With the introduction of large language models (LLMs), automatic math reasoning has seen tremendous success. However, current methods primarily focus on providing solutions or using techniques like Chain-of-Thought to enhance problem-solving accuracy. In this paper, we focus on improving the capability of mathematics teaching via a Socratic teaching-based LLM (\texttt{SocraticLLM}), which guides learners toward profound thinking with clarity and self-discovery via conversation. We collect and release a high-quality mathematical teaching dataset, named \texttt{SocraticMATH}, which provides Socratic-style conversations of problems with extra knowledge. Also, we propose a knowledge-enhanced LLM as a strong baseline to generate reliable responses with review, guidance/heuristic, rectification, and summarization. Experimental results show the great advantages of \texttt{SocraticLLM} by comparing it with several strong generative models. The codes and datasets are available on \url{https://github.com/ECNU-ICALK/SocraticMath}.

本研究解决了当前大型语言模型在数学教学应用中的不足，尤其是缺乏深度引导的对话模式。通过引入基于苏格拉底教学法的模型（SocraticLLM），并推出高质量的数学教学数据集（SocraticMATH），本文展示了该模型在促进学习者深度思考方面的有效性和优势。实验结果表明，SocraticLLM在生成可靠响应的能力上显著优于现有的多种生成模型，具有潜在的教育影响和应用价值。

利用苏格拉底方法增强大型语言模型以进行数学对话教学