Impact of Virtual Reality on the Visualization of Partial Derivatives in a Multivariable Calculus Class

Keegan Kang,Wong Wei Pin,Jacob Chen Shihang,Omar Ortiz,Sergey Kushnarev

doi:10.1109/access.2020.2982972

Abstract

Multivariable calculus is one of the core subjects which engineering students study at university. Students may end up memorizing formulae in multivariable calculus due to the lack of ability in visualizing 3D surfaces, and hence not gain much intuition for the subject. We developed an in-house virtual reality (VR) application with the intention for students to visualize concepts in Multivariable Calculus. In order to evaluate the effectiveness of the VR application (which we term as the treatment), we performed a blinded randomized controlled trial with n = 312 students, where we divided them into a control group of n CO = 187 students and treatment group of n TR = 125 students. We gave both groups of students a test immediately after the treatment, as well as asking them to fill in anonymous survey questions using a Likert scale. Our findings show that students perform worse on some questions after using the VR application, and for some other questions students have similar performance to the treatment group. We hypothesize some reasons why this is so, opening the door for future research. We also give recommendations for future developers of VR applications.

Highlights

Multivariable calculus is one of the first math courses taught in most engineering programmes in higher education
The only difference was that students in the treatment group perceived virtual reality (VR) as being more helpful than the slides in the control group
We summarize the t-tests in Table 1, and can only conclude that the students in the treatment group had a higher perceived benefit of VR than the students in the control group had for slides

Summary

Introduction

Multivariable calculus is one of the first math courses taught in most engineering programmes in higher education. Some students enter engineering programmes having a weak grasp of the concept of functions [3]–[5], moving on from onevariable functions to two-variable functions requires more scaffolding [6], [7]. Animated or interactive plots on computers, where a threedimensional object can be rotated and seen from different angles, as well as physical models, may constitute better tools to present the geometric ideas behind calculus. Recent techniques such as virtual and augmented reality have

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