On Jul 9, 2014, at 6:20 PM, Joe Niederberger <firstname.lastname@example.org> wrote:
> One child may get a particular concept immediately, another may need an entirely different explanation because of some hang up.
No child gets any concept immediately. And multiplication is not a particular concept, it is a large phenomenon. Like a whole branch of phonetics in reading. You have to do a lot of multiplication before it even exists in your head and before you start conceptualizing it.
I am not sure what your question is because children learn addition over a rather long period of time which includes direction, contemplation, exercise and experience. These things are not *explained* to them in the way you seem to be using the word. You have to develop a visceral feeling for the phenomenon first and the explanation, at this age, is mostly just language and labeling. Later it turns to theory and formal thinking.
I don?t have a word for it, but we have a tendency, after we thoroughly understand something, to want to create a perfect explanation for it. But perfect explanations are only sharable with and appreciable by others who have nearly that same level of experience. Thus, providing explanations along the way doesn?t teach multiplication. Multiplication teaches multiplication. Providing explanations along the way is part of the teaching of reason and mathematical justification, but at these ages it is mostly the language training aspect of that. You should only provide explanations at this age (and probably any age) when the child is ready for the explanation. Obviously, a lot of experience must precede that.
In that light, the answer to your first question above is that there are many ways and it isn?t the rightness of the ways that matter but do they connection with the experience. It is really mostly about language, not reason.