My teaching philosophy is that every student can learn when a caring teacher or tutor remediates deficiencies and develops confidence and rapport with the student.

I would want to establish a rapport with a student, understand what he/she is having difficulty with, and try to come up with a plan so the student can successfully learn and have confidence with the mathematical material.

After a few sessions, I would suggest some external resources. Once a foundation of knowledge is laid, that students could go to online resources in order to support their own knowledge and understanding.

Students gain motivation when they start to see that they can perform. When understanding starts occurring, confidence is built, and more knowledge is generally desired by way of wanting new challenges.

I would try to assess what foundational skills the student does know, remediate deficiencies in the foundational skill, and then try to re-teach the concept with the foundational knowledge being built upon.

I think leading questions (lots of formative assessment) and vocabulary review could do a great job in building reading comprehension.

Establishing rapport and letting students know that you are going to be there for them with their struggles are the best way to begin with a student. A content expert's knowledge is going to come through to the student through the content review part of tutoring, so it is more important to develop trust when starting to work with the student and/or the student's parents.

I would try to find out what subject or topics (in school or out of school) interests or motivates the student and try to use as many real-world examples pertaining to the student's interests to engage with mathematics.

Formative assessment is the best way to gauge a student's understanding, so lots of questions should be asked by the tutor in the sessions to ensure that a student is understanding the material.

At each step/milestone that a student has success, a tutor should acknowledge that success. That builds confidence, self-worth, and self-efficacy in the student, and they generally like to be given more difficult material after some foundation is laid in mathematics.

After you establish trust with a student, they will be more likely to share what they have difficulty with, and will seek a content expert's help in those areas. If the student is shy, a tutor might have to use diagnostic assessment tools to evaluate student deficiencies and needs.

By listening to the student and/or his parents, by using results of diagnostic tests, and by adjusting your own approach when necessary, based upon the foundational knowledge that the student comes in with.

I use a lot of paper and a document camera. At times, when appropriate, I will also use manipulatives. I like the student to understand algebra, for instance, graphically, algebraically, kinesthetically, and theoretically where appropriate.