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Smoothly Incorporating Maple into the Mathematics Classroom

Gregory A. Moore, Cerritos College, Norwalk, California
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Maple mathematics software is a powerful teaching partner to the mathematics instructor. Used imaginatively, Maple can help students learn better and faster, can illuminate theory, bring clarity to the abstract, and help prepare them for using mathematics technology that they will need throughout their lives.

With such a versatile tool, the challenge for the teacher is how to navigate the immense possibilities and channel the power of Maple into your teaching. With so many commands, so many options and so much flexibility, you might wonder where to start.

In what follows is a series of steps designed to make your transition as smooth and natural as possible. This plan is based on my first-hand experience and assumes you have no experience in Maple. At the end, you may be teaching specialized Maple courses… and enjoying yourself as never before.

Step 1. Get Acquainted
If you’re new to Maple, get acquainted with it. Have some fun and see what it can do. Learn how to type commands and get responses. The Maple Essentials Tutorial at http://www.MapleApps.com/tutorial.html will get you started on the basics of arithmetic computations, solving equations, simplifying expressions, defining and using functions and making graphs. Your own experimentation will be the basis of a comfortable familiarity.

Step 2. Classroom Demonstrations
When you’ve mastered some tasks, it’s time for a public performance using Maple. You can demonstrate in front of your class on a projection monitor, or just have students crowd around behind a computer monitor. Some simple demonstrations of what you have learned will suffice to awe students with the power at your fingertips. Later, you’ll want to demonstrate concepts that relate to the material you are teaching. For example, you might discuss how changing the parameters in a function affects its graph, and show both the original and the new version simultaneously on the same set of axes. Or show an animation of a graph’s tangent line rolling along the graph as the independent variable increases. There are endless possibilities.

You can also visit the Postsecondary Mathematics Education site at http://www.MapleApps.com/postsec.html for ready-made examples that I’ve created. They illustrate mathematical ideas using Maple, with a clear effort to demonstrate creative uses of the technology. Because they are simply Maple worksheets, you can alter them as you see fit.

As I crafted materials for demonstration, I found that I was gaining a deeper understanding of topics that I had been teaching for ten years. It was a personal joy to discover new nuances to even familiar topics.

Step 3. Create Student Projects
As your Maple demonstration worksheets become more detailed, the next step is to transform them into student projects.

This will work out best if you take the class into a computer lab and spend an hour with them. It’s important to have an experienced Maple person – you – there to assist with any little impediments to enlightenment. As you develop more materials, you can make this a regular part of the class, perhaps even an hour per week. In my experience, students enjoy this much more than sitting in class doing real’ work.

You don’t need to develop all of this from scratch. The worksheets available at http://www.MapleApps.com/postsec.html can be used as a starting point for many projects. Some of them are meaty enough to be split into several days worth of work and provide exercises.

The essential method is to write up an example with detailed explanations of the commands being used and then ask the students to report what they can deduce.

Then, ask them to go through the same procedure with other examples. In this way, they get exposure to a modern mathematical software package, while learning mathematical concepts. Learning through discovery and exploration has a greater impact than looking over someone’s shoulder.

Step 4. Attach a Laboratory Component to Math Classes
After a few semesters of practice, consider attaching a laboratory component to your math classes - much like a chemistry lab accompanies a chemistry lecture. It’s recognized in the sciences that theory and practical application must be intimately connected by way of lecture and lab. The same should apply to mathematics. For example, a one-unit “Maple For Calculus 1” could be used as the lab component for Calculus 1.

Step 5. Full Seamless Integration
The ultimate step in this evolving process is to integrate Maple fully into existing mathematics classes. Imagine a classroom with both computers and writing surfaces. Each day’s class would be a combination of traditional lecture and problem solving, along with examples using Maple demonstrated to the class, or worked out on individual workstations. The lessons of the day could be preloaded on a network, so students need only open the files and work through the instructions. In general, the use of software would be as natural and relevant as the use of pencil and paper.

I believe this is the future of all mathematics teaching. Many of us can still remember when a technical diagram in an engineering class or a spreadsheet in an accounting class meant reams of scratch paper with the help of a slide rule. Of course, computer software has become an integrated part of those tasks now, and the old ways of doing things seem ridiculously antiquated. The day will soon be upon us when mathematics will make a similar transformation -where the use of the technology is part and parcel of learning the subject matter. All of the tools are in place and remain only to be utilized by those on the cutting edge of modern teaching.

*Excerpt from "Integrating Maple into the Math Curriculum: A Sensible Guide for Educators, " by Gregory A. Moore, published by Maplesoft 2001.

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