Wednesday, September 20, 2006


The students in the class I teach had their first quiz on Monday. It came entirely from lecture notes that the professor publishes on the web and consisted of 25 multiple choice questions. In other words, an 'A' was within easy reach for anyone who put in an hour or so worth of time studying. As you might expect, however, there were students asking for a curve after class today (the class average, by the way, was 80%, which is about what it "should" be if a 'C' is "average").

In general, I think curving quizzes and tests is a horrible idea. Quizzes are meant to evaluate student performance. It's how the professor knows whether they've been bothering to learn anything or not. Now, granted, a given quiz may turn out to be a poor measure of student ability, and one way of knowing that it was a pure measure might, indeed, be that the students generally did badly on it. But it seems to me that in such a case the professor should simply scrap the quiz - or else remove from the final score those questions that are, in his opinion, unfair. In any case, the fact that the average on a quiz was bad does not in and of itself indicate that there was anything wrong with the quiz. True, I think it means the professor needs to review, among other things, how well he presented the material, whether the quiz was indeed a fair measure, and whether there might be external factors that would explain it (were an undue number of students absent recently, etc.). But if, in his honest opinion, the quiz was fair, then the grades should stick. As one of my students last semester said - defending me when I gave this (obviously highly unpopular opinion) in discussion section, "you gotta have standards." And that's the point: if we know before we even give the quiz how the class is going to do on it, then there's really no point to giving the quiz at all! However statistically true it is that distributions of grades in large classes tend to follow a bell curve, the operative word is still "tend." There is no a priori reason why any given class in any given situation should necessarily follow this pattern, and so it is annoying when students approach the professor as though it's his fault when they do poorly, as happened today.

The solution the professor offered was to allow an optional fifth quiz at the end of the semester for students who want to replace one of their grades (I told him I wouldn't let him curve it! :-) ). As things go, this is a reasonable solution. It is not, however, ideal. Frankly, I think educational standards are falling, and this is simply one of the symptoms.

The more troubling symptoms show up on a more general level. Today in the paper, for example, there was an article about the enrollment rates for black students at IU (mysteriously unavailable online - instead there is some garbage about how they will throw even more money at athletic programs). Apparently, they're down. Which, from any fair-minded perspective, is no cause for alarm, considering that they reached a peak last year, and considering that enrollment of students from other minority groups is way up, and especially considering that the dropout rate for blacks at IU is rougly 65% anyway (which would tend to indicate that the standards for admission for this group are already artificially low). And yet, the Black Student Organization wants IU to simultaneously address the problem of low admissions for blacks and the low graduation rate. Which really just amounts to asking for a free ride through college.

It operates on the same premise as quiz curves. x% of students typically get As on a given quiz, ergo whatever quiz we give should have this number of As. If it doesn't, we adjust our definition of 'A' to fit our preconceived notions. It has nothing to do with actual performance on the quiz and everything to do with the need to fit some purely cosmetic standard. Ditto black enrollment. x% of Indiana's population is black, so many want to conclude that x% of the student body also should be. Any argument for "injustice" here depends on a preconceived outcome. But that's ridiculous: enrollment should depend entirely on which students manage to meet IU's (embarassingly low) admissions standards. We can well ask, if an inadequate number of black people end up enrolled in the incoming class, why they are not meeting the admissions requirements to the same proportion of their population that other segments of the public manage to do, but there's no basis for concluding that there's an injustice of any kind going on here. And indeed - there are reasons to believe that blacks in general have an easier time getting admitted to university in America than other groups.

As serendipity would have it, there's a post on Samizdata today about this very issue in England. It seems like some have suggested that the only way to significantly increase minority representation at university is to throw away admissions standards altogether. Which at least has the virtue of showing that the reductio ad absurdum argument against "diveristy" enrollment is not merely an imaginative hypothetical but a very real danger.

I can't personally believe that such things are seriously considered, but then, I also have trouble understanding why anyone bothers to assign quizzes that grade imaginary classes rather than the one that actually turns up to take it. I think of Hamlet shouting "Anything but to the point!" And that seems to be the trend in education these days. Virtually any suggestion is on the table as long as it cannot be construed in any was as common sense.

My humble suggestion is that we stop being afraid of letting people fail. If a degree is to mean anything at all, it has to be given out solely on the basis of whether or not the person bearing it in fact has the credentials it claims. Likewise, if tests are to mean anything at all, then they must be graded solely on the basis of whether or not the taker performed to the required level of achievement. Equally, if we're going to bother to have admissions standards at all, then they should solely evaluate whether or not the prospective student in question has the academic qualifications necessary to attend the university. Degrees given out for free are mere pieces of paper. Quizes with predetermined outcomes measure nothing but rank within the class (which ought to be irrelevant). Admissions standards that take race into account are not academic standards and are, bluntly, racist.

None of us likes to see people fail. We fail ourselves sometimes and know how depressing it can be. I do think that society could do with giving people more second chances. For example, in Germany you are free to take courses as many times as you like until you get the grade you need. Grades at the university I attended there were reported by the students - so you got a slip of paper with the professor's stamp on it and took it to the appropriate office. If you didn't like your grade, you simply retook the course. This strikes me as a more reasonable way of dealing with it. Course standards are not up for negotiation, but in return a student is free to try, try again until he gets it right. We know that admissions standards are already like this. If you don't get in where you want to go, you are free to enroll in a community college and try again next year. And as for quizzes, I don't know how to fix that except to say that there are usually plenty of them, so if you don't like your grade on one, feel free to study harder for the next.

Predetermined outcomes are a terrible thing for a society. What we want is a meritocracy. And that is only possible if merit is, in fact, the first consideration.

[Update - Noah has a very insightful comment to make about this post, so please check the comments section. For some reason, I'm feeling mentally exhausted today, really brain-lazy. I'm not going to completely think through whether or not I agree with him about the SAT etc. just now for that reason - but I'm inclined to say that I do, that's he's right about this, and that it is an aspect of this problem I overlooked. He may post about this later when the IDS article in question is available online.]


At 5:10 PM, Blogger noahpoah said...

Damn you, Josh! I was going to blog about the IDS article, but I wanted to wait until it was linkable. Oh well.

I do have a nit to pick with the post, though. While curving quizzes and tests for a given class is basically fitting it to preconceived notions, there are legitimate testing situations in which a curve is expected. The terminology in testing circles makes the distinction obvious:

Norm-referenced tests (such as the SAT, ACT, etc...) have scores that are defined with reference to the mean and variance of the gigantic sample of test-takers. In fact, the scores for both of these tests are just transformed z-scores. If my testing teacher at UH was right, they are transformed so that half the population doesn't get negative scores and feel overly sorry for themselves.

Criterion-referenced tests (such as quizzes in typical college classes, the driver's license exam, etc...) have scores that are defined with reference to the information taught and, in theory, learned.

Forcing the scores on a criterion-referenced test to fit a curve is indeed silly, as is the related notion of expecting (and implementing policy to ensure) that social group X will be represented in each cross-section of society in proportion to their numbers in society at large.

As you point out with regard to curved quizzes, norm-referenced tests tell you someone's rank, not their absolute ability or knowledge. This isn't always bad, though. The most obvious example where this would be useful relates to other parts of this post - admission standards. It seems to me that it makes good sense to restrict the set of potential students to those that rank above a certain level with respect to the population at large (or the population of high-schoolers that take the SAT, ACT, or whatever).


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