Tall, Dark, and Mysterious


Math in the news

File under: Sound And Fury, Queen of Sciences, I Read The News Today, Oh Boy. Posted by Moebius Stripper at 1:09 pm.

Via Chris Correa via Kimberly Swygert, an article from NPR about innumeracy among journalists. It’s got some useful tips (which Kimberly discusses further) about how to interpret polls and such, though you first have to read past the rather blasé introduction about how journalists don’t really care about numbers, and that’s life, what can you do. (Hint: you can start reacting in the same way that you react toward journalists who don’t care about other sorts of facts, rather than shrug off the inability of a lot of journalists to do their damned jobs. Start setting high standards, and you just might see results.)

Another symptom of innumeracy among journalists: the fact that while they routinely fail to present math as something that’s relevant to everyone’s day-to-day life (medicine, polling data, finance), they nevertheless - to the embarrassment of many - jump at the chance to report some faux-esoteric non-story that presents mathematicians as Professor Frink wannabes:

THERE’S grim news for people who worry that if something can go wrong, it will go wrong. A new mathematical formula has proved Murphy’s Law really does strike at the worst possible time.

Ordinary people have long known that computers crash on deadline and cars break down in emergencies, while previous studies have shown the law, also called Sod’s Law, is not a myth and toast really does fall buttered side down.
But now a panel of experts has provided the statistical rule for predicting the law of “anything that can go wrong, will go wrong” - or ((U+C+I) x (10-S))/20 x A x 1/(1-sin(F/10)).

Wow, it’s got a trig function and everything, it must be true.

I’m hoping this is a practical joke, though that just means that the journalists are dupes rather than the “panel of experts” being nerds.

Where to begin? First of all, I love the contrast between “ordinary people” and the geniuses who tested their claims. But geez, mathematical equations do not prove real-life observations (what the hell does that mean? ahhh, my brain), they merely model them, and the good ones model them well. I’m not even going to go into how people will notice rush-hour traffic being bad when they’re already late but won’t notice it going well when they’re late or going badly when they’re on time; or how big projects tend to have bigger problems; or how your hot-water heater is probably working overtime in cold weather to begin with; or how IF YOU SUCK AT SOMETHING, YOU PROBABLY WON’T DO IT VERY WELL.

Some concluding tips from the department of “this guy has a Ph.D. and I don’t??”:

Project psychologist Dr David Lewis said: “…if you haven’t got the skill to do something important, leave it alone. If something is urgent or complex, find a simple way to do it. If something going wrong will particularly aggravate you, make certain you know how to do it.”

Wow, that’s some smart mathematical formula.

Women in math - the intersection of sexism with crappy pedagogy

File under: Those Who Can't, XX Marks the Spot, Queen of Sciences. Posted by Moebius Stripper at 10:26 am.

I started posting a big response to the women in math screed, but it got big enough to merit its own big post.

Joshua H. asks, How exactly do you think high-school level math ought to be reformed? I started to ask if Joshua H. (hi Josh!) meant in general, or in terms of the male/female divide - but then I realized that it’s not necessarily so easy to distinguish between those two. There’s a good post with good comments over at Learning Curves on the subject of how to educate prospective middle school math teachers that leads nicely into a lot of this. Rudbeckia Hirta describes a business math course at her school that sounds an awful lot like just about every high school math class I’m aware of: “Look at the formula. Watch me use the formula. You practice the formula. Next formula.”

And there’s half the problem with math education right there. I routinely get students cutting me short in the middle of an explanation and asking, well, sure, that’s all well and good, but what’s the formula I need to memorize in order to do this sort of problem? And my students, almost to the individual, are woefully ill-equipped to handle any math problem that doesn’t follow the very rigid templates of problems that they’ve memorized. This is the first thing I’d change. But that’s a symptom of something more serious - a cautious approach to doing things in general - “I’m not going to try anything different without permission” - which is something that’s encouraged in girls far more so than in boys:behave, and follow instructions.

Last year, there was this article in a local paper describing a pair of new, experimental, sex-segregated math and English classes at a local Island junior high school. I had no strong feelings a priori about segregating boys and girls in schools, but my jaw dropped when I read that there would be completely different approaches to teaching math to the boys and girls. “The boys’ class will be more hands-on,” boasted the principal, “while girls prefer to read about math before they do it.”

In other words, the boys get to actually think creatively about the problems they’re working on, and try to think of new approaches to questions whose structures they haven’t yet encountered. Meanwhile, the girls will never ever have to try out math problems that they haven’t had explained to them in detail beforehand. The girls will be allowed to continue learning math by learning formulas, while the boys will be taught how to deal with new concepts.

It should be pointed out that the two different curricula weren’t developed by misogynists who think that boys are inherently better than girls at math. They were developed by well-meaning morons who really wanted to help the girls do better in math, but who had no idea what it meant to do mathematics. If any of the curriculum developers had any credentials in math or math education, the article’s writer didn’t see fit to mention them.

Back in the 70’s, the women’s movement was centred largely around getting women involved in male-dominated fields of study. In the decades that followed, the numbers of women in law, medicine, and science skyrocketed. Today, we’re seeing the focus shift away from getting women involved in so-called masculine disciplines and more toward valuing careers, styles of work, and interests that have been traditionally disparaged as feminine. In some ways this is good (being interested in cooking is just as valuable as being interested in automotive repair), and in some ways it’s downright idiotic (being uninterested in science is just as valuable as being interested in science). Among the most egregious examples of the latter are Carol Gilligan’s book In a Different Voice, and the similar Women’s Ways of Knowing, both of which glorify the conventionally “feminine” learning style of sitting still and being cautious and not trying anything new without near-complete context and information. Whether or not this is an accurate assessment of gender-based learning differences I am in no position to gauge; unlike the authors, I did not conduct dozens - yes, dozens - of interviews with upper-middle-class college students in order to draw my sweeping conclusions. I do know, however, that this cautions, personal, social style of learning that is highly inconducive to doing real math.

Back when I was in grade eight, my father gave me some of his old grade nine geometry notebooks. I was amazed, as well as envious of the level of work that was expected of my parents’ generation. Students were presented with problems that didn’t follow exactly the templates of the examples they’d seen in class. They got a feel for the sorts of lines they’d sometimes have to construct in order to find a certain angle or prove a certain property. Formulas were used sparingly.

When my students come into my office, I’ll guide them minimally with questions. Often they’ll say something like “well, I’d look for a common denominator but I don’t think that’s what you did in class” and then look to me for an answer. They’re looking for permission. Four times out of five, it’s the female students who want to know if they’re allowed to do what they’re doing. They look at the steps of solving problems in terms of what they have permission to do, rather than what is mathematically correct. They don’t want to try something that might not work. “Okay,” I’ll say, “let’s try getting this over a common denominator.” Sometimes it’s the right approach (well - a right approach) and sometimes it isn’t. If so - great. If not - they’ve hopefully gained some insight into why it’s a wrong approach.

(One of my students told me that she gets confused when I don’t tell her the single correct method to solve a problem. “Often there are several, and you have a choice of which one to use on tests,” I told her. This bothered her a lot.)

So there’s this movement to get girls interested in and involved in math; there’s also a trend toward a very formula-driven mathematics curriculum. I’m above the correlation/cause conflation, but it’s worth mentioning that there are proponents of the latter who specifically mention that girls’ learning styles need to be respected in order for them to learn math.

Perhaps so. But the learning style of sitting still, being cautious, and not doing anything new without validation, is inherently inconducive to doing mathematics. It’s not a feminine learning style, it’s a deficient one, one that needs not to be respected but discouraged.