Bayesian Knowledge Tracing

src/lib/knowledge-tracing.ts implements classic BKT with two modern extensions: temporal decay and prerequisite-aware content selection.

The model

For each knowledge component, BKT maintains P(L) — the probability the learner has mastered it — updated after every observation:


correct:    P(L | obs) = P(L)·(1 − pSlip) / [ P(L)·(1 − pSlip) + (1 − P(L))·pGuess ]
incorrect:  P(L | obs) = P(L)·pSlip / [ P(L)·pSlip + (1 − P(L))·(1 − pGuess) ]
then:       P(L)' = P(L | obs) + (1 − P(L | obs))·pTransit

Default parameters

src/lib/knowledge-tracing.ts


export const DEFAULT_BKT_PARAMS: Readonly<BKTParams> = {
  pL0: 0.1,       // prior probability of initial mastery
  pTransit: 0.15, // probability of learning per opportunity
  pGuess: 0.25,   // probability of guessing correctly without mastery
  pSlip: 0.1      // probability of erring despite mastery
}

Temporal decay

Mastery decays exponentially when no practice occurs, with a half-life of 14 days — a skill untouched for two weeks drops to half its estimated mastery contribution, prompting review.

Recommendation reasons

The selector explains why it recommends an item:


reason: 'low-mastery' | 'high-uncertainty' | 'prerequisite-gap' | 'decay'

low-mastery — P(L) below threshold
high-uncertainty — too few observations to be confident
prerequisite-gap — a prerequisite concept (from the concept graph) is weak
decay — mastery has decayed since the last practice

These feed the Course View’s next-item selection and the DLP Monitor’s display.