Wednesday, March 09, 2005

Up Where We Belong

Yesterday's entry seems to have awakened a few things in me again. Like, f'rinstance, the feeling that no matter how good I may seem to be at this programming game, or at math, electronics, and so forth, I'll never be more than a grunt. That is, I can do the job and do it well, but I'll never be counted in the ranks of people who go beyond mere competence. Yeah, I've had a few good ideas, but this game is all about creativity and exploration. Or at least it should be.

There is one thing, though, that I'm more than just good at, and that's teaching. It wasn't something I went into on purpose. I was an avionics technician in the Canadian Forces (they used to be Armed, but that sounds a little bit too aggressive for Canadian tastes — I'm sure they'd get rid of the "Force" part if they could find another word) when the decision was made to close the small base I was posted to. (It's entirely coincidental, I'm sure, that both Rocky and I were doing pretty much the same job at the same time.) There was an opening at the Canadian Forces School of Communications and Electronics for an instructor in the basic electronics stream, so that's where I was sent. My contribution to the decision was the fact that I couldn't come up with a reasonable objection to the order.

As a student, I never had much use for the classroom, and in the few classes I sat in on before being loosed on my first group of students, I quickly realised why. The guys I watched hit every teaching point in the lesson plan, all right, and I could even tell what the really important points were — they read the lesson plan a little more loudly at those points. Okay, there was more going on than reading from the lesson plan, but not much more. I was determined to do better.

You've probably heard it said that those who can, do, and those that can't, teach. That may be true to a great extent, but it absolutely not the way it should be. If students are to understand what is being taught, most need to be able to relate the new information to concepts thay already have in hand. Understanding is object-oriented; new concepts ought to extend the old. The challenge in teaching is determining the "base class" upon which one's students can build, and since every student comes into the class with a unique set of interests and experiences, an off-the-shelf analogy will rarely be as effective as one would like. A good teacher, then, needs to be at least somewhat connected to the world the students inhabit, must be willing to engage his or her students at a level that makes it possible to see where working analogies can be drawn from, and needs to know enough about the subject matter to create relationships between what the students know and what they need to learn. To a young private who has been assigned archery as a compulsory hobby while in training (welcome to the military, kid), a strung longbow is a perfect model for explaining FM radio spectrum signatures. A good teacher of FM theory should know that, and know why — and should know why somebody who has never drawn a bowstring wouldn't get it.

I've done a lot of things for a living over the years, from sweeping streets, shining shoes and flipping hamburgers to playing jazz saxophone, from graphic design to programming computers. All of those have been the answer to the question, "what do you do?" There has only ever been one occupation in my life that answers, "what are you?" I am a teacher. It's what I do best. It's what I enjoy most.

Now I have to figure out how to get back into the classroom.

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".