arXiv:2604.04036cs.IRcs.CL2026-04

针对新手数学教师的误解诊断难题,提出双超图RAG框架提升教学反馈精准度。

MisEdu-RAG: A Misconception-Aware Dual-Hypergraph RAG for Novice Math Teachers

  • 构建概念与错题双超图,关联教学知识与真实错误案例
  • 在MisstepMath上提升F1值10.95%,响应质量最高增15.3%
  • 适合新手教师培训及AI辅助教学场景,实证反馈具可操作性

新手数学教师常面临学生错误难以诊断和纠正的问题,尤其是认知误区更需清晰解释。现有大语言模型虽能生成教学反馈,但知识与错误关联松散,指导性不足。为此,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,真实学生错误案例构建为实例超图。查询时,系统分两阶段检索双层证据,并生成基于实证与教学原则的回应。在包含数学错误与教师解法配对的MisstepMath数据集上评估显示,相比基线模型,MisEdu-RAG提升token-F1达10.95%,响应质量最高提升15.3%,尤其在多样性与赋能维度表现突出。通过221名教师问卷及6位新手访谈的试点研究,结果表明该框架能提供高需求场景下的诊断结论与具体教学策略。整体展现出在教师培训与智能教学中的应用潜力。代码已开源:https://github.com/GEMLab-HKU/MisEdu-RAG。

原文摘要 · Abstract (English)

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.

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