用检索引导多阶段推理，精准识别学生数学解题中的误解
MiRAGE: Misconception Detection with Retrieval-Guided Multi-Stage Reasoning and Ensemble Fusion
- 通过检索缩小候选范围，再分步推理暴露逻辑漏洞
- 在数学数据集上平均精度达0.82~0.93，优于单一模块
- 适合教育评估系统，提升诊断可解释性
检测开放回答中的学生误解是长期挑战，需语义精准与逻辑推理。我们提出MiRAGE——一种基于检索引导的多阶段推理与集成融合的数学误解检测框架。该框架分三步：(1) 检索模块从大量候选中筛选语义相关项；(2) 推理模块通过思维链生成揭示学生解答中的逻辑矛盾；(3) 重排序模块结合推理结果优化预测。三者通过集成融合策略统一，提升鲁棒性与可解释性。在数学数据集上，MiRAGE在水平1/3/5的平均精度分别为0.82/0.92/0.93，持续优于单个模块。通过检索引导与多阶段推理结合，显著降低对大规模语言模型的依赖，提供可扩展、高效的教育评估方案。
原文摘要 · Abstract (English)
Detecting student misconceptions in open-ended responses is a longstanding challenge, demanding semantic precision and logical reasoning. We propose MiRAGE - Misconception Detection with Retrieval-Guided Multi-Stage Reasoning and Ensemble Fusion, a novel framework for automated misconception detection in mathematics. MiRAGE operates in three stages: (1) a Retrieval module narrows a large candidate pool to a semantically relevant subset; (2) a Reasoning module employs chain-of-thought generation to expose logical inconsistencies in student solutions; and (3) a Reranking module refines predictions by aligning them with the reasoning. These components are unified through an ensemble-fusion strategy that enhances robustness and interpretability. On mathematics datasets, MiRAGE achieves Mean Average Precision scores of 0.82/0.92/0.93 at levels 1/3/5, consistently outperforming individual modules. By coupling retrieval guidance with multi-stage reasoning, MiRAGE reduces dependence on large-scale language models while delivering a scalable and effective solution for educational assessment.
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