'Real-world' concrete examples don't make math any easier

Washington, Apr 25 : The idea of teaching math using 'real life' concrete examples may not help students learn the subject, says a new study.

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

However, when they first learned the concept with abstract symbols, they were much more likely to apply that knowledge.

"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 Centre for Cognitive Science at Ohio State.

"The belief in using concrete examples is very deeply ingrained, and hasn't been questioned or tested," he added.

During the study, the students were asked to learn basic mathematical properties such as commutativity and associativity - the fact that you can change the order of elements without changing the results. For instance, 3+2 and 2+3 both equal 5.

Some students learned these principles using generic symbols, in which combinations of two or more symbols resulted in a predictable resulting symbol.

Others were presented with one or more concrete examples that involved this same concept. The students viewed three images of measuring cups with varying levels of liquid and were told to determine the remaining amount when different cups of liquid were combined.

Two other examples involved how many slices of pizza in a pizza pie were overcooked, and the other how many tennis balls were in a container.

After learning this math concept using the concrete examples or abstract, generic symbols, the students took a multiple-choice quiz demonstrating that they learned the principles involved. And in all cases, the study showed that most undergraduate students picked up the knowledge easily.

However, when they were asked to apply the same principles in a totally different setting, described to them as a children's game from another country, they kept guessing.

Out of 80 students, those who learned the generic symbols nearly 80 percent of the questions right and those who learned one, two or even three concrete examples did no better than chance in selecting the right answers.

"They were just guessing," said Kaminski.

In another 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, which suggested that only some benefit from direct comparison of learned concrete examples.

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

ANI