Teaching Philosophy

A list of generalizations such as this should begin with a disclaimer, limiting the authority and imposition of the generalizations. Learning is individual. Different people learn in different ways and form different structures in their brains. Insisting on the same style of teaching and learning for all people makes no more sense than requiring everyone to wear trousers of the same (average, presumably) waist and inseam. The general style and techniques of teaching that I am about to present represent only what I try first; there is no limit to how much I will modify and adapt teaching to the individual I am working with.
I believe that saying too much is worse than saying too little. My goal is to get a student's fingers moving as soon as possible; I say as little as is needed to get the student thinking and working.
I like to introduce a topic with a very brief description of, and motivation for, the problem. I check the student's background, detour into preliminary material; all discussions should start with something the student is familiar with. I do a simple illustrative example, then the student does a similar problem. We repeat this cycle, gradually increasing complexity. For students being tutored on a regular basis, it is desirable to repeat the types of problems from previous lessons; this puts knowledge into long-term memory and gives students the pleasure of feeling on top of a subject.
All discussions are done, as much as possible, with the Socratic method of eliciting or discovering ideas through questions.
All activities are predicated on the premise that mathematics is intrinsically worthwhile.
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