As I see, one aspect conspiring many girls (and boys as well, here in Italy) is the sense "mathematics (science in general) is not worth the effort". After all, why to embrace a career or get literacy on something demanding a high investment, and guaranteeing little return if any at all?
The problem is (at least) twofold.
On one side, current image of science (and scientists) in society conspire to make it less attractive. On the other, instrumental, ideological, irresponsible or insensitive uses of (mathematics and) science cripple trust in them.
I try to proceed in an orderly manner...
Science image: an urgent need of revision
In relation to science, one of the hardest pressures girls face is the self-inflicted assumption they are not for science, and science is not for them.
This, in my perception, has a lot to do on how “science” is valued: * Impersonal * Arid * Abstract * Insensitive to consequences of discovery * Doggedly competitive * Narrow-minded * Unrespectful of actual people needs and wills * …
The actual list is much longer, and you may easily add points to it. I imagine all your personal addition will not alter a key point: the whole picture is all but “feminine”. And as girls feel pressured to be accepted, they stay carefully away from something so dangerous. How not to understand them?
The actual point is, this image of “science” has very little to do with what science actually is. Or, al least, what it might be, would we accept a bit different standpoint.
Last year I discovered a book: “Lifting the veil: the feminine face of science”, by Linda Shepherd. It’s a wonderful pearl, and I recommend you warmly.
There you’ll find something so movingly simple and “obvious” I feel you’ll have really little to do to accept it: it is not science itself to be arid and insensitive. Are the people practicing and teaching it that sometimes are.
And, there are many ways to look at it. For me, this book was healing and revealing. It also had shown me I’m not alone in my way of conceiving science, itself a wonderful way to attribute a shareable and non-ideological meanings to reality.
Now, can science image be changed in the minds and hearts of people?
Of course, yes. It may take a lot of effort by any of us interested, but I’m convinced the answer remains positive.
And: should science image be changed?
My answer, as objectionable as it surely is: yes. Once more again. We have to, as a tiny contribution to change things by day-to-day restructuring of values.
We have to work hard, both in a myth-dismantling and in alternate constructions more akin to the souls of real people, girls "not excluded".
As many of you/us feel, "stories" (and practical cases) which can be shared and understood are of paramount importance. I'll try to tell some of them, in following posts I've somewhat planned. And, I'll be glad of any yours.
One of the most powerful pressures in favor or against mathematics and physics comes in a sense from inside people. It has much to do on how actually valuable (and, emotionally close) these disciplines are perceived to be.
Not seldom, mathematics and other hard sciences are felt as "distant" from self, under a general assumption of them to be "hard to trust". They are perceived as manipulative, and sometimes this way of thinking is rationalized as "an expression of dominating power", something one should escape as quickly as possible.
This is false, and the corresponding view disempowering (for girls and women especially, although not exclusively).
But on the other side, this view is highly motivated. By an irresponsible use of science, as I understand it.
An example is worth hundreds of difficult theoretical considerations.
Imagine you are a little child, sitting at your desk with an IQ test in front of you.
Your current item is: “Complete the following list with the next number: 2, 5, 10, 17. Please write the answer here: __”.
As you are quite smart, it takes little time for you to realize (what kind of a stuffed shirt the idiot inventing this exercise was, and) all numbers in list are squares augmented by 1. Assuming this, you arrive at the conclusion the next number must be 26. Right answer.
Now, put in the shoes of another child. You know, the problem is not trivial. You feel under time pressure (you know the test must absolutely completed within twenty minutes, and you already used 12 of them). Guess you remember this - it happened to me so many times.
My emotional reaction would have rather been “Oh my dear! What that does mean!? Time is passing! Time is passing! The clock, the clock! Why this damned numbers? Whops…” - right to the imaginable disaster.
But as I wanted to give an answer anyway, say I wrote 35 or something like that).
Well, is the smart child right answer so right? From a mathematical standpoint, I mean?
The answer, surprisingly, is a yes-and-no.
Yes, 26 is a right answer.
But also my “35” is!
In fact, mathematically, infinite answers are possible. “Mathematically speaking”, as you are able to exhibit a mathematical rule (say, a polynomial) justifying your 35, then you have found one right answer (of the many possible).
And this rule exists! If you want to exhibit one of the many possible, you may just take the interpolating polynomial. Just a random choice.
Sure, the new rule seems much more complicate (you may try it on yourself - if you are like me, a computer algebra system like Maxima may help). But it's a rule, and that's all what counts.
And, what actually "less complicate" means? It's about using less symbols? No, of course, the polynomial may be expressed in another "basis" than ordinary power, say Hermite polynomials. Change basis, and the "simple" rule may become horribly complex. Would simplicity be definable, it should in my opinion be at least invariant with respect of basis choice. But, it isn't!
In the end, we have to admit a dreadful thing: the only difference between the "simple" and "complicate" rule is purely subjective, and has to do with the IQ test designer's own sense of attractiveness in formulae. This sense may be conditioned by "commonsense", yet remains subjective.
Now, sorry, this is not a joke. It may seem an intellectual puzzle and, I know, may seem a bit intimidating to so many of us (me included).
What really concerns me more is not the example per se (I know it’s all but rigorous). Are its implications, on very basic emotional grounds.
Has mathematics be abused in this case?
Sure, one of the two children has been tamed unfit, stupid.
And not just as a personal judgement (hard to accept from a beloved person, but “singular”, informal, and in the end recoverable): a “test” has been administered under controlled conditions (a clock, first of all), with a numerical output.
Numbers always convey an image of absolute objectivity, even when it is not the case. This may be one of these cases.
Allowing subjectivity to seep unacknowledged into something apparently objective seems to me profoundly dishonest, even though not originating from bad intentions.
Imagine statement like this are repeated many times, and you will shape an enduring, sad self image of “me, stupid” (and, I add en passant, unfit to mathematics).
“Dear, you’re so sensitive! Have you thought taking a literature class?”
In a sense, what this example reveals to me is: mathematics, applied in an uncaring manner, may turn from a problem-solving and modeling tool into a weapon. Something someone may use at will to justify an already taken decision, not necessarily limpid, varnishing it in a bath of apparent objectivity.
In this example, improper and unthoughtful application of mathematics crippled both a person self-image and her own value of mathematics.
Are young girls especially vulnerable to this kind of treatment? This point is open to exploration.
My opinion is the answer is, sadly, “yes” (with a more precise identification: “yes, for most girls and some boys”).
A systematic effort is clearly due, to identify any possible misuse of mathematics directly affecting children (and “most girls and some boys” especially). These misuses, as I said, undermine the worth of mathematics and science, presenting them as dishonest manipulation methods rather than valuable knowledge tools.