'Real World' Examples Don't Make Math Any Easier

THURSDAY April 24, 2008 -- The use of "real-world" concrete examples doesn't help students learn math, according to an Ohio State University study that challenges the widespread use of this approach in classrooms.

The study found that college students who learned a mathematical concept with concrete examples couldn't apply that knowledge to new situations, while students who learned the same concept through abstract examples were much more likely to be able to transfer that knowledge to different situations.

The study is published in the April 25 issue of the journal Science.

"These findings cast doubt on a long-standing belief in education. The belief in using concrete examples is very deeply ingrained and hasn't been questioned or tested," study co-author Vladimir Sloutsky, professor of psychology and human development and director of the Center for Cognitive Science at Ohio State, said in a prepared statement.

Examples of concrete learning include story problems often given to math students, such as the classic one of two trains that leave different cities and head toward each other at different speeds.

"The danger with teaching using this example is that many students only learn how to solve the problem with the trains," study leader Jennifer Kaminski, a research scientist at the Center for Cognitive Science, said in a prepared statement. "If students are later given a problem using the same mathematical principles, but about rising water levels instead of trains, that knowledge just doesn't seem to transfer."

"It is very difficult to extract mathematical principles from story problems," Sloutsky added. "Story problems could be an incredible teaching instrument for testing what was learned. But they are bad instruments for teaching."

Story problems and the use of visual aids such as marbles or containers of liquid seem to help students learn math concepts more quickly, so it's easy to understand why they're so popular. But extraneous information included in this kind of concrete learning may divert attention from the real mathematics in the lesson, the researchers said.

"We really need to strip these concepts down to very symbolic representations such as variables and numbers. Then students are better prepared to apply those concepts to a variety of situations," Kaminski said.

More information

The Ontario Ministry of Education offers advice to parents on how to help their children learn math.

Posted: April 2008


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