thnik again!

My special pleasure in mathematics rested particularly on its purely speculative part. – Bernard Bolzano

I’m a mathematical optimist: I deal only with positive integers. – Tendai Chitewere

I certainly do care about measuring educational results. But what is an ‘educational result?’ The twinkling eyes of my students, together with their heartfelt and beautifully expressed mathematical arguments are all the results I need. – Keith Devlin

Mathematicians care no more for logic than logicians for mathematics. - Augustus De Morgan

Suppose that you want to teach the ‘cat’ concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractible claws, a distinctive sonic output, etc.? I’ll bet not. You probably show the kid a lot of different cats, saying ‘kitty’ each time, until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience. - R P Boas

There are two versions of math in the lives of many Americans: the strange and boring subject that they encountered in classrooms and an interesting set of ideas that is the math of the world, and is curiously different and surprisingly engaging. Our task is to introduce this second version to today’s students, get them excited about math, and prepare them for the future. – Jo Boaler

This site is not about making mathematics easy because it isn’t. It is about making it make sense because it does. – Mathematics for Teaching

One and one and one is three. - The Beatles

If a ‘religion’ is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one. - John Barrow