Vector dot product: Enhancing understanding and motivation through immersive augmented reality (AR)

Students often struggle to understand the vector dot product, which is a foundational operation used in mathematics and engineering. To improve undergraduate engineering students’ understanding of the dot product, we developed and tested the effects of an augmented reality (AR) app. The app utilized scaffolding and storyline narration to cover: (1) computation of the angle between vectors, and (2) the projection of a force vector onto a line. Students were randomly assigned to either a treatment group to utilize the AR, or a control group for traditional peer collaboration. Pre/post testing was conducted using a 14-item, 100-point test. 61 pairs of pre/posttest data (AR n = 25, control n = 36) were analyzed using ANCOVA. The 20.9-point improvement in the AR group's mean test scores was significantly larger than the 9.33-point increase in the control group. The effect size (partial η 2 = 0.135) was considered medium to large. The Instructional Materials Motivation Survey assessed motivation from 12 students in each group. Motivation of the AR group was 19.3% larger than that of the control. The difference was significant with a large effect size. The results suggest that the 3D visualization and immersive qualities of AR may improve learning of vector operations in STEM disciplines.