Thursday, December 1, 2011

The only answer to the Eternal (student) Question

Now that it's December, I am well into the parts of my mathematics classes that become challenging for my students. For example, in my algebra 2 class, I am teaching them about rules for exponents and the like (e.g., x^a * x^b = x^(a + b)). This joyful experience comes on the heels of an entire chapter on functions, including recursive functions, and is where I recently was asked the inevitable (and annual) questions:

What good is this stuff for?  When are we ever going to use this?

Now, every person who has ever written a blog on teaching has a post somewhere in their writings about this very question. English teachers who lament the question "Why are we reading Shakespeare?". History teachers who are driven mad by "What does the 30 Years' War have to do with us?". And on and on.

The contents of these posts usually fall into one of several categories:
  • The "these kids today..." post. If the kids would just shut up and eat their broccoli, they'd appreciate it later, like we (teachers) did.
  • The "I want to change things, but my administration/parents/board of trustees won't let me" post. Self-explanatory.
  • The "I don't have a good answer for the kid, so what do I tell them?" post. Searching for answers to questions they should already know the answers to.
  • The "Why don't the kids understand that we don't know what the future will bring, so we need them to know everything (about my subject)?" This is a variant on the first category, and while it has the value of being ostensibly in the kids' best interest, it's still, in my opinion, weak - since no one knows the future, how can we say that the particular combination of things that we teach kids is the optimal one for the future? In fact, can't we argue that what we do ISN'T optimal?
Occasionally, and more interestingly, I see the following:
  • The "I teach this because 100+ years ago people thought it was a good idea, and it was, but it isn't so much any more" post (see: Descartes' Rule of Signs, for example)
The mathematics curriculum in the USA has not changed overmuch in the preceding ninety or so years (-ish). This paper provides a brief summary of the debates and discussions that have gone on since the beginning of the 20th century, and the history of these debates illustrates that, truly, there is little to nothing new under the sun. There has been a constant tension between "practicality" and "theory", there has been debate over who should take algebra (everyone vs. "the elite"), etc.

My reaction to the Eternal Question (when are we ever...) is different from all of these, I hope. Because I think all of the other possible reactions, in their own ways, have value, but I also think they are considering the question from an obsolete viewpoint.  But I'll begin by giving the answer that I hope I will have the courage to completely express someday....

The answer, and the only honest answer, that you can give a student who asks you that big question after facing something mathematical and abstract that they really struggle with, and when you know that they are asking it honestly and from the depths of their adolescent souls, is:
"When will you use this? You probably won't. What is this good for? Well, if you are going to be an engineer/physicist/mathematician/chemist (maybe), you'll need to have excellent algebra skills, which include knowing IN YOUR GUTS (or if you want to be fancier, ON AN ANIMAL, VISCERAL LEVEL) all of the things I'm trying to teach you. Otherwise, it's not going to do you much good, except to prepare you for the SATs and your college mathematics entrance exam."
Now, this answer really doesn't accomplish much, per se, except that you are now obeying the ancient dictum "First do no harm." And I would argue that before you actually give such an answer, you'd better be sure you know your kids. Unless you and they have mutual respect, this approach could obviously, well, backfire. Regardless of whether you go down this road, however, you still need to keep a few things in mind about the answer you do decide to give:

If you make grandiose claims about the value of whatever you're teaching, you'd better be damn sure you can back them up. Students need and deserve that level of honesty. If you can't give a reason why, but you think there must be one somewhere, you'd better go find it (that night!). Here's an observation from 13 years of teaching: most of the time the reason you hope to find isn't actually out there.

So anyway. Long live the revolution and all that, fine, whatever. But the big truth behind that eternal student question is the real heart of the problem. The big truth behind the endless years of "why are we learning this?" questions is that the educational system is an industrial system. Its job is to turn people (yes, 5 and 6 and 12 and 16-year olds are people) into uniform products (and yes, I mean products), otherwise known as "consumers".

We take every student, with all of their talents and interests and uniqueness and force them through the exact same mold. Now that NCLB is less than 3 years from the insane goal of 100% proficiency in math and English nationwide, the screws on these kids will only get tighter and tighter. More and more material, more and more testing....and yet, I wait for the time when someone can give me a really compelling argument why EVERY student must learn logarithms, or about the proper use of a gerund, or about the colonization of South America, or Newton's Laws (and this pains me to write, as a former physicist). And then I'll ask them why every student must also all learn the other 12 gazillion things that they are supposed to learn. As a start, I'd like to take the Common Core Standards and go line by line and ask "why?" to the developers. I suspect their answers would be amusing.

In some ways, I relish getting that question every year. Because it gives me a chance, a little bit, to tell the students what I really think: that they are learning it because our district, the state, the Federal Government, the College Board, and whomever else I can think of at the moment think it's a good idea. Not because the material will be practical, and not because it's connected to anything else, but because someone else thought they should learn it. (Side note: for a fun exercise, determine a coherent organizational scheme behind an algebra 2 textbook. Any algebra 2 book. The entire book, not just individual chapters. Post a comment when you figure it out.) The students are learning X because policymakers using models of education that were developed early in the Industrial Age can't think of anything better, and have no real interest in exploring anything else.

Human beings are curious by nature, and yet it depresses astonishes me how incurious most of our educational "leaders" can be. I hope for better - our kids deserve that.

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