Girls and mathematics

This was about the third Ockham's talk that I ever did.

This all began when I rang Halina Szewczyk. At that time, I had done two Ockham's Razors programs with her as producer, and I thought she would recognise my voice when she heard it over the phone. So when she picked up her phone and said "Science Unit", I simply said, "This is Peter Macinnis".

There was dead silence from the other end. I wondered: had I offended in some strange way? No, there was no unusual offence that I had given, not that I could remember. Surely it would not be so: after all, I'm even notable as one of the few people who can spell Szewczyk. Obviously, I was less memorable than I had thought.

So I started to explain to Halina who I was, and that I had done a couple of Ockham's Razors with her. Then Halina cut in, as she no doubt thought, reassuringly.

"No, that's all right, I know who you are," she said. "I'm chopping you up at this very moment."

It was my turn to go strangely silent. Until I recalled that the last recording session, some weeks earlier, had involved several fluffs, a few coughs, a scattering of paper rattles, and other things that never come out on air. My being chopped up obviously referred to the fact that a tape with fragments of my talk was strewn all over the cutting-room floor.

We joked over the coincidence, discussed our business, and then I hung up. It was only later that I started to muse over the special language that is used in different professions. We talk about the Americans being speakers of a different language, but there are times when I wonder how far we have gone to evolving different species of English in our own seemingly monolithic Australian society.

Part of it is a question of connotation, or is it context? "The bar" has one meaning for a lawyer, and another altogether for a ballet dancer. For both, it is a place of work, as it is for a publican. But not so, of course, for a drinker. And for a deep-sea fishing crew, the bar is an impediment to be crossed before going to work. For the standover-man, the bar is a tool of trade.

"Fix" is another multiple word. We can be in a fix, fix a drink, fix a broken leg, fix a person, or set up a fix. If somebody comes home and says "I've been at the bar all day fixing things", we are well short of the total picture. The crooked lawyer, the balleto-medico, and the cocktail mixer could all use the expression. Obviously, the context is important.

Sometimes, it's a matter of words dying out, or being revived. In my immediately post-school days, I was a Public Service clerk in lowly orders, a sort of junior Bristow. Given a task to do which was already in hand, I innocently wrote on the file that the matter was in train, and referred the reader to another file, meaning that the rest of the story would be found there.

As quick as a cockroach, my own particular Mr. Fudge was upon me, thumping a dirty fingernail down on the offending page of the offending file. In what train, he demanded, had I left it, and why had I done so?

Until I saw what he meant, I was nonplussed. Then, as the light dawned, but to no avail, I pointed out that my note featured a perfectly valid form of expression, and that "in train" meant "in the process of being done". The trouble was, the only thing that looked like being done right then was me.

Quick as a sewer rat, the boss flourished a dictionary under my nose, to show that there was no reference to "in train" in his dictionary. Given the chance, I would have wagered a few pounds that the word "impossible" was in his dictionary, though, if only as a personal descriptor.

Whatever else he was, he was my superordinate. So I was careful to be gentle in pointing out that his tiny pocket dictionary was fit only for children. I would have liked to add, or people with brains commensurate with that dictionary. But I didn't try to blind him with science, nor did I try to blind him with words. If I had, I might have got my eyes poked out.

It didn't work. What dictionary, he enquired sweetly, would do? Simple, I responded: look you to the OED. As quick as a rather dim flash, he was off and back with a Concise Oxford, and it was already opened.

The gleam in his eye made my heart sink, so I got in first. No, no, I said, that is a handy tool, but I really did mean the big one, the Big OED. And there I was temporarily safe, for nobody in the office had a Shorter Oxford, let alone the full fourteen-volume OED.

But my boss wasn't very happy, and neither was I. So that night, safe in the security of my home, I consulted my Shorter Oxford. And drew a blank. Well, to cut a long story short, the phrase "in train" is only mentioned in the huge Oxford Extravaganza, the fourteen-volume monster, as it was then, the one for which I still yearn. And there, when you turn it up, "in train" is listed as an archaic legal term.

While I was writing the notes that eventually became this talk, I heard somebody who is neither archaic nor legal using the expression. In the past year, I must have heard it a dozen times.

Round my neck of the woods, the phrase is alive, well, and definitely kicking. But I wonder: if I used the phrase in the streets of Oxford, would they know what it was I was talking about? I hate to think that they might accuse me of archaic language. Maybe they would, but I hope not.

I would have to concede, though, that there is one sense in which I most certainly do use archaic language. It happens almost every time that I talk about discrimination.

You see, I am probably one of the few people who was employed by the Government to encourage discrimination, and I will never be stomped on by the Anti-Discrimination people for my actions, either. The sort of discrimination that I practised and fostered is both legal and desirable. I used to look after tests and examinations.

Just as it was once desirable to have a discriminating palate, so test constructors prefer to ask questions which discriminate. The questions that they write need to distinguish between good and poor students. To be precise, concise and to the point, the questions must discriminate between better and poorer students.

Of course, test and examination people don't wish to discriminate on the grounds of race, sex, religion, colour, et cetera. So they have declared that sort of thing off limits, out of bounds, beyond the Pale, and they give that sort of discrimination a special name. They have dubbed it test bias and test bias is held to be undesirable.

Now here I would like to get down to tin tacks, and enunciate a heresy. I think that there are times when we ought properly to use biased tests for genuine research purposes.

My little corner of the educational world, which included, and still includes, such things as science and mathematics, is beset by sociologists. These poor, generally innumerate creatures hop onto all sorts of bandwagons, rolling or otherwise, and from that secure position, they roost and bleat. They are, to say the least of it, mixed-up beasties, the sociologists.

One of the newest roosting points for the sociologists is the thing about girls and science, technology and mathematics. In a broad-brush gratuitous insult to all girls, they assert that girls don't do as well in these areas as boys. From this delightfully data-free vantage point, they then generate all sorts of fascinating theories to explain why this is so.

These are all nice theories, usually of the conspiracy variety. Male teachers, aggressive boys, the media, textbook writers, all of these can be the villains. A quick tweak here, and a minor twitch there, and you can tailor a set of ideas that will pander to any prejudice you may care to dream up.

There's just one problem: they never actually investigate any of their theories in an unbiased manner. Nor do indeed do they generate their theories in an unbiased manner. But they could, if only they would use the occasional biased test.

In both science and mathematics, in all subjects in fact, there are questions which are better answered by boys. Equally, there are other questions which are better answered by girls. There seems to be no way of predicting in advance which questions will do what, or to whom, but the differences are there, and the differences seem to be quite stable.

Note that I said you can't predict things in advance. No, that wasn't a clumsy tautology: I meant what I said, for after the question has been tried out, prediction is dead easy. Even though you can't look at a question and say "Aha! that one will stitch up the girls", you can look at the statistics for a question once it has been used on a sample population, and say, "It fixed them last time, it will fix them this time." You can, with the right information, construct a marvellously biased test.

Now the strictures of the sociologists notwithstanding, there are girls who do well on tests in science and mathematics, girls who can even top the whole group, even on a biased test. So suppose we make up two biased tests, one designed to be anti-Boy, and another one which is anti-Girl, and run each test on a randomly selected group of boys and girls.

Now that is done, we are ready to go somewhere that the sociologists dare not venture: into number-crunching land. What I want is for somebody to find out who the girls are that do well against the odds, and then to try and find out why.

Forget about the sociological weeping and wailing and wringing of hands over the unfortunate state of girls' science and maths performance. That gains us nothing at all. Instead, let's find a few causes! After all, isn't that what science is about?

If there is some measurable or identifiable cause of poor performance in science or mathematics, it ought to show up more commonly in the girls who do poorly in the anti-Girl test, and less often in the girls who beat the bias in the anti-Girl test. And I suspect that we could get a whole extra load of information from a study of the boys' performances on the tests as well, and from the girls' performances on the anti-Boy test.

How could we investigate causes from this information? Well, the first thing to do would be to make up a list of all the possible causes. Things like having experience with tools, having older brothers or sisters (or not having them, or even having no brothers at all), or maybe having graduate parents, or male (or female) teachers, or anything else that had ever come into anybody's theory.

If somebody says that lead levels are relevant, we may even throw in a few blood tests as well. You could even check hormone levels, as long as there was a good theoretical reason to do so. I don't see it, but if somebody can make a case for it, test it, even if people start crying heresy at the mere suggestion. After all, if the notion really is fatuous, as I suspect, then we should prove this, once and for all, rather than sticking our heads in the sand!

Then once we have identified the possible "causes" for our specimen youngsters, we would do a bit of cook-book statistics, to find out what matches up best with ability in mathematics for each of boys and girls, and then for kids in general.

Then we would take a second sample, carry out the necessary measures, and check their predicted test scores and their actual test performance. If the original work was well done, we should have close to a perfect prediction measure.

By the way, the statistical method that we would use is called (wait for it!) discriminant analysis. But I don't plan to wend my way back through all the steps to Square One and the cutting-room floor of Ockham's Razor, back to the use of "discriminate". I just want to urge somebody to do a bit of proper science.

Of course, some people might say that what I propose isn't science at all. It was Lord Rutherford who is supposed to have said, "If your experiment needs statistics, then you ought to have done a better experiment."

Lord Rutherford was an old-style physicist, of course, so we know what experiments he thought highly of, and what he meant when he said that there are "...two kinds of science: Physics and Stamp-collecting...". I am just a quiet and peaceable sort of researcher, not really a scientist at all, but a researcher who thinks that the present knowledge about girls, technology, science and mathematics is regrettably and unnecessarily incomplete.

There can be no doubt that girls are not participating in these areas, and there can equally be no doubt that some of our very best chaps are actually, when you come down to it, chapesses. We need some clear indications about what causes this, so that we can do something about it.

The woolly mammoth is extinct: so, too, should be the woolly-minded sociologist. Whether it is real science or just stamp-collecting, we are wasting far too much good talent out there.

Yet despite this crying need, the investigations that have been carried out so far can't even be called an imitation of science. I hope you will agree, though, that my proposal is at the very least a sincere form of philately.

Just for the record, the boss with the dirty fingernail was a clerk in lowly orders, the original 'Udson with a haitch -- I am fairly sure that the person who created the genial advertising character was somebody I worked with, and that he was using the evil bastard as a linguistic model.


This is one of a set of talks which were originally heard on ABC Radio National in Australia. All of the talks are copyright © Peter Macinnis, 2001, but permission will be readily granted on request for educational and most non-profit purposes. Contact Peter Macinnis specifying the talk(s) you want, and the purpose to which they will be put. For the rest of the talks, go to Six Months of Sundays.

Note that the message will go astray if you do not put my first name at the front of the address.

corrections made, December 13, 2007.