The Unsolvable Gender Equation in Mathematics
Wednesday, March 2, at 2 p.m., U.S. Eastern time
Lawrence H. Summers, president of Harvard University, said at an economics conference in January that "intrinsic" differences in aptitude between the sexes may be an important reason that men dominate the science-and-engineering work force. The remarks sparked widespread protests, in and out of academe, and Mr. Summers quickly apologized.
But a growing body of research suggests that there is some truth in his comments: That something in the brains of boys may predispose them to perform better on certain standardized tests of mathematical abilities. Hormones in women -- and in men -- apparently alter how well they can do particular cognitive tasks. And there may be biological differences that lead mathematically gifted men toward careers in science and engineering while pointing mathematically gifted women in other directions.
The research, conducted by psychologists and education experts, bothers academics who brook no discussion of innate cognitive differences between the sexes, but many scientists consider it persuasive. One psychologist says that a blind devotion to the concept of equal abilities "gets in the way of figuring out what makes us tick."
Other researchers, however, say that whatever biological factors exist, they pale in comparison to the pervasive social forces that push young women away from math courses and, later, from math careers. One female mathematician, who graduated summa cum laude from Harvard, says, "I no longer ask why there are so few women in mathematics; I ask why there are so many. I can think of few male mathematicians who would have stayed in the field if they had faced the prejudice and discrimination female mathematicians deal with."
What should we make of these conflicting views? What should colleges seeking to hire more women in math, the sciences, and engineering do differently? What role should academic departments play? Does Mr. Summers's experience suggest that research in this area is so highly charged as to be a risky career move? And do Mr. Summers's critics owe him an apology?
» Primed for Numbers (3/4/2005)
» Where's Larry? (3/4/2005)
David C. Geary, a professor of psychology at the University of Missouri at Columbia, is the author of Male, Female: The Evolution of Human Sex Differences (American Psychological Association, 1998). He suggests that evolution has led to innate differences in the abilities and interests of men and women, but he also says social forces play an important role in shaping how people develop.
Rich Monastersky (Moderator):
Welcome to The Chronicle's live chat regarding the gender gap in the math and science workforce in the United States. My name is Richard Monastersky and I wrote the article "Primed for Numbers," which ran in this week's issue of The Chronicle. The article explored some of the potential environmental and biological factors that might explain the gender gap. Our guest today is David C. Geary, a professor of psychology at the University of Missouri at Columbia and author of Male, Female: The Evolution of Human Sex Differences. This is a controversial topic and I've heard various reactions to the story, from people who appreciate it to others who are offended by it. Whatever your viewpoint, I encourage you to send in a question to Dr. Geary.
Question from Frank Forman, U.S. Department of Education:
What is the exact data-driven *positive* evidence FOR innate equality between the sexes regarding math and science ability? I am not asking this on behalf of the U.S. Dept. of Education, but it is a precise one.
David C. Geary:
This is an important question and brings up an essential point. There is no mathematics or science as we define it today in our evolutionary history. The academic fields of mathematics and the sciences emerged over the past 2,000 years and would not exist today without extensive social and cultural supports. For simple quantitative abilities that may have an inherent basis, there are no sex differences. However, spatial abilities and an intuitive understanding of tools and simple mechanics are likely to have an evolutionary history and these very basic abilities combined with enough training and basic intelligence contribute to the development of some competencies in mathematics and the sciences. Sex differences in these spatial and mechanical areas are related in part to prenatal exposure to male hormones. In this sense, any inherent sex differences are "remotely" related to mathematics and science.
As for innate equality. Achievement in any area of mathematics and the sciences requires focus and intelligence, and there do not appear to be sex differences in average IQ, or intelligence.
Of course, it is important to remember that all of these statements refer to group means and not individuals. Women who achieve in the mathematics and the sciences are very similar to their male peers in the same fields, in terms of mathematical ability, intelligence, and interest patterns. These groups are equal in many respects, but there are fewer women than men.
Question from Patricia Schwarz:
Why do so many men in science seem to believe that being completely empty of human feeling is the same thing as being completely filled with logic?
David C. Geary:
Many men in science, and this is also true but perhaps to a lesser extent of women in science, have a bias toward thinking about the world in terms of abstractions, and often focus more on mechanical rather than social things in the world.
The brain and cognitive systems that allow for sensitivity to social (e.g., facial expressions) and emotional cues in others are almost certainly different than those brain and cognitive systems that allow sensitivity to mechanical aspects of the world. All of these are different than the systems that underlie logic and intelligence.
In other words, in many cases they really don't understand people in the same way others do. This has social costs for them and those around them but focuses them on solving other types of problems that can ultimately benefit many people.
Question from Marc Mayerson, UCLA:
While there may be some indication that genetics may have a negative factor on accumulating an equivalent pool of potential female scientists and mathematicians, nevertheless a critical mass of female scientists and mathematicians DO obtain doctorates and apply for ladder positions, critical enough to equalize the staffing of even the most highly respected research universities. Can you agree that, at such point, genetics could not possibly affect the hiring and promotion process, and if so, how would you account for the dearth of female professors in science and mathematics departments?
David C. Geary:
I'd rather not say genetics, because it is a long way from gene products to a PhD in science. Still there do appear to be biological influences on some sex differences that contribute to this attainment.
To your question: In absolute numbers, yes there are many talented women with PhDs in mathematics and the sciences that could staff many of these positions. But, if you have two male applicants for every female applicant and assumed that choices were not based on gender but on other factors such as content of research area, then the result would be more men than women in these positions.
I would not like to see any type of quota on the numbers of men and women hired in these important positions.
Rather, if the goal is to increase the number of women on mathematics and science faculties, then one potential solution is to create positions in subareas in which their are as many women as men, or more women than men. In the biological sciences, there are as many women (maybe more) primatologists as men. One way then - without any bias one way or the other to hire a man or woman - to increase the number of women on the biological faculty is to hire more primatologists.
To get two women, you may have to make three hires (assuming an open search based solely on merit), but wealthy universities can afford to do this. These would be new faculty lines that do not take away from existing positions and thus would not create tension in the hiring department.
I told know about mathematics, but there may be more women in number theory than in geometric areas. If so, create more positions in number theory.
Question from Joseph B. Powell, UC Santa Barbara:
Given that "rising" in any discipline is a thoroughly social process, e.g. in-group recognition, wouldn't any demonstrable differences in male and female achievement (presumably we are talking about a specific social-cultural group and not universal Male and Female)have more to do with the social history of female exclusion from math, science, and many other socially organized disciplines?
David C. Geary:
I don't believe that anyone who studies biologically-based sex differences believes that social influences are not enormously important, especially when it comes to long-term occupational choices and achievements. They clearly are.
If your suggestion is correct, then we would not have seen significant increases in the number of women entering medical school, a clearly science-based occupation.
Many of these women who choose to become physicians and many others who choose other, once male dominated fields, such as business could enter academic fields in mathematics and the sciences. And, more of them are than in past decades, but the gap in absolute numbers remains.
Research on these choices suggest that mathematically- and scientifically capable women have broader and more socially-oriented interests than their more narrowly focused male peers. These interest patterns influence which in-groups are important to you and which are not, and appear to be influenced in part by hormones. In other words, many of the women who could enter the lab believe that other work settings, such as a hospital providing direct care, would be more satisfying. Long-term studies suggest that these women are just as happy with their choices as women who enter the academic world.
Question from Ph. D student, College of William and Mary:
No doubt there are intrinsic differences between men and women, but is that the primary reason that there are so few women in math and science. I believe that this is an easy excuse to avoid looking more closely at society and the educational system itself. Are we teaching and testing students in a manner that is fair and understandable to a variety of learning styles? Or do we just expect students to adapt to the dominant teaching methodology in a field? To whom does the dominant teaching methodologies and practices in science and math appeal to? Could science and math be taught more humanistically? Could students be encouraged to use and develop their minds in a more holistic way? Would that make a difference in our world?
David C. Geary:
It is not yet known the relative influences of biology and society on career choices. If we look at education rates, numbers of boys and girls in special education, and other indicators of not adapting well to the school environment, then one would have to conclude that schools are better serving girls than boys. Why more girls than boys in undergraduate programs, for instance?
It is not a question of what students, boys or girls, find appealing. It is a question of what the most effective methods of instruction are, and whether these differ for boys and girls. I suspect that as you increase appeal you decrease effectiveness, or at least there is some type of trade off. The educational system in this country is undeserving both girls and boys, that is, resulting in much wasted potential in the name of catering to student-centered and often untested assumptions about learning styles.
In any case, once we more fully understand how girls and boys think about and solve math and science problems and differences in these strategies as related to long-term outcomes, then we can begin to devise different ways to teach boys and girls. I suspect that for the most part, what is good for girls is good for boys, and vice versa.
Question from carol Moore Lyndon state college:
What is the growing body of information?
David C. Geary:
One of the most interesting and on going studies in this area is that of David Lubinski and Camilla Benbow. They continue to add to the empirical data base on similarities and differences in the career trajectories of gifted men and women who have the potential to succeed in mathematics and the sciences.
As for sex differences in general, new research is published monthly in many different scientific journals. A literature search on PsychInfo to Biological Abstracts will reveal many, many studies.
Question from Female professor, small university:
Do we have sufficient data to provide answers to these important questions? Should we be investing time and energy in obtaining the biopsychological (including genetic and physiological) data required to answer these and related questions?
David C. Geary:
We have a lot of information and clues to many likely influences, biological and social. Yes, we should study long-term occupational outcomes of men and women, and if there are sex differences we should find out why.
Question from Mary Anne Holmes, U-Nebraska-Lincoln:
The old chestnut "mentally rotating three-dimensional objects" surfaces repeatedly when discussing whether there are innate differences between male and female cognitive abilities. How exactly do we measure the ability to "mentally rotate 3-dimensional objects"? Are we still measuring this in a darkened room with the subject and an examiner? Have the results been repeated? What do the results actually mean in terms of how humans learn and what humans can or cannot learn? Much is made of this difference, and I am not convinced that the method of measurement gives us any information that is useful. What, exactly, is being measured, and what, if anything, does it signify?
David C. Geary:
These are measured many ways. An often used test is a paper and pencil version of the procedure you mention. The results are VERY consistent across age ranges, cultures, and historical periods. New methods of testing navigation in a virtual or real, large scale 3-D maze reveal larger sex differences than this standard 3-D mental rotation test.
Rich Monastersky (Moderator):
We're a little over halfway through the chat, so don't delay if you want to ask a question.
Question from Tom, southern medical center:
While I won't completely disregard the "genetic" factors that govern how men and women can think differently, I am interested in your comments on any reasons why some women seem to be successful in certain subdisciplines of the sciences (specifically biological and medical research) and not others (physical sciences). Even within the subdiscipline of medicine, there are certain areas where women (pediatrics) tend to excel better than men (surgery).
David C. Geary:
Great question. I suspect that much of the difference can be related to where women and men lie on a broad dimension of interests ranging from highly social to mechanical/theoretical. This maps onto a a broader interest in living things at one end and non-living things at the other.
Women tend more toward the social/living things end, on average, and men toward the mechanical/non-living things men.
I suspect that these differences any an evolutionary history, but won't elaborate here (see articles on my web page, which I'll post later). But, biologically and medicine map onto the living things end of the spectrum and physical sciences to the non-living spectrum. Both are very important!
Pediatrics, I suspect, relates to women's greater interest in children and "whole organisms" and surgery toward the "parts" that is the "machinery"
Question from Carol B. Muller, MentorNet & Stanford University:
"A growing body of research suggests that genetic factors predispose women to avoid those fields..." Here's my question: Who is pushing this agenda? The reason I ask it is that this kind of statement represents a real misreading of the research findings and their limitations.
The research cited in your background material has to do with test performance. Research over the last couple of decades has clearly shown that test performance can readily be influenced by environmental factors (see research on "stereotype threat," for example); a close reading of much of this kind of research shows fallacious inferences that children's test performance as 12-year-olds reflects "genetic" differences -- in 12 years of life, a huge amount of socialization has occurred, and social expectations influencing performance established.
Furthermore, no study has shown any correlation between the extreme upper end of the distribution on mathematics test scores and professional success in mathematics and science fields. If we look at sex differences in the brain from birth, we find a number of hormonal differences. If what is meant is that testosterone has become the predominant factor in the social construction of fields like math, science, and engineering, with hyper-competition and bullying aggressive behavior the predominant norms in educational and work settings, then one could agree that "genetic factors predispose women to avoid these fields."
But one might want to question, whether such behavioral norms are needed for scientific discovery and technology development, or perhaps a remnant of a society which historically severely limited women's opportunities to pursue education and employment despite their considerable talents and brainpower.
Rich Monastersky (Moderator):
As the person responsible for that sentence, I should probably explain it. The story discusses data that suggest there are biologically based gender differences in interests, which of course get modified heavily by cultural forces.
But at one day old, boys show a preference for looking at mechanical mobiles over looking a human face, whereas girls show the opposite. Later in the story, I discuss some research results showing that mathematically gifted young women also tend to be more gifted (than their mathematically gifted male peers) in verbal skills.
Not surprisingly, these exceptional young women have broad interests matching their broad abilities. They enter the math-and-science educational pipeline in lower numbers than mathematically gifted young men, who on average have narrower abilities and interests. Also, the data on students suggests that girls in high-school are more interested in careers that help people than are high-school boys.
Has the prevailing culture influenced these choices? Obviously, the answer is yes. But there also seems to be some innate component to the differences in interest, which would account for the data from 1-day-old infants, and may also account for the higher verbal skills in mathematically gifted young women (although environment could also play a big role there, too). My story also discusses ways to attract more women--and men--with broad interests to enter the science track.
David C. Geary:
I agree with Rich's response. I might also note that test performance in high school and earlier does in fact predict long term success in many fields, including mathematics and sciences. And, so do some dimensions of personality and social background. Stereotype threat seems to be important but does not explain the gap, especially at the high end of the math distribution.
Question from Andrew Mytelka, Chronicle of Higher Ed:
Underlying some of the criticism of Lawrence Summers's comments seemed to be the sense that there are some subjects that are so sensitive -- so potentially hurtful, to individuals and to society -- that they should not be studied. If research could verify that "intrinsic" differences explain the gender disparity in math, and if such a finding could hobble the progress of women in the field, the thinking goes, then maybe the research should not be attempted. Similar things were said a decade ago, when The Bell Curve posited that black people were less intelligent than white people. But in the aftermath of 9/11, biological scientists have agreed that they should not conduct research that would create dangerous viruses or that would make existing microbes more lethal. Could the same policy be developed for research on race or gender? Do you think that would be wise -- or just an evasion of the truth?
David C. Geary:
Good question. Any "intrinsic" influences on sex differences will emerge whether we discuss their causes or not, and whether or not we understand these causes. Intrinsic does not mean unchangeable. If we understand biological influences on the expression of sex differences and how these influences interact with experience, social context, etc, then we may be in a better position to make change. Creating a culture in which researchers will be socially or otherwise (e.g., loss grant funding) punished for studying these differences will ensure that any intrinsic biases will be expressed in future generations.
Question from Rich Monastersky:
I've heard from a female mathematician who objects to this whole line of research. Her point is that 20 years ago, she had to battle prejudices based on incorrect "proof" of innate differences. For example, in the early 1980s, there were 13 boys to every girl who scored 700 on the math section of the SAT at age 13. At the time, that finding was used to show that there are genetic differences in math abilities between boys and girls. Now, that ratio is 2.8 to 1, a drop that reveals how important cultural factors are in influencing abilities. So should researchers who look at innate differences face an exceptional responsibility and burden of proof before they publish results?
David C. Geary:
Researchers should look at all potential influences on any phenomenon that is of importance. There is no doubt that schooling influences math and science achievement and that girls and women have made great strides in recent decades and will likely continue to do so.
I don't have the raw data, but I wonder whether any of the change in the 13:1 to 2.8:1 ratio is related to change in test items or the recent recentering of the SAT (to adjust the mean back up to 500). As I understand recent changes, the number of correct items that produce a score of 700 is now lower, which will reduce the ratio without change at the high end. To know what is fully going on, we need to see raw test scores for the exact same items for the SAT in the 1980s and now.
Question from Mike Fulford, Georgia Tech:
Do colleges such as Harvard truly understand the power of the social constructs they have created throughout history in relation to gender, race, etc.?
David C. Geary:
You mean do people in high-profile institutions such as Harvard understand the potential social power they have with their statements and claims? Well, they certainly do now. What is unclear is whether these claims have real long-term effects on the career choices of gifted men and women. My bet is these budding stars have better things to do and aren't paying much attention to the debate.
Question from Dianne, southern HBCU:
What accounts for the increase in males from other countries in the math and sciences, even as students, and the drop in white males?
David C. Geary:
This one is easy. A very poor educational system in mathematics and the sciences in the US, especially in later grades and for gifted students. The relative proportion of US educated students, including white males, that can fill high-paying math/science jobs is decreasing as the number of these jobs is increasing. This creates an opportunity for well educated students, male or female, from other countries.
Question from Don Williams, Florida Hospital College of Health Sciences:
I am curious as to why this creates a firestorm when males score lower on other scales on standardized tests and in light of the downward trends in male participation and success in higher education?
David C. Geary:
Great question, I wonder the same thing. The magnitude of the advantage than boys and men have in some areas of math and in some areas of the sciences is about the same magnitude as the advantage that girls and women have on tests of writing ability. Girls and women also have an advantage on reading tests, but the gap is a bit smaller. As stated, there are now more women than men in undergraduate programs. If there are sex biases, they are working against boys and men too.
Question from Emil Chuck, Duke University:
Do any of these surveys take differences in international culture or education into account?
David C. Geary:
Yes. The magnitude of the sex difference in math varies across content areas and women in some countries outperform men in others. Within countries there is a small advantage for males, but this too varies. But, there does appear to be a consistent male advantage in math areas that require visualization and spatial abilities, especially as related to the solving of novel problems.
Rich Monastersky (Moderator):
That's all our time for today. Thank you all for participating in The Chronicle's live chat. And I also want to thank David Geary for taking the time to answer our questions.
David C. Geary:
I have a number of articles on the development of mathematical competencies, including sex differences, as well as articles on sex differences in general available on my web page.
http://web.missouri.edu/~psycorie/
Copyright © 2008 by The Chronicle of Higher Education