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Some of my best friends are math teachers. And in the beginning, computers in schools were the province of the math department. They were, after all, devices for computing, which is what math teachers do. Math teachers were always in the lead with computing in our schools. I was a social studies teacher in the early days of computers, and never did much with math. But recent encounters with math teachers and computers have led to this week's article.

In helping a school of engineering to put their teaching program online, I have enjoyed to opportunity to work with teachers who use mathematics every day in their work, a high level of math of a type I never expected my sixth-graders to learn, and that seldom confronts a professor of communication. Integrals, sums, sinusoidal functions and fast Fourier transforms find their way into the everyday speech of these teachers. Through my work with them, I have found that while the rest of us in the humanities have all become computer users over the last two decades, the math teachers have maintained their lead. They use computers in ways that go far beyond what the rest of us do.

The tools they use

They've come a long way from paper, pencil, chalk, and blackboard. The math teachers, the engineers, and the mathematicians that I see do much of their work on the computer. There's a computer on their desk, and one in the classroom. More often than not, it's the same one, a laptop that they take with them wherever they go. And the software I see them using includes:

Animation. The sine function seemed to draw itself across the x and y axes, like a wave swooping up and down in a smooth continuous motion. But now the wave is sampled into a series of discontinuous dots, thus teaching an important concept in signal processing. The teacher built this animation in Flash to help him teach students a difficult but basic idea in a memorable way. The animation proved the concept in ways that would have been impossible on the pages of a textbook or on the chalkboard.

Simulation. The same teacher wanted to go farther, and let his students change certain factors such as the frequency of the sine function or the rate of sampling, and see the results for themselves. So he modified the animation to turn it into a simulation that allowed students to test the concept interactively. This too was built with Flash, but here he needed a Flash programmer -- one of his students -- to help him with the scripting. Going deeper, this teacher then assigned his students to use MatLab -- which can simulate just about any mathematical process on the computer screen -- to explore the concept in more detail.

Equations. Math people use equations to tell their stories. While the rest of us use words made up of the 26 letters on the keyboard, the mathematicians use equations made up of strange symbols that you will be hard-pressed to find on your keyboard. Seldom do they write these equations with pencil on paper -- I see them instead composing the equations for their students' homework problem sets with Microsoft Word, using Word's Equation Editor to enter their favorite math symbols carefully organized on the page to tell the story. (For more information on how to do that see the article in this series called Math Equations in Word and PowerPoint.) And apparently the more dedicated among them use a more powerful equation-writer called MathType.

Calculators. Yes, they still use the computer to compute, but ever since mathematics moved beyond arithmetic their calculations became more than mere numbers and sums. They enter an equation and see it calculated and graphed in an instant. They change a variable and see the display of the function move on the display. They cut, copy, paste, print, and email the results of the calculations. The graphing calculator, all the rage in the high school math classroom a few years ago, has given way to the personal computer with built-in calculation software that's more powerful and flexible.

Spreadsheets. When they do work with numbers and quantities and statistical data, I see them using as their tool of choice the lowly spreadsheet. The same copy of Microsoft Excel that came with your computer is used by the math mavens to organize information, numbers, names, data, anything they can enter into the cells. And then to work with the data: apply formulas to it, add, subtract, sum, and compare it, and graph it. I've even seen math lessons built on the spreadsheet, for students of all ages.

Presentation. Another tool form the Microsoft Office suite, PowerPoint, shows up on their math desks and in their classrooms. I see the engineers prepare their lectures not for the chalkboard but for the projector, delivered as PowerPoint slide shows. With the same equations, beautifully scaled and presented and visible across the classroom. With text that explains the math. And with graphs copied from the calculator to illustrate the concepts. The PowerPoint file ends up on the Web, where students may access it from anywhere, at any time.

Where did they learn all this? Not from their own math teachers, in most cases. They went to the Web, to places like the Math Forum at http://mathforum.org. And when they want to help their students learn, they send them to the Web also, to programs like MathXL at http://www.mathxl.com/support/features.htm, that provide tutorials and tools for learning math with these new-fashioned tools.

You may not be a math teacher, but your field most likely has developed some new tools of the trade over the last few years, based on the personal computer. How do you learn about them? How do you learn to use them? How do you bring them into the act of teaching?

Today's tools, yesterday's teaching

What do these new tools portend for the future? When all the math teachers and all the math students bring these computers into the classroom, what will it look like? How will the environment change? How will teaching be different? "I'm not sure I like it," remarked a math teacher sitting in his office. "They'll be paying attention to what's on their computer rather than looking at me. I'm afraid I'll lose control of their train of thought. I think I'll stick to paper and pencil and chalk in the classroom."

If this teacher's view results in a banning of the new tools from the math classroom, we will see a disconnect between the tools of math used in labs and on the desks of real mathematicians, and those used for teaching in the classroom. Will this be good for our students?