Monday, April 28, 2008

time to throw concrete math instruction out the window?

This... could hurt.
In the first experiment, involving 80 students, some participants were given one concrete example before testing on the children’s game, while some were given two or three examples. One group only learned the generic symbols.

When tested on the children’s game, the group that learned the generic symbols got nearly 80 percent of the questions right. Those who learned one, two or even three concrete examples did no better than chance in selecting the right answers.

“They were just guessing,” Kaminski said.

In a second experiment, the researchers gave 20 participants two concrete examples and explained how they were alike. Surprisingly, this still did not help students apply the concept any better and they still did no better than chance when tested later about the game.

In a third experiment, the researchers presented 20 students with two concrete examples and then asked them to compare the two examples and write down any similarities they saw. After this experiment, about 44 percent of the students performed well on the test concerning the children’s game, while the remainder still did not perform better than chance.

This suggests that only some students, not all, benefit from direct comparison of learned concrete examples.

Finally, in a fourth experiment involving 40 students, some learned the concrete example first followed by the generic symbols, while others learned only the generic symbols. The thought here was that the concrete example would engage the students in the learning process while the generic symbols would promote transfer of that knowledge.

But even in this experiment, students who learned only the generic symbols performed better on subsequent testing than those who learned the concept using the concrete example and then the generic symbols.

The authors said that students seem to learn concepts quickly when they are presented with familiar real objects such as marbles or containers of liquid, and so it is easy to see why many advocate this approach. “But it turns out there is no true insight there. They can’t move beyond these real objects to apply that knowledge,” said Sloutsky.
Compare that with, say, the recent math-athon in the North Thurston district.
Pre-calculus students at North Thurston High School will show display boards of photographs of everyday objects that are examples of conics — circles, parabolas, ellipses and hyperboles.

“I just wanted them to see real math in the real world,” said their teacher, Julie Cassidy.

Boards showed photographs of nail polish bottles, mustard containers, bicycle racks, basketballs, garden hoses, shoe soles and more.

“I really liked it because it kind of gives you a more hands-on idea of math. I’m the type of person who likes to get out and experience in the world. I can’t sit at a desk and remember it,” said junior Raewyn Heim, 17.
Obviously, further studies are needed to see if Heim has it right. It could be that the hands-on aspect provides greater motivation for learners who aren't already college undergrads, the subjects of the OSU experiment. Also, if Piagetian principles are at play, the older students might just be more facile in the realm of abstraction. Still, as an English teacher, I have to go with this quote by one of the experimenters: "Story problems could be an incredible instrument for testing what was learned. But they are bad instruments for teaching."

Now you have a scientific reason to hate story problems.

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