[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
http://chronicle.com/colloquy/2005/03/math/
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
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?
» [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.
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.
[45]http://web.missouri.edu/~psycorie/
References
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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