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Children’s Developing Understanding of Number: Mind, Brain, and Culture

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The Developmental Relations among Mind, Brain and Education

Abstract

This chapter describes and extends Robbie Case’s contributions to the field of children’s numerical development. Case postulated a theory of numerical development that results from an integration of two schemas essential to understanding quantity relations. These schemas depict children’s intuitions about numerical concepts that involve counting objects and comparing quantities. A conceptual structure that supports a new way of thinking emerges from this integration – a qualitatively different way of viewing the quantitative world. This new structure is termed a central numerical structure, which serves as a focal hub for children’s understandings of a broad range of numerical activities and situations that are culturally defined. The current chapter takes these ideas in two directions: one is to explore the potential origins of the counting and quantity schemas and the other is to examine the development of central numerical structures in cultural contexts. The former presents an argument that the two, initial structures parallel the two “core” systems of number for infants: Recent findings from cognitive sciences and neurosciences show that infants may possess such systems of number that allow them to represent discrete numerosity (similar to the counting schema) and approximate numerical magnitudes (similar to the quantity schema). For the latter, the chapter presents evidence from two cross-national studies that showed equivalent patterns of development of central numerical structures between American and Japanese children, despite large achievement differences in mathematics. The chapter ends with an attempt to link recent developments in neurosciences to cognitive and cultural studies of the numerical mind.

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Notes

  1. 1.

    This is in accord with Weber’s Law that states that discriminability of two quantities is a function of their ratio.

  2. 2.

    Infants’ precision improves. The ratio of success at 9 months is 2:3 (e.g., Lipton & Spelke, 2003).

  3. 3.

    Carey and colleagues refer to this system of representation as “parallel individuation.”

  4. 4.

    Macaque monkeys are able to track up to four items (e.g., Hauser, Carey, & Hauser, 2000).

  5. 5.

    Ross-Sheehy, Oakes, and Luck (2003) reported that infants were able to hold four units.

  6. 6.

    There is evidence that older children and adults use an analog magnitude system to assess numerical magnitudes when prevented from counting (see, for example, Barth, Kanwisher, & Spelke, 2003).

  7. 7.

    Due to neural plasticity, neural connections may be altered reflecting life experiences.

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Acknowledgments

I thank Marion Porath, Michel Ferrari, Ljiljana Vuleti, Gregory Jarrett, and John Jabagchourian for their helpful comments on earlier versions of this manuscript.

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  1. Department of Education, University of California, Santa Barbara, CA, USA

    Yukari Okamoto

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  1. Ontario Inst. Studies in Education, Dept. Human Development &, University of Toronto, Bloor Street West 252, Toronto, M5S 1V6, Ontario, Canada

    Michel Ferrari

  2. Ontario Inst. Studies in Education, Dept. Human Development &, University of Toronto, Bloor Street West 252, Toronto, M5S 1V6, Ontario, Canada

    Ljiljana Vuletic

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Okamoto, Y. (2010). Children’s Developing Understanding of Number: Mind, Brain, and Culture. In: Ferrari, M., Vuletic, L. (eds) The Developmental Relations among Mind, Brain and Education. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3666-7_6

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