>>> I had the extreme luck of having excellent teachers around me. That helps one from running astray.
>>> More than rudimentary intelligence is assumed to be present, because ordinary students can master this material only when assisted by patient teachers.
I can't comment on my intelligence per se without being either self promoting or self deprecating. ;-) But I'm indebted to having good teachers for getting me through college math and physics, and for a professor to teach me how to do research. Working against whatever intelligence I possessed, was my lack of organization and focus, and the structure of the academic environment was vital for me.
Oddly enough, there were other things that I learned easily on my own such as electronics and programming. So I can't say that all things need to be taught by teachers, or even that a single person can follow a single heuristic.
> But I'm indebted to having good teachers for getting me through college math and physics
As a visual learner, I didn’t really understand linear algebra or differential equations until 3Blue1Brown came along through my YouTube. I got through that advanced college maths, but it was all just a pattern matching game back then. Seeing these equations move with life flipped the switch.
>>> More than rudimentary intelligence is assumed to be present, because ordinary students can master this material only when assisted by patient teachers.
I can't comment on my intelligence per se without being either self promoting or self deprecating. ;-) But I'm indebted to having good teachers for getting me through college math and physics, and for a professor to teach me how to do research. Working against whatever intelligence I possessed, was my lack of organization and focus, and the structure of the academic environment was vital for me.
Oddly enough, there were other things that I learned easily on my own such as electronics and programming. So I can't say that all things need to be taught by teachers, or even that a single person can follow a single heuristic.