I have strong opinions on how Calc should be introduced - visually.

I think we don't cover basics like the distributive rule in school very well, and that it should be a much more nuts n bolts visual / measuring / counting experience.

Ive attempted to outline how I think this stuff should be taught, by making a video tour of the concepts - from Counting, to Distributive rule / algebra, to Quadratics then the Derivative, here :

https://www.youtube.com/playlist?list=PLEInJ-Z4qBKYxbK1Mm13g...

All of these things are covered in some great books :

  W W Sawyer Vision in Elementary Mathematics
  Algebra by Gelfand
  Calculus by Thomas