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Cognitive Play and Mathematical Learning in Computer Microworlds

Chapter

Abstract

Based on the constructivist principle of active learning, we focus on children’s transformation of their cognitive play activity into what we regard as independent mathematical activity. We analyze how, in the process of this transformation, children modify their cognitive play activities. For such a modification to occur, we argue that the cognitive play activity has to involve operations of intelligence which yield situations of mathematical schemes.

We present two distinctly different cases. If the first case, the medium of the cognitive play activity was a discrete computer microworld. We illustrate how two children transformed the playful activity of making pluralities into situations of their counting schemes. In the second case, the medium was a continuous microworld. We illustrate two children’s transformation of the playful activity of making line segments (“sticks”) into situations of their counting schemes. We explain one child’s transformation as a generalizing assimilation because it was immediate and powerful. The transformation made by the other child was more protracted, and social interaction played a prominent role. We specify several types of accommodations induced by this social interaction, accommodations we see as critical for understanding active mathematics learning. Finally, we illustrate how a playful orientation of independent mathematical activity can be inherited from cognitive play.

Keywords

Number Sequence Teaching Session Mathematical Activity Counting Scheme Segmented Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bickhard, M.: 1992, “How does the environment affect the person?”, in L. T. Winegar, J. Valsiner (eds.), Children’s Development Within Social Contexts: Metatheoretical, Theoretical, and Methodological Issues, Lawrence Erlbaum, Hillsdale, NJ, pp. 63–92.Google Scholar
  2. Cobb, P., Wood, T., Yackel, E.: 1990, “Classrooms as learning environments for teachers and researchers”, in R. B. Davis, C. A. Maher, N. Noddings (eds.), Constructivist Views on the Teaching and Learning of Mathematics, National Council of Teachers of Mathematics, Reston, VA, pp. 125–146.Google Scholar
  3. Cooper, R. G. Jr.: 1991, “The role [of] mathematical transformations and practice in mathematical development”, in L. P. Steffe (ed.), Epistemological Foundations of Mathematical Experience, Springer, New York, pp. 102–123.CrossRefGoogle Scholar
  4. Hilgard, E. R., Bower, G. H.: 1966, Theories of Learning, Appleton-Century-Crofts, New York.Google Scholar
  5. Kieren T. E., Pirie S.: this volume, “Growth in mathematical understanding: How can we characterize it and how can we represent it?” Educational Studies in Mathematics.Google Scholar
  6. Marton, F., Neuman D.T: 1990, “Constructivism, phenomenology, and the origin of arithmetic skills”, in L. P. Steffe, T. Wood (eds.), Transforming Children’s Mathematics Education: International Perspectives, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 62–75.Google Scholar
  7. Papert, S: 1980, Mindstorms: Children, Computers, and Powerful Ideas, Basic Books, New York.Google Scholar
  8. Piaget, J.: 1962, Play, Dreams and Imitation in Childhood (Translated by C. Gattegno and F. M. Hodgson), W. W. Norton & Company, New York.Google Scholar
  9. Piaget, J.: 1980, “The psychogenesis of knowledge and its epistemological significance”, in M. Piattelli-Palmarini (ed.), Language and Learning: The Debate Between Jean Piaget and Noam Chomsky, Harvard University Press, Cambridge, MA, pp. 23–34.Google Scholar
  10. Sinclair, H.: 1990, “Learning: The interactive recreation of knowledge”, in L. P. Steife,T. Wood (eds.), Transforming Children’s Mathematics Education: International Perspectives, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 19–29.Google Scholar
  11. Steffe, L. P.: 1988, “Modifications of the counting scheme”, in L. P. Steffe and P. Cobb, Construction of Arithmetical Meanings and Strategies, Springer, New York, pp. 284–322.Google Scholar
  12. Steffe, L. P.: 199la, “Operations that generate quantity”, Learning and Individual Differences 3(1), 61–82.Google Scholar
  13. Steffe, L. P.: 1991b, “The constructivist teaching experiment: Illustrations and implications”, in E. von Glasersfeld (ed.), Radical Constructivism in Mathematics Education, Kluwer Academic Publishers, Boston, MA., pp. 177–194.Google Scholar
  14. Steffe, L. P.: 1991c, “The learning paradox: a plausible counterexample”, in L. P. Steffe (ed.), Epistemological Foundations of Mathematical Experience, Springer, New York, pp. 26 11.Google Scholar
  15. Steffe, L. P.: 1992, “Schemes of action and operation involving composite units”, Learning and Individual Differences 4 (3), 259–309.CrossRefGoogle Scholar
  16. Steffe L. P., Cobb, P.: 1988, Construction of Arithmetical Meanings and Strategies, Springer, New York.CrossRefGoogle Scholar
  17. Steife, L. P., von Glasersfeld, E.: 1985, Child Generated Multiplying and Dividing Schemes: A Teaching Experiment. NSF Grant No. MD-8550463.Google Scholar
  18. Steife, L. P., von Glasersfeld, E., Richards, J., Cobb, R: 1983, Children’s Counting Types: Philosophy, Theory, and Application, Praeger, New York.Google Scholar
  19. Thompson, P.: 1991, “To experience is to conceptualize: A discussion of epistemology and mathematical experience”, in L. P. Steffe (ed.), Epistemological Foundations of Mathematical Experience, Springer, New York, pp. 260–281.CrossRefGoogle Scholar
  20. Von Glasersfeld, E.: 1981, “An attentional model for the conceptual construction of units and number”. Journal for Research in Mathematics Education 12 (2), 83–94.CrossRefGoogle Scholar
  21. Von Glasersfeld, E.: 1983, “Learning as constructive activity”, in J. C. Bergeron, N. Herscovics (eds.), Proceedings of the Fifth Annual Meeting of PME-NA, Université de Montreal, Montreal, Canada, pp. 41–63.Google Scholar
  22. Von Glasersfeld, E.: 1989, “Constructivism in education”, in T. Husen, N. Postlethwaite (eds.), The International Encyclopedia of Education, Pergamon Press, Oxford, pp. 162163.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  1. 1.Department of Mathematics EducationUniversity of GeorgiaAthensUSA

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