I am 28 years old. That means I am not so far removed from the time when I was a student getting tutored. I was always pretty smart, quick, bright, or whatever you want to call it, but when I got to college things got really hard and it happened so fast I needed some extra help. As it turns out, I graduated from Carnegie Mellon University with a BS in Physics. I have very strong math skills, but it was the field theory that I needed help with. Learning from different teaching styles and working in groups of 2 or more got me through the program.
I would describe my style as goal-oriented and hands on. I believe that "but I'm never going to use this" is always wrong and I can prove it. Once, when a calculus student of mine said that about derivatives, I took them out to her car and explained how acceleration, velocity, and distance are all calculus terms we think about in the car while she drove us around.
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