Novice math teachers often encounter students' mistakes that are difficult to diagnose and remediate. Misconceptions are especially challenging because teachers must explain what went wrong and how to solve them. Although many existing large language model (LLM) platforms can assist in generating instructional feedback, these LLMs loosely connect pedagogical knowledge and student mistakes, which might make the guidance less actionable for teachers. To address this gap, we propose MisEdu-RAG, a dual-hypergraph-based retrieval-augmented generation (RAG) framework that organizes pedagogical knowledge as a concept hypergraph and real student mistake cases as an instance hypergraph. Given a query, MisEdu-RAG performs a two-stage retrieval to gather connected evidence from both layers and generates a response grounded in the retrieved cases and pedagogical principles. We evaluate on \textit{MisstepMath}, a dataset of math mistakes paired with teacher solutions, as a benchmark for misconception-aware retrieval and response generation across topics and error types. Evaluation results on \textit{MisstepMath} show that, compared with baseline models, MisEdu-RAG improves token-F1 by 10.95\% and yields up to 15.3\% higher five-dimension response quality, with the largest gains on \textit{Diversity} and \textit{Empowerment}. To verify its applicability in practical use, we further conduct a pilot study through a questionnaire survey of 221 teachers and interviews with 6 novices. The findings suggest that MisEdu-RAG provides diagnosis results and concrete teaching moves for high-demand misconception scenarios. Overall, MisEdu-RAG demonstrates strong potential for scalable teacher training and AI-assisted instruction for misconception handling. Our code is available on GitHub: https://github.com/GEMLab-HKU/MisEdu-RAG.

翻译：新手数学教师常会遭遇学生难以诊断和纠正的错误。误解问题尤为棘手，因为教师必须解释错误成因并提供解决方案。尽管现有的大语言模型平台能辅助生成教学反馈，但这些模型对教学知识与学生错误之间的关联性较为松散，可能导致指导建议对教师而言缺乏可操作性。为弥补这一空白，我们提出MisEdu-RAG——一种基于双超图的检索增强生成框架，将教学知识组织为概念超图，将真实学生错误案例组织为实例超图。当收到查询时，MisEdu-RAG通过两阶段检索从两个层级中收集关联证据，并基于检索到的案例与教学原则生成回答。我们在《MisstepMath》数据集上展开评估——该数据集包含数学错误及其对应教师解决方案，可作为跨主题与错误类型的误解感知检索及回答生成基准。在《MisstepMath》上的评估结果显示，与基线模型相比，MisEdu-RAG的token-F1值提升了10.95%，五维回答质量最高提升15.3%，其中在“多样性”与“赋能性”维度上增益最为显著。为验证实际应用可行性，我们进一步通过对221名教师的问卷调查与6名新手教师的访谈开展试点研究。结果表明，MisEdu-RAG能为高需求的误解场景提供诊断结果与具体教学策略。总体而言，MisEdu-RAG在规模化教师培训与AI辅助误解处理教学中展现出巨大潜力。我们的代码已开源：https://github.com/GEMLab-HKU/MisEdu-RAG。