I’ve been truly enjoying Dan’s blog post series (from last year!) on the “Fake World.” I’d highly recommend you go read those posts if you haven’t already. It deftly exposes the fallacy of authenticity-as-engagement. I would like to offer a defense (three, really) of applied mathematical tasks.He offers three arguments. Here's the third:

Also, by dismissing the “real-world” as a lever to engagement, you’re giving teachers a kind of out. I’ve had conversations with sanctimonious math teachers and district instructional coaches that cite Paul Lockhart as a reason to keep doing what they’re doing. I’ve read Lockart. I love Lockhart. But his books aren’t about instructional practice. While much of “Measurement”, say, can and should be handed over to students to explore, it’s frustrating to kids who have only experience math in the abstract.Of the three, this is the only of his argument that draws blood for me. If you love math, you end up loving the fake world, and it's tempting to think that others will share that love. But the fake world is tough for kids. It's very, very different from the world in which they inhabit.

But so is the real world, no? Dan's done a great job making that case. So if the fake world isn't real for kids, and the real world isn't real for kids, then that means that...

...the world is fake for kids.

And that sounds closer to the truth for me. The world, as experienced by a mathematician, is very different than it is for your average civilian. You learn a bunch of math, and you start seeing things differently. You talk differently. You find yourself asking all these questions that nobody else asks.

And that's because

**no content is a "natural" context for mathematics**. Or rather, no content is inherently engaging, and the world needs a different language for talking about student interest than engagement with content.

We have to change the conversation. Content isn't engaging, not all on its own. Pedagogy partnered with dumb content can only take you so far. What we need is a way to talk about partnering great content with effective pedagogy, what I'm calling "teaching" until someone comes up with a better term for it.

(Heavily influenced by this post from Larry Cuban.)

"What I'm calling teaching..."

ReplyDeleteZing!

:)

That last paragraph is a really helpful.

ReplyDeleteA test-case for your distinction between content and pedagogy.

ReplyDeleteI've been reading this discussion as it's been going on, and wanting to write about it, but my post would be positively war-like, because lord, a bunch of math geeks twiddling over the beauty of math has zero relevance to teaching high school math, and the fact that so many people think so strikes me as a problem. But I can't remember if I commented on that before. I must have, it sounds like me.

ReplyDeleteAnyway, I am completely out of synch with the values of these math teachers who love math, and the problems they see in teaching math are utterly non-problems.

And then you say this: "Or rather, no content is inherently engaging, and the world needs a different language for talking about student interest than engagement with content."

and I'm like well, yeah. That seems to me so completely obvious, so completely why I have been scratching my head over the conversation, that I have to think that most of the people participating didn't know it already. (you did, apparently).

Engagement is a false god, although as I said recently, I no longer discount it. But the solution is not "make the problem engaging", it's "make the kids want to work at math". Because other teachers won't necessarily engage them, so they have to come up with their own internal motivations, the belief that if they work they can figure it out--whatever it is, whatever the goal, applied or "fake".

It's tempting to look at a lesson that went really well and say, hey, what I did there was create an opportunity for kids to experience this wonderful content. In this framework, what I end up doing is removing stumbling blocks that get in the way of a kid experiencing what's inherently interesting about the world.

DeleteThat's the framework that I'm pushing back against. This is a bit more subtle, to my mind, than the problem of the math-enamored teacher that you describe, but the response is pretty much the same.

So, nothing in the world is inherently engaging. Then how do we make math class interesting?

I typed up a whole answer and everything, and then it didn't make sense, so I'll offer restraint for the moment.

"Then how do we make math class interesting?"

ReplyDeleteI suspect you know my answer:

You don't. You make math class *doable*. You start there. And that's not the same thing as removing stumbling blocks, or giving them nothing but worksheets. I think my byline is going to be "rigorous, but manageable".

"Doable" means many different things, depending on student ability. If I have a student who just wants to regurgitate algorithms, I make them do more work without algorithms. If I have a really active, really engaged kid, I delight him by showing him what he can do. If, as is usually 50 or more % of my class, I have kids who simply are convinced they can't do math, I convince them otherwise.

These challenges, at which I like to think I am moderately successful, are so far away from the "should it be real life or Memorex" or "making kids love math" or "is this equation inherently interesting" that I am constantly flummoxed by the debate. What on earth are these other teachers teaching?

And when I go and see what they are teaching, it is always either much too hard, much too idealistic, much too All About Them to succeed (as is evidenced by their depression and despair) or evidence that they are teaching an entirely different demographic from the one I work with.

I love your last paragraph as well...and it reinforces what I've observed, and that is a need for math teachers to have stronger content knowledge. Further...I find that the curiosity that could be fostered in a student gets taken away b/c some teachers feel that concepts need to be "taught" before they can pose a particular problem. So...this moves towards an answer getting sort of pedagogy, instead of an answer seeking one.

ReplyDelete