Home » Order Irrelevance Principle

Category: Order Irrelevance Principle

Order-Irrelevance Principle – The Order of the Count Doesn’t Matter

The order-irrelevance principle refers to the understanding that the order in which objects are counted is not important. It doesn’t matter whether the counting procedure is carried out from left to right, from right to left or from somewhere else, so long as every item in the collection is counted once and only once. 

For example:
In a collection of three buttons there may be a red, green and blue one. I may start counting with a blue button the first time but the next time I may begin with the red button. Whichever button I begin, with I will always arrive at the same number.
This seems like a simple concept to understand but children often have to recount the set if you ask them to begin counting from a different object.


  • When counting, some children may assume that the number they tag an object with stays with that object and is not ‘temporary’
     For example:
     If we go back to the previous button example. Children may start with counting the blue button and         tag or label it as ‘one’. Some children will insist that it is ‘one’ and that’s where they must start                   counting from.

Source: Origin One

Recent research by LeFevre and others, 2008, indicates that from Foundation through to about Year 2 the application of conventional counting rules (left to right and top to bottom) was related to higher numeration skill. At this age, the order-irrelevance principle appeared to impact negatively on children’s working memory and therefore, their ability to count proficiently.

However, from Year 3 onward, children’s numeration knowledge was unrelated to whether they had acquired order-irrelevance. Although the order-irrelevance principle is an important understanding for children to have, some children do not fully develop this understanding until they are around eleven years of age. 

The research suggested that only when counting becomes automatic might there be the opportunity for children to accept that it is not necessary to count a set in a strict order.

Thus, for children who are still developing their counting skills, the principle of order irrelevance
might be logical, but it is not necessarily practical.


Have children count objects in their every day environment in a variety of different ways. Ensuring that they touch the object as they do so.
Constant exposure to counting helps develop this skill as well as making a game out of it by “mixing up” objects in a set to see if the numbers change.
  •  Count left to right and right to left with the same row of objects
  •  Count the same set but starting with a different “one” each time, for example, the middle object
  •  For a greater challenge, ask the children to count all the objects, making the middle object ‘5’
  •  Re-arrange the objects so they are no longer in a row and ask the child to count from a particular object
  • Ensure that sets for counting contain, not only sets with the same objects but also sets that have miscellaneous objects without any commonality.


Until next time,