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.
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References
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.
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.
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.
Edwards, L.: 1991, ‘A Logo microworlds of transformation geometry’, in Hoyles, C. and Noss, R. (eds.), Learning Mathematics and Logo, MIT Press, Cambridge.
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.
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.
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.
Hoyles, C. and Noss, R.: 1989. The Computer as a catalyst in children's proportion strategies’, Journal of Mathematical Behaviour 8, 53–75.
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.
Hoyles, C. and Sutherland, R.: 1989, Logo Mathematics in the Classroom, Routledge, London.
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.
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.
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.
Lave, J.: 1988, Cognition in Practice, Cambridge University Press, Cambridge.
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.
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.
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.
Papert, S.: 1980, Mindstorms, Basic Books, NY.
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.
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.
Weir, S.: 1987, Cultivating Minds: A Logo Casebook, Harper and Row, New York.
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Hoyles, C., Noss, R. A pedagogy for mathematical microworlds. Educ Stud Math 23, 31–57 (1992). https://doi.org/10.1007/BF00302313
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DOI: https://doi.org/10.1007/BF00302313