From: Reuters
Published April 24, 2008 05:05 PM

Hold the marbles: Abstract approach best for math

By Julie Steenhuysen

CHICAGO (Reuters) - Frustrated math students may have a good excuse -- some of the teaching methods meant to make math more relevant may in fact be making it harder to understand, U.S. researchers said on Thursday.

They said students who were taught abstract math concepts fared better in experiments than those taught with real-world examples, such as story problems.

Adding extraneous details makes it hard for students to extract the basic mathematical concepts and apply them to new problems, they said.


"We're really making it difficult for students because we are distracting them from the underlying math," said Jennifer Kaminski, a research scientist at Ohio State University, whose study appears in the journal Science.

The findings cast doubt on the widely used practice among elementary and middle schools in the United States and elsewhere of using friendly, concrete examples to teach abstract math concepts.

For example, a teacher might use a bag of colored marbles to explain probability, or teach a formula about distance with the classic example of two trains departing from different cities and traveling at different speeds.

"The danger with teaching using this example is that many students only learn how to solve the problem with the trains," Kaminski said.

To find out the best methods of teaching basic math concepts, the researchers conducted several experiments using college students in which some students were taught concepts using basic symbols, while others were taught with concrete examples.

For example, they studied different approaches at teaching the basic mathematical property of commutativity -- that you can switch up the order of elements and still get the same answer, as in 3 + 2 or 2 + 3 equals 5.

Some students learned the concepts using generic symbols. Others were taught with concrete examples such as pictures of measuring cups filled with liquid, or slices of pizza or tennis balls in a container.

While all of the students were able to master these concepts easily, the students who first learned math concepts using abstract symbols were better able to transfer that learning to other problems when tested.

That is not to say story problems should disappear. Kaminski said story problems offer a good way to test whether a student has mastered the abstract concept.

"Story problems aren't out, but they are probably not the way we want to go about introducing concepts or problem solving," she said in a telephone interview.

"That would be best done through symbolic math."

(Editing by Maggie Fox and Mohammad Zargham)

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