Why Cannot Children See as the Same What Grown-Ups Cannot See as Different?— Early Numerical Thinking Revisited

Abstract

Based on close observations of two 4-year-old children responding to their parents' requests for quantitative comparisons, we offer a "participationist" account of the origins and development of numerical thinking, one that portrays numbers as a product rather than a pregiven object of human communication. In parallel, we propose a participationist reinterpretation of relevant past research, most of which has been guided by the metaphor of learning-as-acquisition (of mental schemes, of concepts, etc.). The point of departure for our analyses is the assumption that thinking can be usefully conceptualized as a special case of activity of communicating and that learning arithmetic can be thought of as a development of a specialized discourse. We claim that the development of this discourse involves the ability to see as "the same" things that, so far, could only be seen as different. In the longer run, this ability will lead to the objectification of the discourse-that is, to the use of number words as if they signified discourse-independent entities "out there" in the world. This development commences in child's ritualized participation in arithmetical routines of grown-ups and continues in a gradual transformation of the rituals into genuine explorations. Paraphrasing Vygotsky (1978), we conclude that the numerical discourse that begins as an interpersonal affair turns in the growing mind into a matter of one's relation with human-independent world. We also claim that this kind of development is a 1-way process, and the change from the interpersonal to between-person-and-the-world outlook, once accomplished, can hardly be reversed.