Tuesday, March 08, 2005

Girls & Math & Stuff

As is her customary practice, our Jess has provoked me so severely as to make me blog. Okay, let's get it all out in the open -- she is the only reason I started this silly site. There's only so much prodding a fellow can take.

Anyway, the subject of today's discussion is, "Do girls suck at math genetically, or have they learned to be stupid?" (At this point, I duck and cover, waiting for the slings and arrows of outrageous Fortune -- who is also a girl, if you believe your mythology -- to stop flying overhead.)

Frankly, I think it's about time that someone had the intestinal fortitude to propose the question, and I'm sorry to see Dr. Summers attacked the way he has been for merely offering the idea for exploration. You'd think that by now somebody would have noticed that people are not interchangeable, that gender (I hate that term -- words have genders, people have sexes, but politically correct is the order of the day, what?) equality does not necessarily mean that there are not differences between men and women or between boys and girls. As long as we pretend that there are no differences, there can never be true equality.

I approach this particular issue wearing a couple of hats. On the one hand, I have gone through life with a bit of an aptitude, one might say, for matters mathematical (I understand equations, both the simple and quadratical, about Binomial Theorem I am teeming with a lot of news --with many cheerful facts about the square of the hypoteneuse). Like most of the people I have met who have my talent, I learned mathematics as highly abstracted concepts, to which I could usually attach practical uses by intuition as much as anything else. I didn't learn maths by practical application, I learned by symbology, and the practical application was something I did with the knowledge I had. When one progresses beyond mere arithmetic in school, that is pretty much the way mathematics is taught.

On the other hand, though, I have been a teacher of mathematics, and I know that many students do not learn that way. Many will spend what I consider far too much time learning to manipulate the symbols, a task that does not come naturally to them, gradually working themselves to the point that they can do symbolic calculations well enough to get most of them right on a test. Yet, after all of that work, those symbols have no real meaning. These people tend to complain of an inability to do "word problems", and wonder why their marks should be based on something that bears so little relationship to the concepts they broke their heads learning. Well, those unfair word problems are what math is all about, boys and girls.

On the gripping hand, I eventually became a teacher who found that if you take the time to teach from the practical to the abstract instead of the other way around, a whole bunch more people start to grok the math. And, frankly, the girls in the class tend not to be quite so stupid when you teach that way. Yes, "learning styles" lie on a continuum, but I have found that more women than men need to know what the problem they are trying to solve is before they can deal with the symbology. And the guys don't suffer at all from the treatment -- only a slightly larger fraction of males than females appear to learn well in the abstract space alone. When you strip away all of the people of both sexes who haven't learned well enough and aren't motivated by a desire to learn more of the same in the same way, that slightly larger fraction can account for the disproportionate number of men going into physics, engineering and mathematics even though more women are progressing to higher education as a whole.

But what about sensitivity? Girls aren't dumb, they're just treated as if they are. Right? Sorry, Charlie. You can be as sensitive, caring and understanding as you want to be, you can spend more time being encouraging than teaching the material, but if what you are teaching has no meaning to your students, they still aren't going to learn as well as they should. Most teachers who know enough about mathematics to be effective teachers of the subject learned abstractly, and truly can't fathom that other people don't learn that way. Most don't mean to intimidate -- they have taught as well as they know how to, and those students who can't understand that way do seem hopelessly lacking.

How about the idea that women should teach girls in order to take "gender bias" out of the equation? You know, that might work -- if the women teaching are sensitive to the REAL issue. Taking fear out of the classroom is a great idea, but fear won't go far if the material is taught in a way that doesn't breed understanding. And let's face it, there will be two kinds of women teaching -- some who learned easily from abstract symbols, and who will therefore expect that anyone else should be able to learn the same way once the evil condescending men are removed, and those who didn't learn well enough from the abstract concepts and who can't explain the practicalities. The first group will be no less oppressive than men who learned the same way, and the second group, well-meaning as they might be, are not qualified to teach real mathematics, no matter how hard they have worked to pass a few tests.

I am certain that this is a fair description of the problem and the solution. I may be flattering myself, but I'm pretty sure I can teach anyone of average intelligence most of the math I've ever understood -- but you know I'm just one teacher who has had some limited success with a relatively small number of students. Unless and until the problem is properly studied with a large enough number of students, male and female, of varying social backgrounds, we'll never know for sure. As long as people mistake equality for sameness (even in math, things can be equal without being congruent, and congruent without being identical) and let defensiveness get in the way of reason, we'll never have the opportunity to find out for sure.

And you know what? If it turns out I'm right, not only will the girls get smarter, a lot of the sweat hogs in shop class will get a lot smarter too. As much as we need tradespeople in this world, the old "menial" trades involve a lot more than a good set of hands these days. So, if I am right in my analysis, and the necessary corrections are made, then maybe it's a good thing that girls today are "stupid".


Jess said...

"but I have found that more women than men need to know what the problem they are trying to solve is before they can deal with the symbology"

That's interesting too... everyone knows that no matter how much I love mathematics, I'm terrible at it. YET, take geometric proofs. We figure out the answer, and also have to step-by-step how we arrived there. I ACED every single geometry class I ever took (ironically, I'm good at pool. That's just geometry too!)

I love geometry so much because we have to explain how we arrived at the answer, through each step. In some cases, you are given the answer, and must prove it that way. Now THAT'S fun stuff.

Speaking of being bad at math, I also agree that while everyone should get an equal opportunity to prove their talent, that still won't automatically GIVE them that talent. :-)

Anonymous said...

An interesting thread and I'm in some, but not entire, agreement.

There are indeed the 2 kinds of people you describe and they are mainly split by gender, but there are exceptions. Even though I'm male, I regard myself as falling into the female style you describe. I like that way of learning much better. I've always excelled at teaching stuff to girls, but have problems keeping the attention of boys...who just want to jump straight to the answer.

All very interesting...


Scott Good said...

I totally agree with you, Stan. Math is often taught in a way that makes it hard to understand.

Like, Jess, apparently, I more or less despised math until I got to Geometry when, all of a sudden, it all made sense. It was like I was suddenly able to sneak a peek through the keyhole and understand why I'd spent all that time standing outside the door.

From there, Algebra II, Calculus, etc., all were both fun (ok, funish) and interesting.

I think there's a similar problem in the teaching of computer programming where the organization of the information is such that you have to slog through a whole lot of boring and apparently unrelated information before you can ACTUALLY DO SOMETHING.

It's kind of like explaining the theory of vulcanization and Dalton's law of partial pressure states in answer to the question, "how do I know if my tires are too low?" Maybe it's important information, but maybe, also, you don't need it right out of the chute.

In my experience, teaching technology is about building on small victories. Here's a button that does something simple. See that? Now, what if you needed it to do something a little more sophisticated? Ah...then you'd need to think about this...

Stan Rogers said...

Which is, of course, why your LotusScript and JavaScript tutorials in Lotus Advisor (and on the subsequent "best of" cd) should be considered required reading for newbies.

Anonymous said...

I agree with most of your comment, but I'd like to offer some other explainations as to why girls get better grades but score 30-50 pts lower on the SAT tests. (And why the gap seems to be growing) Has anyone thought that maybe the immature nature of adolescent boys ciould cause them not to do homework and to skip studying, thus getting lower grades? I've taught high school math for decades and I know for a fact that girls are much more attentive to classwork and homework than boys are. consequently, they get better grades. But better grades do not necessarily confer better understanding or talent in the area of study. Some of my more promising students do not get great grades because they lack the maturity to excel, at least not at that point in their lives. Boys fall into this category at a much larger rate than do girls, I can tell you that. Perhaps the question would be better phrased "What could we do to engage males in schoolwork at an earlier age, and what kind of talent is this country throwing down the drain because of a matriarchical education system? But I guess that would not be politically correct...