A Contingency Analysis of LeActiveMath’s Learner Model

  • Rafael Morales
  • Nicolas Van Labeke
  • Paul Brna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4293)


We analyse how a learner modelling engine that uses belief functions for evidence and belief representation, called xLM, reacts to different input information about the learner in terms of changes in the state of its beliefs and the decisions that it derives from them. The paper covers xLM induction of evidence with different strengths from the qualitative and quantitative properties of the input, the amount of indirect evidence derived from direct evidence, and differences in beliefs and decisions that result from interpreting different sequences of events simulating learners evolving in different directions. The results here presented substantiate our vision of xLM is a proof of existence for a generic and potentially comprehensive learner modelling subsystem that explicitly represents uncertainty, conflict and ignorance in beliefs. These are key properties of learner modelling engines in the bizarre world of open Web-based learning environments that rely on the content+metadata paradigm.


Mass Distribution Belief Function Intelligent Tutor System Competency Level Mathematical Competency 


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  1. 1.
    Self, J.A.: Bypassing the intractable problem of student modelling. In: Proceedings of ITS 1988, Montréal, Canada, pp. 18–24 (1988)Google Scholar
  2. 2.
    Lee, M.H.: On models, modelling and the distinctive nature of model-based reasoning. AI Communications 12, 127–137 (1999)MathSciNetGoogle Scholar
  3. 3.
    Koedinger, K.R., Anderson, J.R.: Intelligent tutoring goes to school in the big city. International Journal of Artificial Intelligence in Education 8, 30–43 (1997)Google Scholar
  4. 4.
    Conati, C.: Toward comprehensive student models: Modeling meta-cognitive skills and affective states in ITS. In: Lester, J.C., Vicari, R.M., Paraguaçu, F. (eds.) ITS 2004. LNCS, vol. 3220, p. 902. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Burton, R.B.: Diagonising bugs in a simple procedural skill, ch. 8. In: [13], pp. 157–183Google Scholar
  6. 6.
    Corbett, A.T., Anderson, J.R.: Knowledge tracing: Modeling the acquisition of procedural knowledge. User Modeling and User-Adapted Interaction 4, 253–278 (1995)CrossRefGoogle Scholar
  7. 7.
    LeActiveMath Consortium: Language-enhanced, user adaptive, interactive elearning for mathematics (2004)Google Scholar
  8. 8.
    Organisation for Economic Co-Operation and Development: The PISA 2003 Assessment Framework (2003)Google Scholar
  9. 9.
    Burton, R.B., Brown, J.S.: An investigation of computer coaching for informal learning activities, ch. 4. In: [13], pp. 79–98Google Scholar
  10. 10.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)MATHGoogle Scholar
  11. 11.
    Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66, 191–234 (1994)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Morales, R., van Labeke, N., Brna, P.: Approximate modelling of the multi-dimensional learner. In: Ikeda, M., Ashley, K.D., Chan, T.-W. (eds.) ITS 2006. LNCS, vol. 4053, pp. 555–564. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Sleeman, D.H., Brown, J.S. (eds.): Intelligent Tutoring Systems. Academic Press, New York (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rafael Morales
    • 1
  • Nicolas Van Labeke
    • 2
  • Paul Brna
    • 2
  1. 1.Sistema de Universidad VirtualUniversidad de GuadalajaraGuadalajara, JaliscoMexico
  2. 2.The SCRE CentreUniversity of GlasgowGlasgowUnited Kingdom

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