Math is hard! *

Here is a YouTube video posted by M.J. McDermott, a weather girl in Seattle who went back to college to get a degree in atmospheric sciences. She soon discovered that her old-school arithmetic was a lot better than her fresh-out-of-high-school classmates'. She talks about college students who can't calculate 4x6 without a calculator.

I'm going to ignore the selection problems -- that she's a highly motivated, adult student, and that her classes were almost certainly diluted by a bunch of people who had no business attending college at all. (I'm also going to ignore that she's talking about arithmetic, not mathematics.) Instead, I'm going to focus on her diagnosis: that the way math is taught is a failure.

To make her point, she pages through a few junior high math books, highlighting the fact that there's not much math in them. There's a lot of multi-cultural diverso-nonsense, of course. Never hurts to saddle up that hobby horse for a quick gallop. But when it comes to actual calculations, the curricula McDermott shows seem to mostly wave their hands and leave it up to the student to get the basic idea.

For many students, this is undoubtedly a terrible way to learn to do multiplication or long division. They need a reliable algorithm they can memorize and that will work every time. One example she shows is a book that suggest multiplying by breaking the numbers into clusters, so 26x31 becomes (20x31)+(5x31)+(1x31). If you would have struggled with the traditional approach to multiplication, I'm sure cluster problems are simply more than you can handle. They're abstract, they're subjective, and they require more thinking. However, speaking as somebody who works in a very math-intensive industry, I can tell you that this is exactly how people who are good at math think about the problem. Furthermore, it's unlikely that you'll never actually need to multiply 31 and 26 without a calculator. I can see the new-math-people's point: Why are we wasting everybody's time teaching a method that has pretty much no application?

That statement was hard for me to make, because it's so obvious that as a first approximation all the changes in curriculum for the last forty years have had one of two goals in mind:
a) to indoctrinate students to a certain point of view (e.g., history becomes social studies,

or (mostly) b) to make life easier for teachers (e.g., Shakespeare is expunged, phonics is given the hook). But like I said, I can kind of see the point in this case.

Nobody needs multiplication algorithms. If you're doing math in your head, its good enough to know that 26x31 is about 800 (26 is about 25, which is one quarter of 100. 31 is almost 32, which divided by 4 is 8. 8x100=800.). If that's not close enough, you really should use a calculator. Actually, nobody who's doing math uses a calculator anymore either. You should plug the numbers into Excel.

Once again, it depends what you think the point of school is.

If you think school is about getting everybody up to a certain minimum level, then you better stick with the tried-and-true algorithms. They work, and pretty much anybody can learn them. On the other hand, if you think school is about educating people according to their abilities, so the smart kids do one thing, the average kids do something else, and the dull kids do something else again, then the answer is different.

* Misquote from Teen Talk Barbie. She actually said, "Math class is tough!" No less true.