\section{Transitioning from ``high school math'' to ``real math''}
A key function of an introductory college math course
(esp.:
 calculus course
 multi-variable calculus
 intro to real analysis
 intro to algebra)
...is to help students transition from high school math to real math.

This is very hard; it involves learning new perspectives along with new
material, unlearning old habits, etc.

Key points:
- writing proofs
- understanding/reasoning mathematically, not just symbol shuffling
  (eg., $\int x^n = \frac{1}{n+1}x^{n+1} + C$ is pure symbol shuffling)
