Friday, May 11, 2007

Ask an Applied Mathematician, Math Education Edition

Devoted reader Tony asked (in this entry):
I am very interested in hearing more about these inadvertent sexist syntaxes. I constantly strive to eradicate biased behavior from myself, and since I am planning to become a math/science teacher, this issue has become even more important to me. I am especially concerned with the attitudes that today's young woman have toward mathematics and I certainly want to make things better, not worse. Could you maybe do an Ask an Applied Mathematician post about fairness in the classroom?

Sure, Tony. I am not an educator myself, but I have been educated, and based on my experience I have a few ideas of what not to do:

When introducing the different sets of numbers (e.g. the reals, the integers, the complex, the irrational numbers), end the lesson by discussing your favorite set of numbers: Cindy Crawford's measurements. (True story, happened to my sister at a math/science/technology high school magnet program.)

When male classmates humiliate your best pupil, making fun of her for being female and being interested in joining the computer club, stand idly by and let her take care of it herself. (Happened to me in 7th grade.)

Frame an otherwise entertaining story about computing the power usage of your computer within the context of your math-illiterate wife blaming you for the high power bill. For extra bonus points, explicitly tell the students that women can't do math. (This happened in a classroom I was observing.)

When handing back exams, place the person's exam on their desk, but then grab it back, leaf through to problem number three, and exclaim, "Oh yeah, don't do problem number three [this way]. Only a stupid person would do it that way." (True story, I was the "stupid person" in question, although it goes without saying that you shouldn't do this to anybody, independent of their gender.)

Of course I think you are not likely to do any of the above, based on what I know of you. But there are subtler things that can occur to discourage girls in the math/science classroom.

The classroom should be a safe place, a place where no one is judged on their gender, race, religion, sexual orientation, etc., and I would encourage you to strive for that. I think that girls will thrive in a class where they feel safe from harassment, intimidation, etc. coming from their peers. I know that I performed a lot better when I knew that the teacher would come down hard on the people who made fun of me outside of class. I also felt a lot more comfortable when I knew the teacher wasn't going to pick on me, either. Basically I guess I liked the teachers who were benevolent dictators.

There's a phenomenon known as stereotype threat, in which people, when reminded of their status as members of traditionally underperforming groups, perform worse on exams. They don't even have to believe that any stereotypes about their groups are true; they still perform worse than they would have if they hadn't been reminded. The more the differences are played up, the worse the members of the threatened group perform. It even works on white males, if they're told just before taking a math test that Asians perform better on the test. Stereotype threat accounts for at least some of the underperformance that we see in the scores of certain groups on standardized tests, such as the SAT. But it does not account for all.

Unfortunately, society reinforces the idea that women cannot do math in many ways. There was the talking Barbie who declared that "Math is hard!" There are the pajamas for toddlers I saw at the store; you could choose from the "boy" designs with astronauts, athletes, and engineers, and the "girl" designs with ballerinas, pop stars, and fashion models. And the toy section with a doctor's kit aimed at boys and a nurse's kit aimed at girls, despite the fact that in this country, there are more women in medical school than men. And the articles in the newspaper depicting particle physics as a fun game that men play. And the online brochures for math and science departments, depicting their glorious department full of white (and sometimes Asian) men.

There's not much that you can do in the classroom to counter the sexism ingrained in our society. But you can make your classroom a safe space, where the sexism gets checked at the door. And taking at least a little bit of time to discuss the accomplishments of women mathematicians, and women scientists could at least help the girls who are interested in math and science feel less like freaks.

I think this is probably a very incomplete answer, and I wish I could make it more complete. I'm cross-listing this entry with the scientiae carnival, in hopes that others will contribute more ideas for you. Comments are very welcome.

Got a question for the Applied Mathematician? Leave it as a comment, or e-mail me!


Tony said...

Thanks for the tips.

Sally said...

I was thinking of another issue. I'm not sure how to say it well, but I'll try.

I think that one important thing in the math classroom is the ability to explain things in different ways so that different types of thinkers can be successful. In the past, this would have been described in gender-biased terms (girls think differently, etc..), but I don't think that's necessary. There are girls and boys who think like mathemeticians, and there are girls and boys who don't. All those kids need to learn.

Usually, math teachers were kids who found math to be easy (duh). They teach it the way they learned it, and very successfully connect with like-minded thinkers.

I think the reason some girls and some boys think math is intimidating is because it's explained in a way that's harder for them to understand. They (we! I'm one too!) find it frustrating to see all the people around us who are one type of thinker quickly grasping a concept when the teacher explains it their way. See that often enough and you begin to believe you are a slower or lesser thinker, when you are actually just different.

In my case, I had a high-school teacher who only had one teaching style. He'd work example problems on the board without explanation. All the "good at math kids" could follow what he was doing and transfer the one example to different, related problems. I couldn't.

I'm smart. I know I'm smart, but I don't think that way. I'd take the calculus book home and read the explanation of the process, then I'd literally teach myself. If he asked me a question in class the first day - right after he worked a problem that in his mind should have "taught" me - I could never answer. I could have answered the next day, after I'd read the book and done the homework myself, but he never asked questions then.

It was frustrating and reinforced his belief that I was slow at math and didn't belong in the class. I was one of three girls in the class. I wonder how many of the other girls who could have been in that class thought the way I do but were less stubborn and self-motivated to teach themselves?

Rebecca said...

Sally, you are absolutely right. It is definitely important to teach to all the students, not just one subset. And catering to the many different styles of learning can help that a great deal.

It sounds like your high school teacher was kind of closed-minded, too. It's too bad that you had that experience.

Anonymous said...

One thing you should try to do: Treat people as individuals, not as members of their specific group. E.g. avoid compliments like: this was pretty good for a girl.

In my high school I had a teacher who would tell everyone that the first time he saw me I was explaining physics to all the guys around me. To him, this was obviously something astounding and unusual. While this was clearly meant as a compliment for me, it also made it clear that normally, girls are just not as good as boys.
Since at the time I was also often being mocked for not being a "real girl", it also reinforced the feeling that I was a weird freak.

By the way, Rebecca, I really like your blog a lot.
I guess I'll go back to lurking again now.

Rebecca said...

Anonymous, thank you for delurking to make that point. Sometimes people think it's praise to tell you that you are good at something despite your gender. And comments like that can do more harm than good, because they're reinforcing the stereotype that girls aren't as good as boys are at math/science.

Like I read that in some ways, Marie Curie did not help the cause of women in science, because then the men in power expected all women to be that brilliant, and anyone who wasn't (namely, the rest of the female population) was dismissed outright. I'm looking forward to the day that a mediocre female scientist can advance as far as a mediocre male scientist.

Ginger said...

My experience with math was a bad one. I was always allowed to get by with mediocrity, especially in math, because girls are typically better at language skills..which was true for me. I noticed in college that I did better in math classes when they were taught by a woman. It seemed as though the male teachers taught as though everyone loved math as much as they did. I didn't. It was simply a drudgery I had to endure. Women taught so people learned math. Oddly enough, it seems as though it's getting easier for me in my old age.

ScienceWoman said...

Your tips are good ones (and the things not do are atrocious). There are links to other good resources at Fairer Science.

Jenny F. Scientist said...

Sciencewoman, great link!

The thing that really gets me in academic settings- and I know this is the last thing to worry about, once all the 'Math is hard!' Barbies have gone to a special little Barbie hell and Congress reflects the population- but anyhow, highly gendered or aggressive word choices really, really annoy me. Like describing things as 'seminal'. Or saying that it's 'a hard science' or a 'macho approach' or whatever. Drives me nuts. I've heard better ones but they've all dropped out of my brain.

Marius said...

Good post and good comments! I am wondering about the relation betwen the questions 'Why are there more men in maths' and 'why are many clever people bad at maths'. As some people pointed out, math is taught an specific way that might unnecessarily discourage people, and this might hit girls harder since the teachers tend to be men.

Personally I get the impression that it is not the math that scares girls away form exact sciences, but
more a lack of interest in exact disciplines that discourages interest in math. After all, if you're not involved in applications of math, you're going to miss both motivation AND a lot of extra practice, from different angles.

I think adults tend to reason that, since most people outside exact profession are bad at maths, being good or bad at maths was a reason to choose exact interest, while the opposite, being good as result of interests is just as important.

Applied to girls I believe this practice-makes-perfect causes most of the 'girls have language skills and boys math skills' effect. If we want more women in math and exact sciences, I think focussing on math education is not the most efficient direction. I think we should get girls interested in exact-related subjects from avery young age. Perhaps Legos with less stereotypical boys' themes would be the best step.

Of course, that still means that math teachers should behave fair to everyone.

Arwen said...

In terms of teaching styles: I did extremely poorly in calculus until, in calculus 2, a tutor pinned an index card to an orange and my brain lit up. I got such a great mark on the final they pulled me in to make sure I wasn't cheating. I know you can't always demonstrate math concretely - but sometimes, you can, and man did it help.

As for the women in science thing, I cannot claim I would have gone on to a PhD if it hadn't happened, but one particularly bad experience with a particularly misogynist/pushy professor who was supervising my work as a research assistant really did sour me. He obviously respected my (male) peers more than myself, and I was told not to ask such stupid questions twice.

I am not particularly thick skinned. Or rather, I've internalized some bullshit about women being second rate in math and science, and it is logic and not emotion that I use to fight that internalization. When hit on that plank, it's hard not to feel innately disabled by ovaries.

I also tend to agree with Marius, that a lot of our gendered kids toys end up showing up in University. Women seem to have taken biology by storm, but "hard" sciences are still seen as a boy-nerd's game. Frankly, in CompSci, the fact that I was a female who was into role playing and computer games *definitely* exposed me to the field, and that subculture has some messages about womanhood that turns some girls away.

Another anecdote: I was doing my RAship in computing bioinformatics, and was told by another student that "that is a good place for girls, since biology is soft science." Like bioinformatics somehow softened comp sci enough that my head wouldn't explode on all the pointy algorithms. (I told him to go bang rocks.)

Lisa said...

I do think like a mathematician, so I can't speak to some of the content of the comments. But I'm beginning to realize to what degree my success and interest in math and science is driven by the need to prove everyone wrong. "I'm the only girl in my class... and I'm better than they are."

Perhaps because of the encouragement I had as a child, perhaps because even the encouragement had gendered aspects ("don't let them tell you that because you're a girl..."), my gut response to "that was good for a girl" is "yeah, and I'd like to see you do any better".

This seems to be related to the Marie Curie thing that was mentioned. The girls in my high-level physics classes are all very, very good at it - because if they weren't they'd've given up on it. The mediocre ones are almost entirely male.

kostis said...

hello rebecca...i can't stop reading your blog since i found it(common interests ...role playing and mathematics).So i would like to ask
as applied mathematician to applied mathematician , what's your opinion about nullity (the theory in which x/0=Φ (capital phi) with x!=0 and Φ a number outside the number line)? For more information:
i would really like to know your views on the matter.
cheerz ,

Rebecca said...

Kostis, I had never actually heard of that, but it's certainly very interesting to think about. I don't know that I agree with Dr. Anderson's idea outright but I would certainly be interested in understanding its implications.