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BKT Study Guide parrot Bayesian Knowledge Tracing Study Guide

Selector simulator

How to read the simulator

Section titled “How to read the simulator”

Left panel — P(L) for each of the 9 micro-skills. This is the probability that the student has mastered the corresponding micro-skill (P(mastered)).

Centre — the task the selector currently puts first. It is the top-1 of all 20 tasks ordered by closeness of the computed P(solve)P(\text{solve}) to the target value 0.7 (zone of proximal development).

Right panel — top-3 candidates with their justification: the task’s P(solve)P(\text{solve}) (geometric mean over its micro-skills — see Multi-skill tasks) and the distance from the ZPD target 0.7.

The Solved / Wrong buttons apply the BKT update to the P(L) of all the chosen task’s micro-skills (formula from Bayes step by step) and re-compute the recommendations.

Student:
Skill mastery, P(L)
L1 — additive (+/−)0.20
L1 — multiplicative (×/÷)0.20
L1 — mixed0.20
L2 — additive (+/−) + context0.20
L2 — multiplicative (×/÷) + context0.20
L2 — mixed + context0.20
L3 — additive (+/−) + 3+ quantities0.20
L3 — multiplicative (×/÷) + 3+ quantities0.20
L3 — mixed + 3+ quantities0.20
Current task (top-1)
MD-19 · L3 · P(solve) = 0.34
The 2nd number is 2 times greater than the 1st. The 3rd is 6 greater than the 1st. The 4th is 3 less than the 2nd.
Canonical definition
Let I number = x
II = 2x
III = x + 6
IV = 2x − 3
Top-3 candidates
MD-19 · L3P=0.34 · score=0.02
The 2nd number is 2 times greater than the 1st.
distance from ZPD 0.7: 0.36
MD-20 · L3P=0.34 · score=0.02
Bianca is 5 years older than Alexandra.
distance from ZPD 0.7: 0.36
MD-01 · L1P=0.34 · score=0.02
One number is greater than another by 5.
distance from ZPD 0.7: 0.36

Things to try

Section titled “Things to try”
  1. Newbie → 5 correct in a row. You can see the selector gradually raise the difficulty — from L1 to L2 — as the base skills’ P(L) grows.
  2. Strong +/−, weak ×/÷. The geometric mean “drags down” the joint P(solve)P(\text{solve}), so the selector avoids tasks where the multiplicative skill is one of the core micro-skills. The top fills with L1.add / L2.add tasks — as expected.
  3. Confident L1 → wrong on T2.add. A single wrong answer steers recommendations into the same ZPD pocket: the selector keeps working exactly where the student “leaked”.

How it differs from BktSimulator

Section titled “How it differs from BktSimulator”

BktSimulator (on the Step by step page) teaches the math of a single micro-skill: one P(L), one chart, the ”✓/✗” buttons update only that one. It is an explanation of the algorithm’s internals.

MatrixSelectorSim is the whole system: 9 P(L) at once, 20 tasks, ranking by ZPD, penalty for recently-shown tasks, geometric mean across micro-skills. The same thing web/lib/bkt.ts does in the /api/recommend route — only in the browser, with no server.

What this simulator does not cover

Section titled “What this simulator does not cover”
  • Per-step ingest. If the worksheet were scanned step-by-step, an error on “subtract from both sides” would only update that micro-skill, not the entire “constellation” of the task. Here, only the aggregate outcome (solved or not) is observed.
  • BKT parameters are shared (P(L₀)=0.2, P(T)=0.1, P(S)=0.1, P(G)=0.2). The real engine may vary them per micro-skill.
  • Fatigue. The selector does not know that the current task is the fifth in a row on the same skill.

All of that lives outside the hackathon scope, but everything is visible in the code (web/lib/bkt.ts) and discussed in the Inside the code section.

Where to go next — practising the solving

Section titled “Where to go next — practising the solving”

Companion: MATx. The simulator above picks a defining microskill — which modeling task to give the student. Solving the resulting equation is a different domain (computation), and Tom Kabel has a separate tool for that. The page Bridge to MATx has the exact transition map: “after mastering our T2.add the student is ready for Tom’s vorrandid.lihtsad-vorrandid”.