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Educational Studies in Mathematics

, Volume 23, Issue 1, pp 31–57 | Cite as

A pedagogy for mathematical microworlds

  • Celia Hoyles
  • Richard Noss
Article

Abstract

In this paper we attempt to map out some relationships between pedagogy and student behaviour in a mathematical microworld. We illustrate our analysis by a series of episodes which occurred in a Logo-based microworld constructed around the notions of ratio and proportion. We explore the patterns of pedagogy associated with on and off-computer activities and suggest how the teacher has significant roles in both settings; particularly in helping pupils to bridge the discursive disjuncture between the practices of Logo- and schoolmathematics.

Keywords

Significant Role Student Behaviour Mathematical Microworld 
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. Balacheff, N.: 1991, ‘Treatment of refutations: Aspects of the complexity of a constructivist approach to mathematics learning’, in VonGlasersfeld, E. (ed), Radical Constructivism in Mathematics Education, Kluwer, Dordrecht, pp. 89–110.Google Scholar
  2. Bell, A., Greer, B., Grimson, L. and Mangan, C.: 1989, ‘Children's performance on multiplicative word problems: Elements of a descriptive theory’, Journal of Research in Mathematics Education 20(5), 434–449.Google Scholar
  3. Carraher, T. N., Schliemann, A. D. and Carraher, D. W.: 1988, ‘Mathematical concepts in everyday life’, in Saxe, G. B. and Gearhart (eds.), Children's Mathematics, Jossey-Bass, San Franciso, pp. 71–87.Google Scholar
  4. Edwards, L.: 1991, ‘A Logo microworlds of transformation geometry’, in Hoyles, C. and Noss, R. (eds.), Learning Mathematics and Logo, MIT Press, Cambridge.Google Scholar
  5. Hillel, J. and Kieran, C.: 1987, ‘Schemas used by 12-year-olds in solving selected turtle geometry tasks’, Recherches en Didactique des Mathematiques 8(1,2), 61–102.Google Scholar
  6. Hoyles, C. and Noss, R.: 1987a, ‘Synthesising mathematical conceptions and their formalisation through the construction of a Logo-based school mathematics curriculum, International Journal of Mathematics Education in Science and Technology 18(4), 581–595.Google Scholar
  7. Hoyles, C. and Noss, R.: 1987b, ‘Children working in a structured Logo environment: From doing to understanding’, Recherches en Didactique de Mathematiques 8(1.2), 132–174.Google Scholar
  8. Hoyles, C. and Noss, R.: 1989. The Computer as a catalyst in children's proportion strategies’, Journal of Mathematical Behaviour 8, 53–75.Google Scholar
  9. Hoyles, C. and Noss, R.: 1991, ‘Deconstructing microworlds’, in Ferguson, D. L. (ed.), Advanced Technologies in the Teaching of Mathematics and Science, Springer-Verlag, Berlin.Google Scholar
  10. Hoyles, C. and Sutherland, R.: 1989, Logo Mathematics in the Classroom, Routledge, London.Google Scholar
  11. Hoyles, C.: 1987, ‘Tools for learning — insights for the mathematics educator from a Logo programming environment’, For the Learning of Mathematics 7(2), 32–37.Google Scholar
  12. Hoyles, C., Noss, R. and Sutherland, R.: 1991, ‘The ratio and proportion microworld’, Final Report of the Microworlds Project, Volume III, Institute of Education, University of London.Google Scholar
  13. Hoyles, C., Noss, R. and Sutherland, R. (eds.): 1986, Proceedings of the Second International Conference for Logo and Mathematics Education, Institute of Education, University of London.Google Scholar
  14. Lave, J.: 1988, Cognition in Practice, Cambridge University Press, Cambridge.Google Scholar
  15. Noss, R.: 1991, ‘The social shaping of computing in mathematics education’, in Pimm, D. and Love, E. (eds.), The Teaching and Learning of School Mathematics, Hodder & Stoughton.Google Scholar
  16. Noss, R. and Hoyles, C.: 1991, ‘Looking back and looking forward’, in Hoyles, C. and Noss, R. (eds.), Learning Mathematics and Logo, MIT Press, Cambridge.Google Scholar
  17. Noss, R., Sutherland, R. and Hoyles, C.: 1991, ‘Teacher attitudes and interactions’, Final Report of the Microworlds Project, Volume 2, Institute of Education, University of London.Google Scholar
  18. Papert, S.: 1980, Mindstorms, Basic Books, NY.Google Scholar
  19. Thompson, P.: 1987, ‘Mathematical microworlds and intelligent computer assisted instruction’, in Kearsley, G. E. (ed.), Artificial Intelligence and Instruction: Applications and Methods, Addison-Wesley, pp. 83–109.Google Scholar
  20. Vergnaud, G.: 1982, ‘Cognitive and developmental psychology and research in mathematical education: Some theoretical and methodological issues’, For the Learning of Mathematics 3(2), 31–41.Google Scholar
  21. Weir, S.: 1987, Cultivating Minds: A Logo Casebook, Harper and Row, New York.Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Celia Hoyles
    • 1
  • Richard Noss
    • 1
  1. 1.Department of Mathematics, Statistics & Computing Institute of EducationUniversity of LondonLondonUK

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