Each node is a skill in a prerequisite curriculum graph. An AI tutoring engine picks the learner's next question using Bayesian Knowledge Tracing (BKT): it tracks each skill's mastery as a probability and updates it after every attempt with a real Bayes-rule posterior, then applies a fixed transit probability.
P(correct) = m·(1−slip) + (1−m)·guess
m' = correct ? m(1−slip) / [m(1−slip)+(1−m)guess]
: m·slip / [m·slip+(1−m)(1−guess)]
m_next = m' + (1−m')·p(transit)
Hover any node to read its exact mastery probability, prerequisite-readiness state, and attempt history. Click a ready (non-grey) node to answer it yourself instead of waiting for the AI tutor.
- Skill nodes — size of the curriculum graph; more nodes means longer prerequisite chains to traverse.
- Learning rate p(transit) — probability mastery advances one notch after an attempt; higher values mean faster mastery growth.
- Target success (proximal zone) — the AI tutor picks whichever ready skill has predicted success probability closest to this value, keeping every question inside the learner's zone of proximal development.
- Attempt pace — how fast the AI works through the graph (visualization speed only; doesn't affect manual clicks).
- Mode toggle — switches the AI's question-picking policy between adaptive (proximal-zone targeting) and random ordering among unlocked skills, so you can compare how much faster the graph turns gold with real personalization.
Real-world relevance: this is the same core idea behind adaptive curricula engines and mastery-learning platforms — estimate per-skill mastery probabilistically with Bayes' rule, and always route the learner to the next-best skill instead of a fixed, one-size-fits-all lesson order.