I found this article in the New York Times yesterday interesting, especially in light of a recent post on the Arborparents Yahoo group on the same topic.
The message on the Yahoo group was written by a parent who said he chose to send his child to a private school because he did not like the math method used by Ann Arbor Public Schools. AAPS uses "Everyday Mathamatics," which is a controversial math program that emphasizes problem-solving with everyday applications. (Here's an article that goes into great detail explaining Everyday Math.)
The private school uses the "Saxon" also a new method, but a more traditional one.
The Times article is about a new study that suggests students learn math better without concrete examples. It doesn't specifically mention Everyday Math, but it seems to me that concrete examples are the essence of the program. From the story:
In the experiment, the college students learned a simple but unfamiliar mathematical system, essentially a set of rules. Some learned the system through purely abstract symbols, and others learned it through concrete examples like combining liquids in measuring cups and tennis balls in a container.
Then the students were tested on a different situation -- what they were told was a children's game -- that used the same math. "We told students you can use the knowledge you just acquired to figure out these rules of the game," Dr. Kaminski said.
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.
The problem with the real-world examples, Dr. Kaminski said, was that they obscured the underlying math, and students were not able to transfer their knowledge to new problems.
"They tend to remember the superficial, the two trains passing in the night," Dr. Kaminski said. "It's really a problem of our attention getting pulled to superficial information."
I recently talked to a friend who has a high-schooler in the Ann Arbor schools about the Everyday Math program, and she said that she and her husband always did plenty of traditional math instruction at home. Hmmm. It'll be interesting to learn more about this as Belle starts school in the fall.