groups: Facilitating and inhibiting solving an ambiguously worded insight problem

We extend research on the priming of insight by studying group problem solving. Groups of 2–4 participants tried to solve an ambiguously worded problem in the presence of a prime that reinforced the dominant but incorrect interpretation of the problem, a prime that reinforced the uncommon but correct interpretation, or no prime. The paradigm involved participants asking questions of the experimenter that could only be answered “yes” or “no.” In Experiment 1, the prime was present throughout the solving period; in Experiment 2, it was removed prior to the solving period. In both experiments, the primes had their predicted effects. Patterns in the time taken to solve the problem supported the idea that groups stuck at the impasse were more or less able to restructure the problem, depending on the environmental context. Data from the questions asked and questionnaires converged with time taken to solve the problem, consistent with the view that restructuring a problem is an automatic process that produces insight. A comparison of the group data in Experiment 1 with individually tested participants’ data revealed that the insight of the groups benefited from their being able to recognize lines of questions to follow, to listen to answers to questions asked, and to evaluate and reject errors or assumptions.     

Multiple paths to transfer and constraint relaxation in insight problem solving

In two experiments participants received various training methods designed to relax constraints present in the Four-Tree problem (deBono, 1967 deBono, E. 1967. The use of lateral thinking, London: Jonathan Cape.  [Google Scholar]), a difficult insight problem. Geometry misconceptions were corrected via direct instruction. Participants’ difficulty with developing three-dimensional representations was addressed via spontaneous analogical transfer (Experiment 1) or via cued analogical transfer (Experiment 2). We found that, while both training methods were effective, alleviating multiple constraints was more effective than the alleviation of single constraints via training programmes (c.f. Kershaw & Ohlsson, 2004 Kershaw, T. C. and Ohlsson, S. 2004. Multiple causes of difficulty in insight: The case of the nine-dot problem. Journal of Experimental Psychology: Learning Memory and Cognition, 30: 3–13. doi: 10.1037/0278-7393.30.1.3[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Providing single difficulty hints was ineffective in promoting solution. Implications for multiple paths to transfer (Nokes, 2009 Nokes, T. J. 2009. Mechanisms of knowledge transfer. Thinking & Reasoning, 15: 1–36. doi: 10.1080/13546780802490186[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Nokes & Ohlsson, 2005 Nokes, T. J. and Ohlsson, S. 2005. Comparing multiple paths to mastery: What is learned?. Cognitive Science, 29: 769–796. doi: 10.1207/s15516709cog0000_32[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and multiple constraints are discussed.     

Swinging into thought: Directed movement guides insight in problem solving

Can directed actions unconsciously influence higher order cognitive processing? We investigated how movement interventions affected participants’ ability to solve a classic insight problem. The participants attempted to solve Maier’s two-string problem while occasionally taking exercise breaks during which they moved their arms either in a manner related to the problem’s solution (swing group) or in a manner inconsistent with the solution (stretch group). Although most of the participants were unaware of the relationship between their arm movement exercises and the problem-solving task, the participants who moved their arms in a manner that suggested the problem’s solution were more likely to solve the problem than were those who moved their arms in other ways. Consistent with embodied theories of cognition, these findings show that actions influence thought and, furthermore, that we can implicitly guide people toward insight by directing their actions.     

Incentives improve performance on both incremental and insight problem solving

An increasing number of studies are showing a connection between emotion and motivation and cognitive processes. Most of these studies, however, have been correlational in nature, limiting the conclusions that can be drawn. We directly manipulated motivation through the use of an incentive and investigated its effects on insight and incremental problem solving. In four experiments we found that an incentive (the opportunity to leave the experiment early) increased problem-solving performance for all problems presented, regardless of problem type. Additionally, we found evidence that the incentive increased recall memory, indicating more thorough processing for participants in the incentive condition. This study provides evidence that incentives influence problem solving and implies that motivation should not be ignored when investigating cognitive processes.     

Stepping out of history: mindfulness improves insight problem solving

Insight problem solving is hindered by automated verbal-conceptual processes. Because mindfulness meditation training aims at "nonconceptual awareness" which involves a reduced influence of habitual verbal-conceptual processes on the interpretation of ongoing experience, mindfulness may facilitate insight problem solving. This hypothesis was examined across two studies (total N=157). Participants in both studies completed a measure of trait mindfulness and a series of insight and noninsight problems. Further, participants in Study 2 completed measures of positive affect and a mindfulness or control training. The results indicated that (a) trait mindfulness predicts better insight but not noninsight problem solving (both studies), (b) this relation is maintained when controlling for positive affect (Study 2), (c) mindfulness training improves insight but not noninsight problem solving (Study 2) and (d) this improvement is partially mediated by state mindfulness (Study 2). These findings are the first to document a direct relation between mindfulness and creativity.     

Investigating the effect of mental set on insight problem solving

Mental set is the tendency to solve certain problems in a fixed way based on previous solutions to similar problems. The moment of insight occurs when a problem cannot be solved using solution methods suggested by prior experience and the problem solver suddenly realizes that the solution requires different solution methods. Mental set and insight have often been linked together and yet no attempt thus far has systematically examined the interplay between the two. Three experiments are presented that examine the extent to which sets of noninsight and insight problems affect the subsequent solutions of insight test problems. The results indicate a subtle interplay between mental set and insight: when the set involves noninsight problems, no mental set effects are shown for the insight test problems, yet when the set involves insight problems, both facilitation and inhibition can be seen depending on the type of insight problem presented in the set. A two process model is detailed to explain these findings that combines the representational change mechanism with that of proceduralization.     

Incentives improve performance on both incremental and insight problem solving

An increasing number of studies are showing a connection between emotion and motivation and cognitive processes. Most of these studies, however, have been correlational in nature, limiting the conclusions that can be drawn. We directly manipulated motivation through the use of an incentive and investigated its effects on insight and incremental problem solving. In four experiments we found that an incentive (the opportunity to leave the experiment early) increased problem-solving performance for all problems presented, regardless of problem type. Additionally, we found evidence that the incentive increased recall memory, indicating more thorough processing for participants in the incentive condition. This study provides evidence that incentives influence problem solving and implies that motivation should not be ignored when investigating cognitive processes.     

Using another's gaze as an explicit aid to insight problem solving

Research has shown that implicitly guiding attention via visual cues or unrelated tasks can increase the likelihood of solving insight problems. We examined whether following another person making specific skin-crossing saccades could induce similar attentional shifts and increase solution rates for Duncker's ((1945) Duncker, K. 1945. On problem solving. Psychological Monographs, 58 (5, Whole No. 270)[Crossref] , [Google Scholar]) radiation problem. We presented 150 participants with one of three 30-s eye movement patterns from another problem solver: (a) focusing solely on the central tumour; (b) naturally making skin-crossing saccades between the outside area and the tumour from multiple angles; or (c) making deliberate skin-crossing saccades between the outside area and the tumour from multiple angles. Following another person making skin-crossing saccades increased the likelihood of solving the radiation problem. Our results demonstrate that another person's eye movements can promote attentional shifts that trigger insight problem solving.