And where does the idea that proofs are limited to geometry come from?!?
Math and multiple choice questions. How... sad.
Yes to everything you wrote.
The better mathematics textbooks in the US have proofs outside of geometry as well. Unfortunately, the mainstream textbooks in this category tend to be older. For example, the high school math textbooks by Richard Brown include proofs outside of geometry (
see Algebra 2 here) . Newer programs like
AoPS are outstanding math courses and textbooks.
Yes-- it's just that in the US, high school geometry was a sort of last bastion of the form (constructing proofs, I mean).
Seeing it pass from core instructional practice even
there is beyond the pale for me personally.
I do not find mathematics "easy" by any means, either.
