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Thinking Through Diagrams: Discovery in Game Playing

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Book cover Spatial Cognition IV. Reasoning, Action, Interaction (Spatial Cognition 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3343))

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Abstract

Diagrams often play an important role in human problem solving. A diagram can make a task more difficult, however, when it obscures important problem features, or requires repeated effort to interpret what it represents. Moreover, the nature and origin of diagrams can be as important as their exploitation during problem solving. This paper chronicles the complex interleaving of visual cognition with high-level reasoning in three subjects. Their diagrams and subsequent verbal protocols offer insight into human cognition. The diversity and richness of their response, and their ability to address the task via diagrams, provide an incisive look at the role diagrams play in the development of expertise. This paper recounts how their diagrams led, and misled, them; how their diagrams both explained and drove explanation; and how a spatial approach reported here can lead to deeper understanding of other simple games.

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References

  1. Amarel, S.: On Representations of Problems of Reasoning about Actions. In: Michie, D. (ed.) Machine Intelligence, vol. 3, pp. 131–171. Edinburgh University Press, Edinburgh (1968)

    Google Scholar 

  2. Anzai, Y., Simon, H.: The Theory of Learning by Doing. Psychological Review 36, 124–140 (1979)

    Article  Google Scholar 

  3. Cheng, P.C.-H.: Unlocking conceptual learning in mathematics and science with effective representational systems. Computers in Education 33, 109–130 (1999)

    Article  Google Scholar 

  4. Cheng, P.C.-H., Simon, H.A.: Scientific discovery and creative reasoning with diagrams. In: Smith, S., Ward, T., Finke, R. (eds.) The Creative Cognition Approach, pp. 205–228. MIT Press, Cambridge (1995)

    Google Scholar 

  5. Cross, N., Christaans, H., Dorst, K. (eds.): Analyzing Design Activity. John Wiley and Sons, Chichester (1996)

    Google Scholar 

  6. Epstein, S.L.: Toward an Ideal Trainer. Machine Learning 15, 251–277 (1994)

    MATH  Google Scholar 

  7. Falkenhainer, B.C., Michalski, R.S.: Integrating Quantitative and Qualitative Discovery. Machine Learning 1, 367–401 (1986)

    Google Scholar 

  8. Gelernter, H.: Realization of a Geometry-Theorem Proving Machine. In: Feigenbaum, E.A., Feldman, J. (eds.) Computers and Thought, pp. 134–152. McGraw-Hill, New York (1963)

    Google Scholar 

  9. Hadamard, J.: The Psychology of Invention in the Mathematical Field. Dover Publications, New York (1945)

    MATH  Google Scholar 

  10. Hegarty, M.: Mental Visualizations and External Visualizations. In: Gray, W., Schunn, C. (eds.) Proceedings of the 24th Annual Meeting of the Cognitive Science Society, pp. 40–45. Lawrence Earlbaum, CA (2002)

    Google Scholar 

  11. Kaplan, C.A., Simon, H.A.: In Search of Insight. Cognitive Psychology 22, 374–419 (1990)

    Article  Google Scholar 

  12. Kotovsky, K., Hayes, J.R., Simon, H.A.: Why are some problems hard? Cognitive Psychology 17, 248–294 (1985)

    Article  Google Scholar 

  13. Langley, P., Zytkow, J.M., Simon, H.A., Bradshaw, G.L.: The Search for Regularity: Four Aspects of Scientific Discovery. In: Michalski, R.S., Carbonell, J.G., Mitchell, T.M. (eds.) Machine Learning 2: An Artificial Intelligence Approach, pp. 425–469. Tioga Publishing, Palo Alto (1986)

    Google Scholar 

  14. Larkin, J.H.: Display-based Problem Solving. In: Klahr, D., Kotovsky, K. (eds.) Complex Information Processing: The Impact of Herbert A. Simon, pp. 319–341. Lawrence Erlbaum Associates, Hillsdale (1989)

    Google Scholar 

  15. Pascal, B.: Pensées de Pascal. Éditions Garnier Frères, Paris (1964)

    Google Scholar 

  16. Pearson, D., Alexander, G.C., Webster, R.: Working Memory and Expertise Differences in Design. In: Gero, J.S., Tversky, B.T., Purcell, T. (eds.) Visual and Spatial Reasoning in Design II. Key Centre of Design Computing and Cognition, pp. 237–251. University of Sydney, Sydney, Australia (2001)

    Google Scholar 

  17. Poincaré, H.: La Valeur de la Sciènce. Flammarion, France (1970)

    Google Scholar 

  18. Saariluoma, P., Maarttola, I.: Spatial Mental Content and Visual Design. In: Gero, J.S., Tversky, B.T., Purcell, T. (eds.) Visual and Spatial Reasoning in Design II. Key Centre of Design Computing and Cognition, University of Sydney, Sydney, Australia, pp. 253–268 (2001)

    Google Scholar 

  19. Suwa, M., Tversky, B.T., Gero, J.S., Purcell, T.: Seeing into sketches: Regrouping Parts Encourages New Interpretations. In: Gero, J.S., Tversky, B.T., Purcell, T. (eds.) Visual and Spatial Reasoning in Design II. Key Centre of Design Computing and Cognition, University of Sydney, Sydney, Australia, pp. 207–219 (2001)

    Google Scholar 

  20. Tversky, B.T.: Multiple Mental Models. In: Gero, J.S., Tversky, B.T., Purcell, T. (eds.) Visual and Spatial Reasoning in Design II. Key Centre of Design Computing and Cognition, University of Sydney, Sydney, Australia, pp. 3–13 (2001)

    Google Scholar 

  21. Zaslavsky, C.: Tic Tac Toe and Other Three-in-a-Row Games, from Ancient Egypt to the Modern Computer. Crowell, New York (1982)

    Google Scholar 

  22. Zhang, J.: The nature of external representations in problem solving. Cognitive Science 21, 179-217 (1997)

    Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Epstein, S.L. (2005). Thinking Through Diagrams: Discovery in Game Playing . In: Freksa, C., Knauff, M., Krieg-Brückner, B., Nebel, B., Barkowsky, T. (eds) Spatial Cognition IV. Reasoning, Action, Interaction. Spatial Cognition 2004. Lecture Notes in Computer Science(), vol 3343. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11397977_16

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  • DOI: https://doi.org/10.1007/11397977_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25048-7

  • Online ISBN: 978-3-540-32255-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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