What's funny, is that I think my radical acceleration in math is what saved me from learning stuff wrong. I puttered along in school, taking Algebra I in 8th grade, then did Algebra II, Trig, Geometry, and Analytical Geometry that summer at a camp for gifted kids, and took Calculus in the fall. (Actually, I didn't take Geometry, I just tested out of it. They didn't teach Geometry, and the test was really, really hard. I pestered the head of the program to let me take the test, which was in two parts. She agreed to give me part one, and told me that part two would depend on how I did on part one. I'm sure she expected me to bomb it and then she could tell me she told me so. Instead I got 100%, and a 96% on part two, so they had to support me in not taking it.)
My school gave me credit for all of them, but only after I slogged through every homework assignment and test. My calculus teacher very kindly agreed to grade it all (which I bet he regretted when I didn't do much of it until after the Calculus AP exam, and then I started blowing through multiple chapter tests and homework per day). Thirty years later, I still vividly remember fretting all night because I knew I had fudged a step in a proof when I couldn't figure out a way to do it rigorously, and him marking it correct without even noticing.
But it all meant that all my teaching before calculus was from math graduate students who knew exactly how to do the math right and didn't know anything about pedagogical reasons for dumbing it down. It was awesome.
