What is your teaching philosophy?

Albert Einstein is often quoted having said, "insanity - doing the same thing over and over again and expecting different results." I believe this statement applies best to my teachings, meaning that students will not merely cover the approaches to mathematical solutions discussed in the classroom, but also be able to approach problems from a logical standpoint by which they understand.

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

In a first session, I would like to better understand the student - his or her interests, hobbies, talents, etc. This will aid me in strategizing a way to excite the student about mathematics, by applying these problems in areas that he or she enjoys. Also, I would like to know how he or she is doing in current mathematical curriculum. This will allow me to understand where exactly the student is struggling with the material.

How can you help a student become an independent learner?

Everyone thinks differently, and mathematics is not an exception to this rule of thought process. Students will become independent learners by better understanding how he or she approaches mathematical problems and gaining the confidence to succeed on one's own.

How would you help a student stay motivated?

The applications of mathematics are limitless! By introducing real-life situations in areas of particular interest for him or her, the student will gain an appreciation for mathematics.

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

Since higher mathematics is more abstract, it can be difficult to conceptualize what exactly is happening on paper. Therefore, I would break it down to the rudimentary level and explain what is happening in terms of how the student thinks, whether it be graphically, algebraically, numerically or verbally.