An augmented reality application and experiment for understanding and learning spatial transformation matrices

Understanding spatial transformations and their mathematical representations is essential in computer-aided design, computer graphics, 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. In this paper, we evaluated the BRICKxAR/T as a learning intervention using LEGO models for physical and virtual manipulatives in an experiment. The experiment 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 to assess students' learning gains. All participants math scores significantly improved 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.