LOOKING FOR THE ROOTS OF STATISTICAL DISPARITIES

Aug. 25, 1995 The Valley Times, Pleasanton, Calif.

Ask why more men than women excel at mathematics, and you will get two kinds of answers.

One sort of answer says society and culture are to blame, that women would do just as well as men if it weren't for the different expectations families and schools have for girls and boys.

The other sort says it's in the genes, that despite the vast range of abilities displayed by both men and women, the persistent statistical disparities in their achievements result in part from biological differences that exist from the moment of conception.

Ask me, and I say both kinds of answers offer part of the explanation, and in fact, reinforce each other. Yes, there are cultural stereotypes that tend to discourage girls from studying mathematics and science at all or from doing as well in those subjects as they could. Anyone who has survived junior high school can testify to that.

But the reason these particular stereotypes exist, rather than their opposites, is that it's much easier for cultural patterns to amplify biological predispositions than to counteract them.

The cultural explanations are emotionally appealing, and they're popular because they're easy to understand. Earlier this month, Stanford University professor Claude M. Steele presented his research on what he calls "stereotype vulnerability" at the annual convention of the American Psychological Association in New York and stirred up a flurry of media attention.

Steele studies the deleterious effects of believing in stereotypes, especially for women in mathematics and for African-Americans. In one experiment, he gave a difficult math test to two groups of women. One group was told the test showed gender differences, and for them it did. The other was told it didn't, and for them, indeed, it didn't.

These and similar experiments with minority students have convinced Steele that people tend to live up -- or down -- to what is expected of them. Anxiety prevents them from achieving their full potential, or sometimes even trying.

"When anxiety occurs on a chronic basis," Steele told The Chronicle of Higher Education, "what a person can do to protect him- or herself from that anxiety is to stop caring about that domain."

So far, so good. Students are more likely to thrive with academic support programs that challenge them instead of treating them like idiots.

But Steele also said he believes that the achievement gap will vanish once students are taught that it's merely a matter of expectations.

That's too simplistic, and a study by Larry Hedges and Amy Nowell, "Sex Differences in Mental Test Scores, Variability, and Numbers of High-Scoring Individuals," published in the July 7 issue of the weekly magazine Science illustrates why.

Hedges and Nowell's paper analyzes a number of large national studies, and concludes "although average sex differences have been generally small and stable over time, the test scores of males consistently have larger variance."

Well, that's not the kind of sound bite that gets you on the evening news. "Variance," the measure of how much a standard bell curve is all bunched up in the middle, is not in most people's everyday vocabulary.

Men's scores, on a wide variety of intelligence and achievement tests but especially those of quantitative and spatial ability, spread out more than women's. Not by much, but a small difference in variance makes a big difference far out on the tail of the bell curve, among the people who have particularly high or low scores.

Among the people who win National Merit Scholarships, for instance, where the smaller number of female winners is a perennial cause of outrage.

The customary explanation is bias in the tests, or more generally discrimination against women. People like to believe that, but the problem is that the phenomenon Hedges and Nowell describe is symmetrical. If it's discrimination that is pushing the test scores of above-average women down, then the same discrimination is simultaneously pushing the test scores of below-average women up. That's harder to believe.

There are many more men than women also at the lower end of the bell curve, but since they're not usually applying for college, they don't show up in the results for the Scholastic Assessment Test.

The further out on the curve one looks, the larger the differences are. For the mathematics part of a large study called "Project Talent," the male-female sex ratios were:

1.3-to-1 for the top 10 percent

2.1-to-1 for the top 3 percent

7.0-to-1 for the top 1 percent

Most of the people who are "poised to succeed in the sciences" come from the top 10 percent, the authors note.

"The achievement of fair representation of women in science will be much more difficult if there are only one-half to one-seventh as many women as men who excel in the relevant abilities."

But what's "fair"? If young men and women of comparable ability are equally able to aspire to success and to achieve it, that meets my definition of fairness, and I don't care whether they are born in equal numbers.

Nor do I see what we could reasonably expect to do about it if they are not.

What can we reasonably do? It's not constructive to put all the blame on discrimination. Internalizing the assumption that you're not really very good at math may be damaging, as Steele says, but so is the assumption that everybody's out to get you.

There's no easy answer to the question I began with, but students deserve our best attempts to provide an honest one.