메뉴 건너뛰기




Volumn 44, Issue 1-3, 2000, Pages 5-23

Proof, explanation and exploration: An overview

Author keywords

Dynamic geometry; Proof; Technology; Visualization

Indexed keywords


EID: 27544492987     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1023/A:1012737223465     Document Type: Article
Times cited : (239)

References (37)
  • 1
    • 84967713486 scopus 로고
    • Responses to "theoretical mathematics": Towards a cultural synthesis of mathematics and theoretical physics
    • Atiyah, M., et al.: 1994, 'Responses to "theoretical mathematics": Towards a cultural synthesis of mathematics and theoretical physics', Bulletin of the American Mathematical Society 30(2), 178-207.
    • (1994) Bulletin of the American Mathematical Society , vol.30 , Issue.2 , pp. 178-207
    • Atiyah, M.1
  • 3
    • 52849103899 scopus 로고    scopus 로고
    • Teaching proof
    • Barnard, T., et al.: 1996, 'Teaching proof, Mathematics Teaching 155, 6-39.
    • (1996) Mathematics Teaching , vol.155 , pp. 6-39
    • Barnard, T.1
  • 4
    • 0002611102 scopus 로고
    • Visual information and valid reasoning
    • W. Zimmerman and S. Cunninghan (eds.), The Mathematics Association of America, Washington
    • Barwise, J. and Etchemendy, J.: 1991, 'Visual information and valid reasoning', in W. Zimmerman and S. Cunninghan (eds.), Visualization in Teaching and Learning Mathematics, The Mathematics Association of America, Washington, pp. 9-24.
    • (1991) Visualization in Teaching and Learning Mathematics , pp. 9-24
    • Barwise, J.1    Etchemendy, J.2
  • 5
    • 0040504849 scopus 로고    scopus 로고
    • Heterogeneous logic
    • G. Allwain and J. Barwise (eds.), Oxford University Press, New York
    • Barwise, J. and Etchemendy, J.: 1996, 'Heterogeneous logic', in G. Allwain and J. Barwise (eds.), Logical Reasoning with Diagrams, Oxford University Press, New York, pp. 179-201.
    • (1996) Logical Reasoning with Diagrams , pp. 179-201
    • Barwise, J.1    Etchemendy, J.2
  • 6
    • 0002122056 scopus 로고
    • A study of pupils' proof-explanations in mathematical situations
    • Bell, A.: 1976, 'A study of pupils' proof-explanations in mathematical situations', Educaation Studies in Mathematics 7, 23-40.
    • (1976) Educaation Studies in Mathematics , vol.7 , pp. 23-40
    • Bell, A.1
  • 8
    • 52849103023 scopus 로고    scopus 로고
    • Visible structures in number theory
    • Texas Instruments Incorporated
    • Borwein, P. and Jorgenson, L.: 1997, 'Visible structures in number theory', in http://www.cecm.sfu.ca/loki/Papers/Numbers/node3.html. Cabri Geometry II (computer software).: 1996, Texas Instruments Incorporated.
    • (1996) Cabri Geometry II (Computer Software)
    • Borwein, P.1    Jorgenson, L.2
  • 9
    • 4544306190 scopus 로고
    • The role and function of proof in mathematics
    • de Villiers, M.: 1990, 'The role and function of proof in mathematics', Pythagoras 24, 17-24.
    • (1990) Pythagoras , vol.24 , pp. 17-24
    • De Villiers, M.1
  • 13
    • 0007242525 scopus 로고
    • Epistemology of visual thinking in elementary real analysis
    • Giaquinto, M.: 1994, 'Epistemology of visual thinking in elementary real analysis', British Journal for the Philosophy of Science 45, 789-813.
    • (1994) British Journal for the Philosophy of Science , vol.45 , pp. 789-813
    • Giaquinto, M.1
  • 14
    • 52849116071 scopus 로고
    • Comments on Susanna Epp's chapter
    • A. Schoenfeld (ed.), Lawrence Erlbaum Associates, Hillsdale, NJ
    • Greeno, J.: 1994, 'Comments on Susanna Epp's chapter', in A. Schoenfeld (ed.), Mathematical Thinking and Problem Solving, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 270-278.
    • (1994) Mathematical Thinking and Problem Solving , pp. 270-278
    • Greeno, J.1
  • 16
    • 0002952407 scopus 로고
    • Some pedagogical aspects of proof
    • Hanna, G.: 1990, 'Some pedagogical aspects of proof, Interchange 21(1), 6-13.
    • (1990) Interchange , vol.21 , Issue.1 , pp. 6-13
    • Hanna, G.1
  • 17
    • 0009613925 scopus 로고    scopus 로고
    • Proof and proving
    • A. Bishop, K. Clements, C. Keitel, J. Kilpatrick and C. Laborde (eds.), Kluwer Academic Publishers, Dordrecht
    • Hanna, G. and Jahnke, H.N.: 1996, 'Proof and proving', in A. Bishop, K. Clements, C. Keitel, J. Kilpatrick and C. Laborde (eds.), International Handbook of Mathematics Education, Kluwer Academic Publishers, Dordrecht, pp 877-908.
    • (1996) International Handbook of Mathematics Education , pp. 877-908
    • Hanna, G.1    Jahnke, H.N.2
  • 19
    • 0012012692 scopus 로고
    • Proving is convincing and explaining
    • Hersh, R.: 1993, 'Proving is convincing and explaining', Educational Studies in Mathematics 24(4), 389-399.
    • (1993) Educational Studies in Mathematics , vol.24 , Issue.4 , pp. 389-399
    • Hersh, R.1
  • 20
    • 84967787254 scopus 로고
    • "Theoretical mathematics": Towards a cultural synthesis of mathematics and theoretical physics
    • Jaffe, A. and Quinn, F.: 1993, '"Theoretical mathematics": Towards a cultural synthesis of mathematics and theoretical physics', Bulletin of the American Mathematical Society 29(1), 1-13.
    • (1993) Bulletin of the American Mathematical Society , vol.29 , Issue.1 , pp. 1-13
    • Jaffe, A.1    Quinn, F.2
  • 24
    • 52849095894 scopus 로고    scopus 로고
    • Truth, rigour, and common sense
    • H.G. Dales and G. Oliveri (eds.), Oxford University Press, Oxford
    • Manin, Yu.: 1998, 'Truth, rigour, and common sense', in H.G. Dales and G. Oliveri (eds.), Truth in Mathematics, Oxford University Press, Oxford, pp. 147-159.
    • (1998) Truth in Mathematics , pp. 147-159
    • Manin, Y.U.1
  • 25
    • 52849117523 scopus 로고
    • Questions about geometry
    • D. Pimm and E. Love (eds.), Holder and Stoughton, London
    • Mason, J.: 1991, 'Questions about geometry', in D. Pimm and E. Love (eds.), Teaching and Learning Mathematics: A Reader, Holder and Stoughton, London, pp. 77-99.
    • (1991) Teaching and Learning Mathematics: A Reader , pp. 77-99
    • Mason, J.1
  • 26
    • 0003425267 scopus 로고
    • National Council of Teachers of Mathematics (NCTM), Commission on Standards for School Mathematics, Reston, VA
    • National Council of Teachers of Mathematics (NCTM): 1989, Curriculum and Evaluation Standards for School Mathematics, Commission on Standards for School Mathematics, Reston, VA.
    • (1989) Curriculum and Evaluation Standards for School Mathematics
  • 27
    • 0003865802 scopus 로고    scopus 로고
    • National Council of Teachers of Mathematics (NCTM), Commission on Standards for School Mathematics, Reston, VA
    • National Council of Teachers of Mathematics (NCTM): 2000, Principles and Standards for School Mathematics, Commission on Standards for School Mathematics, Reston, VA.
    • (2000) Principles and Standards for School Mathematics
  • 28
    • 0039648255 scopus 로고
    • Structure and ideology in the mathematics curriculum
    • Noss, R.: 1994, 'Structure and ideology in the mathematics curriculum', For the learning of mathematics 14(1), 2-10.
    • (1994) For the Learning of Mathematics , vol.14 , Issue.1 , pp. 2-10
    • Noss, R.1
  • 29
    • 1542357016 scopus 로고    scopus 로고
    • The visualization of mathematics: Toward a mathematical exploratorium
    • Palais, R.S.: 1999, 'The visualization of mathematics: Toward a mathematical exploratorium', Notices of the AMS 46(6), 647-658.
    • (1999) Notices of the AMS , vol.46 , Issue.6 , pp. 647-658
    • Palais, R.S.1
  • 31
    • 0010424484 scopus 로고    scopus 로고
    • Why do we prove theorems?
    • Rav, Y: 1999, 'Why do we prove theorems?', Philosophia Mathematica 7(3), 5-41.
    • (1999) Philosophia Mathematica , vol.7 , Issue.3 , pp. 5-41
    • Rav, Y.1
  • 32
    • 0030096114 scopus 로고    scopus 로고
    • Justification in the mathematics classroom: A study of prospective elementary teachers
    • Simon, M.A. and Blume, G.W.: 1996, 'Justification in the mathematics classroom: A study of prospective elementary teachers', The Journal of Mathematical Behavior 15, 3-31.
    • (1996) The Journal of Mathematical Behavior , vol.15 , pp. 3-31
    • Simon, M.A.1    Blume, G.W.2
  • 34
    • 0347376740 scopus 로고
    • Mathematical explanation
    • Steiner, M.: 1978, 'Mathematical explanation', Philosophical Studies 34, 135-151.
    • (1978) Philosophical Studies , vol.34 , pp. 135-151
    • Steiner, M.1
  • 37
    • 0000266833 scopus 로고    scopus 로고
    • The mathematician and the mathematics education reform
    • Wu, H.: 1996, 'The mathematician and the mathematics education reform', Notices of the American Mathematical Society 43(12), 1531-1537.
    • (1996) Notices of the American Mathematical Society , vol.43 , Issue.12 , pp. 1531-1537
    • Wu, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.