I had a student last semester who was giving me a hard time by acting strangely and giving weird excuses for not completing assignments on time. After a brief investigation, administration determined she was not taking her medication and so all her classes were dropped. She reappeared, with another girl in tow, several weeks later and registered for my course again, for this semester. Surprisingly (or not?), her performance is exceptional this semester -- she has a strong A average right now. However, because she is taking this course online, I don't know whether to attribute this success to (a) her medication or (b) "help" from a friend.
It's a math course and I do my best to randomize problems assigned to each student, so they can't "share" answers. However, I am not aware of an effective way to prevent "outsiders" from helping students. Any ideas?