On Nov 9, 2012, at 12:50 PM, Joe Niederberger <firstname.lastname@example.org> wrote:
> I agree with Clyde - children learn to count, and even to count perhaps in pure numbers. Its a game, with its own rhythm, like skipping rope. But expressions like "how many" beg for an object: "how many apples". Beginning arithmetic such as addition has always been greatly aided by grounding in real world objects. That's how children > begin to understand expressions like 3 + 5; they relate it to a real-world situation, like "3 apples + 5 apples"
I repeat my question, now to all three of you. WHEN do these games stop and the math begins?