Recap from Last Time: People use a set of relationships to help make decisions all the time called an ambient filter; some people might call the same set common sense. Stereotypes are a part of common sense.
Something’s not quite settling about the foundations I’ve detailed in the last post. It looks like the only thing we could say about women using ambient filters is that society conditions women to be bad at math (either by depriving them of the ability to hold tenured positions due to sexism, providing hostile working and learning environments, etc). Ah, but that ignores the nature of human existence. Like our filters, which can add or drop a relationship any time, our environment is not fixed.
This might sound a little Marxist to you; it should: Vygotsky (who got it from Engels who was inspired by Marx) loved the idea that man can shape his environment in order to shape himself. Whoa. Let’s pause a moment to digest the educational implications of that statement.
I’m told that in olden times, a person might tie a red or white string on his finger in order to remind himself to do something. Apparently, this was before they had paper and pencil and could write notes. Regardless of the specifics of the method, the general process and effect are the same: make something on the outside to trigger a response on the inside. This the the all-powerful idea of the sign. And if you dig deep enough, you can say all sorts of interesting things about social (as well as societal) effects on learning. Marx said the use of the tool makes us characteristically human; Vygotsky argues in favor of the sign. (Personally, I like the sign better.)
I know, I know, we’re moving slowly. So I’ll speed it up.
Now back to math: who were the principal investigators of mathematics since very early on? Men. And who developed the system of notation and verbal description we commonly use today? Men. And is it very likely that those who study a field of knowledge (which, by the way, may be entirely blind to the natural inclinations of its investigators) are going to devise a method of symbology that makes sense to them? Yes. And is it very likely that these representations of knowledge are going to make sense to its authors precisely because these representations automatically exploit their personal frameworks for understanding? Yes. (That is, would anyone ever record something that he understands in a way that cannot understand? No—at least not on the community-level.) Ah, then would you grant me that if there are biological differences between the way men and women think, doesn’t it make sense that because men have dominated math forever that the language of mathematics as we know it will necessarily be kinder to the male intellect than to its female counterpart? Sure it does.
So what have we learned through our very heavy-handed Socratic dialogue? It is very possible that while real mathematical knowledge doesn’t care what gender a person is, the representations we use today (in the symbols, language, and presentation at large) are biased in favor of men. Weirdly enough, that means there are innate difference between math and women. Exposition of mathematics has changed very little in the past century. The curriculum and its implementation exist primarily for historical reasons. The way people form common sense about math, therefore, hasn’t changed much, either. The trick, if what I say is correct and its effects are large, is to recast the relationships we use to describe math, and the methods by which we establish them, in a way that is meaningful to a larger audience. Of course, uprooting blatantly sexist myths about the role of women in math and science couldn’t hurt, either.
But here’s the really interesting part: we’ve shown that common sense doesn’t exist exclusively within the mind. Instead, we can leave it on the outside, in what we say, write, draw, make, build—in anything, even tangible things!—and that a throrough treatment of creative problem solving (and thought more generally) has to take into consideration the external consciousness we store in everyday objects.
(Yes, Lauren, I know. Historians have long recognized this fact. Ulrich studies teapots, I get it. Archaeologists, too. Sure. But is there anything new under the sun?)
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It is very possible that while real mathematical knowledge doesn’t care what gender a person is, the representations we use today (in the symbols, language, and presentation at large) are biased in favor of men.
There are women who have achieved great heights in math … and Chinese women seem to do pretty well.
Weirdly enough, that means there are innate difference between math and women.
More likely innate differences between males and females. You know, like how there are differences in protein expression in the brain mediated by the presence of XX or XY (at least in mice) and the fact that testosterone production is switched to high levels in males from week 8 of gestation.
An investigation of CAH females might reveal interesting results in this regard.
Exposition of mathematics has changed very little in the past century. The curriculum and its implementation exist primarily for historical reasons. The way people form common sense about math, therefore, hasn’t changed much, either. The trick, if what I say is correct and its effects are large, is to recast the relationships we use to describe math, and the methods by which we establish them, in a way that is meaningful to a larger audience.
Why? Math is an activity engaged in by individuals who use the methods and terminology bequethed to them by others and sometimes develop their own methods and terminology.
If (some) women find that not to their liking they are free to develop their own techniques and terminology.
We will know by their achievments which approach is better.
Anything else is just whining that the world is not fair.
In any event, given that math research is engaged in by individuals who are 3+ SDs above the mean, any changes are going to be largely irrelevant to 99.8% or more of the population.