3D Printed Manipulatives in a Multivariable Calculus Classroom

Abstract

As three-dimensional (3D) printing technology is fast becoming more affordable and accessible, calculus instructors can now consider using 3D printing and 3D printed models to actively engage students in core concepts relating to objects in ${\mathbb{R}}^3$. This article describes three lessons for a multivariable calculus class in which students interact with 3D models to learn concepts relating to surfaces, solids, and multivariable functions. With each lesson are discussions and examples of student work based on the author’s experience. Finally, the article includes a brief section on practical considerations for mathematics instructors thinking of using 3D printing technology in their classrooms.

KEYWORDS:

• Multivariable calculus
• 3D printing
• manipulatives
• inquiry-based learning

ACKNOWLEDGEMENTS

The author wishes to thank Bill Jacob and Monica Mendoza for their suggestions, particularly on the structure of the lesson on solid regions and volume.

Additional information

Funding

The purchase of the 3D printer and printing materials used in developing and executing the lessons presented here was supported by funds from the Honors Program in Letters and Sciences at UC Santa Barbara.

Notes on contributors

Stepan Paul

Stepan Paul is a preceptor at Harvard University. He earned a Ph.D. in mathematics in 2013 from University of California, Santa Barbara, specializing in algebraic geometry and commutative algebra. More recently, he has focused his efforts on the scholarship of teaching and learning at the undergraduate level. When he is not doing math, Stepan can often be found running on some trail, cycling on some road, or swimming in some ocean.