I'm dreaming of a curriculum where students start to program their own computer algebra system in 9th grade (or earlier), say, using Python or Clojure. Starting by teaching it to solve simple equations for x, then proceed over the next 4 years by extending it to know about binomial formulas, solving quadratic euations, perform gaussian elimination, symbolic differentiation and integration, etc. I guess the world isn't ready for that idea, yet ;)
Automatic differentiation by dual number! Really, after I learned it, I wondered why symbolic differentiation isn't taught this way by default. Good use case of operator overloading, by the way.
