What is your teaching philosophy?

The number one rule of teaching is that there are no rules. A good teacher is able to adapt his or her methods for each student. In order to do this, the teacher has to listen to the student and try to understand how the student thinks. From my experience, the two most common methods that work are: 1) encourage the student until he or she can figure out the material on his or her own. 2) walk the student through a sample problem step by step. Afterwards, guide the student to repeat the same steps on his or her own. After a few repetitions, challenge the student to solve a similar problem that requires a slightly different set of steps.

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

In the first session, the tutor needs to gain the student's trust and assess the student. These can both be accomplished by listening to the student.

How can you help a student become an independent learner?

By building the student's confidence and enthusiasm for the subject. This can be done by having material that is at the right level for the student. If it is too hard, the student will get discouraged. If it is too easy (or un-creative) the student will not find it enjoyable.