Conservation of Cream Cheese Theorem

“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.”

“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.

We have four people in our family

“We have two people.”

Timon, who is 3 years old, holds up 2 fingers on the same hand.

“What if Mommy comes back? Then we have three people. See? Three people.”

Timon holds up 3 fingers on the same hand and then says, “And if Thanasis comes too? Then we have four people. Four people.”

Timon holds up four fingers on one hand for emphasis. Then he giggles and holds up two fingers on one hand and two fingers on the other hand and says “See four people?”

I ask, “And what if Grandpa comes? How many people then?”

Timon says quickly, without any obvious counting with his fingers, “Five!” and then holds up all five fingers on one hand. Here, I notice him counting on rather than counting from one.

“What if Grandma comes too?”, I ask.

Timon, without speaking runs up and shows me five fingers on one hand and one finger on his other hand and then says, “Six people.”

And then he’s done with this game and moves on.

Later I ask him again how many people are in our family and he holds up five fingers, looks at them and says, “I need to take one away. Four people” and folds his thumb up next to his hand.

This is the use of three different representations of numbers from 1 through 6, specifically the oral naming of the numbers, the use of his fingers to show the numbers, and then actual number of people being represented, and Timon is moving between the three representations fluently.

But he’s also only doing this for the first six numbers and I know that he doesn’t know the symbols for these six numbers yet. I’m also not sure yet that in every instance of these numbers appearing around him that he’s as fluent as when he is counting people. And as I recall with my older son, he was fluent with counting people before he was able to count other things.

I especially noticed this interaction because this is the first time I have seen him move between number representations greater than 4 things so effortlessly.