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Visualizing Change

Calculus Activities for The Geometer's Sketchpad[1]

NCTM National Conference, Washington DC, April 1998

by Scott Steketee ssteketee@keypress.com
& Nicholas Jackiw njackiw@keypress.com

Key Curriculum Press

Introduction

Calculus—the mathematical study of change—is best taught in a way that reflects its dynamic character. This is not easy to do with traditional materials, though some newer textbooks, which take advantage of dynamic technology resources (especially graphing calculators), have begun to change classroom approaches to calculus significantly[2]. For many topics, the larger screen size and greater power of a computer can make possible more effective and compelling calculus activities, but relatively little work has been done thus far in developing and publishing such activities.

Since many calculus topics can effectively be visualized using geometry or analytic geometry, it's not surprising that dynamic geometry computer software such as The Geometer's Sketchpad can be a powerful aid in teaching calculus. The activities included here use Sketchpad to investigate a number of such topics. They are only a sample of what could be done; many other calculus topics can be taught effectively using similar dynamic activities.

These activities and the sketches they are based on are work in progress. You are welcome to use both the sketches and activities with your own classes, but please do not reprint or distribute them without permission. On the Sidebar you can download the Sketchpad files that go with these activities.

Some of the sketches included with these activities are constructed to be quite flexible, allowing you to vary parameters to change the function being investigated, and containing action buttons that enable various kinds of automatic manipulation. On occasion they may be too flexible for your purposes in getting across a particular point to your students. If so, you can easily remove unwanted functionality from a sketch. For instance, you can hide a slider so students can't change the parameters that define a function, you can hide (or remove) an action button to prevent students from performing an animation, or you can add your own Hide and Show action buttons to draw attention to particular features.

We solicit your comments and suggestions. And we'd also love to see any calculus sketches and activities you create!

Table of Contents

[1] Portions of the work described in this paper were funded under National Science Foundation grant DMI-9623018.
[2] We're particularly indebted to Paul A. Foerster's Calculus: Concepts and Applications (1998, Key Curriculum Press), which inspired several of the activities in this presentation.