What is your teaching philosophy?

I believe strongly that to fully grasp a topic, one must understand the basic reasoning behind that topic. In my experiences, understanding the basis behind the concepts, and knowing how they work, gives a much stronger ability to manipulate and analyze questions related to that topic. In short, my teaching philosophy is "reasoning through understanding".

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

I treat the first session with a new student as if they are taking a diagnostic exam. I provide the student with questions and will observe the way in which they go about answering the questions. I ask myself things such as "Does this student notice all factors to the question?" and "Does the student skip steps in the answering process that are vital to the answer?" Knowing the way in which a student prefers to work is very important, and I use their preferred method of working as a springboard to assist them better.