Getting that A, by means fair and foul

This week’s Capital Times leads with a story on grade inflation at UW-Madison.  I’m with ex-chancellor John Wiley on this:  “Grade inflation is one of those topics that initially seem clear and simple, but become murkier and more confusing the longer you think about them.”  I more or less stand by what I wrote about grade inflation in Slate in 2002.  The discussion on grade inflation has improved since then, actually:  I think people generally understand now that our moral standing doesn’t rest on whether our shorthand for “student did fine, showed they basically learned the material, is about average among classmates” is “B+” or “C.”  The Cap Times focuses on the more important question of whether different grading standards between departments creates weird incentives for undergraduates.

“I’m trying to get into medical school and it’s frustrating,” says Sheala M_____, a junior majoring in pharmacology and toxicology.  “I can work my butt off and come out of school with a 3.5 in my major, and a women’s study major going pre-med can come out with a 3.9 due to a much easier schedule. All of my courses have very strict policies — some where only 10 percent or 20 percent can get A’s.”

If you like statistics and large .pdf files you can look directly at the source of the article’s numbers: the registrar’s data for GPA in every department in Madison in 2008-2009, broken down by course number and class year.  For instance:  Sheala M_____ is required to take statistics, pathology, and biochem, which have average GPAs around 3.  (All give well above 20% A’s.)  The courses in her major, on the other hand, will be  in the pharmaceutical sciences department, where the average undergrad GPA is 3.43 and 46% of the grades are A.  The corresponding figures for women’s studies are 3.5 and 48%; not much of a thumb on the med school admission scales.  (Remember, the women’s studies pre-med has to take orgo too!)  That said:  I think the weird incentives are real and I think they’re bad.

Meanwhile, at my alma mater, Winston Churchill HS in Potomac, MD, up to 50 students may have broken into the school computer system and changed their grades.    The description of WCHS’s current reliance on computer-graded multiple-choice tests is sort of depressing.  But the worst part is I now have to stop making fun of my friends who went to high school with Blair Hornstine.

Deforming Galois representations in Rwanda

I just now learned that my friend Ravi Ramakrishna from Cornell spent a sabbatical term last spring at the Kigali Institute of Science and Technology in Rwanda.  And he blogged his semester.  Good reading for anyone interested in math in the developing world, or who likes awesome pictures of gorillas and volcanoes.  Ravi made a side trip to Uganda with Teach and Tour Sojourners; seems like a nice program, though note that you pay your own way to the continent.

See also:  Dino Lorenzini’s notes on visiting math departments in Africa.

Note:  I don’t know if Ravi actually deformed any Galois representations while in Rwanda.  But come on, if you know the guy, you know he probably did.  He can’t leave those things alone.

well, did we, okay did we determine that Moebius maps were like isometries or whatever?

From the Michigan Corpus of Academic Spoken English, a 16,000 word transcript of an undergraduate math study session.  In case you ever wanted to know what it really sounds like when students work on our homework.

S1: what if- what if A plus B, equals two times Y and C plus D equals two? [S3: yeah. ] it just has to be proportional so you can’t break it up… but if we have A and C being whatever, then let’s make them something that works.

S2: like one?

S1: let’s… like what if you made, A equal Z and C equal one or something.

S2: but they can’t equal whatever because in the bottom A over C has to equal Z.

S1: i know. [S2: okay ] you make it so that it works.

S2: so you want A to be equal to Z, and C to be equal to one.

S1: okay, so what if we do that…? well no then that gives us uh, Z in the Y equation. unless B equals like Y minus Z or something well it could be done… it’s gonna get complicated though… so if A equals Z,

S2: i think this sucks.

Madison Science Pub at Brocach, July 26

A couple of weeks ago at the farmer’s market I ran into some undergrads who were doing science demonstrations on Capitol Square.  I tried to get CJ to drop the ball into the beaker and displace some liquid, but he was too shy.  While I was there, another guy wandered by to see what was happening — turned out he too was in the science popularization biz, and is running a series of science pub nights at Brocach downtown.  This July 26, the guest is  UW bio-anthro prof John Hawks, an expert in population genetics of early humans.

As it happened, CJ demanded we eat lunch at Brocach the same day.  I’d never been in there before and wasn’t sure if it was OK to bring him in, but in fact the place is packed with strollers at Saturday lunchtime, and they have a kids’ menu.  I had the corned beef hash, which was good, but — and coming from me, this means a lot — too big.

If you were a mathematician and you were going to talk at a science pub, what would you talk about?

Fund the Montgomery County math team

Montgomery County is no longer going to fund the county’s participation in ARML, the American Regions Mathematics League. (Funny name, right? In my day, young whippersnappers, it was the “Atlantic Region Mathematics League,” and stopped at Chicago. By the time the rest of the country got in on the competition, the acronym was too well-branded to change. Nowadays, teams from Hong Kong, Taiwan, the Phillipines, and Colombia compete. “All-Encompassing Regional Mathematics League?”)

Montgomery County has been sending a team to ARML since the very first meet in 1976. These days, they send four full teams of 15 students each, plus a separate team of middle-schoolers. So all kinds of kids come, not just the child prodigies and the math obsessives — which is a terrific feature of the “mathletic” culture that our coach, Eric Walstein, has built up over the last thirty years. It would be a shame to see the county ARML team disappear, or radically contract to the 15 superstars only.

I don’t understand the intricacies of school funding well enough to complain knowledgably about Montgomery County’s decision (but feel free to do so in comments!) I think the idea is that MCPS expects the math team to have alumni and friends who can afford to help out with a little money. If you’re one of them, you can send a check made out to “Blair Math Team” to

Eric Walstein
Montgomery Blair High School
51 University Blvd – east
Silver Spring, MD 20901

Please do not write “TNYWR” for the amount.

“His parents think he’s fine. The school system thinks he’s fine. But he’s not fine!”

No sooner do I mention Eric Walstein than Emily Messner’s long profile of him appears in the Washington Post. You get a vivid sense of this devoted and — um, what’s the opposite of soft-spoken? — educator, who’s been wrestling Montgomery kids through math since — well, I don’t know how long, but he was already an old hand when I met him. I was seven. He ran me through some arithmetic problems and bawled me out when I gave him an answer of “Two hundred and six.”

“There is NO SUCH NUMBER AS TWO HUNDRED AND SIX!” he told me. He wrote “206″ on the board. “This number is called TWO HUNDRED SIX.”

OK, in restrospect, I don’t really understand why he needed to insist on this point. But I was tremendously impressed. I’d never met somebody who would have cared in the slightest how properly to pronounce “206.” Let alone somebody who would yell at a seven-year-old kid about it.

The article isn’t just about Walstein, but about the raging battle over how math is to be taught in Montgomery County, one of the fanciest public school systems in the country. Messner is to be commended for going a little deeper than “Are calculators good or bad? Are standardized tests good or bad? Are math education Ph.D.’s good or bad?” which is all one usually gets on this issue.

Also: more memories of Ted Widerski in the comments on Madison’s School Information System blog.

Ted Widerski

I just learned that Ted Widerski died last month. Ted was a long-time math teacher, in Madison and elsewhere in Wisconsin, and the programming director for the city’s gifted and talented program. He was 56.

I didn’t know Ted very well. I met him last year, when I spoke at the Middle School Math Fest he organized in Madison. I expected to lecture to a dozen or so overachieving and dutiful students — instead, I found the CUNA cafeteria packed with close to a hundred pre-teens, still fizzy and enthusiastic after a full morning of math activities led by an equally energetic cadre of teachers and high school students from Madison East. And Ted, fizzier if possible than the pre-teens themselves, at the center of it all. Very few people have the drive and know-how even to put together an event like this, let alone to make it such a success. Madison was lucky to have somebody like Ted helping young students find joy in math; from the Cap Times article linked above, it sounds like the students who learned from Ted in the classroom were pretty lucky too.

We talk a good game, in the higher-ed business, about getting kids in secondary school excited about mathematics. But it’s not easy for us to do, because we’re not in secondary schools. You need to have people in the school district who have a real feeling for math beyond the test, and who can convey that feeling to kids who don’t yet know how to articulate what they’re interested in. I think a lot of grown-ups in math can think of teachers of this kind we were fortunate enough to encounter in our youth. For me, and for a lot of other kids in Maryland, it was Eric Walstein. I think there’s a lot of kids, and former kids, from Madison, who’d say it was Ted Widerski.

Punished by praise

New York Magazine ran a feature story about a year ago, by Po Bronson, warning that telling your kids they’re smart is bad for them. The scientific peg is a series of studies by social psychologist Carol Dweck, in which one group of children was praised for their abilities on a task (“You sure are good at this!”) and the other group for their efforts (“You sure did a good job on this!”) The former group, at follow-up, was less inclined to take on challenging tasks, and more prone to give up after experiencing minor setbacks. Dweck’s explanation: the “abilities” group is getting the message that success is explained by your inherent characteristics. If that’s the case, then any task that presents difficulties must be one you’re inherently bad at, and there’s no point trying to get past the difficulties.

I’m reminded of a very strange argument I had with a tearful first-year calculus student, back when I was teaching at Princeton.

“This class is really hard!” she said.

“Math is supposed to be hard!”

“No, math isn’t supposed to be hard!”

“Yes, I’m the professor, and I say the course is supposed to be hard!”

“But it isn’t supposed to be hard!”

And so on.

When I started teaching I really liked Punished by Rewards, by Alfie Kohn. Kohn isn’t just against praising students’ abilities — he’s against praise of any kind. And he doesn’t like grades, good or bad. His contention is that all these things instill in students the pernicious idea that the goal of learning is to get the reward (the A+, the compliment from the teacher, the approval of the parent) And that the praise rewires you so badly that once you get hooked, you can never really go back to learning for its own sake.

And now? I’m not the radical teacher I used to be. But we do try to avoid imputing to CJ too many inherent attributes. “That was a good song!” not “You’re a good singer!” “We like it when you share,” not “You’re a nice boy.” It’s not as hard as Po Bronson makes it sound.

“Learn Bayes’ theorem, it won’t kill you.”

Great advice from a somewhat surprising source: K. Anthony Appiah, professor of philosophy at Princeton.

He’s right. Is there a reason, other than tradition, that we teach high school students trigonometry and not basic statistics? (I can think of one other reason, which unfortunately sounds like a pretty good one — swapping out an entire year of curriculum for new material would presumably create a massive problem of teacher training.) How pleasant it would be to answer “When are we ever going to use this?” with “You should be using it right now!”

More from Appiah, writing in Slate in 2005:

Many of them [humanities students] don’t know how to evaluate mathematical models or statistical arguments. And I think that makes you incompetent to participate in many discussions of public policy. So I favor making sure that someone teaches a bunch of really exciting courses, aimed at non-majors in the natural and social sciences, which display how mathematical modeling and statistical techniques can be used and abused in science and in discussions of public policy. If there are enough of them and they’re good enough, one or two required courses in this area won’t seem like a chore to students. And even those who grouse will probably be grateful later.

A lot is hiding in the “If” up there: it’s not easy to design or promote such courses. But we have models. For instance, if you don’t know statistics and want to, or if you do know statistics and want to know how to convince others that they’d better learn, you still can’t beat the 1954 classic How to Lie with Statistics.

More genius (there is no math stick)

A bunch of traffic seems to be coming over from Terry’s blog, so while the math people are here, one more comment about why the cult of the genius is bad for mathematics. When a student, especially a first-year, really impresses me, I often suggest that they consider majoring in math. And too often what I get in response is, “My math classes are my favorite ones and I’m really having fun, but I can’t be a math major because I didn’t win the Olympiad / win Intel / take calculus in 4th grade.” I don’t think other fields of study have this problem, at least not as severely — I’ve never heard anyone say “I can’t go to medical school because I’m not like those people who can instantly figure out how to palpate a gallbladder correctly and who knew the diagnostic criteria for a hundred tropical diseases when they were eight.” But in math we’ve unfortunately allowed the impression to persist that all of us in the business are former child prodigies, touched at birth with the math stick.

Consider, for instance, the list of participants in the 1988 International Mathematical Olympiad, which includes both me and Terry. There are lots of notable mathematicians on here — at a quick run-through, I count 13 names I know as working research mathematicians today. This means, of course, that of the many hundreds of excellent mathematicians in our age cohort, only a tiny minority even participated in the IMO. And even among this group of contest-lovers, success in research doesn’t require success at the Olympiad — one of the most distinguished members of the group, Elon Lindenstrauss (now a full professor at Princeton) finished with a score of 17 out of 42, right in the middle of the pack.

If you’re in college and you like learning math, study math! It doesn’t matter that there’s someone out there who’s better at it than you. That’ll be the case no matter what path you choose. And if you decide that the academic life is not for you — and it isn’t for everyone — you’ll be very well-positioned to apply for a wide spectrum of jobs and higher degree programs.