Rude students can be the most disruptive and negative presence in a class room and can have a real effect on those trying to teach them. How you deal with it will determine how other students respect you and whether they believe you have control. Rudeness, more perhaps than open stupid behaviour, is incidious and subtle yet it needs a very direct approach in order for the teacher to gain control.
First ask yourself why a student is rude. Do they want attention? Are they finding a subject hard or beyond their capabilities or are they simply foul-mouthed, mean-minded sloths? Whichever is true, the way to deal with them is relatively straightforward.
A rude student will usually be rude in front of others. They gain something by being rude - whether this is is the momentary break in your train of thought, your unease or discomfort or the reaction of their group of cohorts. You need to make it so they gain nothing from being rude.
Remove a rude student from their comfort zone and usually the rudeness will abate. Instead of allowing the groups to work together in their own predetermined small groups, number them say from 1-6 as they come in and group all the number 1s together, number 2s and so on. This will mean that within each group, there are people from most social groups in the class room, whether it is the nerds, the clever ones, the rude ones or the slightly slower. Mixing groups up helps everyone because the ones who are able, will be allowed to develop leadership skills in getting a task done, those who are usually quiet and feel uneasy about how they sit with will be free from this, the slower ones will be inspired by the quicker ones , especially if you make a competition of the task, and the rude ones will have noone to play with or get to react.
If this does not work - try a tactic I once used. I had a particular student who was rude, feet on desks, disruptive and generally cheeky. He was also very clever but never carried out projects well and invariably gave them in late - and made sure everyone saw him.
After putting up with this behaviour for a long time and getting nowhere even with my tactics above I took him out for lunch - to the school dining area as it happens. I sat him down and stated simply that unless he changed, he would no longer come into my lessons but would work elsewhere on his own. He would have no support from me and I would fail him completely. I told him I thought he was very able and bright but that he was wasting my and his time. I then marched off, giving him no time or chance to reply.
Next lesson I did not expect him to appear but I was astonished when a fresh project - a week early- sailed across my desk. I glanced at it and saw his name on it. I looked up into a grinning face. He said no teacher had ever given him a talking to like that and he intended to change. I was angry with him and did not believe him but the transformation was miraculous and he graduated third in the group in that subject. Sometimes, only a one-to one direct approach works.
The golden rule is to always realise that you do not have to put up with rude students. You have a system, support from colleagues and you are there to teach, not be spoken to rudely. You are the expert, not the students and you should lay down some easy to follow but clearl defined rules and expect these to be followed. If they are not, take action straight away because students react best to definite lines - grey areas are a no-no.
Most students, if you teach well, want to be in the class room, they are able and willing to learn given the right stimulus and one rude student or two must not be allowed to spoil it for others.