UB Graduate School of Education helps students visualize complex calculus concepts

When students begin to study calculus, equations and their graphs are mostly drawn on a “flat” plane. It’s when students proceed to advanced calculus that they find paper and pencil inadequate.

A new project by UB's Graduate School of Education sets out to change that. Instead of students having to learn three-dimensional concepts by memorizing formulas, it uses a dynamic digital resource that plots graphs in a three-dimensional plane, allowing students to look at these underlying principles in a way that better represents the properties and relationships represented in the formulas.

“In short, this project looks to change Calculus III from a course where many students blindly memorize formulas to a course where students are able to ‘see’ the mathematics,” says Deborah Moore-Russo, program director for mathematics education and online gifted education and the director of UB’s Gifted Math Program.

“As a result, they are able to work flexibly with equations, tables and graphs. In short, they have a deeper understanding.”

The project, funded by the National Science Foundation (NSF), is a multi-institutional effort involving UB, Monroe Community College and Robert Morris University in Pittsburgh. UB’s portion is $75,500, Moore-Russo says, with funding starting in September 2015 and ending in August 2018.

The project will look at how images from a digital resource called the 3D Calc Plotter can help calculus students visualize mathematical relationships in three dimensions.

“We have data that has been collected online on how students have used this digital resource, which was created with a previous NSF grant,” says Moore-Russo.

Researchers will analyze data gathered during the study to refine the 3D Calc Plotter and make it more useful for Calculus III students, she says.

“So we are taking a commonly used resource – one that is used across campuses in numerous states already – and making it even better suited to Calculus III students' needs,” says Moore-Russo.

Although the 3D Calc Plotter currently is designed for use with computers, researchers will adapt the digital resource to make sure it is compatible on other platforms so that students can use it easily on handheld devices, such as iPads, tablets and smartphones, she says.

“The grant is important because it is paying for the time and effort to go through rather large amounts of online data,” says Moore-Russo. “It also will refine the 3D Calc Plotter resource, pilot the refined 3D Calc Plotter with a study group to iron out any kinks and then update the computer version of the 3D Calc Plotter.

“Finally, the program will create a version of the 3D Calc Plotter that works on handheld devices."