The core of my approach is to start from the ground up. In the classroom, especially in mathematics, students are expected to have a given set of knowledge and skills; I make no such assumption. If a problem is not understood, I ask why, which may lead to another why, all the way until the root. The root of that may be as fundamental as the rules of addition and multiplication, but once the root is found, we build up together from there. Learning math is like building a wall: You need a solid foundation without any cracks or holes. If you don't build it right, you get to a certain level and the whole wall starts crumbling down. I do not do patchwork as a tutor, I survey the entirety of the wall and work on whatever needs to be worked on. And once the foundation is solid, and every new layer is laid meticulously, there is no limit to how high that wall can be built.

I would first ask what material he or she needs help with. Then, we would begin the diagnosis of precisely what material is troubling, and why it is. Once a sub-topic that needs work is found, we would do some practice problems. Within those practice problems, we would discuss the student's (failed) approach, down to the nitty-gritty. Then we would discover what previously learned and understood math is being misapplied or done incorrectly. Then we would put together a plan of action for what material we need to cover to get the student of track with this sub-topic of the subject. This would be done for all topics eventually, whether or not this could all be done within the first session is a matter of its length and the need of the student.

I am not satisfied with my explanation of an idea until the student understands it enough to explain it to me or someone else. By being that thorough, it takes much longer to cover any depth of material. But it also passes on full understanding, and once that is attained, a critical learner has been created. A student who seeks understanding asks questions and explores knowledge independently.

It is imperative to instill a level of confidence in the progress that is being made. When a student actualizes full understanding of something that was previously confusing and frightening, it is an empowering feeling; one that sustains motivation. That is why I focus so much as a tutor on passing on full comprehension, as it breeds an inner-faith in the ability to conquer whatever materials lie ahead in addition to its other, many benefits.

I would break it down into bite-sized pieces. Ultimately, in math more than in any other subject, a complicated problem is just a million tiny, easy steps all wrapped up into one. These problems will presume that you can see that and execute them all in perfect order fairly quickly, which is what can make them so intimidating! But by taking it one baby-step at a time, I would show my struggling student that he/she really does know how to do it. Students often see a mountain in front of them and are too paralyzed to take the first step, but I explain that we will take that first step and all others one at a time all the way to the top.

Writing is very formulaic and can, as well, be broken down into many, many, many little pieces. In education in general, that is almost always what can be so terrifying: seeing a tremendous mess and not knowing where to begin. But through lesson plan organization and going through one thing at a time, not departing from one concept until it is completely understood, the structure of the written language can learned and mastered.

I am a believer that one does not understand something if he/she cannot explain it. So, simply, my students must be able to explain it to me to show they have full understanding.

I use the student's textbook and any other class materials (homework, handouts, etc.), a whiteboard and marker, and our brains.

Whenever working with any student on a problem, I fast-forward through any parts determined by the student and me to be trivial. That being said, the list of trivial material can be much longer or shorter for some students than others. So for students with less understanding/knowledge, it is more important to alter my tutoring style to reflect the need to walk through problems more thoroughly, at the expense of time, to ensure understanding. With more advanced students, we can skip along to get to the heart of the matter in a much more efficient way.