I think the key difference is that it quickly moves from what's considered problems for kids (Ally had 3 apples, Booby had 2, etc) to abstract tasks and fundame

I think the key difference is that it quickly moves from what's considered problems for kids (Ally had 3 apples, Booby had 2, etc) to abstract tasks and fundamental theorems in algebra, geometry and other areas. The way math was taught in USSR and is still largely taught in Russia is by going as quickly as possible to calculus. I definitely studied limits and derivatives in school (around grade 8 or 9 out of 11 as I recall) and we briefly touched integrals in the last grade. There are some areas they don't really include, although in my opinion they should have, like mathematical statistics, which could be even more useful, but still. That is a common approach recreated in some other subjects. For instances, teaching Russian includes not just basic syntax and phonetics but also just basic linguistic exercises like dissecting complex words and learning classifications, which you don't really need to talk it but they provide a deeper understanding.