Bayesian Knowledge Tracing

BKT is a particular hidden Markov model. The hidden state is binary (skill not learned vs. learned), the transition allows only the unlearned-to-learned move (learn rate, with no forgetting in the classic version), and the emission probabilities are governed by slip and guess. Recognizing BKT as an HMM clarifies why standard HMM fitting (expectation-maximization) and identifiability concerns apply directly. See the related Hidden Markov Model entry.

Slip is the probability a student who has mastered the skill still answers incorrectly (a careless error); guess is the probability a student who has not mastered it answers correctly anyway. They model the noisy link between knowledge and behavior. If they are too large, observations become uninformative and mastery estimates degenerate. Bounding them (commonly below 0.5 or 0.3) keeps the model interpretable, and contextual estimation lets them vary by situation for better accuracy.

BKT is a compact, interpretable HMM with four parameters per skill and explicit assumptions. Deep Knowledge Tracing uses recurrent neural networks to predict the next response from the full interaction sequence, capturing skill interdependencies and richer patterns at the cost of interpretability and data hunger. DKT can outperform BKT in raw prediction on large datasets, but BKT's transparency and modest data requirements keep it widely used, and the two are routinely benchmarked against each other.