Jane has $3.05 in nickels and quarters. If she has 13 more nickels than quarters, how many coins does she have? According to the conventional thinking, real-world examples such as this one are the best way to teach mathematics. When researchers at Ohio State University tested this hypothesis, however, they found the opposite to be true. They showed college students a mathematical pattern using either a concrete example (in this case, measuring cups filled with water) or an abstract example involving symbols, then had them play a game that drew on their new skills. The subjects who saw the abstract example performed significantly better in the game than did those who learned the pattern with measuring cups. Jennifer Kaminski, lead author of the study, hypothesizes that real-world examples might distract students from the mathematics being represented. “We think what’s driving this is attentional focus,” she says. (And by the way, Jane has 29 coins.)
This article was originally published with the title Word Problems.
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Add CommentThe presentation of a problem is more real for those in the process of growth and accumulating experience. After a saturating amount has been
Reply | Report Abuse | Link to thisaccumulated, then the use of abstracts, as symbols can function in the learning process. This implies that variation in absorption of real puzzles and those of symbols depends upon the brain's capability. which denies the mundane application "we are all born equal" and sustains the reality that this can only be true with the flexible factors of God.
The problem with these math questions is that students focus to much on the actual physical problem and do not let their imagination "see" a natural and simple method of discovery of unraveling the question. I solved the question using the traditional "let x" , finding an the equivalent equation in one unknown.....two variables with two equations could also be used here but it would make the question become too heavy (always follow Occam's Razor).
Reply | Report Abuse | Link to thisI then went back to the question to see if i could of done mentally, by visually the algebra and quantities, the same solution drop out in seconds.
Having an open mind for multiple ways of attacking a question is not common at the elementary or secondary level, most teachers want their way or else....I try to show my students many ways in seeing a problem; the original problem will call different people in different ways to solve it....it should be natural to be original, curious and freely discuss each other method or algorithm.