I grade exams problem by problem, with a twist. Basically, I start each exam and grade as far as possible before I have to actually think about point allocation – meaning, essentially, until I hit a problem that will be more than 1 point away from 0 or the maximum, or at least is not obviously out of that category. On some students’ exams this will be the first problem; occasionally I’ll hit one that I go all the way through in one pass. The exams on which I get hung up are put into piles according to which problem I first need to address. After this first pass, I take the pile of exams on which I got hung up the earliest (generally the exams which need the first problem looked at more carefully) and sit to think about how to allocate points. After grading that problem I take each of those exams and continue, which may end with all of them put into the “problem 2” pile but more typically puts many of them in later piles. At the end I will have a stack of exams that just need the final problem graded, and shouldn’t be the whole stack.

Advantages: since the easy-to-grade exams have been pulled out, there is more direct comparison of mistakes and it is easier to be consistent – no going back to try to remember how you graded that one problem that was similar and you didn’t make a note to yourself about. You get a feeling of real progress when you mark three pages in a row on one exam, and I believe at least sometimes you are going faster because you have an easier time comparing and figuring out consistent amounts to take off.

Disadvantages: it is like saving your least favorite food to eat last.

Case study: linear algebra, 24 exams at 10 pages each.
This isn’t the ideal case study because it bottlenecked at the second to last page with a conceptually difficult problem, but it is the one for which I have data. That problem was harder for the students and involved more thought to grade, so all but three of the exams (over 85%) ended up in the pile for that problem. However, reading a bit of each student’s answer to determine it belonged in that pile probably helped in figuring out how to mark.

A “pass” here counts as finishing the first incomplete page and running through each of those exams to the next stuck point. You’ll note no one got stuck on the third page of the exam; it was part (c) of a problem and was straightforward to grade.

pass 1: remaining exams x pages left: 7×9, 2×7, 4×5, 6×4, 4×2, 1×1 (130 total pages left)
pass 2: 5×7, 4×5, 6×4, 8×2, 1×1 (96 pages left)
pass 3: 2×6, 5×5, 6×4, 1×3, 9×2, 1×1 (83 pages left)
pass 4: 6×5, 6×4, 2×3, 9×2, 1×1 (79 pages left)
pass 5: 9×4, 3×3, 10×2, 1×1, 1×0 (66 pages left)
pass 6: 4×3, 18×2, 1×1, 1×0 (49 pages left)
pass 7: 21×2, 1×1, 2×0 (43 pages left)
pass 8: 6×1, 18×0 (6 pages left)
pass 9: done

Except for the first problem and the second to last problem, the most exams I had to deal with at once was 9, under 40% of the total. That amount is easily sorted into piles according to the sort of error made and each pile dealt with quickly after determining the rubric for that kind of error.

I would like to give credit to the person who introduced me to this method, but I have zero recollection of who it was. Thank you, anonymous benefactor.