What is your teaching philosophy?

Stick with the problem until it's mastered. That may mean different approaches; some are visual learners, while others learn by doing.

What might you do in a typical first session with a student?

Figure out their level within the subject and their learning style. There would also be some part of learning about the student, as well as some hobbies and such to try to give more real-world examples for them.

How can you help a student become an independent learner?

Teach them to think about the problems in a different way. It may help to break the problem down, or to rephrase it to something they better associate with.

How would you help a student stay motivated?

Praise them for hard work and remind them of their progress.