# Counting Isn’t an Inherent Concept

We spent our vacation a couple of weeks ago in central Texas. We had lots of fun – including lots of counting.

I noticed that some of the basic counting principles grownups know, aren’t inherently known to kids.

I was observing Daughter as I was counting. She continued to look in deep concentration as I counted from one direction and then recounted from the other. Then I would rearrange the items and count them again. She was still enthralled.

We teach our young children to count to 10, but never realize they don’t know what that means.

### Counting is a way to associate how much with a group of objects.

If there are three things in a bundle, we associate the word “three” and the symbol 3 with that bundle. This number is called the cardinality of the set/bundle and means the number of things in it.

My lone Calculus classmate in high school decided to create her own number system when we were freshmen. Everyone else laughed at her, but I got it. She was noticing that there was no rhyme or reason that we called a set of two objects “two.”

We’ve decided to say out loud “two” and label it two and 2 and that means this many things: X X

### Counting is a way to order things.

A bunch of things can be lined up and counted – even if they aren’t technically in a line. Each subsequent number is associated with another object. These numbers are the ordinal numbers. The final number that you count ends up being the cardinality of the set (from above). In this way you use ordinals to determine the cardinality.

### Counting is a way to compare one group of objects with another.

Take two groups of objects. Pair one object from one group to an object from the other group – set them up in a one-to-one fashion. This shows that the two groups have the same number of objects. It doesn’t determine how many there are, but very young children don’t have to know the numbers to grasp the concept of “the same.”

This eventually leads to the concepts of equality as well as less than and greater than.

This was the craziest concept for me. I noticed this when reading Brown Bear, Brown Bear one night.

To mix it up (to keep my sanity) I would count the children in the book in differnet directions. After 3,000 nights of reading the same book over and over, something occurred to me. There is no reason for a 2 year old to know that counting in one direction will yeild the same number as counting in another direction.

This is taught – not directly, but through experience. After counting a bazillion times, we eventually figure out that no matter which way you count things, you’ll get the same number.

Well, unless Little Brother starts eating those things.

### Counting can be stopped and picked up where you left off.

This is another concept that grownups “just know.” If you can mark your place (and Little Brother isn’t involved), stopping and coming back won’t change the result. This is the forerunner to addition, too.

### Counting is the foundation of all mathematics.

This is the kicker. Counting is the beginning of it all.

If you can get your kiddo to count, the rest is cake. And not just saying, “1, 2, 3, 4, 5, 6, 7, 8, 9, 10,” but really getting him or her to understand the totality of the concepts.

• How much is there?
• Is there an order?
• Does one group have more, less or the same as another group?
• Did the number of objects change when you counted differently?

Grownups get it, but we aren’t born with it. Imagine that you don’t know these things inherently. How does that change the way you observe the world?

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