标题： 一种增强现实应用及用户研究，用于理解和学习空间变换矩阵 显示英文标题

标题： An Augmented Reality Application and User Study for Understanding and Learning Spatial Transformation Matrices

摘要： 理解空间变换及其数学表示在计算机辅助设计、机器人技术等领域中是必不可少的。 这项研究开发并测试了一款增强现实（AR）应用程序（BRICKxAR/T），以增强学生对空间变换矩阵的学习。 BRICKxAR/T利用增强现实的功能，包括信息增强、物理与虚拟物体的互动以及具身学习，为学习创造了一种新颖且有效的可视化体验。 BRICKxAR T通过用户研究作为学习干预措施进行了评估，使用乐高模型作为示例的物理和虚拟操作工具，以评估学生的学习成果。 该研究比较了AR（N=29）与非AR（N=30）学习工作坊，在普渡旋转可视化测试和数学问题上进行了前后测。 参与两种工作坊后，学生的数学成绩显著提高，其中AR工作坊显示出更大的提升趋势。 工作坊后的调查表明，学生倾向于认为BRICKxAR/T是一个有趣且有用的应用程序，并且他们在AR中学习的时间比非AR更多。 显示英文摘要

摘要： Understanding spatial transformations and their mathematical representations are essential in computer-aided design, robotics, etc. This research has developed and tested an Augmented Reality (AR) application (BRICKxAR/T) to enhance students' learning of spatial transformation matrices. BRICKxAR/T leverages AR features, including information augmentation, physical-virtual object interplay, and embodied learning, to create a novel and effective visualization experience for learning. BRICKxAR T has been evaluated as a learning intervention using LEGO models as example physical and virtual manipulatives in a user study to assess students' learning gains. The study compared AR (N=29) vs. non-AR (N=30) learning workshops with pre- and post-tests on Purdue Visualization of Rotations Test and math questions. Students' math scores significantly improved after participating in both workshops with the AR workshop tending to show greater improvements. The post-workshop survey showed students were inclined to think BRICKxAR/T an interesting and useful application, and they spent more time learning in AR than non-AR.