Ordinality and Cardinality

Ordinality and Cardinality

How many times have you seen a parent proudly proclaiming that his child can count to 10, 20, or even more and then prodding the child to demonstrate her mathematical prowess?  Well, don’t be too impressed.  Any child can be trained to recite a series of numbers.  But all children need to have a variety of experiences before they can understand what the numbers mean.

First, there is the concept of ordinality, that is, the fact that numbers represent more than/less than relationships.  Then there is the concept of cardinality, the fact that the last number in a sequence represents the total amount.

It is always amusing to see the parent of a three-year-old ask her, “How many marbles do you have?”

The child replies, “I don’t know.”

The parent says, “Count them.”

The child goes, “One…two…three…four…five…six…seven.”

The parent asks again, “So how many marbles do you have?”

The child cries, “I don’t know!”

We tend to forget that simple concepts we take for granted are not present from birth.  So whether your child can or can’t count to 10 or 100, don’t worry.  As long as she is playing with marbles, beads, and other materials in an art class or climbing and dancing in rhythmic fashion in a gym or music class, she will eventually learn to count.  And in the meantime, she will be learning how and why to count.