Representation of women and the genius myth
In a recent issue of Science, there was an article entitled Belief that some fields require ‘brilliance’ may keep women out (hat tip Gary Cornell) that absolutely resonates with my experiences, both as a mathematician and as a teacher.
Namely, it talks about the extent to which women are discouraged to go into a field because that field is somehow reserved for “geniuses,” and women are rarely if ever bestowed with that label. Mathematics is definitely one of those fields; if you are exceptionally successful in mathematics, people call you a genius, and it’s pretty hard to be successful if people don’t think you’re a genius.
But other STEM fields have less of a reputation for geniuses, and they have correspondingly more women. Biology, for example. Moreover, there are some fields outside of STEM that have way fewer women, which seems unexplained unless you have the “genius” theory. Philosophy is the obvious example here, a very macho field.
In the Science article, they were reporting on a study done by Sarah-Jane Leslie, Andrei Cimpian, Meredith Meyer, and Edward Freeland, in which they surveyed researchers from all sorts of fields in all sorts of research universities and asked them to rate, on a scale of 1-7, statements about their own discipline along the lines of, “Being a top scholar of [discipline] requires a special aptitude that just can’t be taught”. Here’s the critical graph:
STEM subjects above, non-STEM below. The negative correlation is the key to this study. I am particularly struck by the difference between statistics and math.
It’s just one study, and the response rate was small, so the word is not final. Even so, I think this proves that we should look into this more, gather more evidence, and see where it leads.
Personally, I have already spent quite a bit of time trying to deal with this very problem in mathematics. For example, I’ve explained before how I deliberately teach kids an introduction to proof that emphasizes practice over the silly and distracting concept of having an innate gift. It works, and it’s more fun too, for both men and women.
If I were designing a curriculum for STEM subjects I would rely heavily on this idea to inform my approaches to all sorts of things, partly because I think it’s true, but partly because the other things we think might matter are harder to change.
If you think about it, it’s actually a pretty reasonable roadmap for how to attract a more diverse group of people to mathematics or other subjects. You just need to create an environment of learning that emphasizes practice over genius. Actively dispel the genius myth. Achieving that cultural shift gets harder the higher up the research ladder you go, though, partly because it’s hard for older people to give up the “genius” label they worked so hard for. But it’s worth a try.
mathbabe 
Yes, it’s all about genis envy …
LikeLike
An outlier here is literature, where (in English) women have been a substantial presence for 300 years and more or less on par for 200 years, despite the prevalence of “genius” view of the field. Another extreme positive example is musical composition, where the absence of women is stark (I don’t know about extremely recently, but historically) and the “genius” theory is highly dominant.
LikeLike
I think that the discussion about the math-intensity of the field is relevant. I’m surprised that the “Science” article said that philosophy is not math-intensive…at least at the university I attended it was (to the extent that you consider logic a math-related discipline). I would suspect that music composition is substantially more math-intensive than English lit.
LikeLike
Wow, philosophers seem to have a special smugness that just can’t be taught.
LikeLiked by 1 person
Judging by the graph, all 58 philosopher respondents must have agreed at a level of 5! (or close to that). In fact, eyeballing it, the x-coordinate of the dot looks more like 5.1, which is impossible. Anyway, an extraordinary level of agreement among philosophers endorsing a viewpoint that certainly seems very unphilosophical.
LikeLike
The simple explanation is that the question about “Field-Specific Abilities” was asked on a 7 point scale, not a 5 point scale (from the supplemental materials).
LikeLike
oh whoops. my bad, I will fix that.
On Fri, Jan 16, 2015 at 9:07 AM, mathbabe wrote:
>
LikeLike
I find this very interesting, but I think a degree of caution is needed in interpreting the result, because the degree-of-genius parameter also seems to correlate strongly with where a subject fits (in my perception, and I presume therefore other people’s too) on a pure/applied spectrum. I have always thought of the sciences that I learned at school as arranged in a line that goes maths, physics, chemistry, biology. Computer science would probably come pretty close to physics, and so on.
So is it that women are put off by the view that you have to be a genius to do certain subjects (which I object to because (i) it is false and (ii) even if it were true, there is no evidence that women cannot be that kind of genius), or is it that for complicated social reasons they tend to prefer subjects towards the applied end of the spectrum, and that happens to correlate well with the perception that genius is less necessary?
The two explanations are not incompatible of course — the perceptions about genius could be one of the complicated social reasons.
LikeLike
I tend to use the Italian example. As various Italian mathematician women have explained to me – and there are a lot of Italian mathematician women – in Italy it is not all that prestigious to be a mathematician, and in fact to do so you basically go through the same school as high school math teachers, but then you continue on past a masters to get a Ph.D.. So in that case it has nothing to do with the level of abstractness, and everything to do with whether it’s considered special.
On Fri, Jan 16, 2015 at 9:26 AM, mathbabe wrote:
>
LikeLike
But whether or not it is prestigious is not the same as whether or not there is a belief that you have to be a genius to do it properly. So although I agree that the Italian example does weaken my alternative hypothesis (since whether or not maths is a pure subject does not vary from culture to culture) it’s not clear what one should conclude from it. It seems highly unlikely that the reason the Italian system was set up the way it was is that in that country they don’t think that one needs to be a genius to do mathematics. It seems more plausible that it is just a historical accident that overrides other factors.
It’s interesting to compare maths with music. In music there is a widespread perception that to be a brilliant performer you have to be some kind of genius — merely doing lots of practice isn’t enough. But music is full of incredible female performers. Nowadays there are also lots of very successful female composers as well, even if that has not always been the case.
LikeLike
Yes, I agree, it’s not a perfect answer, but it does show how much expectations play a part. I’d also argue that “historical accidents” can be fixed if they are inconsistent with social values.
As for the music example, I think it’s a pretty good one, but keep in mind that a) in music people obviously know about practice vs. genius, and b) the blind orchestra audition has made huge improvements in the gender makeup of orchestras. The question is, how do we build a blind orchestra audition in other fields?
LikeLike
This type of shift is being very actively pursued in primary and secondary school math education, which I know well. I can’t speak to other fields, so it is possible similar things are happening elsewhere.
There are three prongs to the attack:
(1) change language and attitudes from a fixed mindset (talent is innate, results come instantaneously) to a growth mindset (effort and practice are key, results develop over time)
(2) explicitly recognize that there are many valuable skills that combine to an interesting mathematical result: asking good questions, formulating definitions, gathering data, testing hypotheses, finding a range of approaches, communicating mathematically, etc. This sounds a bit vague, but stands in contrast to the historical caricature that mathematical skill was one-dimensional and consisted only of (quickly) getting the *right* answer or, in more mature form, finding the proof. One other natural consequence of the current thinking is that collaborative/group work is prized, encouraged, and respected.
(3) recognize that different teaching styles, approaches, and models are valid, that students should be exposed to a range and encouraged to actively think about what makes sense themselves.
Now, I don’t really know how widely and sincerely these ideas are implemented. An alert reader would notice that point (2), particularly, stands in contrast to universal testing practice. When have you seen a standardized test that asked: make 5 conjectures inspired by this picture? or had prep instructions: please list the members in your working group at the top of the paper?
LikeLike
They report the answers to this question broken down into women and men respondents by field (Suppl. Materials p. 12). Mostly men believe it more strongly than women, though it depends strongly on the field. E.g. in Math on average women believe this 4.4 and men believe it 4.74; in engineering it’s 3.69 to 4.44 and in statistics it’s 3.65 to 4.49. On the other hand in anthropology women believe it 3.9 and men believe it 3.39, and in Music it’s 4.68 to 4.28 but I think those are the only fields where there is a large difference in that direction. (I’m not checking statistical significance.)
They also report a measure of composite GRE scores, in terms of standard deviations away from the norm (I think). The outlier in the positive direction is philosophy 1.35 sd’s above the norm and the outlier in the negative direction is Computer Science 1.10 sd’s below the norm. Whether this says something about computer scientists or something about the meaningfulness of the GRE is another question.
LikeLike
Computer Science appears to be somewhat an outlier, but actually I think it might fit the theory too. In CS, the lack of gender-balance is already extreme at Bachelors level, and at that level, the focus isn’t on “being a top shcolar” but on being a great practitioner. And I think the belief in “innate ability” is especially strong for being a great practitioner of computing (eg a great programmer); much more than for being a scholar of CS.
LikeLike
Fascinating and very true. Physics does have a certain problem in this direction. One colleague once told me that in effect there are only a few “great men” who move the field forward and everyone else’s work is just basically useless. This is a ridiculous opinion especially now in times of big collaborations, but it was ridiculous even before if you look at the history of big ideas.
That being said, after working for 10 years in academia as a physicist, the worst condescending macho asshole that I have ever met is still a philosopher who informed me that physics is just a “religion”. Philosophers seem to think that they are geniuses hovering far above the rest of us, and I can well imagine why philosophy might be a far tougher field to be in as a woman than physics, especially since in physics the person with the best arguments often wins eventually, which is clearly not the case in philosophy.
LikeLike
So it seems like we can all agree that philosophers are assholes.
LikeLike
That was a joke, by the way. There are some very nice philosophers. And some very not nice ones.
LikeLike
I haven’t known many philosophers, but those I have known have been strikingly sweet people, and not particularly more arrogant than anyone else.
LikeLike
Artists and musicians probably give another set of examples. Just after reading this post, for some unrelated reason I found myself going through Rolling Stone’s online list of “100 greatest guitarists.” I couldn’t help but be amazed that, unless I missed one, there are no women in at least their TOP 60 (I got tired of checking after that). I imagine that an equivalent “top 60” list for ANY of the fields mentioned in the Science article wouldn’t be as bad as that (and I’m sure people have commented on this before). If you read RS’s blurbs about each guitarist, the “genius myth” is everywhere.
LikeLike
As regards music, which Gowers also raised, it is striking that “Music composition” in the chart above is way below the line; it is apparently not particularly thought of, by its practicioners, as a “genius” activity, but the percentage of women PhD’s (about 15%) is by a long shot the lowest of the humanities; eyeballing it, it even looks slightly lower than physics and CS, the worst of the sciences.
LikeLike
Yes, it is way below the line, with many fewer women than predicted by attitudes, but it is quite strongly thought of as requiring genius. It is in third place, ahead of physics!
LikeLike
In terms of music performers, rock music, particularly in the early days, was notorious for featuring “the man and his guitar”, sometimes with an admiring chanteuse in the background. (There are exceptions.) Women have had a much larger place as classical performers for a long time. But not as composers until recently, as Gowers mentioned; if you find some list of classical composers before 1970 or so, you would probably have to go down to about 100 before you reach Clara Schumann or someone. Worse than practically any of the other arts or probably even the sciences.
LikeLike
Data for orchestral music for 2010-11 is here:
Click to access ORR_1011.pdf
Among the 25 most often played composers, there is not a single woman.
Among the 25 most often played living American composers, there are only 2 (judging by first name): Joan Tower is 3rd on the list and Jennifer Higdon is tied for 7th.
LikeLike
Years ago, I heard that it was teachers who were discouraging women from STEM. Recently, female math and computer science majors at my university tell me that they were never discouraged by teachers. When they were 12 – 14 they were discouraged by other 12 – 14 year old girls from doing well in STEM. That’s more insidious – we have some hope of raising the consciousness of teachers – but of 12 – 14 year olds?
LikeLike
Yeah the discouragement from girls is really difficult to deal with. As a teen girl I was way ahead in math (my parents both taught me a ton) and my teachers in my honors high school considered me exceptional. But the term genius was used as a negative snide remark by the other girls.
LikeLike
It’s also possible that very little of the supposed “genius effect” involves DIScouraging women, and the unbalancing is predominantly from ENcouraging men who are (perhaps delusionally) more drawn to the genius model and the PhD-precursors that correlate with it, such as competitions and accelerated education.
For example, the study could have surely found a similar correlation by looking at fields where “competitions and accelerated education” (or comparable early performance) play a large role. This is consistent with music composition, theoretical science, and computer programming being majority male, and laboratory science and social/historical subjects having more women.
Studies that look only at the relative number of men and women in the field cannot distinguish male-encouragement from female-discouragement. Or the discouragement being endogenous (women not wanting to be around genius-wannabe males) rather than disparities in the treatment of men and women.
LikeLike
The “competitions and accelerated education” explanation hardly applies to philosophy, as far as I know. Musical _performance_ (not listed here, because no PhDs) where the genders are fairly well balanced, has a lot more competitions and accelerated education than musical _composition_ where the gender imbalance is acute.
In any case, I’m not sure how what kind of data could distinguish between encouragement of men and discouragement of women. The data show a relative effect; men are encouraged more than women.
LikeLike
I think many women are definitely put off by the perception that one must be a genius to enter math (and other fields). This was my experience decades ago when I was the only girl left in the top math class in my high school, despite having several peers who were more capable than many boys who remained. Currently, the young woman who asked Cathy, “How do I know if I’m good enough to go into math?” was expressing the same hesitancy.
Women tend to underestimate their own ability, whereas so many men (very confidently) overestimate theirs. Add the general tendency in our society to judge that a woman with identical ability/experience is less able than her male counterpart. Is it any wonder that both internal and external pressures keep women out of fields in which the genius-myth is perpetuated?
LikeLike
My observation has been pretty much in line with what you wrote, Kari. My solution, at least as far as my own daughters w.r.t. STEM, was to encourage and to answer: “Yes, you are more than just smart enough. You are brilliant.” Rather than bust the “genius-myth,” our job as parents and as educators is to provide young girls with encouragement and to boost their confidence. One young woman at a time.
LikeLike
Maybe you have more credibility with your daughter than my father had with me, or than I have with my daughter….I did not see myself as a “genius,” which I definitely thought one should be do be a mathematician (I went into medicine). Fortunately my daughter (who lacks the confidence to accept the positive input she has received on her abilities) has taken to heart that hard work and persistence are the key, given a certain level of natural ability (which is all she will believe she has).
LikeLike
I agree it’s easier to think “I can work hard” than it is to think “I am a genius,” even if people are telling you both things. Personally I never thought I was a genius, it was more like, “people are still letting me do this!”.
On Sun, Jan 18, 2015 at 8:23 AM, mathbabe wrote:
>
LikeLike
Everyone’s experience is different, but as parents we need to encourage our children. As a teacher, I’ve seen the difference between parents who encourage and care, even if just at the “capable” level, and parents who don’t. I’ve also seen the debilitating effect of parents who call their children stupid.
LikeLike
Maths (and music composition) do seem to be especially ‘blessed’ with foundation myths about geniuses (CF Gauss, Galois, Mozart, Beethoven). Maths also has hagiographers such as ET Bell. Statistics, as an example, seems less replete with genius myths, even if the giants of statistics were/are exceptionally able people. I suppose WS Gosset has to take some blame here, due to publishing anonymously, but possibly also there is some unease about some of the founders’ role in also founding eugenics – for that reason alone, it’s hard to imagine the Karl Pearson biopic getting greenlit.
LikeLike
Let them keep the label genius just like an athlete is still called an athlete but remind people that genius is created by hard work just as great athletes are created by practicing.
And then remind people with their genius kids that its super great that their kid loves spending all day doing mathematics but that people who earn their PhD at 22 are just thrust into the adult world of postdocs younger and get no particular advantages over those who finish at 25 or 27. In fact, they can have more difficulty landing a job.
Last of all remind people that a whole ton of top quality mathematicians went to public universities as undergraduates and that getting into an Ivy League is not necessarily the best prerequisite for becoming a scientist.
LikeLike
I just now came across a wonderful old article titled “The importance of stupidity in scientific research”
http://jcs.biologists.org/content/121/11/1771.full
___________________
Unrelated comment:
I might be taking a sentence from your post out of context, or misreading it, but you wrote about mathematics: “it’s pretty hard to be successful if people don’t think you’re a genius.” What? I guess if your definition of success is becoming a Harvard professor or a Fields medalist, then okay. But for me personally success would mean being a professor at any old place, and publishing papers that are small contributions to my field. I hope that can be done without people thinking I’m a genius (and I know I am stupid, and several professors have said effectively that about me (but not directly to me)).
____________________
Unrelated comment:
The people (men and women) that I’ve known that have left math or math grad school realized that there are more worthwhile (for them personally) things to do with their life than spend the time required to pursue pure math (and a lot of that time is spent alone and being frustrated – even for the best mathematicians). Over at http://www.quora.com/What-is-a-good-tagline-for-pure-mathematics
it was asked, what is a good tagline for pure mathematics, and the most popular answer, by a long shot, is
“Bringing solutions which nobody understands to questions nobody asked.” (paraphrasing of Dr. Bernard Beauzamy)
LikeLike
It seems to me that the emphasis on “being a top scholar” is unhealthy by itself. I really don’t know what it takes to be a Deligne, Kontsevich, Tao or Thurston. (Although I know that Terry has written some very good posts on this issue https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/ https://terrytao.wordpress.com/career-advice/work-hard/ ).
I can definitely say that I know lots of people who hold tenured positions and do interesting research who do not strike me as geniuses. For me, one of the most important realizations was that I want to do research which people find useful and or beautiful, and I want to help my students grow in ability and confidence, and that I don’t need to be at the top to do those things.
LikeLike
David, that’s an odd thing to say considering that you, and half of the co-authors listed in your bibliography page, excelled in math/science competitions. That’s true for both the male and female collaborators. That is, a large percentage showed the intimidating sorts of precocity associated with “expectations of brilliance”, as this study calls them.
A majority of Cathy O’Neil’s co-authors (on math papers) participated the International Math Olympiad.
JSE and Terry Tao and (pretty much everyone else getting high profile research done but writing online that genius is over-rated) have similar collaboration statistics.
Those rates are much higher than the representation of former genius/precocious folks in the pool of potential co-authors. The actual explanation is that people who showed precocity continued to have a far higher productivity as researchers and are thus overrepresented. “Genius” qualifications are not everything, but the things they measure often do count for a lot in mathematical fields, and not all of those differences conveniently disappear as the cohort gets older.
LikeLike
Captain Obvious, there’s a selection bias going on here. People who don’t do well with competitions often leave math. So what we’re not seeing is all the wonderful people who are bad at competitions that should have been my collaborators but left. Not to state the obvious.
LikeLike
That bias may exist, but is beside the point that you are citing it to address.
That point, again, was that from the pool of potential collaborators who did NOT leave math, somehow the child-genius types are drastically over-represented in
writing papers with you, JSE, Terry Tao — and a similar
level of over-representation when looking at prizes and citations and grants that are based predominantly on the actual work, not “being a genius”.
There is a different selection effect, that y’all being in Top 20 departments, there are more former genius types around as potential collaborators, and networking effects. But none of this seems like enough to explain the actual huge levels of overrepresentation observed.
LikeLike