I am an engineer and an MBA by education, and work as a business architect with a software company in Philly. Basically, I'm a physics and math enthusiast and I teach because I love it - the teaching, and the subject, a bit more (I'm inspired by Richard Feynman and his methods). I prefer to also talk about the practical utility of mathematical and physics ideas because that's the kind of background information that makes the topic sensible and its methods easy to remember.
There's nothing more satisfying than evangelizing a perspective on a subject of one's passion. I find that discussing physics or math is in itself fulfilling, and when that helps someone in the process, it is all the more satisfying.
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I think that a close understanding of the student's comfort in the subject, and of his/her immediate goals is crucial. After discussing these topics, I also prefer to understand the student's broader context or longer term goals to identify the most suitable approach for the individual. Sometimes, I find it insightful to pose a counter question the first few times that the student has a question. This phase of discovery usually lasts 30 minutes or less, but it allows us to go into the course with greater confidence about what approach is most suitable.
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