So this is one of the week 3 Blogger Initiation prompts and at first I shied away from it because Steve’s post was so good, my post would be lame compared to it. However, I do think it is important for me to reflect on, and as no other prompt really caught my attention, I figured I’d try to refine my own answer to this question. It is especially important for me to think about it because the one math class I teach is Precalculus–often the final class required in many a student’s math career, and yet, as another of the prompts put it, a “hodgepodge of ideas”.

So why do we learn math? The answer I often give to students is that math exercises the brain, much as playing any sport exercises the body. Being able to use logic is a skill that takes time and the more you work at math, the more your brain will be able to work in other, seemingly unrelated areas of life.

“But I just don’t see how it relates to real life.” When I was younger I would have “soccer practices” where we would not touch a soccer ball, but we would simply run. We’d run laps, we’d wind-sprints, we’d run up and down hills. We might have complained, but we continued to run. Why? Because we knew that even though we weren’t working with a soccer ball, we were improving our soccer game and our ability to play and win through conditioning. Math is analogous to running without a soccer ball. Even though math doesn’t *look* like solving problems in the “real world” (whatever that is), it helps work and expand our mind so that we can more readily see answers and solutions when we come to a situation outside of the math classroom.

However, there is a very big assumption behind this answer. One that I did not realize I made until I started reading blogs and thinking about the way I teach. The assumption is that math teachers are teaching students to be *problem solvers*, not just memorizers of formulas or “plug and chug” machines. Yes, you must learn many formulas as a math student, but all of my classrooms were of the “lecture->practice” format, and there were very few (if any) open-ended problems, which really teach students to *think*. One of my personal goals this year is to get my math class to match the answer I give to the above question by teaching students to learn (I’ll work on doing this in Chemistry next year…). And I’m not sure it’s going to come from me categorizing problem-solving strategies and making them memorize those categories: it’s going to come from them learning how to solve problems with *limited* help from me. So wish me luck!

One of my answers to The Question is much like the one you describe here, and your soccer practice analogy is better than any I’ve come up with so–ta da!–consider it adopted. (Soccer also happens to be my favorite sport, though I know very little about the professionals, so don’t ask. My daughter and I play on recreational teams, and my son is just starting to play HS soccer–he’s a freshman this year.)

As for your last paragraph, I am on the same quest this year in my Geometry classes. I want my students to be problem solvers, and experimenters, and justifiers. No more just filling their empty brains with knowledge (though I may still joke about that). “Be less helpful,” as Dan Meyer says.

Good luck to both of us on that!

I like that: “Be less helpful.” I used to believe (before I started teaching) that I could explain all of math so well that all my students would be able to understand everything clearly, but I’m starting to realize that a “good explainer” and a “good teacher” are very different things.

Oh, I totally hear you about thinking a crystal clear explanation is all you need. I started out with the same frame of mind. At this point, “I taught it; you just didn’t learn it” no longer sounds acceptable.