Creativity As a Source of Difﬁculty in Problem Solving

bundet

138 Lubart and Mouchiroud deﬁnition of a problem, divergent thinking, synthesis, the use of heuris- tics, remote association, the reorganization of information, as well as eval- uation and analysis of information (see Lubart, 2000 – 2001 ; Mumford, Mobley, Uhlman, Reiter-Palmon, & Doares, 1991 ). For example, the sub- process of forming remote associations may involve spreading activation through previously established links in semantic memory (Mednick, 1962 ), random chance-based connections that lead to coherentidea conﬁgurations (Simonton, 1988 ), or emotional resonance (Lubart & Getz, 1997 ). According to the emotional resonance model, each person has stored in memory a di- verse set of emotional experiences associated with objects, places, people, and situations that have been encountered. These emotional traces, called endocepts, are activated during problem solving and may resonate with each other, thereby activating cognitively remote but emotionally related concepts in memory. A person may, in turn, notice the simultaneously acti- vated concepts and form an association that is perhaps more idiosyncratic, and unusual in the population, than those formed through cognitive paths. Empirical tests of this model show that the emotional richness with which a concept is characterized explains signiﬁcant variance of originality in as- sociative thinking tasks based on the concept, beyond that explained by rich cognitive descriptions of the same concept (Getz & Lubart, 2000 ). Beyond the growing body of work concerning subprocesses involved in creativity, few studies have speciﬁcally addressed how the creative pro- cess as a whole differs from the noncreative or barely creative process. For example, are certain subprocesses present in very creative problem solv- ing and absent or reduced in less creative problem solving? Do different orders of the subprocesses lead to differences in the creative level of the outcome? Mumford et al. ( 1991 ) suggested that the creative problem solving pro- cess and the “canned,” noncreative process differ in four main ways. First, creative problem solving involves ill-deﬁned problems more than routine problem solving. This places an emphasis on the problem construction phase in creative work. Second, in the creative process people must gen- erate new, alternative solutions that involve divergent and convergent thinking. In routine problem solving, people apply previously acquired procedures, search for ready-made solutions, and tend to satisﬁce, all of which involve mainly convergent thinking (see also Mayer, 1999 ). Third, the creative process involves active, attention-demanding processing with multiple cycles of divergent and convergent thought, whereas the “stan- dard” process proceeds in an “additive fashion” with more direct activa- tion, generation, and application. Fourth, in the creative process existing information is restructured, reorganized, or combined. In routine, non- creative problem solving, information is recalled and understood using existing categories. Thus the subprocesses of combination and reorganiza- tion of category information as well as problem construction differentiate Creativity: A Source of Difﬁculty 139 creative and standard problem solving. Within the creative process, differ- ent levels of creativity result, in part, from the skill or quality with which each of the involved subprocesses is executed. Consider now some studies that begin to address how differences in the process as a whole contribute to the individual differences in creativity. For example, Getzels and Csikszentmihalyi ( 1976 ) observed art students as they made a drawing based on a set of objects that were provided (e.g., a manikin, a book, a hat, a glass prism). A panel of expert judges rated the originality of the drawings. All the art students handled the objects to set up their still-life composition. However, some students manipulated only a few objects and did not examine much these objects, whereas other stu- dents explored in detail many of the proposed objects. Furthermore, some students rearranged the still-life composition after having begun to draw what they had initially set up. The number of objects manipulated and the extent to which each object was explored in detail correlated signiﬁcantly ( r>. 50 ) with originality, as did problem formulation behaviors during the drawing phase. Thus, differences in the quality and quantity of problem ﬁnding as well as when it occurred during the drawing task were related to originality. Using a think-aloud methodology, Goor and Sommerfeld ( 1975 ) exam- ined differences in the subprocesses used by “creative” and “noncreative” students preselected based on performance on divergent thinking tasks. The students thought aloud while solving three insight-type problems (making four triangles with six matches, killing a tumor without destroy- ing healthy cells, solving a problem concerning the selection of colored pebbles by chance). Problem-solving protocols were divided into brief in- tervals, and seven categories of verbal behavior were noted (e.g., generat- ing new information or hypotheses, self-reference or self-criticism, silence). The high creative group spent more time than the low creative group on generating new information or hypotheses, working on these hypotheses, and self-reference or self-criticism. There were also some group differences on the sequences of activities. For example, following self-reference or self- criticism, the high creative group tended to engage in generating new infor- mation or developing hypotheses, whereas the low creative group entered a period of silence. Finally, Lubart ( 1994 ) examined the nature of the creative process, by looking at the role of idea evaluation. The evaluation of the strengths and weaknesses of potential ideas and problem solutions under development serves as a ﬁlter in creative work. In natural work situations, we ﬁnd that some people auto-evaluate their ideas early on in their work. Others tend to make later auto-evaluations. Finally, there are those who engage in auto- evaluations at regular intervals. Based on these interindividual differences, two studies using an experimental methodology were conducted with uni- versity student participants. 140 Lubart and Mouchiroud In the ﬁrst study, the students composed short stories and created drawings based on provided objects; the creativity of these two types of productions was judged by graduate-level teaching assistants in, respec- tively, literary composition and studio art. During their work, the students were brieﬂy stopped at various times and instructed to evaluate for them- selves their production in progress. The moment and the quantity of these auto-evaluations were controlled. There were groups of subjects that car- ried out their auto-evaluations relatively early in the work, relatively late in the work, or at regular intervals throughout the work. Additionally, there was a control group that engaged in other activities at the indicated times and that was not explicitly encouraged to auto-evaluate. For the writing composition task, the results showed that early auto-evaluations were the most effective for creativity, in comparison with late auto-evaluations or auto-evaluations at regular intervals, and with the results of the control group. In a second study, these results were replicated, in general, with various methods for inducing auto-evaluations and with a different story-writing composition task. For the drawing task, no clear effect of the synchroniza- tion of auto-evaluations was found. This may be due to the fact that last- minute changes to a drawing could greatly inﬂuence its overall appearance, whereas the story task tended to be more linear, increasingly constrained as one progresses in elaborating the plot (“surprise” endings invented at the last minute tended to be inadequate). Finally, for the various tasks (short stories and drawings), no effect of the quantity of auto-evaluations was observed. These results indicate that differences in the sequence of cognitive ac- tivities can inﬂuence the level of creativity observed, at least for certain tasks. Thus, creative problem-solving seems to depend on having certain cognitive-conative resources and using them at appropriate points in the problem-solving process. It may well be that some potentially creative peo- ple who have relevant capacities and traits do not produce creative ideas because they fail to put their resources into action during the problem- solving process, with the optimal use of these resources being domain or task speciﬁc. creativity as a source of difficulty in problem solving: another look Up to this point, we have developed the idea that creativity is a source of difﬁculty in problem solving because some problems require original solutions and these solutions are not easy to generate. They require a set of cognitive and conative factors that are used at appropriate moments in the course of problem solving. In this ﬁnal section, we consider brieﬂy a rather different way in which creativity is a source of difﬁculty in problem solving. Creativity: A Source of Difﬁculty 141 Consider the following case that a physics professor submitted to his col- league, whom he requested to be an impartial judge: The physics professor asked on an exam how one could measure the height of a building using a barometer. The student replied that one could take the barometer to the top of the building, attach it to a cord, slowly let the barometer down along the side of the building and once the barometer was on the ground, bring it back up and measure the length of the cord to determine the height of the building. This answer was given a zero; it did not use any of the formulas taught in class. However the student claimed that the answer deserved full credit. The impartial colleague of the student’s professor decided to give the student a second chance and asked the student to respond to the ques- tion using his knowledge of physics. After several minutes without any response the impartial professor asked the student if he had found a so- lution. The student said that he had several and was trying to choose the best one. Soon after, he proposed putting the barometer on the roof and dropping it from the building. The height of the building can be found by applying a formula that takes into account the time it took the barometer to reach to ground and the gravitational constant. The impartial professor decided that this response deserved full credit. Seeing how the student had considered several answers, the impartial professor was curious to know what were the others. The student explained that one could put the barometer in the sun and measure its shadow as well as the building’s shadow, and then compare the two using a simple proportion. He noted several other solutions as well, such as one in which the barometer could be used as part of a pendulum with measures taken at the top and bottom of building. Finally, the student proposed that one could offer the building’s superintendent a barometer as a gift if he would give the height of the building. At the end of this exam, the impartial professor asked the student whether he knew which answer his professor had expected. The student replied that he did but he was fed up with having to spit back information to get a good grade. The student, by the way, was Niels Bohr, who went on to win the Nobel Prize in physics. The impartial professor was Ernest Rutherford. Ogden Nash, the modern American poet, summed up the point of the story in his work entitled Reﬂections on Ingenuity : “Sometimes too clever is dumb.” In other words, being creative can get one into trouble if “canned” problem solving is requested. Every year there are cases of students who claim that they deserve credit for their creative answers to test items, be- cause their responses are valid but do not correspond to the designated cor- rect answer. In this vein, Cropley ( 1996 ) described the case of a teacher who asked his class of 5 -year-olds to provide examples of “workers in wood.” Several answers were proposed, such as cabinet maker or carpenter. Then, 142 Lubart and Mouchiroud one child proposed “termites.” The teacher became angry at the child and told him to be silent if he was not able to propose a valid answer. Employ- ing creative thinking when a canned problem solving mode is requested can be, itself, a problem. Using the Ideal Child Checklist, which consists of a series of 66 traits to be evaluated as desirable or not for an ideal child, studies by Kaltsounis ( 1977 a, 1977 b) and Torrance ( 1975 ) have compared the teachers’ opinions with those of a panel of experts in the ﬁeld of creative personality. The results were striking: The traits characterizing an ideal student for ele- mentary school teachers were not at all similar to creativity experts’ de- scriptions of an ideal creative child’s proﬁle. For example, teachers favored traits such as “considerate of others” or “doing work on time,” whereas creativity experts saw “courage in convictions,” “curiosity,” and “indepen- dent thinking” as the most valuable characteristics. Kaltsounis reported that there was only 4 % of shared variance between the rankings given by teachers and creativity researchers. Another study involving student teach- ers showed that they valued highly “obedience/submission to authority” and did not value “unwillingness to accept things on mere say-so,” which are obviously antithetical to creativity. Such ﬁndings suggest that at least some school settings do not particularly emphasize creative problem solv- ing, and may even sanction it. Thus, we see how the environment is im- portant for providing a setting that favors or inhibits creative problem solving. conclusion All problem solving is not creative problem solving. Although we have contrasted “creative” and “canned” problem solving, there exists a con- tinuum between the two extremes; some problem solving relies heavily on existing procedures but requires some novelty, some enhancements to existing structures (Sternberg, 1999 ). In any case, the ability to come up with new and useful ideas applies to a wide range of problem situations (“creative” and “partially canned” ones) and represents one of the most valuable human assets. At the level of the individual, creativity relates to coping abilities, leadership, self-actualization, and psychological health (Carson & Runco, 1999 ). At the societal level, creative solutions contribute to major cultural advancements. Why is creative problem solving often difﬁcult? First, because creative thinking involves a large set of cognitive and conative factors. Second, these factors must be used appropriately during task completion, the problem solving process. Third, some environments are hostile toward new ideas and may even view creative thinking as a hindrance. Identifying difﬁ- culties associated with creative problem solving is one thing, overcoming these difﬁculties is another. Both of these endeavors should be pursued Creativity: A Source of Difﬁculty 143 because, in our view, there is much to problem solving beyond “canned” solutions. references Amabile, T. M. ( 1983 ). The social psychology of creativity . New York: Springer- Verlag. Amabile, T. M. ( 1996 ). Creativity in context . Boulder, CO: Westview. Amabile, T. M. ( 1997 ). Entrepreneurial creativity through motivational synergy. Journal of Creative Behavior, 31 ( 1 ), 18 – 26 . Baer, J. ( 1991 ). Creativity and divergent thinking: A task-speciﬁc approach . Hillsdale, NJ: Erlbaum. Baer, J. ( 1998 ). Gender differences in the effects of extrinsic motivation on creativity. Journal of Creative Behavior, 32 ( 1 ), 18 – 37 . Barron, F., & Harrington, D. M. ( 1981 ). Creativity, intelligence, and personality. Annual Review of Psychology, 32, 439 – 476 . Brophy, D. R. ( 1998 ). Understanding, measuring, and enhancing individual creative problem-solving efforts. Creativity Research Journal, 11 ( 2 ), 123 – 150 . Busse, T. V., & Mansﬁeld, R. S. ( 1980 ). Theories of the creative process: A review and a perspective. Journal of Creative Behavior, 14 ( 2 ), 91 – 103 . Cagle, M. ( 1985 ). A general abstract-concrete model of creative thinking. Journal of Creative Behavior, 19 ( 2 ), 104 – 109 . Carson, D. K., & Runco, M. A. ( 1999 ). Creative problem solving and problem ﬁnding in young adults: Interconnectionswithstress, hassles, and coping abilities. Journal of Creative Behavior, 33 ( 3 ), 167 – 190 . Cattell, R. B., Eber, H. W., & Tatsuoka, M. M. ( 1970 ). The handbook for the Sixteen Personality Factor (16PF) Questionnaire . Champaign, IL: Institute for Personality and Ability Testing. Cawelti, S., Rappaport, A., & Wood, B. ( 1992 ). Modeling artistic creativity: An empirical study. Journal of Creative Behavior, 26 ( 2 ), 83 – 94 . Collins, M. A., & Amabile, T. M. ( 1999 ). Motivation and creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 297 – 312 ). Cambridge: Cambridge University Press. Conti, R., Coon, H., & Amabile, T. M. ( 1996 ). Evidence to support the componen- tial model of creativity: Secondary analyses of three studies. Creativity Research Journal, 9 ( 4 ), 385 – 389 . Cropley, A. J. ( 1996 ). Recognizing creative potential: An evaluation of the usefulness of creativity tests. High Ability Studies, 7 ( 2 ), 203 – 219 . Cropley, A. J. ( 1999 ). Creativity and cognition: Producing effective novelty. Roeper Review, 21 ( 4 ), 253 – 260 . Csikszentmihalyi, M. ( 1988 ). Society, culture, and person: A systems view of creativity. In R. J. Sternberg (Ed.), The nature of creativity: Contempo- rary psychological perspectives (pp. 325 – 339 ). New York: Cambridge University Press. Csikszentmihalyi, M. ( 1999 ). Implications of a systems perspective for the study of creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 313 – 335 ). Cambridge: Cambridge University Press. 144 Lubart and Mouchiroud Davidson, J. E., & Sternberg, R. J. ( 1984 ). The role of insight in intellectual giftedness. Gifted Child Quarterly, 28, 58 – 64 . de Alencar, E., & Bruno Faria, M. ( 1997 ). Characteristics of an organizational envi- ronment which stimulate and inhibit creativity. Journal of Creative Behavior, 31 ( 4 ), 271 – 281 . Dellas, M., & Gaier, E. L. ( 1970 ). Identiﬁcation of creativity: The individual. Psycho- logical Bulletin, 73, 55 – 73 . Dudek, S. Z., & Hall, W. B. ( 1991 ). Personality consistency: Eminent architects 25 years later. Creativity Research Journal, 4 ( 3 ), 213 – 231 . Ebert, E. S. ( 1994 ). The cognitive spiral: Creative thinking and cognitive processing. Journal of Creative Behavior, 28 ( 4 ), 275 – 290 . Eisenberger, R., & Armeli, S. ( 1997 ). Can salient reward increase creative perfor- mance without reducing intrinsic creative interest? Journal of Personality and Social Psychology, 72 ( 3 ), 652 – 663 . Eisenberger, R., & Cameron, J. ( 1996 ). Detrimental effects of reward: Reality or myth? American Psychologist, 51 ( 11 ), 1153 – 1166 . Eisenberger, R., & Cameron, J. ( 1998 ). Reward, intrinsic interest, and creativity: New ﬁndings. American Psychologist, 53 ( 6 ), 676 – 679 . Eysenck, H. J. ( 1994 ). Creativity and personality: Word association, origence, and psychoticism. Creativity Research Journal, 7 ( 2 ), 209 – 216 . Eysenck, H. J. ( 1995 ). Genius: The natural history of creativity . Cambridge: Cambridge University Press. Eysenck, H. J., & Eysenck, S. B. G. ( 1975 ). Manual of the Eysenck Personality Ques- tionnaire . London: Hodder & Stoughton. Feist, G. J. ( 1998 ). A meta-analysis of personality in scientiﬁc and artistic creativity. Personality and Social Psychology Review, 2 ( 4 ), 290 – 309 . Feist, G. J. ( 1999 ). The inﬂuence of personality on artistic and scientiﬁc creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 273 – 296 ). Cambridge: Cambridge University Press. Feldhusen, J. F. ( 1995 ). Creativity: A knowledge base, metacognitive skills, and personality factors. Journal of Creative Behavior, 29 ( 4 ), 255 – 268 . Feldman, D. H., Csikszentmihalyi, M., & Gardner, H. ( 1994 ). Changing the world: A framework for the study of creativity . Westport, CT: Praeger. Finke, R. A., Ward, T. B., & Smith, S. M. ( 1992 ). Creative cognition: Theory, research, and applications . Cambridge, MA: MIT Press. Frensch, P. A., & Sternberg, R. J. ( 1989 ). Expertise and intelligent thinking: When is it worse to know better? In R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 5 , pp. 157 – 188 ). Hillsdale, NJ: Erlbaum. Gerrard, L. E., Poteat, G. M., & Ironsmith, M. ( 1996 ). Promoting children’s creativity: Effects of competition, self-esteem, and immunization. Creativity Research Journal, 9 ( 4 ), 339 – 346 . Getz, I., & Lubart, T. I. ( 2000 ). An emotional-experiential perspective on creative symbolic-metaphorical processes. Consciousness & Emotion, 1 ( 2 ), 89 – 118 . Getz, I., & Lubart, T. I. ( 2001 ). Psychologie, economie et cr´eativit´e: Exploration de leurs interactions [Psychology, economics and creativity: Exploration of their interactions]. Psychologie Franc¸aise, 46 ( 4 ), 365 – 378 . Getzels, J., & Csikszentmihalyi, M. ( 1976 ). The creative vision: A longitudinal study of problem-ﬁnding in art . New York: Wiley-Interscience. Creativity: A Source of Difﬁculty 145 Goor, A., & Sommerfeld, R. E. ( 1975 ). A comparison of problem-solving processes of creative students and noncreative students. Journal of Educational Psychology, 67 ( 4 ), 495 – 505 . Goswami, A. ( 1996 ). Creativity and the quantum: A uniﬁed theory of creativity. Creativity Research Journal, 9 ( 1 ), 47 – 61 . Gough, H. G. ( 1987 ). California Psychological Inventory: Administrators’ guide . Palo Alto, CA: Consulting Psychologists Press. Gray, C. E. ( 1966 ). A measurement of creativity in western civilization. American Anthropologist, 68, 1384 – 1417 . Guastello, S. J., Shissler, J., Driscoll, J., & Hyde, T. ( 1998 ). Are some cognitive styles more creatively productive than others? Journal of Creative Behavior, 32 ( 2 ), 77 – 91 . Guilford, J. P. ( 1967 ). The nature of human intelligence . New York: McGraw-Hill. Helson, R. ( 1999 ). A longitudinal study of creative personality in women. Creativity Research Journal, 12 ( 2 ), 89 – 101 . Hennessey, B. A., & Amabile, T. M. ( 1998 ). Reward, intrinsic motivation, and cre- ativity. American Psychologist, 53 ( 6 ), 674 – 675 . Hennessey, B. A., Amabile, T. M., & Martinage, M. ( 1989 ). Immunizing children against the negative effects of reward. Contemporary Educational Psychology, 14, 212 – 227 . Hennessey, B. A., & Zbikowski, S. ( 1993 ). Immunizing children against the neg- ative effects of reward: A further examination of intrinsic motivation training techniques. Creativity Research Journal, 6, 297 – 308 . Israeli, N. ( 1962 ). Creative processes in painting. Journal of General Psychology, 67 ( 2 ), 251 – 263 . Israeli, N. ( 1981 ). Decision in painting and sculpture. Academic Psychology Bulletin, 3 ( 1 ), 61 – 74 . Kaltsounis, B. ( 1977 a). Middle Tennessee teachers’ perception of ideal pupils. Per- ceptual and Motor Skills, 44, 803 – 806 . Kaltsounis, B. ( 1977 b). Student teachers’ perceptions of ideal pupils. Perceptual and Motor Skills, 44 , 160 . Kasof, J. ( 1997 ). Creativity and breadth of attention. Creativity Research Journal, 10 ( 4 ), 303 – 315 . King, M. J. ( 1997 ). Apollo 13 creativity: In-the-box innovation. Journal of Creative Behavior, 31 ( 4 ), 299 – 308 . Lubart, T. I. ( 1994 ). Product-centered self-evaluation and the creative process . Unpub- lished doctoral Dissertation, Yale University, New Haven, CT. Lubart, T. I. ( 1999 a). Componential models. In M. A. Runco & S. R. Pritsker (Eds.), Encyclopedia of creativity (Vol. 1 , pp. 295 – 300 ). New York: Academic Press. Lubart, T. I. ( 1999 b). Creativity across cultures. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 339 – 350 ). Cambridge: Cambridge University Press. Lubart, T. I. ( 2000 – 2001 ). Models of the creative process: Past, present and future. Creativity Research Journal, 13 ( 3 – 4 ), 295 – 308 . Lubart, T. I., & Getz, I. ( 1997 ). Emotion, metaphor, and the creativeprocess. Creativity Research Journal, 10, 285 – 301 . Lubart, T. I., & Sternberg, R. J. ( 1995 ). An investment approach to creativity: Theory and data. In S. M. Smith, T. B. Ward, & R. A. Finke (Eds.), The creative cognition approach (pp. 271 – 302 ). Cambridge, MA: MIT Press. 146 Lubart and Mouchiroud MacKinnon, D. W. ( 1962 ). The nature and nurture of creative talent. American Psy- chologist, 17, 484 – 495 . Marchant, G., Robinson, J. P., Anderson, U., & Schadewald, M. ( 1991 ). Analogi- cal transfer and expertise in legal reasoning. Organizational Behavior and Human Decision Processes, 48 ( 2 ), 272 – 290 . Martinsen, O. ( 1995 ). Cognitive styles and experience in solving insight problems: Replication and extension. Creativity Research Journal, 8, 291 – 298 . Martinsen, O. ( 1997 ). The construct of cognitive style and its implications for cre- ativity. High Ability Studies, 8 ( 2 ), 135 – 158 . Martinsen, O., & Kaufmann, G. ( 1999 ). Cognitive style and creativity. In M. A. Runco & S. R. Pritsker (Eds.), Encyclopedia of creativity (Vol. 1 , pp. 273 – 282 ). New York: Academic Press. Mayer, R. ( 1999 ). Problem solving. In M. A. Runco & S. R. Pritzker (Eds.), Encyclo- pedia of creativity (Vol. 2 , pp. 437 – 447 ). New York: Academic Press. Mayer, R. E. ( 1983 ). Thinking, problem solving, cognition . New York: Freeman. Mednick, S. A. ( 1962 ). The associative basis of the creative process. Psychological Review, 69, 220 – 232 . Mehr, D. G., & Shaver, P. R. ( 1996 ). Goal structures in creative motivation. Journal of Creative Behavior, 30 ( 2 ), 77 – 104 . Mouchiroud, C., & Lubart, T. I. ( 2000 ). The development of social creativity: Analysis of its speciﬁcity in children . Paper presented at the XVIth Biennal Meeting of the International Society for the Study of Behavioural Development, Beijing, China. Mouchiroud, C., & Lubart, T. I. ( 2002 ). Social creativity: A cross-sectional study of 6 -to 11-year-old children. International Journal of Behavioral Development, 26 ( 1 ), 60 – 69 . Mumford, M. D., Baughman, W. A., Maher, M. A., Costanza, D. P., & Supinski, E. P. ( 1997 ). Process-based measures of creative problem-solving skills: IV. Category combination. Creativity Research Journal, 10 ( 1 ), 59 – 71 . Mumford, M. D., Costanza, D. P., Threlfall, K. V., & Baughman, W. A. ( 1993 ). Person- ality variables and problem-construction activities: An exploratory investigation. Creativity Research Journal, 6 ( 4 ), 365 – 389 . Mumford, M. D., & Gustafson, S. B. ( 1988 ). Creativity syndrome: Integration, ap- plication, and innovation. Psychological Bulletin, 103 ( 1 ), 27 – 43 . Mumford, M. D., Mobley, M. I., Uhlman, C. E., Reiter-Palmon, R., & Doares, L. M. ( 1991 ). Process analytic models of creative capacities. Creativity Research Journal, 4 ( 2 ), 91 – 122 . Mumford, M. D., Supinski, E. P., Baughman, W. A., Costanza, D. P., & Threlfall, K. V. ( 1997 ). Process-based measures of creative problem-solving skills: V. Overall prediction. Creativity Research Journal, 10 ( 1 ), 73 – 85 . Noppe, L. D. ( 1996 ). Progression in the service of the ego, cognitive styles, and creative thinking. Creativity Research Journal, 9, 369 – 383 . Ochse, R. ( 1990 ). Before the gates of excellence . New York: Cambridge University Press. Osborn, A. F. ( 1953 ). Applied imagination . New York: Charles Scribner’s Sons. Raidl, M.-H., & Lubart, T. I. ( 2000 – 2001 ). An empirical study of intuition and cre- ativity. Imagination, Cognition and Personality, 20 ( 3 ), 217 – 230 . Romer, P. M. ( 1994 ). The origins of endogenous growth. Journal of Economic Perspec- tives, 8 , 3 – 22 . Creativity: A Source of Difﬁculty 147 Rothenberg, A. ( 1996 ). The Janusian process in scientiﬁc creativity. Creativity Re- search Journal, 9 ( 2 – 3 ), 207 – 231 . Runco, M. A. ( 1987 ). The generality of creative performance in gifted and non-gifted children. Gifted Child Quarterly, 31, 121 – 125 . Runco, M. A., & Chand, I. ( 1995 ). Cognition and creativity. Educational Psychology Review, 7 ( 3 ), 243 – 267 . Runco, M. A., & Dow, G. ( 1999 ). Problem ﬁnding. In M. A. Runco & S. R. Pritsker (Eds.), Encyclopedia of creativity (Vol. 2 , pp. 433 – 435 ). New York: Academic Press. Runco, M. A., Nemiro, J., & Walberg, H. J. ( 1998 ). Personal explicit theories of creativity. Journal of Creative Behavior, 32 ( 1 ), 1 – 17 . Ruscio, J., Whitney, D. M., & Amabile, T. M. ( 1998 ). Looking inside the ﬁshbowl of creativity: Verbal and behavioral predictors of creative performance. Creativity Research Journal, 11 ( 3 ), 243 – 263 . Shalley, C. E., & Oldham, G. R. ( 1997 ). Competition and creative performance: Effects of competitor presence and visibility. Creativity Research Journal, 10 ( 4 ), 337 – 345 . Simonton, D. K. ( 1984 ). Genius, creativity, and leadership . Cambridge, MA: Harvard University Press. Simonton, D. K. ( 1988 ). Creativity, leadership, and chance. In R. J. Sternberg (Ed.), The nature of creativity: Contemporary psychological perspectives (pp. 386 – 426 ). New York: Cambridge University Press. Stein, M. I. ( 1974 ). Stimulating creativity: Individual procedures . New York: Academic Press. Sternberg, R. J. ( 1985 ). Beyond IQ: A triarchic theory of human intelligence . New York: Cambridge University Press. Sternberg, R. J. ( 1997 ). Thinking styles . Cambridge: Cambridge University Press Sternberg, R. J. ( 1999 ). A propulsion model of types of creative contribution. Review of General Psychology, 3 ( 2 ), 83 – 100 . Sternberg, R. J., & Davidson, J. E. (Eds.). ( 1995 ). The nature of insight . Cambridge, MA: MIT Press. Sternberg, R. J., & Lubart, T. I. ( 1991 ). An investment theory of creativity and its development. Human Development, 34, 1 – 31 . Sternberg, R. J., & Lubart, T. I. ( 1995 ). Defying the crowd: Cultivating creativity in a culture of conformity . New York: Free Press. Sternberg, R. J., & Lubart, T. I. ( 1996 ). Investing in creativity. American Psychologist, 51 ( 7 ), 677 – 688 . Sternberg, R. J., & O’Hara, L. A. ( 1999 ). Creativity and intelligence. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 251 – 272 ). Cambridge: Cambridge University Press. Taylor, I. A. ( 1959 ). The nature of the creative process. In P. Smith (Ed.), Creativ- ity: An examination of the creative process (pp. 51 – 82 ). New York: Hastings House Publishers. Taylor, I. A., Austin, G. A., & Sutton, D. F. ( 1974 ). A note on “instant creativity” at CPSI. Journal of Creative Behavior, 8 ( 3 ), 208 – 210 . Tesluk, P. E., Farr, J. L., & Klein, S. R. ( 1997 ). Inﬂuences of organizational culture and climate on individual creativity. Journal of Creative Behavior, 31 ( 1 ), 27 – 41 . Torrance, E. P. ( 1975 ). Ideal Child Checklist . Athens, GA: Georgia Studies of Creative Behavior. 148 Lubart and Mouchiroud Wallas, G. ( 1926 ). The art of thought . New York: Harcourt, Brace. Ward, T. B., Smith, S. M., & Finke, R. A. ( 1999 ). Creative cognition. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 189 – 212 ). Cambridge: Cambridge University Press. Weisberg, R. W. ( 1999 ). Creativity and knowledge: A challenge to theories. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 226 – 250 ). Cambridge: Cambridge University Press. Wiley, J. ( 1998 ). Expertise as mental set: The effects of domain knowledge in creative problem solving. Memory and Cognition, 26 ( 4 ), 716 – 730 . Witkin, H. A., Dyk, R., Faterson, H. F., Goodenough, D. R., & Karp, S. A. ( 1962 ). Psychological differentiation . New York: Wiley. Woodman, R. W., & Schoenfeldt, L. F. ( 1990 ). An interactionist model of creative behavior. Journal of Creative Behavior, 24 ( 4 ), 279 – 291 . 5 Insights about Insightful Problem Solving Janet E. Davidson Many years ago, I tried to go night skiing with some friends. We were driving to the mountain wishing we had checked the ski report to ﬁnd out whether there would be snow, when suddenly we found ourselves in a blizzard. Cars were skidding off the road and getting stuck in large snowdrifts. The car I was in also went off the road, but the driver, who had never before driven in a blizzard, somehow managed to get it back on course. (I cannot tell you how he did this because I had my eyes closed.) A similar situation occurs when people try to solve nonroutine prob- lems. Nonroutine problems can be difﬁcult because we do not possess preexisting procedures for solving them (Mayer, 1995 ). This difﬁculty is compounded when the givens, goals, and obstacles in the problems are not well speciﬁed. Under these conditions, there are times when we all go off track. Some people manage to get on course and successfully solve the problem; others remain stuck. In this chapter I claim that the ability to get on track when solving nonroutine problems often involves conceptual change and insight. In addition, getting on track in one’s problem solving, after being off course, is frequently accompanied by a feeling of suddenly knowing what to do. Insight has long been associated with creative thoughts and products. For example, Graham Wallas ( 1926 ) proposed four stages involved in the creative process. These stages are ( 1 ) preparation, where the problem solver gathers relevant information and begins conscious work on a problem; ( 2 ) incubation, which is a period of time away from consciously working on the problem; ( 3 ) illumination or insight, when the problem solver suddenly “sees” or knows how to solve the problem; and ( 4 ) veriﬁcation, where the solution is worked out and checked for accuracy. Many important contributions to the world have been attributed to the third stage, where insight or illumination occurs (Gruber, 1981 ). If major, or even minor, ac- complishments do stem from insightful problem solving, then it seems im- portant to understand the nature of these seemingly sudden realizations. In 149 150 Davidson addition, our general understanding of how successful problem solving occurs would be incomplete if we did not consider the role, if any, of insight. But what exactly is insight? This surprisingly controversial question has been around since the early 1900 s, and several different approaches have tried to answer it. Four of these approaches are discussed in this chapter. Each approach has its own goals and methodology, and each one tells a different part of the story of insight. First, the Gestalt approach sets the his- torical context for the later approaches. Gestalt psychologists introduced the concept of insightful problem solving, and many aspects of it that are still being studied today. Second, the nothing-special approach tests the null hypothesis that insight does not actually exist. This approach exam- ines some of the Gestaltists’ assumptions and attempts to illustrate how nonroutine problems could be solved using routine processes. Third, the puzzle-problem approach uses perplexing riddles and mathematical prob- lems to examine empirically the mental processes and subjective feelings involved in insight. Finally, the great-minds approach analyzes, usually retrospectively, the commonalties in societally recognized demonstrations of insight. In the concluding section of this chapter, these approaches are critiqued and integrated to highlight what is and is not known about insightful problem solving. historical context for insight: the gestalt approach Our story of insightful problem solving begins with the Gestalt psycholo- gists. Prior to this time, problem solving was thought to begin with trial and error applications of preexisting responses. It was believed that people au- tomatically form associations during trial and error learning and that these associations result in reproductive thinking. When problem solvers receive a routine problem, they simply reproduce a solution that they have pre- viously associated with success on the problem (Thorndike, 1911 ). When faced with a novel problem, they extend or modify their associations. In other words, nothing completely new is ever created. In sharp contrast to this associationist view, the Gestaltists felt that in- sightful problem solving occurs through productive thinking. In produc- tive thinking, the problem solver goes beyond old associations and views a problem in a completely new way (Kohler, 1925 ; Wertheimer, 1945 / 1959 ). A novel solution is produced, often preceded by an “Aha!” experience or a feeling of suddenly knowing what needs to be done. In other words, in- sight occurs when a problem solver moves from not knowing how to reach a problem’s goal to a deep understanding of the problem and its solution (Maier, 1940 ). The Gestaltists were interested in the conditions that do and do not pro- mote insight. They believed that people’s inability to produce an insightful Insightful Problem Solving 151 solution for a problem is often due to their ﬁxation on past experience and associations. For example, in what is now seen as a classic insight problem, Karl Duncker ( 1945 ) gave people three small cardboard boxes, candles, matches, and thumbtacks. The participants’ task was to mount a candle vertically on a screen so that it could serve as a reading lamp. The solution is to light a candle, melt wax onto the top of a box, stick the candle into the wax, and tack the box to the screen. Individuals who were given boxes ﬁlled with tacks, matches, and candles had much more difﬁculty solving the problem than did people who received the same supplies outside of the boxes. According to Duncker, seeing a box serve the typical function of a container made it difﬁcult for problem solvers also to view the box as a structural support. This phenomenon became known as functional ﬁxedness and has been replicated in a variety of studies (e.g., Adamson, 1952 , Adamson & Taylor, 1954 ; DiVesta & Walls, 1967 ; Scheerer, 1963 .) According to the Gestalt view, functional ﬁxedness is not the only type of ﬁxation, or mental block, that interferes with insightful problem solv- ing. Fixation on previous solution procedures can also inhibit insightful thinking. For example, Luchins ( 1942 ; Luchins & Luchins, 1950 ) had sub- jects use three hypothetical water jugs of varying capacity to obtain precise quantities of water. Problems within a set all required the same solution procedure. When a new problem was introduced that could be solved us- ing either a new, simple solution procedure or the complicated one that had been established, Luchins found that most participants did not notice the simple solution. In other words, ﬁxation can keep people from chang- ing their problem-solving strategies, even when old procedures are not as relevant to the present situation. The Gestaltists speculated that breaking ﬁxations, or mental blocks, allows problem solvers to view a situation in a new way and, therefore, reach an insightful solution. Richard Mayer ( 1995 ) derived four other sources of insightful problem solving, in addition to the source of overcoming ﬁxation, that were intro- duced by Gestalt psychologists. For example, in the early 1900 s, Otto Seltz proposed that insightful problem solving could occur when the problem solver discovers how to complete a mental schema for a problem. Com- plete schemas are important because they allow the problem solver to ﬁll in gaps between the given elements and the goals of a problem, thus making the path to solution more obvious. Seltz (see Frijda & de Groot, 1982 ) provided empirical support for his view by asking problem solvers to think aloud as they solved word-association problems, such as naming a superordinate of newspaper (e.g., publication) or a subordinate of the tool category (e.g., ax). Selz found that problem solvers did not solve these problems simply by generating a series of word associations. Instead, they performed goal-directed cognitive operations in an attempt to create a coherent, integrated structure (or schema) for the given elements and desired outcome imbedded in a problem. 152 Davidson According to Mayer ( 1995 ), another Gestalt source of insightful prob- lem solving involves the spontaneous restructuring of visual information related to a problem’s goal. This view highlights the relationship between Gestalt views of problem solving and Gestalt principles of perception. Sudden changes in how information is perceived are similar to ﬁgure- ground reversals where “elements at one moment are seen as one unity, at the same moment, another unity appears with the same elements” (Ellen, 1982 ,p. 324 ). For example, Wolfgang Kohler ( 1925 ) observed a chimpanzee trying unsuccessfully to reach a bunch of bananas hung above his reach. Fortunately, the chimpanzee was able to view the crates in his cage as the makings of a set of stairs. By stacking the crates and climbing the ﬁnished structure, he successfully reached the bananas. Kohler concluded that the chimpanzee’s cognitive reorganization of information in his visual ﬁeld allowed him to reach an insightful solution. A third source of insight that was introduced by the Gestalt psychol- ogists involves the reformulation, or restructuring, of a problem’s com- ponents so that the problem is viewed in a new way. Reformulation can occur multiple times as an individual moves from general to speciﬁc mental representations of a problem. It can also occur in one of two parts of a prob- lem. A suggestion from above involves the reformulation of a problem’s goal or desired outcome. Although this view is most often attributed to Duncker ( 1945 ), Max Wertheimer provides a simple example ( 1945 / 1959 , pp. 169 – 181 ). Suppose two boys of different ages played multiple games of badminton and the older boy consistently beat the younger one. The younger, less talented player refuses to play again, even though the older boy desperately wants to continue. How can the older boy get the younger one to play? One possible solution would be for him to change the goal of the game from a competition to a cooperative effort. In other words, the boys could now focus on keeping the badminton bird in play as long as possible, counting their number of consecutive hits. As their proﬁciency increased, they could move to more difﬁcult shots. A suggestion from below involves reformulating, in a productive way, the given elements of a problem. Consider, for example, the two-string problem used by Maier ( 1930 , 1931 , 1970 ), where the problem solver is asked to tie together two strings that are hanging from the ceiling. Be- cause the strings are too far apart to be held at the same time, one of them needs to be reformulated as a potential pendulum. The solution is to tie a moderately heavy object to one of the strings, set it into mo- tion, and then grasp the other string. When the pendulum is caught on its upswing, the two strings can be tied together. Reformulations of a problem’s given elements can occur if the problem solver spontaneously views them in a new way or if external hints are provided. For example, Maier found that most participants solved the two-string problem when the experimenter bumped into one of the strings and set it into motion. Insightful Problem Solving 153 Interestingly, these problem solvers were usually unaware that a hint had been provided. Finally, according to the Gestalt psychologist Max Wertheimer ( 1945 / 1959 ), insight can occur when a problem solver ﬁnds an analogue to a problem he or she is trying to solve. Unlike ﬁxation, where one has to overcome a reliance on prior experience, here the problem solver cap- italizes on his or her prior knowledge and experience. In other words, a connection is seen between the structural organization of a familiar situ- ation and the structural organization of a new problem. This connection allows the problem solver to understand the new problem’s solution. Wertheimer ( 1945 / 1959 ) provided empirical support for his view of problem formulation in part through the use of problems requiring stu- dents to ﬁnd the area of parallelograms. First, he gave students one of two types of training. One type focused on the formula for ﬁnding a paral- lelogram’s area, but not on a conceptual understanding of the structural nature of the problem. The second type of training capitalized on students’ prior knowledge about ﬁnding the area of rectangles. Students were shown how to remove the triangle found at each end of a parallelogram and to combine these two triangles into a rectangle. By computing the areas of the two rectangles that comprise a parallelogram and adding them to- gether, they would have the parallelogram’s total area. When students were given transfer problems that were somewhat different from the ones used during training, Wertheimer found that type of training inﬂuenced problem-solving performance. Most students who were merely taught the formula were unable to solve the transfer problems; they did not know where to begin. In contrast, the students who understood the structural relationship between a parallelogram and a rectangle successfully applied their knowledge to the new problems. The Gestalt approach raised important questions about insightful prob- lem solving but provided few answers about exactly what insight is and how it occurs. Gestalt descriptions of insight as resulting from acceler- ated mental processes, a short-circuiting of conventional reasoning, or un- conscious leaps in thinking, for example, are vague and do not specify what insight is or precisely how it takes place (Perkins, 1981 ). In other words, no coherent, falsiﬁable theory of insightful problem-solving de- veloped from this approach. In addition, the research has been criticized for not being scientiﬁcally rigorous or representative of problem-solving situations (Ohlsson, 1984 a, 1984 b; Weisberg, 1986 ). Only one problem was used in some of the studies and it was presented under artiﬁcial circumstances. It should be emphasized, however, that the Gestalt psychologists left behind a powerful legacy. They introduced many of the ideas about in- sight being studied today and they created some of the “insight” problems that are still being used. In addition, and perhaps most important, the 154 Davidson Gestalt approach led us to consider whether nonroutine problems are solved in a different manner than routine ones. the nothing-special approach As mentioned earlier, the prevailing view prior to the Gestalt approach was that all problem solving occurs through reproductive, associative think- ing. Just as the Gestaltists left behind a legacy, associationism inﬂuenced a current approach to insight that is sometimes called the nothing-special approach (Davidson & Sternberg, 1984 ; Sternberg & Davidson, 1982)orthe memory position (Finke, Ward, & Smith, 1992 ). In contrast to the Gestalt approach,the nothing-special view of insight proposes that insightful prob- lem solving is basically the same as routine problem solving (Langley & Jones, 1988 ; Perkins, 1981 ; Weisberg, 1986 ). What we think of as insights, according to the nothing-special view, are merely signiﬁcant products that come from ordinary mental processes. This would mean that “insight” problems, such as the candle problem and the two-string problem men- tioned above, are inaccurately named. Such problems mostly measure the retrieval and application of problem-speciﬁc prior knowledge. For exam- ple, Robert Weisberg and Joseph Alba ( 1981 ) asked participants to solve “classic” insight problems, such as the “nine-dot” problem. In the nine-dot problem, individuals are each given a 3 × 3 matrix of nine equally spaced dots and asked to connect the nine dots with four straight lines without lifting their pencils from the paper. What was unusual about Weisberg and Alba’s experiment was that participants were given a crucial clue that is needed to solve the problem: They were told that the problem could be solved only by drawing the lines beyond the implicit boundaries formed by the dots. Unlike Maier’s two-string experiment ( 1930 , 1931 , 1970 ), where participants beneﬁted from an external clue, Weisberg and Alba’s hint did not help their participants. Even when problem solvers were essentially told how to reformulate the nine-dot problem’s elements, they had difﬁculty ﬁnding the answer. However, they were much better at solving it after they had been trained on highly similar problems. From their results, Weisberg and Alba conclude that the retrieval of relatively speciﬁc prior knowledge about a problem, rather than insightful thinking, is the key to successful problem solving. Therefore, according to their view, the terms ﬁxation and insight do not belong in theories of problem solving. Weisberg and Alba ( 1982 ) do note, however, differences in how prior knowledge is applied to routine and nonroutine problems. Retrieval of problem-speciﬁc past experience is only the ﬁrst step in solving a problem; the problem solver then attempts to apply this ex- perience to the new problem. To the degree that the present problem is novel, solutions to previous problems will not completely solve Insightful Problem Solving 155 it. Therefore, the problem solver will be confronted with mismatches between past experience and the present problem. These mismatches serve as the basis for further searches of memory in the same way as the initial presentation of the problem initiated a memory search. These mismatches between the old solution and the new problem are new problems to be solved. The person attempts to solve these mis- match problems through further memory search, which may result in retrieval of information that will enable the person to eliminate the mismatch. This would result in a modiﬁcation of the old solution in such a way as to solve the new problem. (p. 328 ) In other words, multiple memory searches and the resulting variety of so- lution attempts can lead problem solvers to restructure nonroutine prob- lems. However, this type of restructuring does not involve the spontaneous reorganization of previously unrelated experiences that the Gestaltists proposed. Weisberg and Alba’s claim that the retrieval of prior knowledge has a major inﬂuence on successful problem solving is similar to conclusions that have been drawn about how and why experts in a domain differ from novices. Several researchers (e.g., Chase & Simon, 1973 ; Chi, Feltovich, & Glaser, 1981 ; Larkin, McDermott, Simon, & Simon, 1980 ) have found that large, well-organized knowledge structures, rather than unique mental processes, allow experts to outperform novices when they solve standard domain-speciﬁc problems. In addition, Perkins ( 1981 ) and Weisberg ( 1986 ) argue that the solution of nonroutine problems, as well as routine ones, takes place in incremental steps, rather than through spontaneous reformulations of the problems or leaps of insight. As support for this view, Perkins analyzed individuals’ retrospective reports of how they solved the following problem: A dealer in antique coins got an offer to buy a beautiful bronze coin. The coin had the emperor’s head on one side and the date 554 b.c. on the other. The dealer examined the coin, but instead of buying it, he called the police. Why? Very few problems solvers reported “Aha!” experiences, where they sud- denly realized that the date was impossible because the coin’s maker could not anticipate when, or even if, Christ would be born. The majority of par- ticipants verbalized a series of incremental steps involving ordinary un- derstanding and reasoning skills. Partly based on this analysis, Perkins is skeptical of the Gestalt notion that solutions to novel problems are based on special mental processes that cannot be verbalized. Further support for the nothing-special view comes from a set of com- puter programs that reproduced major scientiﬁc discoveries in a variety of domains (Langley, Simon, Bradshaw, & Zytkow, 1987 ). What is intriguing 156 Davidson about these programs is that they used the same recognition processes that are used to solve routine problems. No special processes were needed for these computer-generated creative discoveries. In sum, arguments for the nothing-special view are essentially argu- ments by default: Because insight processes have not been found, they must not exist. After repeated failures to identify a construct empirically, ascribing the failure to the nonexistence of the construct seems like a nat- ural response. Such a response has two potential beneﬁts. First, theories of problem solving are more parsimonious if the same mental processes can be used to explain performance on a variety of problems. Second, researchers who believe that insightful problem solving does differ from other types of problem solving are challenged to provide concrete empirical support for their view. Vague descriptions, anecdotal evidence, and lack of scientiﬁc rigor associated with the Gestalt approach cannot counteract the arguments and alternative explanations proposed by the nothing-special theorists. There are, however, some methodological weaknesses connected with the nothing-special approach. Finding no differences between insightful and routine problem solving does not mean that signiﬁcant differences do not exist. Consider, for example, the computer programs developed by Langley et al. ( 1987 ) to replicate important scientiﬁc discoveries. Writing computer programs that reproduce already known discoveries might well require processes that differ from those used by the scientists who origi- nally deﬁned the problems, created mental representations for them, and searched for and found the novel solutions (Kuczaj, Gory, & Xitco, 1998 ; Sternberg & Davidson, 1999 ). Furthermore, some researchers have questioned Weisberg and Alba’s in- terpretationof the resultsfromtheir experiment using the nine-dot problem (e.g., Davidson & Sternberg, 1986 ; Dominowski, 1981 ; Ellen, 1982 ; Lung & Dominowski, 1985 ; Ohlsson, 1984 a). These critics argue (a) that some prob- lems, such as the nine-dot problem, may require more than one insight or restructuring, and (b) that Weisberg and Alba oversimpliﬁed the Gestalt notions of ﬁxation and insight, then rejected these notions by asserting the null hypothesis (see Weisberg, 1993 , for additional discussion). Finally, recent research (e.g., Siegler, 2000 ; Siegler & Stern, 1998 ; Smith & Kounios, 1996 ) does not support David Perkins’s ( 1981 ) view that solutions to novel problems occur in incremental steps that can be described by prob- lem solvers. Robert Siegler and Elsbeth Stern, for example, found that the majority of second graders in their study abruptly generated an arithmetic insight at an unconscious level before they were able to verbalize it. the puzzle-problem approach Unlike the Gestalt approach, the puzzle-problem approach tends to use several constrained riddles and problems that are administered to a large Insightful Problem Solving 157 number of participants in well-controlled settings. Several aspects of the Gestalt view of insight have been tested using this empirical approach. These aspects include ﬁxation, incubation, and subjective feelings of sud- denness associated with insight. In addition, the puzzle-problem approach has been used to identify speciﬁc mental processes involved in insightful problem solving. To avoid problems of inconsistency found in past research, puzzle prob- lems should meet certain criteria when they are used to study insight (Weisberg, 1995 ). First, their solutions must not be obvious to the peo- ple solving them. In fact, these puzzles are often nonroutine problems that are disguised as routine ones; they are designed to mislead solvers into taking incorrect solution paths. Consider the following problem: You have blue stockings and red stockings mixed in a dresser drawer in the ratio of 4 to 5 . How many stockings must you remove in order to guarantee that you have a pair that is the same color? Many people incorrectly assume that this is a ratio problem and, therefore, that they must compute the answer using the 4 : 5 information. The second criterion is that the puzzle problems cannot be solved simply through a careful reading of the problems. An example of a problem not conducive to insight would be the following one about eggs. “Is it more correct to say the yolk is white or the yolk are white? ” For a problem to foster insight, its solution must result from the formation of a new mental representation of the problem, not simply a careful reading of it. Consider a problem that is conducive to insight: Water lilies double in area every 24 hours. At the beginning of the summer, there is one water lily on a lake. It takes 30 days for the lake to become completely covered with water lilies. On what day is the lake half covered? Most problem solvers attempt to solve this problem by working forward from the ﬁrst day. To reach the correct solution of day 29 , they must switch to a mental representation of the problem that involves working backward from the last day. The ﬁnal criterion is that solution of the problems cannot be dependent on labor-intensive computations or domain-speciﬁc prior knowledge. The puzzles should be solved when problem solvers change their mental repre- sentations of the givens, goals, and obstacles found in the problems, rather than through the application of knowledge that might be available only to individuals of certain ages, cultures, or educational backgrounds. Mental Processes If changes in the mental representations of problems are crucial for in- sightful problem solving, how do these changes occur? According to the 158 Davidson three-process theory of insight (Davidson, 1995 ; Davidson & Sternberg, 1986 ), the mental processes of selective encoding, selective combination, and selective comparison are used to restructure one’s mental representa- tions. When individuals do not have a routine set of procedures for solving a problem, they often search through a space of alternative ways of solving it (Newell & Simon, 1972 ). Selective encoding, selective combination, and selective comparison help guide this search and lead to a change in the internal representation of the givens, the relations among the givens, or the goals found in a problem. Each of the three processes are discussed in turn. Selective Encoding Insightful encoding occurs when a person ﬁnds in a stimulus, or set of stimuli, one or more elements that previously have been nonobvious. Sig- niﬁcant problems generally present an individual with large amounts of information, only some of which is relevant to problem solution. Selective encoding contributes to insight by restructuring one’s mental represen- tation so that information that was originally viewed as being irrelevant is now seen as relevant for problem solution. Also, information that was originally seen as relevant may now be viewed as irrelevant. The problem of the two colors of stockings mixed in the ratio of 4 to 5 that was mentioned above illustrates how selective encoding can occur. Some individuals ﬁrst try to use the ratio information and realize their computations lead to an absurd answer. They then review the problem and realize the ratio information is irrelevant. By focusing on the relevance of the two colors, they can imagine what would happen if they took stockings out of the drawer one at a time. After two drawings, they may not have a matching pair but the third drawing guarantees that they will have two stockings of the same color. Ignaz Semmelweis’s discovery of the importance of asepsis is a famous example of a selective encoding insight in science. While on the staff of the general hospital in Vienna, Semmelweis noticed that more women on the poor ward were dying from infection during childbirth than were women on the rich ward. He encoded that doctors, even if they came straight from working on cadavers, seldom washed their hands before they had contact with the poor women, and he realized the relevance that this had for spreading puerperal fever. Unfortunately, Semmelweis was ridiculed for this insight and committed suicide before others accepted the relevance of his discovery. Selective Combination Insightful combination occurs when an individual discovers a previously nonobvious framework for the relevant elements of a problem situation. In many problems, even when the relevant features have been identiﬁed, it is Insightful Problem Solving 159 often difﬁcult (a) to know that these features should be combined and (b) to ﬁnd a procedure to combine them appropriately. Consider the following example: Using six matches, make four equilateral triangles with one complete match making up t

bundet

he side of the triangle. Most problem solvers initially try to build a two-dimensional structure with the matches. When this fails to meet the problems’ requirements, some individuals discover that they can combine the matches to form the three-dimensional structure of a tetrahedron. Kary Mullis’s Nobel prize–winning invention of polymerase chain re- action (PCR) seems to have involved an insight of selective combination. “There was not a single unknown in the scheme. Each step involved had been done already” (Mullis, 1998,p. 9 ). While driving his car and thinking about science, Mullis suddenly realized that the steps could be combined to replicate short sequences of DNA. He was surprised that the majority of his colleagues did not see the relevance his combination would have for producing abundant supplies of speciﬁc DNA sequences. Selective Comparison Insightful comparison occurs when one suddenly discovers a nonobvi- ous connection between new information and prior knowledge. It is here that analogies, metaphors, and models are used to solve problems. (Selec- tive comparison is related to Wertheimer’s [ 1945 / 1959 ] view, mentioned earlier, that insight can occur when the structural organization of one prob- lem is used to solve a new problem.) The person having an insight sud- denly realizes that new information is similar to old information in some ways and then uses this similarity better to understand the newly acquired information. Consider the following problem: A jar contains 3 different sizes of buttons; there are 15 small buttons, 20 medium buttons, and 10 large buttons. You need 3 buttons of the same size. How many buttons must you take out of the jar in order to make sure that you will have 3 small, 3 medium, or 3 large buttons? If individuals know how to solve the “two colors of stockings” problem mentioned earlier and see its relation to this new problem, they will ignore the quantities of each size button and imagine the longest sequence of drawings needed to ensure three of the same size (i.e., 7 ). Archimedes’s theory of “speciﬁc gravity” is a famous example of a se- lective comparison insight. While trying to determine whether silver had been put into King Hiero’s crown, Archimedes supposedly took a bath. He noticed that the amount of water that was displaced in the bathtub was equal to the volume of his body that was under water. By drawing an analogy between his bath and the problem with the crown, Archimedes 160 Davidson suddenly knew how to determine the purity of the crown. He could com- pute the crown’s volume by placing it in water and measuring the amount of displaced water. The crown could then be weighed against an equal volume of gold. (But ﬁrst, according to legend, he was compelled to run naked through the streets of Syracuse shouting “Eureka!”) In sum, these three processes form the basis for a theory of insightful problem solving. Selection and relevance are important to all three of these mental processes. In encoding, one is selecting elements from the often numerous possible elements that constitute the problem situation; the key is to select the relevant elements. In combination, an individual is select- ing one of many possible ways in which elements of information can be combined or integrated; the key is to select a relevant way of combining the elements in a given situation. Selective comparison involves selecting one (or more) of numerous possible old elements of information to which to relate new information. There is any number of relations that might be drawn; the key is to select the relevant comparison or comparisons to make for one’s purposes. Note, however, that not every instance of selective encoding, selective combination, or selective comparison is an insight. To be referred to as insightful, the relevant selections must not occur to people immediately upon presentation of a problem. After individuals reach an impasse, they must spontaneously search for and discover previously overlooked rele- vant elements, methods for combining elements, or connections between prior knowledge and the problem situation. Also, successful search for this relevant information must result in an abrupt change in the problem solver’s mental representation of the problem. In contrast, routine encod- ings, combinations, and comparisons do not require the self-management of a nonobvious search nor do they lead to a restructuring of one’s mental representation of a problem. In other words, the proposed theory is pro- cess, rather than product, oriented. Nonroutine problems are more likely than routine problems to elicit insightful problem solving. However, one individual may correctly solve a nonroutine problem by having an insight, whereas another individual may solve the same problem correctly without having an insight. The difference between these two individuals lies in the nature of the processes they use, rather than in the outcome. In studies conducted with children and adults, it was found that se- lective encoding, selective combination, and selective comparison play an important role in the solution of nonroutine problems and in individual dif- ferences in intelligent behavior. More speciﬁcally, individuals who solved the puzzle problems correctly were more likely than those who solved the problems incorrectly (a) to have above average intelligence, (b) to apply spontaneously the three insight processes, © to switch mental represen- tations as a result of these processes, and (d) to take longer to solve the problems (Davidson, 1986 , 1995 ; Sternberg & Davidson, 1982 ). The last Insightful Problem Solving 161 ﬁnding supports the view that successful insights can require a great deal of preparation time and veriﬁcation (Wallas, 1926 ). In addition, it was found that insightful problem solving can be trained on the basis of the three mental processes, and that the training effects are transferable and durable (Sternberg & Davidson, 1989 ). It should be noted that individuals who correctly solved routine prob- lems were also more likely than those who solved them incorrectly to have above average intelligence. In fact, intelligence test scores were more highly correlated with performance on routine problems than with perfor- mance on nonroutine problems, probably because standard tests of gen- eral intelligence emphasize routine problem solving. However, very little restructuring of mental representations occurred while participants were solving the routine problems, and restructuring was not related to accu- racy. In addition, correct and incorrect solutions for routine problems took approximately the same length of time (Davidson, 1995 ). In sum, insightful problem solving, unlike other types of problem solving, involves searching for and selecting previously overlooked rel- evant encodings, combinations, and comparisons of information and then restructuring one’s mental representation of the problem based on this search. Highly intelligent individuals are better at this search and restructuring than individuals of average intelligence. The Roles of Incubation According to Wallas’s four stages of creative problem solving described earlier, incubation often precedes illumination or insight. To understand how incubation can lead to insight, it helps to understand why novel prob- lems are often difﬁcult for us to solve. There are at least two reasons for their difﬁculty (Kaplan & Davidson, 1988 ). One reason is stereotypy. In this case, the problem solver becomes ﬁxated on an incorrect solution procedure. As mentioned earlier, a property of many novel, nonroutine problems is that, on the surface, they appear to be routine ones. Unfortunately, applying routine procedures leads to obvious, but incorrect, solutions. Even when problem solvers realize that they are approaching a problem incorrectly, they often cannot break their focus on this approach in order to develop a more worthwhile plan for solution. In other words, ﬁxation keeps indi- viduals from changing their problem-solving strategies, even when they know that old procedures are not relevant to the current situation. The other main source of problem difﬁculty involves the inability to generate any paths to solution. If a problem is sufﬁciently novel or complex, the solver may not know where to begin. For example, consider the task of cutting a hole in a 3 × 5 index card of sufﬁcient size to put one’s head through. If problem solvers do not have the insight to cut a spiral out of the card, they often cannot generate any strategies for solving this problem 162 Davidson (Davidson, 1995 ). In research using a range of problems, Schooler and Melcher ( 1995 ) found that problem solvers gave more statements about reaching an impasse on “insight” problems than on analytic problems. In other words, these individuals could generate more strategies for the analytic problems. The role of incubation, or a break in conscious problem solving that results in illumination, has been tested in two ways using the puzzle- problem approach. One method, related to stereotypy, is to examine when a break in problem solving does and does not reduce ﬁxation and lead to insightful solutions. The other method is to examine whether information provided during an incubation period helps the problem solver generate new strategies for solving a problem and, therefore, overcome an impasse. Each of these methods is discussed in turn. Forgetting According to Woodsworth ( 1938 ), “incubation consists in getting rid of false leads and hampering assumptions so as to approach the problem with an open mind” (p. 823 ). In other words, a break in problem solving allows unproductive ﬁxations to weaken and more useful associations to surface. This implies that problem solvers must ﬁrst have a sufﬁcient period of preparation time on a problem, where incorrect assumptions can be formed and false solution paths pursued. If an incubation period occurs too early, individuals may not have adequately encoded the problem, let alone attempted its solution. A premature interruption would, therefore, hinder problem solving if elements of the problem, rather than false leads and assumptions, were forgotten. Similarly, if individuals are already pursuing a productive solution path, an interruption may hinder problem solving by causing them to lose track of this path (Murray & Denny, 1969 ). However, if individuals become ﬁxated on incorrect solution procedures, a break from problem solving allows them to forget their ﬁxations and approach the problem in a new way (Smith, 1995 ). For example, Smith and Blankenship ( 1989 ) used rebus problems (picture-word puzzles) to examine the relationship between ﬁxation and incubation. Correct solutions to rebuses are common phrases or idioms that ﬁt the situation depicted in a problem. For example, the solution to “ timing tim ing”is“ split second timing ” because the second word in the problem is divided into two parts. Misleading cues, such as “clock,” were given along with the rebuses in order to block problem solvers’ access to the correct solution. Smith and Blankenship found that relatively long in- cubation periods decreased individuals’ memory of the misleading cues and increased their chances of accessing the correct solutions. The explanation that an incubation period provides an opportunity for problem solvers to forget their ﬁxation on incorrect procedures can account for some improvements in individuals’ performance after they have had Insightful Problem Solving 163 time away from a problem (Mednick, Mednick, & Mednick, 1964 ; Smith & Blankenship, 1989 , 1991 ). However, forgetting cannot explain how in- cubation effects occur when no incorrect procedures are pursued during initial exposure to a problem. How can a break in problem solving help individuals generate paths to a problem’s solution? Opportunistic Assimilation According to Colleen Seifert and her colleagues (Seifert, Meyer, Davidson, Patalno, & Yaniv, 1995 ), when motivated problem solvers cannot generate a path or strategy for solving a problem, their long-term memory systems store “failure indices” that mark the problem as unsolved. These indi- viduals then move from the preparation stage of problem solving to the incubation stage, where they no longer consciously work on the problem. However, the “failure indices” in long-term memory cause them uncon- sciously to process the environment in light of the unsolved problem. Infor- mation that might be relevant to solving the problem now receives special attention, whereas this same information might have been ignored prior to the problem-solving impasse. If a piece of relevant information provides a potential solution path, problem solvers move from the incubation stage to the illumination (or insight) stage of problem solving. Seifert et al. ( 1995 ) used two different paradigms to test the opportunistic-assimilation model of insight. In one, participants were ex- posed to target items and asked to judge whether the items were words or nonwords. They were not told that, at times, the target items would be related to general information questions they attempted to answer earlier. When old and new general information questions were given to partici- pants a day later, the relevant target items helped them answer the ques- tions they had previously failed. However, neither mere passage of time nor prior exposure to target items that were related to new general infor- mation questions improved problem-solving performance. In a memory- for-problems paradigm, participants were more likely later to remember puzzle problems when they had reached an impasse in solving them than when they had reached successful solutions or been interrupted prior to reaching an impasse. Results from both paradigms are consistent with the opportunistic-assimilation model of insightful problem solving: Impasse on a problem causes a failure index to be stored in long-term memory, and this index allows new information to be assimilated and used to overcome the impasse. The Role of Affect Insight is often deﬁned as a sudden realization of a problem’s solution (e.g., Duncker, 1945 ; Kaplan & Simon, 1990 ; Kohler, 1969 ; Worthy, 1975 ). In support of this deﬁnition, Janet Metcalfe ( 1986 a, 1986 b; Metcalfe & Weibe, 164 Davidson 1987 ) found that steady increases in feelings of conﬁdence (or warmth) that one is nearing a solution negatively predict correct solution of insight problems but positively predict correct solution of routine, algebra prob- lems. In other words, individuals who felt they were gradually getting closer to solving insight problems tended to arrive at incorrect solutions, whereas individuals who felt they were far from solving the insight prob- lems and then suddenly felt they knew the answers tended to give correct solutions. Metcalfe concludes that insight problems are correctly solved by a subjectively catastrophic process rather than by incremental processes. In a follow-up to Metcalfe’s work, Davidson ( 1995 ) asked adults to solve puzzle problems requiring selective encoding, selective combination, and selective comparison, and routine problems that had clear paths to their solution. In some cases, participants were given cues pointing to solution- relevant information in the problems. In addition to objective performance measures, Metcalfe’s ( 1986 a) subjective measure of problem solvers’ feel- ings of conﬁdence about nearing solution was used. Results showed that sudden, dramatic increases in conﬁdence ratings coincided with the se- lection of appropriate information on the uncued insight problems. Some- times searching for and ﬁnding the relevant information was sufﬁcient for problem solvers immediately to know the answer to a problem. In these cases, a dramatic increase in conﬁdence ratings was immediately followed by the correct solution. At other times, especially on problems requiring se- lective combination, an abrupt increase in conﬁdence ratings was followed by a gradually increasing (incremental) pattern of ratings. The abrupt in- crease occurred when participants changed their mental representations and discovered a path to solution; the incremental ratings were given as problem solvers followed the path and worked out the answer. This last ﬁnding agrees with the view that veriﬁcation or further work often follows illumination (Dominowski & Dallob, 1995 ; Wallas, 1926 ). In contrast, participants showed an incremental pattern of conﬁdence ratings when they were explicitly given cues about the relevant encodings, combinations, and comparisons in the insight problems. Apparently, feel- ings of sudden realization occur only when problem solvers need to search for and select relevant information that will change their mental represen- tations and help them solve the problems. Similarly, incremental patterns of conﬁdence ratings preceded incorrect solutions on the insight problems and both correct and incorrect solutions for routine problems. In sum, the puzzle-problem approach uses a range of challenging prob- lems in well-controlled settings to test various theories about insight. This approachhas allowed researchersto move beyond the anecdotes, vague de- scriptions, and methodological weaknesses associated with the Gestaltist psychologists and empirically examine the mental processes, individual differences, and subjective feelings related to insightful problem solving. The resulting research indicates that insight is a multifaceted phenomenon. Insightful Problem Solving 165 It can come from a variety of mental processes, such as the selective en- coding, selective combination, and selective comparison of nonobvious relevant information. A break in problem solving can enhance the use of these processes by allowing problem solvers to forget their ﬁxation on irrelevant information or opportunistically assimilate new information. These seemingly sudden changes in what information is and is not used allow individuals to restructure their mental representations of a problem and, therefore, approach the problem in a new way. Furthermore, the re- structuring of a mental representation is often accompanied by sudden, subjective feeling of conﬁdence that one is reaching solution. In contrast, routine problem solving usually does not involve the same restructuring of representations and is often accompanied by incremental feelings that one is nearing solution. Even though the puzzle-problem approach has increased our knowl- edge about insightful problem solving, it has at least two weaknesses. First, the views are mainly descriptive and do not fully explain how in- sight occurs. For example, the three-process theory of insight (Davidson, 1995 ; Davidson & Sternberg, 1986 ) does not specify how individuals search for relevant elements, combinations, and prior knowledge and distinguish them from irrelevant information. It also does not establish whether the three processes constitute three independent sources of individual differ- ences or are interrelated because of their derivation from one or more higher-order processes. Similarly, Smith’s ( 1995 ) intriguing view of forget- ting does not specify how a break in problem solving allows the activation of misleading information to decay or how this decay changes one’s men- tal context for, and representation of, the problem. Also, the opportunistic- assimilation model of insight (Seifert et al., 1995 ), though highly plausi- ble and supported by data, does not establish exactly how, or by what mechanism, individuals detect the relevant information that moves them from the incubation stage of problem solving to the illumination phase. In other words, future in-depth work needs to be conducted on the speciﬁc mechanisms problem solvers use to search for nonobvious information, to distinguish this information from irrelevant material, and to apply this relevant information to their mental representations and reformulations of problems. The second weakness to this approach, oddly enough, originates from advantages found in the empirical use of puzzle problems. Among the advantages are that the puzzles come in a variety of forms (e.g., spatial, verbal, and numerical), do not require specialized prior knowledge on the part of the problem solver, and lend themselves to cuing and other forms of manipulation. As a consequence, solving these puzzles probably does not require the same motivation, social interaction, preparation time, restructuring, and solution procedures that individuals need to solve sig- niﬁcant, real-world problems. In addition, the puzzle-problem approach 166 Davidson provides problem solvers with ready-made problems; no information is obtained on how individuals ﬁnd new problems or how the discovery of a problem might inﬂuence insightful problem solving. At some point, the three-process theory and other theories of insight need to be tested using more consequential nonroutine problems, and research participants need to be given opportunities to ﬁnd their own problems. the great-minds approach Unlike the puzzle-problem approach, the great-minds approach does ex- amine how signiﬁcant insights occur in the real world. Structured inter- views, case studies, and observations take us beyond an experimental con- text and provide perspective on insightful problem solving that society recognizes as valuable. Some common themes about insight come out of in-depth examinations of creative, accomplished problem solvers. Three of these themes are discussed here: intrinsic motivation, identiﬁcation of an impasse, and social interaction. Intrinsic Motivation Most individuals who have signiﬁcant insights also have the motivation to acquire relevant knowledge, overcome numerous obstacles, and persist in the face of problem impasses. One reason that persistence is important is that, unlike solving puzzle problems in laboratory experiments, major breakthroughs typically require about ten years of preparatory work in at least one domain (Hayes, 1989 ). As Dean Simonton notes ( 1995,p. 479 ), even someone as talented as Mozart did not compose masterpieces until he spent ten years writing music. However, the length of preparation is not the same for all types of in- sights. Mihaly Csikszentmihalyi and Keith Sawyer ( 1995 ) make an im- portant distinction between insights that occur when individuals solve problems that are given to them and insights that ﬁrst involve ﬁnd- ing a previously unknown problem. (The Gestalt, nothing-special, and puzzle-problem approaches focus on presented problem-solving insights.) From their interviews with 91 accomplished individuals in a wide range of domains, Csikszentmihaly and Sawyer found that presented problem- solving insights involve a relatively short amount of preparation time in a single domain. Short periods of incubation, illumination, and elaboration follow the preparation period. In contrast, problem-ﬁnding insights, which tend to be more revolutionary than presented problem-solving insights, in- volve a relatively extended preparation period and are characterized by the synthesis of information from more than one domain. For this type of insight to occur, individuals must (a) acquire knowledge of one or more do- mains, (b) become immersed in a ﬁeld that practices the domain, © focus Insightful Problem Solving 167 on a problematic situation in the domain and internalize information rel- evant to this situation, (d) use parallel processing to let the relevant in- formation interact at a subconscious level with information from other domains, (e) recognize a new conﬁguration emerging from this interaction of information that helps solve the problem, and (f) evaluate and elaborate the resulting insight in ways that are valued and understood by colleagues (Csikszentmihalyi & Sawyer, 1995 , pp. 358 – 359 ). The problem-solving cycle for problem-ﬁnding insights can take a year or longer. A second reason that intrinsic motivation is important is that real-world insights often involve many failures before an insight is achieved. Because the correct approach to a signiﬁcant nonroutine problem is not obvious, multiple solution paths are often followed before the correct one is found (Csikszentmihalyi & Sawyer, 1995 ; Simonton, 1995 ). In his in-depth study of Darwin’s accomplishments, Howard Gruber ( 1981 ) points out that the best predictor of great discoveries is a prolonged and passionate dedication to a subject. Individuals must have enough devotion to endure ambiguity and initial problem-solving failures. Closely related to intrinsic motivation is the ability to maintain in- tense concentration and undivided attention while working on a problem. Mihaly Csikszentmihalyi ( 1996 ) refers to this highly focused state of con- sciousness as “ﬂow.” Individuals who have experienced periods of ﬂow often report being completely immersed in what they are doing and los- ing track of time. Csikszentmihalyi and his colleagues (Csikzentmihalyi, 1996 ; Csikszentmihalyi, Rathunde, & Whalen, 1993 ) found that creative adolescents and adults often achieved ﬂow states while working in do- mains that match their interests and abilities. These ﬂow states increase the likelihood that material within a domain will be mastered and insights will occur. Individuals who achieve ﬂow tend to be curious, sensitive to sensory information, and open to new experience. Identiﬁcation of an Impasse Unfortunately, intrinsic motivation alone does not lead to insight. In fact, persistence can be harmful if one is pursuing an incorrect solution. How- ever, conceptual change and insightful solutions often occur not long after problem solvers realize that they, or the ﬁeld in which they are working, are on an unproductive path for solving a particular problem. For exam- ple, Kevin Dunbar ( 1995 , 2001 ) found that experienced scientists usually abandoned their hypotheses after obtaining inconsistent or unexpected ev- idence that indicated they were on the wrong track. Immediately after the unexpected results were deemed valid, these scientists often made major shifts in their reasoning. Similarly, problem-ﬁnding insights occur when individuals identify an impasse within a domain and then recognize a new reconﬁguration that overcomes it (Csikszentmihalyi & Sawyer, 1995 ). 168 Davidson How does recognition of an impasse lead to conceptual change? While observing scientists at a wide range of laboratories, Dunbar ( 2001 ) found that these individuals often turn to analogies to help them understand and move beyond obstacles in problem solving. For example, after obtaining a series of unexpected results, molecular biologists and immunologists often draw analogies to different types of models and mechanisms. These analo- gies are still within the same general domain of the research but involve connections to work conducted by other laboratories studying different organisms. In contrast, Csikszentmihalyi and Sawyer ( 1995 ) propose that revolu- tionary problem-ﬁnding insights involve the random convergence of ideas from different symbolic domains. Impasses are processed serially using conscious attention, and then a semiconscious ﬁlter determines which rel- evant information will enter a subconscious network. Unlike the serial nature of conscious processing, subconscious processing allows connec- tions between ideas to be generated and tested in parallel. Insights occur when a new conﬁguration of ideas from different domains emerges from the subconscious and enters consciousness. Social Interaction The Gestalt, nothing-special, and puzzle-problem approaches treat insight as a solitary, cognitive event. Research participants are given problems and asked to solve them independently, without interacting with other prob- lem solvers. However, ﬁndings from the great-minds approach indicate that signiﬁcant insights are embedded within an important social context. Even though the actual insights usually occur when people are alone, the preparation, evaluation, and elaboration stages surrounding the insights depend on interaction with, and input from, one’s colleagues. According to Csikszentmihalyi and Sawyer ( 1995 , pp. 334 – 335 ), “Although the mo- ment of creative insight usually occurs in isolation, it is surrounded and contextualized within an ongoing experience that is fundamentally social, and the insight would be meaningless out of that context.” Csikszentmihalyi ( 1988 ) adopts a “systems” model that takes into ac- count both social and cognitive factors related to creativity. According to this model, creativity involves a positive interaction among an indi- vidual, a domain, and a ﬁeld. It occurs when (a) an individual’s knowl- edge, talents, and interests are a good match for the particular domain to which the individual contributes and (b) knowledgeable judges in the larger ﬁeld, or context, of the domain favorably evaluate the individual’s contributions. Similarly, Dunbar ( 1995 ) found that the social structure of weekly labo- ratory meetings plays a crucial role in conceptual change and scientiﬁc insights. Questions from colleagues during these meetings seem to be Insightful Problem Solving 169 particularly important. For example, conceptual change often occurs when scientists are asked questions that cause their thinking to move from one level to another. In addition, researchers often consider alternative expla- nations that can lead to insights when the interpretations of their results are challenged or even when they face the prospect of publicly admitting an impasse. According to Dunbar, the most constructive laboratory meet- ings occur when group members have different backgrounds and sources of knowledge. In sum, the great-minds approach provides information about the cog- nitive and social mechanisms that foster signiﬁcant insights in real-world settings. This approach, unlike the other three discussed here, focuses on a wide range of factors that inﬂuence insight but that cannot easily be studied in an experimental setting. In particular, the in-depth examination of great thinkers indicates that prolonged hard work and social interac- tions within one or more domains provide an important foundation for insightful problem solving. However, the great-minds approach does not permit the controls and empirical manipulations that play an integral part in experimental re- search. Even though some of the ﬁndings are followed up in laboratory experiments (Dunbar, 2001 ), it is not clear how far the results from the great-minds approach generalize to other populations. In addition, it is not yet obvious how to incorporate the ﬁndings into existing models of in- sight. For example, current theories of insight cannot account for the social factors that inﬂuence insight. conclusions Four approaches to insightful problem solving were reviewed in this chap- ter. On the surface, these approaches seem quite different from each other because each one has its own goals and methodologies. The Gestalt ap- proach attempted to demonstrate productive thinking by using novel problems that need to be viewed and solved in new ways. The emphasis was on the interpretation and reinterpretation of a problem’s components and structure, rather than on the mental mechanisms or processes used to achieve a reinterpretation. The nothing-special approach, by showing that nonroutine problems can be solved using knowledge retrieval and routine procedures, focuses on the null hypothesis that insight does not exist as a distinct cognitive construct. The puzzle-problem approach empirically tests theories and models of insight by examining the selection, retrieval, and application of relevant information related to puzzle problems. Fi- nally, the great-minds approach focuses on the insight processes used by accomplished thinkers in the context of their work. This view obtains “real- world” information on all four stages of the creative process: preparation, incubation, illumination, and veriﬁcation. 170 Davidson There are, however, some common themes that have come out of these different approaches. For example, all four attach some degree of impor- tance to the retrieval and application of prior knowledge. The Gestaltists proposed that the application of previously learned analogues is one source of insight; insightful problem solving can occur when the struc- tural organization of an old situation is used to understand and solve a new problem. Proponents of the nothing-special view use knowledge retrieval and its application as evidence that solving “insight” problems requires routine information and procedures, rather than insight. The puzzle-problem researchers address the retrieval and application of prior knowledge in several ways. One way is through the mental process of selective comparison, where one successfully searches for old informa- tion that is similar in some way to new information and then uses this similarity to solve a problem. Another is through the view that incu- bation allows problem solvers to forget ﬁxations that are blocking their access to relevant information that they have in memory. Similarly, the opportunistic-assimilation model of insight proposes that failure indices in long-term memory allow us to assimilate and remember information that is related to problem solving impasses. Finally, researchers who fo- cus on great thinkers have found that large amounts of knowledge within and across domains play a crucial role in real-world instances of insight- ful problem solving. In other words, ﬁndings from these four approaches indicate that old knowledge can help individuals view problems in new, insightful ways. Another common theme is that the restructuring of mental represen- tations, or conceptual change, plays an important role in the solution of nonroutine problems. Impasses in problem solving often lead problem solvers to search for new ways of approaching a problem. Research gener- ated by all four approaches has found that prior knowledge and its match (or mismatch) with new information can lead to the restructuring of a non- routine problem. Research from three of the approaches – the Gestalt, the puzzle-problem, and the great-minds approaches – has found that other factors also inﬂuence changes in problem solvers’ mental representations. In addition, researchers using these three approaches propose that refor- mulations of a problem are related to insight and to the subjective feeling of suddenly understanding how to solve a problem. Insight does not require unique mental processes but does involve using mental processes in novel ways in order to create new mental representations. If these approaches have one common weakness, it is that they all lack sufﬁcient speciﬁcation. The Gestalt approach never went beyond labels and rather vague descriptions of insightful behavior. As Mayer ( 1995 ) points out, the Gestaltists asked difﬁcult questions without having the knowledge and technology we have today to answer them completely. The nothing- special approach does not specify what type of evidence, if any, could Insightful Problem Solving 171 ﬁrmly establish that insightful problem solving does not exist. Showing that special processes are not needed to solve classic insight problems does not mean that special processes are never used. As mentioned earlier, the puzzle-problem approach does not specify exactly how relevant informa- tion is distinguished from irrelevant information, how irrelevant informa- tion is forgotten, and how mental processes are used to restructure the problem and change the context of solving it. The great-minds approach does not specify how current models of insight should incorporate the social factors related to insightful problem solving. Given this common weakness, how insightful are these approaches to insightful problem solving? If one’s deﬁnition of insight includes the re- structuring of a problem (Dominowski & Dallob, 1995 ; Duncker, 1945 ; Wertheimer, 1945 / 1959 ), then the answer is that they are quite insight- ful. The Gestaltists provided many questions about insight but few of the answers. When impasses were reached and these questions about insight could not be addressed in their original form, the form was changed. For example, the nothing-special approach turned the question of what is in- sight into the question of whether insight exists as a distinct, cognitive phenomenon. This reformulation of the question generated new research and a conﬂict in the answers. In some cases, different conclusions were drawn from evidence that was collected using the same stimuli (Weisberg, 1995 ). This conﬂict in interpretations has prompted some researchers to examine insight as a multifaceted construct, rather than a singular one, and to study individual differences in insightful-thinking skills. In other words, reformulations of the questions about insightful problem solving have moved the ﬁeld forward in constructive directions. However, if one’s deﬁnition of insight includes the sudden realization of a solution (Duncker, 1945 ; Kaplan & Simon, 1990 ; Kohler, 1969 ; Worthy, 1975 ), then these four approaches, even in combination, have not yet in- sightfully discovered the full nature of insight. There are still questions about how insight occurs and what role it plays in problem solving. But the search for answers about insight is well under way, and these approaches have narrowed the space of possible solutions. references Adamson, R. E. ( 1952 ). Functional ﬁxedness as related to problem solving: A rep- etition of three experiments. Journal of Experimental Psychology, 44, 288 – 291 . Adamson, R. E., & Taylor, D. W. ( 1954 ). Functional ﬁxedness as related to elapsed time and set. Journal of Experimental Psychology, 47, 122 – 216 . Chase, W. G., & Simon, H. A. ( 1973 ). The mind’s eye in chess. In W. G. Chase (Ed.), Visual information processing (pp. 215 – 281 ). New York: Academic Press. Chi, M. T. H., Feltovich, P., & Glaser, R. ( 1981 ). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121 – 152 . 172 Davidson Csikszentmihaly, M. ( 1988 ). Society, culture, and person: A systems view of cre- ativity. In R. J. Sternberg (Ed.), The nature of creativity (pp. 325 – 339 ). Cambridge, U.K.: Cambridge University Press. Csikszentmihaly, M. ( 1996 ). Creativity: Flow and the psychology of discovery and inven- tion. New York: Harper Collins Publishers. Csikszentmihalyi, M., Rathunde, K., & Whalen, S. ( 1993 ). Talented teenagers: The roots of success and failure. New York: Cambridge University Press. Csikszentmihaly, M., & Sawyer, K. ( 1995 ). Creative insight: The social dimension of a solitary moment. In R. J. Sternberg, & J. E. Davidson (Eds.), The nature of insight (pp. 329 – 363 ). New York: Cambridge University Press. Davidson, J. E. ( 1986 ). Insight and intellectual giftedness. In R. J. Sternberg & J. E. Davidson (Eds.), Conceptions of giftedness (pp. 201 – 222 ). New York: Cambridge University Press. Davidson, J. E. ( 1995 ). The suddenness of insight. In R. J. Sternberg, & J. E. Davidson (Eds.), The nature of insight (pp. 125 – 155 ). New York: Cambridge University Press. Davidson, J. E., & Sternberg, R. J. ( 1984 ). The role of insight in intellectual giftedness. Gifted Child Quarterly, 28, 58 – 64 . Davidson, J. E., & Sternberg, R. J. ( 1986 ). What is insight? Educational Horizons, 64, 177 – 179 . DiVesta F. J., & Walls, R. T. ( 1967 ). Transfer of object-function in problem solving. American Educational Research Journal, 63, 596 – 602 . Dominowski, R. L. ( 1981 ). Comment on “An examination of the alleged role of ‘ﬁxation’ in the solution of ‘insight’ problems.” Journal of Experimental Psychology: General, 110, 199 – 203 . Dominowski, R. L., & Dallob, P. ( 1995 ). Insight and problem solving. In R. J. Sternberg, & J. E. Davidson (Eds.), The nature of insight (pp. 33 – 62 ). New York: Cambridge University Press. Dunbar, K. ( 1995 ). How scientists really reason: Scientiﬁc reasoning in real-world laboratories. In R. J. Sternberg, & J. E. Davidson (Eds.), The nature of insight (pp. 365 – 395 ). New York: Cambridge University Press. Dunbar, K. ( 2001 ). The analogical paradox: Why analogy is so easy in naturalis- tic settings, yet so difﬁcult in the psychological laboratory. In D. Gentner, K. J. Holyoak, & B. Kokinov (Eds.), The analogical mind: Perspectives from cognitive sci- ence . Cambridge, MA: MIT Press. Duncker, K. ( 1945 ). On problem solving. Psychological Monographs, 58 ( 5 ), Whole No. 270 . Ellen, P. ( 1982 ). Direction, past experience, and hints in creative problem solv- ing: Reply to Weisberg and Alba. Journal of Experimental Psychology: General, 111, 316 – 325 . Finke, R. A., Ward, T. B., & Smith, S. M. ( 1992 ). Creative cognition: Theory, research and applications . Cambridge, MA: MIT Press. Frijda, N. H., & de Groot, A. D. (Eds.). ( 1982 ). Otto Selz: His contribution to psychology . The Hague: Mouton. Gruber, H. E. ( 1981 ). On the relation between “Aha! experiences” and the construc- tion of ideas. History of Science, 19, 41 – 59 . Hayes, J. R. ( 1989 ). The complete problem solver ( 2 nd ed.). Hillsdale, NJ: Erlbaum. Insightful Problem Solving 173 Holyoak, K. J. ( 1984 ). Analogical thinking and human intelligence. In R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 2 , pp. 199 – 230 ). Hillsdale, NJ: Erlbaum. Kaplan, C. A., & Davidson, J. E. ( 1988 ). Hatching a theory of incubation effects. Technical Report , CIP No. 472 , Carnegie-Mellon University. Kaplan, C. A., & Simon, H. A. ( 1990 ). In search of insight. Cognitive Psychology, 22, 374 – 419 . Kohler, W. ( 1925 ). The mentality of apes ( 2 nd ed.). New York: Harcourt Brace. Kohler, W. ( 1969 ). The task of Gestalt psychology . London: Routledge & Kegan Paul. Kuczaj, S. A. II, Gory, J. D., & Xitco, M. J. ( 1998 ). Using programs to solve problems: Imitation versus insight. Behavioral and Brain Sciences, 21, 695 – 696 . Langley, P., & Jones, R. ( 1988 ). A computational model of scientiﬁc insight. In R. J. Sternberg (Ed.), The nature of creativity: Contemporary psychological perspectives (pp. 177 – 201 ). New York: Cambridge University Press. Langley, P., Simon, H. A., Bradshaw, G. L., & Zytkow, J. M. ( 1987 ). Scientiﬁc discovery: Computational explorations of the creative process . Cambridge, MA: MIT Press. Larkin, J. H., McDermott, J., Simon, D. P., & Simon, H. A. ( 1980 ). Expert and novice performance in solving physics problems. Science, 208, 1335 – 1342 . Luchins, A. S. ( 1942 ). Mechanization in problem solving. Psychological Monographs, 54 ( 6 ), Whole No. 248 . Luchins, A. S., & Luchins, E. S. ( 1950 ). New experimental attempts at preventing mechanization in problem solving. Journal of General Psychology, 42, 279 – 297 . Lung, C., & Dominowski, R. L. ( 1985 ). Effects of strategy instructions and practice on nine dot problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 11, 804 – 811 . Maier, N. R. F. ( 1930 ). Reasoning in humans: I. On direction. Journal of Comparative Psychology, 12, 115– 143 . Maier, N. R. F. ( 1931 ). Reasoning in humans: II. The solution of a problem and its appearance in consciousness. Journal of Comparative Psychology, 12, 181 – 194 . Maier, N. R. F. ( 1940 ). The behavior mechanisms concerned with problem solving. Psychological Review, 47, 43 – 53 . Maier, N. R. F. ( 1970 ). Problem solving and creativity . Belmont, CA: Brooks/Cole. Mayer, R. E. ( 1995 ). The search for insight. In R. J. Sternberg, & J. E. Davidson (Eds.), The nature of insight (pp. 3 – 32 .) New York: Cambridge University Press. Mednick M. T., Mednick, S. A., & Mednick, E. V. ( 1964 ). Incubation of creative performance and speciﬁc associative priming. Journal of Abnormal Psychology, 69, 84 – 88 . Metcalfe, J. ( 1986 a). Feeling of knowing in memory and problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 12, 288 – 294 . Metcalfe, J. ( 1986 b). Premonitions of insight predict impending error. Journal of Experimental Psychology: Learning, Memory, and Cognition, 12, 623 – 634 . Metcalfe, J., & Weibe, D. ( 1987 ). Intuition in insight and noninsight problem solving. Memory & Cognition, 15, 238 – 246 . Mullis, K. ( 1998 ). Dancing naked in the mind ﬁeld . New York: Vintage Books. Murray, H. G., & Denny, J. P. ( 1969 ). Interaction of ability level and interpolated activity (opportunity for incubation) in human problem solving. Psychological Reports, 24, 271 – 276 . 174 Davidson Newell, A. & Simon, H. A. ( 1972 ). Human problem solving . Englewood Cliffs, NJ: Prentice-Hall. Ohlsson, S. ( 1984 a). Restructuring revisited: I. Summary and critique of the Gestalt theory of problem solving. Scandinavian Journal of Psychology, 25, 65 – 68 . Ohlsson, S. ( 1984 b). Restructuring revisited: II. An information processing theory of restructuring and insight. Scandinavian Journal of Psychology, 25, 117 – 129 . Perkins, D. ( 1981 ). The Mind’s Best Work . Cambridge, MA: Harvard University Press. Scheerer, M. ( 1963 ). Problem solving. Scientiﬁc American, 208, 118 – 128 . Schooler, J. W., & Melcher, J. ( 1995 ). The ineffability of insight. In S. Smith, T. Ward, & R. Finke (Eds.), The creative cognition approach (pp. 97 – 133 ). Cambridge: MIT Press. Seifert, C. M., Meyer, D. E., Davidson, N., Patalno, A. L., & Yaniv, I. ( 1995 ). De- mystiﬁcation of cognitive insight: Opportunistic assimilation and the prepared- mind perspective. In R. J. Sternberg & J. E. Davidson (Eds.), The nature of insight (pp. 65 – 124 ). New York: Cambridge University Press. Siegler, R. S. ( 2000 ). Unconscious insights. Current Directions in Psychological Science, 9, 79 – 83 . Siegler, R. S., & Stern, E.( 1998 ). Conscious and unconscious strategy discoveries: A microgenetic analysis. Journal of Experimental Psychology: General, 127, 377 – 397 . Simon, H. A. ( 1986 ). The information processing explanation of Gestalt phenomena. Cognitive Psychology, 2, 241 – 255 . Simon, H. A., Newell, A., & Shaw, J. C. ( 1979 ). The process of creative thinking. In H. A. Simon (Ed.), Models of thought (pp. 144 – 174 ). New Haven: Yale University Press. Simonton, D. K. ( 1995 ). Foresight in insight? A Darwinian answer. In R. J. Sternberg, & J. E. Davidson (Eds.), The nature of insight (pp. 465 – 494 ). New York: Cambridge University Press. Smith, R. W., & Kounios, J. ( 1996 ). Sudden insight: All-or-none processing revealed by speed-accuracy decomposition. Journal of Experimental Psychology : Learning, Memory, and Cognition, 22, 1443 – 1462 . Smith, S. M. ( 1995 ). Getting into and out of mental ruts. In R. J. Sternberg, & J. E. Davidson (Eds.), The nature of insight (pp. 229 – 251 ). New York: Cambridge Uni- versity Press. Smith, S. M., & Blankenship, S. E. ( 1989 ). Incubation effects. Bulletin of the Psycho- nomic Society, 27, 311 – 314 . Smith, S. M. & Blankenship, S. E. ( 1991 ). Incubation and the persistence of ﬁxation in problem solving. American Journal of Psychology, 104, 61 – 87 . Sternberg, R. J., & Davidson, J. E. ( 1982 ). The mind of the puzzler. Psychology Today, 16, 37 – 44 . Sternberg, R. J., & Davidson, J. E. ( 1989 ). A four-prong model for intellectual skills development. Journal of Research and Development in Education, 22, 22 – 28 . Sternberg, R. J., & Davidson, J. E. ( 1999 ). Insight. In M. Runco (Ed.), Encyclopedia of creativity . San Diego, CA: Academic Press. Thorndike, E. L. ( 1911 ). Animal intelligence: Experimental studies. New York: Macmillan. Wallas, G. ( 1926 ). The art of thought . New York: Harcourt, Brace. Weisberg, R. W. ( 1986 ). Creativity: Genius and Other Myths . New York: W. H. Freeman & Co. Insightful Problem Solving 175 Weisberg, R. W. ( 1993 ). Creativity: Beyond genius and other myths . New York: Freeman. Weisberg, R. W. ( 1995 ). Prolegomena to theories of insight. In R. J. Sternberg, & J. E. Davidson (Eds.), The nature of insight (pp. 157 – 196 ). New York: Cambridge University Press. Weisberg, R. W. & Alba, J. W. ( 1981 ). An examination of the alleged role of “ﬁxation” in the solution of “insight” problems. Journal of Experimental Psychology: General, 110, 169 – 192 . Weisberg, R. W. & Alba, J. W. ( 1982 ). Problem solving is not like perception: More on Gestalt theory. Journal of Experimental Psychology: General, 111, 326 – 330 . Wertheimer, M. ( 1945 / 1959 ). Productive thinking . Chicago: University of Chicago Press. (Original work published 1945 .) Woodsworth, R. S. ( 1938 ). Experimental psychology . New York: Henry Holt. Worthy, M. ( 1975 ). Aha! A puzzle approach to creative thinking . Chicago: Nelson Hall. 6 The Role of Working Memory in Problem Solving David Z. Hambrick and Randall W. Engle The combination of moment-to-moment awareness and instant re- trieval of archived information constitutes what is called the working memory, perhaps the most signiﬁcant achievement of human mental evolution. (Goldman-Rakic, 1992,p. 111) Working memory plays an essential role in complex cognition. Every- day cognitive tasks – such as reading a newspaper article, calculating the appropriate amount to tip in a restaurant, mentally rearranging furniture in one’s living room to create space for a new sofa, and com- paring and contrasting various attributes of different apartments to decide which to rent – often involve multiple steps with intermediate results that need to be kept in mind temporarily to accomplish the task at hand successfully. (Shah & Miyake, 1999,p. 1 ) More than 25 years ago, Baddeley and Hitch ( 1974 ) lamented, “Despite more than a decade of intensive research on the topic of short-term memory (STM), we still know virtually nothing about its role in normal informa- tion processing” (p. 47 ). The primary concern for Baddeley and Hitch was the presumed centrality of limited-capacity short-term memory in con- temporary models of memory, including Atkinson and Shiffrin’s ( 1968 ) “modal model.” For example, Baddeley and Hitch described a patient with brain-damage (K.F.) who exhibited grossly deﬁcient performance on tests of short-term memory but normal performance on long-term learning tasks. Logically, this could not occur if information passes from short-term memory to long-term memory. Baddeley and Hitch also reported a series of experiments in which participants performed various reasoning tasks while concurrently performing a task designed to place a load on short- term memory. For example, in one experiment, the task was to verify sen- tences purporting to describe the order of two letters (e.g., A is not preceded by B–AB ) while repeating the word “the,” a predictable sequence of digits, 176 Role of Working Memory 177 or a random sequence of digits. Surprisingly, short-term memory load had very little effect on reasoning. How could these ﬁndings be reconciled with the view that short-term memory is the central bottleneck in information processing? Baddeley and Hitch ( 1974 ) proposed that short-term memory is not a single, capacity- limited store, but rather a more complex system consisting of three compo- nents: two “slave” systems – the phonological loop and visuospatial sketchpad , devoted to temporary storage and maintenance of information – and a central executive responsible for control processes such as reasoning, plan- ning, and decision making. This model could easily handle empirical results that Atkinson and Shiffrin’s ( 1968 ) modal model could not. For example, K.F. exhibited deﬁcient performance on short-term memory tasks but normal long-term learning, because only the phonological loop com- ponent of his working memory system was impaired. K.F.’s central ex- ecutive was intact. Similarly, in the experiments described by Baddeley and Hitch, decrements in reasoning performance emerged only when the storage load imposed by the secondary task exceeded the capacity of the phonological loop. Otherwise, the limited resources of the central execu- tive could be devoted exclusively to reasoning. Thus, Baddeley and Hitch demonstrated that short-term memory is merely one component of an in- formation processing system involving not only storage limitations but processing limitations as well. the goal and organization of this chapter As the quotations at the beginning of this chapter suggest, working mem- ory has emerged as one of the most important and intensively researched constructs in cognitive psychology. However, we believe that there is still much to be learned about the role of working memory in real-world cog- nitive functioning. Indeed, one might conclude that despite nearly three decades of intensive research, we still know relatively little about the role of working memory in “normal information processing.” For example, a lit- erature search revealed only 12 publications devoted to working memory and problem solving during the 25 -year period from 1975 through 1999 . Furthermore, in a recent review, Kintsch, Healy, Hegarty, Pennington, and Salthouse ( 1999 ) noted that tasks studied by researchers interested in work- ing memory are often simple and artiﬁcial, and cannot be considered what Hutchins ( 1995 ) termed “cognition in the wild” – complex cognitive tasks encountered in everyday settings. Thus, the goal of this chapter is to speculate about the role of work- ing memory in problem solving. The chapter is organized into three major sections. In the ﬁrst section, we establish the scope of the chapter by consid- ering the question, “What is a problem?” Research on problem solving is sometimes viewed as a narrow area of scientiﬁc inquiry restricted to “toy” 178 Hambrick and Engle tasks such as Tower of Hanoi, but we suggest that many cognitive tasks and activities can be considered examples of problem solving in the sense that they involve purposeful, goal-directed behavior. Or as Anderson ( 1985 ) observed: “It seems that all cognitive activities are fundamentally problem solving in nature. The basic argument . . . is that human cognition is always purposeful, directed to achieving goals and to removing obstacles to those goals” (pp. 199 – 200 ). In the second section of the chapter, we examine the role of working memory in various cognitive tasks. Evidence from two traditions of work- ing memory research is considered. The ﬁrst tradition is associated with work in Europe, primarily by Baddeley and his colleagues, and concerns the role of the phonological loop and visuospatial sketchpad “slave” sys- tems in cognitive performance. The second tradition has been pursued by researchers, primarily in North America, interested in individual dif- ferences in working memory capacity and their relation to cognitive per- formance. In the third section, we consider the question of when working memory capacity should be expected to play an important role in problem solving. what is a problem? A problem is often deﬁned as a goal that is not immediately attainable. For example, Duncker ( 1945 ) proposed that “a problem exists when a living organism has a goal but does not know how this goal is to be reached” (p. 2 ). Consistent with this deﬁnition, problem-solving research has tradi- tionally focused on so-called insight problems. The Tower of Hanoi task is a prototypical example. In the version of this task illustrated in Figure 6 . 1 , there are three pegs ( 1 , 2 , and 3 ) and three disks (A, B, and C). The initial state is that the disks are set on Peg 1 , with the smallest disk (Disk A) on the top and the largest disk (Disk C) on the bottom. The goal is to move the disks from Peg 1 to Peg 3 , but the rules state that only one disk can be moved at a time, that only the top disk can be moved, and that a disk can never be placed on a smaller disk. Once the target conﬁguration of pegs is achieved, the problem is solved. Perhaps the most salient aspect of tasks such as Tower of Hanoi is that the solution must be discovered. That is, although the initial state and the goal state are clear, how to transform the initial state into the goal state is unclear. By contrast, proﬁciency in more routine problem-solving tasks involves execution of well-learned skills and procedures. For example, success in a reading comprehension task depends not so much on ﬁguring out the most effective way to read the material, but rather on the efﬁciency and effectiveness of processes already in place. As another example, how one should proceed in order to mentally calculate the answer to an arithmetic problem such as 1,356 – 234 = ? is probably clear for any educated adult. The Role of Working Memory 179 A B C A B C 1 2 3 1 2 3 Initial Goal Tower of Hanoi figure 6.1. The Tower of Hanoi problem. solution 1,122 is not discovered; rather, it is derived. In short, as Anderson ( 1993 ) noted, “Some activities, like solving a Tower of Hanoi problem or solving a new kind of physics problem, feel like problem solving, whereas other more routine activities, such as using a familiar computer application or adding up a restaurant bill, do not” (p. 39 ). Working Memory as a Unifying Construct How, though, are tasks such as Tower of Hanoi and other cognitive tasks similar, and how can they be compared at a theoretical level? Our view is that success in many tasks is predicated on the ability to maintain goals, action plans, and other task-relevant information in a highly activated and acces- sible state, and when necessary, to inhibit activation of irrelevant or distracting information. For example, during performance of the Tower of Hanoi task, what one must keep active are the rules of the task and subgoals created en route to the solution. In addition, discovery of a solution may depend on the ability to activate information from multiple, unsuccessful solution at- tempts, and to maintain that activation until the information is integrated. Similarly, a fundamental requirement of understanding the meaning of a difﬁcult passage about an unfamiliar topic is the ability to maintain some representation, either verbatim or gist, from clause to clause, sentence to sentence, and paragraph to paragraph (Kintsch & van Dijk, 1978 ). Finally, in a mental arithmetic task, intermediate sums must be kept active in order 180 Hambrick and Engle to compute the correct answer. To sum up, the argument is that working memory is a fundamental determinant of proﬁciency in a wide range of tasks. Working Memory and Problem Solving Research on working memory has proceeded along two theoretical paths during the past 25 years. Working memory research in Europe has concen- trated primarily on the slave systems of the Baddeley-Hitch model. More speciﬁcally, what is the role of the phonological loop and the visuospatial sketchpad in working memory, and how are they involved in performance of tasks such as reasoning and comprehension? In contrast, working mem- ory research in North America has focused primarily (although not ex- clusively) on the central executive component of working memory. More speciﬁcally, what is the nature of individual differences in central executive functioning, and how are they related to individual differences in perfor- mance of various cognitive tasks? Scholars from the European and North American traditions of working memory research have also tended to rely on different methodological approaches. Generally, working memory re- search in Europe is experimental, whereas working memory research in North America is more often correlational. Theoretical and methodological differences aside, results from both tra- ditions of research are informative about the role of working memory in higher level cognition. We review a subset of these ﬁndings in the context of the Baddeley-Hitch model of working memory. To review, Baddeley and Hitch ( 1974 ) conceptualized the phonological loop as a store for holding speech-based information and a subvocal rehearsal process responsible for reinstantiating or refreshing the information. Similarly, the visuospa- tial sketchpad refers to a memory store for holding visual or spatial infor- mation and a mechanism responsible for reinstantiating the information (Logie, 1995 ). The third component of the model, the central executive, is a general-purpose, attention-based entity responsible for control pro- cesses such as planning, reasoning, decision making, and coordination of the slave systems. This organizational scheme provides a context for the discussion, given that much of the research that is reviewed below concerns the Baddeley- Hitch model. However, an important difference between the view of work- ing memory set forth in this model and our view is that we conceptualize working memory as a system in which phonological and spatial formats are but two of many ways of representing information (see, e.g., Engle, Ka

bundet

ne, & Tuholski, 1999 ). More speciﬁcally, we assume that working memory con- sists of two primary components. The ﬁrst component – short-term memory – refers to long-term memory representations activated above threshold as a means of temporary maintenance. Long-term memory representations can Role of Working Memory 181 become activated through an external event or because an internal event (i.e., a thought) spreads activation to the representation. Furthermore, rep- resentations can be maintained in many different formats, including not only phonological and visual or spatial, but also orthographic, lexical, se- mantic, tactile, and so forth. Therefore, the phonological loop and the visu- ospatial sketchpad are different representational formats and not distinct storage modules (see Cowan, 1995 , for a similar view). Finally, periodic attention to the representations is necessary to keep them active above a threshold, below which the information would have to be retrieved from long-term memory. In many circumstances, this is not a problem if retrieval can be carried out quickly and with little chance of error. By contrast, main- tenance of information in the active state above threshold is particularly important under conditions in which retrieval from long-term memory is slow or error prone because of interference. The second component of our model – working memory capacity –isa concept that has emerged from a synthesis of a number of ideas. For exam- ple, working memory capacity corresponds to individual differences in the capability of the central executive of Baddeley and Hitch’s ( 1974 ) model. Therefore, it is assumed to play an important role in a wide range of tasks. In addition, it is similar to Kahneman’s ( 1973 ) notion of effortful processing. That is, working memory capacity refers to a limited-supply cognitive re- source that can be allocated ﬂexibly depending on the demands of the task at hand. Finally, working memory capacity is reminiscent of what Cattell ( 1943 ) termed ﬂuid intelligence , because it is thought to reﬂect a general and relatively stable cognitive ability. However, the speciﬁc function of working memory capacity is to bring memory representations into the focus of attention, and to maintain these representations in a highly activated and accessible state. Thereby, working memory capacity underlies what Horn and Masunaga ( 2000 ) recently described as the ability to maintain focused concentration. Working memory capacity may also be called on when it is necessary to suppress, inhibit, or otherwise remove memory representations from the focus of attention (see Hasher & Zacks, 1988 , for a somewhat similar view). The Slave Systems One way that the so-called slave systems have been studied is through use of concurrently performed secondary tasks thought to interfere with the slave system believed to be important to the primary task. That is, participants perform a primary task (e.g., reasoning) while concurrently performing a secondary task designed to prevent storage of information in either the phonological loop or the visuospatial sketchpad. For exam- ple, a phonological secondary task might involve repeating a predictable sequence of digits (e.g., 1 to 6 ) or the word “the,” whereas a visuospatial secondary task might require tracking a visual target. If performance of 182 Hambrick and Engle the primary task is impaired in the secondary task condition relative to a no-interference control condition, then involvement of the targeted slave system is suggested. Of course, a fundamental problem with this technique is the problem inherent in all methodological approaches that rely on subtractive logic (Donders, 1868 / 1969 ) to isolate the role of a component process (e.g., the action of a slave system) in performance of a complete task. To be exact, when a secondary task produces a decrement in primary task performance, one cannot be sure that this decrement reﬂects involvement of only the tar- geted slave system. For example, even a very simple task such as repeating the word “the” may require some level of central executive resources, in addition to the slave system in question. Despite this limitation, research using a secondary task approach has contributed to the theoretical under- standing of working memory. A brief review of this research follows. Comprehension Comprehension – the ability to understand the larger meaning of a set of events or words – is a fundamental aspect of cognitive functioning. For ex- ample, a person would have little hope of success in a task such as Tower of Hanoi unless he or she ﬁrst comprehended the instructions. Indeed, Kintsch ( 1998 ) proposed that comprehension is fundamental for under- standing many different types of cognition. What, then, is the role of the slave systems in comprehension? Not surprisingly, much of the research germane to this question has focused on storage of speech-based informa- tion in the phonological loop. For example, Baddeley, Elridge, and Lewis ( 1981 ) found that a phonological secondary task interfered with partici- pants’ ability to detect errors of word order in sentences such as: We were to that learn he was a very honest person, even though he loved money. Waters, Caplan, and Hildebrandt ( 1987 ) replicated this result and also found that the detrimental effect of articulatory suppression was greater for sentences with multiple propositions than for sentences with a single proposition. Finally, Baddeley, Vallar, and Wilson ( 1987 ) found that patients with brain damage who had deﬁcits in phonological processing had difﬁculty com- prehending long sentences but not shorter ones. Much less is known about the role of the visuospatial sketchpad in com- prehension, but there is some evidence to suggest that this slave system contributes to comprehension of high-imagery prose. For example, in a study by Glass, Eddy, and Schwanenﬂugel ( 1980 ), participants read and veriﬁed sentences that were either concrete and highly imageable (e.g., The star of David has six points ) or abstract (e.g., Biology is the study of living matter ). In addition, for half of the trials, participants concurrently maintained a vi- sual pattern and indicated whether it matched a pattern presented after the sentence. Glass et al. found that, although maintaining the visual pattern Role of Working Memory 183 did not selectively disrupt veriﬁcation of the high-imagery sentences, ver- iﬁcation of the high-imagery sentences impaired pattern matching. Thus, Glass et al. concluded that comprehension of the high-imagery sentences involved the visuospatial sketchpad. Reasoning The contribution of the phonological loop and the visuospatial sketchpad to reasoning has been investigated in a number of studies. For example, using a phonological secondary task similar to the one described above, Evans and Brooks ( 1981 ), Halford, Bain, and Maybery ( 1984 ), and Toms, Morris, and Ward ( 1993 ) found no evidence for involvement of the phono- logical loop in a conditional reasoning task in which participants evaluated conclusions for rules stated in the form “if p then q” – for example, If I eat haddock, then I do not drink gin. I drink gin. I do not eat haddock. Toms et al. also reported that reasoning was unimpaired by concurrent performance of a spatial secondary task. Similarly, Gilhooly, Logie, Wetherick, and Wynn ( 1993 ) found no effect of either phonological or spatial secondary tasks on syllogistic reasoning. Thus, in contrast to comprehension, there is lit- tle evidence to suggest that the slave systems play an important role in reasoning. Insight Tasks The preceding review indicates that the slave systems may play a limited role in comprehension, but perhaps play no role at all in reasoning. What is the role of the slave systems in tasks, such as Tower of Hanoi, tradi- tionally studied in research on problem solving? One possibility already mentioned is that the phonological loop inﬂuences performance of such tasks through comprehension of instructions. Furthermore, for tasks such as choosing a move in a chess game, it seems reasonable to suggest that the visuospatial sketchpad may contribute to performance, at least when a spatial visualization strategy is used. Consistent with this speculation, in a study of chess, Robbins et al. ( 1996 ) found that a spatial secondary task (pressing keys in a repetitive counterclockwise fashion) had a detrimental effect on performance in a “choose-a-move” task in which chess players were shown an unfamiliar chess position and attempted to generate an optimal move. But how important are the slave systems for tasks such as Tower of Hanoi or choosing a move in a chess game? This question can be consid- ered in light of evidence concerning reasoning already considered. More speciﬁcally, reasoning about the potential effectiveness of different ways to approach a task can probably be considered a critical aspect of performance in many complex tasks, at least when immediate retrieval of a solution from 184 Hambrick and Engle long-term memory is not possible. If this is true, then the slave systems might be expected to play a minor role in tasks such as Tower of Hanoi relative to the third component of the Baddeley-Hitch model – the central executive. That is, a consistent ﬁnding is that secondary tasks designed to tap the central executive impair reasoning. For example, Gilhooly et al. ( 1993 ) and Klauer, Stegmaier, and Meiser ( 1997 ) found that reasoning suf- fered when participants performed a putative central executive secondary task in which they were asked to generate random numbers (e.g., from the set 1 – 9 ) at a constant rate. Similarly, Robbins et al. ( 1996 ) found that chess players were virtually unable to perform the aforementioned chose- a-move task while concurrently performing a random-letter-generation task. Summarized, our speculation is that the processes subsumed by the central executive represent one important determinant of success in a wide range of problem-solving tasks. The next section discusses research that has investigated this claim from an individual-differences perspective. The Central Executive In North America, interest in working memory gained momentum in the early 1980 s with the development of a reliable measure of working memory capacity , the Daneman and Carpenter ( 1980 ) reading span task. Consistent with Baddeley and Hitch’s ( 1974 ) conception of the central executive, this task was designed to emphasize simultaneous storage and processing of information. Brieﬂy, the goal of the reading span task is to read a series of sentences while remembering the ﬁnal word from each sentence. Work- ing memory capacity (or “span”) is then operationalized as the number of sentence-ﬁnal words recalled. Hence, the reading span task is actually a dual task because the subject must read sentences while trying to remem- ber the word following each sentence. The goal of a similar task, called operation span (Turner & Engle, 1989 ), is to solve a series of arithmetic questions and to remember a word following each for recall. Measuresof working memory capacity, such as operation span and read- ing span, predict performance in a wide range of tasks, including language comprehension (Daneman & Merikle, 1996 ), learning to spell (Ormrod & Cochran, 1988 ), math (Adams & Hitch, 1997 ), following directions (Engle, Carullo, & Collins, 1991 ), vocabulary acquisition (Daneman & Green, 1986 ), and writing (Benton, Kraft, Glover, & Plake, 1984 ). Clearly, then, working memory tasks “work” in the sense that they exhibit predictive validity. But why do they work? In other words, as illustrated in Figure 6 . 2 , what accounts for the correlation between individual differences in working memory capacity and individual differences in various cognitive tasks? The premise of what we have labeled the task-speciﬁc hypothesis is that measures of working memory capacity capture acquired skills in- volved in performance of the criterion task. For example, according to Role of Working Memory 185 Working Memory Capacity Cognitive Performance That is, what accounts for common variance? figure 6.2. Why do measures of working memory capacity work? this hypothesis, the reading span task predicts reading comprehension because both tasks involve reading. Consequently, a key prediction of the task-speciﬁc hypothesis is that a working memory task will exhibit predictive validity only when it captures the speciﬁc skills involved in the criterion task. By contrast, the basic idea of the general capacity hypothesis is that measures of working memory capacity capture domain-general information-processing capabilities that can be brought to bear on many tasks. Therefore, a key prediction of the general capacity hypothesis is that operations unique to a particular working memory task (e.g., reading sen- tences) are largely unimportant in accounting for the relationship between working memory capacity and cognitive performance. Instead, working memory tasks are thought to be imperfect indicators of a construct involved in the execution of a wide range of tasks. Comprehension Daneman and Carpenter ( 1980 ) were the ﬁrst to demonstrate a relation- ship between central executive functioning and individual differences in comprehension. Their participants read a series of narrative passages and then answered different types of questions. For example, the ﬁnal sentence of each passage contained an ambiguous pronoun, and the participants’ task was to supply the referent, which occurred at some earlier point in the passage. Daneman and Carpenter found a strong positive correlation between reading span and this index of comprehension, particularly when several sentences separated the pronoun and referent. There were positive correlations between reading span and other indexes of comprehension as well, including memory for facts and verbal SAT score. Daneman and Carpenter argued that the relationship between reading span and read- ing comprehension occurs simply because both measures capture reading skill. That is, by virtue of more efﬁcient and automatic reading strategies, 186 Hambrick and Engle participants with high levels of reading skill were able to devote more working memory resources to remembering the sentence-ﬁnal words. Thus, Daneman and Carpenter ( 1980 ) argued that reading span is a consequence of reading skill. The results of a large number of subsequent studies from our laboratory run counter to this argument. We describe the results of two such studies. Turner and Engle ( 1989 ) reasoned that if the correlation between working memory span and reading comprehension reﬂects the fact that both measures index reading skill, then the strength of the relationship between the two measures should vary depending on the nature of the processing component of the span task. Following this logic, participants completed four working memory tasks in which the pro- cessing task was either reading sentences or solving arithmetic equations. The measures of reading comprehension were scores on the Nelson-Denny reading test and verbal SAT. Turner and Engle found that the processing component manipulation (sentences vs. equations) had little effect on the relationship between working memory span and reading comprehension. Engle, Cantor, and Carullo ( 1992 ) conducted a more systematic investi- gation of the relationship between working memory capacity and reading comprehension. In a series of experiments, participants performed either the operation span task or the reading span task using a moving window technique in which each equation-word (operation span) or sentence-word (reading span) stimulus was presented one element at a time. The time re- quired to advance through the equation or sentence was used as an index of skill in executing the processing component of the task; verbal SAT served as a measure of comprehension. Engle et al. reasoned that if skill in the pro- cessing component of the span tasks accounted for the correlation between working memory capacity and verbal SAT, then controlling for processing skill would eliminate the correlation. This was not the case: Controlling for processing skill had no effect on the correlation between working memory capacity and comprehension. One possible interpretation of the evidence reviewed thus far is that working memory capacity reﬂects a domain-general capability instead of skills and procedures applicable to a particular task or class of tasks. Re- cently, however, Ericsson and Kintsch ( 1995 ) and Kintsch ( 1998 ) suggested a viewpoint more in line with the task-speciﬁc hypothesis. In particular, they suggested that what the reading span task measures is the efﬁciency of comprehension. For example, Kintsch stated, “What the reading span measures is the efﬁciency with which readers can comprehend sentences and hence store them in long-term memory” (p. 239 ). To support their claim, Ericsson and Kintsch reviewed evidence suggesting that long-term memory contributes to performance in the reading span task. For exam- ple, using a version of the reading span task, Masson and Miller ( 1983 ) found a positive correlation between recall of the sentence-ﬁnal words and cued recall of words from earlier in the sentences. There were also positive Role of Working Memory 187 correlations of each measure with reading comprehension. Assuming that participants could not maintain all of the sentences in temporary storage, it seems clear that the sentences were stored in long-term memory. Nevertheless, a critical point about the original Daneman and Carpenter ( 1980 ) reading span task, and the version of this task used by Masson and Miller ( 1983 ), is that the sentence-ﬁnal “span” words were not separate from the sentences themselves. The problem with this task is that it is not possible to disentangle working memory capacity and reading skill. Indeed, recall of the sentence-ﬁnal words may in part reﬂect the efﬁciency with which readers can comprehend sentences and store them in long-term memory (Kintsch, 1998 ). By contrast, in the version of the reading span task used by Engle et al. ( 1992 ), the span words were separate from the sentences. Hence, it was possible to examine effects of reading span on comprehension controlling for skill in the processing component of the task. To reiterate, reading skill did not account for the relationship between working memory capacity and comprehension. Based on this evidence, we believe that the ﬁndings cited by Ericsson and Kintsch ( 1995 ) are important, but they are not sufﬁcient to falsify the claim that measures of working memory capacity reﬂect a general capacity that transcends task-speciﬁc skills. Multiple Working Memory Capacities? A study by Shah and Miyake ( 1996 ) is also relevant to the present dis- cussion. The major question of this study was whether working memory capacity represents a single cognitive resource or whether domain-speciﬁc pools of working memory resources can be distinguished. To investigate this issue, Shah and Miyake had participants perform two working mem- ory tasks, one verbal and one spatial. The Daneman and Carpenter ( 1980 ) reading span task served as the verbal working memory task. The spatial working memory task involved simultaneous maintenance and process- ing of spatial information. For each trial, participants indicated whether the orientation of a letter was normal or mirror-imaged. Then, after a num- ber of trials, the objective was to recall the orientation of each letter. Verbal SAT score was used as a measure of verbal ability, and spatial visualization tests were used to measure spatial ability. Shah and Miyake ( 1996 ) found that the spatial working memory measure correlated moderately with spa- tial ability, but near zero with verbal SAT. Conversely, the verbal working memory measure correlated moderately with verbal SAT, but near zero with spatial ability. In addition, the correlation between the two working memory measures was weak ( r = . 23 ). The same basic pattern of results was replicated in a second study. Shah and Miyake therefore concluded, “The predictive powers of the two complex memory span tasks seem to be domain speciﬁc … ” (p. 11 ). Nevertheless, the results of these studies should be evaluated in light of two potential methodological limitations. First, the sample sizes were