Experience Summary
As an undergraduate, I used to be frustrated with the idea that a teacher "knows his stuff but can't teach well". For me,the true proof of knowledge is to be able to communicate it, especially to those who have a different background.
This personal philosophy drove me into a state of personal inquiry that is perhaps different from other teachers or students approach- studying with a view to explaining the concept to someone of limited knowledge in the area of discipline
Teaching Style
Start with what the student knows and gradually into the new and unknown material. This way the student is guided seamlessly into the unknown using what he knows as a "bait".
Math, and calculus for that matter, is best mastered by practice. As such, I prefer to guide the student into problem-solving immediately after the concepts are taught. This way misconceptions and erroneous interpretations are exposed through the errors made during the problem-solving.This goes to solidify the students overall learning experience an understanding.