A Retrieval-Augmented Question Answering Framework for Mathematics Education Based on Knowledge Graph Optimization and Multi-path Recall

Time: 2026-09-22 22:34:00

To address insufficient domain knowledge coverage, unstable mathematical reasoning, and inadequate external evidence in large language model-based question answering for mathematics education, this paper proposes a retrieval-augmented question answering framework based on knowledge graph optimization and multi-path recall, named KGMR-QA. The framework cleans, segments, and structures multi-source data to construct a text knowledge base, a question-answer knowledge base, and a mathematics knowledge graph. It then adapts an embedding model to the mathematics domain through InfoNCE-based contrastive learning and Low-Rank Adaptation (LoRA). A progressive entity disambiguation mechanism based on vector recall, connected-subgraph construction, and large language model judgment is used to address synonymous and context-dependent mathematical expressions. Finally, knowledge graph retrieval, BM25 retrieval, and dense semantic retrieval are integrated with Reciprocal Rank Fusion (RRF), reranking, and Small2Big context expansion. Experiments on mathematics questions from primary, junior high, and senior high school show that the accuracy on senior high school multiple-choice and fill-in-the-blank questions increases from 77.8% to 82.8% compared with Pure LLM. For senior high school solution questions, the comprehensive LLM-Judge score increases from 4.33 to 4.77, and the sub-question accuracy increases from 83.4% to 92.9%. Under different knowledge-source configurations, KGMR-QA achieves an accuracy of 84.3%. Under the current dataset and evaluation metrics, the framework yields better knowledge retrieval and answer-quality results.

References：

[1] 祝智庭, 戴岭, 赵晓伟. “近未来”人机协同教育发展新思路[J]. 开放教育研究, 2023, 29(5): 4-13. Zhu Z T, Dai L, Zhao X W. New Iideas Ffor the Ddevelopment of Nnear-Ffuture Hhuman-Mmachine Ssynergistic Eeducation[J]. Open Education Research, 2023, 29(5): 4-13. 

[2] Ahn J, Verma R, Lou R, et al. Large language models for mathematical reasoning:p Progresses and challenges[C]//Proceedings of the 18th Conference of the European Chapter of the Association for Computational Linguistics: Student Research Workshop. St. Julian’'s, Malta: Association for Computational Linguistics, 2024: 225-237.

[3] Anh-Hoang D, Tran V, Nguyen L M. Survey and analysis of hallucinations in large language models:a Attribution to prompting strategies or model behavior[J]. Frontiers in Artificial Intelligence, 2025, 8: 1622292.

[4] Lewis P, Perez E, Piktus A, et al. Retrieval-augmented generation for knowledge-intensive NLP tasks[C]//Advances in Neural Information Processing Systems 33. Red Hook, NY: Curran Associates Inc., 2020: 9459-9474.

[5] Gao Y, Xiong Y, Gao X, et al. Retrieval-augmented generation for large language models:a A survey[EB/OL]. (2023-12-18)[2026-06-14]. https://arxiv.org/abs/2312.10997. DOI: 10.48550/arXiv.2312.10997.