What is your teaching philosophy?

My teaching philosophy is that any idea, no matter how complex, can be broken down into pieces small enough for anyone to understand. Breaking these ideas down and learning by building them back up into the main idea give an insight into how and why something is, and gives greater understanding that simply memorizing answers.

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

Use practice problems to discover where the student is having trouble and where they can improve. Also, lead them in discussions of the subject to see if they actually hold an interest in any particular area, and try to incorporate that interest in future sessions.

What techniques would you use to be sure that a student understands the material?

I would create my own set of practice problems and concept questions specifically targeted to the student, focused on the parts of the material that has caused the most problems.

How would you help a student stay motivated?

By showing the student that they can understand the material. I would discern what they know and test them on what they're comfortable with. After that, I would ramp up the difficulty at a slow enough pace that they don't lose motivation, but are still challenging themselves.

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

If using a real world example to describe the concept doesn't work, I would break it down into its most simple parts. Once you break down a concept into individual parts, they are more easily understood, and once each of the parts are understood, putting them back together into the whole concept is much easier.