Tall, Dark, and Mysterious

1/17/2005

Oh, I do believe I’ve already addressed this.

File under: Righteous Indignation, XX Marks the Spot. Posted by Moebius Stripper at 9:55 pm.

I had a long and only vaguely coherent post about the President of Harvard’s comments about the relative number of men and women in the mathematical and physical sciences, but then I realized that I’d already posted about it. Three months ago:

…no meaningful or productive discussion of [low ratio of males to females in the mathematical and physical sciences] can take place without acknowledging that there are far, far fewer women than men who are both interested in, and qualified to do, higher mathematics. Unfortunately, no discussion of that fact can take place - at least not in my presence - without someone pointing that the likely culprit is socialization, not biology - as though this is some profound insight that only those enlightened, self-proclaimed gender experts have ever considered - and one that renders any further discussion on the topic of women in mathematics completely moot. Social problem, not biological, the absence of women in math is a result of sexism, not hormones, nothing to see here.

What else did I say back then - oh, yeah, this:

‘“[W]e must increase the numbers of women in math!” has become the dominant battle cry of mathematicians and career feminists alike - the former of whom (mostly men, mostly older) typically have limited understanding of the life experiences of girls, and the latter of whom typically know next to nothing about math. The former accept the latter’s simplistic notion that the women-in-math problem would be solved if only we consciously countered our latent sexist beliefs and actively tried to recruit adult women into math programs and positions.

So I’ll leave the career feminists and male scientists to this one, and resume my role as math-chick-in-fishbowl. Honestly. Because if I don’t, I might have to explain why I can’t get too worked up over the fact that

[t]he president of Harvard University, Lawrence H. Summers… said that innate differences between men and women might be one reason fewer women succeed in science and math careers.

And I might also have to overlook Summers’ dumbass statement about his daughter’s feminine way of playing with toy trucks and how that is apparently related to women’s allegedly poor mathematical abilities, because that’s already been soundly eviscerated - by, among others, people who counter the “biology may be one of several factors” claim with fairytales like this one, cut from whole cloth:

I’ll tell you how much of a role discrimination plays in limiting female professors in so-called “elite” universities: 100%. There is no shortage of brilliant women scientists…but there is a dearth of jobs and we still have bigoted ignoramuses like Summers standing guard over the gateways.

So, there are just as many qualified women with Ph.D.’s in the physical biological sciences as there are men, or close enough? Come again? Can I please see the data on this one, because all I’ve heard on the subject in the last decade or so is that there IS a shortage of women in the above fields? Must be convenient to be able to peg the small number of tenured female scientists on the likes of Summers (who certainly isn’t the person I’d choose to head a top university) rather than doing the work to keep girls studying math and science so that they can BECOME brilliant women scientists.

I said that, too, a few months ago. Or something like it.

I might also have to say something about how it’s a crying shame that the brilliant women scientists listening to Summers’ speech (which he was invited to make by virtue of his qualfications as a leading economist - why, exactly?) walked out on him, rather than countering his claims with the data from the groundbreaking MIT study that rigourously revealed that, all other things being equal, female professors at MIT were paid and promoted less than their male colleagues. It’s a pity that they chose to walk out instead of giving data that backs up the belief they hold so strongly - that women would be men’s equals in the sciences, but for social conditioning to the contrary. It’s a shame that neither Summers nor his critics took the opportunity to outline how one could measure the impact of social conditioning versus the impact of genetics on academic performance; clearly they diverge on this issue, and it’s an interesting one to explore. I’m sure there could have been a lively discussion, had it gone that way. Instead, it became a circus, consisting of specious, deliberately provocative claims, countered not by arguments but by indignation. Welcome to Harvard, where the nation’s greatest minds are challenged, or something.

That RSS feed that I still don’t know how to use

File under: Meta-Meta. Posted by Moebius Stripper at 3:01 pm.

Someone’s set up Livejournal syndication for this blog. I don’t know who did this (though I have a few guesses, based on my referral logs), and it makes me feel all self-important to know that not only would someone want to set up a feed for this site, but that they’d do it without consulting me. I mean, this is how, say, the Dilbert and Savage Love feeds got set up: their fans just did it for them. It’s like I’m an unapproachable celebrity! (Seriously, though - thanks to whoever did this. I never did get around to figuring out how to use that handy rss2 thing that Wordpress generously provides, and I’m glad that someone did.)

Grade inflation

File under: Those Who Can't, Home And Native Land, I Read The News Today, Oh Boy. Posted by Moebius Stripper at 2:33 pm.

Education Wonk wants to hear from Canadian educators about grade inflation. I’ve got some stuff to say about that, mostly anecdotal, but the statistics support me:

A recent National Post survey of 25 universities including SFU found that only 14 of 81 faculties handed out lower grades than they did five or 10 years ago. It also found that the average grade in most faculties is a B.

SFU, the article mentions, seems to be immune to this trend, but the article doesn’t give much insight as to why that is. Pity.

Some subjects suffer more than others. I think I read the print version of this article when it first came out:

Using information on first-year university grades from across Ontario, we examine whether or not there has been grade inflation by discipline. In a survey of seven universities for the periods 1973-74 and 1993-94, we find significant grade inflation in various Arts and Science programs. The rate of inflation is not uniform. Some subjects, such as Mathematics experienced little or no change in average grades at most universities, while English and Biology experienced significant grade inflation.

A former camper of mine from Toronto told me about one local high school - I don’t remember the name - in which students routinely graduated with averages of 100%. One by one, they would flunk out of college, and eventually it got to the point that some universities would no longer accept graduates of this school. Those high marks meant nothing.

There’s a lot of talk about grade inflation, but measuring it is not easy. Addressing it is even more difficult.

For instance, EdWonk’s query was inspired by an article about a British math(s) exam, linked here, in which a grade of 17% translated into a B. Having not seen the test, I can’t say if this is an example of grade inflation: it’s possible that the exam was preposterously difficult, and that B students in the 1950’s would have received grades of 17% on it as well. What is clear is that if that’s the case, then the exam was unreasonable. Kimberly Swygert puts it well:

…it’s possible that a 17% on the higher-level paper really is B work…However, it doesn’t seem very useful to have an exam in which even the A scorers get half the questions wrong, because all those additional items go to waste. It would make far more sense to assemble the exam to have many more of the B level items, which would both raise the percent-passing level for a B (thus satisfying the public) and better discriminate among B and A level students. There can still be a few impossible items on there to sort out the A from the A* kids, but there don’t need to be many of such items, if they’re well-chosen.

This reminds me of a second-year physics exam I took as an undergrad: I scored an A+ on the midterm; the class average was a D. Most of us anticipated that the final exam would be a cakewalk, so as to bring up the average grade. We couldn’t have been more wrong. There were seven questions on the final; I (of the A+ midterm) understood what three of them were asking. I spent the entire three hours in the exam room anyway, figuring that I might as well make the prof suffer when he graded my paper. It paid off, and my final grade in the course was an A. I should qualify that: it paid off, provided the only thing I cared about was my letter grade in the course. I’d like to say that I also cared about what I learned in the course, but I’m not so sure I did at the time.

And that’s a big part of the problem when it comes to analysing these things: judgements about the suitability of a grade or a test are typically made based on little other than the actual numerical or letter grade received on various tests. If a 17% translates into a B, then grades are being inflated. If a class average was 57%, then the test was too hard. If students are averaging 75%’s in a math class, then the tests are too easy.

At the two universities where I’ve taught, the only supervision neophyte teachers received from the senior faculty came in the form of making sure that the marks - the average marks we gave in our classes were okay. Every few weeks, I’d be asked how it was going, and how my students were doing.

“They wrote their second test the other day,” I’d say.

“How did they do?”

“Class average was 62%.”

“Not bad - 65% would be better, but 62% is fine. Next time aim for a bit higher.”

That’s me being addressed in that last quote: the implication is that the marks (the average marks, anyway) that my students receive are entirely under my control. No wonder grades are being inflated.

(ETA - Outside the Beltway has more along those lines.)

In truth, a mark that is higher than it “should” be can mean any number of things. It could mean that my test was too easy, as has certainly been the case at times. It could mean that my students are smarter than last year’s. It could mean that my students worked extremely hard - this is what happened in my discrete math class last term: I gave difficult tests, and the kids blew me away. It could mean that I am the most effective teacher the school has ever hired. It could mean that one student hacked into my computer and distributed copies of the test to their classmates ahead of time. Simply designing a more difficult test would be the right course of action in the first of these situations, but not in the others.

It’s hard for a new teacher to know why a class has performed better or worse than they “should”. I consider myself a pretty decent teacher, but I am an inexperienced one. There is no class that I’ve taught more than three times. I would wager that a teacher would have to teach a course ten time or more before they could get a reliable idea of how one group of students should be doing relative to another, and whether, for instance, it was justified that the class of ‘02 had an average of 68% while the class of ‘97 had an average of 63%. At the university level, I suspect that relatively few instructors have taught a single class that many times. University instructors are an intellectually restless bunch, who grow bored teaching the same material over and over again. In other words: it’s very difficult for individual teachers, even highly talented ones, to ensure that their students are receiving the grades they deserve, the grades that their parents would have received with comparable understanding of the material.

For this reason, among others, I support standardized testing, particularly in math - cross-referencing standardized test marks against class marks over the years can paint a decent picture of whether students are receiving higher or lower marks than they would have received several years ago. However, this too is fallible: for obvious reasons, it’s unwise to simply give the same standardized test to students year after year, as both students and teachers will respond by learning how to answer the specific questions on the test and not the actual subject matter. Altering the standardized test significantly from year to year gets around this problem, but only by relaxing control over the samples.

(Do not misread these previous paragraphs to say that I think that uncertainty exists and that therefore, one can never really know anything about things in general and grade inflation in particular; I do teach statistics, after all. All I’m saying is that accurately measuring - never mind correcting - grade inflation is a tricky affair, one that requires attentiveness to any number of variables. I gather Kimberly and her ilk may have more to say about the specifics of this problem.)

However, the difficulty of applying consistent standards from year to year does not explain why, by most accounts, grades measured over long periods of time are increasing rather than decreasing or regressing to the mean. I’d be interested in what others have to say about this; I can speculate, though.

At the risk of waxing nostalgic over an era during which I was but a twinkle in my parents’ eye: the last several decades have given rise to two changes in attitude, which are almost certainly related: the notion that a university education is necessary in order to ensure success in life; and the idea that a university education is a commodity to be purchased in exchange for eventual employment. (I’ve discussed the tension between the goals of the academy with the perceived (and actual) importance of university education at Jobs are for the little people.)

Students are told - and told correctly, to a large extent - that they’ll be terminally unemployed and unemployable if they don’t go to university. University, for them, is not an option; it’s a requirement. Since decent marks are needed in order to get into university, they too are a requirement. Grade inflation is merely the right-hand side of that equation.

Every university instructor will tell you stories about the clueless student who indignantly proclaims that the B they received on that essay or the C they received on that test wasn’t good enough, and would the teacher please reconsider. I’ve read several such stories on blogs, and I’ve told a number of them here. The fact that my students can’t add fractions is no reason, apparently, for me not to give them at least B’s. After all, they’re trying. And they need these marks.

When these stories appear on my elders’ blogs, they’re almost invariably accompanied by commentary of the form well I never - “Back when I was a student,” the bloggers write, “I’d never have even considered complaining about my marks…”

In the most extreme cases, students have sued, or attempted to sue, professors. A fellow grad student of mine once taught a calculus class in which one student hadn’t achieved the grade he needed to keep his scholarship. The student complained to my classmate. My classmate held his ground. The student complained to the course coordinator. The course coordinator replied that he wasn’t going to change the grade unless Grad Student did. At this point, the student’s father called Grad Student, who, while agitated, didn’t buckle. Finally, Dad called Course Coordinator, and while I don’t know exactly what transpired during that phone call, Dad must have been pretty pursuasive, because the next thing anyone knew, Course Coordinator was backpedalling furiously and demanded that Grad Student alter his pupil’s grade. When Grad Student argued, Course Coordinator pointed out that he was under no obligation to rehire disobedient graduate students as instructors for the following term.

(This never happened to me, by the way, but at one point I actually hoped it would. If I were ever told that keeping my job was contingent upon me dishing out high grades on demand, I would have gone straight to the media with my story. Whose job is on the line now, huh, Course Coordinator?)

While every marginally principled instructor will decry the attitudes of Kids (and their parents) These DaysTM, the fact of the matter is, it’s stressful to be continually under attack by students whose inflated grades are surpassed only by their senses of entitlement. There’s also the pressure of teaching alongside teachers who buckle under the pressure: should we standardize our grades to be in line with theirs, or should we stand firm and give out the marks we think our students deserve? My students were competing for scholarships and such with the students of an instructor who gave B’s for attending class and A’s for doing a modicum of homework. The committees assessing our students aren’t administering math tests to measure their abilities; the assumption is that we’ve already done this, and that the grades we gave reflect the students’ relative standings. The committees don’t know that the Nice Teacher and I could have wildly different standards. I ended up scaling grades at the end of the term to bring mine in line with my colleague’s, but I didn’t enjoy having to do so. Again - this is certainly an argument for some level of standardization.

In terms of preparing students for future academic programs, the job market, and such, inflating grades is a prisoner’s dilemma of sorts. If the other teachers are inflating grades, you should, too, so as not to place your students at a disadvantage. If the other teachers aren’t inflating grades and you do, then your students have an edge in admissions and scholarship committees; not only that, but they’ll also like you more. But it’s best for everyone if no one inflates grades.

And as any student of the prisoner’s dilemma knows, we generally can’t trust multiple parties to cooperate; someone’s likely to defect and inflate their students’ marks, and I believe the data bear this out. But are we instructors willing to relinquish our autonomy and allow a third party to verify that our students’ grades are fair? And if we do, is there any assurance that that will help?

I don’t know - do you?

(I can’t close this post without linking to one site I found in searching on the terms “Canada grade inflation”. The irony is truly a thing to behold.)