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Original Articles

Representing numbers: prime and irrational

Pages 207-217 | Received 20 Jul 2004, Published online: 20 Feb 2007

References

References

  • Tall , D and Vinner , S . 1981 . Concept image and concept definition in mathematics with particular reference to limts and continuity . Educational Studies in Mathematics , 12 : 151
  • Zazkis , R and Liljedahl , P . 2004 . Understanding primes: The role of representation . Journal for Research in Mathematics Education , 35 ( 3 ) : 164
  • Lesh R Behr M Post M 1987 Rational number relations and proportions In: C. Janvier (Ed.) Problems of Representation in the Teaching and Learning of Mathematics Hillsdale NJ Lawrence Erlbaum Associates pp. 41–58
  • Zazkis R Gadowsky K 2001 Attending to transparent features of opaque representations of natural numbers In: A. Cuoco (Ed.) The Roles of Representation in School Mathematics Reston VA NCTM pp. 146–165
  • Zazkis R Sirotic N 2004 Making sense of irrational numbers: Focusing on representation Proceedings of 28th International Conference for Psychology of Mathe-matics Education 4 Bergen Norway pp. 497–505
  • Cuoco A (Ed.) 2001 The Roles of Representation in School Mathematics Reston VA NCTM
  • Goldin G Janvier C (Eds) 1998 Representations and the psychology of mathematics education, Parts I and II. Special Issue Journal of Mathematical Behavior 17 1 2
  • Skemp R 1986 The Psychology of Learning Mathematics 2nd Edn New York Penguin
  • Sirotic N Zazkis R 2004 Irrational numbers: Dimensions of knowledge Proceedings of the North American Chapter Conference for Psychology of Mathematics Education Toronto pp. 171–177
  • Lamon SJ 2001 Presenting and representing: From fractions to rational numbers In: A. Cuoco (Ed.) The Roles of Representation in School Mathematics Reston VA NCTM pp. 41–52
  • Friedlander A Tabach M 2001 Promoting multiple representations in algebra In: A. Cuoco (Ed.) The Roles of Representation in School Mathematics Reston VA NCTM pp. 173–184
  • Janvier C 1987 Representation and understanding: The notion of function as an example In: C. Janvier (Ed.) Problems of Representation in the Teaching and Learning of Mathematics Hillsdale NJ Lawrence Erlbaum Associates pp. 67–72
  • Even , R . 1998 . Factors involved in linking representation of functions . Journal of Mathematical Behavior , 17 ( 1 ) : 105
  • Kaput J 1991 Notations and representations as mediators of constructive processes In: E. von Glasersfeld (Ed.) Radical Constructivism in Mathematics Education Dordrecht Kluwer Academic pp. 53–74
  • Dubinsky E 1991 Reflective abstraction in advanced mathematical thinking In: D. Tall (Ed.) Advanced Mathematical Thinking Boston Kluwer pp. 95–123
  • Sfard , A . 1991 . On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin . Educational Studies in Mathematics , 22 : 1 – 36 .
  • Rissland EL 1991 Example-based reasoning In: J.F. Voss, D.N. Parkins and J.W. Segal (Eds) Informal Reasoning in Education, Lawrence Erlbaum Associates pp. 187–208
  • Mason , J and Pimm , D . 1984 . Generic examples: Seeing the general in the particular . Educational Studies in Mathematics , 15 : 277
  • Lakoff G 1987 Women, Fire and Dangerous Things Chicago University of Chicago Press
  • Mason J Burton L Stacey K 1982 Thinking Mathematically Wokingham UK Addison-Wesley
  • Pólya G 1973 How to Solve it? 2nd Edn Princeton NJ Princeton University Press
  • Hazzan , O . 1999 . Reducing abstraction level when learning abstract algebra . Educational Studies in Mathematics , 40 : 71
  • Zazkis , R and Campbell , S . 1996 . Prime decomposition: Understanding uniqueness . Journal of Mathematical Behavior , 15 : 207
  • Sirotic N 2004 An inquiry into prospective teachers’ understanding of irrational numbers Unpublished M.Sc. Thesis Simon Fraser University Canada
  • Zazkis , R . 1998 . Odds and ends of odds and evens: An inquiry into students' understanding of even and odd numbers . Educational Studies in Mathematics , 36 : 73
  • Watson A Mason J in press Learners Generating Examples, Lawrence: Erlbaum

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