What is your teaching philosophy?

I believe that one shouldn't learn to know; one should learn to understand. Learn the overarching concept, and the little facts that come with the concepts will come along.

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

You have to figure out a baseline. You need to know where the student is and where they want to be. Afterwards, an appropriate plan can be made.

If a student has difficulty learning a skill or concept, what would you do?

Take a different approach. There are many ways to climb a tree. Assure the student that just because they had trouble one way does not mean they'll have trouble with others.

What techniques would you use to be sure that a student understands the material?

Give them questions that test conceptual knowledge rather than mere reproduction of a skill.