My approach to teaching is to provide real-life situations which demonstrate the concept, and then to work through numerous and varying examples and problems until the concept has been thoroughly mastered.

Each student learns differently. My primary goal in the first meeting is to understand how they learn, what their current understanding is of the course content, and what they wish to gain by personal tutoring. This may involve determining where the student believes their shortfall in understanding of the subject matter is. On some occasions, the student may not know where their shortfall is, so I will need to determine that with the help of the student. It may also be helpful to talk the student's parents (if a high-school student) to determine the shortfall.

Independent learning comes from a couple of things - self-discipline and self-confidence. A student that is confident in their ability to learn, having learned the self-discipline to study on their own, will be more successful.

Everyone learns at their own pace, and learns differently. The key is to understand the individual student. The first step in helping a student learn a difficult concept is for me as the tutor to gain an understanding of what they understand of the subject, and then to identify where the shortfall is. We can then take a couple of different pathways, whether using textbook problems to gain repetitive understanding, or real-life examples to reinforce learning.

Simply re-reading the text likely won't help. The lack of comprehension can be overcome through examples, bridging the gap and identifying ways to overcome.

Students often get excited and engaged in subjects in which they do well. Rarely will you see someone get excited about something they're struggling with. Often, understanding large concepts starts with understanding simple ones first. And in understanding more simple concepts, we create a foundation for further understanding, and that's where engagement comes from.

If a student can explain a concept back to me in a manner which demonstrates understanding, that's a start. And some of that will be demonstrated through mastery of problems and examples. Repetition of success in that vein will lead to success and overall understanding.

Success builds confidence, and success comes from understanding. My job is to build that understanding via mastery of problems and examples.

My first approach is going to be to what the student believes their needs are. Often, a student will know where they are struggling. What they may not know are the specifics of why they are struggling at a particular point in their learning. And determining that takes a keen understanding of the subject matter involved.

Different students learn in different ways. The key to success, whether in individual tutoring or in the classroom setting, is for the instructor to adapt. That may mean more theory and reading that works for one student may not necessarily work for another. That second student may learn better through verbal explanation, examples, problem solving, etc.

Practice problems, guided learning, short examples building to larger examples and repetition.

Written problems, ad-hoc examples, and printed material.