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Glossary

Concept map

flowchart TB
  subgraph pred["Prediction"]
    PL(["P(L) — skill mastered?"])
    PS(["P(solve) — solves task?"])
  end
  subgraph params["Four parameters"]
    PL0["P(L₀)"]
    PT["P(T)"]
    PSl["P(S)"]
    PG["P(G)"]
  end
  subgraph ui["Product"]
    SEL["Task selector"]
    HM["Class heatmap"]
    EXP["Explainability"]
  end
  PL --> PS
  PL0 --> PL
  PT --> PL
  PSl --> PS
  PG --> PS
  PS --> SEL
  PL --> HM
  SEL --> EXP

Terms

Term	Definition
BKT	Bayesian Knowledge Tracing — tracks, per (student, micro-skill), the probability the skill is mastered; updates after each response via Bayes + a learning step (P(T)).
Micro-skill	Smallest useful unit of competence (e.g. “expand brackets”); each gets its own BKT state.
(P(L))	Probability the student has mastered the skill right now (latent state).
(P(L_0))	Initial (P(L)) before the first attempt on that skill (prior).
(P(T))	Probability of learning in one attempt after working a problem (transit).
(P(S))	Slip — “knows the skill but answered wrong” (careless error).
(P(G))	Guess — “doesn’t know but picks the right answer”.
(P(solve))	Probability of solving the current problem given (P(L)): (P(L)(1-P(S))+(1-P(L))P(G)).
ZPD	Zone of Proximal Development — “hard but doable”; selector targets (P(solve) \approx 0.7).
Selector	`recommend()` — ranks pool tasks by closeness to target (P(solve)) plus a weak-skill bonus.
Geom. mean across skills	For multi-skill tasks, joint (P(solve)) is the geometric mean per skill — weak links dominate vs arithmetic mean.
Class heatmap	Students × skills matrix coloured by (P(L)).
Explainability	Teacher-facing “why this task” text from templates + BKT numbers (facts not LLM-guessed).
JupyterLite	In-browser Jupyter (Pyodide/WASM); deployed here at `/lab/`.
IRT	Item Response Theory — models item difficulty and ability (\theta); great for tests, weaker than BKT for learning over time.
EM / Baum–Welch	Fits BKT parameters from answer sequences (HMM-style).

See also