Women, maths, and gender stereotypes

Above: a meeting of Portuguese mathematicians

Cordelia Fine’s book “Delusions of Gender” finds that a repeated theme in arguments about biologically-determined inequalities is that girls and women are worse at maths, and mathematically-structured fields like physics.

The “compensating” claim is that girls and women are, supposedly, biologically determined to be better at empathy and caring.

The nearest to a “proof” of this claim is the results for “mental rotation performance”, “the largest and most reliable gender difference in cognition”. Males are usually found to do better, on average, than females in telling rotations of three-dimensional shapes apart from mirror-reflections.

Fine reports research with Italian high school students who were told, before being tested, that “women usually perform better than men in this test”. The women then performed just as well as the men.

Even if the difference were real, why would that generate difference in maths more than in, say, visual arts, design, and architecture?

Aside from visual dexterity, the other qualities required for maths are, if you think about it, ones stereotypically identified as “feminine”: precision, attention to detail, neatness, imagination, ability to hold onto many ideas simultaneously, persistence and stamina, self-critical attitudes (most mathematicians get most things wrong most of the time), and sociability and cooperativeness (maths is the most social of sciences).

The quality cited as essential for maths and supposedly “masculine” is logical, analytic, systematic thinking.

In the first place, why would logical, analytic, systematic thinking be less important for law than for maths? Yet the photo which my younger daughter has just put on her Instagram account of herself with the other Judge’s Associates at the Supreme Court of Queensland (the top-end just-graduated law students there) shows 13 women and 5 men.

In the second place, different people are good at maths in many different ways. Some can “see” mathematical relations quickly by visualisation; others can get little from diagrams. Some are brilliant calculators; others are quick at seeing possible approaches, but relatively slow at checking them out by calculation…

And some excel at painstaking logical analysis, while others excel at leaps of intuition and imagination. (See here for an example: Heaviside and Schwartz).

I see no evidence that women are systematically “good at maths” in different ways from men. But even if they were, they would still be “good at maths”.

The “mental rotation” test, as above, should identify women as worse at visual studies as much as at maths. Yet in British universities, 65% of students in creative arts and design subjects are women, 50% of architecture students (and 62% of law students). In all those fields, men do better at the best-paid senior end, but that can hardly be because of aptitudes biologically imprinted from babyhood.

Yet in the UK still only 37% of university maths students are women. (Only 21% of uni maths lecturers, and only 9% of professors).

Things are better elsewhere, and, oddly, not necessarily in countries where women’s equality is generally better.

Possibly best in the world is Portugal, where 46% of university maths and computer science students are women, 68% of maths Ph D students, 50% of maths lecturers, and 32% of maths professors.

Fine reports that in Armenia close to 50% of university students specialising in computer science are women (UK: 17%). The explanation which Fine got from Hasmik Gharibyan, an Armenian woman professor of computer science now working in the USA, is unexpected:

“In Armenia, ‘there is no cultural emphasis of having a job that one loves… The source of happiness for Armenians is their family and friendships, rather than their work… [So] there is a determination to have a profession that will guarantee a good living’.”

Fine explains how “stereotype threat” – the need to use mental energy fending off negative stereotypes – hurts in maths.

“Stereotype threat hits hardest those who actually care about their maths skills… and thus have the most to lose by doing badly, compared with women who don’t much identify with maths. Also, the more difficult and non-routine the work, the more vulnerable its performance will be to the sapping of working memory”.

She also quote findings from Shelley Correll in 1988 that among US high school students, boys tended to rate themselves as better at maths than girls would, at each level of actual achievement. There wasn’t the same male self-overrating, and female self-underrating, on verbal skills.

“Boys do not pursue mathematical activities at a higher rate than girls do because they are better at mathematics. They do so, at least partially, because they think they are better”.

Heather Mendick, who did a Ph D study on maths and gender in UK schools and came to talk with one of my classes about it in July 2018, found the same: girls are more reluctant to call themselves “good at maths”.

I think this may have shifted, or at least that more subtle mechanisms are operating.

Ten of my students were in class when Heather came, five girls, five boys. I asked them at the end: “Do you think you are good at maths?” Four of the girls said yes; one said she was just “ok”. Only one of the boys said “yes”; four said they were just “ok”. I’ve had similar responses elsewhere.

When in the course of the discussion Heather said something like: “Of course, maths isn’t easy for anyone”, the whole class immediately responded by laughing and indicating one of the girls: “Except for some!”

At least at some level, I think that girl knows she’s brilliant. In fact, most of my classes at that school have included girls recognised by me and by their classmates, and, at least eventually, by themselves, as stars.

Yet I’ve always found that the boys are more likely to attempt prize problems, outside the syllabus, than the girls. The boys are less worried by the risk of falling flat on their face with such problems.

My reading is that girls are more likely (on average! for socially-conditioned reasons!) to think that they’re good, even very good… but maybe not quite good enough. Boys are more likely to think that they’re maybe not brilliant… but good enough.

Fine’s argument about “stereotype threat” would fit into that picture.

Shortage of confidence (even at the level of thinking “I’m very good… but may still not good enough”) is a bigger difficulty in maths than in other subjects, I think. Asked to write an essay on the rise of Hitler, even the least confident student is likely to write something (and then can be told: “This is good!”) Asked to show, say, that in every right-angled triangle with whole-number sides, the three sides multiplied together must make a number divisible by 60, the less confident student is likely just to freeze and write nothing, while the more confident will make attempts, not be too worried if some attempts are way off the mark, and probably come up with at least some good ones.

The examples of Armenia and Portugal suggest that winning equality for girls and women in maths is not just a straightforward subsection of winning general equality. But it can be done.