Ten years ago, Larry Summers, a former Treasury Secretary and at the time president of Harvard University, gave a set of remarks to a conference on diversifying the science and engineering workforce in which he posed some hypotheses about why there were so few women in science and engineering fields. He ventured three hypotheses. The first was that the career pressures of such positions were not as attractive to married women as they were to married men. The second was that there were more men than women possessing the “aptitude” to work at the highest levels of mathematics. The third was that men and women were “inclined” for various reasons to go into other fields. While all three claims feel strangely ignorant for a person in Summers’ position to suggest, it was the second of his hypotheses that really struck a nerve with the public at large. While Summers’ defenders in the media brouhaha that followed pointed out that he wasn’t saying that all women are innately less mathematical than all men nor even that the average woman is less capable than the average man, when you parse his words and shift them from the language of academia to the language of everyday communication, he was basically saying he thought that as a matter of biological difference fewer women than men might be capable of doing math at the highest levels.
Now, I’m ideologically suspicious of any biological claims made regarding the general superiority of one person or group over another. Usually, such claims are deployed – consciously or not – in a way that justifies a person or people’s position of power over others by claiming some inherent betterness in themselves. And if you look at Summers in this context - a white male economist moving in the upper echelons of academic, economic, and political power in America – such an alignment fits. He basically said within those remarks that women have neither the interest nor the capacity to handle the kind of work he does. He even made a spurious claim about how his twin daughters, despite not being given dolls, transformed other playthings into mothers and babies as a way of justifying his hypothesis on the differing inclinations of women and men. Hey Larry, did your children not go to preschool or have a nanny or play with other kids or watch TV? Where do you think ideas about gender roles come from? A child’s parents are only one out of a great many sources.
Anyway, the whole Larry Summers episode was brought back to my mind recently when Polly told me about the math groups in her kindergarten class. Polly has a good feel for numbers and, for reasons I’ll discuss in a few moments, is way ahead of the average kindergartener in handling the basic functions of mathematical thinking. As such she is working in the most advanced math group in her class and, as it turns out, all the other members in her group are boys. Now, the highest level reading group in her class has an even mix of boys and girls. Why should the math group be any different? It’s an anecdotal result that would cheer Larry’s heart and one that makes me shake my head. I had hoped things would be better than this by now.
In one chapter of his book Outliers, Malcolm Gladwell talks about hockey players and an interesting pattern that can be observed when one looks at which players ultimately make it into the highest levels of the sport. Interestingly, many have birthdays that come early in the year. Gladwell looked a bit more closely at this and found that Jan 1 corresponded with the cut-off date for kids joining youth hockey leagues in Canada. In other words, the kids who had birthdays early in the year – those who were at the oldest end of the league spectrum – tended to have a greater chance of developing the skills and talent necessary to play the sport at higher and higher levels. Gladwell attributes this correlation to the idea that the older kids were bigger, stronger, and more capable and thus garnered more developmental attention from coaches, got more playing time in games, and attained the kind of early success that keeps one interested in doing more. While Gladwell argued that one’s birthdate was no guarantee of success, it did create a slightly more favorable set of conditions and thus more of those players eventually made it into the professional ranks.
I’ve been thinking about Gladwell and Summers together because it seems to me that much of Summers’ argument regarding the distributions of mathematical thinking at the highest levels could be explained by a Gladwell-type argument. While I don’t know why the distribution in Polly’s class is the way it is, I can see how it would propagate from there all the way up through the ranks into the highest levels of math and science. The kids in the advanced group are getting the same kind of feedback that Gladwell’s older hockey players are. They are getting the extra attention. They are encountering the success that makes one want to keep going and doing more. They are not all going to be great mathematicians, but the odds say good mathematical thinkers are more likely to come from one of these kids than from kids in any of the other groups. They essentially have a head start that can increase with time.
Before I had children I always thought of kindergarteners as little kids not that far removed from infanthood. They still have their entire school careers in front of them. They were, I thought, a blank slate waiting to absorb the world. However, that’s just not the case. By the time they turned 5 both Polly and Pip were well established as people. Their personalities were solidly in place. What they’re willing to do and not do were largely set. Their aptitudes and interests had a solid form. Their school years will certainly be a time of adding and molding, but the foundations regarding who they are and what they know about themselves are already poured.
This reality makes me think that all the effort put forth in later years to bring more women into math and science fields, while not a waste of time, is something of a rear-guard action. The real ground where much of these relationships is getting decided is in the zero to 5 age group. It turns out, I think, that if you really want to head off the cultural influences that shape girls’ relationships to mathematical thinking, you have to get to them really early. You have to get to them when they are learning to speak, when their brains are making the transition from basic stimuli response to conscious and considerate thought. From what I’ve seen with my kids, there is a sweet zone in the 2-4 range where so much of their basic thinking is worked out. If you can get to them then, you can shape a good deal of their capabilities later.
And this is why Polly is in the highest math group in her class. I started doing simple math work at home with Pip when he was four and Polly was two (we used Singapore Math but I don’t think any particular program really makes that much difference). She looked over his shoulder for a full year then after he went to kindergarten the following year, I started her on the same program. By the time she entered kindergarten she’d had two full years of math already and was doing subtraction with three-digit numbers and substitutions. (She’s actually slipped a little since then because she hasn’t kept doing it). Polly is now good at math which makes all the stuff she’s doing in school easy. And because its easy, she does it well and she likes doing it. That momentum is going to carry her a long way. I don’t think she’ll be a math genius or necessarily pursue a career where math is central – right now she wants to be a veterinarian or zoologist or something else where she would work with animals – but, if we take the Gladwell effect seriously – and I do – she will be on the front end of her class in math from the rest of her academic career.
I think this will probably be true for another reason as well. I’ve consciously made her aware of the ideas Summers was espousing, and this has given her a bit of a chip on her shoulder. It was Polly who brought to my attention to the fact that she was the only girl in the highest math group. And she took relish in telling me last week about how she was already done with her math sheet and the boys still had at least half the page to go. They weren’t serious enough about doing the work, she said with a touch of disdain.
This chip is going to keep her working and that is something I don’t mind feeding. I even took advantage of her moment of triumph over the boys to start giving her one math problem a day when she comes home. We’re not going to do new material until the summer, but I’d like to get her back up to where she was this past fall. That way we can plow forward come summertime and Polly will be well situated for another year of math to come.
I don’t know why the distribution of mathematical prowess in Polly’s class is the way it is. At this time, I don’t have the data to completely rule out Summers hypotheses regarding biological differentiation. However, I don’t think they’re right. Polly is not in the most advanced math group in her class by accident. She was not freakishly inclined towards mathematical thinking from the start. She was exposed to math principles early on and has been doing math work regularly ever since. This kind of socialization is more fundamental than any biological differences one may find.