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.
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References
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.
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.
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.
Hilgard, E. R., Bower, G. H.: 1966, Theories of Learning, Appleton-Century-Crofts, New York.
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.
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.
Papert, S: 1980, Mindstorms: Children, Computers, and Powerful Ideas, Basic Books, New York.
Piaget, J.: 1962, Play, Dreams and Imitation in Childhood (Translated by C. Gattegno and F. M. Hodgson), W. W. Norton & Company, New York.
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.
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.
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.
Steffe, L. P.: 199la, “Operations that generate quantity”, Learning and Individual Differences 3(1), 61–82.
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.
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.
Steffe, L. P.: 1992, “Schemes of action and operation involving composite units”, Learning and Individual Differences 4 (3), 259–309.
Steffe L. P., Cobb, P.: 1988, Construction of Arithmetical Meanings and Strategies, Springer, New York.
Steife, L. P., von Glasersfeld, E.: 1985, Child Generated Multiplying and Dividing Schemes: A Teaching Experiment. NSF Grant No. MD-8550463.
Steife, L. P., von Glasersfeld, E., Richards, J., Cobb, R: 1983, Children’s Counting Types: Philosophy, Theory, and Application, Praeger, New York.
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.
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.
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.
Von Glasersfeld, E.: 1989, “Constructivism in education”, in T. Husen, N. Postlethwaite (eds.), The International Encyclopedia of Education, Pergamon Press, Oxford, pp. 162163.
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© 1994 Springer Science+Business Media Dordrecht
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Steffe, L.P., Wiegel, H.G. (1994). Cognitive Play and Mathematical Learning in Computer Microworlds. In: Cobb, P. (eds) Learning Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2057-1_1
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DOI: https://doi.org/10.1007/978-94-017-2057-1_1
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