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

Jinwen Tang, University of Missouri

Qiming Guo, Texas A&M University – Corpus Christi

Date

08/2025

AI Overview

Why it matters

Students struggle to recognize missing prerequisite concepts they need to learn, while expert instructors often overlook foundational steps. Existing AI tutoring tools require students to articulate their gaps rather than identifying them dynamically.

Study at a glance

Question: Can AI dynamically uncover hidden prerequisite knowledge gaps and build personalized learning paths using simple binary assessments?
Setting and data: Demonstration case query on backpropagation in neural networks; no human participants or datasets evaluated.
Method: System development and prototype demonstration (Recursive Prerequisite Knowledge Tracing)
AI tools: Recursive Prerequisite Knowledge Tracing (RPKT), GPT-4o

Key findings

The prototype recursively mapped multi-level dependencies across domains, tracing a neural network query down to foundational calculus and linear algebra concepts.
Replacing open-ended question formulation with simple binary self-assessments allowed the system to expand unknown topics inline without requiring pre-built curricula.
The system synthesized assessment results to generate customized explanations that reviewed identified missing prerequisites before explaining the target topic.

Summary drafted with AI from the full paper and may contain errors. See the full paper for details.

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.