Mathematical Animations as a Medium for Teaching and Learning Mathematics

Abstract

DESCRIPTION AND THE ACTIVITIES:
We will discuss the role of mathematical animation in teaching and learning mathematics. We will use the computer algebra system Mathematica to create our animations. However, no prior experience of Mathematica is assumed from the participants. The following items are covered.

1. Introduction:
We will start with a brief overview on the general computer algebra systems and its impact on the teaching and learning of mathematics. In particular, we will make some introductory remarks on Mathematica.

2. Arithmetic and Algebra with Mathematica:
Before creating animations, we must first illustrate the basic syntax of Mathematica by performing some arithmetical and algebraic calculations. Among the items we cover include exponentiation, square roots, absolute values, approximations, factoring and expanding algebraic expressions, solving equations, functional notation, and lists.

3. Two and Three Dimensional Graphing:
This is probably the main Mathematica ingredient one needs to understand in order to create animations. Starting with graphing a simple function, we will discuss several aspects of graphing. Among them include the plot options, such as "PlotStyle", "AspectRatio", "Axes", "AxesLabel", "Frame", "PlotLabel" etc. We will also discuss three dimensional graphing.

4. Animations and Simulations
First, we will explain the essential mathematical idea behind a simple animation. The simplest animations are created by changing a single parameter. We will then create many animations covering different areas of mathematics such as, college algebra, precalculus, calculus, linear algebra, and applied mathematics. Special emphasis is placed on locus problems in coordinate geometry, and generation of classical Greek curves such as cycloid and astroid. We will discuss the role of animations in mathematics instruction and research. Some of our animations will lead into nice mathematical conjectures! The audience will get a chance of enjoying themselves by making their own two and three dimensional animations, and some simple Mathematica movies. We will also explain how to generate sounds within Mathematica and to integrate with motion.

EQUIPMENT NEEDED: I need Windows compatible computers with Mathematica 3.0 for myself and for the participants. I also need an overhead projector for the transparencies and a video projector for the computer. Also needed are a CD-ROM drive and sound output with a speaker system.

REFERENCES: de Alwis, T. (1993). Effective Use of Mathematica – Pattern Recognition, Conjecture Making and Simulations. Proceedings of the International Conference on Technology in Mathematics Teaching, University of Birmingham, UK.
Gray, T. and Glynn, J. (1991). Exploring Mathematics with Mathematica. Redwood City, CA: Addison Wesley.
Wolfram, S. (1996). Mathematica Book, 3rd ed. Cambridge, UK: Cambridge University Press.