If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.

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

The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing.

Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. [...] To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery.

If there is a problem you can't solve, then there is an easier problem you can't solve: find it.

When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.