Friday, December 20, 2002

A Grader's Complaint
So, my last work, done yesterday, was grading for the 7b final, and given the fact that I was already running on empty, my grading there probably did not represent my best work. However, if you do it right, grading can be pretty mechanical; the trick is properly setting the mileposts for people to be awarded points (my own grading scheme being somewhat of a hybrid between the holistic grading scheme that we're supposed to use in 7b, where points are assigned on the level of understanding that the student exhibits, and the more traditional "assign a point value to every important step" method; while the former is a really nice idea, it's a lot harder to implement in practice than the latter, so I often use accomplishing a particular step as a proxy for reaching a certain level of understanding, thus nicely tying the two together).

Unfortunately, I (in strict accordance with some law or another) got awarded the most unpleasant problem to grade. On the first midterm, the professor had posed a problem involving a submerged lead ball; as a result of the buoyant force, it had an apparent weight less than its real weight. Then, everything was heated up, so that the lead ball expanded (the water, too), changing the apparent weight. So far, so good. Now, the professor wrote the problem such that there was a certain percentage change in the temperature, figuring that this would cause all of the other variables to cancel out and leaving you with a percentage change of the apparent weight, obviating the need to, say, provide the other variables. A fine idea, except that it didn't work -- you still needed to know some of the initial variables in order to get the percentage. So, you would think he had learned his lesson. But no. On the final, he did the exact same thing -- posted a problem in which the initial percentage change was given, and no other variables, figuring that the variables would cancel -- but again, they didn't. This resulted in his having to issue a clarification midway through the exam, and subsequent student confusion, which was reflected in the exams I had to grade.

That wasn't really the worst of it, though. The most annoying thing was that, fundamentally speaking, there were two ways to do the problem: a right way and a wrong way. (For those interested in the technical details: The problem asked for the change in resonant frequency in an LC circuit when the position of a dielectric in the capacitor was changed by a little amount. The right way was to use the Chain Rule to obtain dw/dx. The wrong way was to compute the old capacitance and the new capacitance, subtract the two, and attempt to find the change in the resonant frequency.) Now, for people who went the right way, if they erred, it was pretty easy to identify where they had strayed from the path and award partial credit appropriately. Unfortunately, those people were significantly in the minority behind people who went the wrong way. Now, it is possible to get the right answer using the wrong way (it does work, just not very well, if you carry everything through very carefully), and so of course I had to give full credit to people who did manage to make it all the way through to the final answer this way. But if you went astray along that path, things got unpleasant really quickly, making it impossible to determine really how much credit they deserved; their understanding was completely obscured. So I had to just assign a uniform partial credit to the large number of people who suffered that fate.

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