In the old way, you never showed your personal compositions to your composition teacher. So, when Alban and Anton showed up to Prof. Schoenberg's class, they did exercises. They did a lot of model writing, harmony exercises, counterpoint, etc. One of the good things about this approach is the respect for the students integrity. There is a very real place where I can't speak to what a student should write.
I'm not completely sure when it changed, but the general pattern now is for students to primarily bring in their own compositions. I know that Roger Sessions went through a pretty drastic change in his approach from the older European model to one focussed more on student compositions.
For me, I've always tried a balancing act. I look at student compositions, but we also do some sort of exercises. Mostly I use 16th century counterpoint. This semester, I'm using the Bach chorales. I learned this exercise from Robert Helps (a Sessions pupil). He said, "You copy out the soprano melody, make your own harmonization, and compare it to Bach...to see how much you suck. You will find that he will always do something that is more daring and adventurous than you."
So my students are doing Bach chorales this semester. I'd love to hear ideas about what other people use.