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.
Most large, transport category airplanes use a device known as a tiller to steer the airplane while taxiing. This usually takes the form of a small steering wheel or lever in the cockpit, often one for the pilot and one for the co-pilot. However, they differ from the tiller on a ship.