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Summary of Reference

Author:
Maclellan, Effie

Title:
The Importance of Counting

Bibliographic data:
Maclellan, E. (1997). The importance of counting. In I.Thompson (Ed.). Teaching and learning early number (pp.33-40). Buckingham, UK : Open University Press.

Summary: 
Although counting has been dismissed as being of little value (because it does not help children in their construction of the concept of number), more recent research has suggested that counting is both a more sophisticated and a more powerful phenomenon than earlier conceived.

Counting can develop as young as 2-3 years of age, but the skill takes a number of years to develop. A principal task for the young child is to learn that number words are used in different ways in our society and that these will have different meanings depending on the context in which they are used.

There are, it seems, five counting principles used to construct the meaning of counting:

  • The one-one principle. This means that children understand that discrete and different groups of objects have different numbers assigned to them.

  • The stable-order principle. Without consistent order there can be no transfer of meaning.

  • The cardinal principle. Numerosity is a property of all countable entities and an understanding that a given quantity always has the same number assigned to it (rather than having to be recounted) is fundamental.

  • The abstraction principle. This is an understanding that the first three principles (the counting principles) can be applied to any array or collection of entities.

  • The order irrelevance principle. The order in which an array is counted is not relevant so long as all elements are counted and counted only once.

    Knowledge of these counting principles is fundamental to understanding of number. This understanding may be developed before school. It is the teacher’s job to reinforce the already held knowledge and to ensure that it is not lost.