I've often said that the "Why" we teach something informs the "How."

"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:

1. seek and recognize patterns
2. explore the relationship between things
3. see similarities and also distinctions
4. analyze logically but with a deep sense that there is a right answer and a set ideal worth detecting
5. compare and contrast
6. see things in black and white
7. see infinite shades of grey and therefore avoid jumping to conclusions
8. seek evidence for conclusions and check opinion with first-hand research
9. put his own pen to paper before accepting what society tells him
10. seek for absolutes
11. 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."