I taught Astronomy to the people in the years below me (a school tradition because it was optional), and it was absolutely exhausting trying to plan good lessons that didn't involve getting them to memorise stuff by wrote. I ""derived"" Kepler's laws for a bunch of 14-15 year olds who didn't even know logarithms yet and it was pretty brutal intellectually.
Also, I think teaching mathematics "intuitively" requires a bit of cooperation from the student - not in the sense of intelligence, just that for for every guy (or girl) who watches 3Blue1Brown (and looks deeper into the pure mathematics) there's another who's just along for the ride. I think the frequencies of those personalities are a product of how they were taught, but it's very difficult to convince people in "teaching time" as opposed to naturally (I was in the lowest maths group for years until I picked up a calculus book on a whim, but no teacher could've convinced old me that mathematics can be beautiful)
Quick Edit: To quote Tim Minchin, "Be a teacher". I might come across as moaning in the above but it's really interesting to explain things (in my experience at least - I love writing documentation!), and a good bullshit-test on yourself
I taught Astronomy to the people in the years below me (a school tradition because it was optional), and it was absolutely exhausting trying to plan good lessons that didn't involve getting them to memorise stuff by wrote. I ""derived"" Kepler's laws for a bunch of 14-15 year olds who didn't even know logarithms yet and it was pretty brutal intellectually.
Also, I think teaching mathematics "intuitively" requires a bit of cooperation from the student - not in the sense of intelligence, just that for for every guy (or girl) who watches 3Blue1Brown (and looks deeper into the pure mathematics) there's another who's just along for the ride. I think the frequencies of those personalities are a product of how they were taught, but it's very difficult to convince people in "teaching time" as opposed to naturally (I was in the lowest maths group for years until I picked up a calculus book on a whim, but no teacher could've convinced old me that mathematics can be beautiful)
Quick Edit: To quote Tim Minchin, "Be a teacher". I might come across as moaning in the above but it's really interesting to explain things (in my experience at least - I love writing documentation!), and a good bullshit-test on yourself