It's a bit worse than just having no experience teaching algebra, I didn't have the same experience as most kids trying to learn it. I was kind of a freak. I was the weird quiet kid in the back of the class who always knew the answer to every question. (Other kids tended to not like that, but I'm also very disarming (in person) and so I did alright.) One year, I was misplaced into a basic geometry class, and the teacher very kindly let me pick out some calculus textbooks and sit in the back of the class teaching myself calculus. (Some bureaucratic reason for why I couldn't transfer, or the calc classes were full, or we didn't have any, or something, I forget.) Learning math for me feels like remembering things I always knew.

So, yeah, maybe I should keep my mouth shut when it comes to teaching normal people how to do math.

Or maybe we should try to figure out what my brain is doing and how to teach people to do that too?

Maybe I have a normal brain and I'm just using it differently than most people?

I like that idea better, because then, instead of a freak, I'm a front-runner. And, in addition, there's hope for a great improvement in didactic technique and humanity's general "numeracy" level, eh? If we could teach people to math like i do we could compress basic math education (up to calculus) into just a year or so.

"Something self-referential and hopefully unsnarky about how this is a thread on a how-to-math-better article." ~me, failing at rhetoric.

And for kicks, here's Iconic Math: http://iconicmath.com/ (No affiliation with me. I'm just trying to end on an upbeat, constructive note.)