Andrew Hacker in the NY Times:
There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic.
Dan Willingham: Hacker is wrong.
The inability to cope with math is not the main reason that students drop out of high school. Yes, a low grade in math predicts dropping out, but no more so than a low grade in English.
He also argues that Hacker's suggestion, teaching practical stuff instead of algebra, won't work.
Because if you teach students the significance of the Consumer Price Index they are not going to know how to teach themselves the significance of projected inflation rates on their investment in CDs. Their practical knowledge will be specific to what you teach them, and won't transfer.
The best bet for knowledge that can apply to new situations is an abstract understanding--seeing that apparently different problems have a similar underlying structure. And the best bet for students to gain this abstract understanding is to teach it explicitly. (For a discussion of this point as it applies to math education in particular, see Anderson, Reder, & Simon, 1996).
But the explicit teaching of abstractions is not enough. You also need practice in putting the abstractions into concrete situations.
Hacker overlooks the need for practice, even for the everyday math he wants students to know.
The MCAS is a 10th grade exam with algebra and geometry. Our students have done well. It does take a lot of practice though.
Does anyone know of any spectacular "practical math" courses for high school students? We've experimented, but it's rough sledding.
Here's one example.