[Paleopsych] Chronicle Colloquy: (Summers) The Unsolvable Gender Equation in Mathematics

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The Unsolvable Gender Equation in Mathematics
The Chronicle: Colloquy Live Transcript

    Wednesday, March 2, at 2 p.m., U.S. Eastern time
    The topic
    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
    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
    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?
      » [43]Primed for Numbers (3/4/2005)
      » [44]Where's Larry? (3/4/2005)
    The guest
    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.

                      A transcript of the chat follows.

    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.

    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
    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

    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
    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

    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
    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
    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

    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
        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.


   43. http://chronicle.com/free/v51/i26/26a00102.htm
   44. http://chronicle.com/free/v51/i26/26a00101.htm
   45. http://web.missouri.edu/~psycorie/

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