Another big problem is that there are very few high school math teachers who have a good idea of what mathematicians do It's a massive problem in America, the

Another big problem is that there are very few high school math teachers who have a good idea of what mathematicians do It's a massive problem in America, the undereducation of teachers. There is a lovely book, "Easy as π?" (https://www.springer.com/us/book/9780387985213 https://www.springer.com/us/book/9780387985213), it grew from an overview course in elementary mathematics for teachers of secondary-level math in Russia. The idea is to have the teachers know their math and the reasoning behind it. Try that in America, the students will complain to the administration that they learn too much, instead they will take all sorts of strange classes at their School of Education.