So Grant Wiggins threw down the gauntlet. And Patrick Honner, as Patrick Honner is wont to do, picked it up. And then Grant Wiggins -- I'm not totally sure what traditionally happens to a gauntlet at this point -- did some other gauntlet-related thing in reply. It was fast and furious. Actually, it was incredibly civil and well considered, which spirit I will try to preserve here.
For the tl;dr crowd, Wiggins posted a celebratory 100th-blog-post rant against Algebra (the course, not the content). In that post he challenged Algebra teachers to name Four Big Ideas contained in the curriculum. And Honner responded with some pretty solid candidates:
- Algebraic Structure
- Binary Relations
- The Cartesian Plane
Wiggins quasi-stipulates to a couple (binary relation, Cartesian Plane) -- with much qualification -- and more or less dismisses the others (quite politely). It seems that Wiggins agrees all those ideas are important, but he has a very particular notion of what makes for a Big Idea:
So, I wish to up the ante. To me a big idea is big for both: I am looking for those ideas that are big – powerful and fecund – for both novice and expert.
I always return to this simple example from soccer: Create dangerous space on offense; collapse dangerous space on defense is a big idea at every level of the game, from kid to pro. And it is transferrable to all space-conquest sports like lacrosse, hockey, and basketball. Truly big. [emphasis in original]
I'm not interested in debating the general lifelessness of high school Algebra, which strikes me as largely uncontroversial at this point in the conversation. In fact, the same rant could just as easily be applied to mathematical instruction at almost any level (Wiggins even includes the obligatory quotation from A Mathematician's Lament). I'm also not interested in trying to produce more convincing examples. Nope, I'm interested in talking about soccer.
I think the soccer analogy is on the verge of making it impossible to have a meaningful discussion about math education. Not just Algebra, but mathematics. And here's why: the creating and collapsing of dangerous space might be the only Big Idea in soccer. I submit that, if that's the standard for bigness, then there just aren't four Big Ideas to be had.
If soccer were taught like math, then you might take a course called Moving Without the Ball I as a freshman. And in that class there would be a unit about Overlapping Runs. And you would probably hate it, because it would be an awful lot of running, and you wouldn't ever be sure why you were doing all this goddamn running, because maybe your coach isn't overly concerned about unveiling to you the beautiful truth that a good, long overlapping run pulls a defender way down into the corner and stretches the whole defense and creates some dangerous space for a midfielder to run into. And you would moan and check the calendar for when you were starting the Passing Into Space unit, because you heard it was totally easy -- mostly just standing around and pushing nice, easy passes toward cones. But that really says more about your coach's ability/willingness to keep your eye on the Truly Big Idea (because hey, he's pretty much coaching the way he was coached in the first place, back when kids just shut up and did their Backwards Jogging homework without complaint) than it does about the bigness of the Pretty Big Ideas that you're working your way through, because the Truly Big Idea is just too ungodly huge to be useful in making you a better soccer player. After all, there's just the one.
In an attempt at analogic involution, I'm going to try to come up with a mathematical analogy for the soccer analogy for math:
I always return to this simple example from mathematics: Create structure when you're building; look for structure when you're exploring is a big idea at every level of the subject, from kid to professional mathematician. And it is transferrable to all structure-having systems like language, chemistry, and logic. Truly big.
Maybe structure is the only big idea in math. At least the only one Wiggins might agree to. And that's just too big. What we really need in Algebra are some Pretty Big Ideas. So here's my gauntlet, which is admittedly significantly lighter than the one that's currently being kicked around: what are four Pretty Big Ideas in Algebra? Honner got you started.