Series: Ideas at Work

What Do We Mean by Counting Principles and What Do Early Childhood Educators Need to Know?

What Do We Mean by Counting Principles and What Do Early Childhood Educators Need to Know?

Counting is a part of young children’s everyday life. They love to count everything from the stairs they climb to the crackers they eat. But what is counting?

To adults, counting seems very simple, but it is actually quite complex. Counting is a precise, step-by-step procedure governed by rules. In order for counting to work—that is, in order to use it and get the right number—children have to coordinate all of these rules at the same time into one set of actions.

As a teacher, it can be helpful to know about these rules so you can be more specific about what each child is working on and how you can help. There are 5 Counting Principles:

  1. Stable Order
  2. One-to-One Correspondence
  3. Cardinality
  4. Order Irrelevance
  5. Abstraction

This article focuses on the first three, since they are absolutely required for a counting procedure to be accurate.

What’s the stable order principle?

Counting words must be said in the same order every time. As they learn, children often skip numbers, or get them out of order. They may even get the sequence right one day but mix it up the next! This is a normal part of the development of counting skills.

Put this into practice:

One of the best ways to help children clarify the sequence of the number words is with counting rhymes and songs that incorporate using fingers to indicate amounts. Young children love to recite these stories—whether about ducks, sausages, or elephants!—and become invested in remembering which number comes next. Using their fingers to show each number as they say it out loud adds an element of meaningful understanding. If they can show “four,” they must “know” four!

Math at your Fingertips: Songs and Fingerplay for Preschoolers

What’s the one-to-one correspondence principle?

Each object in the set to be counted must be counted once, and only once. Keeping track of which objects you’ve already counted and which ones remain to be counted is an additional task children have to learn to manage. As they learn, they may count some objects twice, skip objects, or even skim their finger across the whole set as they recite counting words.

Put this into practice:

Modeling and supporting precise counting is key. Children need opportunities to see a mature counter slowly and deliberately tracking objects as they count. They can benefit, too, from the suggestion to point at each object or move objects to the side as they are counted. Helping children become accurate in this way supports their success and will inspire confidence.

Visual tools such as the number path seen below support both the stable order principle and one-to-one correspondence. Placing one object in each corresponding box can support children’s ability to keep track of the count.

One-to-One Correspondence

Ask young children, “How does this tool help you keep track of your count?” An empty egg carton is a useful tool as well.

Number paths – a visual model of our counting system

What is the cardinality principle?

The last word in the counting sequence indicates the total amount. It’s not obvious to young children that they should use the last number they say to describe the total amount. They are often so absorbed in getting the sequence of words right and not missing any of the objects to be counted that they arrive at the last number and simply stop. If you ask them, “how many is that all together?” they may even start their counting procedure over from one, as though producing a counting procedure is what you want them to do.

Put this into practice:

Asking “how many is that all together?” after children count a set is the key here. If you find they don’t know, you can model and support their understanding by demonstrating the cardinality principle yourself, “for example, “…three, four, five…that’s five crayons.” If you make a habit of this, they will eventually get it.