How Children Individualize Numerical Routines: Elements of a Discursive Theory in Making

Conceptualizing numbers as discursive constructs generated in, and for the sake of, communication, we investigated the development of the numerical discourse of Milo, a boy who was 2 years and 8 months old when we first met him and whom we then followed for 18 months. Our analyses of the child’s evolving responses to the question “Where is there more X?” (WiTM) corroborated the basic theoretical tenet, according to which numerical thinking begins in our culture with the independent appearance of (1) the quantitative–non-numerical discourse and (2) numerical–non-quantitative discourse. In Milo’s case, these two discourses, although constantly evolving, remained separate for months. A number of clearly distinguishable developments preceded the eventual consolidation of the independent numerical and quantitative “rituals” the child performed in response to WiTM-question into one compound routine of quantitative–numerical comparison. It is at this point that the numerical and quantitative ways of thinking began coalescing into a single discourse and the initial binary relation of order gave rise to the unary relation of cardinality. All this is summarized in a three-stage model of the development of numerical discourse. Three additional case studies that corroborated this model are reported briefly.