the difference between generalization and prejudice

[chhotii]

A generalization would be, for example, to observe that on average, females show poorer performance in doing math than males. It makes me cringe to admit this, but I've heard that statistics such as average SAT scores, numbers of women vs. men enrolling in engineering programs, etc., support the hypotheses that females, as a group, have worse math skills.

Prejudice is to say "oh, she's a girl, she can't do math." I will take my perfect 800 on the math section of the GRE and beat anyone who says this into a pulp.

The problem with generalizations is that they lead to prejudice. Generalizations are useful because they allow for snap judgments. Like, if someone runs in exclaiming "Quick! Somebody prove that cos(A+B) = cosAcosB - sinAsinB before the house burns down!" then you will probably find the person who looks most like a "math geek" to direct this problem to, and that stereotype is male (and scrawny, wearing glasses and a pocket protector). OK, so that example is absurd and far-fetched. But more useful generalizations might suggest who you should pull out of line to search at airport security: the young man from Saudi Arabia or the old lady from Minnesota. (But, then again, this makes it kind of suck to be a perfectly innocent young man from Saudi Arabia.)

Why do generalizations lead to prejudice? When one has to make a snap judgment, is prejudice any more effective than generalization? I think not; prejudice is too inflexible to allow one to recognize and adapt when one has encountered a math-geek chick, or a little old lady terrorist from Minnesota, or a deficit-spending Republican.

Discuss.

Comments

[tb]

Yet another interesting topic that can't be properly discussed in lj, but I'll throw out a few paragraphs. Of course, all my points are simplified generalizations...

Humans are pattern-matchers. This is a survival skill; we often don't have time to completely evaluate a situation before we must react. Much of our long childhood is spent learning about patterns. Humans are also pattern-seekers and pattern-creators. These are also useful but can be misleading, as demonstrated by everything from optical illusions to generalizations to prejudice.

Prejudice is a subset of generalization. I've rarely heard it applied to judgements about non-humans and I've also rarely heard it applied to positive generalizations. Prejudice is usually used to describe the limitations and perceived inferiority of some group of people that the speaker if not a member of.

I think prejudice comes out of another basic human survival-skill form of pattern matching, the need to distinguish between "us" and "them." Back in our hunter-gatherer days, the tribal band was "us", providing safety and survival, and other humans were "them", dangerous competitors for limited resources. At best "we" could form an uneasy alliance with some of "them" to exchange mates and co-operate against other, even scarier "thems."

I don't think the us/them dichotomy will ever be eliminated from human nature, nor does it need to be so long as we acknowledge that it's there and can learn to modify and ameliorate it when needed to deal with the larger and more diverse societies that technology tends to encourage. So long as we see some people as different from us, we will tend to rank those differences as either good or bad (another human habit; we like to dichotomize and rank things).

I've had to come to terms myself with the difference between observing statistically real trends in groups and the abilities and desires of individuals. For example, there's a difference between saying "most women want to be mothers" and "all women want children." The first statement is a generalization, the second is limiting and prejudicial, especially in the stuff that usually follows it: that motherhood is all women are good for and that there's something wrong with women who don't want children.

The big difference is in how you treat the exceptions. If, hypothetically, 99% of women suck at math and don't want to be engineers and suchlike, what do you do about the remaining 1%? You can do the "easy", prejudicial thing and deny their existence, telling them "tough, girls can't do math, go do something feminine" or you can make sure that engineering training is open to anyone who can and wants to learn it.

[klingonlandlady.livejournal.com]

I was just whining at P last night, about being sick of being people's educational experience by way of counterexample to some stereotype. I've been doing this role ever since I could talk (would answer in complete grammatical sentences the little old ladies who were baby talking at me.) It can be fun, but more often it's irritating and tiring.

P hasn't been on the receiving end of that much, but reminds me there are a lot of preconceptions white males get to deal with; that they are strong, stoic, in charge, should to be able to earn enough money to support other people, etc.

I guess, the more counterexamples people have to deal with, the better.

[lyonesse.livejournal.com]

I've heard that statistics such as average SAT scores, numbers of women vs. men enrolling in engineering programs, etc., support the hypotheses that females, as a group, have worse math skills.


just fyi, a few points about this specifically:

1. it's cultural. american and israeli girls have lower sat scores than american and israeli boys. thai and kuwaiti girls outscore thai and kuwaiti boys.

2. relative to boys, girls get better grades in math class than their sat scores would predict. so it's difficult to interpret what this means in terms of their actual math skills -- is the test harder on girls in some way that has nothing to do with their math, or do they get better grades for some reason besides their actual skills?

i guess my point is that even generalizations need to be made with a lot more care than we typically offer them. prejudices, of course, the more so.

[chhotii.livejournal.com]

It makes sense to me that this is largely cultural. I think the relavant points about math are that a) it is difficult and b) it takes perserverance to get very far in it. So cultural expectations and self-esteem have a big impact. The preface to Thomas Garrity's book, All the Mathematics You Missed [But Need to Know for Graduate School], is worth quoting at length on this point:

Math is hard. Unfortunately, people are just not that good at mathematics... I know of no serious mathematician who finds math easy. In fact, most, after a few beers, will confess as to how stupid and slow they are... This is one of the hurdles... namely how to deal with the profundity of mathematics in stark comparison to our own shallow understandings of mathematics.

My own experience is that math is wicked hard. Alone with a math textbook, without any external feedback, I quickly come to the conclusion that I am the stupidest bit of goo in the universe. But then I get all this assurance from standardized tests and from my college professors that, really, I am really amazingly good at math... So then I grant that maybe, perhaps, it might be worthwhile to keep tackling the subject.

On the other hand, someone who has internalized both "I am female" and "girls are bad at math", when faced with the difficulty of math, is going to just give up too quickly. In a culture in which math skills are considered un-feminine, boys would be more likely than girls to keep plugging away, which is what is really needed because nearly nobody finds math to be falling-off-a-log easy. But... but I guess in a culture that doesn't contain the "girls suck at math" meme, girls would expect themselves to understand the math they're taught in school as well as they understand other subjects. So the prejudice regarding girls and math is really insideous and self-perpetuating. Has anyone studied attitudes on this subject in Thailand and Kuwait, whether math is considered less un-feminine in those countries?

My own reactions to the 2 statements that got most chicks to give up on math long ago:

I am female: I am a gender-neutral soul that happens to be inhabiting a female body, which seems so irrelevant when I'm trying to focus on math not sex.

Girls are bad at math: They should stop being wimps and try harder.

I have no insight on the discrepancy between test scores and class grades, though.

[quietann.livejournal.com]

Broad generalizations ahead, but...

I've met some women who were truly brilliant mathematicians. I've met more men who were truly brilliant mathematicians. I am not a brilliant mathematician, although I did very well in all my math classes until I got to calculus, and my job is more or less "working with numbers". I am missing some essential "bit" that truly brilliant mathematicians seem to have.

On the "math is hard" bit: Perhaps girls are fine at math, but they have other priorities? A lot of girls -- including the really bright ones -- get their heads more into friends and boys and the social aspects of life. Boys (at least the ones who are "good at math") are stereotypically socially incompetent in comparison, and probably spend a lot less time in the intricacies of friendships and relationships. I don't think that it's entirely coincidence that my willingness to "pursue" math declined as my social life improved.

I've spoken with Dale quite a bit about the "math genius" thing, since he is, arguably, a math genius. He's pointed out to me that it's a very solitary pursuit, and not one that would lend itself to interruptions by children, partners, etc. One complaint I hear a *lot* from men who are "in the sciences" (including math) is that their female peers/students/etc. are great colleagues until they have kids and get distracted from the scientific world. (read: "can no longer work 16 hour days or drop their babies in order to work out a complicated proof or experiment or run back to the lab at 3 a.m. to check on something") Women -- at least married women with kids -- Just Don't Do That according to societal norms. Most of the female brilliant mathematicians I know don't have kids. The same is not true for their male colleagues.

BTW, for more on the larger issue (genius in academe') you really should have a look at Rebecca Goldstein's novel "The Mind-Body Problem."

[hammercock.livejournal.com]

The other thing that bugs me is that people often assume the math score discrepancy to look like this:

---- ----
/ \ / \
--/ \-- --/ \--
F M

...when actually it's more like this:

-------
/ / \ \
--/--/ \--\--
F M

(about as well as I can do overlapping bell curves in ASCII right now)

I mean, I am one of those math-challenged, math-phobic women. In compensation, my verbal skills are great. But sheesh, that's just me; I'm only one combination of many possible combinations.

[chhotii.livejournal.com]

You have enough mathematical intuition to understand the issue exactly... (If you're saying what I think you're saying. The ASCII art Just Didn't Work, even in lynx.)

[marmota.livejournal.com]

Consider that a generalization can be a result without being a conclusion. The result may indicate something else entirely... for example, perhaps that on average women buy into the prejudice that they're poor at math skills, and so don't try as hard to learn as hard as they otherwise would have without that preconception?