Adapted from *Young Children's Mathematics: Cognitively Guided Instruction in Early Childhood Education*

By: Thomas P. Carpenter, Megan L. Franke, Nicholas C. Johnson, Angela Chan Turrou, and Anita A. Wager

Capturing a child’s understanding of the cardinal principle while they are counting can be challenging, as children don't necessarily end the process of counting by explicitly stating the total amount that they have in their collection. A child may know that counting objects involves reciting a sequence of numbers, but not that the outcome of this process is a number that represents the total quantity. A child may say “1,2,3,4” as they count a collection of four, but this does not necessarily mean that the child understands that there is a quantity of four objects. Applying the cardinal principle requires that children name the set according to the last number used in their count. In this case, that last number used was four, so there are four objects in the collection. Because the process of counting and what the count tells you are not necessarily the same thing, figuring out what a child knows about the cardinal principle often requires waiting for a child to complete their count and then asking a question like, “So, how many do you have in your collection?” Other ways to get at the cardinal principle could include saying to the child: “Here are some blocks. How many are there?” Or “Do you have enough to give me 4?” Asking children to make a group of counters of a given size rather than counting a given collection also can focus them on the cardinal principle.

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