AI Tutor Uses Skill Dependency Graph to Pinpoint Where Students Truly Struggle

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A developer built an AI-powered tutoring tool that maps academic skills as a dependency graph to identify the root cause of a student's learning gaps rather than re-teaching surface-level topics. The system models 58 skills across five layers, from exam-level tasks down to basic arithmetic, with each skill linked to the prerequisite skills it depends on. An LLM generates targeted questions while the graph determines which skill to probe next, drilling downward until the underlying broken concept is found. To ensure the hand-authored graph remained valid, the developer implemented cycle detection using a three-colour depth-first search algorithm. An initial breadth-first traversal approach proved impractical, as a struggling student could face up to 42 questions before the diagnostic walk completed.

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