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.

将数字概念化为在交流中生成的话语结构，并为了进行交流，我们调查了米洛（Milo）的数字话语的发展，这个男孩在初次见到他时才2岁8个月，然后跟随他18个月。我们对孩子对“哪里有更多X？”这个问题不断演变的反应的分析。（WiTM）证实了基本的理论宗旨，根据该宗旨，数值思维在我们的文化中开始独立出现（1）定量-非数值话语和（2）数值-非定量话语。在米洛的情况下，这两种话语虽然不断发展，但相隔数月之久。在将孩子响应WiTM问题而执行的独立的数字和定量“仪式”最终合并为一个定量与数字比较的复合程序之前，出现了许多明显可区分的发展。正是在这一点上，数字和定量的思维方式开始融合为一个单一的论述，而秩序的初始二元关系产生了基数的一元关系。所有这些都总结在数字话语发展的三个阶段模型中。简要报告了证实该模型的另外三个案例研究。正是在这一点上，数字和定量的思维方式开始融合为一个单一的论述，而秩序的初始二元关系产生了基数的一元关系。所有这些都总结在数字话语发展的三个阶段模型中。简要报告了证实该模型的另外三个案例研究。正是在这一点上，数字和定量的思维方式开始融合为一个单一的论述，而秩序的初始二元关系产生了基数的一元关系。所有这些都总结在数字话语发展的三个阶段模型中。简要报告了证实该模型的另外三个案例研究。