Advanced Mathematics Exercise Recommendation Based on Automatic Knowledge Extraction and Multi-Layer Knowledge Graph

Higher education is rapidly growing in the online learning landscape. However, current personalized recommendation techniques struggle with precise extraction of complex mathematical semantics, hindering accurate perception of learners' cognitive states and relevance of recommendations. This paper proposes a framework for extracting complex mathematical semantics and providing personalized exercise recommendations. We design a tree-based position encoding method to enhance the accuracy of positional representation for mathematical expressions in pre-trained model, aiming to improve the performance of downstream tasks. We propose an automatic method for extracting knowledge attributes based on expert annotations, enabling interpretable cognitive diagnosis. Furthermore, we employ sequential pattern mining to discover the knowledge usage patterns in exercises, generate learning paths using a multi-layer knowledge graph, and leverage cognitive diagnostic results to enhance the relevance of recommendations. Experimental results show a 2.0% improvement in mathematical symbol embedding on mathematical formula retrieval tasks, and knowledge attribute extraction accuracy ranging from 66.5% to 81.7%. Learners' post-test scores significantly improve during group testing, with good consistency between online cognitive diagnosis and self-diagnosis.