So here's my idea. I pull out something that I have: something good, established, thoughtful. Maybe it's not even my own material, but I like it for its value in my classroom. And then I ask myself, "WHY?"

"Why is this piece of content important? Why does this lesson design seem good to me? Why should my students care about this?" etc.

So far the thought experiments have been eye-opening.

I looked at a unit on writing linear equations in slope intercept form. "Of course writing linear equations is important," I thought to myself. "If they can't write linear equations, then they won't be able to write quadratic, or exponential, or rational, or radical equations. It's the foundation of equation writing!"

Whoa. Who cares? Honestly, I hate to admit it, but I don't even care. Outside of math class, how often do even I find occasion to write and solve an equation? Sure: I'm pretty sure some engineers, or physicists or scientists of one sort or another write equations every day... but what about everyone else? After all, algebra is required for everyone! And so, it turns out, this is an excellent question for me: "Why ARE linear equations important?"

My thoughts eventually turned to recognizing and describing patterns. I notice something seems to be happening in the same way over and over again, so I predict it will happen that way again next time. But when I am able to generalize the pattern, I can not only predict what's next, but what will happen at ANY point in the future and that's powerful. And then my brain takes me a step further to the importance of communication. If I can take my generalized pattern and explain it to you, then we can both predict the future. And if the computations are tough, I can even communicate my pattern to a machine with no brain... as long as I speak in a language that it is programmed to recognize.

And suddenly my unit on writing linear equations in slope intercept form becomes a unit on predicting the future and building robots. And THAT'S something that interests me.

I've had other game-changing moments lately too:

- An assessment about coordinate geometry and triangle properties (how DO you rationalize incenter, orthocenter, circumcenter, and centroid?) became an end-cap to a unit about apprenticeship and tool mastery.
- An already rich unit on multiple solution methods got even richer when I refocused on presentation skills: a solution to a problem illustrates, generalizes, communicates, and verifies the results. An answer is just a number.
- And a simple lesson on using LCD to simplify rational equations became an integral part of a unit about elegance.

I love your math blog. I like reading articles which cause me to think. Hmmmm, all math is based on patterns. Isn't it wonderful?

ReplyDeleteThank you

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