The University's official policy on cheating is available here, as presented by the UW-Madison Dean of Students Office.
Cheating is a topic with a lot of associated urban mythology. Many TA's can tell you stories involving a friend of a friend, or the story about this one TA who... The Center for Academic Integrityis dedicated to fighting ignorance. How much of a problem?
- As a math graduate student, you have probably found it easy to do well in mathematics classes. Many of your students may not feel that way. This is particularly true in courses the student is taking only as a requirement, not something he/she is really interested in. In a required course the student may also question whether the material will ever be of use, i.e. whether there is any real point to learning it other than to get a grade. Such a student may find it very tempting to try to get the grade without the learning... Every year there are quite a few instances of attempted cheating in our math classes! So you do need to be vigilant. At the same time an honest student may get very nervous and not do well on an exam if you are breathing down his neck, or otherwise telling him you think he is likely to cheat.
The best way to deal with cheating is to deny the students opportunities to do it. Your lecturer will probably have their own techniques for this (exam seating and different versions of the test are the norm). One thing you can (and should!) do as a TA is watch the students while they are taking an exam. Exams are not study halls for you. You are still on the job and have responsibilities. Doing so not only will give the honest ones a chance to ask questions when they are confused, but will also discourage students from looking at other's papers. While it is not practical to make multiple versions of a quiz, this is another time you should watch your students instead of reading the newspaper.
Regarding cheating on homework, you should assume that your students have and are using a copy of the student solutions manual. Thus, if you are going to grade homework for correctness it makes more sense to do this for even problems (or problems you write yourself). Some TAs will instead grade based on completion, which gives the students an incentive to do the work without feeling as much pressure to have it all be correct.
Another potential source of trouble is students who want test questions regraded. One method is to return tests during the discussion sessions, tell them to check your arithmetic and finally tell them to ask you questions about grading before they leave. Allowing them to return later to have problems regraded affords them more of an opportunity to change what was written. If you do not have time to review questions immediately, feel free to collect exams from students who have questions, and address those later.