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Volumn 61, Issue 1-2, 2006, Pages 67-101

A semiotic perspective of mathematical activity: The case of number

Author keywords

Development of number understanding; Foundations of number; History of number; Mathematical activity; Mathematical signs; Mathematics; Mathematics education; Number; Numerical calculation; Semiotics; Teaching and learning mathematics

Indexed keywords


EID: 33645682885     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-006-6423-7     Document Type: Review
Times cited : (63)

References (77)
  • 5
    • 0006449695 scopus 로고
    • Benacerraf, P. and Putnam, H. (eds.), Englewood Cliffs, Prentice-Hall, New Jersey
    • Benacerraf, P. and Putnam, H. (eds.): 1964, Philosophy of Mathematics: Selected Readings, Englewood Cliffs, Prentice-Hall, New Jersey.
    • (1964) Philosophy of Mathematics: Selected Readings
  • 7
    • 0004146270 scopus 로고
    • Harvard University Press, Cambridge, Massachusetts
    • Bruner, J.: 1960, The Process of Education, Harvard University Press, Cambridge, Massachusetts.
    • (1960) The Process of Education
    • Bruner, J.1
  • 8
    • 0003809019 scopus 로고
    • Harvard University Press, Cambridge, Massachusetts
    • Bruner, J.: 1964, Towards a Theory of Instruction, Harvard University Press, Cambridge, Massachusetts.
    • (1964) Towards a Theory of Instruction
    • Bruner, J.1
  • 10
    • 0003027491 scopus 로고
    • The development of addition and subtraction problem-solving skills
    • T.P. Carpenter, J.M., Moser, and T.A. Romberg (eds.), Erlbaum, Hillsdale, New Jersey
    • Carpenter, T.P. and Moser, J.M.: 1982, The development of addition and subtraction problem-solving skills,' in T.P. Carpenter, J.M., Moser, and T.A. Romberg (eds.), Addition and Subtraction: A Cognitive Perspective, Erlbaum, Hillsdale, New Jersey.
    • (1982) Addition and Subtraction: A Cognitive Perspective
    • Carpenter, T.P.1    Moser, J.M.2
  • 12
    • 0009960234 scopus 로고
    • Understanding of number concepts in low attaining 7-9 year olds (parts I and II)
    • Denvir, B. and Brown, M.: 1986, 'Understanding of number concepts in low attaining 7-9 year olds (parts I and II),' Educational. Studies in Mathematics 17, 15-36, 143-164.
    • (1986) Educational. Studies in Mathematics , vol.17 , pp. 15-36
    • Denvir, B.1    Brown, M.2
  • 13
    • 0004505721 scopus 로고
    • The contextualising of mathematics: Towards a theoretical map
    • M. Harris (ed.), Schools, Falmer press, London
    • Dowling, P.: 1988, The contextualising of mathematics: Towards a theoretical map', in M. Harris (ed.), Schools, Mathematics and Work, Falmer press, London, pp. 93-120.
    • (1988) Mathematics and Work , pp. 93-120
    • Dowling, P.1
  • 16
    • 27544505912 scopus 로고    scopus 로고
    • Semiotics, mathematics and mathematics education
    • Ernest, P.: 1997, 'Semiotics, mathematics and mathematics education', The Philosophy of Mathematics Education Journal, 10 (http://www.ex.ac.uk/~PErnest/) .
    • (1997) The Philosophy of Mathematics Education Journal , vol.10
    • Ernest, P.1
  • 18
    • 33645669680 scopus 로고    scopus 로고
    • The relation between personal and public knowledge from an epistemological perspective
    • F. Seeger, J. Voigt and U. Waschescio (eds.), Cambridge University Press, Cambridge
    • Ernest, P.: 1998b 'The relation between personal and public knowledge from an epistemological perspective', in F. Seeger, J. Voigt and U. Waschescio (eds.), The Culture of the Mathematics Classroom, pp. 245-268, Cambridge University Press, Cambridge.
    • (1998) The Culture of the Mathematics Classroom , pp. 245-268
    • Ernest, P.1
  • 19
    • 3042811773 scopus 로고    scopus 로고
    • Forms of knowledge in mathematics and mathematics education: Philosophical and rhetorical perspectives
    • Ernest, P.: 1999, 'Forms of knowledge in mathematics and mathematics education: philosophical and rhetorical perspectives', Educational Studies in Mathematics 38(1-3), 67-83.
    • (1999) Educational Studies in Mathematics , vol.38 , Issue.1-3 , pp. 67-83
    • Ernest, P.1
  • 20
    • 33645670124 scopus 로고    scopus 로고
    • The Epistemic subject in mathematical activity
    • M, Anderson, A. Saenz-Ludlow, S Zellweger and V.V. Cifarelli (eds.), Legas Publishing, New York, Ottawa and Toronto
    • Ernest, P.: 2003, 'The Epistemic subject in mathematical activity', in M, Anderson, A. Saenz-Ludlow, S Zellweger and V.V. Cifarelli (eds.) Educational Perspectives on Mathematics as Semiosis: From Thinking to Interpreting to Knowing, Legas Publishing, New York, Ottawa and Toronto, pp. 81-106.
    • (2003) Educational Perspectives on Mathematics as Semiosis: From Thinking to Interpreting to Knowing , pp. 81-106
    • Ernest, P.1
  • 21
    • 84860860296 scopus 로고    scopus 로고
    • Agency and creativity in the semiotics of learning mathematics
    • forthcoming. M. Hoffmann, J. Lenhard and F. Seeger, (eds.), Kluwer, Dordrecht
    • Ernest, P., (2005) in 'Agency and creativity in the semiotics of learning mathematics' forthcoming. M. Hoffmann, J. Lenhard and F. Seeger, (eds.), Activity and Sign, - Grounding Mathematics Education (Festschrift for Michael Otte), Kluwer, Dordrecht.
    • (2005) Activity and Sign, - Grounding Mathematics Education (Festschrift for Michael Otte)
    • Ernest, P.1
  • 26
    • 0001706315 scopus 로고
    • The subject and power
    • H.L. Dreyfus and P. Rabinow (eds.), Harvester Press, Brighton
    • Foucault, M.: 1982, 'The subject and power', in H.L. Dreyfus and P. Rabinow (eds.), Michel Foucault: Beyond Structuralism and Hermeneutics, Harvester Press, Brighton, pp. 208-226.
    • (1982) Michel Foucault: Beyond Structuralism and Hermeneutics , pp. 208-226
    • Foucault, M.1
  • 27
    • 0002975018 scopus 로고
    • Analysis of the counting-on procedure
    • T.P. Carpenter, J.M. Moser, and T.A. Romberg, (eds.), Erlbaum, Hillsdale, New Jersey
    • Fuson, K.C.: 1982, 'Analysis of the counting-on procedure', in T.P. Carpenter, J.M. Moser, and T.A. Romberg, (eds.), Addition and Subtraction: A Cognitive Perspective, Erlbaum, Hillsdale, New Jersey.
    • (1982) Addition and Subtraction: A Cognitive Perspective
    • Fuson, K.C.1
  • 30
    • 34347193348 scopus 로고
    • Über formal unentscheidbare sätze der principia mathematica und verwandter systeme I
    • Trans. in Heijenoort, 1967
    • Gödel, K.: 1931, 'Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte, fur Mathematik und Physik 38, 173-198 (Trans. in Heijenoort, 1967), pp. 592-617.
    • (1931) Monatshefte, fur Mathematik und Physik , vol.38 , pp. 173-198
    • Gödel, K.1
  • 34
    • 0003691342 scopus 로고
    • Heijenoort, J. van, (ed.). Logic, Cambridge, Harvard University Press, Massachusetts
    • Heijenoort, J. van, (ed.).: 1967, From Frege to Gödel: A Source Book in Mathematical. Logic, Cambridge, Harvard University Press, Massachusetts.
    • (1967) From Frege to Gödel: A Source Book in Mathematical
  • 38
    • 33645672168 scopus 로고
    • Happy numbers
    • D. Lingard (ed.), Derby: Association of Teachers of Mathematics, 1981
    • Jeffrey, B.: 1981, 'Happy numbers', in D. Lingard (ed.). Mathematical. Investigations in the Classroom, Derby: Association of Teachers of Mathematics, 1981, pp. 8-11.
    • (1981) Mathematical. Investigations in the Classroom , pp. 8-11
    • Jeffrey, B.1
  • 43
    • 85061659351 scopus 로고    scopus 로고
    • The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics
    • L. English (ed.), Mahwah, Erlbaum, New Jersey, 1997
    • Lakoff, G. and Nunez, R.: 1997, 'The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics', in L. English (ed.), Mathematical. Reasoning: Analogies, Metaphors and Images, Mahwah, Erlbaum, New Jersey, 1997, pp. 21-89.
    • (1997) Mathematical. Reasoning: Analogies, Metaphors and Images , pp. 21-89
    • Lakoff, G.1    Nunez, R.2
  • 45
    • 33645686414 scopus 로고    scopus 로고
    • Number words and language origins
    • Lambek, J.: 1996, 'Number words and language origins,' The Mathematical. Intelligencer 18(4), 69-72.
    • (1996) The Mathematical. Intelligencer , vol.18 , Issue.4 , pp. 69-72
    • Lambek, J.1
  • 48
    • 33645665956 scopus 로고
    • Mathephobia
    • P. Ernest, (ed.), Falmer Press, London
    • Maxwell, J.: 1989, 'Mathephobia', in P. Ernest, (ed.), Mathematics Teaching: The State of the Art, Falmer Press, London, pp. 221-226.
    • (1989) Mathematics Teaching: The State of the Art , pp. 221-226
    • Maxwell, J.1
  • 50
    • 0002339782 scopus 로고
    • Ethnomathematics and everyday cognition
    • D.A. Grouws (ed.), Macmillan, New York
    • Nunes, T.: 1992, 'Ethnomathematics and Everyday Cognition", in D.A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York, pp. 557-574.
    • (1992) Handbook of Research on Mathematics Teaching and Learning , pp. 557-574
    • Nunes, T.1
  • 54
    • 33645688681 scopus 로고
    • Concepts and the mangle of practice: The case of quaternions
    • Ed. by B. H. Smith and A. Plotinsky, (Spring 1995)
    • Pickering, A.: 1995, 'Concepts and the mangle of practice: The case of quaternions', South Atlantic Quarterly, (Special issue: Mathematics, Science and Postclassical Theory, Ed. by B. H. Smith and A. Plotinsky), 94(2), 417-465 (Spring 1995).
    • (1995) South Atlantic Quarterly, Special Issue: Mathematics, Science and Postclassical Theory , vol.94 , Issue.2 , pp. 417-465
    • Pickering, A.1
  • 56
    • 33645679068 scopus 로고
    • Ghent, Belgium: Kultuur, Kennis en Integratie (Communication and Cognition)
    • Pinxten, R.: 1987, Towards a Navajo Indian Geometry, Ghent, Belgium: Kultuur, Kennis en Integratie (Communication and Cognition).
    • (1987) Towards a Navajo Indian Geometry
    • Pinxten, R.1
  • 57
    • 0040147341 scopus 로고
    • Decomposition and all that rot
    • Plunkett, S.: 1979, 'Decomposition and all that rot,' Mathematics in School 8, 2-7.
    • (1979) Mathematics in School , vol.8 , pp. 2-7
    • Plunkett, S.1
  • 58
    • 0004268176 scopus 로고
    • Routledge and Kegan Paul, London (Revised edn. 1964, Harper and Row, New York)
    • Polanyi, M.: 1958, Personal Knowledge, Routledge and Kegan Paul, London (Revised edn. 1964, Harper and Row, New York).
    • (1958) Personal Knowledge
    • Polanyi, M.1
  • 59
    • 33645690440 scopus 로고    scopus 로고
    • Pre-Print Series, No. 1, School of the Sciences of Education, University Laurentienne, Sudbury, Ontario
    • Radford, L.: 1998, On Signs and Representations a Cultural Account, Pre-Print Series, No. 1, School of the Sciences of Education, University Laurentienne, Sudbury, Ontario.
    • (1998) On Signs and Representations a Cultural Account
    • Radford, L.1
  • 63
    • 3042735052 scopus 로고
    • Stanford University Press, Stanford California
    • Rotman, B.: 1993, Ad Infinitum, Stanford University Press, Stanford California.
    • (1993) Ad Infinitum
    • Rotman, B.1
  • 64
    • 0003771802 scopus 로고
    • Payot, Paris (Trans. by W. Baskin, Philosophical Library, New York, 1959)
    • Saussure, F. de: 1916, Course in General Linguistics, Payot, Paris (Trans. by W. Baskin, Philosophical Library, New York, 1959).
    • (1916) Course in General Linguistics
    • De Saussure, F.1
  • 66
    • 0002328292 scopus 로고
    • The earliest precursor of writing
    • Schmandt-Besserat, D.: 1978, 'The earliest precursor of writing', Scientific American 238(6).
    • (1978) Scientific American , vol.238 , Issue.6
    • Schmandt-Besserat, D.1
  • 67
    • 33645695817 scopus 로고
    • Seeger, F. and Steinbring, H. (eds.), IDM, University of Bielefeld, Bielefeld, Germany
    • Seeger, F. and Steinbring, H. (eds.): 1990, The Dialogue between Theory and Practice in Mathematics Education, IDM, University of Bielefeld, Bielefeld, Germany.
    • (1990) The Dialogue between Theory and Practice in Mathematics Education
  • 68
    • 0000935350 scopus 로고
    • Humanities students and epistemological obstacles related to limits
    • Sierpinska, A.: 1987, 'Humanities students and epistemological obstacles related to limits', Educational Studies in Mathematics 18, 371-397.
    • (1987) Educational Studies in Mathematics , vol.18 , pp. 371-397
    • Sierpinska, A.1
  • 69
    • 0002155120 scopus 로고
    • Relational understanding and instrumental understanding
    • Skemp, R.R.: 1976, 'Relational understanding and instrumental understanding', Mathematics Teaching 77, 20-26.
    • (1976) Mathematics Teaching , vol.77 , pp. 20-26
    • Skemp, R.R.1
  • 70
    • 0008978989 scopus 로고
    • Smith, D.E. (ed.) (2 Vols.), Dover Press, New York
    • Smith, D.E. (ed.) 1959, A Source Book in Mathematics (2 Vols.), Dover Press, New York.
    • (1959) A Source Book in Mathematics
  • 71
    • 0003981065 scopus 로고
    • Steffe, L.P. and Gale, J. (Eds.), Erlbaum, Hillsdale, New Jersey
    • Steffe, L.P. and Gale, J. (Eds.): 1995, Constructivism in Education, Erlbaum, Hillsdale, New Jersey.
    • (1995) Constructivism in Education
  • 72
    • 84937180998 scopus 로고    scopus 로고
    • The influence of structural aspects of the English counting word system on the teaching and learning of place value
    • Thompson, I.: 1998, 'The influence of structural aspects of the English counting word system on the teaching and learning of place value', Research in Education 59, 1-8.
    • (1998) Research in Education , vol.59 , pp. 1-8
    • Thompson, I.1
  • 74
    • 0004115808 scopus 로고
    • Cambridge, Harvard University Press, Massachusetts
    • Vygotsky, L.: 1978, Mind in Society, Cambridge, Harvard University Press, Massachusetts.
    • (1978) Mind in Society
    • Vygotsky, L.1
  • 77
    • 0006987968 scopus 로고
    • Prindle, Weber and Schmidt, Boston
    • Zaslavsky, C.: 1973, Africa Counts, Prindle, Weber and Schmidt, Boston.
    • (1973) Africa Counts
    • Zaslavsky, C.1


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