I wonder how receptive students would be to more abstract mathematical concepts, and how they could be implemented in American schools.

Throughout my school career, the number of kids that actually "liked" math was really small. Of course, in the normal teach-me-some-math-so-I-can-get-out-of-here classes, the math hating sentiment was strong, but even in the more advanced classes, it was still commonplace. We did a couple things that weren't normal math, like fractals, for instance, and people had fun with it, but mainly because it wasn't plugging a bunch of numbers into equations and writing proofs. I learned many abstract and strange types of math in my programming classes, because we had to solve puzzle with them in a way, and even then, a lot of my peers felt like they were making things more complicated than they felt like dealing with.

On top of that, I'm no teacher, but a lot of school curriculum, at least in America, is based on getting good scores on tests. I got to hear all about my teachers, as well as others on the internet, complain about having to cram in order to cover a checklist of topics in the short amount of time available. Even a couple snow days would seem to throw a a big wrench in plans. Unless there was a reform on how exactly education was planned in America, how could more irrelevant (in respect to the tests that the lessons are geared towards) topics be implemented in a classroom? I saw a lot of teacher do fun things after finals and end-of-course exams, but that was maybe a week of class time in the end; cut down even further due to weird scheduling around end-of-year events during school.

It would be great to dedicate more time to the "fun" parts of math. However, I don't know if there's enough time or a great enough level of interest among students that could make it work.