I grade three problems on each homework assignment. Sometimes, students will complain, “You only graded those I got wrong!” Really? How do you know the others are right? Do you think I care enough about you go go through your homework to find which ones you got wrong and grade only those?
One of my colleagues has a student who said that she knows she is dying of cancer, because she diagnosed herself on the Internet. Because of this, she should get a good grade. Huh? Even assuming she is correct, the last thing she should worry about if she is dying is a grade in a math class. But even if the student believes this is the one thing she wants to do before she dies, the teacher is correct to grade the work and not the student.
I like teaching math, partly because there is very little ambiguity when grading. Of course the question of how much part credit to give can be a problem, but I try to be consistent. Homework is easy, because each problem is worth two points. Two points if it’s right, one point if it is attempted, but wrong, and zero for it not being attempted.
I have enough trouble keeping up with my workload. I’m not going to increase it by going after particular students. I grade papers, not students. It’s really not personal.