\chapter{Material versus Method: the Key Problem of Calculus and Linear Algebra}
calc and linear algebra are taught b/c the *material* is very useful,
but they are a poor place to learn the *method* of math.
\emph{Yes,} abstract reasoning is a key part of math
(discrete math, esp. basic number theory and algebra,
is the best place to teach this)
Conflict between *material* and *method/way-of-thought*:
resolutions:
- teach method beforehand
This is the long-term solution
- teach something other than calc and linear algebra
good solution for poets,
not for chemists or economists
- give special attention to the thinking/approach
[huge grind of 1st rigorous math classes]
- cookbooks
ok if that's what you want