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.     

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.     

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.     

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.     

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.     

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)) 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.     

Individual differences in working memory and reasoning-remembering relationships in solving class-inclusion problems

In the present experiment, we evaluated the effects of individual differences in reading span and variation in memory demands on class-inclusion performance. One hundred twenty college students whose reading spans ranged from low to medium to high (as indexed by a computerized version of the Daneman and Carpenter [1980] reading-span task) solved 48 class-inclusion problems. Half of the subjects had the solution information available when the problems were presented; the other half performed a detection task between solution information and problem presentation. The results from both standard statistical analyses and from a mathematical model indicated that differences in reading span and memory load had predictable, similar effects. Specifically, the sophistication of reasoning strategies declined when memory demands increased or when reading spans decreased. Surprisingly, these effects were primarily additive. The results were interpreted in terms of global resource models and findings from the developmental literature.     

The neural basis of insight problem solving: an event-related potential study

The electrophysiological correlates of successful insight problem solving (Chinese logogriphs) were studied in 18 healthy subjects using high-density event-related potentials (ERPs). A new experimental paradigm (learning-testing model) was adopted in order to make subjects find a solution on their own initiative rather than receive an answer passively. Results showed that Successful guessed logogriphs elicited a more positive ERP deflection (P200-600) than did Unsuccessful guessed logogriphs in the time window from 200 to 600 ms after onset of the stimuli. Subsequently Successful logogriphs elicited a more negative ERP deflection than did Unsuccessful logogriphs in the time windows of 1500-2000 ms (N1500-2000) and 2000-2500 ms (N2000-2500). Maps of the P200-600 showed strong activity in the midline parieto-occipital scalp regions. Dipole analysis localized the generator of P200-600 in the left superior temporal gyrus and parietotemporo-occipital cortex areas. The N1500-2000 and N2000-2500 had a distinct activation over left frontal scalp regions. Dipole analysis localized the generator of the N1500-2000 in the anterior cingulate cortex (ACC) and the N2000-2500 in the posterior cingulate cortex (PCC). This result indicates that the parietotemporo-occipital cortex areas might be involved in forming rich associations in the early stage of successful logogriph solving. Then, the ACC might play an important role in the breaking mental set and the forming of novel associations. At last, "Aha" feeling might activate the PCC.     

Acquiring an understanding of design: evidence from children's insight problem solving

The human ability to make tools and use them to solve problems may not be zoologically unique, but it is certainly extraordinary. Yet little is known about the conceptual machinery that makes humans so competent at making and using tools. Do adults and children have concepts specialized for understanding human-made artifacts? If so, are these concepts deployed in attempts to solve novel problems? Here we present new data, derived from problem-solving experiments, which support the following. (i) The structure of the child's concept of artifact function changes profoundly between ages 5 and 7. At age 5, the child's conceptual machinery defines the function of an artifact as any goal a user might have; by age 7, its function is defined by the artifact's typical or intended use. (ii) This conceptual shift has a striking effect on problem-solving performance, i.e. the child's concept of artifact function appears to be deployed in problem solving. (iii) This effect on problem solving is not caused by differences in the amount of knowledge that children have about the typical use of a particular tool; it is mediated by the structure of the child's artifact concept (which organizes and deploys the child's knowledge). In two studies, children between 5 and 7 years of age were matched for their knowledge of what a particular artifact "is for", and then given a problem that can only be solved if that tool is used for an atypical purpose. All children performed well in a baseline condition. But when they were primed by a demonstration of the artifact's typical function, 5-year-old children solved the problem much faster than 6-7-year-old children. Because all children knew what the tools were for, differences in knowledge alone cannot explain the results. We argue that the older children were slower to solve the problem when the typical function was primed because (i) their artifact concept plays a role in problem solving, and (ii) intended purpose is central to their concept of artifact function, but not to that of the younger children.     

执行功能对言语顿悟问题解决的影响:基于行为与ERPs的研究

执行功能是否影响顿悟问题解决,顿悟问题解决中的表征重组阶段是否涉及执行功能仍存在争议。基于此,通过2个研究探讨执行功能对顿悟问题解决的影响。研究1初步探讨执行功能与个体顿悟能力之间的关系,结果发现个体的执行功能与其顿悟问题解决成绩之间存在显著正相关,刷新功能可以显著预测顿悟成绩;研究2使用汉字字谜任务,通过行为与ERPs技术探讨执行功能对言语顿悟问题解决的影响,其中研究2a,行为实验发现高工作记忆刷新能力的个体反应时显著小于低工作记忆刷新能力的个体,说明执行功能中工作记忆刷新亚成分影响顿悟问题解决。研究2b脑电结果发现,"顿悟"条件较之"无顿悟"条件诱发了一个更强的早期成分P2和N2,以及中晚期P3。P2可能主要反映人脑对思维僵局的早期觉察,受到执行功能高低的影响。280~500 ms内,中晚期P3则主要体现以新旧思路交替为特征的僵局打破过程,不受执行功能高低的影响,结果表明汉字字谜顿悟问题的表征重组阶段并未受到执行功能的影响,更倾向认为该阶段为一个突进的过程。综合2个研究说明,执行功能影响顿悟问题解决,其主要作用于顿悟问题解决过程的问题空间搜索阶段,而表征重组阶段是一个突进式的过程。