Educational Psychology Review

, Volume 28, Issue 4, pp 691–716 | Cite as

The Structure of Ill-Structured (and Well-Structured) Problems Revisited

  • Stephen K. Reed
Review Article


In his 1973 article The Structure of ill structured problems, Herbert Simon proposed that solving ill-structured problems could be modeled within the same information-processing framework developed for solving well-structured problems. This claim is reexamined within the context of over 40 years of subsequent research and theoretical development. Well-structured (puzzle) problems can be represented by a problem space consisting of well-defined initial and goal states that are connected by legal moves. In contrast, the initial, goal, and intermediate states of ill-structured (design) problems are incompletely specified. This article analyzes the similarities and differences among puzzles, insight puzzles, classroom problems, and design problems within Gick’s (Educational Psychologist, 21, 99–120, 1986) theoretical framework consisting of representation construction, schema activation, and heuristic search. The analysis supports Simon’s (Artificial Intelligence, 4, 181–201, 1973) claim that information-processing principles apply to all problems but apply differently as problems become more ill structured.


Problem solving Representation Search Analogy Schema 



Work on this manuscript occurred while the author was a visiting scholar at the Center for the Study of Language and Information, Stanford University and at the Department of Psychology, University of California, San Diego. I thank anonymous reviewers for their many helpful suggestions.


  1. Alfieri, L., Nokes-Malach, T. J., & Schunn, C. D. (2013). Learning through case comparisons: a meta-analytic review. Educational Psychologist, 48, 87–113.CrossRefGoogle Scholar
  2. Ash, I. K., & Wiley, J. (2006). The nature of restructuring in insight: an individual-differences approach. Psychonomic Bulletin & Review, 13, 66–73.CrossRefGoogle Scholar
  3. Atwood, M. E., & Polson, P. (1976). A process model for water jug problems. Cognitive Psychology, 8, 191–216.CrossRefGoogle Scholar
  4. Atwood, M.E., Polson, P.G., Jeffries, R., & Ramsey, H.R. (1978). Planning as a process of synthesis. Retrieved from Englewood, CO.Google Scholar
  5. Barsalou, L. W. (1999). Perceptual symbol systems. Behavioral & Brain Sciences, 22, 577–660.Google Scholar
  6. Bassok, M., & Novick, L. R. (2012). Problem solving. In K. J. Holyoak & R. J. Morrison (Eds.), The Oxford Handbook of thinking and reasoning (pp. 413–432). New York: Oxford University Press.Google Scholar
  7. Brewer, W. F., & Nakamura, G. V. (1984). The nature and function of schemas. In R. S. Wyer & T. K. Srull (Eds.), Handbook of social cognition (Vol. 1, pp. 119–160). Hillsdale: Erlbaum.Google Scholar
  8. Carroll, J. M., Thomas, J. C., & Malhotra, A. (1980). Presentation and representation in design problem solving. British Journal of Psychology, 71, 143–153.CrossRefGoogle Scholar
  9. Catrambone, R. (1995). Aiding subgoal learning: effects on transfer. Journal of Educational Psychology, 87, 5–17.CrossRefGoogle Scholar
  10. Catrambone, R., & Holyoak, K. J. (1989). Overcoming contextual limitations on problem-solving transfer. Journal of Experimental Psychology: Learning, Memory and Cognition, 15, 1147–1156.Google Scholar
  11. Chi, M. T. H., Glaser, R., & Rees, E. (1982). Expertise in problem solving. In R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 1, pp. 7–75). Mahwah: Erlbaum.Google Scholar
  12. Chi, M. T. H., & VanLehn, K. (2012). Seeing deep structure from the interaction of surface features. Educational Psychologist, 47, 177–188.CrossRefGoogle Scholar
  13. Cho, A. (2007). Program proves that checkers, perfectly played, is a no-win situation. Science, 317, 308–309.CrossRefGoogle Scholar
  14. Dove, G. (2009). Beyond perceptual symbols: a call for representational pluralism. Cognition, 110, 412–431.CrossRefGoogle Scholar
  15. Dunbar, K., & Blanchette, I. (2001). The in vivo approach to cognition: the case of analogy. TRENDS in Cognitive Sciences, 5, 334–339.CrossRefGoogle Scholar
  16. Duncker, K. (1945). On problem solving. Psychological Monographs, 58(5, Whole No. 270).Google Scholar
  17. Egan, D. E., & Greeno, J. G. (1974). Theory of rule induction: knowledge acquired in concept learning, serial pattern learning, and problem solving. In L. Gregg (Ed.), Knowledge and cognition. Erlbaum: Mahwah.Google Scholar
  18. Engle, R. A. (2006). Framing interactions to foster generative learning: a situative explanation of transfer in a community of learners classroom. The Journal of the Learning Sciences, 15, 451–499.CrossRefGoogle Scholar
  19. Ernst, G. W., & Newell, A. (1969). GPS: a case study in generality and problem solving. New York: Academic Press.Google Scholar
  20. Finke, R. A. (1990). Creative imagery: discoveries and inventions in visualization. Mahwah: Lawrence Erlbaum Associates.Google Scholar
  21. Gentner, D. (1983). Structure-mapping: a theoretical framework for analogy. Cognitive Science, 7, 155–170.CrossRefGoogle Scholar
  22. Gentner, D., Lowenstein, J., Thompson, L., & Forbus, K. D. (2009). Reviving inert knowledge: analogical encoding supports relational retrieval of past events. Cognitive Science, 33, 1343–1382.CrossRefGoogle Scholar
  23. Gentner, D., & Markman, A. B. (1997). Structure mapping in analogy and similarity. American Psychologist, 52, 45–56.CrossRefGoogle Scholar
  24. Gick, M. (1986). Problem-solving strategies. Educational Psychologist, 21, 99–120.CrossRefGoogle Scholar
  25. Gick, M., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive Psychology, 15, 1–38.CrossRefGoogle Scholar
  26. Gick, M., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1–38.CrossRefGoogle Scholar
  27. Gilhooly, K. J., Georgiou, G., & Devery, U. (2013). Incubation and creativity: do something different. Thinking & Reasoning, 19, 137–149.CrossRefGoogle Scholar
  28. Glenberg, A. M., Jaworski, B., Rischal, M., & Levin, J. R. (2007). What brains are for: action, meaning, and reading comprehension. In D. McNamara (Ed.), Reading comprehension strategies: theories, interventions, and technologies (pp. 221–240). Mahwah: Lawrence Erlbaum Publishers.Google Scholar
  29. Goel, V. (2014). Creative brains: designing in the real world. Frontiers in Human Neuroscience, 8(241), 1–14.Google Scholar
  30. Goel, V., & Pirolli, P. (1992). The structure of design problem spaces. Cognitive Science, 16, 395–429.CrossRefGoogle Scholar
  31. Greeno, J. G. (1976). Indefinite goals in well-structured problems. Psychological Review, 83, 479–491.CrossRefGoogle Scholar
  32. Greeno, J. G. (1978). Natures of problem solving abilities. In W. K. Estes (Ed.), Handbook of learning and cognition (Vol. 5). Hillsdale: Elbaum.Google Scholar
  33. Greeno, J. G., Smith, D. R., & Moore, J. L. (1993). Transfer of situated learning. In D. K. Detterman & R. J. Sternberg (Eds.), Transfer on trial: Intelligence, cognition, and instruction (pp. 99–167). Norwood: Ablex.Google Scholar
  34. Hassin, R. R. (2013). Yes it can: on the functional abilities of the human unconscious. Perspectives on Cognitive Science, 8, 195–207.Google Scholar
  35. Hayes, J. R. (1966). Memory, goals, and problem solving. In B. Kleinmuntz (Ed.), Problem solving: research, method, and theory. New York: Wiley.Google Scholar
  36. Hayes, J. R., & Simon, H. A. (1977). Psychological differences among problem isomorphs. In N. J. Castellan, D. B. Pisoni, & G. R. Potts (Eds.), Cognitive theory (Vol. 2, pp. 21–41). Mahwah: Erlbaum.Google Scholar
  37. Helie, S., & Sun, R. (2010). Incubation, insight, and creative problem solving: a unified theory and a connectionist model. Psychological Review, 117, 994–1024.CrossRefGoogle Scholar
  38. Hills, T. T., Todd, P. M., Lazer, D., Redish, A. D., Couzin, I. D., & the Cognitive Search Research Group (2015). Exploration versus exploitation in space, mind, and society. Trends in Cognitive Sciences, 19, 46–54.Google Scholar
  39. Jonassen, D. H. (1997). Instructional design models for well-structured and ill-structured problem-solving learning outcomes. Educational Technology Research and Development, 45, 65–94.CrossRefGoogle Scholar
  40. Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48, 63–85.CrossRefGoogle Scholar
  41. Jones, G. (2003). Testing two cognitive theories of insight. Journal of Experimental Psychology: Learning, Memory, and Cognition, 29, 1017–1027.Google Scholar
  42. Klahr, D., & Simon, H. A. (1999). Study of scientific discovery: complementary approaches and convergent findings. Psychological Bulletin, 125, 524–543.CrossRefGoogle Scholar
  43. Knoblich, G., Ohlsson, S., Haider, H., & Rhenius, D. (1999). Constraint relaxation and chunk decomposition in insight problem solving. Journal of Experimental Psychology: Learning, memory and cognition, 25, 1534–1555.Google Scholar
  44. Kohler, W. (1925). The mentality of apes. New York: Harcourt.Google Scholar
  45. Kohler, W. (1947). Gestalt Psychology. New York: Liveright Publishing Corporation.Google Scholar
  46. Lobato, J. (2012). The actor-oriented transfer perspective and its consequences to educational research and practice. Educational Psychologist, 47, 232–247.CrossRefGoogle Scholar
  47. MacGregor, J. N., Ormerod, T. C., & Chronicle, E. P. (2001). Information processing and insight: a process model of performance on the nine-dot and related problems. Journal of Experimental Psychology: Learning, Memory, and Cognition, 27, 176–201.Google Scholar
  48. Marshall, S. P. (1995). Schemas in problem solving. New York: Cambridge University Press.CrossRefGoogle Scholar
  49. McCaffrey, T. (2012). Innovation relies on the obscure: a key to overcoming the classic problem of functional fixedness. Psychological Science, 23, 215–218.CrossRefGoogle Scholar
  50. Metcalfe, J., & Wiebe, D. (1987). Intuition in insight and noninsight problem solving. Memory & Cognition, 15, 238–246.CrossRefGoogle Scholar
  51. Moyer, P. S. (2002). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47, 175–197.CrossRefGoogle Scholar
  52. Murray, O. A. R. (1923). The administration of a fighting service. Journal of Public Administration, 1, 216–217.Google Scholar
  53. Newell, A., & Simon, H. A. (1972). Human problem solving. Englewood Cliffs: Prentice-Hall.Google Scholar
  54. Nokes-Malach, T. J., & Mestre, J. P. (2013). Toward a model of transfer as sense-making. Educational Psychologist, 48, 184–207.CrossRefGoogle Scholar
  55. Norman, D. A. (2013). The design of everyday things: revised and expanded edition. New York: Basic Books.Google Scholar
  56. Ormerod, T. C., MacGregor, J. N., & Chronicle, E. P. (2002). Dynamics and constraints in insight problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 28, 791–799.Google Scholar
  57. Patsenko, E. G., & Altmann, E. M. (2010). How planful is routine behavior? A selective-attention model of planning in the Tower of Hanoi. Journal of Experimental Psychology: General, 139, 95–116.CrossRefGoogle Scholar
  58. Reed, S. K. (1987). A structure-mapping model for word problems. Journal of Experimental Psychology: Learning, memory and cognition, 13, 124–139.Google Scholar
  59. Reed, S. K. (2010). Thinking Visually. New York: Taylor & Francis.Google Scholar
  60. Reed, S. K. (2012). Learning by mapping across situations. The Journal of the Learning Sciences, 21, 353–398.Google Scholar
  61. Reed, S. K. (2015). Problem Solving. In S. Chipman (Ed.), Oxford handbook of cognitive science. Oxford: Oxford Chapters Online.Google Scholar
  62. Reed, S. K., & Abramson, A. (1976). Effect of the problem space on subgoal facilitation. Journal of Educational Psychology, 68, 243–246.Google Scholar
  63. Reed, S. K., Ernst, G. W., & Banerji, R. (1974). The role of analogy in transfer between similar problem states. Cognitive Psychology, 6, 436–450.CrossRefGoogle Scholar
  64. Reed, S. K., & Johnsen, J. A. (1977). Memory for problem solutions. In G. H. Bower (Ed.), The psychology of learning and motivation (pp. 161–201). New York: Academic Press.Google Scholar
  65. Reitman, W. R. (1965). Cognition and thought. New York: Wiley.Google Scholar
  66. Richey, J. E., & Nokes-Malach, T. J. (2015). Comparing four instructional techniques for promoting robust knowledge. Educational Psychology Review, 27, 181–218.CrossRefGoogle Scholar
  67. Richland, L. E., Holyoak, K. J., & Stigler, J. W. (2004). Analogy use in eighth-grade mathematics classrooms. Cognition and Instruction, 22, 37–60.CrossRefGoogle Scholar
  68. Rittel, H. W. J., & Webber, M. M. (1973). Dilemmas in a general theory of planning. Policy Sciences, 4, 155–169.CrossRefGoogle Scholar
  69. Rittle-Johnson, B., & Star, J. R. (2009). Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. Journal of Educational Psychology, 101, 529–544.CrossRefGoogle Scholar
  70. Silver, E. (1981). Recall of mathematical problem information: solving related problems. Journal for Research in Mathematics Education, 12, 54–64.CrossRefGoogle Scholar
  71. Simon, H. A. (1973). The structure of ill-structured problems. Artificial Intelligence, 4, 181–201.CrossRefGoogle Scholar
  72. Simon, H. A. (1975). The functional equivalence of problem solving skills. Cognitive Psychology, 7, 268–288.CrossRefGoogle Scholar
  73. Simon, H. A., & Reed, S. K. (1976). Modeling strategy shifts in a problem-solving task. Cognitive Psychology, 8, 86–97.Google Scholar
  74. Sio, U. T., & Ormerod, T. C. (2009). Does incubation enhance problem solving? A meta-analytic review. Psychological Bulletin, 135, 94–120.CrossRefGoogle Scholar
  75. Smith, S. M., Ward, T. B., & Schumacher, J. S. (1993). Constraining effect of examples in a creative generation task. Memory & Cognition, 21, 837–845.CrossRefGoogle Scholar
  76. Sun, R., & Zhang, X. (2006). Accounting for a variety of reasoning data within a cognitive architecture. Journal of Experimental & Theoretical Artificial Intelligence, 18, 169–191.CrossRefGoogle Scholar
  77. Sweller, J., Mawer, R. F., & Ward, M. R. (1983). Development of expertise in problem solving. Journal of Experimental Psychology: General, 112, 639–661.CrossRefGoogle Scholar
  78. Vallacher, R. R., Coleman, P. T., Nowak, A., & Bui-Wrzosinska. (2010). Rethinking intractable conflict: the perspective of dynamical systems. American Psychologist, 65, 262–278.CrossRefGoogle Scholar
  79. van Tonder, G. J., & Vishwanath, D. (2015). Design insights: Gestalt, bauhaus, and Japanese gardens. In J. Wagemans (Ed.), The Oxford handbook of perceptual organization. New York: Oxford University Press.Google Scholar
  80. VanLehn, K. (1989). Problem solving and cognitive skill acquisition. In M. I. Posner (Ed.), Foundations of cognitive science (pp. 526–579). Cambridge: MIT Press.Google Scholar
  81. Wallas, G. (1926). The art of thought. New York: Harcourt, Brace.Google Scholar
  82. Ward, T. B., Patterson, M. J., & Sifonis, C. M. (2004). The role of specificity and abstraction in creative idea generation. Creativity Research Journal, 16, 1–9.CrossRefGoogle Scholar
  83. Weisberg, R. W. (2009). On “out-of-the-box” thinking in creativity. In A. B. Markman & K. L. Wood (Eds.), Tools for innovation (pp. 23–47). New York: Oxford University Press.CrossRefGoogle Scholar
  84. Wickelgren, W. A. (1974). How to solve problems: elements of a theory of problems and problem solving. San Francisco: Freeman.Google Scholar
  85. Wiley, J., & Jarosz, A. F. (2012). Working memory capacity, attentional focus, and problem solving. Current Directions in Psychological Science, 21, 258–262.CrossRefGoogle Scholar
  86. Yu, R., Gu, N., & Lee, J. H. (2013). Comparing designers' behavior in responding to unexpected discoveries in parametric design and geometry modeling environments. International Journal of Architectural Computing, 11, 393–414.CrossRefGoogle Scholar
  87. Zedelius, C. M., & Schooler, J. W. (2015). Mind wanderig "Ahas" versus mindful reasoning: alternative routes to creative solutions. Frontiers in Psychology, 6, 834.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.PsychologySan Diego State UniversitySan DiegoUSA
  2. 2.CRMSESan Diego State UniversitySan DiegoUSA
  3. 3.Department of PsychologyUniversity of California, San DiegoLa JollaUSA

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