I mentioned a few posts back that Steven Pinker’s book “The Blank Slate” convinced me that there probably are SOME behaviorally genetic differences between human males and human females. He cited a number of excellent examples, including very convincing work involving people who were sexually reassigned as infants tending to spontaneously gender-identify with their biological sex.
Meanwhile, some time ago I had done some comics on teaching math to girls. I was, and still am, of the opinion that it is not obvious that one gender should be superior at math. Math is such a diverse field of study, whose areas require such various suites of skills, that it just seems unlikely to me that one sex should be better in all areas. Some people have tried to deal with this issue in a way I don’t agree with. Notably, Danica McKellar wrote several math books for girls titled “Math Doesn’t Suck” and “Kiss My Math.” While I like the idea of appealing to middle school girls about math, I question the attitudes being layered with the math.
I actually looked through these books, and here’s what I found: Essentially, these are standard algebra texts, but the word problems are often about fashion and shopping, there are asides about relationships, and (the only truly damning thing) there are “math horoscopes.” I dislike this because I believe math is in essence genderless. It is a matter of understanding how reality works. I also dislike the implicit assumption that girls will be more apt to get into math if it’s about shopping. I don’t think I’d be comfortable buying a math book “for boys” that involved guns and the trajectory questions of peeing while standing up. Bottomline, I think the goal should be to change the way young girls are taught (are allowed!) to think, rather than changing math to suit young girls.
That said, if there are behavioral genetic differences, it seems to me that it’s reasonable to suspect the route by which you arrive at good results (i.e. more women enjoying math and mathematical sciences) might lie in harnessing those differences. One of Pinker’s claims is that women are more likely to be interested on social issues. I don’t know if this is true, but for the sake of argument, let’s say it is.
Reading that idea made me think of another book, different in time and focus – A Tree Grows in Brooklyn, by Betty Smith. If you haven’t read this book, you should. It’s excellent, and was once standard middle school/high school reading. More importantly for this discussion, it focuses on a young girl (Francie) who is intellectually precocious. For example, the book describes the girl working her way alphabetically through all the books at the library. I believe she gets through “B.” Not bad. It also describes why she liked doing arithmetic.
From the book:
“She liked numbers and sums. She devised a game in which each number was a family member and the “answer” made a family grouping with a story to it. Naught was a babe in arms. He gave no trouble. Whenever he appeared you just “carried” him. The figure 1 was a pretty baby girl just learning to walk, and easy to handle; 2 was a baby boy who could walk and talk a little. He went into family life (into sums, etc.) with very little trouble. And 3 was an older boy in kindergarten, who had to be watched a little. Then there was 4, a girl of Francie’s age. She was almost as easy to “mind” as 2. The mother was 5, gentle and kind. In large sums, she came along and made everything easy the way a mother should. The father, 6, was harder than the others but very just. But 7 was mean. He was a crotchety old grandfather and not at all accountable for how he came out. The grandmother, 8, was hard too, but easier to understand than 7. Hardest of all was 9. He was company and what a hard time fitting him into family life!
When Francie added a sum, she would fix a little story to go with the result. If the answer was 924, it meant that the little boy and girl were being minded by company while the rest of the family went out. When a number such as 1024 appeared, it meant that all the little children were playing together in the yard. The number 62 meant that papa was taking the little boy for a walk; 50 meant that mama had the baby out in the buggy for an airing and 78 meant grandfather and grandmother sitting home by the fire of a winter’s evening. Each single combination of numbers was a new set-up for the family and no two stories were ever the same.
Francie took the game with her up into algebra. X was the boy’s sweetheart who came into the family life and complicated it. Y was the boy friend who caused trouble. So arithmetic was a warm and human thing to Francie and occupied many lonely hours for her time.”
If you’re dork enough, you see not only an interesting technique, but a young mind pulling on big threads. She’s intuitively discovered differences between odds and evens, identities, and even has a sense (note the crotchety old number 7) of the weirdness of primes.
(Incidentally, lest you think the fact that the males tend to be more ‘complex’ is sexist, the technique is a bit out of context. Without giving away plot points, suffice it to say that the males in the book tend to be less reliable and good than the women.)
Having this thought in my head, it occurred to me that if I had daughters, it might be worthwhile to give them this technique. If young girls really are interested in social situations, this seems like a hell of a good way to to backdoor in some math. In fact, not only does it backdoor in some math, it has a built in way of thinking mnemonically. If you learn this technique, you remember numbers, even big ones, as having special qualities. It’s easy to imagine Francie learning advanced math and wrapping it in bigger and bigger stories
Then the part of my brain that deals in social taboos said “isn’t that sexist?” “Aren’t you being a hypocrite to say McKellar is doing it wrong now?” Let me address both points.
Is it sexist? I don’t think so, and here’s why. First, it seems to me that a fact cannot be sexist. I don’t know whether such a teaching mode would work or not, but I don’t think that has a bearing on how you valuate men and women.
Second, I can think of comparable examples that nobody would call sexist. For instance, it’s said that Feynman saw certain symbols as having colors. That is, alpha is blue, gamma is brown, psi is green, et cetera. He felt this improved his ability to work equations. If you found out an all-girls school was teaching this technique, you might be tempted to call it sexist – “why can’t girls just be taught math? Why are we teaching them that 4 is pink?!” So you see things depend a bit on framing. Would we call Feynman “girly” if we found out he saw delta as baby pink? I suspect not. And, I suspect the same would be true if we found out he thought of 7 as an angry grandpa.
The McKellar question I find more troubling, especially as I believe we’re largely on the same side of this issue. But, I would argue that there is a nuanced, but still important, distinction.
McKellar is talking about middle school girls who presumably already have socially and genetically formed views on lots of things. They’re designed to appeal to girls who’ve decided they don’t like math, or who are at risk of doing so. What bothers me is that I think this doesn’t deal with the root problem – the common notion that math isn’t “for” girls. In that it creates a safe place for some girls to enjoy math, I appreciate it. But it seems like we’d do better to start earlier – to cure the problem, if it is a problem, rather than palliate it.
I believe a big part of being successful at math is a lack of fear. A lot of people, male and female, genuinely fear math. But, what if you could make math just part of your everyday experience from childhood? Then, I suspect, books about how math is like shopping, wouldn’t be necessary.
Let’s assume, as many socially liberal parents I know have been disappointed to discover, that girls tend to like babydolls and boys tend to like guns. There’s nothing inherently more mathy about either of these. But they’re both ways to sneak in math. The gun comes with a chance to talk about trajectory, momentum, drag, and even chemical energy storage. But the babydoll is no less replete with possibilities. It’s an opportunity to talk about game theory, or to organize social affairs as logical chains.
My hope would be that once you’ve made mathematical thinking part of this individual’s brain, by the time they’re older the stigma would be less of a problem. That is, by saying “social relations? That’s behavioral economics!” and “Relationships? That’s discrete mathematics!” you might be able to break someone of that fear of math as The Other. If you can achieve that, then the gender issues become irrelevant – you’ve shown them the beautiful world of math. With luck, that could mean that they’ll love math abstractly, without dressing it up for them.
Because, of course, math is best enjoyed in naked form.
Disclaimer: The above is just some morning thoughts I had that somehow grew into a 1600 word article. I suspect I’m being a bit hypocritical and haven’t properly sourced everything. I’m still analyzing how I think about gender and mathematics, and hoping it’ll be more of a fun point of discussion than anything. Please please tell me I’m stupid, and provide citations.