Adaptive Learning Basics: Bayesian Knowledge Tracing Simulator

Cohort

Students per group 60

Bayesian Knowledge Tracing

Learn rate P(T) 0.12

Guess P(G) 0.20

Slip P(S) 0.10

Adaptive P(L)

--%

Fixed-pace P(L)

--%

Adaptive mastered

--%

Questions answered

How it works

Each student's true skill answers a question of difficulty d correctly with logistic probability, then Guess/Slip noise is applied. An adaptive engine tracks an estimate P(L) of mastery with Bayesian Knowledge Tracing and targets the next question just inside the student's own "productive struggle" zone; the fixed-pace group gets one shared textbook difficulty for everyone, regardless of individual ability.

P(correct | L) = P(L)(1−S) + (1−P(L))G
P(L | correct)  = P(L)(1−S) / [P(L)(1−S) + (1−P(L))G]
P(L | incorrect)= P(L)S / [P(L)S + (1−P(L))(1−S)]
P(Lₙ) = P(L | evidence) + (1 − P(L | evidence))·T·cf
cf(desirable difficulty) peaks when true success chance ≈ 75%

Students per group — cohort size simulated in parallel for each strategy.
Learn rate P(T) — probability of transitioning from "not known" to "known" after any attempt.
Guess P(G) — chance of answering correctly without knowing the skill.
Slip P(S) — chance of answering incorrectly despite knowing the skill.

Real-world use: platforms like Khan Academy, DreamBox and ALEKS run this loop per skill per learner to pick the next best exercise instead of a fixed syllabus.

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