Advances in large language models (LLMs) offer new possibilities for enhancing math education by automating support for both teachers and students. While prior work has focused on generating math problems and high-quality distractors, the role of visualization in math learning remains under-explored. Diagrams are essential for mathematical thinking and problem-solving, yet manually creating them is time-consuming and requires domain-specific expertise, limiting scalability. Recent research on using LLMs to generate Scalable Vector Graphics (SVG) presents a promising approach to automating diagram creation. Unlike pixel-based images, SVGs represent geometric figures using XML, allowing seamless scaling and adaptability. Educational platforms such as Khan Academy and IXL already use SVGs to display math problems and hints. In this paper, we explore the use of LLMs to generate math-related diagrams that accompany textual hints via intermediate SVG representations. We address three research questions: (1) how to automatically generate math diagrams in problem-solving hints and evaluate their quality, (2) whether SVG is an effective intermediate representation for math diagrams, and (3) what prompting strategies and formats are required for LLMs to generate accurate SVG-based diagrams. Our contributions include defining the task of automatically generating SVG-based diagrams for math hints, developing an LLM prompting-based pipeline, and identifying key strategies for improving diagram generation. Additionally, we introduce a Visual Question Answering-based evaluation setup and conduct ablation studies to assess different pipeline variations. By automating the math diagram creation, we aim to provide students and teachers with accurate, conceptually relevant visual aids that enhance problem-solving and learning experiences.

本研究解决了数学教育中视觉化不足的问题，探讨了使用大型语言模型（LLMs）自动生成数学图形的新方法。通过定义自动生成SVG格式数学图形的任务和开发相应的LLM提示管道，我们的研究发现使用矢量图形可以有效提升数学问题解决中的视觉辅助效果，进而改善学生的学习体验。

从文本到视觉：利用大型语言模型生成数学图形与矢量图形