Every dot on the ring is a skill node with a fixed difficulty b. The AI tutor core in the centre estimates the learner's ability θ and, each round, fires a practice beam at whichever unmastered skill is closest in difficulty to θ — exactly like an adaptive item-response (IRT) tutoring system.
P(correct) = 1 / (1 + e^(−a·(θ − b))) a = tutor targeting focus
selection weight(skill i) ∝ e^(−a·(θ − b_i)²) · (1 − mastery_i)
correct → mastery_i += 0.35·(1 − mastery_i); θ += η·(0.3 + 0.7·max(0, b_i − θ + 0.3))
incorrect → θ -= 0.3·η
every skill: mastery_i -= forgetting·mastery_i·dt (spaced-repetition decay)
- Ability growth rate (η) — how fast the learner's estimated ability θ moves after each graded attempt; the beam colour (green/red) is the auto-graded result of that attempt.
- Tutor targeting focus (a) — how tightly the AI tutor concentrates on the skill nearest the learner's current edge versus spreading practice across the ring.
- Forgetting rate — how fast an unreviewed skill's mastery decays, forcing the personalized path to loop back for spaced repetition.
- Practice pace — how many auto-graded practice attempts the tutor sends out per second.
This 2D map mirrors the same adaptive-learning mechanics as the 3D version: an IRT-style ability estimate drives item selection, correct/incorrect answers are auto-graded instantly, and a forgetting model keeps re-scheduling review.