Student Knowledge Diagnosis Using Item Response Theory and Constraint-Based Modeling

One of the most popular student modeling techniques currently available is Constraint Based Modeling (CBM), which is based on Ohlsson's theory of learning from performance errors. It focuses on the domain principles to correct faulty knowledge and assumes that a student will reach a correct solution without violating these fundamental domain concepts. However, even though this is a powerful and computationally simple technique, most student models of CBM-based tutors handle simple long-term models or based on heuristics to quantitatively estimate the knowledge measured. In this paper we propose a student knowledge diagnosis model which combines CBM with the Item Response Theory (IRT). IRT is a probabilistic and data-driven theory which guarantees accurate and invariant student knowledge estimations. By means of this synergy between CBM and IRT we suggest the construction of long-term student models composed of the estimations of their knowledge. This paper also includes an experiment we have carried out with real students, which explores the validity of the diagnoses made with our model.