Why we built the BKT mastery map
A binary 'lesson completed' flag is a lie. Mastery is probabilistic. Here's why that matters for spaced practice.
When we first shipped the site, every lesson had a single "Mark as complete" toggle. After a few weeks of using it ourselves, that toggle felt wrong. You can complete a lesson and remember 80% of it; you can complete the same lesson next week and remember 95%. The toggle is the same Y/N either way.
Bayesian Knowledge Tracing — Corbett and Anderson, 1995 — models this honestly. Each Knowledge Point gets a probability p(known). Every correct answer pushes it up; every wrong answer pulls it down. The math has four params (p_init, p_learn, p_slip, p_guess) and they all matter.
What changes when you start tracking p(known)
- Review scheduling stops being random. The 14-Day Plan rebalances every visit to front-load the lowest-p KPs.
- Mastered KPs drop out of practice. No more re-doing what you already know cold.
- The map glows the right amount. Faint tint at 30%, full color at 80%, soft halo at 90%+. You can see where you're weak at a glance.
The map at /plan/map is the most-checked page on the site for our team. Once you start tracking like this you can't go back.