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Summary of Reference

Thomas, Noel

Understanding the Number System

Bibliographic data:
Thomas, N. (1996). Understanding the number system. In J. Mulligan & M. Mitchelmore (Eds.). Children’s Number Learning, (pp. 89-106). Adelaide : The Australian Association of Mathematics Teachers.

The fundamental basis of numeration is the notion of treating a group as a unit. It seems that there is considerable chaos in the way children construct mathematical meaning, more so than would be expected from a study of the mathematics.

This paper reports on the results of research, attempting to ask three questions:

  • What is the relationship between children’s understanding of counting, the formulation of equivalent groups, and the base ten numeration system?
  • How is the structure of the numeration system reflected by children’s representations?
  • What is the relationship between children’s representations and their understanding of the formal base ten structure?

It appears that many children in grades 1-6 are familiar with concrete materials used to represent groups of numbers, but still rely on unitary counting. They may show good performance on two-digit calculations but generally use poor methods and cannot extend their success to numbers with more digits. There is generally a weak awareness of structure and, in particular, of the multiplicative nature of this structure.

It could be that there is too much emphasis in the early years on addition and not sufficient on multiplication (splitting, partitioning and grouping). If this is so, there are implications for early classroom teaching.