The meaning attached to counting is the most important idea on which all other number concepts are developed.

**Counting Involves at Least Two Separate Skills:**

- A child must be able to produce the standard list of counting words in order: “one, two, three, etc.” This must be learned by rote memory.
- The child must be able to connect this sequence in a one-to-one manner with the items in the set being counted. In other words, each item must get one and only one count. This important understanding is called
**one-to-one correspondence**.

**Meaning Attached to Counting:**

There is a difference between being able to count as explained above and knowing what the counting means. When we count a set, the last number word used represents the **magnitude** or the ** cardinality** of the set. When children understand that the last count word names the quantity of the set, they are said to have the

**cardinality principle**.

Give a child a set of objects and ask, “How many”? After counting, if the child does not name how many are there (as, “There are 7 of them,”), then ask again, “How many?” If a child can answer without recounting, it is clear he or she is using the cardinal meaning of the counting word. Recounting the entire set again usually means that the child interprets the question “How many?” as a command to count.

**Almost any counting activity will help children develop cardinality. **

- Have the child count several sets where the number of objects is the same but the objects are very different in size. Ask the child to talk about this.
- Have the child count a set of objects, and them rearrange the objects. Ask, “How many now?” (If the child sees no reason to count again, likely the child has a good sense of number and has developed cardinality.)

Happy counting!

Mathematically yours,

Carollee