The Interaction Between Knowledge and Practice in the Acquisition of Cognitive Skills
Abstract
The role of prior knowledge in skill acquisition is to enable the learner to detect and to correct errors. Computational mechanisms that carry out these two functions are implemented in a simulation model which represents prior knowledge in constraints. The model learns symbolic skills in mathematics and science by noticing and correcting constraint violations. Results from simulation runs include quantitative predictions about the learning curve and about transfer of training. Because constraints can represent instructions as well as prior knowledge, the model also simulates one-on-one tutoring. The implications for the design of instruction include a detailed specification of the content of effective feedback messages for intelligent tutoring systems.
Keywords
Production Rule Skill Acquisition Constraint Violation Procedural Knowledge Training TaskPreview
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References
- Abelson, R. P., Aronson, E., McGuire, W. J., Newcomb, T. M., Rosenberg, M. J., & Tannenbaum, P. H., (Eds.), (1968). Theories of cognitive consistency: A sourcebook. Chicago, IL: Rand McNally.Google Scholar
- Anderson, J. R. (1976). Language, memory, and thought. Hillsdale, New Jersey: Erlbaum.Google Scholar
- Anderson, J. R. (1983). The architecture of cognition. Cambridge, MA: Harvard University Press.Google Scholar
- Anderson, J. R. (1986). Knowledge compilation: The general learning mechanism. In R. S. Michalski, J. G. Carbonell, & T. M. Mitchell, (Eds.), Machine learning: An artificial intelligence approach (Vol. 2, pp. 289–310). Los Altos, CA: Kaufmann.Google Scholar
- Anderson, J. R. (1987). Skill acquisition: Compilation of weak-method problem solutions. Psychological Review, 94, 192–210.CrossRefGoogle Scholar
- Anderson, J. R. (1990). The adaptive character of thought. Hillsdale, NJ: Erlbaum.Google Scholar
- Anderson, J. R. (1993). Rules of the mind. Hillsdale, NJ: Erlbaum. In press.Google Scholar
- Anderson, J. R., Boyle, C. F., Corbett, A. T., & Lewis, M. W. (1990). Cognitive modeling and intelligent tutoring. Artificial Intelligence, 42,7–49.CrossRefGoogle Scholar
- Anderson, J. R., Boyle, C. F., Farrell, R., & Reiser, B. J. (1987). Cognitive principles in the design of computer tutors. In P. Morris, (Ed.), Modeling cognition. New York, NY: Wiley.Google Scholar
- Anderson, J. R., Kline, P. J., & Beasley, C. M., Jr. (1979). A general learning theory and its application to schema abstraction. In G. H. Bower, (Ed.), The psychology of learning and motivation: Advances in research and theory (Vol. 13, pp. 277–318). New York, NY: Academic Press.Google Scholar
- Anderson, J. R., & Schooler, L. J. (1991). Reflections of the environment in memory. Psychological Science, 2,396–408.CrossRefGoogle Scholar
- Angluin, D., & Smith, C. H. (1983). Inductive inference: Theory and methods. Computing Surveys, 15, 237–269.MathSciNetCrossRefGoogle Scholar
- Anzai, Y., & Simon, H. A. (1979) The theory of learning by doing. Psychological Review, 86,124–140.CrossRefGoogle Scholar
- Berkson, W., & Wettersten, J. (1984). Learning from error: Karl Popper’s psychology of learning. La Salle, IL: Open Court.Google Scholar
- Bloom, B. S. (1984). The 2 sigma problem: The search for methods of group instruction as effective as one-to-one tutoring. Educational Researcher, 13(6), 4–16.Google Scholar
- Brownell, W. A. (1947). An experiment on "borrowing" in third-grade arithmetic. Journal of Educational Research, 41,161–263.Google Scholar
- Brownell, W. A., & Moser, H. E. (1949). Meaningful vs. mechanical learning: A study in Grade III subtraction. Durham, NC: Duke University Press.Google Scholar
- Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press.Google Scholar
- Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. In C. B. Cazden, (Ed.), Review of Research in Education (Vol. 1, pp. 3–56). Washington, D. C: American Educational Research Association.Google Scholar
- Cormier, S., & Hagman, J., (Eds.), (1987). Transfer of learning: Contemporary research and applications. New York, NY: Academic Press.Google Scholar
- Duhem, P. (1991/1914). The aim and structure of physical theory (2nd ed.). Princeton, NJ: Princeton University Press.Google Scholar
- Ebbinghaus, H. (1964/1885). Memory: A contribution to experimental psychology. New York, NY: Dover.Google Scholar
- Evans, J. St. B. T. (1982). The psychology of deductive reasoning. London, UK: Routledge & Kegan Paul.Google Scholar
- Feigenbaum, E. A., & Feldman, J. (1963). Computers and thought. New York, NY: McGraw-Hill.MATHGoogle Scholar
- Festinger, L. (1957). A theory of cognitive dissonance. Standford, CA: Stanford University Press.Google Scholar
- Fikes, R. E., & Nilsson, N. J. (1971). STRIPS: a new approach to the application of theorem proving to problem solving. Artificial Intelligence, 2,189–208.MATHCrossRefGoogle Scholar
- Forgy, C. L. (1982). Rete: A fast algorithm for the many pattern/many object pattern match problem. Artificial Intelligence, 19,17–37.CrossRefGoogle Scholar
- Gardenfors, P. (1988). Knowledge influx: Modeling the dynamics of epistemic states. Cambridge, MA: MIT Press.Google Scholar
- Gelman, R., & Gallistel, C. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.Google Scholar
- Gelman, R., & Meck, E. (1983). Preschoolers’ counting: Principle before skill. Cognition, 13, 343–359.CrossRefGoogle Scholar
- Gelman, R., & Meck, E. (1986). The notion of principle: The case of counting. In J. H. Hiebert, (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 29–57). Hillsdale, NJ: Erlbaum.Google Scholar
- Gelman, R., Meck, E., & Merkin, S. (1986). Young children’s numerical competence. Cognitive Development, 1,1–29.CrossRefGoogle Scholar
- Gensler, W. J. (1987). Impossibilities in chemistry: Their rise, nature, and some great falls. In P. J. Davis and D. Park, (Eds.), No way: The nature of the impossible (pp. 73–89). New York, NY: Freeman.Google Scholar
- Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1–38.CrossRefGoogle Scholar
- Gick, M. L., & Holyoak, K. J. (1987). The cognitive basis of knowledge transfer. In S. M. Cormier & J. D. Hagman, (Eds.), Transfer of learning: Contemporary research and applications (pp. 183–215). San Diego, CA: Academic Press.Google Scholar
- Glaser, R. (1976). Components of a theory of instruction: Toward a science of design. Review of Educational Research, 46, 1–24.Google Scholar
- Glaser, R. (1982). Instructional psychology: Past, present, and future. American Psychologist, 37, 292–305.CrossRefGoogle Scholar
- Hall, R. (1988). Learning by failing to explain: Using partial explanations to learn in incomplete or intractable domains. Machine Learning, 3, 45–77.Google Scholar
- Hayes, J. R., & Simon, H. A. (1977). Psychological differences between problem isomorphs. In J. Castellan, D. B. Psioni, and G. Potts, (Eds.), Cognitive theory (Vol. 2, pp. 21–41). Hillsdale, NJ: Erlbaum.Google Scholar
- Hayes-Roth, F., Klahr, P., & Mostow, D. (1981). Advice taking and knowledge refinement: An iterative view of skill acquisition. In J. Anderson, (Ed.), Cognitive skills and their acquisition (pp. 231–253). Hillsdale, NJ: Erlbaum.Google Scholar
- Hewson, P. W., & Hewson, M. G. A. (1984). The role of conceptual conflict in conceptual change and the design of science instruction. Instructional Science, 13,1–13.CrossRefGoogle Scholar
- Holland, J., Holyoak, K., Nisbett, R., & Thagard, P. (1986). Induction: The processes of inference, learning, and discovery. Cambridge, MA: MIT Press.Google Scholar
- Hull, C. L. (1943). Principles of behavior. New York, NY: Appleton-Century-Crofts.Google Scholar
- Judd, C. H. (1908). The relation of special training and general intelligence. Educational Review, 36,28–42.Google Scholar
- Katona, G. (1940). Organizing and memorizing: Studies in the psychology of learning and teaching. Morningside Heights, NY: Columbia University Press.Google Scholar
- Kieras, D. E., & Bovair, S. (1984). The role of a mental model in learning to operate a device. Cognitive Science, 8, 255–273.CrossRefGoogle Scholar
- Klahr, D., Langley, P., & Neches, R., (Eds.), (1987). Production system models of learning and development. Cambridge, MA: MIT Press.Google Scholar
- Kocabas, S. (1991). Conflict resolution as discovery in particle physics. Machine Learning, 6,277–309Google Scholar
- Kuhn, T. (1970). The structure of scientific revolutions (2nd ed.) Chicago, IL: University of Chicago Press.Google Scholar
- Laird, J. (1986). Universal subgoaling. In J. Laird, P. Rosenbloom, & A. Newell, Universal subgoaling and chunking: The automatic generation and learning of goal hierarchies (pp. 3–131). Boston, MA: Kluwer.Google Scholar
- Lane, N. (1987). Skill acquisition rates and patterns: Issues and training implications. New York, NY: Springer-Verlag.CrossRefGoogle Scholar
- Langley, P. (1985). Learning to search: From weak methods to domainspecific heuristics. Cognitive Science, 9, 217–260.CrossRefGoogle Scholar
- Langley, P. (1987). A general theory of discrimination learning. In Klahr, D., Langley, P., & Neches, R., (Eds.), (1987). Production system models of learning and development (pp. 99–161). Cambridge, MA: MIT Press.Google Scholar
- Leinhardt, G. (1987). Development of an expert explanation: An analysis of a sequence of subtraction lessons. Cognition and Instruction, 4, 225–282.CrossRefGoogle Scholar
- Leinhardt, G., & Ohlsson, S (1990). Tutorials on the structure of tutoring from teachers. Journal of Artificial Intelligence in Education, 2,21–46.CrossRefGoogle Scholar
- Lyons, J. (1988). Origins of language. In A. Fabian, (Ed.), Origins: The Darwin College lectures (pp. 141–166). Cambridge, MA: Cambridge University Press.Google Scholar
- Mazur, J., & Hastie, R. (1978). Learning as accumulation: A reexamination of the learning curve. Psychological Bulletin, 85, 1256–1274.CrossRefGoogle Scholar
- McCrone, J. (1992). The ape that spoke: Language and the evolution of the human mind. New York, NY: Avon Books.Google Scholar
- McDermott, D., & Doyle, J. (1980). Non-monotonic logic I. Artificial Intelligence, 13, 41–72.MathSciNetMATHCrossRefGoogle Scholar
- Minton, S. (1988). Learning search control knowledge: An explanationbased approach. Boston, MA: Kluwer.CrossRefGoogle Scholar
- Moore, J. D., & Ohlsson, S. (1992). Educating migraine patients through on-line generation of medical explanations. Proceedings of the 14h Annual Conference of the Cognitive Science Society. July 29-August 1, Bloomington, Indiana, USA. In press.Google Scholar
- Mostow, D. J. (1983). Machine transformation of advice into a heuristic search procedure. In R. S. Michalski, J. G. Carbonell, & T. M. Mitchell, (Eds.), Machine learning: An artificial intelligence approach (pp. 367–404). Palo Alto, CA: Tioga.Google Scholar
- Mostow, J., & Bhatnager, N. (1987). Failsafe—a floor planner that uses EBG to learn from its failures. In Proceedings of the International Joint Conference on Artificial Intelligence (pp. 249–255), Milan, Italy: UCAI.Google Scholar
- Mostow, J., & Bhatnager, N. (1990). Heuristic detection, explanation, and avoidance of failures as an approach to intractability in explanation-based learning of search control knowledge (Technical Report No. 171). Rutgers, NJ: Rutgers University.Google Scholar
- Murray, F. B., Ames, G. J, & Botvin, G. J. (1977). Acquisition of conservation through cognitive dissonance. Journal of Educational Psychology, 69, 519–527.CrossRefGoogle Scholar
- Newell, A. (1969). Heuristic programming: Ill-structured problems. In J. Aronofsky, (Ed.), Progress in operations research (Vol. III, pp. 360–414). New York, NY: Wiley.Google Scholar
- Newell, A. (1980). Reasoning, problem solving and decision processes: The problem space as a fundamental category. In R. Nickerson, (Ed.), Attention and performance VIII (pp. 693–718). Hillsdale, NJ: Erlbaum.Google Scholar
- Newell, A. (1990). Unified theories of cognition. Cambridge, MA: Havard University Press.Google Scholar
- Newell, A., & Rosenbloom, P. (1981). Mechanisms of skill acquisition and the law of practice. In J. Anderson, (Ed.), Cognitive skills and their acquisition (pp. 1–55). Hillsdale, NJ: Erlbaum.Google Scholar
- Newell, A., & Simon, H. (1972). Human problem solving. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
- Nilsson, N. J. (1980). Principles of artificial intelligence. Palo Alto, CA: Tioga.MATHGoogle Scholar
- Ohlsson, S. (1987a). Transfer of training in procedural learning: A matter of conjectures and refutations? In L. Bolc, (Ed.), Computational models of learning (pp. 55–88). Berlin, West Germany: Springer-Verlag.CrossRefGoogle Scholar
- Ohlsson, S. (1987b). Truth versus appropriateness: Relating declarative to procedural knowledge. In D. Klahr, P. Langley, & R. Neches, (Eds.), Production system models of learning and development (pp. 287–327). Cambridge, MA: MIT Press.Google Scholar
- Ohlsson, S. (1992a). Artificial instruction. A method for relating learning theory to instructional design. In P. Winne & M. Jones, (Eds.), Foundations and frontiers in instructional computing systems. New York, NY: Springer-Verlag. In press.Google Scholar
- Ohlsson, S. (1992b). The impact of cognitive theory on the practice of courseware authoring. In R. Lewis, (Ed.), Authoring environments for computer-based courseware. New York, NY: Springer-Verlag. In press.Google Scholar
- Ohlsson, S. (1992c). The learning curve for writing books: Evidence from Professor Asimov. Psychological Science. In press.Google Scholar
- Ohlsson, S., Ernst, A. M., & Rees, E. (1992). The cognitive complexity of doing and learning arithmetic. Journal of Research in Mathematics Eduation. In press.Google Scholar
- Ohlsson, S., & Rees, E. (1991a). The function of conceptual understanding in the learning of arithmetic procedures. Cognition and Instruction, 8,103–179.CrossRefGoogle Scholar
- Ohlsson, S., & Rees, E. (1991b). Adaptive search through constraint violation. Journal of Experimental and Theoretical Artificial Intelligence, 3, 33–42.CrossRefGoogle Scholar
- Pearl, J. (1984). Heuristics: Intelligent search strategies for computer problem solving. Reading. MA: Addison-Wesley.Google Scholar
- Piaget, J. (1971). Biology and knowledge: An essay on the relation beween organic regulations and cognitive processes. Edingburgh, UK: Edinburgh University Press.Google Scholar
- Piaget, J. (1985). The equilibrium of cognitive structures: The central problem of intellectual development. Chicago, IL: University of Chicago Press.Google Scholar
- Popper, K. (1972/1935). The logic of scientific discovery. London, UK: Hutchinson.Google Scholar
- Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). Accomodation of a scientific conception: Toward a theory of conceptual change. Science Education, 66,211–227.CrossRefGoogle Scholar
- Psotka, J., & Massey, L. D., & Mutter, S. A., (Eds.), (1988). Intelligent tutoring systems: Lessons learned. Hillsdale, NJ: Erlbaum.Google Scholar
- Quine, W. V., & Ullian, J. S. (1978). The web of belief (2nd ed.). New York, NY: Random House.Google Scholar
- Reason, J. (1990). Human error. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
- Reif, F. (1987). Interpretation of scientific or mathematical concepts: Cognitive issues and instructional implications. Cognitive Science, 11, 395–416.CrossRefGoogle Scholar
- Reiser, B. J., Kimberg, D. Y., Lovett, M. C., & Ranney, M. (1991). Knowledge representation and explanation in GIL, an intelligent tutor for programming. In J. H. Larkin & R. W. Chabay, (Eds.), Computer assisted instruction and intelligent tutoring systems: Shared issues and complementary approaches (pp. 111–149). Hillsdale, NJ: Erlbaum.Google Scholar
- Resnick, L. B., & Omanson, S. F. (1987). Learning to understand arithmetic. In R. Glaser, (Ed.), Advances in instructional psychology (Vol 3, pp. 41–95). Hillsdale, NJ: Erlbaum.Google Scholar
- Rose, D., & Langley, P. (1986). Chemical discovery as belief revision. Machine Learning, 1,423–452.Google Scholar
- Rosenbloom, P. (1986). The chunking of goal hierarchies. A model of practice and stimulus-response compatibility. In J. Laird, P. Rosenbloom, & A. Newell, Universal subgoaling and chunking: The automatic generation and learning of goal hierarchies (pp. 135–1282). Boston, MA: Kluwer.Google Scholar
- Rychener, M. D. (1983). The instructable production system: A retrospective analysis. In R. S. Michalski, J. G. Carbonell, & T. M. Mitchell, (Eds.), Machine learning: An artificial intelligence approach (pp. 429–460). Palo Alto, CA: Tioga.Google Scholar
- Schank, R. (1982). Dynamic memory: A theory of reminding and learning in computers and people. Cambridge, MA: Cambridge University Press.Google Scholar
- Schank, R. (1986). Explanation patterns: Understanding mechanically and creatively. Hillsdale, NJ: Erlbaum.Google Scholar
- Singely, M., & Anderson, J. (1989). The transfer of cognitive skill. Cambridge, MA: Harvard University Press.Google Scholar
- Sleeman, D., & Brown, J. S., (Eds.), (1982). Intelligent tutoring systems. New York, NY: Academic Press.Google Scholar
- Smith, E. E., & Goodman, L. (1984). Understanding written instructions: The role of an explanatory schema. Cognition and Instruction, 1, 359–396.CrossRefGoogle Scholar
- Solomons, T. (1988). Organic chemistry (4th ed.). New York, NY: Wiley.Google Scholar
- Sorum, C. H., & Boikess, R. S. (1981). How to solve general chemistry problems. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
- VanLehn, K. (1982). Bugs are not enough: Empirical students of bugs, impasses and repairs in procedural skills. Journal of Mathematical Behavior, 3, 3–71.Google Scholar
- VanLehn, K. (1988). Toward a theory of impasse-driven learning. In H. Mandl & A. Lesgold, (Eds.), Learning issues for intelligent tutoring systems (pp. 19–41). New York, NY: Springer Verlag.CrossRefGoogle Scholar
- VanLehn, K. (1990). Mind bugs: The origins of procedural misconceptions. Cambridge, MA: MIT Press.Google Scholar
- Winograd, T. (1975). Frame representations and the declarative/procedural controversy. In D. Bobrow and A. Collins, (Eds.), Representation and understanding: Studies in cognitive science (pp. 185–210). New York, NY: Academic Press.Google Scholar