AI 中文总结
该研究通过访谈18名几何教师、审查33款工具，发现数字工具在几何证明正式教学中存在不足，进而提出四项教育证明工具的设计准则。
AI 中文摘要
几何证明是数学中基础性却富有挑战性的主题，要求学生整合视觉、逻辑与符号表达技能。尽管技术已在其他数学领域提升了学习效果，但其对几何证明的影响仍有限。为探究这一差距，我们访谈了18名几何教师，以明确教育类证明工具的技术需求。这些需求为我们审查33款商业及研究工具提供了依据。我们的研究发现存在关键不匹配：教师虽重视部分数字工具用于初始规划与探索活动，但在正式证明阶段仍回归纸笔，因为纸笔支持图表标注，且提供多种解题方法的空间。图表标注是解题流程的关键组成部分，现有工具均未支持。我们针对教育类证明工具提出四项以技术和人为中心的设计准则，以大规模满足教师需求：整合图表与证明、自动生成问题与反馈、支持多种证明格式、降低用户体验中的意外复杂度。
英文摘要
Geometric proof is a foundational yet challenging topic in mathematics, requiring students to integrate visual, logical, and notational skills. While technology has enhanced learning in other mathematical domains, its impact on geometric proof remains limited. To investigate this gap, we interviewed 18 geometry teachers to establish the technical requirements of educational proof tools. These requirements inform our review of 33 commercial and research tools. Our findings reveal a critical mismatch: while teachers value certain digital tools for initial planning and exploration activities, they revert to pen-and-paper for formal proof because it supports diagram annotation and provides space for multiple approaches to proof-solving. Annotating the diagram is a key component of the proof-solving workflow that existing tools do not support. We propose four technical and human-centered design guidelines for educational proof tools to meet teacher needs at scale: integrating diagram and proof, generating problems and feedback automatically, supporting multiple proof formats, and reducing accidental complexity in the user experience.
