"To teach it now as if it were A Rule, or (even more intimidating), The Law, is to pretend that what took years of experimenting and ingenuity is as obvious as your nose. And then, because you never really had a chance to understand what was going on, whenever you need this rule again it will come as just that - an arbitrary fiat, enforced by Them. And so the whole integrity of mathematics is compromised. The only reasonable conclusion for a struggling student to draw from such pretense is that he is irremediably stupid, or that Mathematics works in mysterious ways, its wonders to perform."
and further down the page:
"...and so a teacher, who is supposed to develop our powers of inquiry, becomes instead a messenger of Received Truth."
There are many other incredible little tidbits in this book and, so far, it is making a pretty good case for a spot in my preferred reading list. As I read the above passage, I was reminded of something that I have been thinking about a lot lately (and even alluded to at the end of this post). We talk a lot about the importance of context in math education. There are many benefits to situating mathematics into some nice context that students find engaging/relevant (mostly, it seems beneficial to help students see that math can help them describe and understand their world) and there are some sites/people that are doing this very well.
But simply using an exciting context does nothing to remedy the fact that often the "whole integrity of mathematics" can still be compromised. I mean, you can start with a really interesting and perplexing question and still completely miss the boat when it comes to helping students do their own mathematics; it just becomes a better way of teaching "The Law." These types of questions could (and should) drive a whole unit because then we can explore different parts of the problem, honor different approaches and ways of thinking, and ultimately, help students create their own math along the way.