**by Raji Jayaraman and Peter N Burns***

We both have daughters who are good at math, but opted out of advanced math. In so doing, they effectively closed off entry into math-intensive fields of study at university such as physics, engineering, economics, and computer science. They used to be enthusiastic about math, but as early as grade three this enthusiasm waned, and they weren’t alone. It was a pattern we observed repeatedly in their female friends during those early school years, as boys slowly inched ahead.

This turns out to be something of a statistical regularity. Girls don’t start school hating math or doing worse at it than boys. Then, somewhere in elementary school, this changes for many girls and in some (though not all) countries, a gender gap in math performance appears. The reasons why girls sometimes begin to dislike or slip behind in math are important, wide-ranging and controversial, with scientists, psychologists, sociologists, and others all weighing in. What often starts as small fissure in test performance in childhood seems to be locked in by the onset of puberty. At this stage kids hit high school where they get to choose their subjects, and the great divergence is set in motion. Girls disproportionately opt out of math-intensive subjects. From there, there’s really no turning back. Girls tend to study subjects, and graduate with degrees in fields, that have lower math requirements. In the U.S., women receive only about a quarter of bachelor’s degrees in physics, engineering and computer science; the pattern persists in graduate school. That there are tragically few women in these professions, is a logical consequence.

What is remarkable about this great divergence is that the size of the initial gender gap in average math performance is itself, pretty unremarkable—typically under a quarter of a standard deviation depending on the country. In fact, in many countries, girls do at least as well as boys on average, and girls are well represented in the top tail of the math performance distribution. In short, girls do well in math by many metrics, both in absolute terms and relative to boys, and yet they opt out of math. Why is that?

As it turns out, girls who are good at math also have good verbal skills, and many have a *comparative *advantage in English, meaning they are good at English *relative *to math. Girls’ comparative advantage in English is thought to explain three-quarters of the gender gap in the intention to study math. This may well be a logical choice if girls are, in fact, better at English than they are at math. Still, girls don’t start off with this comparative advantage so the question remains: why does girls’ interest and their performance in math often wane as they progress through school?

We might begin with the contention most famously expressed by Larry Summers, former President of Harvard University, that this is an “issue of intrinsic aptitude”. This was widely rejected, including by his own psychology professors, as not supported by any evidence. Even the demonstrated ability of boys to develop superior spatial skills, which might conceivably have an evolutionary foundation (and for reasons we cannot fathom, is supposed to give them an advantage in math) can be reversed or eliminated with appropriate training. In his defence, Summers claimed to draw on his own experience as a parent: “there is reasonably strong evidence of taste differences between little girls and little boys that are not easy to attribute to socialization.”

The bit he got right is that understanding the influence of socialization is by no means easy. For example, while it is true that parents with a son preference tend to have daughters who underperform in math, the same is not the case for societies in general. On the contrary, countries with some of the biggest sociocultural, economic, and educational gender gaps produce grade four girls with the biggest advantage in math skills over their boy peers. The 2015 TIMSS study of more than half a million children in fifty-seven countries placed Saudi Arabia, Oman, Jordan, Bahrain, and Kuwait among the countries with highest gender difference in mathematics achievement in favour of girls. Conversely, when asked if they “liked mathematics”, the maximum gender disparity in favour of boys for fourth graders was in France, which in the World Economic Forum’s Global Gender Gap Report ranked among top eleven countries for gender equality. All of which is to say that social influences on gender disparities in education outcomes work in mysterious ways. So, where to next?

Back to the classroom, perhaps, where teachers, often themselves undertrained and uncertain of their own math skills, are delivering a curriculum that is the result of a decades long tug of war between educators, politicians and mathematicians. Perhaps because it has long been seen as a place to ‘learn how the think’, the math class is a bit of a battlefield, with reforms such as the ‘new math’ of the 1960s now considered toxic to politicians who instead incant ‘back to the basics’, whatever this call to undefined arms may mean.

One thing it certainly means is that teaching focuses on students’ performance at testing, and there is strong evidence that this in itself is responsible for driving a wedge between genders. Girls and women underperform when tested in a competitive, mixed gender environment, even though their abilities are equal when tested separately. Girls and boys with the same math test scores have very different assessments of their relative ability, with girls consistently underestimating themselves. A possible explanation for why the performance gap is greater for math than for verbal testing is that a math question has a right and a wrong answer and is therefore more sensitive to competitive stress. In fact, perhaps girls aren’t opting out of math because they actually have a comparative advantage in English at all; maybe the way math evaluations are structured gives them the false impression that they do. Sadly, the results of such testing become predictive of future performance.

That math assessments should be structured like this is not self-evident. Why should a discipline that seeks to develop the ability to abstract ideas and to manipulate them logically or analytically always have a right or wrong answer? How is logical or analytic thinking reflected in the ability to recite the nine times table? If a child were instead asked to think about the set of all living things, plants, animals and humans and draw their subsets and intersections, for example, would that reduce gender bias in testing? We do not know, and we will likely never know, because such experiments do not seem possible in a world where the teaching of mathematics has become a target of the same reactionary ideologies that threaten women’s rights in other areas. One thing we do know is that children’s educational ability in math is malleable; if only the system that teaches them were too.

Things could be different. If school curricula were not shaped by performance evaluations, or if the potential for mathematics were assessed more reasonably, maybe we could blunt the choice confronting our children and allow them to select a path based on their interest and aptitude, instead of grades. We could integrate the teaching of math- and language-based courses rather than treating them as diametric opposites. We could require that all kids take the same (high) level of a set of core subjects, including math and English. Universities could do away with high school course prerequisites for admission. Employers could stop placing a premium on certain types of specialization.

Unfortunately, this is not the world we live in. Our daughters and their peers are forced into a binary choice in high school —stick with math-intensive subjects or drop them. This suggests that increasing female representation will involve convincing a large number of girls that *would* have dropped math, to stick with it. There are thousands of wonderful programs that try to do this, including math camps that challenge girls, or fun activities to engage girls. Many such programs are successful at improving performance in math, feeding interest in it, or at least reducing anxiety about it, and that’s invaluable. It’s even possible that there’s a program out there so effective that it would have been successful at flipping our daughters, but that’s a tall order. If we ran such a program and our main goal was to increase women’s representation in math-intensive fields, our daughters wouldn’t be in our target group at all. The reason is not because they are privileged or are reasonably good at math (although these are also sound reasons to exclude them). Rather, it is because it would have taken an awful lot to get them to change their minds.

Instead, we would target girls who are on the fence. Girls who could easily go either way when it comes to math, because they like it as much as they like other subjects, or because they’re equally good or equally bad at math as they are in other subjects. A well-designed girls-and-math program targeted at these kids and their math-esteem, early enough, might very well tip the scales in favour of math. We hope there are lots of girls sitting on that fence because then maybe, just maybe, we stand a fighting chance of improving gender representation in math-intensive fields before it’s too late.

***

*Peter Burns trained as a mathematician and is now professor and former chair of the Department of Medical Biophysics at the University of Toronto. His research focuses on using ultrasound and microbubbles to image and treat the microcirculation in cancer.