A mathematics teacher is a midwife to ideas.

There are many questions which fools can ask that wise men cannot answer.

It may be more important in the mathematics class how you teach than what you teach.

What is the difference between method and device? A method is a device which you use twice.

The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. ... Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.

Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself

A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise.