Two competing claims in the mainstream newspapers:
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.
Hacker overlooks the possibility that the mathematics learned in school, even if seldom applied directly, makes students better able to learn new quantitative skills. The on-the-job training in mathematics that Hacker envisions will go a whole lot better with an employee who gained a solid footing in math in school. […]
[In] teaching the specific skills that people need, you had better be confident that you’re going to cover all those skills. 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.