Approximate Modelling of the Multi-dimensional Learner

  • Rafael Morales
  • Nicolas van Labeke
  • Paul Brna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4053)


This paper describes the design of the learner modelling component of the LeActiveMath system, which was conceived to integrate modelling of learners’ competencies in a subject domain, motivational and affective dispositions and meta-cognition. This goal has been achieved by organising learner models as stacks, with the subject domain as ground layer and competency, motivation, affect and meta-cognition as upper layers. A concept map per layer defines each layer’s elements and internal structure, and beliefs are associated to the applications of elements in upper-layers to elements in lower-layers. Beliefs are represented using belief functions and organised in a network constructed as the composition of all layers’ concept maps, which is used for propagation of evidence.


Mass Function Belief Function Subject Domain Competency Level Mathematical Competency 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Advanced Distributed Learning: Sharable Content Object Reference Model Version 1.2: The SCORM Overview (2001)Google Scholar
  2. 2.
    LeActiveMath Consortium: Language-enhanced, user adaptive, interactive elearning for mathematics (2004),
  3. 3.
    National Information Standards Organization: Understanding Metadata (2004)Google Scholar
  4. 4.
    Institute of Electrical and Electronics Engineers: IEEE 1484.12.1 Draft Standard for Learning Object Metadata (2002)Google Scholar
  5. 5.
    Organisation for Economic Co-Operation and Development: The PISA 2003 Assessment Framework (2003)Google Scholar
  6. 6.
    Self, J.A.: Dormorbile: A vehicle for metacognition. AAI/AI-ED Technical Report 98, Computing Department, Lancaster University, Lancaster, UK (1994)Google Scholar
  7. 7.
    Zapata-Rivera, J.-D., Greer, J.E.: Inspecting and Visualizing Distributed Bayesian Student Models. In: Gauthier, G., VanLehn, K., Frasson, C. (eds.) ITS 2000. LNCS, vol. 1839, pp. 544–553. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66(2), 191–234 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)zbMATHGoogle Scholar
  10. 10.
    Sentz, K., Ferson, S.: Combination of evidence in dempster-shafer theory. Sandia Report SAND2002-0835, Sandia National Laboratories (2002)Google Scholar
  11. 11.
    Shenoy, P.P., Shafer, G.: Axioms for probability in belief-function propagation. In: Shachter, R.D., Levitt, T.S., Kanal, L.N., Lemmer, J.F. (eds.) Proceedings of the Fourth Anual Conference on Uncertainty in Artificial Intelligence, pp. 169–198. North-Holland, Amsterdam (1990)Google Scholar
  12. 12.
    Conati, C., Gertner, A., VanLehn, K.: Using bayesian networks to manage uncertainty in student modeling. User Modeling and User-Adapted Interaction 12(4), 371–417 (2002)zbMATHCrossRefGoogle Scholar
  13. 13.
    Bunt, A., Conati, C.: Probabilistic student modelling to improve exploratory behaviour. User Modeling and User-Adapted Interaction 13(3), 269–309 (2003)CrossRefGoogle Scholar
  14. 14.
    Jameson, A.: Numerical uncertainty management in user and student modeling: An overview of systems and issues. User Modeling and User-Adapted Interaction 5(3–4), 193–251 (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rafael Morales
    • 1
  • Nicolas van Labeke
    • 1
  • Paul Brna
    • 1
  1. 1.The SCRE CentreUniversity of GlasgowGlasgowUnited Kingdom

Personalised recommendations