Advertisement

A Teaching Model Exploiting Cognitive Conflict Driven by a Bayesian Network

  • K. Stacey
  • E. Sonenberg
  • A. Nicholson
  • T. Boneh
  • V. Steinle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2702)

Abstract

This paper describes the design and construction of a teaching model in an adaptive tutoring system designed to supplement normal instruction and aimed at changing students’ conceptions of decimal numbers. The teaching model exploits cognitive conflict, incorporating a model of student misconceptions and task performance, represented by a Bayesian network. Preliminary evaluation of the implemented system shows that the misconception diagnosis and performance prediction performed by the BN reasoning engine supports the item sequencing and help presentation strategies required for teaching based on cognitive conflict. Field trials indicate the system provokes good long term learning in students who would otherwise be likely to retain misconceptions.

Keywords

Computer Game Bayesian Network Item Type Teaching Model Cognitive Conflict 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bell, A.: Principles for the design of teaching. Educational Studies in Mathematics 24 (1993) 5–34CrossRefGoogle Scholar
  2. 2.
    Light, P., Glachan, M.: Facilitation of individual problem solving through peer interaction. Educational Psychology 5 (1985) 217–225CrossRefGoogle Scholar
  3. 3.
    Swan, M.: Teaching Decimal Place Value: A Comparative Study of ‘Conflict’ and ‘Positive Only’ Approaches. Shell Centre for Mathematical Ed., Nott. Univ. (1983)Google Scholar
  4. 4.
    Klawe, M.: When does the use of computer games and other interactive multimedia software help students learn mathematics? In: NCTM Standards 2000 Technology Conference. (1998)Google Scholar
  5. 5.
    Conati, C., Gertner, A., VanLehn, K., Druzdzel, M.: On-line student modeling for coached problem solving using Bayesian Networks. In: UM97 — Proc. of the 6th Int. Conf. on User Modeling. (1997) 231–242Google Scholar
  6. 6.
    Conati, C., Gertner, A., VanLehn, K.: Using Bayesian Networks to manage uncertainty in student modeling. User Modeling and User-Adapted Interaction 12 (2002) 371–417zbMATHCrossRefGoogle Scholar
  7. 7.
    Mayo, M., Mitrovic, A.: Optimising ITS behaviour with Bayesian networks and decision theory. Int. Journal of AI in Education 12 (2001) 124–153Google Scholar
  8. 8.
    VanLehn, V., Niu, Z.: Bayesian student modelling, user interfaces and feedback: a sensitivity analysis. Int. Journal of AI in Education 12 (2001) 154–184Google Scholar
  9. 9.
    Horvitz, E., Breese, J., Heckerman, D., Hovel, D., Rommelse, K.: The Lumiere project: Bayesian user modeling for inferring the goals and needs of software users. In: Proc. of the 14th Conf. on Uncertainty in AI. (1998) 256–265Google Scholar
  10. 10.
    Sleeman, D.: Mis-generalisation: an explanation of observed mal-rules. In: Proc. of the 6th Annual Conf. of the Cognitive Science Society. (1984) 51–56Google Scholar
  11. 11.
    Stacey, K., Steinle, V.: A longitudinal study of childen’s thinking about decimals: a preliminary analysis. In Zaslavsky, O., ed.: Proc. of the 23rd Conf. of the Int. Group for the Psych. of Math. Education. Volume 4., Haifa, PME (1999) 233–241Google Scholar
  12. 12.
    Resnick, L.B., Nesher, P., Leonard, F., Magone, M., Omanson, S., Peled, I.: Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education 20 (1989) 8–27CrossRefGoogle Scholar
  13. 13.
    Sackur-Grisvard, C., Leonard, F.: Intermediate cognitive organization in the process of learning a mathematical concept: The order of positive decimal numbers. Cognition and Instruction 2 (1985) 157–174CrossRefGoogle Scholar
  14. 14.
    Stacey, K., Steinle, V.: Refining the classification of students’ interpretations of decimal notation. Hiroshima Journal of Mathematics Education 6 (1998) 49–69Google Scholar
  15. 15.
    Brown, J., van Lehn, K.: Repair theory: A generative theory of bugs in procedural skills. Cognitive Science 4 (1980) 379–426CrossRefGoogle Scholar
  16. 16.
    Boneh, T., Nicholson, A., Sonenberg, L., Stacey, K., Steinle, V.: Decsys: An intelligent tutoring system for decimal numeration. Technical Report 134, School of CSSE, Monash University, Australia (2003)Google Scholar
  17. 17.
    Steinle, V., Stacey, K.: The incidence of misconceptions of decimal notation amongst students in grades 5 to 10. In Kanes, C., Goos, M., Warren, E., eds.: Teaching Mathematics in New Times, MERGA 21. MERGA (1998) 548–555Google Scholar
  18. 18.
    Nicholson, A., Boneh, T., Wilkin, T., Stacey, K., L. Sonenberg, Steinle, V.: A case study in knowledge discovery and elicitation in an intelligent tutoring application. In: Proc. of the 17th Conf. on Uncertainty in AI, Seattle (2001) 386–394Google Scholar
  19. 19.
    McIntosh, J., Stacey, K., Tromp, C., Lightfoot, D.: Designing constructivist computer games for teaching about decimal numbers. In Bana, J., Chapman, A., eds.: Mathematics Education Beyond 2000. Proc. of the 23rd Annual Conf. of the Mathematics Education Research Group of Australasia, Freemantle (2000) 409–416Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • K. Stacey
    • 1
  • E. Sonenberg
    • 1
  • A. Nicholson
    • 1
  • T. Boneh
    • 1
  • V. Steinle
    • 1
  1. 1.The University of MelbourneParkvilleAustralia

Personalised recommendations