What is your teaching philosophy?

My role is to help you develop the strategies of mind and study required to work out and understand, on a fundamental level, the concepts and material which mathematics hopes to analyze and build upon. In plainer terms, I believe it is better to teach you how to ask the right questions, and whom/what to ask them of, than to give you the answer straight away.

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

Basic introductory stuff like names, interests, Q&A about what their goals are, find out what's in/not in their subject comfort zone, and discuss desired scheduling. Depending on what falls out of the first part, get to work on whatever seems to be the good first step, whether that's current homework the student is struggling with or exploring a basic concept like logarithms, time permitting.

How would you help a student stay motivated?

Ideally, find ways to relate their work in math to other interests discussed/discovered during our first session. Lots of math (not to mention the sciences, broadly) has been built in response to actual questions about actual material realities. What is the angle between the earth and a star? Where does a photon go when it hits your eyeball? How do we maximize our output from a given input? Sometimes realizing that the (now) abstracted concept the student is struggling with related to a real problem is interesting enough to keep them curious. Conversely, relating mastery of the subject to any professional goals they might have in the future can be effective as well, clarifying the struggle now as a means to their desired reward later. Finally, I find that actually loving the material, and in particular the struggle/eureka/repeat cycle of learning more, is a pretty infectious quality in educational situations.

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

Try, try again. Isolate bits and pieces of the problem until we find what's stuck, and then work everything back together one piece at a time. Find new ways of formulating the thought. Ask them to try explaining it to me as though they're the tutor. And if all that doesn't work, try some more.