User Modeling and User-Adapted Interaction

, Volume 4, Issue 4, pp 253–278 | Cite as

Knowledge tracing: Modeling the acquisition of procedural knowledge

  • Albert T. Corbett
  • John R. Anderson
Article

Abstract

This paper describes an effort to model students' changing knowledge state during skill acquisition. Students in this research are learning to write short programs with the ACT Programming Tutor (APT). APT is constructed around a production rule cognitive model of programming knowledge, called theideal student model. This model allows the tutor to solve exercises along with the student and provide assistance as necessary. As the student works, the tutor also maintains an estimate of the probability that the student has learned each of the rules in the ideal model, in a process calledknowledge tracing. The tutor presents an individualized sequence of exercises to the student based on these probability estimates until the student has ‘mastered’ each rule. The programming tutor, cognitive model and learning and performance assumptions are described. A series of studies is reviewed that examine the empirical validity of knowledge tracing and has led to modifications in the process. Currently the model is quite successful in predicting test performance. Further modifications in the modeling process are discussed that may improve performance levels.

Key words

Student modeling learning empirical validity procedural knowledge intelligent tutoring systems mastery learning individual differences 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andersen, J. R.: 1993,Rules of the mind. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  2. Anderson, J. R., C. F. Boyle, A. T. Corbett, and M. W. Lewis: 1990, Cognitive modeling and intelligent tutoring.Artificial Intelligence,42, 7–49.Google Scholar
  3. Anderson, J. R., F. G. Conrad, and A. T. Corbett: 1989, Skill acquisition and the LISP Tutor.Cognitive Science,13, 467–505.Google Scholar
  4. Anderson, J. R., F. G. Conrad, A. T. Corbett, J. M. Fincham, D. Hoffman, and Q. Wu: 1993, Computer programming and transfer. In J. Anderson (ed).Rules of the mind. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  5. Anderson, J. R., A. T. Corbett, J. M. Fincham, D. Hoffman, and R. Pelletier: 1992, General principles for an intelligent tutoring architecture. In J. Regian & V. Shute (eds.)Cognitive approaches to automated instruction. Hillsdale, NJ: Erlbaum.Google Scholar
  6. Anderson, J. R., A. T. Corbett, K. R. Koedinger, and R. Pelletier: in press, Cognitive tutors: Lessons learned.Journal of the Learning Sciences.Google Scholar
  7. Anderson, J. R. and B. J. Reiser: 1985, The Lisp Tutor.Byte,10, (4), 159–175.Google Scholar
  8. Atkinson, R.C.: 1972, Optimizing the learning of a second-language vocabulary.Journal of Experimental Psychology,96, 124–129.Google Scholar
  9. Atkinson, R. C. and J. A. Paulson: 1972, An approach to the psychology of instruction.Psychological Bulletin,78, 49–61.Google Scholar
  10. Block, J. H. and R. B. Burns: 1976, Mastery learning. In L. S. Shulman (ed.)Review of research in education, Volume 4. Itasca, IL: F. E. Peacock (AERA).Google Scholar
  11. Bloom, B. S.: 1968, Learning for mastery. InEvaluation Comment, 1. Los Angeles: UCLA Center for the Study of Evaluation of Instructional Programs.Google Scholar
  12. Carroll, J. B.: 1963, A model of school learning.Teachers College Record,64, 723–733.Google Scholar
  13. Corbett, A. T. and J. R. Anderson: 1993, Student modeling in an intelligent programming tutor. In E. Lemut, B. du Boulay & G. Dettori (eds.)Cognitive models and intelligent environments for learning programming. New York: Springer-Verlag.Google Scholar
  14. Corbett, A. T., J. R. Anderson, V. H. Carver, and S. A. Brancolini: 1994, Individual differences and predictive validity in student modeling. In A. Ram & K. Eiselt (eds.)The Proceedings of the Sixteenth Annual Conference of the Cognitive Science Society. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  15. Corbett, A.T., J. R. Anderson and A. T. O'Brien: in press, Student modeling in the ACT Programming Tutor. In P. Nichols, S. Chipman and B. Brennan (eds.)Cognitively Diagnostic Assessment. Hillsdale, NJ: Erlbaum.Google Scholar
  16. Duncan, D., P. Brna, and L. Morss: 1994, A Bayesian approach to diagnosing problems with prolog control flow. In B. Goodman, A. Kobsa & D. Litman (eds.)User Modeling: Proceedings of the Fourth International Conference. Bedford, MA: The MITRE Corporation.Google Scholar
  17. Goldstein, I. P.: 1982, The genetic graph: A representation for the evolution of procedural knowledge. In D. Sleeman and J.S. Brown (eds.)Intelligent tutoring systems. New York: Academic.Google Scholar
  18. Guskey, T. R. and T. D. Pigott: 1988, Research on group-based mastery learning programs: A meta-analysis.Journal of Educational Research,81, 197–216.Google Scholar
  19. Hyman, J. S. and A. Cohen: 1970, Learning for mastery: Ten conclusions after 15 years and 3,000 schools.Educational Leadership,37, 104–109.Google Scholar
  20. Keller, F. S.: 1968, “Good-bye teacher....”Journal of Applied Behavioral Analysis,1, 79–89.Google Scholar
  21. Kessler, K.: 1988,Transfer of programming skills in novice LISP learners. Unpublished doctoral dissertation, Carnegie Mellon University, Pittsburgh, PA.Google Scholar
  22. Kieras, D. E. and S. Bovair: 1986, The acquisition of procedures from text: A production system analysis of transfer of training.Journal of Memory and Language,25, 507–524.Google Scholar
  23. Kulik, C. C., J. A. Kulik, and R. L. Bangert-Drowns: 1990, Effectiveness of mastery learning programs: A meta-analysis.Review of Educational Research,60, 265–299.Google Scholar
  24. Kulik, J. A., C. C. Kulik, and P.A. Cohen: 1979, A meta-analysis of outcomes studies of Keller's Personalized System of Instruction.American Psychologist,34, 307–318.Google Scholar
  25. McKendree, J. E. and J. R. Anderson: 1987, Effect of practice on knowledge and use of basic Lisp. In J.M. Carroll, (ed.)Interfacing thought. Cambridge, MA: MIT Press.Google Scholar
  26. Newell, A.: 1990,Unified theories of cognition. Cambridge, MA: Harvard University Press.Google Scholar
  27. Pennington, N. and R. Nicolich: 1991, Transfer of training between programming subtasks: Is knowledge really use specific? In J. Koenemann-Belliveau, T. Moher & S. Robertson (eds.)Empirical studies of programmers: Fourth workshop. Norwood, NJ: Ablex.Google Scholar
  28. Reed, S. K., A. Dempster, and M. Ettinger:1985, Usefulness of analogous solutions for solving algebra word problems.Journal of Experimental Psychology: Learning, Memory and Cognition,11, 106–125.Google Scholar
  29. Resnick, L. B.: 1977, Assuming that everyone can learn everything, will some learn less?School Review,85, 445–452.Google Scholar
  30. Resnick, L. B. and D. P. Resnick: 1992, Assessing the thinking curriculum: New tools for educational reform. In B. Gifford & M. O'Connor (eds.)Changing assessments: Alternative views of aptitude, achievement and instruction. Boston: Kluwer.Google Scholar
  31. Self, J. A.: 1988, Bypassing the intractable problem of student modeling. In C. Frasson (ed).Intelligent Tutoring Systems: The proceedings of the of ITS-88. Montreal: The University of Montreal.Google Scholar
  32. Shepard, L. A.: 1991, Psychometrician's beliefs about learning.Educational Researcher,20, 2–16.Google Scholar
  33. Singley, M. K.: 1986,Developing models of skill acquisition in the context of intelligent tutoring systems. Unpublished doctoral dissertation, Carnegie Mellon University, Pittsburgh, PA.Google Scholar
  34. Singley, M. K. and J. R. Anderson: 1989,The transfer of cognitive skill. Cambridge, MA: Harvard University Press.Google Scholar
  35. Slavin, R. E.: 1987, Mastery learning reconsidered.Review of educational research,57, 175–213.Google Scholar
  36. VanLehn, K.: 1990,Mind bugs: The origins of procedural misconceptions. Cambridge, MA: The MIT Press.Google Scholar
  37. Wenger, R. H.: 1987, Cognitive science and algebra learning. In A. Schoenfeld (ed.)Cognitive science and mathematics education. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Albert T. Corbett
    • 1
  • John R. Anderson
    • 2
  1. 1.Human Computer Interaction Institute, School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA
  2. 2.Psychology and Computer Science DepartmentsCarnegie Mellon UniversityPittsburghUSA

Personalised recommendations