Probability estimation and a competence model for rule based e-tutoring systems

In this paper, we present a student model for rule based e-tutoring systems. This model describes both properties of rewrite rules (difficulty and discriminativity) and of students (start competence and learning speed). The model is an extension of the two-parameter logistic ogive function of Item Response Theory. We show that the model can be applied even to relatively small datasets. We gather data from students working on problems in the logic domain, and show that the model estimates of rule difficulty correspond well to expert opinions. We also show that the estimated start competence corresponds well to our expectations based on the previous experience of the students in the logic domain. We point out that this model can be used to inform students about their competence and learning, and teachers about the students and the difficulty and discriminativity of the rules.