Psychonomic Bulletin & Review

, Volume 14, Issue 2, pp 249–255 | Cite as

Cognitive Tutor: Applied research in mathematics education

  • Steven Ritter
  • John R. Anderson
  • Kenneth R. Koedinger
  • Albert Corbett
Applying cognitive psychology to education

Abstract

For 25 years, we have been working to build cognitive models of mathematics, which have become a basis for middle- and high-school curricula. We discuss the theoretical background of this approach and evidence that the resulting curricula are more effective than other approaches to instruction. We also discuss how embedding a well specified theory in our instructional software allows us to dynamically evaluate the effectiveness of our instruction at a more detailed level than was previously possible. The current widespread use of the software is allowing us to test hypotheses across large numbers of students. We believe that this will lead to new approaches both to understanding mathematical cognition and to improving instruction.

References

  1. Aleven, V. A. W. M. M., &Koedinger, K. R. (2002). An effective metacognitive strategy: Learning by doing and explaining with a computer-based Cognitive Tutor.Cognitive Science,26, 147–179.CrossRefGoogle Scholar
  2. Anderson, J. R. (1983).The architecture of cognition. Cambridge, MA: Harvard University Press.Google Scholar
  3. Anderson, J. R. (1990).The adaptive character of thought. Hillsdale, NJ: Erlbaum.Google Scholar
  4. Anderson, J. R. (1993).Rules of the mind. Hillsdale, NJ: Erlbaum.Google Scholar
  5. Anderson, J. R. (2002). Spanning seven orders of magnitude: A challenge for cognitive modeling.Cognitive Science,26, 85–112.CrossRefGoogle Scholar
  6. Anderson, J. R., Bothell, D., Byrne, M. D., Douglass, S., Lebière, C., &Qin, Y. (2004). An integrated theory of the mind.Psychological Review, 111, 1036–1060.CrossRefPubMedGoogle Scholar
  7. 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
  8. Anderson, J. R., Boyle, C. F., Farrell, R., &Reiser, B. J. (1987). Cognitive principles in the design of computer tutors. In P. Morris (Ed.),Modelling cognition (pp. 93–133). Chichester, U.K.: Wiley.Google Scholar
  9. Anderson, J. R., Conrad, F. G., &Corbett, A. T. (1989). Skill acquisition and the LISP tutor.Cognitive Science,13, 467–505.CrossRefGoogle Scholar
  10. Anderson, J. R., Corbett, A. T., Koedinger, K. R., &Pelletier, R. (1995). Cognitive tutors: Lessons learned.Journal of the Learning Sciences,4, 167–207.CrossRefGoogle Scholar
  11. Anderson, J. R., &Lebière, C. (1998).The atomic components of thought. Mahwah, NJ: Erlbaum.Google Scholar
  12. Cen, H., Koedinger, K. R., &Junker, B. (2005). Learning Factors Analysis: A general method for cognitive model evaluation and improvement. In M. Ikeda, K. Ashley, & T. Chan (Eds.),Intelligent Tutoring Systems 8th International Conference (pp. 164–175). Berlin: Springer.Google Scholar
  13. Corbett, A. T., &Anderson, J. R. (1995a). Knowledge decomposition and subgoal reification in the ACT programming tutor. In J. Greer (Ed.),Artificial intelligence and education, 1995: The proceedings of AI-ED 95 (pp. 469–476). Charlottesville, VA: AACE Press.Google Scholar
  14. Corbett, A. T., &Anderson, J. R. (1995b). Knowledge tracing: Modeling the acquisition of procedural knowledge.User Modeling & User-Adapted Interaction,4, 253–278.CrossRefGoogle Scholar
  15. Corbett, A. T., Koedinger, K. R., &Anderson, J. R. (1997). Intelligent tutoring systems. In M. G. Helander, T. K. Landauer, & P. Prabhu (Eds.),Handbook of human-computer interaction (2nd ed., pp. 849–874). Amsterdam: Elsevier.CrossRefGoogle Scholar
  16. Corbett, A. [T.], McLaughlin, M., Scarpinatto, K. C., &Hadley, W. H. (2000). Analyzing and generating mathematical models: An Algebra II cognitive tutor design study. In G. Gauthier, C. Frasson, & K. van Lehn (Eds.),Intelligent Tutoring Systems: Fifth international conference (pp. 314–323). Berlin: Springer.Google Scholar
  17. Corbett, A. T., Trask, H. J., Scarpinatto, K. C., &Hadley, W. S. (1998). A formative evaluation of the PACT Algebra II Tutor: Support for simple hierarchical reasoning. In B. P. Goettl, H. Halff, C. Redfield, & V. Shute (Eds.),Intelligent Tutoring Systems: Fourth International Conference, ITS ’98 (pp. 374–383). New York: Springer.Google Scholar
  18. Gluck, K. A. (1999). Eye movements and algebra tutoring.Dissertation Abstracts International,61, 1664B.Google Scholar
  19. Junker, B. W., Koedinger, K. R., & Trottini, M. (2000, July).Finding improvements in student models for intelligent tutoring systems via variable selection for a linear logistic test model. Paper presented at the 65th Annual Meeting of the Psychometric Society, Vancouver.Google Scholar
  20. Koedinger, K. R., &Anderson, J. R. (1990). Abstract planning and perceptual chunks: Elements of expertise in geometry.Cognitive Science,14, 511–550.CrossRefGoogle Scholar
  21. Koedinger, K. R., &Anderson, J. R. (1993). Effective use of intelligent software in high school math classrooms. InProceedings of the Sixth World Conference on Artificial Intelligence in Education (pp. 241–248). Charlottesville, VA: Association for the Advancement of Computing in Education.Google Scholar
  22. Koedinger, K. R., &Anderson, J. R. (1998). Illustrating principled design: The early evolution of a cognitive tutor for algebra symbolization.Interactive Learning Environments,5, 161–180.CrossRefGoogle Scholar
  23. Koedinger, K. R., Anderson, J. R., Hadley, W. H., &Mark, M. (1997). Intelligent tutoring goes to school in the big city.International Journal of Artificial Intelligence in Education,8, 30–43.Google Scholar
  24. Koedinger, K. R., Corbett, A. T., Ritter, S., & Shapiro, L. J. (2000).Carnegie Learning’s Cognitive Tutor: Summary research results. Pittsburgh: Carnegie Learning. Available at www.carnegielearning .com/web_docs/CMU_research_results.pdf.Koedinger, K. R., & Nathan, M. J. (2004). The real story behind story problems: Effects of representations on quantitative reasoning.Journal of the Learning Sciences,13, 129-164.Lebière, C. (1999). The dynamics of cognition: An ACT-R model of cognitive arithmetic.Kognitionswissenschaft,8, 5-19.Google Scholar
  25. Mark, M. A., & Koedinger, K. R. (1999). Strategic support of algebraic expression writing. InProceedings of the Seventh International Conference on User Modeling (pp. 149-158). Available at www.cs.usask.ca/UM99/Proc/mark.pdf.Google Scholar
  26. Morgan, P., &Ritter, S. (2002).An experimental study of the effects of Cognitive Tutor Algebra I on student knowledge and attitude. Pittsburgh: Carnegie Learning. Available at www.carnegielearning.com/web_docs/morgan_ritter_2002.pdf.Google Scholar
  27. Nathan, M. J., &Koedinger, K. R. (2000a). An investigation of teachers’ beliefs of students’ algebra development.Cognition & Instruction,18, 209–237.CrossRefGoogle Scholar
  28. Nathan, M. J., &Koedinger, K. R. (2000b). Teachers’ and researchers’ beliefs about the development of algebraic reasoning.Journal for Research in Mathematics Education,31, 168–190.CrossRefGoogle Scholar
  29. National Research Council (2003).Strategic education research partnership (M. S. Donovan, A. K. Wigdor, & C. E. Snow, Eds.). Washington, DC: National Academies Press.Google Scholar
  30. Newell, A. (1973). You can’t play 20 questions with nature and win: Projective comments on the papers of this symposium. In W. G. Chase (Ed.),Visual information processing (pp. 283–310). New York: Academic Press.Google Scholar
  31. Newell, A. (1990).Unified theories of cognition. Cambridge, MA: Harvard University Press.Google Scholar
  32. Ritter, S., &Anderson, J. R. (1995). Calculation and strategy in the equation solving tutor. In J. D. Moore & J. F. Lehman (Eds.),Proceedings of the 17th Annual Conference of the Cognitive Science Society (pp. 413–418). Hillsdale, NJ: Erlbaum.Google Scholar
  33. Rittle-Johnson, B., &Koedinger, K. R. (2002). Comparing instructional strategies for integrating conceptual and procedural knowledge. In D. S. Mewborn, P. Sztajin, D. Y. White, H. G. Wiegel, R. L. Bryant, & K. Nooney (Eds.),Proceedings of the 24th Annual Meeting of the North American Chapters of the International Group for the Psychology of Mathematics Education (pp. 969–978). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.Google Scholar
  34. Rittle-Johnson, B., &Koedinger, K. R. (2005). Designing better learning environments: Knowledge scaffolding supports mathematical problem solving.Cognition & Instruction,23, 313–349.CrossRefGoogle Scholar
  35. Rittle-Johnson, B., &Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. In C. Donlan (Ed.),The development of mathematical skills: Studies in developmental psychology (pp. 75–110). Hove, U.K.: Psychology Press.Google Scholar
  36. Rittle-Johnson, B., Siegler, R. S., &Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process.Journal of Educational Psychology,93, 346–362.CrossRefGoogle Scholar
  37. Sarkis, H. (2004).Cognitive Tutor Algebra 1 program evaluation: Miami-Dade County public schools. Lighthouse Point, FL: The Reliability Group. Available at www.carnegielearning.com/web_docs/sarkis_2004.pdf.Google Scholar
  38. Siegler, R. S., &Crowley, K. (1991). The microgenetic method: A direct means for studying cognitive development.American Psychologist,46, 606–620.CrossRefPubMedGoogle Scholar
  39. Siegler, R. S., &Shipley, C. (1995). Variation, selection, and cognitive change. In T. J. Simon & G. S. Halford (Eds.),Developing cognitive competence: New approaches to process modeling (pp. 31–76). Hillsdale, NJ: Erlbaum.Google Scholar

Copyright information

© Psychonomic Society, Inc. 2007

Authors and Affiliations

  • Steven Ritter
    • 1
  • John R. Anderson
    • 2
  • Kenneth R. Koedinger
    • 2
  • Albert Corbett
    • 2
  1. 1.Carnegie LearningPittsburgh
  2. 2.Carnegie Mello UniversityPittsburgh

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