What should I do as a teaching assistant when I find cheating behavior from actual grading? Update:

I found 8 students cheating in today's quiz despite stern warning and personal threatening to kick them out of the classroom if I notice cheating behavior again. 4 of them also likely cheated last time. The main reason is I left 5 minutes to fetch old quiz from last time. 

I have reported this to the instructor and the two chairs of the department as well as sending the quiz sheets. I am very upset even though it "is not my fault". I have asked the professors explicitly that I do not to see these students in classroom again. 



I work as a probability&amp;statistics TA. During actual grading of the quiz papers submitted by students, I suspect some students are involved in cheating. The question is what I should do. I should note that my relationship with students is not the best judged from past experience.  

The evidence that support my claim students were cheating in the quiz was follows:


During the quiz, I noticed students A, B, C, D, E, F, etc sitting very close to each other. I pulled their chairs apart and minutes later their chairs were close again. While I did not suspect cheating, I felt this is quite strange. In the end I have to pull their chairs apart three times. I also noticed they talking to each other, but I am not sure if they were borrowing the calculator or something. I simply did not suspect cheating. 
During the actual grading I found the students A, B, C, D, E, F, etc all submitted work of very low quality and they made identical elementary mistakes like 1+1=3 on their exam sheets. This elementary mistake was carried through to the second part of the exam, such that a few of them did not bother to give any derivation to the wrong results in the test paper. 


I have reported this to the professor, who avoided my email on any discussion with this topic. My questions are as follows:


If I want to report cheating, how do I make sure students A, B, C, D, E, F, etc all cheated? Of course there is a small chance that they all made the "stupid mistake" due to some random misunderstanding. For example, maybe students E, F did not cheat; they simply misunderstood the problem or their Casio calculator malfunctioned. Who knows? 


For example, when I was an undergraduate, I was wrongly accused for cheating, and I knew such accusations makes people psychologically very uncomfortable even if turned out false in the end. While I am quite confident with what I found, I do not want to be the mean professor who treated me that way. I checked the university honor code and it says "the instructor should communicate with the students regarding the nature of the charge and the evidence...". I simply do not know what to say in this case. Should I simply say "I am suspecting you of cheating behavior, please explain yourself", or something? 


More importantly, what I should do for the future to the class to prevent cheating? I put "cheating behavior means -10 points and an invitation to visit the Dean" in every exam sheet. But I could not prevent this situation from happening again in future. I felt very uncomfortable that I am preparing lecture for students who paid negative amount of input to the class material. To me a student walking out of the classroom and believe my lecture was tedious is okay; one do not need to take the class if one already knew the material. 


But cheating behavior is far worse; it makes the normal Q&amp;A process break down, and I simply do not know what feedback should I give to the students who cheated. It also makes life very unfair for students who made an huge effort but did not do as well as cheaters. I find it very difficult to prepare the lecture in the same mood again and pretend that this have not happened. 


In the extreme case, if the professor took no action at all, what should I do next? Should I waste many hours coming back and forth on this "trivial" issue and facing various committees, or should I simply turn a deaf ear on it because this is first time offense? To me, this seems a black and white situation. But I am still quite confused.
Disclaimers: Firstly, how cheating is treated varies a lot among different countries, so what I'm going to say might not be applicable to your case. Secondly, you actually ask several questions, and I shall concentrate just on the following one:


  More importantly, what I should do for the future to the class to prevent cheating?


The students' behaviour you describe in point 1) should be cut off directly during the exam, and not discussed afterwards. In general, I enforce the following rules:


Students are not allowed to talk to each other. If I find two or more students trying to talk to each other, I warn them once, but the second time they're out.
Students should bring their own calculators and cannot borrow calculators from other students. If a students forgets her/his calculator, too bad, she/he can employ the good ol' pencil and paper method of calculation. 
We don't have movable chairs, but, in case: if you're too close, the first time I come to pull you apart and warn you; the second time, that's the door and you're welcome to walk out of it.