A question that is often asked is "What is your teaching philosophy?". First and foremost it is important that the student learn about music; how to read it as well as the theory behind it. It is necessary to learn from method books in order to develop sound basic skills, but once this is accomplished, the student is encouraged to work on pieces that are of their own choosing to supplement the other materials that they are studying. By working on pieces they choose, this allows the student some "recreational" material to help keep them motivated in their studies.
Another way to put it is that these are music lessons, not just lessons on the student’s chosen instrument, so that they develop the skills to understand music beyond just being able to play a particular piece on a particular instrument. These skills then enable them to apply what they have learned to any instrument. Understanding the theory behind what you are doing allows you to apply what you have learned in new ways, in new situations. This is much better than rote memorization of a particular piece, without any understanding of what is being played.
The main thing is that the student learn good basic skills, and theory, while still playing the style that they want as soon as possible, so that they are not only learning, but having fun doing it. That combined with good practice habits will allow them to progress in a steady manner toward what ever their musical goal may be. There is no substitute for good practice habits, without which, no matter how good the teacher may be, the student will not be able to make good, consistent progress.