Bayesian Knowledge Tracing

Bayesian knowledge tracing (BKT) is a model that estimates, after each problem a student attempts, the probability that the student has mastered the underlying skill. Introduced by Corbett and Anderson for intelligent tutoring systems, it is a two-state hidden Markov model: the latent variable is whether the skill is learned or not, and observed correct/incorrect responses update that latent state through Bayesian inference. With just four parameters — initial knowledge, learning, slip, and guess — BKT drives the mastery decisions that tell a tutor when a student can move on.