Constructing and understanding of place value in numerical notation

Abstract

The purpose of this study was to investigate how children aged five to nine gradually build up an understanding of the characteristics of place-value inherent in the written number system. The task consisted in presenting collections of chips, asking children to produce the corresponding two-digit numerals, and then questioning them in a structured clinical interview about the possible numerical meaning (in terms of correspondence to a number of chips) of each of the digits in the numeral. Results show that the idea that parts of the notation must correspond to mutually exclusive parts of the collection is but slowly built up, and that subsequently it is fleshed out by the use of knowledge concerning oral numeration_— written numeration correspondences. Intuitions concerning «groups of ten» arise later. A fair proportion of eight-year-olds and all nine-years-olds saw the two-digits as corresponding to, on the one hand, a number of units, and on the other, a number of groups of units.