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Modeling Individualization in a Bayesian Networks Implementation of Knowledge Tracing

  • Zachary A. Pardos
  • Neil T. Heffernan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6075)

Abstract

The field of intelligent tutoring systems has been using the well known knowledge tracing model, popularized by Corbett and Anderson (1995), to track student knowledge for over a decade. Surprisingly, models currently in use do not allow for individual learning rates nor individualized estimates of student initial knowledge. Corbett and Anderson, in their original articles, were interested in trying to add individualization to their model which they accomplished but with mixed results. Since their original work, the field has not made significant progress towards individualization of knowledge tracing models in fitting data. In this work, we introduce an elegant way of formulating the individualization problem entirely within a Bayesian networks framework that fits individualized as well as skill specific parameters simultaneously, in a single step. With this new individualization technique we are able to show a reliable improvement in prediction of real world data by individualizing the initial knowledge parameter. We explore three difference strategies for setting the initial individualized knowledge parameters and report that the best strategy is one in which information from multiple skills is used to inform each student’s prior. Using this strategy we achieved lower prediction error in 33 of the 42 problem sets evaluated. The implication of this work is the ability to enhance existing intelligent tutoring systems to more accurately estimate when a student has reached mastery of a skill. Adaptation of instruction based on individualized knowledge and learning speed is discussed as well as open research questions facing those that wish to exploit student and skill information in their user models.

Keywords

Knowledge Tracing Individualization Bayesian Networks Data Mining Prediction Intelligent Tutoring Systems 

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References

  1. 1.
    Atkinson, R.C., Paulson, J.A.: An approach to the psychology of instruction. Psychological Bulletin 78, 49–61 (1972)CrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    Corbett, A., Bhatnagar, A.: Student Modeling in the ACT Programming Tutor: Adjusting a Procedural Learning Model with Declarative Knowledge. In: Jameson, A., Paris, C., Tasso, C. (eds.) Proceedings of the 6th International Conference on User Modeling, pp. 243–254 (1997)Google Scholar
  4. 4.
    Baker, R.S.J.d., Corbett, A.T., Aleven, V.: More accurate student modeling through contextual estimation of slip and guess probabilities in bayesian knowledge tracing. In: Woolf, B.P., Aïmeur, E., Nkambou, R., Lajoie, S. (eds.) ITS 2008. LNCS, vol. 5091, pp. 406–415. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Beck, J.E., Chang, K.M.: Identifiability: A Fundamental Problem of Student Modeling. In: Conati, C., McCoy, K., Paliouras, G. (eds.) UM 2007. LNCS (LNAI), vol. 4511, pp. 137–146. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Reye, J.: Student modelling based on belief networks. International Journal of Artificial Intelligence in Education 14, 63–96 (2004)Google Scholar
  7. 7.
    Chang, K.M., Beck, J.E., Mostow, J., Corbett, A.: A Bayes Net Toolkit for Student Modeling in Intelligent Tutoring Systems. In: Ikeda, M., Ashley, K.D., Chan, T.-W. (eds.) ITS 2006. LNCS, vol. 4053, pp. 104–113. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Ritter, S., Harris, T., Nixon, T., Dickison, D., Murray, C., Towle, B.: Reducing the knowledge tracing space. In: Proceedings of the 2nd International Conference on Educational Data Mining, Cordoba, Spain, pp. 151–160 (2009)Google Scholar
  9. 9.
    Draney, K.L., Pirolli, P., Wilson, M.: A measurement model for a complex cognitive skill. In: Nichols, P.D., Chipman, S.F., Brennan, R.L. (eds.) Cognitively diagnostic assessment, pp. 103–125. Erlbaum, Hillsdale (1995)Google Scholar
  10. 10.
    Pavlik, P.I., Cen, H., Koedinger, K.R.: Performance Factors Analysis - A New Alternative to Knowledge Tracing. In: Proceedings of the 14th International Conference on Artificial Intelligence in Education, Brighton, UK, pp. 531–538 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Zachary A. Pardos
    • 1
  • Neil T. Heffernan
    • 1
  1. 1.Worcester Polytechnic InstituteDepartment of Computer Science 

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