In this scenario, the student is a passive participant in the process. The information learned is impersonal. Clearly, the teacher is in control of the learning process; his or her interests dictate what and how fast the students learn.
The answer in all three cases is that rudder is used to help maintain stability in the roll. A little rudder at just the right time can help keep the nose up in a slow roll or even an aileron roll, as the plane rotates through the sideways portions of the roll when gravity is otherwise not countered.
This is one of sea kayaking's great debates. Most touring kayaks dont need a rudder or a skeg. For long sea kayaks, (over 15 feet in length), a rudder is useful to go straight in a cross wind. Some people like to use a rudder to steer, but that is easily accomplished with your paddle.