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Lamrot Hakol (Despite Everything)

Musings and kvetchings and Torah thoughts from an unconventional Orthodox Jew.

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"I blog, therefore I am". Clearly not true, or I wouldn't exist except every now and then.

Tuesday, July 19, 2005

Grading on a curve

Can someone explain to me how grading on a curve is ever justified?

Correct me if I'm mistaken, but if you grade on a curve, the grade becomes an indicator of how well you did relative to your fellow students. It turns the class or the test or whatever the case may be into a contest between students.

If you don't grade on a curve, the grade is an indicator of how well you learned the material. It's entirely independent of how well or how poorly others may have done.

So what's the goal of education? To do better than the kid you sit next to, or to learn?


Blogger pacatrue said...

I am inclined to agree with you. However, I think the idea behind a curve is to compensate for faulty test design. It assumes that every class should have some good grades, some middle ones, and some bad ones. And if no one can pass a test, then the idea is that there must have been something wrong with the test. It's not a completely dumb idea. If I am supposed to teach algebra, and not a single soul in the class seems able to pass my algebra test, it is possible that I am either a bad teacher or bad test writer. A curve is intended to compensate. Of course, you could just say that the whole class is a bunch of idiots, which is always possible. However, in the long run, as more and more students go through the class and no one figure algebra out, then it is possible it is not the student, but the test.

9:35 PM  
Blogger Old Mountain Goat said...

I agree with pacatrue. A curve is most likely compensation for poor planning on the part of the teacher. The class needs a course correction (pun intended), to become more realistic or to employ new teaching strategies. Teachers who use the curve as a crutch -- semester after semester remaining impervious to feedback -- should change professions.

12:03 AM  
Anonymous Joshua W. Burton said...

I always aimed my tests to avoid grades of 0% or 100%, on the grounds that a question everyone (or no one) can answer fails to show anything useful, and is an unjustifiable waste of every student's time and an abuse of my authority. The ideal outcome was a mean near 50% and a standard deviation around 20%, so that at least 98 students in a class of 100 were showing the limits of their knowledge.

The point of the "curve" in this situation is not to calibrate the students but to calibrate the _test_. If my students surprised me by doing much better than I expected, I wouldn't penalize them: they could count on 70% being a solid A- even if half the class got there. And if they all bilged, I'd give them a break, within reason, on the theory that the test was unfair. But either outcome definitely feeds back into the level to which I aim the _next_ test.

The whole idea of a classroom test is a compromise, of course. In an ideal world, I'd teach only tutorials, and give only one-on-one blackboard exams, where I would calibrate the questions in real-time by telling the student to skip past anything she understood, and back off from anything she didn't. In a well-administered two hour oral, the student should be right at the agonizing edge of her capabilities, unsure how the next 30 seconds will go, for at least an hour and forty minutes. There's no way to do that affordably for a lecture class of a hundred students; an exam calibrated to mean _expected_ performance is the closest second-best. And just as the correct calibration for a one-on-one exam is the student's minute-by-minute performance, the statistically correct calibration for a written exam is the observed curve. Anything else risks wasting many students' time with 0% or 100% wastepaper.

2:26 AM  
Blogger Lisa said...

I hear what you're all saying, and it sounds like it could possibly be okay in theory. But in practice, it doesn't work that way.

When a bright student takes flak from classmates for skewing the curve, that's a serious problem. And curves do that, despite what Josh wrote.

Josh, you seem to have tried to use grading curves in a very atypical, and much better way. But surely you'll concede that what you've described is an extreme exception to the rule, no?

I had a math teacher in high school named Rabbi Kaplan. He was probably the best teacher I've ever had in any subject.

The class was called "telescopics". Telescopics was to honors as honors was to the regular math class. When they first came up with it, the idea was that a student getting an A or a B would get half a grade point bonus in honors, and a full grade point bonus in telescopics.

Rabbi Kaplan agreed to teach the class on condition that students would only get half a grade point bonus on an A or a B. He wanted kids who were there because they wanted to learn more math; not because they wanted a higher GPA.

He used to grade on a curve, and he had to, given his teaching method. His tests were roughly half on the material we'd just learned, and half on stuff we hadn't learned yet. He just wanted to see how far we could stretch on our own.

I remember once getting a 16/31 on one of his tests and it being the highest grade on that particular test. I have a cousin who transferred back to honors because of that kind of thing.

But Rabbi Kaplan and Josh are exceptions. If the class is a bunch of idiots, to use pacatrue's phrase, why should they get grades that don't reflect it? Why should the same student get different grades depending on whether his classmates are generally smart or generally stupid? That's my issue here. What one student does should have no implications whatsoever for the grade that another student gets.

11:04 AM  
Blogger Old Mountain Goat said...

Joshua's method sounds excellent.

Normally the curve means that grade percentages are predetermined going into the class. Idiotic. Any 10 year old would say so. It takes a bureaucracy to embrace the idiotic. And often teachers are bullied by the administration to flunk a certain percentage. And what a handy tool the curve becomes then.

On the hypothetical that a well tuned course receives a "bunch of idiots" by some weird stroke of fate, then they should all flunk. By the same token a "bunch of geniuses" should all get 100%. When the administration comes down on the teacher, he/she should push back because it is most likely the administration's fault for not screening out the bunch of idiots or geniuses.

1:28 PM  
Anonymous Joshua W. Burton said...

What one student does should have no implications whatsoever for the grade that another student gets.

By the same argument, which lab project one student does should have no implications whatsoever for the project another student picks. Except that we've only got one cryostat, four oscilloscopes, two lasers, and one working power supply.

As long as the teacher has to sit a bunch of students down to the same exam, we're talking about economics and compromise; it's not quite the exam she'd give any single student in a tutorial situation. The Platonic ideal toward which the teacher is aiming to grade is "Lisa's mastery of this course." An imperfect approximation is "Lisa's performance on this particular test on this particular day, relative to the teacher's generic expectations for this year's students." Another imperfect approximation is "Lisa's performance on this particular test on this particular day, relative to the teacher's informed expectations for this year's students, based on their observed performance." In general, the latter is a better approximation than the former, because the teacher has better information before deciding what an A or a C is.

The case Lisa is worried about (a minority "throwing off the curve") reflects an abuse of process, or sheer laziness or innumeracy, on the part of the teacher. The teacher should have gone into the exam thinking, "anyone who can solve problem 4 is B+ material or better," and "this is a pretty good class; I bet about a third will get B+'s or better." If the experiment fails, the teacher needs to decide which proposition she believes more strongly, and grade accordingly. Grading to a fixed scale presupposes (1), and grading to a blind statistical curve presupposes (2). A teacher who is neither omniscient nor lazy ought instead to look at the exams before deciding what they show...about her success as a teacher, about the quality of the posed problems, and about each individual student.

More common than curving is retroactive downweighting of (what turn out empirically to be) bad questions. Surely that isn't wrong? To object, I think you'd have to reify "the test" into some infallible oracle that exists independent of the learning process and the particular students. Maybe that works for third-grade arithmetic and spelling, but it doesn't scale.

1:51 PM  
Anonymous Joshua W. Burton said...

Anecdote: the first time I ran my own lecture course, the department head asked me if I had any questions about the administrative stuff. I replied that I had only two. (1) How many students in this first-year required course can I give A's to without getting flak from above? (2) How many can I fail, ditto?

His immediate answer: "100%, and 100%. It's your course, Joshua." I miss that job.

1:56 PM  
Anonymous Anonymous said...

The purpose of grading on a curve is to demonstrate to the students that their success is based not only on mastery of the material, but more complete mastery than their competitors (fellow students). Curve grading is a life lesson that is probably appropriate to begin in high school.

There are two problems with curve grading. First is faulty test design. The second is an underachieving class. Those faults have already been discussed. However,it is possible to use the curve grading to ratchet down every student's grade in the second case, if even the best student has an inadequate grasp of the subject. This is because adjusting grades on the curve is an inherently statistical process. If all grades are adjusted with the same process there is fairness, even if the top grade is a C.


10:11 PM  
Blogger Lisa said...

Anonymous wrote:

The purpose of grading on a curve is to demonstrate to the students that their success is based not only on mastery of the material, but more complete mastery than their competitors (fellow students). Curve grading is a life lesson that is probably appropriate to begin in high school.

It's a terrible life lesson. One of the reasons society is so screwed up nowadays is that people are more worried about doing better than others than they are about excelling on their own terms.

Why should a fellow student be considered a competitor? School is supposed to be for learning. Not for competing. If someone wants to compete, that's what sports and other extracurriculars are for.

10:38 AM  
Anonymous Anonymous said...

I agree with Joshua Burton -- teachers that grade on curves in the way lisa is calling "typical" are being lazy or displaying innumeracy. I may have been fortunate in not having many teachers of that ilk, but I have to say that I disagree that the lazy way is the typical way. The typical way is probably closer to what one would hope for, even if it is even lazier than using XCel to calculate the curve for you.

I believe the typical pedagogue starts by trying to use a standard set of levels for each grade break-point. 90=A, 80=B and so forth (some use a different scale, of course). Now, when the test scores come in, they look for surprises. Too many A's, they probably don't adjust ANYTHING on that test and they make a more difficult test next time. But they wouldn't curve it so that people getting 92 are given a "B".

Note, however, that they should also know that tests with narrow bands of scores are non-diagnostic later in the year when grades might be based on total points. If everyone got 92 on the first test in a course, the teacher might as well throw that test out and tally the scores for all students based on one fewer test.

Okay, now take the opposite example. A test was so beyond the students that the best one scored 50%. Here, most teachers would "grade on a curve" in that they would simply tell students "on this test, anyone who got above 45 is probably doing "A" work. Why would they say this? First off, because they know they're going to calculate a final grade based on total points and because they aren't interested in failing good students when clearly something was lacking going into the test. Again, it's dispersion in test scores that helps a teacher evaluate whether the test was a good one, not the absolute scores of the people in the class. If everyone got 50 on test, that test might as well not count in the final analysis either.

So, what we're really after is whether, at the end of the year, the teacher needs to apply some normalizing function to get to a pleasing bell-shape for the class as a whole.

Here's where the laziness rolls in. The prof has 20 students ranging in total score from 189 to 572. He or she COULD just do the obvious and compare each student's points to the total possible for the term (572 out of 600, say...) and get a percentage. Everyone over 90% gets an "A", and so on. But that would ignore the fact that one of the tests was way too difficult (50% was the high score) and one was way too easy (everybody got 92 or above). So, instead, the prof decides to do some sort of "curve..." For the most part, what they REALLY do is:

1) Look for gaps in the distribution of scores. If they fall in about the right spots, they do the letter grade breaks at those points.

2)Then, if they feel generous, they take people who are close to the edge and move them up a half-letter grade or something.

3)Finally, to avoid complaints, they double check to see that everyone does better this way than if straight percentages were used. So, you NEVER penalize a student who scores low on the curve by giving him or her a lower letter grade than the straight percentages would've.

And what does it all mean? It means that most of the educators I know got to know their students and decided that unless they were surprised at some point by their performance, they knew from pretty early in the year what grade that person was likely to get.

And a truly good educator in that mode would also try to motivate the lower-end students to pick it up a bit. And if they did it, they'd reward that effort. If they didn't, the kid got the grade the teacher figured he or she would get all along.

The reason for this laziness in grading? None of them really care about the GRADES. They care about what you learn. They don't care about evaluating you numerically, they want to teach and have you show that you learned.

And frankly the whole grade thing (and systematic approaches to it) make most educators just plain ill.

Sloppy. Sure.

But it's also rather comforting to know that most of them are concerned more with teaching their students than with placing them in rank order on a list.

7:14 PM  

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