Counting: There's more to it than 1-2-3!

This is a continuation of yesterday’s article, Quantification, which is just a fancy word for figuring out how much you’ve got. To recap, there are three developmental stages of quantification:

• Global quantification – child relies on perception.
• One-to-one correspondence – child matches objects one for one.
• Counting.

Check yesterday’s article, Quantification: How children learn to count, for a review of the first two stages.

Today we’ll focus on the third stage: Counting.

Counting is a not a trivial thing for little ones to grasp. There are three stages a child must come to understand.

1. Knowing the right order of the words. At this stage, it’s about the same as reciting a poem. It’s not the ABC poem but the 123 poem. This is called stable order counting.
   
   Have you ever observed a child count the fingers on one hand and end up with more than 5? They counted properly: 1-2-3-4-5-6, but they counted one finger twice. These children understand stable order counting – all the words were said in the right order - but they haven’t moved on to the next stage, which is…

   
   

2. Knowing that each object may be counted only one time, with one number word said for each object counted. This is an example of one-to-one correspondence: one word for each object.
   
   
3. The third stage is knowing that the last number represents the total. This is formally known as cardinality. This requires the understanding that the last number has two roles: the name assigned to the last item, and the name for the entire set. The pinkie finger is number 5, and the total number of fingers is 5.

To demonstrate the difference between one-to-one correspondence and cardinality, here’s a favorite story:

There was a little boy who was eating cookies with his mom. He counted them in the plate: 1, 2, 3. After he ate one his mom asked, “How many are there now?” “Three!” he replied. Mom asked how could that be, if he ate one? He said that he ate “1”, but not “2” or “3”.

This boy understood that there’s a word for each cookie, but he didn’t understand cardinality. The words for each cookie change when the quantity changes.

Fortunately for him, his mother accepted his answer and didn’t pursue a correct answer. These mistakes should be viewed as windows into a child’s knowledge rather than opportunities for correcting.

Once children grasp these 3 concepts:

• correct word order,
• one word for one object,
• the last word represents the total

then they start using counting as a method of quantification.

And so you see, counting is NOT as easy as 1-2-3!

To your child's success,

Rita