Tuesday, April 29, 2008

Math and writing: I see a pattern here

The New York Times recently had an article about some research done on the way math is taught. It turns out that learning abstract concepts like equations can actually help rather than hinder learning.

The students who learned the math abstractly did well with figuring out the rules of the game. Those who had learned through examples using measuring cups or tennis balls performed little better than might be expected if they were simply guessing. Students who were presented the abstract symbols after the concrete examples did better than those who learned only through cups or balls, but not as well as those who learned only the abstract symbols.

It reminded me of the recent article in the Chronicle about Berkinstein and Graff's book.

Both rely on formulas, in a way, but--and here's the important part--they don't begin and end with formulas. The abstractions allow students to apply the concepts but NOT, as detractors fear, to stop at applying principle A to material B in a bad, evil, wicked, formulaic, five-paragraph essay kind of way to make students march in lockstep as prescribed by Satan's minions who want to stifle creativity. Instead, they allow students to conceptualize ideas in new and different ways.

It's like riding a bicycle. If you had to think about how to ride a bicycle every time you rode one, or reconceptualize it every time lest you not have the "true and authentic" experience of discovery, you'd be exhausted and you'd never get anywhere. You'd be so busy learning to ride that you'd never find the pleasure in riding.

Isn't there room for both discovery and actually learning--all right, even memorizing--a few concepts? I honestly don't see the problem with this.


JM said...

There's been a kerfuffle about the B&G book on WPA-L and TechRet in the past few days. I've been meaning to blog something about it but lo and behold if I just wait a few days I find that you usually say what I was thinking and I can just link to you. :)

But yeah, ditto your last three paragraphs.

Anonymous said...

YES! I figured out how to write English papers in Honors Geometry.
I could not take Honors English (in high school), where one learned to write papers, because it conflicted some years with advanced Spanish and others with advanced French. Not to mention Latin, that horror of our high school to which I also succumbed.

So I couldn't make it into Honors Freshman English in college because I had never written a college prep English paper. However I was able to get an A in Regular College English because I channelled Honors High School Geometry which was very abstract.

undine said...

Great minds, jm, great minds ;-). Writing creatively is hard enough without having to invent new forms every time. And what's the first thing any writer does when tackling a new project? Look for a model, of course.

Cero,that's the first time I've heard empirical--well, anecdotal--proof of this idea. To an extent, they're both about learning and discerning rules and patterns, even if they're not called that.

Professor Zero said...

Here if they fail Algebra (that's a college course, not high school one here) they will also fail their foreign language class because both it and Algebra have to do with the ability to acquire a system.