If a train heading east leaves Chicago at noon and a train heading west leaves New York an hour later, will that make you any better at math? New evidence says "No." In a report in the April 25th issue of the journal Science, researchers from Ohio State University say the preferred method of teaching math just doesn't make the grade. The researchers taught undergraduates mathematical principles they would need to solve future problems. Some were taught using concrete visual examples, like cups filled with water or a pizza cut into slices. Other students learned abstract formulas in terms like "n=x."
When asked to solve new problems using these teachings, major discrepancies appeared. In one case, abstract-learning students scored an average of 80 percent on a test. Their "real-world" counterparts, however, seemed unable to transfer their knowledge to a new situation, posting only a 44 percent average. The researchers say using concrete examples is alluring, because students seem to learn lessons faster. However, students who take the time to get abstract concepts down are able to get on the train before it leaves the station.
Word problems and real world example are the preferred method of teaching? Hmmm, things have changed. I seem to recall being taught by endless repetition of solving "8x = 24" and almost no repetition of "How many 8-slice pizzas do you need if 24 people want one slice each?" Which is good. The former teaches algebra. The latter teaches you to count pizza slices, which is helpful if your dream job is at Papa Gino's.
Wish I could read more about this, to find out exactly how the researchers used "pizzas and cups of water" to teach concepts to undergrad students ("this pizza is an electron with up 1/2 spin...this cup of water is an electron with down 1/2 spin") but I'm too cheap to pay AAAS the $10 for 24 hrs of the article, let alone $144 for a membership when the most scientific thing I get to do any more is ... well, read 60 Second Science feeds.