What is your teaching philosophy?

To not focus as much on the grade, but rather to focus on learning and mastery of the content for the student.

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

After introductions I would immediately give practice problems. That way I can visualize what the student's thought process is, and correct errors wherever they may be.

How can you help a student become an independent learner?

By giving worksheets and more practice problems. Problems are the best way to learn, because they show the student if he or she has successfully mastered the concept. Only the student will know when they feel comfortable.