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.
Either child must already *know* the phenomenon in order to connect to any explanation. If I point to a visual scene, say for example, a harbor, and mention that the ripples at the inlet indicate the direction of the tidal current. You might not yet connect that statement to the scene you are viewing. You may be confused because you don?t know which aspect of the scene is *ripples* or *inlet*, or what *tidal* and *current* even refers to. Then there will be the subtle differences in the ripples when the tide is going out or coming in. There are dozens and dozens of facets and aspects in this scene and *explaining* is the process of pointing out these details and their significance and connecting it all together, with language. In the beginning of such a complicated process, every child isn?t going to pickup on the clues and connect the statements at the same time or in the same order. Their awareness of the details and acuteness will vary. With very *new* explaining it can b! e very hit and miss. Eventually though, barring differences in interest and/or ability and awareness, they will understand all of the explanations. But they need to be looking at the harbor for any of this to occur.
Numbers and arithmetic are a phenomenon, that is imagined. Before you can *explain* the details of this phenomenon, the child must first be able to see it. This is a lengthy process that requires exercise and illustration. And it requires awareness. I cannot over emphasize that last part. If you are not aware of the details and cannot differentiate the details then there is nothing to explain.