Through the Looking Glass: Embracing Visualization in Emergency Remote Linear Algebra
Most students at the University of Arizona experienced an increase in math anxiety during the 2020 transition to online learning [Lanius, et al. 2020]. Because 1 of the 9 items on the psychological assessment tool The Abbreviated Math Anxiety Scale (AMAS) [Hopko et al. 2003] is "watching a teacher work an algebraic equation on the blackboard", we knew that online linear algebra in this time of heightened math anxiety would pose a unique impediment to student learning. We built a curriculum that first grounds every core concept in a geometric picture and secondly introduces a set of symbols with rules for manipulation to bring clarity and precision to that picture.
In this work we will colorfully illustrate more topics, including matrix row operations. A visualization lens embraces online formats for their capacity as a visual medium, rather than treating them as a temporary hindrance to withstand. We find visualization to be a welcoming access point to linear algebra for the algebra-averse student as well as a novel perspective for the established algebraist. Linear algebra is not just powerful; it is visually beautiful mathematics.