Confidence does not mean you are always right, it means you are not afraid to be wrong.
Ideal teachers are those who use themselves as bridges over which they invite their students to cross, then having facilitated their crossing, joyfully collapse, encouraging them to create bridges of their own.
We begin with the hypothesis that any subject can be taught effectively in some intellectually honest form to any child at any age of development.
-Jerome Seymour Bruner, 1960, p.33
Are we teaching mathematics so that all students will be empowered to use it flexibly, insightfully, and productively?
-Trafton and Claus, 1994, p.9