We introduce Augmented Math, a machine learning-based approach to authoring AR explorable explanations by augmenting static math textbooks without programming. To augment a static document, our system first extracts mathematical formulas and figures from a given document using optical character recognition (OCR) and computer vision. By binding and manipulating these extracted contents, the user can see the interactive animation overlaid onto the document through mobile AR interfaces. This empowers non-technical users, such as teachers or students, to transform existing math textbooks and handouts into on-demand and personalized explorable explanations. To design our system, we first analyzed existing explorable math explanations to identify common design strategies. Based on the findings, we developed a set of augmentation techniques that can be automatically generated based on the extracted content, which are 1) dynamic values, 2) interactive figures, 3) relationship highlights, 4) concrete examples, and 5) step-by-step hints. To evaluate our system, we conduct two user studies: preliminary user testing and expert interviews. The study results confirm that our system allows more engaging experiences for learning math concepts.

翻译：我们提出了一种名为“增强数学”的机器学习方法，用户无需编程即可通过增强静态数学教材来创作基于增强现实（AR）的可探索解释。为了增强静态文档，我们的系统首先利用光学字符识别（OCR）和计算机视觉从给定文档中提取数学公式和图形。通过绑定和操作这些提取的内容，用户可以通过移动AR界面看到叠加在文档上的交互式动画。这使得教师或学生等非技术用户能够将现有的数学教材和讲义转化为按需定制的个性化可探索解释。为设计该系统，我们首先分析了现有的可探索数学解释，以识别常见的设计策略。基于研究结果，我们开发了一套可根据提取内容自动生成的增强技术，包括：1) 动态数值，2) 交互式图形，3) 关系高亮，4) 具体示例，以及5) 分步提示。为了评估我们的系统，我们进行了两项用户研究：初步用户测试和专家访谈。研究结果证实，我们的系统能够为学习数学概念提供更具吸引力的体验。