Practices of quantification from a socio-cultural perspective

doi:10.1017/CBO9780511489938.009

7 - Practices of quantification from a socio-cultural perspective

Published online by Cambridge University Press: 22 September 2009

Geoffrey B. Saxe

Edited by

Andreas Demetriou and

Athanassios Raftopoulos

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Geoffrey B. Saxe: Affiliation:
Department of Psychology, University of California, Berkeley, USA
Andreas Demetriou: Affiliation:
University of Cyprus
Athanassios Raftopoulos: Affiliation:
University of Cyprus

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Summary

Children are engaged with mathematics in their everyday activities. Look around you – notice the children chanting numbers as they jump rope or haggling over their scores in handball. Children in urban centres in Brazil buy and sell goods (Carraher, Carraher and Schliemann 1985; Saxe 1991); toddlers in working and middle-class homes in the US play number games and sing number songs with their mothers (Saxe, Guberman and Gearhart 1987); inner-city teenage boys keep track of their statistics in league basketball play (Nasir 2002). Mathematics is interwoven in children's everyday collective activities, and yet the cognitive-developmental study of children's mathematics has often overlooked such activities as sites for analysis. The result is that treatments of development often do not capture adequately the role of children's participation in collective activities, nor the way that children themselves contribute to the mathematical norms, values and conventions that take form in collective life.

The purpose of the chapter is to present a conceptual framework for analysing the interplay between individual and collective activity in cognitive development, using mathematical cognition as an illustrative case. The framework is rooted in an assumption common to psychogenetic treatments, whether structural-developmental (Piaget 1970) or activity-theoretic (e.g. Leontiev 1981): new cognitive developments emerge as individuals create and accomplish goals in daily activities. In this chapter I present an exposition of the framework with particular attention to the ‘what?’, ‘how?’ and ‘why?’ of development.

Throughout the chapter, I limit my discussion of cognitive development to practices of quantification.

Type: Chapter
Information: Cognitive Developmental Change
Theories, Models and Measurement
, pp. 241 - 263

DOI: https://doi.org/10.1017/CBO9780511489938.009 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2005

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References

Butterworth, B. (1999). What counts: how every brain is hardwired for math. New York: The Free Press

Carraher, T. N., Carraher, D. W. and Schliemann, A. D. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology 3, 21–9CrossRef Google Scholar

Case, R. (1985). Intellectual development: birth to adulthood. New York: Academic Press

Case, R. (1992). The mind's staircase: exploring the conceptual underpinnings of children's thought and knowledge. Hillsdale, NJ: Erlbaum

Case, R., Okamoto, Y., Henderson, B. and McKeough, A. (1993). Analyzing diversity in developmental pathways: Methods and concepts. In R. Case and W. Edelstein (eds.) The new structuralism in cognitive development: theory and research on individual pathways (pp. 71–100). Contributions to Human Development, vol. 23. Basel: Karger

Case, R., Okamoto, Y., Griffin, S., McKeough, A., Bleiker, C., Henderson, B. and Stephenson, K. M. (1996). The role of central conceptual structures in the development of children's thought. Monographs of the Society for Research in Child Development, 61 (1–2), serial no. 246CrossRef

Cole, M. (1996). Cultural psychology: a once and future discipline. Cambridge, MA: Harvard University Press

Dasen, P. R. and de Ribaupierre, A. (1988). Neo-Piagetian theories: cross-cultural and differential perspectives. In A. Demetriou (ed.) The neo-Piagetian theories of cognitive development: toward an integration. North Holland: Elsevier

Dehaene, S. (1997). The number sense: how the mind creates mathematics. New York: Oxford

Demetriou, A., Christou, C., Spanoudis, G. and Platsidou, M. (2002). The development of mental processing: efficiency, working memory, and thinking. Monographs of the Society for Research in Child Development, 67(1), serial no. 263

Demetriou, A., Kui, Z. X., Spanoudis, G., Christou, C., Kyriakides, L. and Platsidou, M. (2003). The architecture and development of mental processing: Greek, Chinese, or universal? Unpublished manuscript. University of Cyprus

Gearhart, M., Saxe, G. B., Seltzer, M., Schlackman, J., Ching, C., Nasir, N., Fall, R., Bennett, T., Rhine, S. and Sloan, T. F. (1999). Opportunities to learn fractions in elementary mathematics classrooms. Journal for Research in Mathematics Education 30 (3): 286–315CrossRef Google Scholar

Karmiloff-Smith, A. (1995). Beyond modularity: a developmental perspective on cognitive science. Cambridge, MA: MIT Press

Leontiev, A. N. (1981). The problem of activity in psychology. In J. V. Wertsch (ed.) The concept of activity in Soviet psychology (pp. 37–71). New York: Sharpe

Modell, J. (1996). The uneasy engagement of ethnography and human development. In R. Jessor, A. Colby and R. A. Shweder (eds.) Ethnography and human development: context and meaning in social inquiry (pp. 479–504). Chicago: University of Chicago Press

Nasir, N. S. (2002). Identity, goals, and learning: mathematics in cultural practice. Mathematical Thinking and Learning, 4(2 and 3), 213–47CrossRef Google Scholar

Pascual-Leone, J. (1970). A mathematical model for the transition rule in Piaget's developmental stages. Acta Psychologica, 32, 301–45CrossRef Google Scholar

Pascual-Leone, J. (1988). Organismic processes for neo-Piagetian theories: a dialectical causal account of cognitive development. In A. Demetriou (ed.) The neo-Piagetian theories of cognitive development: towards an integration (pp. 25–64). Amsterdam: North-Holland

Piaget, J. (1965). The child's conception of number. New York, Norton

Piaget, J. (1970). Piaget's theory. In P. H. Mussen (ed.) Carmichael's manual of child psychology (pp. 703–31). New York: Wiley

Piaget, J. (1972). Intellectual evolution from adolescence to adulthood. Human Development, 15(1), 1–12CrossRef Google Scholar

Saxe, G. B. (1991). Culture and cognitive development: studies in mathematical understanding. Hillsdale, NJ: Lawrence Erlbaum Associates

Saxe, G. B. (1999). Cognition, development, and cultural practices. In E. Turiel (ed.) Culture and development: new directions in child psychology (pp. 19–35). San Francisco: Jossey-BassCrossRef

Saxe, G. B., Guberman, S. R. and Gearhart, M. (1987). Social processes in early number development. Monographs of the Society for Research in Child Development, 52(2), serial no. 216CrossRef

Saxe, G. B. and Esmonde, I. (in press). Making change in Oksapmin tradestores: studies in shifting practices of quantification under conditions of rapid social change. South Pacific Journal of Psychology

Saxe, G. B., Gearhart, M. and Seltzer, M. (1999). Relations between classroom practices and student learning in the domain of fractions. Cognition and Instruction, 17 (1), 1–24CrossRef Google Scholar

Saxe, G. B. and Guberman, S. R. (1998). Studying mathematics learning in collective activity. Learning and Instruction, 8(6), 489–501CrossRef Google Scholar

Siegler, R. S. and Crowley, K. (1991). The microgenetic method: a direct means for studying cognitive development. American Psychologist, 46, 606–20CrossRef Google Scholar PubMed

Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Harvard University Press

Vygotsky, L. S. (1986). Thought and language. Cambridge, MA: MIT Press

Vygotsky, L. S. (1987). Thinking and speech. New York: Plenum

Werner, H. and Kaplan, B. (1963). Symbol formation: an organismic-developmental approach to language and the expression of thought. New York: Wiley

Werner, H. and Kaplan, B. (1984). Symbol formation: an organismic-developmental approach to the psychology of language. Hillsdale, NJ: Lawrence Erlbaum Associates

Wertsch, J. V. (1985). Vygotsky and the social formation of mind. Cambridge, MA: Harvard University Press

Wertsch, J. V. (1991). Voices of the mind. Cambridge, MA: Harvard University Press