What are the Principles of Counting?

I have received quite a few messages following some recent posts on my Facebook page which mentioned a few principles of counting. So, what are they and why are they important?

A common understanding is that learning to count is a very simple concept and, that it can be learnt by rote. But, there are 5 principles of counting which lead each child towards effective counting skills and trusting that counting will always give the same answer each time.

So, what are the 5 principles of counting?

• Each number is said only once and in sequential order.

• Each object to be counted is touched only once (or included) as the numbers are said. This is more commonly known as one to one correspondence.

• Objects in a collection can be counted in any order. That is, the starting point and order does not affect how many there are.

• The arrangement of the objects doesn’t impact on how many there are in total collection. This includes the types of objects used - so the collection can be a mixture of erasers and blocks in all different colours or it could be a collection of blocks which are all the same colour.

• The last number said in a counting sequence means ‘how many’ there are in the entire collection.

There is no hierarchical order in developing these principles. However, the first two dot points and the last dot point are usually the easiest to learn and the first learnt.

A child who who does not fully understand and apply all five principles of counting may not choose to count when faced with a real life problem, simply because they don’t always trust counting.

For instance, when asked to get enough spoons for everyone to eat dessert- they may choose to simply hand out a spoon to each person one at a time and collecting them one at a time as well, or guess how many and collect a bunch of spoons and then return to get more if needed or return any extra spoons. This is opposed to counting the number of people and then collecting ‘that many’ spoons, which is more efficient.

The principles of counting are a focus area in the very early years and through to Kindergarten / Foundation. Unfortunately, however, I have come across students in Year 2 and Year 3 who do not yet fully understand and apply all principles of counting. So, if you have a student who seems to have difficulty grasping counting/place value in the middle years, or in applying number/place value concepts to real life Mathematical scenarios where counting is needed - this would be my first check point.

The video below is very quick demonstration on how to assess each principle and what they all might look like.