“I want a knife. Can you give me a knife?”, Timon asked.

“Why do you want a knife?” I responded.

“I want to spread my cream cheese. On my cracker.”

“Why do you want to spread your cream cheese?”

“Because I want more cream cheese,” replied Timon.

I gave Timon a knife and he proceeded to take the cream cheese that was on his cracker and spread it out until it covered much more of his cracker. Then he smiled and ate the cracker.

Timon doesn’t yet know that no matter how he manipulates his cream cheese, there’s always going to be the same amount. He has yet to learn the Conservation of Cream Cheese Theorem.

But he from his actions we can infer what he does understand that the more area of cream cheese there is on his cracker, the more cream cheese there is. This is true, provided the thickness of the cream cheese is constant.

I wonder how much longer he’ll think that he can get more of something by spreading it out.

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Do you think his ‘more’ meant something different than yours? Maybe he meant that he wanted cream cheese covering more of his cracker. Cracker without cream cheese may taste too dry to him. If so, the spreading would get him more of what he likes.

I think this is a good point Sue. Maybe he means more to mean “more cracker covered”. He’s three and so his descriptive language is still developing.

Yes! I once read a critique of Piaget in which the author pointed out how odd Piaget’s questions must have sounded to the kids, and how maybe they were just trying to placate him. The author claimed that kids will correctly determine which pile has more m&m’s, the compact pile with a few more, or the spread out pile.