For the past fifteen years I have worked as a substitute teacher in the public middle schools and high schools of New York City. Before that I was a teaching assistant in graduate school. All told I have eighteen years of experience teaching, either in classrooms or one-to-one, as a tutor.

One of the chief glories of mathematics–its exactness–can also be a source of fear and anxiety for students. When I tutor mathematics I always try to put the student at ease by promoting an atmosphere of open exploration. With a new student I set about learning how the student thinks, what the student finds confusing, what the student finds appealing–and I adjust my teaching method accordingly. Some students prefer a more inductive approach: they want to see many examples. Others are more deductive: they want to see the logical dependence of the ideas. In all cases I show students how a mathematical problem can be broken down into simpler components. Whether I am presenting new mathematical concepts or whether I am developing a student’s mathematical skills, I proceed by persistent, patient, judicious questioning, often answering a question with a question. For though I start with the premise that an understanding of the basics of school mathematics is within the reach of any normally intelligent child, what a child learns will depend largely on his or her personal efforts. I can stimulate and aid these personal efforts, but to learn anything the student must be thrown upon his or her own intellectual resources. In mathematics this means solving many problems: there is no better way to improve one’s knowledge of and skill in mathematics.

Students preparing to take standardized tests in mathematics face different challenges than those needing help with their classes. These tests put a premium on speed and accuracy, not necessarily on understanding. I teach students the best strategy to follow for a particular test, a strategy that may involve estimating, educated guessing, or the skipping of questions.