So much of math builds on what came before. It's very, very easy to fall behind and become lost in later years - I think that's part of why so many students drop it when they can. And, like anything, if one doesn't use it, one forgets.

Finding ways to keep students using what they learned before is important. Dividing math into segregated boxes of Algebra, Trig, Pre-Calculus, etc. doesn't help, I don't think.

Continuing "math in everyday life" type lessons is important. Compound interest; figuring out how much grass seed you need for your lawn; figuring out how many tiles are needed in a bathroom remodel; figuring out payback time for putting in a low-flow toilet; figuring out how to scale up recipes to 47 people; figuring out the commission costs on an investment; etc. Everyone over 18 should be able to do those things cold. Figuring out the volume enclosed by a hyperbolic parabaloid intersecting with a plane - not so much.

I'll have to return to the Times story later. The early part about the kids "working together to figure things out on their own" threw up red flags for me. My first physics class in high school was like that part of the year (we had about 20 substitute teachers that year...). It was extremely frustrating because the teacher didn't seem to understand the proper way to get the answer himself. We'd all try to puzzle out the answers, he'd declare what the correct answer was, and that was that. Not a good way to build a clear foundation if the instructor doesn't know the subject matter cold and be able to explain why (and too many math and science teachers don't).

Thanks.

Cheers,
Scott.