Supporting Students’ Visualization of Multivariable Calculus Partial Derivatives via Virtual Reality

Abstract

Multivariable calculus is a subject undertaken by engineering students as a core module at the freshman level. One of the intended learning outcomes (ILOs) in multivariable calculus is to gain an intuition for visualizing three-dimensional surfaces and deducing their properties. For students to visualize more complex multivariable calculus concepts, a virtual reality (VR) application has been created. Tapping on existing infrastructures, we investigate the effectiveness of visualization through VR usage vis-à-vis a two-dimensional digital screen. We have conducted a controlled trial on a group of N=119 students across two groups. The first group (control group) comprises students who participated in an online quiz (as a baseline test). The second group (treatment group) is given two sets of tests, the first is the same baseline test that the control group participated in, before administering the test questions on the VR platform (termed the treatment test) to the same group of students. Our analysis reveals that students, in general, perform better on questions pertaining to the identification of the sign of partial derivatives in the treatment test, but for other intended learning outcomes linked to other questions, students have performance similar to the baseline test. Furthermore, low-progress students in the treatment group exhibited improvement after the treatment. Our work here has the potential to be developed into a future-ready smart classroom through VR usage.