用大模型生成结构一致的数学题，效果优于人工出题。
Computational Blueprints: Generating Isomorphic Mathematics Problems with Large Language Models
- 基于模板和元生成设计，自动构建结构相同的数学题
- 生成准确率高，错误率比人工低17.8%
- 适合教育平台大规模部署，已服务超六千名学生
个性化数学教育快速发展，对大量相似练习题的需求激增。现有研究多聚焦于训练语言模型的数据增强，而非直接用于教学。为此，我们提出新任务——同构数学题生成（IMPG），旨在生成与原题结构一致的变体题。通过逐步优化的大模型框架，我们建立了计算蓝图系统（CBIT），采用元级生成与模板化选择性变化，在保证数学正确性和结构一致性的同时，显著降低生成成本。实证结果表明，CBIT在大规模生成中兼具准确性与成本效益。最重要的是，其生成题目错误率比专家编写低17.8%，在商业教育平台部署至6,732名学习者，累计产生186,870次互动。
原文摘要 · Abstract (English)
Personalized mathematics education is growing rapidly, creating a strong demand for large sets of similar practice problems. Yet existing studies on mathematics problem generation have focused on data augmentation for training neural language models rather than on direct educational deployment. To bridge this gap, we define a new task, Isomorphic Math Problem Generation (IMPG), designed to produce structurally consistent variants of source problems. Subsequently, we explored LLM-based frameworks for automatic IMPG through successive refinements, and established Computational Blueprints for Isomorphic Twins (CBIT). With meta-level generation and template-based selective variation, CBIT achieves high mathematical correctness and structural consistency while reducing the cost of generation. Empirical results across refinements demonstrate that CBIT is superior on generation accuracy and cost-effectiveness at scale. Most importantly, CBIT-generated problems exhibited an error rate 17.8% lower than expert-authored items, with deployment to 6,732 learners on a commercial education platform yielding 186,870 interactions.
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