I am an undergraduate senior at Drexel University and my major is Physics. I enjoy teaching because it gives me joy to see the moment when a person truly understands a subject and realizes that the math or physics problem was not hard at all in the first place. This is referred to as the "Aaaaah moment" or the "Oooohhhh moment."
My philosophy of teaching in an analogy sums to the following: "There is no way you can expect to have a skyscraper of knowledge with a Swiss cheese foundation." In other words, my teaching method is very individualized and is a bottom-up approach. I first gauge at what the student knows and understands of a subject. I then figure out the strength of the foundations of understanding by specifically giving problems that test those foundations they may or may not have. After the student's foundations are solid and completely filled in, I then start building up with the student. Although this approach may at first glance seem time consuming, it isn't because once a student has firm understanding, he or she soars through the subject at exceptional speed because subjects, for example math and physics, builds upon themselves.
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