A Practical Approach to Bayesian Student Modeling

Abstract

Bayesian modeling techniques provide a rigorous formal approach to student modeling in contrast to earlier ad hoc or certainty-factor based approaches. Unfortunately, the application of Bayesian modeling techniques is limited due to computational complexity, conditional independence requirements of the model, and difficulties with knowledge acquisition. The approach presented here infers a student model from performance data using a Bayesian belief network. The belief network models the relationship between knowledge and performance for either test items or task actions. The measure of how well a student knows a skill is represented as a probability distribution over skill levels. Questions or expected actions are classified according to the same categories by the expected difficulty of answering them correctly or selecting the correct action. With this model only a small number of parameters are required: an expected probability distribution for the skill categories, and the expected conditional probabilities for slips and lucky guesses. By limiting the complexity of the user model in this way, and to a single level of propagation, updating can be performed in time linear to the number of test items and typically only about a half a dozen model parameters are required. Test items can be added or taken away without changing these parameters, provided only that their skill level is specified. We contrast this approach with other uses of Bayesian models in intelligent tutoring systems for diagnostic plan recognition or assessment. Other assessment approaches typically require 100’s of conditional probabilities or an explicit authoring of the structure of the belief network; this approach requires neither.