> On the other hand, if you did not bother, a student might complain and have
> a point.
cover your ass, then. Why should you let random students decide how you grade things? If anyone, teachers need to be independent thinkers.

…
Even if it’s a small (less than 0.5), it seems to me that it may be worth it anyway. This is because there is little to lose by taking some attempt to normalize. On the other hand, if you did not bother, a student might complain and have a point.

All the courses I have taught or graded so far had at most 30 students, not enough statistics to see a clear bi- or even multi-modal distribution. But I do have seen excellent students that still stick out clearly from the good ones. And I have seen students who should have definitely revised their choice of subject…

When I taught my 300-student course last spring, we solved the TA problem by having a single TA teach all 6 sections (all in one day). We had graders to help him. No partial credit, so no ambiguity in grading.

Where we had a problem, that I never solved, is with our quizzes. The only way not to give the students in later sections an advantage was to make 6 different versions of each quiz, one for each section. This was a huge pain and in hindsight a dumb idea.

After wasting so much energy on making 6 equivalent yet different version of the same quiz each week, I was totally disinclined to run stats on the class to check for inequities due, for example, to the 1:00 pm section having 5 more hours to study than the 8:00 am section. Or for any cheating resulting from info about the quiz topics leaking from the early sections to the later ones.

You’re a saint in my view for taking the trouble to check for inequities and to adjust grades accordingly. Me? I’m way too harried by other responsibilities and just too lazy to give a damn.

Hmmmm…so, you want to measure the lumonosity of 300 objects, and you have uncalbrated visible light measurements made by a bunch of independent amateur (but skilled) astronmers. You then measure UV brightness for all the objects, and use that to callabrate the visible measurements. Legit? Seems so, unless there’s some systematic variance in the visible/UV ratio.

By analogy, this system rewards students with low homework/test ratios if there’s any correlation between that and section assignment. Would you think of that as a second order effect? One could make the argument the homework/test ratio measures ‘responsibility,’ which is as much a parameter of individual students as ‘intelligence.’

Interestingly, this should let you test hypothesises about one section being brighter than others…finaly answer that long-standing question if the brighter (or more responsible) students take the morning sections.

Robert–have you ever seen those multiple peaks in practice? When I TA’ed classes (in economics), I’d always predict that grades would have bimodal distributions, and I was always wrong!

Robert, do you believe in those five categories because we recognize five letter grades? Maybe there can be seven categories, like in Newton’s partition of the rainbow. Or perhaps only three, like in the Norse partition. That’s how Professor Jackson grades his advanced math classes: you were active in the class and knew your stuff, and get an A, or you weren’t all that active, were out of it for long periods, and didn’t seem like you knew too much, so you get a B, or you gave up halfway through, don’t know the material and get an F.

You are of course completely right about arithmetic means assuming affine structure. Naturally, assuming each of the assignments you wrote is of equal difficulty to a student who was first exposed to the material in your class, using the arithmetic mean to determine their score is the logical way to reward effort that leads to understanding. On the assumption that you get about the same kinds of students in each of your sections, normalizing sections is probably a good idea. Throwing away the outliers by using the median score to normalize sections is probably even better.

One thing I’m always interested in whenever normalizing grades comes up is, how do you avoid punishing the kids who take time out of their schedules to help other students? A simple normalization method (fitting scores to some kind of curve) would lower their scores by as much as it raises the scores of the people they help- making schooling pointlessly competitive. Students should be encouraged to present material to each other, because teaching is just about the best way to learn.