While I loved his presentation, his advocacy for science, and his style, I had a problem with one thing Neil deGrasse Tyson said during his talk. Now, he’s working on getting deeper into learning, but this wasn’t off the cuff, this was his presentation (and he says he doesn’t say things publicly until he’s ready). So while it may be that he skipped the details, I can’t. (He’s an astrophysicist, I’m the cognitive engineer ;)
His statement, as I recall and mapped, said that math wires brains to solve problems. And yes, with two caveats. There’s an old canard that they used to teach Latin because it taught you how to think, and it actually didn’t work that way. The ability to learn Latin taught you Latin, but not how to think or learn, unless something else happened. Having Latin isn’t a bad thing, but it’s not obviously a part of a modern curriculum.
Similarly, doing math problems isn’t necessarily going to teach you how to do more general problem-solving. Particularly doing the type of abstract math problems that are the basis of No Child Left Untested, er Behind. What you’ll learn is how to do abstract math problems, which isn’t part of most job descriptions these days. Now, if you want to learn to solve meaningful math problems, you have to be given meaningful math problems, as the late David Jonassen told us. And the feedback has to include the problem-solving process, not just the math!
Moreover, if you want to generalize to other problem-solving, like science or engineering, you need explicit scaffolding to reflect on the process and the generality across domains. So you need some problem-solving in other domains to abstract and generalize across. Otherwise, you’ll get good at solving real world math problems, which is necessary but not sufficient. I remember my child’s 2nd grade teacher who was talking about the process they emphasized for writing – draft, get feedback, review, refine – and I pointed out that was good for other domains as well: math, drawing, etc. I saw the light go on. And that’s the point, generalizing is valuable in learning, and facilitating that generalization is valuable in teaching.
I laud the efforts to help folks understand why math and science are important, but you can’t let people go away thinking that doing abstract math problems is a valuable activity. Let’s get the details right, and really accelerate our outcomes.