Using Dynamic Calculus Software to Visualize the Fundamentals of Calculus

Abstract

Dynamic visualization can greatly enhance student understanding of the fundamental topics of calculus: limits and continuity, derivatives, antiderivatives, and definite integrals. Visual images help students construct deep and intuitive representations, and dynamic images are essential when visualizing a branch of mathematics that can be described as "the mathematics of change." When dynamic visualization is combined with hands-on investigation by the student using appropriate computer technology, the results are significantly deeper understanding and greater retention. For maximum benefit, the hands-on investigation should offer students an opportunity to create, observe, and report on the dynamic visualization, and should also challenge students to make and test their own conjectures and to explore open-ended questions related to the topic. This presentation describes the use of one dynamic visualization tool (The Geometer's Sketchpad Version 4) to shed light on the fundamental topics of calculus by means of such hands-on student exploration. Specific student activities will be presented to introduce several of these topics. The student handouts and sketches actually used in the presentation, and similar materials for several additional activities, will be made available to those who attend the presentation.