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

2025-08-15

AI Summary

Educational systems often assume learners can identify their own knowledge gaps, yet students frequently struggle to recognize “unknown unknowns”—fundamental blind spots in their understanding. To address this, we propose a dynamic prerequisite knowledge tracing method powered by large language models (LLMs), eliminating reliance on predefined curricula or static knowledge graphs. Our approach features: (1) a recursive prerequisite discovery mechanism that enables real-time tracing of multi-layered dependency chains and cross-domain foundational concept identification; and (2) an integrated LLM-based extraction pipeline coupled with a binary assessment interface, reducing cognitive load while enabling dynamic boundary delineation and hierarchical learning sequence generation. Empirical evaluation in computer science demonstrates precise identification of deep mathematical prerequisite dependencies and automatic generation of personalized learning pathways, significantly enhancing adaptive instruction capabilities.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Data Mining & Knowledge Management: Conversational Systems for Recommendation & Retrieval
• Search and Optimization: Learning to Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

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.

Problem

• Addresses unknown unknowns in student knowledge gaps
• Dynamically traces prerequisite concepts using LLMs
• Generates personalized learning paths without predefined curricula

Innovation

• Dynamic prerequisite discovery using LLMs
• Recursive tracing to knowledge boundaries
• Personalized learning paths from gaps