Monday, February 20, 2006

How To Do Well In Math

After my last post, I thought I should throw a bone to all those people I tossed into math class hell just so they can graduate. Yesterday's San Jose Mercury News had an article about math education; it was written by a Stanford mathematician who is also the "Math Guy" on National Public Radio.

I admit that I've never heard of this "Math Guy" because I don't listen to National Pravda Radio, but that's a story for a different post =)

Here are some of his comments:

While it sounds reasonable to suggest, as the math-ed community does, that understanding mathematical concepts should precede -- or at least go along hand-in-hand with -- the learning of procedural skills (such as adding fractions or solving equations) -- there is evidence to suggest that this is simply not possible. The human brain evolved into its present state long before mathematics came onto the scene, and did so primarily to negotiate and survive in the physical world. Our brain does not find it easy to understand mathematical concepts, which are completely abstract....

Ask experts at any activity what it took them to acquire their expertise and they'll tell you in one word: practice. Expertise does not come from understanding, it comes from practice. The part of our brain that provides conscious understanding did not evolve to control and direct our detailed actions, it developed to make sense of them -- after the fact. (The benefit of that sense making is that we can make use of our understanding to guide future action at a higher, more strategic level.)

We are not ``natural-born mathematicians,'' but we are well equipped to learn new skills. Initially, we simply follow the rules in a mechanical fashion. Then, with practice, we gradually become better, and as our performance improves, our understanding grows. Anyone who has learned to play chess, play tennis, ski, drive a car, play a musical instrument, play a video game, etc. has experienced this progression from ``following rules,'' through proficiency, on to eventual mastery and understanding. Mathematics is no different....

And anyone who thinks that today's children don't have what it takes to practice for hours until they really ``get it'' has not watched them playing a video game.

5 comments:

ns said...

Darren,

Interesting article. I think the problem here is the two sides are in an "either or" arguement. It is either one or the other. But really, it is both.

You MUST practice, practice, practice! The problem is, practicing takes time and dedication. No one wants to practice a LOT, and then reach the understanding. They want to be given the answers, now.

To many, especially in public school, they do not see education as a journey. It is in walking the path, not the destination, that gives you knowledge. And you cannot get to knowledge without walking that path... and it is a LONG ARDUOUS path.

But in our culture of shortcuts and now, now, now! - no one wants to experience the journey any more.

K T Cat said...

Cool blog. Check out mine. Care for a link exchange?

I liked the Pappy Boyington post. I did one, too.

Old Math said...

Peter Devlin's "The Language of Mathematics: Making the Invisible Visible" is a great read. His latest "The Math Gene" has some interesting ideas, but not nearly enough to fill an entire book.

On this issue: I agree with him wholeheartedly.

cowboylogic said...

I am learning right now the concepts behind everything I was taught years ago. Without the firm foundation set up as far as how it works I would never have even had an inkiling as to why.
I do wonder if there is a better method to teach math: primarily have mathematicians teach math in early grades. Elem ed majors almost never have enough math background in math to truely understand the why (I am still learning the why as a Math major), and as such in elem. school they can only teach the how. If the in lower grades the instructor truely understood the why, the students might be able to get snippets of the truth earlier and more accurately.
By the way Love the blog

Cowboylogic

Darren said...

Cowboylogic, that's exactly what Liping Ma said in her book Knowing and Teaching Elementary Mathematics, in which she contrasted US elementary teachers (college graduates) with mainland Chinese elementary teachers (mostly not college graduates).