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Original Articles

THE NOVICE MATHEMATICIAN'S INQUIRY ABOUT NEW CONCEPTS: BESTOWING MEANING THROUGH AMBIVALENT USES OF GEOMETRICAL METAPHORS

Pages 57-68 | Published online: 12 Feb 2009

References

  • Balacheff , N. 1990 . ‘Beyond a psychological approach: the psychology of mathematics education’ . For the Learning of Mathematics , 10 ( 3 ) : 2 – 8 .
  • Brousseau , G. 1989 . ‘Le contrat cidactique: Le Milieu’ . Recherches en Didactique des Mathématiques , 9 ( 3 ) : 309 – 336 .
  • Burrell , G. and Morgan , G. 1979 . Sociological Paradigms and Organizational Analysis London : Heinemann .
  • Coulthard , M. 1985 . An Introduction to Discourse Analysis London : Longman .
  • Dubinsky , E. 1991 . “ ‘Reflective abstraction in advanced mathematical thinking’ ” . In Advanced Mathematical Thinking Edited by: Tall , D. 95 – 123 . Dordrecht/Boston/London : Kluwer Academic Publishers .
  • Foucault , M. 1973 . The Order of Things: An Archaeology of Human Sciences New York : Vintage Books .
  • Glaser , B. G. and Strauss , A. L. 1967 . The Discovery of Grounded Theory: Strategies for Qualitative Research New York : Aldine de Gruyter .
  • Hall , E. T. 1981/1959 . The Silent Language Doubleday, New York : Anchor Press .
  • Lacan , J. 1977 . Écrits: A Selection London : Routledge .
  • Nardi , E. 1994 . “ ‘Pathological cases of mathematical understanding’ ” . In Proceedings of the 18th International Conference for the Psychology of Mathematics Education Volume III , 336 – 343 . Lisbon, , Portugal
  • Nardi , E. 1995 . “ ‘The novice mathematician's encounter with mathematical abstraction: the case of accumulation point’ ” . In European Research Conference on the Psychology of Mathematics Education 54 – 57 . Osnabrück, , Germany
  • Nardi , E. 1996a . “ The Novice Mathematician's Encounter With Mathematical Abstraction: Tensions in Concept-Image Construction and Formalisation ” . In Unpublished doctoral thesis Oxford : University of Oxford .
  • Nardi , E. 1996b . “ ‘Tensions in the novice mathematician's induction to mathematical abstraction’ ” . In Proceedings of the 20th International Conference for the Psychology of Mathematics Education Volume IV , 51 – 57 . Valencia, , Spain
  • Nardi , E. 1997 . ‘The novice mathematician's encounter with mathematical abstraction: a concept image of spanning sets in vectorial analysis’ . Educacion Matematica , 9 ( 1 ) Grupo Editorial Iberoamerica, Mexico.
  • Sfard , A. 1994 . ‘Reification as the birth of metaphor’ . For the Learning of Mathematics , 14 ( 1 ) : 44 – 55 .
  • Sfard , A. and Linchevski , L. 1994 . ‘The gains and the pitfalls of reification: the case of algebra’ . Educational Studies in Mathematics , 26 : 191 – 228 .
  • Sierpinska , A. 1994 . Understanding in Mathematics London : The Falmer Press .
  • Tall , D. and Vinner , S. 1981 . ‘Concept image and concept definition in mathematics with particular reference to limits and continuity’ . Educational Studies in Mathematics , 12 : 151 – 169 .
  • Vinner , S. 1983 . ‘Concept definition, concept image and the notion of function’ . International Journal of Mathematics Education in Science and Technology , 14 ( 3 ) : 293 – 305 .
  • Vinner , S. 1991 . “ ‘The role of definitions in the teaching and learning of mathematics’ ” . In Advanced Mathematical Thinking Edited by: Tall , D. 65 – 81 . Dordrecht : Kluwer Academic Publishers .
  • Vygotsky , L. S. 1986 . Thought and Language Cambridge, MA : MIT Press .

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