What is your teaching philosophy?

My philosophy is that I should teach my students how to reason, not how to use a formula. Truly understanding a concept better builds a foundation for future learning than does remembering a formula.

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

If a student has problems to work on, we will go through the problems one by one. However, if I find that the student is weak on a particular concept, I take an aside to explain the concept, either through simpler problems or through proofs, that will help them understand. Similarly, if the student had no work to do, I would start from the basic concepts, asking them to explain them to me. If they struggled, I will teach them how to conceptualize the topic. I will give them problems to make sure they are able to apply their understanding to an actual example.

How can you help a student become an independent learner?

Especially when teaching math, I like to break things down into smaller, more manageable parts, or rewrite expressions into ways that help the learner understand better what is happening. When trying to understand a concept, it is important that you convince yourself that the concept is true, rather than just being told it is true. Teaching a student how to approach or rework a problem or concept, as I said I would do above. The student can become an independent learner if he or she can reorganize or break down the conceptual statement into pieces he or she already understands.