Women, men and mathematics

Oh boy.You may recall, back in 2005, some controversial statements from Harvard’s President Laurence Summers on the issue of the underrepresentation of women among the faculty of hard science and mathematics departments in top tier research and higher education institutions. Most of the responses to this event were underinformed on the current social science evaluation of factors as well as facts, but one exception to this trend was a debate held at Harvard on The Science of Gender and Science between the cognitive scientists Steven Pinker and Elizabeth Spelke. Fortunately for me, and maybe you, they filmed and transcribed this event, so feel free to catch up if you have a couple of hours before reading my responses.

They spend most of their time debating mathematical aptitude and gender differences, a subject that is near and dear to my mathematically sensitive heart. Both parties agree that there are statistical differences (i.e. trends, not absolute binaries) between the sexes that have biological bases. The conflict in the debate lies in how we can measure mathematical ability, and what impact is made by implicit descrimination.

As a mathematically inclined female with experience, at least as an undergraduate, in the field of mathematics, I was surprised at both the conclusions of the studies they cited and at their assumptions about success in mathematics, and hard science, in higher education and academia.

1. Apparently approximately half of the mathematics degrees awared at the undergraduate level are awarded to women, at least in the States. That is news to me. I was always in the minority in my math classes at McGill, and when the class size got under 12, I was always the ONLY female in the class (teacher included).

2. Pinker seems to think, like many others, that visual rotation of objects is some fundamental part of most higher mathematics. What? First off, from tutoring people of both sexes, I have the impression that there are usually different approaches to understanding the abstract relationships that are the building components of mathematical reasoning, and the analogies need not be strictly or even partially visual. I won’t say that my math homework never gave me dreams of dancing polygons, but much of the time I didn’t have and didn’t need a spatial representation of whatever I was trying to understand. Were spatial metaphores important to the mix of ideas that allowed me to construct these abstract concepts and relations? Undoubtably, not in the same way that spatial rotation is measured by comparing pairs of 2D representations of block structures in a multiple choice test. Often times, what was more important was the number of different logical statements I could keep in mind at any given moment, a matter of memory and perhaps succinctness of metaphores rather than pictures.

3. Spelke suggests that while there are differences in some abilities that relate to how mathematics is evaluated, they do not all point in the same direction. SAT and GRE mathematics tests have struggled to deal with the fact that some kinds of questions seem to favour male students and other favour female students. In order to properly represent

4. This is a matter of exceptions, not rules. As Pinker states, but then ignores, “Most women aren’t able to become Harvard mathematics professors because most men aren’t able to became Harvard mathematics professors.” In the process of the debate, they spent relatively little time exploring what it actually takes to become a professor of mathematics as opposed to a professor of psychology (with strong female representation since the barrier went down) or an accountant (also predominantly female profession as of this last generation of workers). This is forgivable because they are psychologists, not mathematicians, and so don’t know what they are talking about, but it still brings up my own questions.

The questions of perception derived biases do come up in my own life. I remember being frustrated from the beginning of my mathematical studies by the fact that most of my peers (i.e. students that were performing comparably well in basic algebra and advanced calculus) had benefited from extensive private study of mathematics prior to beginning this degree. They often had a parent (read father) who was a mathematician or engineer, or had been singled out by a high school math teacher and given extra materials and attention to learn outside of the curriculum. In otherwords, many of my (male) peers had mentors in the field already. While I can explain some of this difference by the fact that I went to public schools rather than private, I do recall getting more of that kind of attention in other subjects, such as english and music, and thus can’t really complain. Who knows how much of the difference was circumstance, aptitude, gender bias or obvious overinvolvement in extracurriculars.

Certainly, a big factor in my performance as a math student was a lack of confidence, combined with a fear of competition, which effectively blocked me from working with my peers towards greater understanding. Had I been convinced of my greatness, and had I no alternative source of affirmation, I might have struggled harder and confronted those fears instead of knowingly letting them handicap my education. One fear was tied up in being the sorry representative of this otherwise underperforming sex. I didn’t want to be “the girl that couldn’t” in the minds of my classmates, for the sake of both my pride and my gender. Oddly enough, I think the resulting bluff worked more often than not, perhaps because most math students have serious confidence issues through assuming everyone else is getting all of this “obvious” material.

Anyway, there are plenty more comments to be made on the debate, but my soup is getting cold.

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17 thoughts on “Women, men and mathematics

    1. w1ldc47 says:

      That article is incredibly depressing. On the other hand, it seems to have been written by someone with an immense amount of privilege. I’m not sure in what manner that would colour his opinions, but it seems certain to me that it must.

      1. platypus_herder says:

        Fair points. Note that while I find it personally depressing (because it stamps on some of my career aspirations), I don’t think it globally depressing (inasmuch as it’s saying that a certain population are responding rationally to a market incentive).

        He certainly is very priviledged, and has his biases, but I’m reminded of an Oscar Wilde epigram about the validity of an opinion having nothing whatever to do with the sincerity (or in this case objectivity) of the man who expresses it.

    2. w1ldc47 says:

      I read some more stuff by this guy and I’m starting to suspect he doesn’t know nearly as much as he thinks he does. As someone who sits on the board of trustees of a not-for-profit organization, I have to say he’s kind of full of shit on that topic. I’m starting to suspect that the reason I don’t think he’s full of shit on other topics is just that I don’t know enough about them to realize it.

      1. platypus_herder says:

        A sound judgment, I think. Sadly, people who have been highly successful in one intellectual field do tend to acquire an inflated opinion of their own wisdom. French scientists used to be notorious for it.

        There’s a story I should look up from my first-year pseudo-science course about a historian and a physicist who were asked to examine some pseudo-scientific gobbledygook attempting to justify literal interpretation of the Old Testament (and other foundational stories, but mostly the Old Testament) as a description of actual natural disasters[1]. The historian opined that the documentary scholarship was bunk, but he found the physics interesting. The physicist said exactly the opposite.

        [1] Not all such speculation is pseudo-scientific gobbledygook, but this was.

      2. w1ldc47 says:

        U of T has a first year pseudo-science course? Really? As in a course about pseudo-science? Please tell me that’s true. I will take it!

      3. platypus_herder says:

        At least when I went through the first-year Eng Scis all had to take a “philosophy” course entitled “Science and Pseudoscience” as part of their breadth requirements.

        Note that, unlike Faculty of Arts and Science, Engineering doesn’t generally let outsiders take classes that aren’t part of their required curricula (because we have a prescribed program of courses in Engineering). It’s a bit of a bee in Fred Wilson’s bonnet though, so you might see if he’s teaching any FAS courses with similar content.

    3. finnupham says:

      I’ve had the horror of reading that article before, and while some of his points are good, it doesn’t deal well with non-material motivations for career efforts. If all else fails, I’ll run off to join a non-profit and be happily poor with more flexible working hours.

      1. platypus_herder says:

        And I can head off to Europe or a second-world country. Only then I won’t be able to do the kind of physics my more ambitious self would like to do.

        One good point he does make (and the one that stings the most, for me) is that the non-material motivations we care about now may not be the same ones that matter to our forty-year-old selves. We may sneer at their motivations, and they will shake their heads at ours.

      2. w1ldc47 says:

        Be that as it may, we need to make decisions now based on the information we have now. I’m not going to choose a career that will make my current self miserable just on the chance they my future self will have different priorities. If my future self has different priorities, you know who will be a good person to handle that situation? Future me.

      3. platypus_herder says:

        A perfectly sound answer from someone who is in grad school because they enjoy being a grad student. Unfortunately I know a number of people whose non-material motivation for being in grad school is the hope of a career of discovery and scientific glory. They’re the ones betting that, if and when they discover something cool and get the credit for it (and that’s a bigger if than most people realize), it will have been worth all it took to get there for future them. They’re the ones who get bitter. If that’s not you then my comment absolutely doesn’t apply to you.

      4. w1ldc47 says:

        Hrm, that hadn’t occurred to me. When you say “a career of discovery,” what do you mean by that. I mean, sure, I would love to find a cure for AIDS and win a Nobel prize, but if I spend my life researching the evolution of pathogens in populations and the public health policies that can affect virulence in obscurity at some university or government office somewhere and never get my name in lights, that’s still “discovery” and it’s still better than being a plastic surgeon or psychiatrist, even if I will only make a tenth the money, you know?

      5. platypus_herder says:

        This doesn’t seem to apply to you (good) and it should probably be hashed out viva voce, but I think what I’m getting at is that the budding academics who sneer at material motivations and look forward to a career of solving interesting and important problems often (sometimes unconsciously) judge what problems are important or interesting by peer recognition. Often they were intellectual/academic big fish in high school and undergrad. Consequently, they have little idea of how big the world really is (even just the world of their research field), how hard it is to fight (politically as well as scientifically) for a share of recognition and resources against such a large field of competitors, or how much it will hurt them to be obscure.

        There’s a Montaigne essay (Book 1, XLI, since I shouldn’t just drop names) about how pride and concern for one’s reputation is the hardest weakness to overcome. Even those who make a vow of simplicity want to be remembered. So to find out that you gave up (additional) wealth, weekends, the chance to start a family at a sensible age, love etc in order to keep the respect of your peers (because you confuse that with self-respect) (I’m not exaggerating, I see all of the above sacrifices around me) and that at the end of the day *nobody cares*, can be an unpleasant shock.

        Now let’s talk about something more cheerful.

  1. w1ldc47 says:

    Did the debate mention the phenomenon of stereotype threat at all? Basically, it’s this phenomenon wherein people who are trying to perform a task that their group is stereotyped as being bad at will do worse at that task if the stereotype is made salient to them. The sad fact is that it doesn’t take much to make the stereotype salient, in fact the presence of one single man in a room full of women will adversely affect the women’s math scores (but not English scores).

    1. finnupham says:

      Not specifically, no. They did pull out research that emphasised how the same actions of infants, children and adults are interpreted to have different value depending on the assumed gender. Spelke I think did the research on showing people (maybe specifically parents) a video of an infant playing and being surprised by a jack-in-the-box, and then asking them to interprete the child’s expression. When the child was given the name David, respondents said that “David’s face was angry”, while the others thought that “Jane’s face was fearful”.

      The study that hits the academic arena specifically had professors consider two CV for potential hiring into faculty position. One CV was a gold star obvious shoe in candidate, while the other was pretty good but not amazing. Different groups got different gendered names at the top and here is how it went (to quote Prof. Spekle):

      “People were asked a series of questions: What do you think about this candidate’s research productivity? What do you think about his or her teaching experience? And finally, Would you hire this candidate at your university?

      “For the walk-on-water candidate, there was no effect of gender labeling on these judgments. I think this finding supports Steve’s view that we’re dealing with little overt discrimination at universities. It’s not as if professors see a female name on a vita and think, I don’t want her. When the vita’s great, everybody says great, let’s hire.

      “What about the average successful vita, though: that is to say, the kind of vita that professors most often must evaluate? In that case, there were differences. The male was rated as having higher research productivity. These psychologists, Steve’s and my colleagues, looked at the same number of publications and thought, “good productivity” when the name was male, and “less good productivity” when the name was female. Same thing for teaching experience. The very same list of courses was seen as good teaching experience when the name was male, and less good teaching experience when the name was female. In answer to the question would they hire the candidate, 70% said yes for the male, 45% for the female. If the decision were made by majority rule, the male would get hired and the female would not.”

      What shocks me about this result is that people have trouble admiting this kind of pattern. When a decision isn’t obvious on any issue, tiny little prejudices have a huge impact on nudging between one result or another – that is not just chaos theory, it’s common sense. What sucks is that it may be difference between my being happily employed by an institution or not.

      1. Anonymous says:

        Not that I normally read or refer to it, but the latest issue of the MIT Technology Review has a pertinent short article on page M17. There are probably copies hanging around campus somewhere, the geeks like to read it.

      2. w1ldc47 says:

        I heard about that. I think Sinead talked about it on the most recent Science Dude. Also, there’s data to show that when authors’ names are withheld from reviewers, the frequency of women getting published automagically goes up to representative levels.

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