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April 24, 2008Concrete Examples Don't Help Students Learn Math |
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From EurekAlert! - Breaking News: 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. "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. For example, there is the classic problem of two trains that leave different cities heading toward each other at different speeds. "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. In the various experiments, some students learned these principles using generic symbols, in which combinations of two or more symbols resulted in a predictable resulting symbol. And in all cases, the study showed that most undergraduate students picked up the knowledge easily. However, the true test came later when the researchers asked these students to apply the same principles in a totally different setting, which was described to them as a children's game from another country. The problem may be that extraneous information about marbles or containers might divert attention from the real mathematics behind it all, according to Kaminski. The authors said they doubt this paper will end the debate over approaches to teaching mathematics, but they hope it will generate interest into systematic examination of which ways of teaching mathematics are most effective.
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