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Volumn 1, Issue 2, 1996, Pages 139-168

A critique of the selection of "mathematical objects" as a central metaphor for advanced mathematical thinking

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EID: 0002993649     PISSN: 13823892     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00571076     Document Type: Article
Times cited : (12)

References (49)
  • 2
    • 27844532431 scopus 로고
    • The importance and limits of epistemological work in didactics
    • W. Geeslin and K. Graham (Eds.), Durham, NH
    • Artigue, M. (1992). The importance and limits of epistemological work in didactics. In W. Geeslin and K. Graham (Eds.), Sixteenth Psychology of Mathematics Education, vol. 3 (pp. 195-216). Durham, NH.
    • (1992) Sixteenth Psychology of Mathematics Education , vol.3 , pp. 195-216
    • Artigue, M.1
  • 4
    • 0001141148 scopus 로고
    • Les obstacles epistemolgiques et les problemes en mathematiques
    • Brousseau, G. (1983). Les obstacles epistemolgiques et les problemes en mathematiques. Recherche in Didactiques des Matematiques 4(2): 164-198.
    • (1983) Recherche in Didactiques des Matematiques , vol.4 , Issue.2 , pp. 164-198
    • Brousseau, G.1
  • 5
    • 26444602947 scopus 로고
    • Concepts fondamentaux de didactique: Perspectives apportees par une perspective anthropologique
    • Plestin les Greves, France
    • Chevallard, Y. (1991). Concepts fondamentaux de didactique: Perspectives apportees par une perspective anthropologique. In Lecture at the VIeme Ecole d'Ete de didactique des mathematiques. Plestin les Greves, France.
    • (1991) Lecture at the VIeme Ecole D'Ete de Didactique des Mathematiques
    • Chevallard, Y.1
  • 7
    • 84970241366 scopus 로고
    • A review of the research on student conceptions in mathematics, science and programming
    • C. Cazden (Ed.), Washington, DC: American Education Research Association
    • Confrey, J. (1990). A review of the research on student conceptions in mathematics, science and programming. In C. Cazden (Ed.), Review of Research in Education (pp. 3-56). Washington, DC: American Education Research Association.
    • (1990) Review of Research in Education , pp. 3-56
    • Confrey, J.1
  • 8
    • 0001311877 scopus 로고
    • Splitting, similarity, and rate of change: New approaches to multiplication and exponential functions
    • G. Harel and J. Confrey (Eds.), Albany, NY: State University of New York Press
    • Confrey, J. (1994a). Splitting, similarity, and rate of change: New approaches to multiplication and exponential functions. In G. Harel and J. Confrey (Eds.), The Development of Multiplicative Reasoning in the Learning of Mathematics (pp. 293-332). Albany, NY: State University of New York Press.
    • (1994) The Development of Multiplicative Reasoning in the Learning of Mathematics , pp. 293-332
    • Confrey, J.1
  • 9
    • 0037548806 scopus 로고
    • A theory of intellectual development, Part I
    • Confrey, J. (1994b). A theory of intellectual development, Part I. For the Learning of Mathematics 14(3, November): 2-8.
    • (1994) For the Learning of Mathematics , vol.14 , Issue.3 NOVEMBER , pp. 2-8
    • Confrey, J.1
  • 10
    • 0038699963 scopus 로고
    • Student voice in examining "splitting" as an approach to ratio, proportion, and fractions
    • L. Meira and D. Carraher (Eds.), Recife, Brazil: Universidade Federal de Pernambuco
    • Confrey, J. (1995). Student voice in examining "splitting" as an approach to ratio, proportion, and fractions. In L. Meira and D. Carraher (Eds.), Proceedings of the Nineteenth International Conference for the Psychology of Mathematics Education, vol. 1 (pp. 3-29). Recife, Brazil: Universidade Federal de Pernambuco.
    • (1995) Proceedings of the Nineteenth International Conference for the Psychology of Mathematics Education , vol.1 , pp. 3-29
    • Confrey, J.1
  • 11
    • 0009644368 scopus 로고
    • Splitting reexamined: Results from a three-year longitudinal study of children in grades three to five
    • D. T. Owens, M. K. Reed and G. M. Millsaps (Eds.), Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education
    • Confrey, J. and Scarano, G. H. (1995). Splitting reexamined: Results from a three-year longitudinal study of children in grades three to five. In D. T. Owens, M. K. Reed and G. M. Millsaps (Eds.), Proceedings of the Seventeenth Annual Meeting for the Psychology of Mathematics Education-NA, vol. 1 (pp. 421-426). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
    • (1995) Proceedings of the Seventeenth Annual Meeting for the Psychology of Mathematics Education-NA , vol.1 , pp. 421-426
    • Confrey, J.1    Scarano, G.H.2
  • 12
    • 0347681495 scopus 로고
    • Limits
    • D. Tall (Ed.), Dordrecht: Kluwer Academic Publishers
    • Cornu, B. (1991). Limits. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 153-166). Dordrecht: Kluwer Academic Publishers.
    • (1991) Advanced Mathematical Thinking , pp. 153-166
    • Cornu, B.1
  • 13
    • 84865918050 scopus 로고
    • "Our" notation from their quarrel: The Leibniz-Newton controversy as embodied in calculus textbooks
    • Paper presented October. Minneapolis, MN
    • Costa, S. (1995). "Our" notation from their quarrel: The Leibniz-Newton controversy as embodied in calculus textbooks. Paper presented at the History of Science Society Annual Meeting, October. Minneapolis, MN.
    • (1995) History of Science Society Annual Meeting
    • Costa, S.1
  • 15
    • 26444530519 scopus 로고
    • Functions of a curve: Leibniz's original notion of functions and its meaning for the parabola
    • Dennis, D. and Confrey, J. (1995). Functions of a curve: Leibniz's original notion of functions and its meaning for the parabola. The College Mathematics Journal 26(3, May): 124-131.
    • (1995) The College Mathematics Journal , vol.26 , Issue.3 MAY , pp. 124-131
    • Dennis, D.1    Confrey, J.2
  • 16
    • 0342826636 scopus 로고    scopus 로고
    • The creation of continuous exponents: A study of the methods and epistemology of Alhazen and Wallis
    • in press J. Kaput and E. Dubinsky (Eds.), Providence, RI: American Mathematical Society
    • Dennis, D. and Confrey, J. (in press). The creation of continuous exponents: A study of the methods and epistemology of Alhazen and Wallis. In J. Kaput and E. Dubinsky (Eds.), Research in Collegiate Mathematics Education II Providence, RI: American Mathematical Society.
    • Research in Collegiate Mathematics Education II
    • Dennis, D.1    Confrey, J.2
  • 17
    • 26444494022 scopus 로고
    • Rethinking functions: Cartesian constructions
    • S. Hills (Ed.), Queens University: Kingston Ontario: The Mathematics, Science, Technology and Teacher Education Group
    • Dennis, D., Smith, E. and Confrey, J. (1992). Rethinking functions: Cartesian constructions. In S. Hills (Ed.), Second International Conference on the History and Philosophy of Science in Science Education, vol. 2 (pp. 449-466). Queens University: Kingston Ontario: The Mathematics, Science, Technology and Teacher Education Group.
    • (1992) Second International Conference on the History and Philosophy of Science in Science Education , vol.2 , pp. 449-466
    • Dennis, D.1    Smith, E.2    Confrey, J.3
  • 20
    • 0002505346 scopus 로고
    • Computer use and views of the mind
    • C. Keitel and K. Ruthven (Eds.), New York: Springer-Verlag
    • Dorfler, W. (1993). Computer use and views of the mind. In C. Keitel and K. Ruthven (Eds.), Learning from Computers: Mathematics Education and Technology (pp. 159-186). New York: Springer-Verlag.
    • (1993) Learning from Computers: Mathematics Education and Technology , pp. 159-186
    • Dorfler, W.1
  • 21
    • 0037699863 scopus 로고
    • Tool, object, setting, window: Elements for analysing and constructing didactical situations in mathematics
    • A. J. Bishop and S. Mellin-Olsen (Eds.), Dordrecht: Kluwer Academic Publishers
    • Douady, R. (1991). Tool, object, setting, window: Elements for analysing and constructing didactical situations in mathematics. In A. J. Bishop and S. Mellin-Olsen (Eds.), Mathematical Knowledge: Its Growth Through Teaching Dordrecht: Kluwer Academic Publishers.
    • (1991) Mathematical Knowledge: Its Growth through Teaching
    • Douady, R.1
  • 22
    • 0002573795 scopus 로고
    • Reflective abstraction in advanced mathematical thinking
    • D. Tall (Ed.), Dordrecht: Kluwer Academic Publishers
    • Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 95-126). Dordrecht: Kluwer Academic Publishers.
    • (1991) Advanced Mathematical Thinking , pp. 95-126
    • Dubinsky, E.1
  • 23
    • 0002370194 scopus 로고
    • The nature of the process conception of function
    • G. Harel and E. Dubinsky (Eds.), Washington, DC: Mathematical Association of America
    • Dubinsky, E. and Harel, G. (1992). The nature of the process conception of function. In G. Harel and E. Dubinsky (Eds.), The Concept of Function Washington, DC: Mathematical Association of America.
    • (1992) The Concept of Function
    • Dubinsky, E.1    Harel, G.2
  • 25
    • 0003884779 scopus 로고
    • Washington, DC: Mathematical Assocation of America
    • Harel, G. and Dubinsky, E. (Eds.). (1992). The Concept of Function. Washington, DC: Mathematical Assocation of America.
    • (1992) The Concept of Function
    • Harel, G.1    Dubinsky, E.2
  • 26
    • 0002801627 scopus 로고
    • Microworlds/schoolworlds: The transformation of an innovation
    • C. Keitel and K. Ruthven (Eds.), New York: Springer-Verlag
    • Hoyles, C. (1993). Microworlds/schoolworlds: The transformation of an innovation. In C. Keitel and K. Ruthven (Eds.), Learning from Computers: Mathematics Education and Technology New York: Springer-Verlag.
    • (1993) Learning from Computers: Mathematics Education and Technology
    • Hoyles, C.1
  • 27
    • 26444592870 scopus 로고
    • Out of the cul-de-sac?
    • J. R. Becker and B. J. Pence (Eds.), Pacific Grove, CA: Center for Mathematics & Computer Science Education, San Jose State University
    • Hoyles, C. and Noss, R. (1993). Out of the cul-de-sac? In J. R. Becker and B. J. Pence (Eds.), Proceedings of the Fifteenth Annual Meeting of the Psychology of Mathematics Education-NA, vol. 1 (pp. 83-90). Pacific Grove, CA: Center for Mathematics & Computer Science Education, San Jose State University.
    • (1993) Proceedings of the Fifteenth Annual Meeting of the Psychology of Mathematics Education-NA , vol.1 , pp. 83-90
    • Hoyles, C.1    Noss, R.2
  • 28
    • 3843119222 scopus 로고
    • The historical dimension of mathematical understanding - Objectifying the subjective
    • J. P. daPonte and J. F. Matos (Eds.), Lisbon, Portugal: University of Lisbon
    • Jahnke, H. N. (1994). The historical dimension of mathematical understanding - objectifying the subjective. In J. P. daPonte and J. F. Matos (Eds.), Proceedings of the Eighteenth International Conference of the Psychology of Mathematics Education, vol. 1 (pp. 139-156). Lisbon, Portugal: University of Lisbon.
    • (1994) Proceedings of the Eighteenth International Conference of the Psychology of Mathematics Education , vol.1 , pp. 139-156
    • Jahnke, H.N.1
  • 29
    • 0011447216 scopus 로고
    • A renaissance of Empiricism in the recent philosophy of mathematics?
    • T. Tymockzko (Ed.)
    • Lakatos, I. (1984). A renaissance of Empiricism in the recent philosophy of mathematics? In T. Tymockzko (Ed.), New Directions on the Philosophy of Mathematics (pp. 29-48).
    • (1984) New Directions on the Philosophy of Mathematics , pp. 29-48
    • Lakatos, I.1
  • 31
    • 26444618062 scopus 로고
    • Towards a social theory of mathematical knowledge
    • C. Keitel and K. Ruthven (Eds.), New York: Springer-Verlag
    • Otte, M. (1993). Towards a social theory of mathematical knowledge. In C. Keitel and K. Ruthven (Eds.), Learning from Computers: Mathematics, Education, and Technology (pp. 280-327). New York: Springer-Verlag.
    • (1993) Learning from Computers: Mathematics, Education, and Technology , pp. 280-327
    • Otte, M.1
  • 32
    • 0003997158 scopus 로고
    • New York: Basic Books, Inc.
    • Papert, S. (1980). Mindstorms. New York: Basic Books, Inc.
    • (1980) Mindstorms
    • Papert, S.1
  • 35
    • 0002447711 scopus 로고
    • Operational origins of mathematical objects and the quandary of reification: The case of function
    • G. Harel and E. Dubinsky (Eds.), Washington, DC: Mathematical Association of America
    • Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification: The case of function. In G. Harel and E. Dubinsky (Eds.), The Concept of Function (pp. 59-84). Washington, DC: Mathematical Association of America.
    • (1992) The Concept of Function , pp. 59-84
    • Sfard, A.1
  • 36
    • 0002728845 scopus 로고
    • Reification as the birth of metaphor
    • Sfard, A. (1994). Reification as the birth of metaphor. For the Learning of Mathematics 14(1): 44-55.
    • (1994) For the Learning of Mathematics , vol.14 , Issue.1 , pp. 44-55
    • Sfard, A.1
  • 37
    • 24944477378 scopus 로고
    • The gains and the pitfalls of reification: The case of algebra
    • Sfard, A., and Linchevski, L. (1994). The gains and the pitfalls of reification: The case of algebra. Educational Studies in Mathematics 26: 191-228.
    • (1994) Educational Studies in Mathematics , vol.26 , pp. 191-228
    • Sfard, A.1    Linchevski, L.2
  • 40
    • 0002335783 scopus 로고
    • On understanding the notion of function
    • G. Harel and E. Dubinsky (Eds.), Washington, DC: Mathematical Association of America
    • Sierpinska, A. (1992). On understanding the notion of function. In G. Harel and E. Dubinsky (Eds.), The Concept of Function (pp. 25-58). Washington, DC: Mathematical Association of America.
    • (1992) The Concept of Function , pp. 25-58
    • Sierpinska, A.1
  • 42
    • 3543001950 scopus 로고
    • The psychology of advanced mathematical thinking
    • D. Tall (Ed.), Dordrecht: Kluwer Academic Publishers
    • Tall, D. (1991b). The psychology of advanced mathematical thinking. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 3-21). Dordrecht: Kluwer Academic Publishers.
    • (1991) Advanced Mathematical Thinking , pp. 3-21
    • Tall, D.1
  • 43
    • 0442283783 scopus 로고
    • Reflections
    • D. Tall (Ed.), Dordrecht: Kluwer Academic Publishers
    • Tall, D. (1991c). Reflections. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 251-260). Dordrecht: Kluwer Academic Publishers.
    • (1991) Advanced Mathematical Thinking , pp. 251-260
    • Tall, D.1
  • 44
    • 0009119382 scopus 로고
    • Cognitive growth in elementary and advanced mathematical thinking
    • L. Meira and D. Carraher (Eds.), Recife, Brazil: Graducate Program in Cognitive Psycholgy, Universidade Federal de Pernambuco
    • Tall, D. (1995). Cognitive growth in elementary and advanced mathematical thinking. In L. Meira and D. Carraher (Eds.), Proceedings of the Nineteenth International Conference for the Psychology of Mathematics Education, vol. 1 (pp. 61-76). Recife, Brazil: Graducate Program in Cognitive Psycholgy, Universidade Federal de Pernambuco.
    • (1995) Proceedings of the Nineteenth International Conference for the Psychology of Mathematics Education , vol.1 , pp. 61-76
    • Tall, D.1
  • 45
    • 0002269268 scopus 로고
    • The development of the concept of speed and its relationship to concepts of rate
    • G. Harel and J. Confrey (Eds.), Albany, NY: State University of New York Press
    • Thompson, P. W. (1994). The development of the concept of speed and its relationship to concepts of rate. In G. Harel and J. Confrey (Eds.), The Development of Multiplicative Reasoning in the Learning of Mathematics (pp. 181-236). Albany, NY: State University of New York Press.
    • (1994) The Development of Multiplicative Reasoning in the Learning of Mathematics , pp. 181-236
    • Thompson, P.W.1
  • 46
    • 0010907998 scopus 로고
    • The four-color problem and its philosophical significance
    • Tymoczko, T. (1979). The four-color problem and its philosophical significance. Journal of Philosophy 76(2): 57-82.
    • (1979) Journal of Philosophy , vol.76 , Issue.2 , pp. 57-82
    • Tymoczko, T.1
  • 49
    • 0001243107 scopus 로고
    • Abstract meditations on the concrete and concrete implications for mathematics education
    • I. Harel and S. Papert (Eds.), Norwood, NJ: Ablex Publishing Corp.
    • Wilensky, U. (1991). Abstract meditations on the concrete and concrete implications for mathematics education. In I. Harel and S. Papert (Eds.), Constructionism Norwood, NJ: Ablex Publishing Corp.
    • (1991) Constructionism
    • Wilensky, U.1


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