Visualizing Three-Dimensional Calculus Concepts: The Study of a Manipulative's Effectiveness

Abstract

With the help of the National Science Foundation, the Department of Mathematics at the University of Puerto Rico in Mayaguez has developed a set of manipulatives to help students of science and engineering visualize concepts relating to points, surfaces, curves, contours, and vectors in three dimensions. This article will present the manipulatives that have been developed, describe how they have been used in multivariable calculus classes, and provide the results of initial studies on their effectiveness.

Keywords:

• Visualization
• multivariable calculus
• visual aids
• curves
• surfaces
• vectors
• parametric curves

ACKNOWLEDGMENT

The material in this article is based upon work supported by the National Science Foundation (NSF) under Grant NSF-DUE 0442365. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.