CalcVR Supplemental Materials

Often the largest hindrances to student success in multivariable calculus courses are the student’s inability to visualize the curves, surfaces, and vector fields, as well as the disconnect that this causes between the geometric interpretation and the algebraic calculation. While there are many great tools that are freely available (such as CalcPlot3D) to help students understand these multivariable objects, the rendering is still a two-dimensional picture of a three-dimensional object. To show these objects with visual depth, we created CalcVR, a virtual reality app that is available for free on smartphones (From the Google Play Store¹⁴ or the Apple App Store¹⁵).

To minimize cost to students and faculty, CalcVR requires a minimal amount of additional hardware costs for students. We have made design decisions so that the materials in the CalcVR app would be usable with the lowest cost possible and with minimal hardware requirements. As such, CalcVR can be used with a single button headset and most modern Android and iOS phones. However, the smoothest experience involves a more powerful phone and the addition of a Bluetooth controller. We have created interactive lessons and playgrounds for multivariable calculus topics with the ability for the user to input their own expressions and explore the related figures with inexpensive integrated Bluetooth controllers. More information can be found in the Hardware Recommendations¹⁶.

CalcVR is built from the ground up using the Unity game engine along with the Google Cardboard framework. The use of these technologies has allowed the small team of developers to rapidly update and add new content to the app.

The focus of CalcVR is on geometric understanding of the concepts and notions prevalent to multivariable calculus. While we understand the importance of the algebraic calculations found throughout multivariable calculus, the virtual reality environment is not well-suited to these somewhat tedious calculations. It is, however, the ideal environment to explore the geometric meaning of three-dimensional objects encountered in multivariable calculus. To further the understanding of geometric concepts and to derive connections between these concepts and algebraic calculations we have added a bevy of supplemental activities and explorations (Supplemental Materials). The CalcVR app is designed to be tool for outside of class meeting times and not to be done in a group setting. The Supplemental Materials offer different ways to connect the geometric tools of the CalcVR app to activities and assessments that can be done both in class meetings and outside of class meetings. These activities and assessments are not prescriptive and the CalcVR team welcomes any ideas and improvements you would like to suggest.