One kid just groks the math. One kid groks the fun(){} ...in a perfect world, those brains should just complement each other, I guess.
I do recall when first taking calc they briefly mentioned delta-epsilion proofs and limits but really hand waved past it, which i guess would be hard if you want everything on solid foundations.
As the teacher looked at the results, he said I should receive a Nobel for my work. As my son told me that, I had a very long sigh...
I don't think you deserve a Nobel, but I do think that teaching your son to solve lots of different problems with algorithmic recursion is going to help him much more in life than memorizing the way to solve one problem on a math test.
I don't think I ever understood math except where it was logical, within the bounds of what I could deduce. But when I learned to write recursive algorithms, that capacity for deduction expanded exponentially.
(Eventually math switchs much more to be about proving things [inb4 someone yells howard-curry], but that is more mid-undergrad degree.)
I never passed a math class after my second try at pre-calculus. Before that I never even had to look at a book. Looking back I think it was a failure for me to ask the right questions or a failure of the teachers to help me visualize how to work out the systems starting from basic principles. I couldn't solve anything without starting from scratch. Still can't. I get paid ludicrously well for making a marketable skill out of that form of reasoning, so I can't think it's either a mental flaw or laziness that prohibited me from grokking calculus in 12th grade. Somewhere in there was a failure to provide the reality handle that mapped to something I could reinvent if necessary.
[edit] fwiw I think I've reinvented trigonometry at least six times when I needed to for games. I never remember how it worked the last time.