Of Math and Men

Barbie thought the algebra exam was hard, and Ken didn't do much better. But he's probably more convinced that he aced it.

Much has been made of the math gap--the discrepancy in performance between males and females. But according to Jennifer Gutbezahl, M.S., of the University of Massachusetts, the male superiority in math scores pales beside the gender gap in overconfidence. And believing that you've done well on a math test, it turns out, may bear little relation to how you actually did. Gutbezahl asked students to determine which of two solutions was right for a probability problem (see below) and to indicate how sure they were of their picks. Men and women fared equally badly, choosing the correct answer only a third of the time--worse than chance.

Despite their dismal performance, guys thought they'd done well. But their confidence had little grounding in reality. One speculated he'd earned a perfect score on a 20-problem exam given earlier. Trouble is, he didn't even answer all the questions.

Psychologists have long presumed students benefit from having more faith in their math abilities. But self-esteem gets you no closer to a passing grade, says Gutbezahl: "The people who had a lot of confidence did no better than those who thought they were poor at it."

Educators, take heed. U.S. students are among the world's most confident, yet they perform worse than their counterparts in most industrialized nations. "It's not that our students can't do math," Gutbezahl asserts. "But more energy has been spent making them feel good about it than teaching them how to do it." So when it comes to solving for y, mere self-assurance may not be the answer.

PANCAKE PROBLEM

There are three pancakes in a restaurant kitchen. The first is burnt on both sides: the second is burnt on one side but not the other; and the third is not burnt on either side. A pancake is selected at random and served to you, the customer. You notice that the top side of your pancake is burnt. What are the odds that the bottom is also burnt?

ANSWER

There are three possible sides you could be seeing: the two sides of the double-burnt pancake, and the burnt side of the half-burnt pancake. You're twice as likely to be seeing one of the two sides of the burnt pancake, because there are two sides you can be seeing. Because two out of the three possibilities involve seeing the double-burnt pancake (and thus having the bottom of your pancake also burnt). the odds of the bottom being burnt are two out of three.

PHOTO (COLOR): Against all odds: guys did no better than gals at solving the pancake problem.