RPKT: Learning What You Don't -- Know Recursive Prerequisite Knowledge Tracing in Conversational AI Tutors for Personalized Learning

Educational systems often assume learners can identify their knowledge gaps, yet research consistently shows that students struggle to recognize what they don't know they need to learn-the "unknown unknowns" problem. This paper presents a novel Recursive Prerequisite Knowledge Tracing (RPKT) system that addresses this challenge through dynamic prerequisite discovery using large language models. Unlike existing adaptive learning systems that rely on pre-defined knowledge graphs, our approach recursively traces prerequisite concepts in real-time until reaching a learner's actual knowledge boundary. The system employs LLMs for intelligent prerequisite extraction, implements binary assessment interfaces for cognitive load reduction, and provides personalized learning paths based on identified knowledge gaps. Demonstration across computer science domains shows the system can discover multiple nested levels of prerequisite dependencies, identify cross-domain mathematical foundations, and generate hierarchical learning sequences without requiring pre-built curricula. Our approach shows great potential for advancing personalized education technology by enabling truly adaptive learning across any academic domain.