By: Audrey Malagon, Lead Editor of DUE Point

The  CalcPlot3D graphing applet has been changing the way students interact with multivariable calculus. In this project, Monica VanDieren of Robert Morris University tells us how she and Deborah Moore-Russo (University of Buffalo) joined with CalcPlot3D creator Paul Seeburger (Monroe Community College) to study impacts on student learning, make research-based improvements to the technology, and design classroom activities using this graphing program. 

Tell us how this project came to be, and what you think set your proposal apart for competitive NSF funding.
I had been using the CalcPlot3D applet for years in my multivariable calculus class, and I developed several learning activities which I shared with Paul Seeburger. Eventually, communication turned to collaboration and we asked Deb Moore-Russo, an expert in pedagogical research, to join us.  Through an AWM Mentor Grant, Deb gave me a crash course on mathematics education research. We analyzed some of Paul’s data on student work in CalcPlot3D, which gave us a good foundation to apply for a grant together. It certainly helped that our project was based on a proven and mature learning tool and that the three of us had a track record of synergistic collaboration, with distinct areas of expertise. When finished, our work would widely impact not only teaching and learning of multivariable calculus but also research on student understanding.

How has your work impacted student learning along with improving the applet?
We knew we needed to update to JavaScript so the applet would be accessible on more devices. In addition to updating the code, we took the opportunity to incorporate research-based pedagogical changes.  Deb and I identified trends in student learning by applying variation theory to a qualitative analysis of over 300 students' responses on CalcPlot3D activities. For instance, in the original version of the applet, the cross product activity allowed students to manipulate a red and blue vector in the xy-plane and see the cross product graphed automatically.  In the update, we added the opposite cross product to emphasize non-commutativity of the operation.

One of CalcPlot 3D’s purposes is to allow students to explore and discover geometric relationships in multivariable calculus, so we developed classroom activities and assignments to support these features. For example, the 3D-printing feature of CalcPlot3D enables instructors to print 3D models of surfaces to bring to the classroom for students to tangibly engage with multivariable calculus concepts.

We also developed a vector concept inventory for multivariable calculus which can be used to study student learning not only with regard to this project but in many other contexts.  College faculty and high school teachers have begun to use CalcPlot3D in their classrooms not just for multivariable calculus, but also in differential equations and even chemistry!

What have you personally learned so far in this project? 

I have been exposed to several issues facing undergraduate mathematics education, especially at the MAA SIGMAA on RUME conferences where we have presented our work.  As a result of being more engaged with the mathematics education research, I am a more self-reflective teacher and introduce more evidence-based practices into my work. For example, I am more aware of the importance of culturally responsive pedagogy and the impact that small decisions we make in the classroom can have on marginalized groups. 

Tell us about someone impacted by the project.

Shelby Stanhope is an Assistant Professor in the Department of Mathematical Sciences at the US Air Force Academy who shared that CalcPlot3D has transformed the way she teaches multivariable calculus. She says, “When I was first introduced to the applet, the most exciting aspect that drew me in was the user-friendly and self-explanatory set up. After just a few minutes of clicking through and exploring its capabilities, I was able to recreate a demonstration that animates vector functions, which had previously taken me an entire afternoon to create using another visualization software. During class, I use CalcPlot3D to provide my students with visualizations that can be animated and rotated, to build their visual intuition and conceptual understanding of the material.”  She is excited about the exploration activities developed by this grant and is looking forward to introducing them in her courses. 

Learn more about NSF DUE 1523786 

Full Project Name: Improving Conceptual Understanding of Multivariable Calculus Through Visualization Using CalcPlot3D

Abstract: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1523786

Project Contact: Monica VanDieren, vandieren@rmu.edu 

*Responses in this blog were edited for length and clarity.

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 financial support of NSF DUE Grant #1626337.

Audrey Malagon is lead editor of DUE Point and a Batten Associate Professor of Mathematics at Virginia Wesleyan University with research interests in inquiry based and active learning, election security, and Lie algebras. Find her on Twitter @malagonmath.