Due to unknown reason I was assigned as a grader this semester for a certain proof writing class in my universtiy. The class size is 65 and students took it usually comes from a computer science background. The result is horrible as I often graded them with marks of $2,3$ out of $20$.
The class average is usually $8$ out of $20$ not considering students who do not hand in homework. And if I account students who did not hand in homework with students scored $5$ or less, then usually this constitutes to $25$ or more students. So right now I do not really know what to do.
The reason they are performing really badly is because most of them has no proof writing background. As a result when asked to "show" some result is right, most of them just write hunchs crossing their mind and did not bother to justify their claims. The simplest example might be the professor showed for a graph of order $n$, size $m$, if $m\ge 3n-6$ then it is not planar. When the homework was hand in, I found the majority of the students under cooperation took this as a criterion to judge whether the graph is planar. Then they omitted obvious non-planar cases.
I am wondering what I can do. Grading takes me a lot of time and it is hard to spend any more time in writing out why they are wrong, or having regular office hours. But on the other hand I doubt if they really learned anything in the class in an organized way given their performance in the homework. So some help must be needed. I feel the situation to be quite puzzling because at here there are no review sessions, no discussion groups, and most students cram in homework in a few hours without much studying. I do not know what I can do to improve their performance.
It might be that because I am from a foreign country and my view towards US education is biased. Maybe students are expected to be this bad. But I did my undergraduate studies at US, and most of my classmates know how to write correct mathematical proofs despite they may have trouble in mastering advanced mathematical material or doing research. It might be that most of the students are CS majors, and as non-math major students they do not know how to prove something other than checking a few cases. But during the class the professor covered truth table, etc in the first few weeks. So I thought the basics are there.
I thought about inflating the grades on my part, but was dissuaded by fellow post-docs suggesting they should get what they deserved. However I had been an undergraduate and I know low grade hurts people. What can I do? I asked them to seek help in mathstackexchange, but I doubt if they are even willing to learn latex since they usually do not even bother to read textbook carefully.
My grading policy is as folllows:
4 for completely correct solution with an acceptable proof.
3 for completely correct solution with a flawed proof, and in some case without a proof but showed substantial work.
2 for correct or nearly correct solution without a proof or noticeable work
1 for half correct solutions, or ideas not quite correct but makes some sense.
0 for totally incorrect solutions, or confused with problem definition, wrong problem, wrong strategy, wrong use of the theorem, complete nonsense, etc.
update: I really do not know what to do. The student accused me for not explaining grading policy clearly. She thought finishing a math problem with a proof needs to be explained; She also seemed to be much more interested in grades instead of the course content, as she claimed the 10% homework grade is a lot. The message below was met with the response that "However, it is not my job to share those views. I think it would be better if you email your grading guidelines and any other relevant announcements to the professor to send out to the class." I felt at lost with her utilitarian attitude.
Also I finally got the professor's response as I forward the conversation to him. Instead of giving any suggestions on what we can do to improve student's understanding of mathematics, he boldly suggested:
"I don't think you need to spend so much time writing to a student in the class. A few sentences should suffice. Save your time for grading"
I think I have to give up dreaming I may change something as a grader.