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.

I do agree that there are a lot of factors!

ReplyDeleteAs a woman, I'm apt to resent any suggestion that women are less intelligent than men.

As a parent, I can't help but see that there ARE "inclinations".

I also started reading/math exposure with my son when he was 2. Also used Singapore math and also think that didn't matter so much. My kid ate up Singapore math books - and any math books. He just loves math. He just turned twelve and he's using Thinkwell's Pre-Calc program and enjoying it. ALSO, he's pretty competitive and thrives by conquering, mastering, passing others, etc. There's positive and negative in that. :)

My daughter is 18 months younger. I also did reading and math with her as a young child. She is fine at math but she doesn't eat it up the way her brother does. I recall, when she was age four, asking an educator for advice because it seemed like she was "hitting a wall" in her 1st or 2nd grade math book. The lady said "Your daughter doesn't need extra help. She's four." I just figured my son was "normal" and she would be like he.

It took me a few YEARS, slow learner that I am, to realize that math just isn't her "thing". Reading she is passionate about. She loves writing, art, languages. Math? Just okay. But to add to that, she is far less confident, far less of a go-getter than her brother, too. Not competitive. She loves to make fanciful drawings on the margins of her math book. :)

How much of this is gender, age, birth order, gifting, personality? Don't know!

Exactly right, Tara. There are so many variables involved when it comes to personalities and interests and capacities, it's impossible to know exactly what factors really matter. The hypothesis of biological difference at a population scale, however, is a crude and self-serving argument that reeks of the kind of Social Darwinist thinking that falls apart when subjected to a competent cross-cultural analysis. If we're looking for reasons why there are not more girls working in higher math professions, it seems like biology is a horrible place to start.

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