Why Common Core Math Emphasizes Counting versus Cardinality
To master Common Core Standards in math, children in kindergarten need to learn the sounds and the patterns of the counting words as well as what those words and patterns mean. This helps them learn the difference between counting and cardinality.
When you count a collection of things, the last number you say is the total number of things. Saying the number words in the right order and naming one number per object counted is the process of counting. Meanwhile, cardinality refers to knowing that the last number you mention tells you something about the whole collection.
If you have spent time doing math with small children, you may have witnessed something like the following exchange:
Adult: Can you count these grapes?
Child: [carefully pointing to each grape, saying one word for each grape] One, two, three, four, five, six, seven, eight.
Adult: So how many grapes are there?
Other children will count again when asked, “How many grapes are there?” Both of these — giving nonsense answers, and understanding the question how many as a request to count — are common responses from children who haven’t mastered cardinality.
When you count things, you point to each thing and say a word. You also do this when you show someone a set of crayons — red, orange, yellow, and so on. In the case of the crayon colors, each color word describes (or names) an individual crayon. The last color in the crayon collection is just the last color; it doesn’t say anything about the whole set. The fact that numbers work differently is something important and challenging for young children to grasp.
They do learn it, though. They learn it by counting, by talking about their counting and about how many things they have or that they need, and then by counting some more. In order to extend the range of numbers they can count, kindergarteners count by ones and they count by tens. They practice counting (both forward and backward), starting at numbers other than one in order to prepare to solve simple addition and subtraction problems in first grade.