I enjoy grading written work, tests not so much. Every week my students are required to work somewhat challenging problems and to describe their solutions. They should use correct grammar, state the problem in their own words, and state the answer in a sentence among other requirements.
I think I enjoy grading written work because I feel closer to my students – closer in the sense of nearer to their ways of seeing and thinking and thus their humanity. I get a sense of their effort and perseverance and appreciate them more. And the papers are direct evidence of their engagement with mathematics. I know that for a little while they were thinking math and that makes me happy. We are designed (evolved) for living on planet earth and as such are born with a variety of amazing capabilities. We have tremendous brains. When my students are using these brains for deep thinking I feel that they are somehow fulfilling their destinies. I get the same sense when I give a test. At least for fifty minutes I know my students’ brains are thinking about math. I also envy them (something I don’t usually reveal) because their brains are engaged in solving math problems, something I don’t get to do much of anymore.
Also I don’t like grading tests. After the first page I generally don’t know whose test I am grading. Every problem missed is disappointing. Sometimes after I have finished grading I think everyone has bombed the test. When I do the totals, I find that this is not so. My mind has focused on the missed problems not the successful ones. Of course since I give partial credit, I had to spend more time on the missed problems further skewing my mental sampling.
I enjoy grading writing, tests not so much.