Childrenʹs understanding of the additive composition of number and of the decimal structure: what is the relationship?

Nunes and Bryant (Children doing mathematics, Blackwell, Oxford, 1996) proposed that an understanding of the additive composition of number could be a precursor to an understanding of the decimal structure. If this is so, children should achieve an understanding of additive composition before they can handle the decimal structure. The aim of our study was to determine the developmental timing of these two forms of mathematical understanding. 5- and 6-year-old children each completed both an addition task and Terezinha Carraherʹs (In: Streefland, L. (Ed.), Proceedings of the Ninth International Conference for the Psychology of Mathematics Education, vol. 1. Research Group on Mathematics Education and Computer Centre, State University of Utrecht, Utrecht, The Netherlands, 1985, pp. 288–303) shop task, with concrete materials. The addition task tested an understanding of additive composition by measuring whether children used a counting-all or counting-on strategy to add two quantities. The shop task tested an understanding of the decimal structure by investigating whether or not children could successfully combine tens and ones in producing a given amount of money. Our results suggest that learning about the decimal structure enhances childrenʹs understanding of the general principle of additive composition.