Friday, April 18, 2008

Doing Algebra

I’m doing quite a bit of algebra these days, helping our young mathematician solve homework problems. I last took algebra from Mr. Webb way back in the year 19-mumble-mumble, when President Nixon was still lovingly adding names to his enemies list. My strongest memory from Mr. Webb’s class was that he never learned his students’ names.  He called everyone Babe. No matter who you were, he’d say, “Babe, put the next problem on the board. Thanks, Babe.” But he must have been a pretty good teacher, because after a quick refresher I can solve a basic problem.  And so for the moment I still have a role to play in our teen’s life.

That role is called factoring. You know: through factoring, 4x + 4 becomes 4 times (x + 1).  This week I relearned how to factor the difference of two squares: x² - 16y², that sort of thing. Silly me, I thought the difference of two squares surely must be the traits that allow a person to distinguish one math teacher from another. Now you may wonder if I was one of those kids in the back row who asked Mr. Webb why algebra was worth learning. Well, I’m not going to tell you. I will admit that a “why is this worth learning” gene has been passed on to the next generation of our little clan.

Anyway, as we work on algebra, a pattern emerges. I check the work and sometimes I say, this solution has an error.  Maybe our scholar doesn’t see it, and points to a similar solution in the class notes, and starts simmering.  A little steam rises from the stylish young hair style. Explain the steps to me, I say. More pointing. Tell me how it’s supposed to work, I say. Don’t give up.

Pretty soon the sheet is covered with x to the 2nds and y’s to the 4th and eraser crumbs. Each correction floats up out of the smudge of previous work.  I start to pity the weary eyes of the math teacher.  Maybe Mr. Webb called us all Babe because our homework had made him blind.

Eventually, if neither of us surrenders, we have the basic method in place, something you could memorize if you don’t mind not really knowing what you’re doing.  Now, I say, tell me why this method works.  More steam, more pointing, perhaps, but we talk through the reason, and then we have a method that we both understand.  The next few problems solidify what we’ve learned.

Then the textbook switches to a new kind of problem, and we’re back to the eraser crumbs and smudges. Explain how it works, I say. Explain why. And we pick up speed.  While my offspring learns algebra, I’m constructing an obvious little theory about learning. I see learning as a progression from rote memory to knowing how and onto knowing why, with the real power accumulating fast in the last stage, when you know why.  That’s cool, as we used to say in Nixon’s day, when we weren’t busy questioning authority.

I saw in the New York Times that an ancient Greek technical manuscript was recently translated, and there, scrawled like graffiti in the margin of the text, was the same question young people are still asking today: “Why is this worth learning?” Is there a good answer to that question?  Most people would probably say that you take algebra in order to go to college and get yourself a place in the middle class.  For some people, it’s a step toward a math-oriented career. Some people find mathematics beautiful. Thanks to my recent experience, I have a new answer to the age-old question. Why is algebra worth learning?  So that later on you can help your own kids learn algebra, and eventually they’ll do the same for their kids. It’s the great cycle of life.

Broadcast by Ken Smith on April 18, 2008
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