Exploring Calculus Using Innovative Technology

For the past decade, our Mac-only software package, TEMATH, has been available as a free download from our web site www2.umassd.edu/TEMATH Over the past few years, we have been converting this software package to one that runs on computers with Macintosh OS X, Linux, or current versions of Microsoft Win-dows/NT/XP operating systems that have a Java JVM 1.4.2 (or later installed). We have integrated into the software a robust set of visualization tools, modeling tools, demon-stration tools, numerical tools, and graphical tools. These tools have been class tested in both our single-variable and multivariable calculus classes. The goals of the software are to: • Enhance the teaching and learning of calculus, • Make it easier for teachers to do real applied mathematics in the classroom, • Make mathematics enjoyable for all students, • Increase the active participation of students in the class, • Provide a visual environment for the presentation of mathematical concepts, • Give teachers an easy-to-use set of tools for demonstrating the theorems of calculus, • Include a friendly interface for importing digital images and movies that can be used for generating data which will be modeled by students, and • Allow students to easily model everyday physical phenomenon. Our software gives the instructor another set of technological tools that can be used in the classroom to improve the presentation of calculus. The software is free to all and the new version will be available for download from our web site this summer. We teach calculus as part of the IMPULSE first-year engineering program at UMass Dartmouth. In this program, all classes (Engineering, Physics, and Calculus) are taught in an active learning environment where students work together in teams. A typical class consists of about 40-48 engineering students working in 10-12 teams of four students each. Each team sits at a large table with two computers and each class period is two hours long. Since we teach in the same room as physics and engineering, we have a vari-ety of equipment available to us for performing experiments. Below, we present a set of calculus examples that demonstrate some of the features of TEMATH