How would you help a student stay motivated?

I believe that all students should want to come to tutoring because it is a fun, entertaining, and comfortable environment to learn in. In my experience, the best way to promote student motivation is to provide a comfortable, welcoming environment and help to build their academic confidence.

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

Independent practice is very important. In learning the material, I like to use guided practice and work through the problems with my students. However, when it is time to check understanding, I let them try problems without my help and verify they can work though all on their own.

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

I like to introduce myself and have the student briefly introduce themselves (both academically and personally). I believe that a comfortable relationship is conducive to learning because the student will be more willing to admit to not understanding a topic should they be comfortable with their tutor. Additionally, I would ask the student to briefly explain everything they don't understand. I would then go a step further and personally quiz them and verify that they don't have holes in prior knowledge required for the subject.