I've often said that the "Why" we teach something informs the "How."
Years ago Oliver wrote an introduction to a math course. He articulated "Why"
we learn and teach math, and I think having this vision is not only
inspiring and motivating, but really helps us focus our approach and
methods. He created a list of "values" that clearly articulates the
meaning and purpose of math education, and I share it here with you:
"Mathematics is an integral part of a statesman's education . . . .
Math teaches a person to think in a way that no other field does. As a
person studies math, he learns to:
- seek and recognize patterns
- explore the relationship between things
- see similarities and also distinctions
- analyze logically but with a deep sense that there is a right answer and a set ideal worth detecting
- compare and contrast
- see things in black and white
- see infinite shades of grey and therefore avoid jumping to conclusions
- seek evidence for conclusions and check opinion with first-hand research
- put his own pen to paper before accepting what society tells him
- seek for absolutes
- remain open to surprising new information which makes past conclusions limited though perhaps still accurate
"Now, clearly, the practical art must also be mastered--we want you to
be able to pass any standardized test with the highest marks. But more
importantly, we want you to be able to think like an Archimedes, a
Descartes, a Newton, a Sophie Germain, an Einstein."
Math Values 
