On Oct 30, 2012, at 11:59 AM, Louis Talman <firstname.lastname@example.org> wrote:
> Clyde is right. And it's completely irrelevant that children don't understand the significance of replacing numbers with symbols for arbitrary numbers. (Nor did I claim that they do.) What matters is that they do it. And, perhaps even more important, they do it naturally.
Look at me, I am replacing numbers with letters, naturally, for no other reason but to replace numbers with letters, naturally. That is exactly what it will look like if you teach it to students before they are ready to appreciate it. Silly.
I hate to pick on you like this, but the stuff you are throwing at me recently, doesn't add up. Have you ever taught a student that took to mathematics?