Rebus puzzles as insight problems

Research on insight-the phenomenon of suddenly solving an apparently intransigent problem--has been hampered because stimulus problems have been few, ad hoc, heterogeneous, and difficult to solve. Responding to the need for a larger pool of problems of a similar type and of varying level of difficulty, we report an experiment testing the validity of rebuses as insight problems. A rebus combines verbal and visual clues to a common phrase, such as PAINS ("growing pains"). Solving a rebus requires breaking implicit assumptions of normal reading, similar to the restructuring required in insight. We hypothesized that, the more implicit assumptions are involved, the more difficult the solution. The results of a two-part experiment supported the hypothesis, with participants solving more problems involving one assumption than they did problems involving two or more. Also, rebus performance correlated significantly with self-rated insight and with scores on remote associates, but not with general verbal ability. The findings suggest that rebus puzzles may be a useful source of theoretically grounded insight problems.     

Differentiating insight from non-insight problems

This study aimed to investigate whether a range of tasks that have been generally classed as requiring insight form an empirically separable group of tasks distinct from tasks generally classed as non-insight. In this study, 24 insight tasks, 10 non-insight tasks, and tests of individual differences in cognitive abilities and working memory were administered to 60 participants. Cluster analysis of the problem-solving tasks indicated that the presumed insight problems did tend to cluster with other presumed insight problems, and similarly the presumed non-insight problems tended to cluster with other presumed non-insight tasks. Performance on presumed insight problems was particularly linked to measures of ideational flexibility with a different pattern of results for the non-insight tasks. Spatial insight problems were linked to spatial flexibility and verbal insight tasks were linked to vocabulary scores. The results are discussed in relation to recent developments of dual process theories of thinking.     

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.     

A generalization of the representational change theory from insight to non-insight problems: the case of arithmetic word problems

This paper provides evidence for a possible generalization of Knoblich and colleagues’ representational change theory [Knoblich, G., Ohlsson, S., Haider, H., & Rhenius, D. (1999). Constraint relaxation and chunk decomposition in insight problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 25, 1534-1555; Knoblich, G., Ohlsson, S., & Raney, G. E. (2001). An eye movement study of insight problem. Memory and Cognition, 29, 1000-1009] outside its original scope of application. While this theory has been proposed to explain insight problem solving, we demonstrate here that its main concepts, namely, constraint relaxation and chunk decomposition, are applicable to incremental problem solving. In a first experiment, we confirm, as already shown by problem solving and reasoning researchers, that individuals avoid the construction of alternative representations of the problems when possible. In the second and third experiments, we show that alternative representations of arithmetic problems are easier to construct and maintain when they violate constraints of narrow rather than wide scope. The specificity of insight problem solving is discussed in the light of these new findings.     

Teaching students to solve insight problems: Evidence for domain specificity in creativity training

The purpose of this research was to investigate whether insight problem solving depends on domain‐specific or domain‐general problem‐solving skills, that is, whether people think in terms of conceptually different types of insight problems. In Study 1, participants sorted insight problems into categories. A cluster analysis revealed 4 main categories of insight problems: verbal, mathematical, spatial, and a combination of verbal or spatial. In Studies 2 and 3, participants received training in how to solve verbal, spatial, or mathematical problems, or all 3 types. They were taught that solutions to verbal insight problems lie in defining and analyzing the terms in the problem, solutions to mathematical insight problems lie in a novel approach to numbers, or solutions to spatial insight problems lie in removing a self‐imposed constraint. In both studies, the spatial trained group performed better than the verbal trained group on spatial problems but not on other types of problems. These findings are consistent with the idea that people mentally separate insight problems into distinct types. Implications for instruction in insight problem solving are discussed.     

Improving examples to improve transfer to novel problems

People often memorize a set of steps for solving problems when they study worked-out examples in domains such as math and physics without learning what domain-relevant subgoals or subtasks these steps achieve. As a result, they have trouble solving novel problems that contain the same structural elements but require different, lower-level steps. In three experiments, subjects who studied example solutions that emphasized a needed subgoal were more likely to solve novel problems that required a new approach for achieving this subgoal than were subjects who did not learn this subgoal. This result suggests that research aimed at determining the factors that influence subgoal learning may be valuable in improving transfer from examples to novel problems.     

Optimal trade-offs of multiple factors in transfer pricing problems

Transfer pricing problems have been extensively researched by a number of scholars. It is well recognized that transfer pricing problems have a multiple-criteria (objectives) feature and can be formulated as a model of multiple-criteria linear programming. However, few methods have the capability of dealing with all possible optimal trade-offs of multiple criteria in optimal solutions of the models. In this paper a linear multiple-factor model is developed to provide managers with a more systematic and comprehensive scenario of all possible optimal transfer prices depending on both multiple criteria and multiple constraint levels. The trade-offs of all possible optimal transfer prices can be used as a basis for managers of a corporation to make a high-quality decision in selecting their transfer pricing systems for business competition. © 1998 John Wiley & Sons, Ltd.     

Conceptual and methodological problems in the analysis of self-serving causal attributions of success and failure

The present article examined conceptual and methodological foundations of testing the self-serving hypothesis of causal attributions. This analysis revealed a startling fact that neither major reviews (by Bradley, Miller & Ross; Snyder et al.; Weary & Arkin; and Zuckerman) nor other reports have provided a clear and specific definition of the self-serving attributions. Furthermore, methodological defects exist because of such fundamental errors as the use of between-subjects designs, instead of within-subjects designs, in testing the hypothesis. Therefore, the reported experiments simply reflect the researchers' attempts to interpret subjects' attributions as self-serving or non-self-serving. To better understand the nature and scope of self-serving motives in causal attributions, it is essential (1) to take into account attributors' personal definitions of self-serving attributions, (2) to relate the nonreciprocal attributions to social/cultural values about self-serving behaviors, and (3) to determine the role of intentions in causal attributions of success and failure.     

Information processing and insight: a process model of performance on the nine-dot and related problems

The 9-dot problem is widely regarded as a difficult insight problem. The authors present a detailed information-processing model to explain its difficulty, based on maximization and progress-monitoring heuristics with lookahead. In Experiments 1 and 2, the model predicted performance for the 9-dot and related problems. Experiment 3 supported an extension of the model that accounts for insightful moves. Experiments 4 and 5 provided a critical test of model predictions versus those of previous accounts. On the basis of these findings, the authors claim that insight problem solving can be modeled within a means-ends analysis framework. Maximization and progress-monitoring heuristics are the source of problem difficulty, but also create the conditions necessary for insightful moves to be sought. Furthermore, they promote the discovery and retention of promising states that meet the progress-monitoring criterion and attenuate the problem space.     

How physical interaction with insight problems affects solution rates,hint use,and cognitive load

So-called insight problems are widely studied because they tap into the creative thinking that is crucial for solving real problems. However, insight problems are typically presented in static formats (on paper, computer) that allow no physical interaction with the problem elements, whereas such an interaction might in fact reduce the load on limited cognitive resources, such as working memory (WM) capacity, thereby facilitating solutions. To test this proposition, 124 young adults were allowed to interact physically with nine established insight problems, while another 124 people attempted to solve these problems using paper and pencil. Additionally, hints were provided for three problems that typically no-one solves. No general facilitating effect of physical interaction was found, with only one problem clearly benefitting from it. Furthermore, making use of hints was actually hindered by physical interaction. No difference in perceived task load and correlation with WM capacity was observed between the formats, and subjective ratings of insight were virtually unaffected by presentation format. Overall, physical interaction minimally affected insight problem-solving, which appears to rely strongly on internalized cognitive processing involving WM.     

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.     

Sequential transfer to related oddity problems by nursery school children

The initial learning and subsequent transfer of an oddity principle by children between 4 and 5 years of age were studied. The initial standard oddity problem was learned quickly by most of the children. A high level of performance was maintained on both transfer sets. The results were related to limitations placed on the oddity solutions learned by 4-year-olds by particular aspects of the original learning context.     

Failure to construct and transfer correct representations across probability problems

Previous studies carried out on "purely random" situations (with dice or poker chips) show the difficulties encountered by people in such situations, however simple they may be. In fact, in this type of situation, prior knowledge guides spontaneous representations, and the "errors" observed could be explained by the activation of "implicit models" which form the basis of erroneous representations. 42 statistically na?ve undergraduates were given several variants of a probability problem on which errors are common. In a learning phase, subjects were given four problems involving geometric figures which were pairwise related by complementarity and equivalence relations. In a subsequent transfer phase, they were given a fifth problem involving poker chips, which was structurally isomorphic to the fourth geometric-figures problem. The findings show that people do not realize the relations between problems, and that transfer occurred only for the subset of subjects who performed correctly on the training problems of the learning phase. These results appear to have some significant implications in teaching mathematical concepts.     

Conceptual pragmatism

The paper puts forward the thesis of conceptual pragmatism: that there are pragmatic choices to be made between distinct but similar concepts within various contexts. It is argued that this thesis should be acceptable to all who believe in concepts, whether the believers are platonists, realists or anti-realists. It is argued that the truth of the thesis may help to resolve many long-standing debates, and that in any case it will lead to an extension of philosophical method. The paper then briefly considers the concepts of belief and desire as a case-study, and argues for the recognition of the practical reasoner's stance (to stand alongside Dennett's intentional stance), relative to which we should select concepts of belief and desire which are broadly cartesian.I am grateful to the following for their help (varying from detailed comments and criticisms on earlier drafts, to general advice and encouragement): David Archard, Simon Blackburn, Jack Copeland, Dan Dennett, Susan Levi, Christopher McKnight, Derek Parfit, Michael Slote, Tim Williamson, and Crispin Wright.