What is your teaching philosophy?

Every time I learn a new nugget of knowledge in either area I get really excited because it's usually useful and, more importantly, it tells me that I truly understand the rules and laws that were used to derive that new idea. When I first learned calculus, it required that I had a firm foundation in algebra. During high school and college as well, I saw classmates struggle in calculus because they were not as capable in algebra. I believe that many of the problems students encounter in mathematics are due to some missing piece(s) of knowledge or misunderstanding(s) of some principle(s). Many times, the student will have practiced or "understood" a technique/topic for years before realizing their way of thinking about the idea was incorrect. If a math student has a deep understanding of the previous principles, then adding to their math skills can be like building a brick tower, in that they build upon a firm foundation that can weather difficult problems. However if the student's understanding is shallow or not fully formed then their math skills can be like a house of cards, with a flimsy base that could fall apart at the slightest problem. Physics, similarly, requires a firm foundation in mathematics. However, many physics problems require more varied and sometimes non-intuitive problem solving skills than one encounters in high school mathematics. The student may struggle with any number of issues that can include not fully grasping the scope of a physical phenomenon, a disconnect between drawn representations and equations, or letting personal experience dictate what they can or cannot assume. In order to excel in physics, a student must have a range of skills that goes beyond mathematical knowledge, that is the student must develop diverse problem solving skills.

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

During our first session, I usually try to assess the level of understanding of the student by both asking questions designed to show gaps in knowledge as well as presenting problems that do much the same. Of course, I always include in the assessment where the student feels they are lacking. After the initial assessment, I will typically begin with assisted problem solving, stopping when we get to a step that the student cannot fully explain. We then work through said step together, with me providing simplified versions to work on and build confidence, until the student full grasps the concept in play.