Seeing is Believing : Using 3D Visualization to Strengthen Student Understanding

Guiding students in visualizing mathematical concepts is one of the most challenging aspects of teaching calculus. As such, professors continuously seek out technological tools to aid in these tasks. One tool that has become a staple for both instructors and students across the country is CalcPlot3D, a free online 3D graphics applet used for classroom demonstrations and interactive tasks. Our readers may recall that we chatted with Monica VanDieren back in March 2020 about research that investigated student usage of CalcPlot3D to design an updated version of the app. We recently spent some time with the creator or CalcPlot3D, Paul Seeburger of Monroe Community College, and two of his collaborators, Shelby Stanhope (U. S. Air Force Academy) and Deborah Moore-Russo (University of Oklahoma), who have been instrumental in making the app more broadly accessible and expanding its usefulness across disciplines.

Paul, can you tell us what inspired you to create CalcPlot3D?

Back in 2003 I was using Visual Basic to play around with visualizations of implicit equations and realized I could use the same type of imagery to easily explore and demonstrate spatial concepts in Calculus III. So I first developed CalcPlot3D in Visual Basic, but later recognized that I couldn’t share it across a broad range of devices. Using NSF funding (#0736968) our team converted it to a Java applet in 2008 and expanded its features to allow 3D printing in 2010. Additional NSF funding has allowed us to continue updating and revising CalcPlot3D to expand accessibility, enhance 3D printing applications, and study its impact on student learning experiences.

Shelby, could you describe some of the specific benefits of using CalcPlot3D in courses to not only mathematics students, but also undergraduate mathematics programs?

What makes CalcPlot3D so special is that it was designed to be an exploration environment with built-in features to visualize many concepts in multivariable calculus. All the standard topics covered in multivariable calculus courses nationwide are represented by features which allow the user to simply click a checkbox or slider to visualize concepts. For example, viewing Riemann prisms that estimate volumes requires only a few clicks which result in a powerful demonstration of how the number of prisms can change the estimate.

In end-of-semester surveys my students report that the CalcPlot3D visualizations are not only helpful but enjoyable. It encouraged students here at the U.S. Air Force Academy to take the course, whereas in previous semesters they shied away from the program due to the reputation of its technological challenges. Ultimately, the classroom demonstrations, ease of individual student use, and 3D printing activities resulted in a 9% drop in withdrawals, 3% drop in the failure rate, and an astounding 20% increase in course enrollment.

Outside of multivariable calculus, what are some other areas of mathematics or STEM fields that CalcPlot3D has been or can be used to amplify?

Within mathematics, we’ve found that CalcPlot3D can be used to highlight a wide range of concepts from linear algebra to topology to complex variables. Beyond that, professors have utilized our tool to develop projects in physics, engineering, and chemistry. For example, CalcPlot3D has been used to create an interactive periodic table with graphics that represent the electron orbital structures of atoms. In general, any field that requires 3D visualization can make use of CalcPlot3D. In fact, our latest NSF project proposal outlines a plan to expand the application to better support variable topics in physics and engineering like vector theorems, flux, and Gauss's Law.

Deb, can you share ways in which CalcPlot3D and its related projects promote professional development on college and university campuses?

Besides the obvious uses in classrooms that have adopted CalcPlot3D as an instructional tool, even our tutors here at the University of Oklahoma incorporate the tool into their study sessions. So, we see how the app enhances the effectiveness of everyone put in place to support student learning. Additionally, our team has conducted MAA Open Math workshops over the last two summers. These workshops allowed professors to receive virtual training on how to implement CalcPlot3D into their classrooms. Looking ahead, those interested in learning more about CalcPlot3D can sign up for our Professional Enhancement Program that will take place during the Joint Mathematics Meetings in January 2025. On our website you can also find a wide range of resources for engaging students in dynamic visualizations, guided explorations, 3-D printing projects, and much more.

Author’s Note:

If you would like to know more about this NSF Project, Taking CalcPlot3D to the Next Dimension: Creating 3D Printed Learning Materials (#2121152, 2121133, 2120660), contact Paul Seeburger at Monroe Community College (pseeburger@monroecc.edu).

Jana Talley is a Co-Editor of DUE Point and an associate professor in the Department of Mathematics and Statistical Sciences at Jackson State University.