用大模型生成按认知分类的合成错题，助力个性化教学。
Taxonomy-Targeted Error Generation for Quantitative Reasoning
- 基于布卢姆分类法设计五类错题生成框架，分步验证错误一致性。
- 生成的错题在认知类别上准确率达90%以上，可复用于教学数据集。
- 适合教育研究、智能辅导系统开发人员使用，提升错题分析效率。
个性化辅导、教师培训和教育研究可受益于带有错误机制标注的真实学生错题。但这类带认知标签的错题收集与共享成本高，促使我们探索大模型是否能生成目标分类的合成错题作为补充材料。本文提出一种面向五类布卢姆认知分类的学生错题生成框架：生成代理（GA）根据目标类别生成候选错误解答，评估代理（EA）判断其是否错误且类别一致。该框架提供了一种可复用的方法，可在缺乏真实学生数据时构建类别分层的合成错题数据集。作为辅助诊断，定向错题生成比自由生成更困难，且答案锚定比扩展示例或外部教材内容更具影响力。
原文摘要 · Abstract (English)
Personalized tutoring, teacher preparation, and education research can benefit from worked errors annotated by the mechanisms that produced them. Authentic student errors with such cognitive labels are costly to collect and share, motivating the study of whether LLMs can generate taxonomy-targeted synthetic errors as complementary candidate material. We present a task-specific framework that generates errors targeted to a five-class Bloom-informed student-error taxonomy. A Generation Agent (GA) drafts a candidate erroneous solution conditioned on a target class, and an Examination Agent (EA) judges whether the draft is incorrect and class-consistent. The framework yields a reusable recipe for building class-stratified synthetic error datasets where authentic student corpora are unavailable. As a secondary diagnostic, targeted error generation is substantially harder than free-form incorrect-answer generation, and answer-grounding contributes more than expanded examples or external textbook content.
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