By Katie Haymaker, Co-editor of DUE Point

The use of smartphones during class is commonly a source of exasperation for instructors, but not for Nick Long and Jeremy Becnel, of Stephen F. Austin State University. They created a smartphone app that brings virtual reality visualization tools within reach for students in multivariable calculus. The Calculus and Virtual Reality (CalcVR) Project focuses on the development of interactive calculus lessons in the app, and Nick and Jeremy describe the project in the following Q&A.   

What is the Calculus and Virtual Reality Project? 

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 (like CalcPlot3D) to help students understand these multivariable objects, the rendering is still a two-dimensional picture of a three-dimensional object. In order to show these objects with visual depth, we created a virtual reality app that is available for free on smartphones (Android or iPhone) and requires less than $5 in additional hardware costs for students. We have created interactive lessons and demos 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.

What was the process of bringing this from an initial idea to a funded NSF proposal?

In summer 2017, we received funding from the Provost’s Office of Stephen F. Austin State University (SFA) to build a prototype of the CalcVR app. By August 2017, we had a working app with several lessons and a couple of demos available through the app stores. At this point, we sought out funding from the NSF and began collaboration with faculty across the country involved in undergraduate mathematics education research.

How have students been impacted by the project? 

We have run several classes here at SFA with students using the app to examine a geometrically intensive introduction to material before in-class discussions. Most students find the app helpful and the use of in-class time is improved as students come in with an understanding of the geometric notions and the instructor can then more effectively connect ideas between algebra and geometry. Student feedback has included:

”The VR stuff was helpful for visualizing what is happening.”

“It’s an interesting app. I would love to build a structure in VR.”

What resources are available for multivariable calculus instructors who want to incorporate virtual reality tools in their classes? 

The CalcVR app is free and can be found on the Google Play or Apple app stores. With over 30 lessons and demos available now, we are shifting our efforts to create more explorations and activities to complement the app. We hope to build a community of users who can contribute content and related materials in the near future.

What advice would you give to someone applying for an NSF DUE grant for the first time?

Finding collaborators who can make your project better is difficult and time consuming but absolutely worth it, so keep reaching out to communities that have something to add to your project.  Make sure to utilize your grants/research office and the NSF program officers. You should think about what makes your project special and expand on that aspect. Don’t be afraid to bring people onboard who can help. As mathematicians, we have benefited greatly from bringing in math education researchers and an advisory board of experienced people who have worked on similar projects.

Describe any upcoming developments for the Calculus in Virtual Reality Project.

We recently added new lessons and demos involving multivariable functions and vector fields and have plans for several additional areas of content. Based on feedback from a recent advisory board meeting, we will incorporate enhancements and improvements to the app. The creation and improvement of activities and explorations that complement the app will be a focus in the next year. We are currently testing an exploration into quadric surfaces using a demo in the app. 

Click this link for a video demo of the app with activities including spherical coordinates, vector-valued functions, curves and surfaces, and more.
Learn more about NSF DUE 1820724

Full Project Name: Calculus and Virtual Reality (CalcVR) 

Abstract: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1820724

Project Website: https://calcvr.org

Project Contact: Nicholas Long, longne@sfasu.edu (PI) 

For more information on any of these programs, follow the links, and follow these blog posts. This blog is a project of the Mathematical Association of America, produced with the financial support of NSF DUE Grant #1626337.
*Responses in this blog were edited for length and clarity.

Katie Haymaker is a co-editor of DUE Point and an Assistant Professor of Mathematics at Villanova, where her research interests include coding theory and mastery-based testing in undergraduate mathematics courses.