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.     

Multiple causes of difficulty in insight: the case of the nine-dot problem

Theories of insight problems are often tested by formulating hypotheses about the particular difficulties of individual insight problems. Such evaluations often implicitly assume that there is a single difficulty. We argue that the quantitatively small effects of many studies arise because the difficulty of many insight problems is determined by multiple factors, so the removal of 1 factor has limited effect on the solution rate. Difficulties can reside either in problem perception, in prior knowledge, or in the processing of the problem information. We support this multiple factors perspective through 3 experiments on the 9-dot problem (N.R.F. Maier, 1930). Our results lead to a significant reformulation of the classical hypothesis as to why this problem is difficult. The results have general implications for our understanding of insight problem solving and for the interpretation of data from studies that aim to evaluate hypotheses about the sources of difficulty of particular insight problems.     

Categories of insight and their correlates: An exploration of relationships among classic‐type insight problems,rebus puzzles,remote associates and esoteric analogies

A central question in creativity concerns how insightful ideas emerge. Anecdotal examples of insightful scientific and technical discoveries include Goodyear's discovery of the vulcanization of rubber, and Mendeleev's realization that there may be gaps as he tried to arrange the elements into the Periodic Table. Although most people would regard these discoveries as insightful, cognitive psychologists have had difficulty in agreeing on whether such ideas resulted from insights or from conventional problem solving processes. One area of wide agreement among psychologists is that insight involves a process of restructuring. If this view is correct, then understanding insight and its role in problem solving will depend on a better understanding of restructuring and the characteristics that describe it. This article proposes and tests a preliminary classification of insight problems based on several restructuring characteristics: the need to redefine spatial assumptions, the need to change defined forms, the degree of misdirection involved, the difficulty in visualizing a possible solution, the number of restructuring sequences in the problem, and the requirement for figure‐ground type reversals. A second purpose of the study was to compare performance on classic spatial insight problems with two types of verbal tests that may be related to insight, the Remote Associates Test (RAT), and rebus puzzles. In doing so, we report on the results of a survey of 172 business students at the University of Waikato in New Zealand who completed classic‐type insight, RAT and rebus problems.     

A process model for water jug problems

We develop and evaluate a model for the water jug task in which a subject is required to find a sequence of moves (pouring operations) which produce a specified amount of water in each jug. Experiment 1 was designed to evaluate the meansends, move selection heuristics that are assumed by the model. Experiment 2 tested the model's predictions concerning those aspects of the water jug task that determine problem difficulty.A three stage process model incorporating GPS-like, means-ends heuristics and assumptions concerning the utilization of short- and long-term memory was able to account for differences across problems as well as details of the performance of subjects solving a given problem. We conclude that a GPS-like model that only selects one move at a time (no forward planning of move sequences or setting up of subgoals) can provide a good account of solution behavior in the water jug task.     

Act first, think later: The presence and absence of inferential planning in problem solving

Planning is fundamental to successful problem solving, yet individuals sometimes fail to plan even one step ahead when it lies within their competence to do so. In this article, we report two experiments in which we explored variants of a ball-weighing puzzle, a problem that has only two steps, yet nonetheless yields performance consistent with a failure to plan. The results fit a computational model in which a solver’s attempts are determined by two heuristics: maximization of the apparent progress made toward the problem goal and minimization of the problem space in which attempts are sought. The effectiveness of these heuristics was determined by lookahead, defined operationally as the number of steps evaluated in a planned move. Where move outcomes cannot be visualized but must be inferred, planning is constrained to the point where some individuals apply zero lookahead, which with n-ball problems yields seemingly irrational unequal weighs. Applying general-purpose heuristics with or without lookahead accounts for a range of rational and irrational phenomena found with insight and noninsight problems.     

What makes an insight problem? The roles of heuristics, goal conception, and solution recoding in knowledge-lean problems

Four experiments investigated transformation problems with insight characteristics. In Experiment 1, performance on a version of the 6-coin problem that had a concrete and visualizable solution followed a hill-climbing heuristic. Experiment 2 demonstrated that the difficulty of a version of the problem that potentially required insight for solution stems from the same hill-climbing heuristic, which creates an implicit conceptual block. Experiment 3 confirmed that the difficulty of the potential insight solution is conceptual, not procedural. Experiment 4 demonstrated the same principles of move selection on the 6-coin problem and the 10-coin (triangle) problem. It is argued that hill-climbing heuristics provide a common framework for understanding transformation and insight problem solving. Postsolution receding may account for part of the phenomenology of insight.     

A process model for Missionaries-Cannibals and other river-crossing problems

We extend a model originally developed by Atwood and Polson (1976) for the water jug task to four isomorphs of the Missionaries-Cannibals problem. Our results show that variation in cover story produced no differences in number of legal moves to solution, but caused large differences in illegal moves. A three-stage process model incorporating means-ends heuristics, assumptions about the utilization of memory, and an illegal move-detection process is able to account for both legal and illegal move data from all four versions of the problem.     

Numerosities and space; indeed a cognitive illusion! A reply to de Hevia and Spelke (2009)

de Hevia and Spelke (de Hevia and Spelke (2009). Spontaneous mapping of number and space in adults and young children, Cognition, 110, 198–207) investigated the mapping of number onto space. To this end, they introduced a non-symbolic flanker task. Here subjects have to bisect a line that is flanked by a 2-dot and a 9-dot array. Similar to the symbolic line bisection task, a bias towards the larger numerosity was observed. We re-investigated these results both by creating new flanker stimuli that controlled for different (non-numerical) stimulus properties and by developing a new measurement tool. We demonstrate that the bisection bias was caused by the larger area subtended by the 9-dot array compared to the 2-dot array and not numerosity. Our study puts constraints on the results of the study by de Hevia and Spelke. The role of visual cues in numerosity processing in general is discussed.     

Promoting Insightful Problem Solving

This work assessed whether insightful problem solving could be trained. Specifically, we tested whether solutions to a heterogeneous set of verbal insight problems could be promoted. A training scheme was developed to promote the application of mechanisms that underlie the process of restructuring. Training across the five experiments consisted of different combinations of the following training techniques: advance strategic instructions, varying amounts of practice, practice with different types of feedback, and problem comparison. Results from all five experiments showed that training can promote solutions to verbal insight problems. Facilitation effects ranged from a 14%–24% gain in overall solution rates relative to no‐treatment controls. This work demonstrated that insightful problem solving could be trained at a relatively high level of generality.     

Deconstructing the tower: Parameters and predictors of problem difficulty on the Tower of London task

The Tower of London (TOL) task has been widely used in both clinical and research realms. In the current study, 104 healthy participants attempted all possible moderate- to high-difficulty TOL problems in order to determine: (1) optimal measures of problem solving performance, (2) problem characteristics, other than the minimum moves necessary to solve the problem, that determine participants’ difficulty in solving problems successfully, quickly, and efficiently, and (3) effects of increased task experience on which problem characteristics determine problem difficulty. A factor analysis of six performance measures found that, regardless of task experience, problem difficulty could be captured well either by a single factor corresponding to general quality of solution or possibly by three subordinate factors corresponding to solution efficiency, solution speed, and initial planning speed. Regression analyses predicting these performance factors revealed that in addition to a problem’s minimum moves three problem parameters were critical in determining the problem difficulty: goal position hierarchy, start position hierarchy, and number of solution paths available. The relative contributions of each of the characteristics strongly depended on which performance factor defined performance. We conclude that TOL problem performance is multifaceted, and that classifying problem difficulty using only the minimum moves necessary to solve the problem is inadequate.     

顿悟式组块破解的时间进程：ERP研究

本研究旨在探讨顿悟式组块破解的信息加工机制及神经动态变化。被试完成汉字拆解任务,也即从一个源汉字中移动部件从而得到有效汉字。研究操纵部件之间在空间交错背景下的类别关系：同类（移动部件和剩余部件都是汉字）和异类（移动部件是笔画,剩余部件是汉字）。与此同时记录事件相关电位变化。结果显示,同类条件比异类条件引发了更大的N2波动和减小的LPC波动。早期的N2效应可能提示了组块破解过程中的识别困难,而晚期的LPC效应可能提示了组块破解过程中的知觉转换困难。     

Working memory and syllogistic reasoning

The purpose of this study was to examine the relation between working memory span and syllogistic reasoning performance. In addition, performance for the reasoning task was compared to predictions made by mental model theory and the probability heuristics model. According to mental model theory, syllogisms that require the use of more mental models are more difficult. According to the probability heuristics model difficulty is related to the number of probabilistic heuristics that must be applied, or (for invalid syllogisms) inconsistencies between the derived and correct conclusion. The predictions of these theories were examined across two experiments. In general, people with larger working memory capacities reasoned better. Also, the responses made by people with larger capacities were more likely to correspond to the predictions made by both mental model theory and the probability heuristics model. Relations between working memory span and performance were also consistent with both theories.     

Recollection, fluency, and the explicit/implicit distinction in artificial grammar learning

In this article, the authors propose that both implicit memory and implicit learning phenomena can be explained by a common set of principles, in particular via participants' strategic use of recollective and fluency heuristics. In a series of experiments, it was demonstrated that manipulating processing fluency had an impact on classification decisions in an artificial grammar learning task (Experiments 1, 2, 4, and 7), showing that participants were using a fluency heuristic. Under identical conditions, however, this manipulation had no effect on recognition decisions (Experiments 3 and 5), consistent with a greater default reliance on recollection. Most significant, the authors also showed that a fluency effect can be induced in recognition (Experiments 4-6) and can be eliminated in classification (Experiment 7).     

When insight just won't come: The failure of visual cues in the nine-dot problem

The nine-dot problem is a classic in the field of human problem solving. Cognitive accounts of the problem's difficulty have been criticized on the grounds that the experimental methods on which they rely for support involve a qualitative change to the task requirements of the problem. The three experiments reported here utilize visual and visual-procedural hints to examine the notion that its difficulty is rooted in a mismatch between problem shape and solution shape. Experiment 1 demonstrated that a perceptual cue to the shape of the solution in the form of shading gave rise to only minimal improvements in performance; an additional hint about the relevance of the shading gave rise to modest, but not statistically significant, improvements. Experiment 2 replicated these findings against an additional control condition in which a solely verbal hint to violate the perceptual boundary of the problem shape was given. Furthermore, when both the verbal and visual hints were provided, performance improved only slightly. Experiment 3 provided participants with experience in producing the shape of the correct solution in problem variants closely related to the nine-dot problem. Performance on the transfer task, the basic nine-dot problem, remained at floor, however. These data suggest that visual constraint relaxation is unlikely to be the sole process by which the insight required to find a solution is achieved. The results are interpreted in terms of a previously proposed computational model of performance.     

The dynamics of search,impasse, and representational change provide a coherent explanation of difficulty in the nine-dot problem

The nine-dot problem is often used to demonstrate and explain mental impasse, creativity, and out of the box thinking. The present study investigated the interplay of a restricted initial search space, the likelihood of invoking a representational change, and the subsequent constraining of an unrestricted search space. In three experimental conditions, participants worked on different versions of the nine-dot problem that hinted at removing particular sources of difficulty from the standard problem. The hints were incremental such that the first suggested a possible route for a solution attempt; the second additionally indicated the dot at which lines meet on the solution path; and the final condition also provided non-dot locations that appear in the solution path. The results showed that in the experimental conditions, representational change is encountered more quickly and problems are solved more often than for the control group. We propose a cognitive model that focuses on general problem-solving heuristics and representational change to explain problem difficulty.     

Heuristics made easy: an effort-reduction framework

In this article, the authors propose a new framework for understanding and studying heuristics. The authors posit that heuristics primarily serve the purpose of reducing the effort associated with a task. As such, the authors propose that heuristics can be classified according to a small set of effort-reduction principles. The authors use this framework to build upon current models of heuristics, examine existing heuristics in terms of effort-reduction, and outline how current research methods can be used to extend this effort-reduction framework. This framework reduces the redundancy in the field and helps to explicate the domain-general principles underlying heuristics.     

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.     

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.     

Working in Dyads and Alone: Examining Process Variables in Solving Insight Problems

This study investigated the effects of working in dyads and their associated gender composition on performance (solution rate and time) and process variables (number of impasses, number of passed solutions, and number of problem solving suggestions and interactions) in a set of classic insight problem solving tasks. Two types of insight problems were used: multiple moves available (MMA) and few moves available (FMA) problems. The results showed no effects on number of problems solved or solving time, but group and gender composition effects emerged when looking at process variables such as number of impasses, time to impasse, number of passed solutions, number of problem solving suggestions, and number of interactions between dyad members. Results support prior evidence that process loss in creative problem solving may be due to differences in interpersonal interactions during group problem solving that do not necessarily affect overall problem solving success.     

顿悟体验的特性、结构和功能基础

顿悟体验是伴随顿悟问题解决过程的心理和现象学体验,主要包含伴随题解闪现的啊哈体验和因思维定势自动激活而催生的僵局阶段体验。现有研究显示,顿悟体验可能是多类认知与情绪要素构成,兼具认知和情绪加工特性的多维复合体。加工流畅性可部分解释顿悟体验的产生机制,杏仁核、眶额区和脑岛等情绪和奖赏加工的脑区则可能是其脑功能基础。未来须用多元方法从新旧交替视角深化两阶段顿悟体验的研究。