用大模型自动生成数学题目的矢量图，提升教学可视化效率。
From Text to Visuals: Using LLMs to Generate Math Diagrams with Vector Graphics
- 通过LLM生成SVG格式的数学图表，实现精准可缩放的视觉辅助。
- 实验表明，优化提示策略后生成图的准确率显著提升。
- 适合教育科技开发者和数学教学研究者参考使用。
大型语言模型（LLM）的发展为数学教育提供了新可能，可自动化支持教师与学生。尽管已有研究聚焦于生成数学题目和高质量干扰项，但可视化在数学学习中的作用仍被低估。图表对数学思维与解题至关重要，但手工制作耗时且需专业知识，限制了可扩展性。近期研究探索使用大模型生成可缩放矢量图形（SVG），这是一种以XML表示几何图形的格式，支持无损缩放与适应性调整。教育平台如Khan Academy和IXL已采用SVG展示数学题目与提示。本文探讨利用LLM生成伴随文本提示的数学图表，以中间的SVG表示为桥梁。我们提出三个研究问题：(1) 如何自动创建并评估问题求解提示中的数学图表质量；(2) SVG是否是数学图表的有效中间表示；(3) 何种提示策略与格式能促使大模型生成准确的SVG图表。本研究贡献包括定义自动生成数学提示用SVG图表的任务、构建基于提示的生成流水线，并识别关键优化策略。此外，我们设计了基于视觉问答的评估框架，并开展消融实验分析不同流水线变体的效果。通过自动化图表生成，旨在为师生提供准确且概念相关的视觉辅助，增强解题与学习体验。
原文摘要 · Abstract (English)
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.
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