Teaching the Computer to Save You Time

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Teaching the Computer to Save You Time

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I just talked with a math department head who said her school couldn’t fit any programming into her already full math curriculum. “We’re strapped for time just to get to everything in our current curriculum,” she said. I would suggest that far from being one more thing to add to the pile of things you have to teach in a year, programming would actually reduce the workload and free up time for deeper exploration of topics. Let me give you an example.

A big idea in algebra (and programming) is functions. You put a number in to a function (the input, x) and you get a number out (output, y). In math notation

y = f(x)

There’s a time in algebra when they stop using y and just use f(x), and it’s never explained why. For example, if the function is “multiply the input by two and add 5,” the function looks like this:

f(x) = 2x + 5

So if your input is 3, your output is

f(3) = 2(3) + 5 = 6 + 5 = 11

That’s not so hard to do by hand, but pretty soon you start dealing with quadratics and cubics and higher. This is from an Algebra textbook:

The problems above want you to replace x in the function with the number in the parentheses and go through the arithmetic to find the output. You’re expected to do this with a calculator, but if you need to input another number, you have to go through it all again! This can be done more effectively with Python. For example, the function in problem #4 translates to

The applet above is interactive! When you press the “Run” button (it looks like an arrow) Python will instantly evaluate the function for x = -7 and print the output (5) in the window on the right. You can evaluate the function for any number by typing a different number in the parentheses.

In problems involving compound interest, falling objects and cost of materials, it’s the answer we’re interested in, and not the student’s ability to evaluate ugly functions like this by hand. Press the Run button and you’ll see the answer.

In math class variables are all named with single letters, and it can get confusing. In programming it’s possible (and advisable) to use more descriptive variable names, like this:

Now you can understand the formula just by reading it, and it proves the student understands what’s going on in the function. Run it to solve problem #4 above.

Using programming tests your knowledge of a topic because you have to teach the computer how to solve a problem! It also tests your ability to be precise and it frees up a lot of time which students would otherwise spend evaluating the same functions over and over. That way they can get deeper into math topics.

In the future, I’ll show you some math topics you can’t get into without a computer, like big data and fractals!

-Peter Farrell
September 6, 2016

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