Take some examples of varying severity. In front of the class say,
I have identified many examples of plagairism on the last assignment. Let me show you some...
Then say, "I have identified more than X cases. If you think you may have been one of them, let me know by email, and I'll let you redo the paper and ignore your first submission.
Anyone that I have identified as a plaigairist who does not offer to redo your paper will be failed. If you think you may have quoted too liberally from an unacknowledged source, I would strongly recommend playing it safe and redoing your paper.
Then on the next class come in, pick a random name out of the list of people who have not reached you yet, call that person by name, and ask him or her if he or she wishes to fail the course. After the kid says no, say, "Then are you going to be redoing your paper?" Then to the rest of the class say, "If you should redo the paper and haven't talked with me yet, I suggest doing so soon."
I believe that once expectations are clearly enough set, most of the problem will disappear fairly easily. As for the rest? I have absolutely no problem with failing cheaters as fast as possible.
But the hope is that if you do it right, you only have to do it once.
A huge percentage of her students turn in plagiarized papers; so many that, if she were to follow the school's guidelines on them all, would result in 1/2 to 3/4 of her students failing. The teacher's pass/fail percentage is one of the criteria used to determine whether a teacher gets any more classes, and does not take into account students failed for plagiarism.
So, if she were to fail those students, she would not get any more classes to teach, thus she'd be out of a job. She's forced to keep track of who she's failed what paper for, to spread the bad grades across as many of the plagiarizers as possible, to cut down on the number that outright fail (and thus impact her).
She has gotten absolutely no support from her superiors about this issue. However, another teacher I know at the same school has a slightly milder version of the same problem, but her superiors are more supportive of her, meaning she's not always worried about her position.
It's pretty fucked up, and kind of depressing.
That is fucked up; all the schools I've ever attended require expulsion, not failure, for proven cases of plagarism. Expelled students are basically immediately expunged from the records of any classes they were enrolled in at the time, as if they had never registered for them.
I can't speak for all of Michigan State University, where I got my degrees, but the computer science departments took it pretty seriously. One 101 course got roughly 1/3rd of the people in it failed one semester for copying. All homework assignments went through a turn-in system that examined the programs for plagiarism; details were sketchy for obvious reasons, but I had heard that a simple variable rename would not get past it. (Home-grown and based on what I heard, I believe it existed and worked roughly as described, since I could now write such a tool myself if I had need.)
When I was teaching information security, I literally had more than half of my students turn in heavily plagiarized papers. It was pretty easy to spot suspicious phrases, and Googling would always turn up the sources quickly.
It was actually quite overwhelming figuring out how to deal with it all - the problem was if we gave no marks for that paper, or failed all the students, it would've been pretty disastrous for the university. In the end, we had to punish the most egregious plagiarism with no marks, and give partial marks for the rest, trying to identify and give credit for the original work.
I had not one, but several students come and argue they should get their full marks back, "for fulfilling the requirements of the assignment".