January 22, 2005

Math, Science, & Girls

I've found the recent spate of articles about the brouhaha over the remarks of Harvard's president on math, science, and gender quite curious. I personally found some of the questions he raised intriguing, but I'm not an academic, and I'm sure much of the harsh reaction was part of academic inner sanctum politics, of which I'm blissfully ignorant. Of course, his remarks as they've been reported were phrased in a way that made them so easy to misconstrue, as it seemed like he'd been throwing out some broad generalizations -- and the hazard of generalizations is that people forget they are just generalizations. Making the generalization about the fact that girls do not tend to perform as well at math and science in school and then asking the question if that could be attributed to biological differences could easily be inaccurately construed as saying all females are innately not as capable at math and science -- which is, of course, pure bull and a faulty correlation. And I don't think was actually what he seemed to be saying at all. Of course, there are plenty of brilliant female mathematicians and scientists now and in history (pssst, here's one: Marquise du Chatelet). Just as there are also plenty of males who don't take to math or science, too.

I think of the many articles I've seen recently about this, this article in Slate does one of the better jobs of sorting out and summing up the particulars of the flap: Don't Worry Your Pretty Little Head - The pseudo-feminist show trial of Larry Summers. By William Saletan

I found these parts from the article especially noteworthy and well-put:

"The next reason was that more boys than girls tend to score very high or very low on high-school math tests, producing a similar average but a higher proportion of scores in the top percentiles, which lead to high-powered academic careers in science and engineering."

later:

"By some accounts, Summers referred to 'innate ability' or 'natural ability' as a possible explanation for the sex difference in high-school test scores. This is what set off the furor."

and later:

"Let's be clear about what this isn't. It isn't a claim about overall intelligence. Nor is it a justification for tolerating discrimination between two people of equal ability or accomplishment. Nor is it a concession that genetic handicaps can't be overcome. Nor is it a statement that girls are inferior at math and science: It doesn't dictate the limits of any individual, and it doesn't entail that men are on average better than women at math or science. It's a claim that the distribution of male scores is more spread out than the distribution of female scores—a greater percentage at both the bottom and the top. Nobody bats an eye at the overrepresentation of men in prison. But suggest that the excess might go both ways, and you're a pig."

____

But still, flap or not, some of Summers' provoking questions fascinated me. As I'm not an academic, I was less interested in wondering about how these questions could explain the male/female ratios in the upper echelons of the academic world than in the implications for the general population that such questions do raise. And I am sad to see that the questions themselves raised such a flap that it's likely no one in the academic world will willingly take them on right now. As I'd be curious to see the answers.

The questions raised about contemplating the differences, including possible innate differences, regarding females in relation to their involvement and interest in mathematics and science fascinated me enough to entertain the notion in a bout of pure omphaloskepsis. As I've long wondered about my own apparent failings at high school math, which weren't actual failures, but have haunted me in varying ways ever since.

Let me explain.

I've always been interested in science, but I have never been at all versed in advanced mathematics, which of course has put limits on my understanding of certain aspects of some of the sciences. And when I was in school (20+ years ago), my lack of advanced mathematical knowledge also prevented me from exploring some science courses that would have required an ability to understand or do advanced calculations.

I know for certain that not all females are innately bad at or disinterested in math. I can remember many females I shared math classes with in school who seemed to be intrinsically brilliant at math. I have a female cousin who was in the same math class I was in in 7th grade. She was one of the best, if not the best, students in that class. Her intrinsic grasp of math was obvious and amazing. And she's since gone on to be brilliant in the field of engineering.

Mathematical genuises seem to crop up on my father's side of the family from time to time. My father was a mathematical genius. He used his mathematical gifts in his profession as a chemist. I remember watching him scribble down formulas and equations with an ease of someone making out a grocery list. He could do complex equations in his head and give out the answer accurately and quickly. He was tickled when hand-held calculators came on the market and spent a lot of money to get one of the early models, although he was as good as those calculators himself. He died in 1982, and I've always wondered how excited he probably would have have been had he lived just a few years beyond that and could have been able to buy and play around with his own PC.

I, on the other hand, am not a mathematical genius. In school, I was always entirely competent and adept with basic computational math -- adding, subtracting, multiplying, dividing. I was good with fractions and remember bizarrely enjoying doing math problems where reducing fractions was involved. But decimals (and percentages) threw me sometimes, as I would often mix up the rules about where to place the decimal point in more complex multiplication and division equations with decimals.

Fortunately, these days, I can just use a little calculator and not worry at all about that little failing of mine.

Anyway, although I wasn't brilliant with math, I always got pretty good grades in it until ... until ... I hit a Great Divide in my freshman year in high school. As it was then I was introduced to and conquered by {shudder} algebra.

Algebra traumatized me and scared me off. In retrospect, I know that letting myself be traumatized by algebra and basing subsequent academic choices on honoring that fear was probably both unnecessary and silly. But it was what I did.

Although I actually understood enough of algebra to fake my way through it at the time and end up with a 'B' as a final grade, I knew that I had not understood it really. And that frightened me, as it was the first subject in school I'd ever come across that I felt completely lost in, that I never felt that I'd gotten even a small handle on. It didn't help me out a bit that my father was a mathematical genius either. My attempt to get him to try to explain it to me was one of the traumatic events of my adolescent life. He didn't understand why I didn't get it and was angry with me for not understanding it. When my father thought something was obvious, he was generally pretty impatient with anyone who didn't see the obvious. So, he acted as if my lack of understanding of it was just some deliberate affront on my part.

So. At 14, the end result of my experience with algebra just made me secretly conclude I was just hopelessly stupid at math. Since my high school allowed students to opt out of taking a requisite second or optional third year math class (geometry and trig, respectively) by taking four years of a foreign language, violà, that's what I did, merci beaucoup.

I was told by my friends back then who went on to take geometry that geometry was much easier and actually made sense (where we all had agreed algebra often hadn't).

___

Anyway, even if the academic world is in a tizzy over such questions being brought up at all, the questions relating to possible biological differences playing some part captured my fancy. And so I've been contemplating them in regards to my own trauma with algebra.

Like these:

I was smack in the middle of puberty when I took algebra. Does puberty have any effect on left-brained/right-brained function? Could there be some suppression of left-brained function in females during their puberty or something like that?

I've seen it reported that studies have pointed out that women's brains generally are shown to be better at multi-tasking. Could it be that a brain better at focusing on one task at a time has an edge when it comes to advanced mathematics?

Although I've been posing such questions to myself, I also just stumbled across another possible culprit that could explain my particular problem with algebra. As I'd forgotten whether or not I was taught in the era of "New Math" or not, I did a search before finishing this post to look up when New Math had been an influence.

I found this q&a from The Straight Dope Mailbag: What exactly was the "new math"?

This excerpt from it especially intrigued me:

The following examples may help to clarify the difference between the new and old math.

1960: A logger sells a truckload of lumber for $100. His cost of production is 4/5 of this price. What is his profit?

1970 (Traditional math): A logger sells a truckload of lumber for $100. His cost of production is $80. What is his profit?

1975 (New Math): A logger exchanges a set L of lumber for a set M of money. The cardinality of set M is 100 and each element is worth $1. (a) make 100 dots representing the elements of the set M (b) The set C representing costs of production contains 20 fewer points than set M. Represent the set C as a subset of the set M. (c) What is the cardinality of the set P of profits?

I know this example is partly meant to be facetious, especially as the example goes on to make fun of the more recent ways of teaching math have attempted:

1990 (Dumbed-down math): A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Underline the number 20.

1997 (Whole Math): By cutting down a forest full of beautiful trees, a logger makes $20.

(a) What do you think of this way of making money?
(b) How did the forest birds and squirrels feel?
(c) Draw a picture of the forest as you'd like it to look.

But facetious or not, that example of New Math brought back some bad memories, and I now wonder if some of my horrible experience with algebra, which I did happen to take in the year 1975, could possibly be because maybe the textbooks and lesson plans used in my algebra classes at the time were ones using some New Math concepts.

As looking at that example made me remember a common reaction I often had in my algebra class towards some of the problems presented to us to solve. Namely, I'd often think to myself: "What the hell are they talking about here? What is it I'm supposed to try to solve in this gibberish?" So, I'd spend an inordinate amount of time just trying to unravel what the question to solve actually was before I could get around to even attempting to solve it. Drove me insane.

Perhaps I ought to find a more straightforward kind of algebra tutorial (or even maybe one day attempt to take an intro class) and see what I'd make of it now. Especially to see if my problems with it back then might have been caused more by some of the horrendous "new math" influences than by possible biological influences or just my own innate failure to grasp the logic of algebra.

Which brings up another question -- were studies ever done on the "New Math" to determine any differences in how males or females responded to it? Because if females happened to have done more poorly with the "New Math" than males, that surely might account for the current gap in the upper echelons of academia, given the time frame it would take for an academic to rise to that level. Mightn't it?

Questions, questions, questions.

____

I have had a few other musings related to this topic in recent days, but I'll save them to post another day.