• By Kevin Mount
  • Posted on Thursday 08th May, 2008

Not enough learned from the reality of passing trains?

In a classic episode of the US TV sitcom Cheers, one of the characters, Cliff Clavin, appears on Jeopardy, a TV game show in which contestants are presented with answers and asked to provide the correct corresponding questions. [Watch Cliff Clavin on Jeopardy]The crucial answer in the Cheers episode is “Archibald Leach, Bernard Schwartz, and Lucille le Sueur”. But instead of providing the question “What are the original names of Cary Grant, Tony Curtis, and Joan Crawford?” Cliff asks “Who are three people who have never been in my kitchen?". When Cliff protests that his response is correct, that, indeed, these movie stars have never been in his kitchen, the host responds “Obviously that’s not what we were going for.” “Obvious to who?” Cliff complains. A group of researchers at the Center for Cognitive Science at Ohio State University in the US asked a similar question. Jennifer A. Kaminski and her colleagues were considering how schools teach math. The conventional wisdom is that students learn better when they are presented with familiar situations and objects. So, rather than teaching concepts using abstract numbers or other symbols, math instructors often present real life situations that demonstrate a math concept – remember all those trains moving in opposite directions at different speeds or pies that need to be divided.Kaminski and company’s research calls the wisdom of such an approach into question, on the basis that the math concepts underlying all such hypothetical situations are far from obvious.In a series of randomized controlled studies involving undergraduate students at Ohio State, the researchers found that students who learned a set of mathematical rules with abstract symbols were better able to apply that knowledge to other problems than students who learned the rules through concrete examples such as combining liquids in measuring cups and tennis balls in a container.The problem seemed to be that like Cliff Clavin the students didn’t always know what the questions were driving at. “They tend to remember the superficial, the two trains passing in the night,” Dr. Kaminski said in a New York Times article about the study. “It’s really a problem of our attention getting pulled to superficial information.” Abstract knowledge appears to be more portable than knowledge embedded in a hypothetical situation. The researchers believe their findings might be particularly relevant to young learners who are less able to keep their attention focused when presented with real life situations and to extract the appropriate (or as the Jeopardy host might say, “obvious”) knowledge.[See the New York Times story Study Suggests Math Teachers Scrap Balls and Slices•Summary of “Learning Theory: The Advantage of Abstract Examples in Learning Math” by Jennifer A. Kaminski, Vladimir M. Sloutsky, and Andrew F. Heckler in Science, 25 April 2008, Vol. 320. no. 5875, pp 454 – 455.

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