Concrete examples don't help students learn math, study finds

COLUMBUS, Ohio – A new study challenges the common practice in many classrooms of teaching mathematical concepts by using “real-world,” concrete examples.

Researchers led by Jennifer Kaminski, researcher scientist at Ohio State University’s Center for Cognitive Science, found that college students who learned a mathematical concept with concrete examples couldn’t apply that knowledge to new situations.

But when students first learned the concept with abstract symbols, they were much more likely to transfer that knowledge, according to the study published in the April 25 issue of the journal Science.

“These findings cast doubt on a long-standing belief in education,” said Vladimir Sloutsky, co-author of the study and professor of psychology and human development and the director of the Center for Cognitive Science at Ohio State.

“The belief in using concrete examples is very deeply ingrained, and hasn’t been questioned or tested.”

Kaminski and Sloutsky conducted the study with Andrew Heckler, assistant professor of physics at Ohio State.

Teachers often use real-world examples in math class, the researchers said. In some classrooms, for example, teachers may explain probability by pulling a marble out of a bag of red and blue marbles and determining how likely it will be one color or the other.

But students may learn better if teachers explain the concept as the probability of choosing one of n things from a larger set of m things, Kaminski said.

The issue can also be seen in the story problems that math students are often given, she explained. For example, there is the classic problem of two trains that leave different cities heading toward each other at different speeds. Students are asked to figure out when the two trains will meet.

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

“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,” she said.

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