Whenever I tutor, I always try to explain each point thoroughly and precisely, so that a complete understanding is attained. It is amazing how often teachers will skip over material, believing it to be "understood" or "obvious." Sometimes being thorough will seem like over-explaining, and perhaps it is, but this is a good thing. Over-explaining will allow for a deeper comprehension of the material and it can answer questions the student didn't even know to ask.
A personal story to clarify my point: when I was a younger lad, learning to play golf, I was playing one of my first games with my dad. On one hole he hit the ball and hooked it to the left, and he said something like, "Dang, I hooked it." I asked my dad what a hook is. He told me it was a bad hit.
A few months later I was playing with some fellow students at a golf camp, when I sliced a drive. Copying my father, I said, "Dang, I hooked it." A student corrected me, saying, "No, you sliced." I proceeded to argue with the students over this point, and of course lost the argument and was embarrassed. Thus, the moral of the story is to always be precise when you explain something; a hook is a bad shot, but it is not any bad shot. The same principle of precision when teaching also applies to mathematics.
Good luck,
Patrick  | 
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