Return of the Math Wars
I’d like to respond to Justin’s excellent critique of integrated math. I think we are mostly in agreement about integrated math’s faults. My position is that parents should be able to choose integrated math for their children if they want to, not that integrated math is good.
I think Justin is 100-percent correct (see, I can use numbers in real-life situations!) that math classes treating all answers as equally right aim only to fluff up students’ self-esteem, not to teach them anything. And when students go through school without learning math facts and formulae, they miss out on a basic part of education.
But I think parents should still be able to choose integrated math, for a few reasons. First, there’s disagreement about which curricula constitute integrated math. One of my brothers attended an elementary school that used Everyday Mathematics, by the University of Chicago School Mathematics Project. My brother hated this curriculum, and I thought it had several disadvantages. It encourages calculator use at a young age, some of the activities are pointless, and it presents some concepts in a more complicated way than necessary.
On the other hand, the curriculum emphasizes practice and getting the right answer. And although many critics object to it because the algorithms it teaches aren’t the same ones they learned in school, no one could accuse it of foregoing algorithms altogether, or of allowing students to make up answers. Is Everyday Math "integrated math"? This Wikipedia article says yes. Personally, I think Everyday Math isn’t so bad as the other integrated programs out there, and parents who choose it aren’t necessarily dooming their children to ignorance.
Justin’s suggestion to encourage computer programming, which uses set theory, is a good idea. But some people consider teaching set theory before college to be a "new math" scheme itself. I’ve seen traditional math books that eschew set theory entirely, even at the high school level.
Even curricula that are indisputably integrated might not be harmful in the long term. I went to a public elementary school that taught integrated math. We were always doing creative projects that were only tangentially related to arithmetic. But when I switched to a private school that taught only traditional math, I didn’t really miss anything, because the traditional sixth-grade math curriculum was basically a review of third-, fourth-, and fifth-grade arithmetic.
What about my peers who stayed in the public school? They started using a more traditional curriculum around that time, too. Several of them went on to major in science at college. Sure, our time could have been put to better uses in elementary school, but the fact that you don’t learn long division in one grade doesn’t mean that you’ll never learn it in any other grade. If parents choose integrated math for their kids in the early grades, their kids could still study all the traditional topics when they’re a little older.
In fact, given the pressure some parents put on their five-year-olds to memorize lots of facts, study textbooks, and prepare for first grade, I imagine I would request integrated math if I had little kids in kindergarten. I probably wouldn’t choose it for later grade levels. But if parents want to put off teaching traditional math until second or third grade, I think that should be up to them. And as for the parents who want their kids to study integrated math through high school? I think they should be free to choose that, even though I disagree with them.
If everyone sent their kids to private schools of their choice, we wouldn’t have this dispute about what schools should teach. The math wars (and reading wars, and spelling wars, etc.) are a product of our one-size-fits-all public school system, which forces a few educational approaches on all families. Opening up the system to choice would lead to more diversity, and less arguing.