Design of a Lightweight Adaptive Knowledge Graph Tutoring System for Discrete Mathematics

This paper proposes a lightweight adaptive knowledge graph tutoring system for discrete mathematics, addressing the challenges of knowledge fragmentation, homogenized pedagogical paradigms, and insufficient practical support in traditional instruction. The system formalizes disciplinary knowledge points and associated exercise repositories, constructing an integrated architecture that unifies knowledge graph representation, intelligent recommendation, adaptive assessment, and content delivery. By integrating lightweight cognitive assessment models with heuristic recommendation strategies, an adaptive learning path generation mechanism is built to dynamically quantify learner proficiency based on problem solving interaction traces. Diverging from compute-intensive deep learning paradigms, this method requires no large-scale training, making it convenient for users to adjust parameters according to actual conditions. It preserves the interpretability of learning trajectories and real-time responsiveness while enabling seamless deployment across conventional computing environments. Experiments in authentic educational settings indicate that the system facilitates learners’ problem solving performance and learning efficiency, offering a scalable and cost-effective solution for personalized supplementary instruction in discrete mathematics and broader undergraduate foundational mathematics courses.