Yesssss to the manipulation of parts. Someone must have told me about it, but I was doing that for MathCounts in seventh grade (and used to have some sort of awkward triangular trophy); unlike most of my fellow former literature majors, I don't fear Common Core for that reason, only want it to be taught properly. And I agree that innate tendency/inclination, at least, factors in.

(I am a weirdo lit major who wanted to study ophthalmology right up through first semester of college, when I realized that my grades wouldn't be high enough, so sciency kid but not sciency adult by formal training.)