CalcVR

What it is

CalcVR (Calculus in Virtual Reality) is a free app designed to help university-level students visualise concepts in multivariable calculus through VR. It addresses a core problem in teaching the subject: students’ difficulty visualising curves, surfaces, and vector fields, and the disconnect this creates between geometric interpretation and algebraic calculation.

Who made it

It was created by Nick Long and Jeremy Becnel of Stephen F. Austin State University (SFA) in Texas. Funding came initially from the SFA Provost’s Office, with subsequent support from a National Science Foundation (NSF) grant.

Development timeline

Prototype funding was received in summer 2017, with a working app available by August 2017. Development has been ongoing since, with the NSF grant enabling collaboration with mathematics education researchers across the US.

Platform availability

Available free on Google Play and the Apple App Store. It uses a Google Cardboard headset (v1.0 or v2.0) and supports Bluetooth controllers. It is also available through Oculus Labs.

Content

The app contains over 30 lessons and demos covering topics including 3D coordinate systems (rectangular, cylindrical, spherical), graphs in 3D, lines and planes, quadric surfaces, parametric curves and surfaces, vector-valued functions, velocity, arc length, acceleration, and vector fields. Users can also specify their own objects for visualisation.

Classroom use

It has been used at SFA ahead of in-class sessions, with students working through geometrically intensive introductions before lectures. Instructors report improved use of class time, as students arrive with a grounding in the geometric concepts. Student feedback has been positive, with comments noting it was helpful for visualising what was happening in the mathematics.