Thursday, December 20, 2007

Efficient grading (physics and math)

This will have to be the short version, since I have to do some real work tonight.

My experience is with quantitative subjects like physics and math, but since it seems to have some value for stuff that requires reading (like lab reports), it can probably be adapted for other subject areas. Details below the fold.

The starting point is that you only grade one problem (or even sub-problem or portion of a report) at a time. That was a given when grading 750 final exams in one day, because each person does one problem while piles of papers get pushed around a big conference room table, but it is also how I grade exams solo.

Here I will assume you are grading the entire exam of 40 or 50 papers yourself, maybe 400 distinct problem solutions. There are some differences when you are only going to grade one problem on 750 exams, so I will summarize those at the end.

My exams all have a cover page for the total, version, etc, so the first step is to turn the page to the first problem to be graded and invert the stack so the first papers turned in are at the top. If not, just set it up for the first problem, which might not be problem 1 on the test. If there are multiple versions, set them up so you are grading the "same" problem on all versions. This is key.

I always start grading with an 'easy' problem. I never start with one that might have N-8 distinct wrong answers. Too depressing, and it defeats the key step.

Sort the exams by answer. That is, make one pass through the tests looking only at the bottom line, the answer and its units. Completely correct answers go in one pile, ones with minor numerical variations or missing units go in another, and ones with wrong answers go in a third. Keep exams with the same wrong answer together.

Reassemble into one big stack and work through them starting at the top, or in the middle if your rubric has a key intermediate result or formula identified for that problem. Just because the answer is right does not mean the solution is right! This goes quickly for 'simple' problems, but requires a bit of care for ones where there are ways for two wrongs to make it right. It does take some experience to know which problems are likely to have 'magic' algebra steps where negative signs mysteriously change as needed, for example.

[Side remark: It is crucial that the solution be checked along with the answer. Many of the algebra weaknesses I see could only have made it into physics and calculus because an algebra or trig teacher did not check that they took the square root of a negative number and just made it into the correct real answer. I don't want that kid designing a bridge I have to drive over!]

There are two advantages here. One, the exams that deserve the same partial credit are next to each other. I may make a note on my key to say how certain errors are dealt with just for future reference, but I rarely have to consult them or look back to see how some weird thing got graded. Two, the exams are usually in the optimal order when it comes time to grade the next problem.

Next problem, same process. However, now the odds are that you have correct answers already at the top. The fact that you see a lot of correct exams before getting to the dregs is great for grader morale, which improves my efficiency. You do have to be super careful not to overlook errors on good papers or be too tough on the bottom. When a "top" paper has an error, it goes to the very bottom and when a "bottom" paper has the right answer, it goes to the very top. Sometimes I cut the deck, as it were, just to be sure I am fair (particularly for a long exam like a final).

The key is that you do not look through the entire solution for every paper, just the ones where you need to figure out what they did. Even then, you often get the efficiency of knowing that four papers all made the same kind of error in step 3 or 4 of the solution. You only have to figure it out once. After that, your eyes go directly to the error, flag it, and move on.

Handling each exam twice is more than made up for by less time spent on each one. I am also less likely to overlook an error in units or significant figures if I check that detail in my first pass. That means I also save time by not having to go back and look at an exam that was already graded.

Changes for Really Big Classes:

We would pre-grade a few dozen exams, picking out specific students from our own sections if that was practical. That would set up the rubric and give us some idea of what we had to watch for, but we also kept a sheet of paper with wrong answers listed along with the partial credit it got (and the reason why) when new ones showed up. This makes up for not being able to sort the exams. The basic idea was still the same: work from bottom to middle to top (or bottom to top to middle) of the solution to check the answer, the algebraic process used, and the physics.

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