Hidden Markov IRT model as a generalization of Bayesian Knowledge Tracing

Abstract

To develop learner's ability, a teacher should grasp the learner's knowledge state accurately in a learning process.For this purpose, Bayesian Knowledge Tracing (BKT) has been proposed to infer learner's knowledge state.Although conventional BKT models learner's knowledge state as a discrete value, the learner's knowledge state must be contentious. Based on this idea, we propose a Hidden Markov IRT model as a generalization of Bayesian Knowledge Tracing. In the proposed model, learner's knowledge state takes a continuous value and change according to a Hidden Markov process in a learning process. The proposed model estimates the optimal value of the degree of learner's mastering knowledge from learning data.From some numerical experiments, we demonstrate that the proposed model improves the estimation accuracy of the learner's knowledge state.