The development of number in children is one of the most well documented topics in the literature on developmental processes. In the present chapter we assess the main contributions made in psychology related to early numerical knowledge; we highlight their limitations, and defend the relevance of the Pragmatics of the Object perspective for a critical look at recent studies on the subject. Piaget proposed that the understanding of number involves a slow process of construction that takes place thanks to children's operations on objects (Piaget & Szeminska, La genèse du nombre chez l'enfant, 1941). The criticisms done on that late acquisition made way for research on innate numerical abilities and also on the importance of counting (Carey, Infant Behavior and Development, 37, 416–427, 2009; Dehaene, El cerebro matemático, 2016; Gelman & Gallistel, The child’s understanding of number, 1978; Hirschfeld & Gelman, Cartografía de la mente. La especificidad de dominio en la cognición y en la cultura. Vol 1. Orígenes, procesos y conceptos., 2002). From here we begin our dialogue with the Pragmatics of the Object: from this perspective, we argue that the nativist perspective, which defends the existence of innate numerical knowledge, presents controversial and debatable issues. Number is not a property of objects, but derives from a process of active construction by the subject in interaction with other people; moreover, if number is symbolic by nature, it requires a symbolic treatment for its construction and expression. We also consider that studies on counting do not analyse in detail the fundamental role of social interaction and disregard the variety of semiotic systems that make numerical development possible. With these considerations in mind, we defend the semiotic status of number and the importance of differentiating it from the concept of number defended by the nativist perspective. We illustrate these ideas by presenting the results of a microgenetic study in which we analyse mother-child interaction in three dyads that engage in a game involving number. Our conclusions point out that studies on number cannot obviate the semiotic, social and cultural nature of its construction.

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Early Development of Number: Semiotic and Social Construction

  • Sílvia Cavalcante,
  • Eduardo Martí

摘要

The development of number in children is one of the most well documented topics in the literature on developmental processes. In the present chapter we assess the main contributions made in psychology related to early numerical knowledge; we highlight their limitations, and defend the relevance of the Pragmatics of the Object perspective for a critical look at recent studies on the subject. Piaget proposed that the understanding of number involves a slow process of construction that takes place thanks to children's operations on objects (Piaget & Szeminska, La genèse du nombre chez l'enfant, 1941). The criticisms done on that late acquisition made way for research on innate numerical abilities and also on the importance of counting (Carey, Infant Behavior and Development, 37, 416–427, 2009; Dehaene, El cerebro matemático, 2016; Gelman & Gallistel, The child’s understanding of number, 1978; Hirschfeld & Gelman, Cartografía de la mente. La especificidad de dominio en la cognición y en la cultura. Vol 1. Orígenes, procesos y conceptos., 2002). From here we begin our dialogue with the Pragmatics of the Object: from this perspective, we argue that the nativist perspective, which defends the existence of innate numerical knowledge, presents controversial and debatable issues. Number is not a property of objects, but derives from a process of active construction by the subject in interaction with other people; moreover, if number is symbolic by nature, it requires a symbolic treatment for its construction and expression. We also consider that studies on counting do not analyse in detail the fundamental role of social interaction and disregard the variety of semiotic systems that make numerical development possible. With these considerations in mind, we defend the semiotic status of number and the importance of differentiating it from the concept of number defended by the nativist perspective. We illustrate these ideas by presenting the results of a microgenetic study in which we analyse mother-child interaction in three dyads that engage in a game involving number. Our conclusions point out that studies on number cannot obviate the semiotic, social and cultural nature of its construction.