Each glowing node is a skill in a prerequisite graph (a simplified curriculum knowledge graph). An AI tutoring engine picks the learner's next lesson using Bayesian Knowledge Tracing (BKT): it estimates the learner's mastery of every skill as a probability and updates it after every attempt.
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)
- Skill nodes — size of the curriculum graph; more nodes means longer prerequisite chains to traverse.
- Learning rate p(transit) — probability mastery advances after one attempt; higher values mean the learner masters each skill faster.
- Target success (proximal zone) — the AI mentor picks whichever ready skill has a predicted success probability closest to this value, keeping challenge inside the learner's zone of proximal development.
- Attempt pace — how fast the learner moves through the graph and attempts skills, for visualization speed only.
- Mode toggle — switches the AI's lesson-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, and always route the learner to the next-best skill instead of a fixed, one-size-fits-all lesson order.