[Aerroon]

But the math we teach in school is context-sensitive. It matters what set your inputs are from and what set the output is supposed to be in. We usually don't mention that we're doing math on real numbers, we assume that based on the context.

22 + 8 = 6

This would be incorrect in an average math class, but when you're dealing with the clock then it's something understands. 8 hours after 10 pm is 6 am.

ab = ba

We teach the commutative property as though it is universal, but it isn't. With real numbers? Sure! Swap two matrices though and you're in trouble.

I don't think kids should necessarily be taught differently, but there is definitely (implicit) context involved in math. Even in geometry: the inner angles of a triangle add up to 180 degrees, right? But in spherical geometry the sum of the inner angles of a triangle can be larger.

[zozbot234]

Yes, abstracting away from the context only works if you can tell that the problem really is context-independent. This works well with apples, not so well with e.g. commutativity once you get to things like matrices. So abstraction (from "apples" to "numbers" to "matrices") can sometimes reintroduce context that had previosly been discarded.