"seem perfectly capable at getting at least that across" yeah, that's part of the problem. They already know that 1+1=2, or so you'd think. But you would be hard pressed to find a teacher who can actually explain WHY 1+1=2 (which is based in how our number system was created and using proof by induction). Anyway, that is besides the point, since you won't teach children math with college approaches, but the important thing is that most teachers don't understand what they teach, they just "say what they remember".

And that doesn't pair well with children's insatiable "why" requests, even if they don't utter them. Teaching children is actually harder than teaching adults, because most adults largely gave up on the "why" and just settle on "I gotta remember that, if I want to pass the next exam" (school did a good job with them I guess).

So why 1+1=2? There is a lot of depth in that that is left unanswered and children are forced to memorize the answer. From then on, a sharp decline of cognitive ability follows as they "graduate" through our excellent school systems...