TAs are responsible for answering students' questions. But sometimes there are bad-mannered students who don't treat the TA with respect during the interaction. Should TAs just take it and still answer students with patience? Otherwise, they may be complained about by students. Or do TAs have a right to ask students to behave politely before answering them, or to just simply refuse to meet them?
The TAs in question should speak with the director of the course first and foremost - it will be important to have that person "on their side", and they likely have a better idea of what actions are available to the TA.
In a more general sense, my opinion is that you try to treat those students with a sort of detached professionalism, but you are under no obligation to go the extra mile to help them. And you are absolutely within your rights to ask them to behave politely.
As a TA, you have been granted a degree of authority from the instructor or professor that you are assisting, and in turn, the educational institution that employs you. Your mentality should reflect this responsibility that you have undertaken.
One of the things that I learned from teaching is that your own attitude and professionalism (or lack thereof) is continuously signaled to your students. That's not to say you have to rule with an iron fist in order to have your students' respect, especially in higher education. But if you act like a student that just happens to have teaching responsibilities, you could be setting up a learning environment that opens you up to being disrespected.
When I was a TA, there was only one incident where I had to explicitly establish my authority. During my recitation section, two undergraduates sitting at the back of the classroom were gossiping loudly, to the point where they were clearly disrupting the other students. I stopped mid-sentence, stopped writing on the board, turned around, and simply waited. The other students of course immediately noticed, but it took about 5 seconds for them to realize I had stopped because they were busy listening to each other. Once they had shut up and turned to look at me, I said, quite firmly but calmly, "Nobody is forcing you to be here. If you'd like to continue your conversation, feel free to do it elsewhere, but don't disrupt your classmates who are here to learn." And then I went right back to teaching.
My point is that you have power, and you should not feel shy about using it, so long as you remember that your purpose is to facilitate the education of your students. To the extent that lack of respect or disruptive behavior interferes with that goal, not only are you within your rights to exercise corrective action, I would say you have a duty to do so. However, the nature of your interactions with your students must always be professional. If there is disagreement about course topics, that's fine as long as it stays in the bounds of the concepts being taught. It's not fine if it becomes personal (e.g., "What you said was so obviously wrong! How can you be the TA for this class?" or "You're just an undergrad, and I'm doing my PhD in this stuff so I'm pretty sure I know what I'm talking about here").
First: The TA should try the best to find out the reason(s) behind such behaviour of the students. For example, (1) if the TA is very friendly with the students and has maintained a small distance with the fellow students, then the students might be thinking him as their friend in which case the formality would not come in the class; (2) if TA is not able to do proper teaching or problem solving, then students might take him as granted.
It also depends on the class size.
Second: What can be done?
As @Fomite points out, the TA should speak with the course in-charge to plan out the things to get the students in line. But, be ready with your points to discuss with the Professor as (s)he would definitely ask questions related to my 'First' point.
This is a difficult question to answer, we have to first consider the problem of "what level of respect should the students give the TA ?"
I am a docent in Europe and I have to teach undergrads in tutorials, and there are some things which I just let pass and somethings which I have zero tolerance for. Some things are so extreme that I would not tolerate them for a moment but thank goodness they have never occured.
Consider what you think is reasonable, do you want to expect the students to treat you like a god and even ignore you when you make an error ? If you expect that then sadly you will be very disappointed.
At the other end of the spectrum if a student made a comment about the appearance of a TA and made a sexual remark about them. Then I would strongly hold the view that this is totally unacceptable, as an academic if a TA came to my office and told me such a thing had happened then I would be deeply troubled and the next thing I would be doing would be contacting the HR officer for advice. I have never had a student come on to me in class, I hold a view that sexual relationships between the academic and the undergrad are an exceptionally bad idea.
I would lump racist, sexist or other bigoted abuse into the same bin of horrors which I would blow my lid at. If a student came to me and told me they did not want a white / black / asian / female / gay / muslim / jewish / christain / green / purple / whatever TA,
I would say "tough you are not able to choose the colour (gender / sexuaility / religion) of your TA. Chemistry is the same chemistry regardless of who the TA is. You need to grow up and become less bigoted"
In the middle you have a wide range of behaviours, I have had the class clown who kept on asking very odd questions such as "how long will be DVD player battery last" during a lesson on elctrochemistry (nerst equation). My advice with such people is never lose your cool, stay calm you need at least one adult in the room. One of those adults has to be you ! As long as the class clown does not disrupt the teaching you will just have to tolerate them.
The disruptive student who is chatting away on their phone or otherwise disrupting the lesson. My advice is to tell them to be quiet, and point out that they need to respect the right of others to learn. Also point out that if they want to discuss some sporting event from last night, their social lives or otherthings which are unreleated to the lesson then they can wait until they are not in the class before doing so.
I had a very offensive student who was being exceptionally rude to me and he kept saying "you do not know my name, you can not do anything about me". By chance I found out his name, the way I then dealed with the student was to walk up to him the next time I had to teach in the undergrad lab. I greeted him by name and told him I was glad to see him, I also told him that I hoped that he was going to have a productive and enjoyable day in the lab. This changed him from a horrible pest into a rather likeable little lamb.
Sometimes a good sense of humor is needed for improving the behaviour of students and making them keep their minds on the subject. I was once teaching basic nuclear chemistry to some undergrads. I had one who was swearing a lot and using the "s word". I turned to the class and in a totally deadpan way, I told them that the classic bioassay for determining exposure to airbourne plutonium is to get a feces sample, ash it and then measure the plutonium content in it. Suddenly using the s word was not quite so funny for the student. Human waste was no longer a swear word it was now something else. Sadly there are limited times when you can pull a stunt like that one to get them to focus and stop swearing.
It is important that you lead by example, if you for example want to your classroom to a cuss free zone, then do not litter your speech with colourful language which would make a factory labourer blush (I used to be a factory labourer in my youth).
You need to keep in mind that as a TA you are not there to be their friend, you are there to teach. Be friendly but try to keep a distance from the students. Never use your time as a TA to try to chat up students (ask for date) or arrange your social life with the students. I have seen some people break this rule, it results in a loss of respect from both the students and other people in the university.
One of the other people commented about make sure that they know you know their names as you have power over their grades. I would advise you to divorce in your mind their conduct in the classroom from their homework. If you grade problem sheets or homework, then ignore the name on written work. You should grade merely what is in front of you on the paper, do not care who the person is. Grade the written work in a totally fair way. One thing that this avoids, is if some horrible student who was "mouthing off" at you, conducting their social life in the classroom and calling you every dirty name under the sun spots that you marked them down becuase their were an arse in your lesson, then they have a tool to make your life harder. They now have a means of complaining to your boss.
If you grade them fairly and the student you flunk (one which did poor work) goes moaning to the head of department, the prof or whoever. If this person has a backbone they will tell the student to stop moaning when they see how you have marked their homework fairly.
You may sometimes have to accept that you might get a very gifted but lazy student. Occasionally you might encoutner a genius with a attitude problem who is lazy, unless you are in a subject such as medicine or the nuclear sector where a standard of behaviour (having the right attitude) is required for work then you will have to just put up with the lazy student who makes lifestyle choices which you disapprove of. I hold the view that the genius should use their time in a productive way rather than merely doing what is required of them in 5 minutes when most students need a whole hour to do it before doing no further productive work. But not everyone sees it the same way as me.
From the first moment you start to feel uncomfortable, you should inform either the professor teaching the course (if you are a grader), or your supervising administrator (if you are the instructor of the course, section, recitation section, or lab).
You are part of a system -- you are a cog in a complex machinery system. Each part of the machine plays its role. Part of your job as a TA is to inform your superior when a problem arises. This is exactly one of the problems that can easily arise on campus.
The way the department will deal with the problem will depend on the context in which the uncomfortable interaction occurred -- in the classroom, in your office, in a computer lab, in the library, etc.
To help you visualize yourself as part of a complex system, with support from your department, I'll mention a few possible ways the problem might be addressed:
A veteran TA might be asked to work quietly at another desk in your office.
You might be asked to move your office hours to a larger group office.
You might be advised to refer the student to the professor him or herself, who is better equipped to answer their question(s).
The professor might email the student to request a visit to his or her office hours, where the professor might listen to the student's point of view, and then perhaps explain the basic ground rules of respectful interaction on campus.
The student might be transferred to a different section (if the behavior was serious, or repeated).
If the behavior was egregious, the student might face serious consequences with the university.
I think you will find that over time, as you find that you are consistently supported by your department, your self-confidence will grow, and you'll become more comfortable asserting yourself with minor incidents. But to get from Point A (fear and uncertainty) to Point B (confident assertiveness), you must allow your department to support you. Your department can't support you if you don't report incidents that make you feel uncomfortable.
Now, sometimes there's a gray area and you're not sure whether something is worth reporting. As a new TA, your motto should be: if in doubt, report. Just a simple email or stopping by a supervisor's office to make a mention of what happened.