I was a TA for the department head in CS, and he gave us free reign to handle grading and such however we felt was best. More important things to do, I guess :)

I was a TA for the department head in CS, and he gave us free reign to handle grading and such however we felt was best. More important things to do, I guess :) We had Homework, Quizzes, and Tests, 33.33 each. Homework was graded like you said. Quizzes and Tests were open notes but on a relatively tight timescale. If people missed a homework, they could turn it in late for some linearly scaled penalty. If they missed a quiz or test question, they could come in and demonstrate/defend a solution off the cuff during office hours for 70% credit or something similarly high. Students loved it. They no longer had to stress about getting an A, and they could instead focus on understanding the material, since that was the easiest way to (eventually) get the points. I will say, though, this strategy was very time consuming for a large class. It also requires the TAs to have mastery of the material, which (shocker) is unfortunately not all that common.