Improving Introductory Calculus Education with 3-D Visualizationand Virtual Touch (Haptics)

Despite advances in 3-D computer graphics, students in introductory calculus classes still learn mainly by working with equations and the occasional 2-D diagram. When moving to more complex levels of calculations, we observed a need for aiding the students´ understanding via 3-D visualization, but without the use of powerful, yet complicated, professional math software. In this paper, we will discuss some of the issues that early college students have visualizing 3-D mathematical shapes and graphs in their minds and what the use of 3-D computer graphics and the simulation of touch (computer haptics) can do to help. We are working on a simple and intuitive application that enables a student to enter a mathematical equation and to see and touch its shape in 3-D. This combined view/touch approach may lead students in introductory calculus classes to a better understanding of complex mathematical equations; a study testing this hypothesis is planned for the fall. Further applications using this technology could be adapted to teach visually impaired students about calculus and about 3-D shapes in general.