Having taught undergraduates at the University of Chicago as a teaching assistant and outside as a private tutor for the last four years, I have observed that the biggest hurdle to grasping new concepts in Physics and Mathematics is almost always a tendency to complicate rather than simplify. Mathematics and physics, being essentially logical enterprises, hold no mysteries, and my teaching methodology crucially hinges upon making my students realize this. The first step to this is identifying what the student does not understand. Understanding anything is the construction of a mental picture, and the first stage of discomfort with a new concept always involves our inability to locate where in this mental picture the holes lie. Our lack of understanding at this stage is a "blob". My strategy at this stage is to help my student reduce this blob to a set of "points", and this isolation of a list of "small concepts" hindering the understanding of a "big concept" is, I believe, half the job done. After this stage of identifying what the student does not understand, I will help the student work on these small concepts, and finally add them all up to understand the big concept that the student originally wished to understand. This teaching methodology, to me, is two pronged. At one level, it helps the student understand a particular concept, and at another level, it will train the student's mind to "think simply" about physics and mathematics.
The other crucial aspect of the way I teach is that I frequently employ the Socratic method, a fancy name for "teach by asking rather than by telling". I firmly believe that the final jump from the realm of not understanding something to that of understanding is one that the student takes all alone. The role of the teacher is merely to lead his student upto that point, and the best preparation for that jump, for me, is to allow my students to find their way upto this point by themselves as far as possible, with my role being restricted to correcting them every time they take a wrong turn, and this, I think is an automatic byproduct of teaching by asking, rather than by telling. This helps build up the student's confidence, and goes a long way towards the demystification that I believe is essential to thinking about physics and mathematics.
A little bit about myself. I am a physics graduate student at the University of Chicago, an amateur guitarist who first started playing the guitar because he wanted to play the solo of Hotel California, but long since realized that playing almost anything on the guitar is immense fun, and a firm believer that learning anything should be fun. I find teaching to be one of the most rewarding things I do : the joy of watching the bulb light up inside anyone's brain, with the knowledge that I had a role to play in that, has no parallels. I look forward to being the teacher who makes a difference in the way your child learns.
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