Abstract
Structuralist models of cognition emphasize the role of reasoning principles, invariants, or rules in the organization of thinking and pay little attention to the culturally developed systems of signs and their impact on thinking. However, complex psychological functions, as pointed out by Vygotsky (1962) and Luria (1979), are always carried out with the mediation of historically developed and culturally transmitted systems of signs. Within this perspective, systems of signs have a major role in thinking because they are central to reasoning processes. This chapter presents research that supports the hypothesis that systems of signs play a structuring role in problem-solving activities as they are used to support skilled action.
Two sorts of empirical findings are reviewed. The first line of work analyzes how cultural practices that rely on diverse systems of signs affect their users’ performance as they solve mathematical problems. The second line of work is experimental and examines how the use of different measurement systems affects children’s problem-solving performance. The results reported here suggest that schools need to consider carefully the systems of signs that they select for transmission in school, in terms of both the difficulties they create for learners and their power as tools for thought.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brown, J. S., & Burton, R. R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science., 155–192.
Carraher, T. N. (1985). Exploracoes sobre o desenvolvimento da competencia ortografica em Portugues. [Exploring the development of spelling in Portuguese] Psicologia: Teoria e Pesquisa., 269–285.
Carraher, T. N. (1986). From drawings to buildings: Working with mathematical scales. International Journal of Behavioral Development., 527–544.
Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British Journal of Developmental Psychology., 21–29.
Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1987). Written and oral mathematics. Journal for Research in Mathematics Education, 1., 83–97.
Dickson, L. (1989). Area of a rectangle. In D. C. Johnson (Ed.), Children’s mathematical frameworks 8–13: A study of classroom teachin. (pp. 89–125). Windsor, England: NFER-Nelson Publishing Company.
Douady, R., & Perrin-Glorian, M. J. (1989). Un processus d’apprentissage du concept d’aire de surface plaine [A teaching experience on the concept of the area of a plane surface]. Educational Studies in Mathematics, 2., 387–424.
Gardner, H. (1993). Multiple intelligences: The theory in practice. New York: Basic Books.
Gay, J., & Cole, M. (1967). The new mathematics and an old culture: A study of learning among the Kpelle of Liberia. New York: Holt, Rinehart & Winston.
Grando, N. (1988): A matematica no meio rural: Pequenos agricultures, estudantes e professore. [Mathematics in the rural area: Farmers, students, and teachers]. M.A. Thesis, Mestrado em Psicologia, Universidade Federal de Pernambuco.
Hatano, G. (in press). Learning arithmetic with an abacus. In T. Nunes & P. E. Bryant (Eds.), Teaching and learning mathematics: International perspectives. Falmer, England: Lawrence Erlbaum.
Hughes, M. (1983). What is difficult about learning arithmetic? In M. Donaldson, R. Grieve, & C. Pratt (Eds.), Early childhood development and educatio. (pp. 204–221). Oxford, England: Blackwell.
Lave, J. (1988). Cognition in practice. Mind, mathematics and culture in everyday life. Cambridge, England: Cambridge University Press.
Lawler, R. W. (1990). Constructing knowledge from interactions. In L. P. Steffe & T. Wood (Eds.), Transforming children’s mathematics education. International perspective. (pp. 47–51). Hillsdale, NJ: Lawrence Erlbaum.
Light, P. & Perret-Clermont, A.-N. (1989) Social context effects in learning and testing. In A. Gellatly, D. Rogers, and J. Sloboda (Eds.), Cognition and social world. (pp 99–112). Oxford, England: Clarendon Press.
Luria, A. (1979). Curso de Psicologia Gera. [Course of General Psychology]. Rio de Janeiro: Civilizacao Brasileira.
Nunes, T. (1993). Learning mathematics: Perspectives from everyday life. In R. B. Davis & C. A. Maher (Eds.), Schools, mathematics, and the world of realit. (pp. 61–78). Needham Heights, MA: Allyn and Bacon.
Nunes, T. (1995). Cultural practices and the conception of individual differences. Theoretical and empirical contradictions. New Directions for Child Development, 6., 91–103.
Nunes, T. (1994). Street intelligence. In R. Sternberg (Ed.), Encyclopedia of Intelligence. New York: MacMillan.
Nunes, T., Light, P., & Mason, J. (1993). Tools for thought: The measurement of length and area. Learning and Instruction., 39–54.
Nunes, T., Light, P., Mason, J., & Allerton, M. (1994). Children’s understanding of the concept of area. Research report prepared for the Economic and Social Research Council (ESRC), Institute of Education, University of London.
Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. New York: Cambridge University Press.
Piaget, J. (1962). Play, dreams and imitation in childhood. New York: Norton.
Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child’s conception of geometry. London: Routledge and Kegan Paul.
Plunkett, S. (1979). Decomposition and all that rot. Mathematics in Schools., 2–7.
Reed, H. J., & Lave, J. (1981). Arithmetic as a tool for investigating relations between culture and cognition. In R.W. Casson (Ed.), Language, culture, and cognition: Anthropological perspective. (pp. 437–455). New York: MacMillan.
Schliemann, A. D. (1984). Mathematics among carpenters and apprentices. In P. Damerow, M. W. Dunckley, B. F. Nebres, & B. Werry (Eds.), Mathematics for al. (pp. 92–95). Paris: UNESCO.
Thurstone, L. L. (1938). Primary mental abilities. Psychometric Monograph., 1 (whole no.).
Vergnaud, G. (1983). Multiplicative structures. In R. Lesh and M. Landau (Eds.) Acquisition of mathematics concepts and processe. (pp 128–175). London, England: Academic Press.
Vygotsky, L.S. (1962). Thought and language. Cambridge, MA: MIT Press.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Nunes, T. (1997). What Organizes Our Problem-Solving Activities?. In: Resnick, L.B., Säljö, R., Pontecorvo, C., Burge, B. (eds) Discourse, Tools and Reasoning. NATO ASI Series, vol 160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03362-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-662-03362-3_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08337-2
Online ISBN: 978-3-662-03362-3
eBook Packages: Springer Book Archive