Student engagement is at the core of my teaching style. I believe that the ability to reach a correct answer is only part of truly understanding a subject; rather, I am only satisfied when a student can reach a correct answer and explain how and why they arrived there. As such, lecture style teaching can only take a student so far. When I am tutoring, I treat learning as a continuing conversation rather than a private lecture.

I think the key to getting students engaged in a subject is to relate it to their interests and to the world around them. I have found that students tend to have a hard time in physics and math because they simply don't see any connection to daily life; there isn't any motivation to work hard in a subject that they are struggling in and will seemingly never use to boot. This is why I like to show the connections between these subjects and the world we live in, and use demonstrations of the concepts. It's much easier to get excited about learning an equation when you can see it being acted out.

In general, my gauge for student understanding is how well my student can explain the topic they've learned to me. Doing problems alone is poor measure for understanding, since it is easy to complete a problem without understanding the concept behind it, or regurgitate equations without really knowing what they mean. As I work with a student on a problem, I'll encourage the student to figure out the next steps on their own, and explain to me why they took those steps. When a student arrives at an answer, right or wrong, I first ask them to walk me through how they arrived there. If a student can work through problems and explain their reasoning, I am more confident that understanding has been achieved.

When evaluating a student's needs, I take into account both the student's perception of their needs and their needs as shown by their previous scores and work they have done. Looking at the work they have done and having them explain their work to me helps to uncover subjects needing attention that the student may not have been aware of, like a conceptual misunderstanding that hasn't affected their performance yet but may impact learning later.

In a first session with a student, I like to start by asking the student if there is anything in particular that they want to go over or are struggling with. If not, then I usually spend my first session with a student to assess where they need help, either by going over current material from their class, or going through practice problems. When doing these, I encourage the student to talk their way through the problems and explain their reasoning to me. This helps reveal to me areas where that student may know more than they give themselves credit for, or places where the student may feel confident despite a shaky understanding of the material. It also gives me an idea of what aspects of the subject the student is struggling with in general, so I can better tailor our following sessions to their particular needs.

In order for a student to become an independent learner, it is important that they know how to approach an unfamiliar subject. This is why I try to focus my sessions on how to approach a new problem in general as much as I do on solving individual problems. Especially with subjects such as math and physics, which are heavy on equations, it can be easy to fall back on memorizing equations and when to use them without knowing what they really mean, leaving the student stumped when they face a problem that is formatted differently from what they've seen before. I encourage students, when faced with a new equation, to think about what the equation is trying to "say" before actually using it. What does each variable mean? What does the result mean? Encouraging a student to think about the point of all the calculations aids understanding and helps them learn how to approach a new subject in the future.

I tailor my tutoring to each individual student by paying attention both to what that student struggles with versus what they pick up easily, as well as what types of explanation they respond to best. If a student understands the concept we are reviewing in an abstract sense but has trouble applying that knowledge on assignments, then I will focus more on strategies for approaching problems and test-taking strategies. If they are able to regurgitate equations and do some problems but get stuck on differently formatted problems or cannot explain why they used a certain equation, then I will focus more on the concepts and understanding the material. If a student is a visual learner, as many people are, I will use more visuals, such as graphs and diagrams, in my explanations, and encourage the student to do the same when studying on their own. With kinesthetic learners, I will go through more practice problems and encourage them to do more problems on their own.

In my tutoring sessions, if the student has their class materials, such as a textbook or assignment details, I give preference to those materials over other kinds of practice problems, and supplement with my own references as needed. Basing the lessons off of class materials allows me to ensure that the material we are going over is pertinent to their class, and helps me make sure that the student is capable of answering the kind of questions that their teacher prefers to ask on homework and tests. For additional explanation, I turn to my own references, such as online reference sites, additional practice problems, or my own notes. When tutoring online, I lean heavily on the Whiteboard and Mathboard on the tutoring company's online platform for drawing diagrams and writing out hints and solutions, as many students respond much better to as visual reference alongside a verbal explanation than to a verbal explanation alone.