Definitely get to know the student, especially if we're going to be working together more than once. I'll ask the student about his/her hobbies, interests/passions, and how he/she feels about the material. I really want to make the student feel very comfortable, and make him or her understand that there is no pressure. This will also help me personalize the way I convey the material.

During tutoring sessions, I would aim not only to teach material, but to teach the student how to learn. Ways I would do this: *Outline his/her weaknesses, and give a summary of what he/she should work on. Usually I recommend drills, but I will assign and email HW problems to be done, if needed. *Hopefully make the student enjoy the material by presenting it in an intuitive manner, as opposed to memorization based.

If a student is not motivated, I want to find out why. If a student feels inferior/untalented, I will do my best to change that by talking about my experience of how I did poorly in math early on, and thought I was of low talent/intelligence, but realized that after some extended effort and struggle, it will suddenly come. I want the student to know that progress will surely come. If a student is bored/tired, I'll make the lesson lighter, and try to just focus on simple key concepts in as intuitive a manner as possible. Most importantly, I want the student to believe that if he/she wants to improve, it's 100% possible.

(1) Try a new approach. Make it simpler through analogies. High school math is generally very intuitive in nature, and this shouldn't be too difficult. (2) Try to show the student that the problem is a like a fixed machine/system: do the following, and the following will happen. This is not good for conceptual understanding right away, but after the student masters the "regurgitation/programming," it will be much easier to have a deep understanding of the material later. This is only if (1) fails. Basically, find anything remotely related to the topic at hand that the student can do, and show him/her that this is what needs to be done.

(1) Explain it to me. This is the most effective way; if a student understands the material deeply he/she will be able to teach others, and answer standard questions on the topic. This is the deepest level of understanding. (2) Problems: I will assign HW to test understanding, and go over it the next session, if necessary. (3) Live problems. Having a student work out a problem, while explaining his/her thought process, is extremely telling of understanding.

Build it from the ground up. The foundation must be extremely strong. To do well in higher level math, lower level math must be almost automatic, instinctive. If there are problems in a student's foundation, I will try to help him/her fix them if possible. To avoid damage to confidence, I will tell him/her how I still work on simple problems, just to keep myself experienced and unrusty. I always start out with simple problems and progress from there. This helps a student see that the hard problems are just pieces of the easier problems, with some scarier notation perhaps.