Toward a Theory of Impasse-Driven Learning

  • Kurt VanLehn
Part of the Cognitive Science book series (COGNITIVE SCIEN)


Learning is widely viewed as a knowledge communication process coupled with a knowledge compilation process (Anderson, 1985). The communication process interprets instruction, thereby incorporating new information from the environment into the mental structures of the student. Knowledge compilation occurs with practice. It transforms the initial mental structures into a form that makes performance faster and more accurate. Moreover, the transformed mental structures are less likely to be forgotten. At one time, psychology concerned itself exclusively with the compilation process by using such simple stimuli (e.g., nonsense syllables) that the effects of the communication process could be ignored. The work presented here uses more complicated stimuli, the calculational procedures of ordinary arithmetic. For such stimuli, the effects of the knowledge communication process cannot be ignored. Later in this chapter it is shown that certain types of miscommunication can cause students to have erroneous conceptions. The long-term objective of the research reported here is to develop a theory of the neglected half of learning, knowledge communication. The experimental methods employed are designed to show the effects of knowledge communication and hide the effects of knowledge compilation. Consequently, whenever the term learning appears, it is intended to mean knowledge communication.


Intelligent Tutor System Procedural Skill Local Problem Solver Leftmost Column Core Procedure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Anderson, J. R. (1983). The architecture of cognition. Cambridge, MA: Harvard.Google Scholar
  2. Anderson, J. R. (1985). Cognitive psychology and its implications. New York: Freedman.Google Scholar
  3. Anderson, J. R., Farrell, R., & Saurers, R. (1984). Learning to program in LISP. Cognitive Science, 8, 87–129.CrossRefGoogle Scholar
  4. Anzai, Y., & Simon, H. A. (1979). The theory of learning by doing. Psychological Review, 86, 124–140.CrossRefGoogle Scholar
  5. Ashlock, R. B. (1976). Error patterns in computation. Columbus, OH: Bell & Howell.Google Scholar
  6. Berwick, R. (1985). The acquisition of syntactic knowledge. Cambridge, MA: MIT Press.Google Scholar
  7. Brown, J. S., & Burton, R. B. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2, 155–192.CrossRefGoogle Scholar
  8. Brown, J. S., & VanLehn, K, (1980). Repair Theory: A generative theory of bugs in procedural skills. Cognitive Science, 4, 379–426.CrossRefGoogle Scholar
  9. Brownell, W. A. (1935). Psychological considerations in the learning and teaching of arithmetic. In W. D. Reeve (Ed.), The teaching of arithmetic. New York: Teachers College, Bureau of Publications.Google Scholar
  10. Brueckner, L. J. (1930). Diagnostic and remedial teaching in arithmetic. Philadelphia: Winston.Google Scholar
  11. Burton, R. B. (1982). Diagnosing bugs in a simple procedural skill. In D. H. Sleeman, and J. S. Brown (Eds.) Intelligent Tutoring Systems. New York: Academic Press.Google Scholar
  12. Buswell, G. T. (1926). Diagnostic studies in arithmetic. Chicago: University of Chicago Press.Google Scholar
  13. Cox, L. S. (1975). Diagnosing and remediating systematic errors in addition and subtraction computation. The Arithmetic Teacher, 22, 151–157.Google Scholar
  14. Laird, J. E., Rosenbloom, P. S., & Newell, A. (1986). Chunking in SOAR: The anatomy of a general learning mechanism. Machine Learning, 1, 11–46.Google Scholar
  15. Laird, J. E., Rosenbloom, P. S., & Newell, A. (1987). SOAR: An architecture for general intelligence. Artificial Intelligence, 33, 1–64.CrossRefGoogle Scholar
  16. Lankford, F. G. (1972). Some computational strategies of seventh grade pupils. Charlottesville, VA: University of Virginia.Google Scholar
  17. Minton, S. (1985). Selectively generalizing plans for problem-solving. In Proceedings of IJCAI 85 (pp. 596–599). Los Altos, CA: Morgan-Kaufman.Google Scholar
  18. Newell, A. (1980). Reasoning, problem solving and decision processes: The problem space as a fundamental category. In R. Nickerson (Ed.), Attention and Performance VIII. Hillsdale, NJ: Erlbaum.Google Scholar
  19. Newell, A., & Simon, H. A. (1972). Human problem-solving. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  20. Norman, D. A. (1981). Categorization of action slips. Psychological Review, 88, 1–15.MathSciNetCrossRefGoogle Scholar
  21. Resnick, L. (1982). Syntax and semantics in learning to subtract. In T. Carpenter, J. Moser & T. Romberg (Ed.). Addition and subtraction: A cognitive perspective. Hillsdale, NJ: Lawrence Erlbaum Assoc.Google Scholar
  22. Resnick, L. B., & Omanson, S. F. (1987). Learning to understand arithmetic. In R. Glaser (Ed.), Advances in instructional psychology. Hillsdale, NJ: Lawrence Erlbaum Assoc.Google Scholar
  23. Roberts, G. H. (1968). The failure strategies of third grade arithmetic pupils. The Arithmetic Teacher, 15, 442–446.Google Scholar
  24. Schank, R. (1982). Dynamic memory: A theory of learning in computers and people. Cambridge, England: Cambridge University Press.Google Scholar
  25. Shaw, D. J., Standiford, S. N., Klein, M. F., & Tatsuoka, K. K. (1982). Error analysis of fraction arithmetic-selected case studies (Tech. Report 82–2-NIE). Urbana, IL: University of Illinois, Computer-based Education Research Laboratory.Google Scholar
  26. Siegler, R. S., & Shrager, J. (1984). Strategy choices in addition: How do children know what to do? In C. Sophian (Ed.). Origins of Cognitive Skill. Hillsdale, NJ: Lawrence Erlbaum Assoc.Google Scholar
  27. Sleeman, D. (1984). An attempt to understand students’ understanding of basic algebra. Cognitive Science, 8, 387–412.CrossRefGoogle Scholar
  28. Sleeman, D. H. (1985). Basic algebra revisited: A study with 14-year olds. International Journal of Man-Machine Studies, 22, 127–149.CrossRefGoogle Scholar
  29. Sleeman, D. H., & Smith, M. J. (1981). Modeling student’s problem solving. Artificial Intelligence, 16, 171–187.CrossRefGoogle Scholar
  30. Smith, B. C. (1982). Reflection and semantics in a procedural language (Technical Report MIT-TR-272). Cambridge, MA: M.I.T. Laboratory for Computer Science.Google Scholar
  31. Tatsuoka, K. K., & Baillie, R. (1982). Rule space, the product space of two score components in signed-number subtraction: An approach to dealing with inconsistent use of erroneous rules (Tech. Report 82–3-ONR). Urbana, IL: University of Illinois, Computer-based Education Research Laboratory.Google Scholar
  32. VanLehn, K. (1982). Bugs are not enough: Empirical studies of bugs, impasses and repairs in procedural skills. The Journal of Mathematical Behavior, 3, 3–71.Google Scholar
  33. VanLehn, K. (1983a). Felicity conditions for human skill acquisition: Validating an AI-based theory (Tech. Report CIS-21). Palo Alto, CA: Xerox Palo Alto Research Center.Google Scholar
  34. VanLehn, K. (1983b). Human skill acquisition: Theory, model and psychological validation. In Proceedings of AAAI-83 (pp. 420–423). Los Altos, CA: Kaufman.Google Scholar
  35. VanLehn, K. (1986). Arithmetic procedures are induced from examples. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics. Hillsdale. NJ: Lawrence Erlbaum Assoc.Google Scholar
  36. VanLehn, K. (in press). Cognitive procedures: The acquisition and mental representation of basic mathematical skills. Cambridge, MA: MIT Press.Google Scholar
  37. VanLehn, K., Brown, J. S., & Greeno, J. G. (1984). Competitive argumentation in computational theories of cognition. In W. Kintsch, J. Miller, & P. Poison (Ed.), Methods and tactics in cognitive science. Hillsdale, NJ: Lawrence Erlbaum, Assoc.Google Scholar
  38. Wexler, K., & Culicover, P. (1980). Formal principles of language acquisition. Cambridge, MA: MIT Press.Google Scholar

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© Springer-Verlag New York Inc. 1988

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  • Kurt VanLehn

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