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Foiled by fractions: Children make more accurate comparisons than adults

Learning fractions in elementary school can be pretty traumatic but for all the gnashing of teeth, it turns out children are intuitively better than adults at comparing fractions. This ability comes from a youthful misperception of how numbers are spaced. In one context the misperception turns out to be helpful.

"If you have a hard problem making a salary decision, you might consult your five year old," says John Opfer, professor of psychology at Ohio State University.

OK, maybe he's not quite serious on that point, but Opfer says that children compare certain fractions more accurately than adults do. So if your salary offers are given as fractions-- like dollars per day or dollars per month, your five year old probably does have an advantage.

Opfer studies how children perceive the world, and how that changes over time. Lately he's been working on how they think about numbers. To find out how children, adolescents and adults think numbers are spaced, he uses a number line exercise.

"Imagine a very long line that runs from left to right," Opfer said. "And on one end of the line will be, say, zero. And on the other side of the line will be another number, say a thousand. And then we just ask children to place a number on the line, say where would a hundred go, where would ten go, where would five hundred go, and so forth."

In this task, children reveal a fundamental misperception about numbers. They space small numbers farther apart, and crunch the big numbers together. On the line, they place 100 closer to 1000 than to 1.

By sixth grade or so, they usually have it sorted out, and place 100 closer to the 1 where it belongs.

Take the inverse of all these numbers, though, and the tables are turned. If the number line is flanked by fractional values rather than whole numbers or decimals, it's the grown-ups who get confused.

Faced with a number line that went from 1/1 to 1/1000, adults generally thought that 1/100 belonged at the 1/1 end. Oops. They were ignoring the fact that 1/100 and 1/1000 are both really tiny numbers, and spaced the fractions based on the spacing of the denominators.

Kids also placed the fractions based on the denominators. But because they thought 100 was closer to 1000, two wrongs made a right and their fractional placements were accidentally accurate.

"They weren't dead on because in truth 1/100 and 1/1000 are both really close to zero so they should be very close together," Opfer said. "And children didn't put it very close together but they put it pretty close together and so the result is they were a lot better than adults."

When the number line problems were stated in dollars instead of plain fractions, the kids still did better. For example, they made more accurate placements of the relative value of earning a dollar per day versus a dollar per hundred days than did adults.

When the fractions are converted to decimals, the adults are back in the game. They also do just fine if fractions have a common denominator. Adults can compare dollars per day to pennies per day it's dollars per day versus dollars per hundred days that poses the problem.

Opfer says this discovery about the way people perceive numbers has implications for understanding how they interpret prices and discounts and how they manage their money.

"Numbers are the very stuff that finance is made of," he said. "Just take away the dollars and it's all a numbers game."

So if the financial decisions require comparing fractions-- adults, stand forewarned. Convert those fractions to decimals, or find a second grader.

Opfer presents his findings in Nashville this week at the annual meeting of the Cognitive Science Society.