I am a university marker TA. The instructor requires TAs to meet students if they have marking issues. But I found most students just come to meet me for better grades, not to ask questions, and some are tough to handle; they just insist they should get better grades.
I feel that is annoying. Is it a better idea to handle the cases by email, and let them talk to the instructor if they have further questions?
Part of the rite of passage of being a graduate student is having to deal with insistent students in person.
If students ask for more marks, you can firmly but politely state that marks are not subject to negotiation, but that you'll gladly discuss the contents of the answer.
Aside: learn early to be firm for otherwise word will spread you are soft and you will invite more headaches. Being firm can lead to awkward silences as you may rapidly reach a point when there is nothing more to say. If you reach a dead end you can always close by firmly but politely ask if there are other topics to discuss.
While the situation is indeed annoying, think of it as a training opportunity: by dealing with these insistent students you are getting really good practice in standing up for yourself in a professional environment (moreover, in a low stakes situation where nothing much other than your ego is at stake, and where you are the person in authority, which makes things a lot easier). The skills you will develop through this practice will be really valuable for you later on in life when the stakes can be much higher -- say, when you are asking for a promotion or a raise, or arguing an important technical point with a colleague or superior. So, the next time you hold office hours think of it as "I am going to my `assertiveness class'" instead of "I am going to be attacked by hostile students". This subtle change in perspective could end up making the experience a lot more tolerable, even fun.
I strongly recommend publishing and adopting the following policies:
Publish detailed grading rubrics describing how you assign partial credit. Follow them slavishly when handling regrade requests.
Regrade requests must be submitted in writing at most X days after the graded work has been returned. Each request must include a brief written explanation of why the grade is incorrect. (Note: not "...why they deserve more points.")
While you are happy to discuss answers and even grades in person, you will not change any grades in the students' presence. Or maybe even within 24 hours of meeting with the student requesting the regrade. Maybe add an exemption for arithmetic / recording errors.
Your responses to regrade requests are final. Further appeals will be automatically forwarded to the instructor. (If the instructor bounces them back to you, that means they're happy with your earlier decision.)
Finally, ask the instructor to announce these policies on the course web page. Better yet, ask the instructor to forbid you to change grades in the students' presence, or to regrade the same submission more than once.
As for demands from students for higher grades: Look them straight in the eye and tell them that giving them anything less than the fair and honest evaluation that they (or their parents) have paid for would be grossly unfair, not only to other students or future employers, but to the students themselves. Refer all complaints about your grading rubric to the instructor. Unless they want to discuss the substance of their work, gently but firmly kick them out of your office.
These headaches are a reason us educators have a job.
Depending on the person and the work I like to look at their exams again and explain why they lost marks and where they could do better, in the rare case that this doesn't do them justice I make it clear that on this exam, today, right now they do not deserve the marks they're asking for. I'll typically throw a few tips at them and tell them to prepare better so they can make up the marks next time.
I like to be open-minded when it comes to a kid's marks because I know a lot of incredibly bright students who make silly and sad mistakes I know they could've avoided. Totally shutting them out and saying things like "marks are not up for negotiation" can really destroy the self-esteem of these students and make them lose hope throughout your course.