Bayesian Knowledge Tracing Study Guide

Bayesian Knowledge Tracing explained hands-on. Interactive primer for the MATx team and the presidential education hackathon.

Start from the problem Glossary Estonian pitch

What’s inside

BKT — foundation

Core model: probabilistic student state per micro-skill, Bayes’ rule, ZPD.

Selector & explainability

How the next task is chosen and why we can explain it to the teacher.

Notebooks & JupyterLite

Static chapters plus live notebooks at /lab/ (Pyodide in the browser).

Inside the code

The real implementation in web/lib/bkt.ts, line by line.

Companion: MATx

Tom Kabel’s MATx teaches solving the equations our book teaches modeling. The mapping is on the Bridge to MATx page.

Study map

%%{init: {'theme': 'base','flowchart': {'nodeSpacing': 96,'rankSpacing': 108,'padding': 40,'curve': 'basis','useMaxWidth': true}}}%%
flowchart LR
  subgraph model["Model"]
    BKT["BKT / P(L)"]
  end
  subgraph engine["Engine"]
    SEL["Selector / ZPD"]
    EXP["Explainability"]
  end
  BKT --> SEL
  SEL --> EXP

Live Mermaid diagrams appear here and in chapters (glossary, BKT, selector).

Stack

Astro Starlight — static site, locales ru / et / en.
KaTeX — math rendering.
Mermaid — flow diagrams.
React + Recharts + Framer Motion — interactive widgets.
JupyterLite — full Jupyter in the browser, no backend.
Cloudflare Pages — deploy at bkt-study-guide.tyche.institute.

Who writes this

The guide evolves alongside the MATx Teacher product. Source of truth: web/lib/bkt.ts — every example uses the same model as production.