I believe in instilling curiosity and wonder in my students. Math and physics may seem intimidating to many students, but once they see that they CAN do it, and they see that that it can actually be fun, they want to know more. Further, once they see that it helps explain the world around them, it opens up a whole new world for them. Hopefully this will motivate them to independent pursuits, or to ask questions about "why things are the way they are."

On my first session I typically try to understand where the student’s interests and aptitudes lie. If he or she is "scientifically inclined" I like to challenge them with fundamental questions such as “why do you think the moon doesn't fall out of the sky?". If they are more humanities oriented I like to suggest how math can be used to develop critical thinking, understand history, and how physics is actually in some sense a form of philosophy.

Students learn best when they are driven by their own curiosity. A technique in developing independent study skills is to give students questions to answer or problems to solve, that are interesting on the face of them. For example, most people wonder at some point why the sky is blue. AN AP physics question may be to write a qualitative paragraph or two why that is so. This approach motivates the student to examine a question they may have considered superficially at some point, and independently address it.

In my opinion the key to keeping a student motivated is to ensure they are making progress, let them know they are making progress, and to help them "congratulate" themselves for correct answers and results. Positive reinforcement is key to them building confidence and continuing forward.

Go back to first principles and using everyday analogies. An algebra student cannot factor a polynomial if he or she does not have a working facility with basic algebraic rules. In physics analogies to the world around us as well as some simple demonstrations are helpful.

It is critical that they understand the vocabulary of what they are reading. If they do not understand a word or words they must look them up, and then proceed. Equally important is that they understand that they can take their time and not get frustrated.

The initial sessions are getting familiar what the student's prior knowledge and strengths lie, as well as what "mental blocks" or conceptual difficulties they may have. For example some students may have difficulty visualizing 3D problems while others may have computational difficulties. Some simple assessments as well as informal chats or questions can help us understand this so we can address them accordingly.

I like to relate the subject to everyday situations they encounter. For example, math is all around us: how much paint to buy for a room, how much will a tank of gas cost, how long will it take to drive to the beach, etc. I find when students see practical use for a subject, they tend to develop more interest and find a reason to work through their difficulties.

Ongoing informal assessments such as short quizzes, pop questions, and Socratic dialogues.