How should we teach our kids math?

The NY Times is reporting on the lagging math skills of US kids and efforts to change, yet again, how we teach math. I'm sympathetic to the desire to teach math in a way that doesn't turn people off. Too many people (including some people who grow up to be biologists) go through their education feeling very, very insecure about their ability to do and understand math.

What's tough about this problem is that you just can't teach the concepts and let kids figure out for themselves how to solve the problems. Understanding is good, but in math, understanding is not a substitute for the ability that comes with lots and lots of practice. This is different from many other fields of study, where if you understand the basic ideas and arguments you can work out a lot for yourself. To actually do math well, you need regular, sometimes mind-numbing practice - you can't just reinvent the wheel (i.e., derive your results from first principles) every time you need to solve a problem.

Gaining proficiency in math is similar to being able to do the NY Times crossword puzzle or play arpeggios on the piano - you simply need a lot of repetitive practice. You may know what an arpeggio is, but that's different from being able to play them over the entire keyboard, in all major and minor keys at a fast tempo.

Just like with the piano, kids will like math more when they are actually reasonably good at it. And there is no reason that most kids can't be fairly good at the kind of basic math we'd expect every educated person to know. Our teaching needs to reflect that - it's good to encourage understanding, but proficiency will never come without plenty of practice.