> In the countries that excel over the United States in mathematics instruction, proof is part of every mathematics course, not just part of geometry, for example.
There's room to wonder about how much of a causative role this has, and how much it reflects consumer demand. When my sister started taking algebra, my parents asked me to help her, and I was careful to provide proofs of all the algebraic properties of exponents (e.g. x^m * x^n = x^{m+n}; x^0 = 1; like that). That's not usual in the US, and didn't feature in her textbooks or supplements, but I did it basically just because it was important to me.
There's room to wonder about how much of a causative role this has, and how much it reflects consumer demand. When my sister started taking algebra, my parents asked me to help her, and I was careful to provide proofs of all the algebraic properties of exponents (e.g. x^m * x^n = x^{m+n}; x^0 = 1; like that). That's not usual in the US, and didn't feature in her textbooks or supplements, but I did it basically just because it was important to me.