My teaching philosophy is developing the concept from the ground up.

I am very reluctant about making assumptions about the student's background because that discourages the student's participation (I have realized this from my first-hand experience as a student). I start from the very basic of principles (axioms) and tend to show the whole derivation of things if the student prefers or asks me to show it. There is no such thing as a stupid question. I welcome every question equally and address them as many times and in as many different ways as it takes to make the student understand it.

I am a very visual person. Therefore, I draw a lot of pictures and use a lot of physical examples to show the application of concepts. Furthermore, I like the study sessions to be as interactive as possible. Therefore, I ask a lot of questions to the students to make sure that they are understanding things as we move along. I also ask the students to come up with their own questions so that we can go through them together because that breaks the mindset of limiting oneself to just the problems in the book. This, I believe, also helps to foster creativity and problem solving.

I usually introduce myself, give my background, ask for their academic background, their interests, the topics they love and hate, and the reasons behind loving or hating them. Then, I usually start with a few easy problems to assess the student's background in that subject.

I focus on developing the core principles that apply in problem solving rather than actually solving a couple of problems and being done. I also give a lot of visual examples to help the students picture things better in their heads.

I believe doing so helps the student become an independent learner.

I am the kind of person who cannot stay motivated in learning something unless that thing has something of practical value to offer. This is because I will forget it if I never get to use it. I think showing the student the practical application of any idea being taught keeps them focused and motivated in learning that concept.

If a student has difficulty learning a skill or concept, I first dissect the concept into steps and go through each step with the student to see where the problem lies. Then, I reinforce the concept by giving/doing as many examples as needed.

The main problem about reading comprehension that I faced early on during my undergraduate years was not knowing what is important and what is not in a given problem. So, with the help of my instructors and learning centers on campus, I learned about how to break a problem into pieces, analyze each piece, and extract relevant information from it, which I could then use in the next step- planning a solution. I think a systematic approach like this will help the students struggling with reading comprehension because it has helped me in the past.

Introducing myself to them properly and asking them about what they are finding problematic and what their background (and future aspirations) is really helps to form a bond with the student. Furthermore, doing some simple practice problems will help me to accurately gauge the concepts they are having a problem with.

Showing the real life application of the concept, and how they can use it always helps students stay motivated. Furthermore, doing word problems rather than simple "Solve"-problems also gives them clarity and keeps them engaged in the subject.

Breaking a concept into numerous small digestible pieces and giving simple problems that correspond to each of those pieces really helps students understand the material. The final step then should be solving harder problems that require all of those small ideas to solve.

I believe that confidence comes from practice over time. So, increasing the complexity of the practice problems gradually should build a student's confidence in the subject.

The first thing one must do to evaluate a student's needs is to ask the student about why they signed up for a tutor and what their expectations are from the tutoring session. Apart from this, giving them a few practice problems in the beginning also helps in evaluating their needs in a much more concrete fashion.

Each individual has their own style of learning. Some learn more by looking at proofs while others learn more by solving more problems. If a student is in more of the first category, I will change my style to focus more on showing why something is true. Whereas if the student has more inclination towards the second category, I will focus more on demonstrating how something is done.

I usually use practice problems and a book (if available) during a tutoring session.