Using Augmented Reality and Artificial Intelligence to Improve Teaching and Learning Spatial Transformations in STEM Disciplines

用于描述空间变换的数学对于本科生来说可能非常困难。 虽然在物理世界中移动某些东西可能很容易理解，但在数字世界中用数学描述相同的操作可能会令人望而生畏。 该项目将利用增强现实 (AR) 和人工智能 (AI) 开发新技术，以改善 STEM 学科中这些困难概念的教学和创造性工作。 该项目将测试新的 AR/AI 技术的使用，以增强学生对空间变换背后的数学的学习。 这将改善 AR/AI 支持的物体精确运动跟踪的使用，这些跟踪可以收集高分辨率的原位运动和场景数据，以增强学习分析。该项目将确定 AR 功能，帮助学生构思、连接和比较运动的数学表示，以克服学生在学习空间变换时面临的有据可查的困难。 加强这项技能将支持他们在许多 STEM 学科中的持续发展。将开发一个 AR/AI 驱动的创新学习环境，并评估其对欧几里德空间中教学和学习主要轮换和方向表示的影响。 将测试不同级别的抽象，包括轴角、欧拉角、矩阵和四元数。在研讨会上，参与者将尝试并改造 3D 打印的几何模型，以评估 AR/AI 技术的有效性。该项目将通过比较研讨会前后测试中的数学技能与不使用 AR/AI 技术完成相同任务的学生的数学技能来评估学生的学习成果。该项目将通过探索以下内容，促进跨空间和数学教学学科的知识进步：a）新颖的 AR 交互的作用，它允许物理和虚拟操作之间的相互作用，让学生参与具体学习； b) AR 能够使困难的隐形概念变得可见，以支持对空间推理和数学公式的直观和形式理解； c) AR 的功能可以帮助学生了解空间操作和数学运算之间的关系； d) 使用 AR 辅助数学学习时空间变换中个体差异的潜在影响。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

The mathematics that are used to describe spatial transformations can be very difficult for undergraduate students. While moving something in the physical world may be easy to understand, describing the same operation with math in the digital world can be daunting. This project will develop new technology using Augmented Reality (AR) and Artificial Intelligence (AI) to improve the teaching and learning of these difficult concepts in STEM disciplines as well as creative endeavors. The project will test the use of new AR/AI technology to enhance students’ learning of the mathematics behind spatial transformations. This will improve the use of AR/AI-powered precise motion tracking of objects that can collect high resolution in-situ motion and scene data to enhance learning analytics. The project will identify the AR capabilities that can help students conceive, connect, and compare mathematical representations of motion to overcome the well-documented difficulties students face when learning spatial transformations. Strengthening this skill will support their continued development across many STEM disciplines.An AR/AI-powered innovative learning environment will be developed and evaluated for its effects on teaching and learning major rotation and orientation representations in the Euclidean space. Different levels of abstraction, including Axis-Angle, Euler Angles, Matrices, and Quaternions will be tested. In workshops participants will play with and transform 3D-printed geometry models to evaluate the effectiveness of the AR/AI technology. The project will assess student learning outcomes by comparing math skills in pre- and post-workshop tests compared to students working through the same tasks without the use of the AR/AI technology. The project will contribute to advancing knowledge across disciplines of spatial and mathematical pedagogies, by exploring: a) the role of novel AR interaction that allows the interplay between physical and virtual manipulatives to engage students in embodied learning; b) the capabilities of AR to make difficult invisible concepts visible for supporting an intuitive and formal understanding of spatial reasoning and mathematical formulation; c) the features of AR that help students see relationships between spatial manipulations and mathematical operations; and d) the potential impact of individual differences in spatial transformations when using AR-assisted mathematical learning.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.