Learning 3D Matrix Algebra Using Virtual and Physical Manipulatives: Qualitative Analysis of the Efficacy of the AR-Classroom

The AR-Classroom application aims to teach three-dimensional (3D) geometric rotations and their underlying mathematics using virtual and physical manipulatives. In an efficacy experiment, undergraduates completed six 3D matrix algebra rotation questions and were assigned to interact with virtual (N = 20) or physical (N = 20) manipulatives in the AR-Classroom. While completing these rotation questions, researchers documented the participants’ reported thoughts, feelings, and perceptions (i.e., qualitative data). A thematic analysis of participants’ reports revealed four prevalent themes regarding participants’ learning experience: (1) Difficulty using traditional methods, (2) Reliance on resources, (3) Pattern recognition, and (4) Developing an understanding of 3D matrix algebra. Participants struggled to complete rotation matrices when only using information from the question and the model; when unsure how to solve the matrix, participants utilized any available resources. Moreover, participants could identify similarities among matrices, demonstrated after using AR-Classroom repeatedly. The findings indicate that the AR-Classroom may aid students in improving their mathematical skills. Suggestions for future research on the AR-Classroom and efficacy experiments are discussed.