I'm not sure that adults learning differently from children is vital here. I think it just comes into play that adults already learned these things and have an

I'm not sure that adults learning differently from children is vital here. I think it just comes into play that adults already learned these things and have an expectation to know them; children are looking fresh and are allowed to not know things. I think many adults would benefit from relearning math to use grids and chunks. To this day I think about arithmetic using my own analogues to the grid and chunk methods. They're far closer to the intuitive meanings of the operators and are more useful when you start generalizing. They get at the heart of the divide between meaning and representation. (And for that, see GEB) Algebra is representation of abstract objects via formal computational procedures (sort of). The formal procedures are the mechanism for proof, but really have no weight of meaning. I to this day cannot long divide (without regenerating the rules anyway) and get weird stares when I tell people that. But then I stare back: how many ways can you describe what division means?