메뉴 건너뛰기




Volumn 44, Issue 1-3, 2000, Pages 55-85

Providing a foundation for deductive reasoning: Students' interpretations when using dynamic geometry software and their evolving mathematical explanations

Author keywords

Appropriation of learning; Computer environments; Deductive reasoning; Dynamic geometry software; Geometry; Mathematical explanation; Mathematisation; Mediation of learning; Quadrilaterals; Secondary school; Sociocultural theory

Indexed keywords


EID: 4544259846     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1023/a:1012789201736     Document Type: Article
Times cited : (124)

References (56)
  • 2
    • 0003113837 scopus 로고
    • Aspects of proof in pupils' practice of school mathematics
    • D.Pimm (ed.), Hodder and Stoughton, London
    • Balacheff, N.: 1988b, 'Aspects of proof in pupils' practice of school mathematics', in D.Pimm (ed.), Mathematics, Teachers and Children, Hodder and Stoughton, London, pp. 216-235.
    • (1988) Mathematics, Teachers and Children , pp. 216-235
    • Balacheff, N.1
  • 4
    • 52849112087 scopus 로고
    • Epistemological domain of validity of microworlds: The case of Logo and Cabri-géomètre
    • R. Lewis and P. Mendelsohn (eds.), Elsevier, Amsterdam
    • Balacheff, N. and Sutherland, R.: 1994, 'Epistemological domain of validity of microworlds: the case of Logo and Cabri-géomètre', in R. Lewis and P. Mendelsohn (eds.), Lessons from Learning, Elsevier, Amsterdam.
    • (1994) Lessons from Learning
    • Balacheff, N.1    Sutherland, R.2
  • 8
    • 2342515820 scopus 로고
    • Instructional implications of students' understanding of the differences between empirical verification and mathematical proof
    • Judah L. Schwartz, Michal Yerushalmy and Beth Wilson (eds.), Lawrence Erlbaum Associates, Hillsdale, N.J.
    • Chazan, D.: 1993, 'Instructional implications of students' understanding of the differences between empirical verification and mathematical proof, in Judah L. Schwartz, Michal Yerushalmy and Beth Wilson (eds.), The Geometric Supposer: What is It a Case of, Lawrence Erlbaum Associates, Hillsdale, N.J.
    • (1993) The Geometric Supposer: What Is It a Case Of?
    • Chazan, D.1
  • 10
    • 0040705305 scopus 로고    scopus 로고
    • A student's learning of geometry using the computer
    • Choi koh, S.S.: 1999, 'A student's learning of geometry using the computer', The Journal of Educational Research 92(5), 301-311.
    • (1999) The Journal of Educational Research , vol.92 , Issue.5 , pp. 301-311
    • Choi Koh, S.S.1
  • 11
    • 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
  • 12
    • 0343982012 scopus 로고
    • The role and function of a hierarchical classification of quadrilaterals
    • de Villiers, M.: 1994, 'The role and function of a hierarchical classification of quadrilaterals', For the Learning of Mathematics 14(1), 11-18.
    • (1994) For the Learning of Mathematics , vol.14 , Issue.1 , pp. 11-18
    • De Villiers, M.1
  • 13
    • 85070599154 scopus 로고    scopus 로고
    • An alternative approach to proof in dynamic geometry
    • R. Lehrer and D. Chazan , Lawrence Erlbaum Associates, Hillsdale, N.J.
    • de Villiers, M.: 1998, 'An alternative approach to proof in dynamic geometry', in R. Lehrer and D. Chazan, Designing Learning Environments for Developing Understanding of Geometry and Space, Lawrence Erlbaum Associates, Hillsdale, N.J., pp. 369-393.
    • (1998) Designing Learning Environments for Developing Understanding of Geometry and Space , pp. 369-393
    • Villiers, M.1
  • 16
    • 1042300390 scopus 로고    scopus 로고
    • Geometry from a cognitive point of view
    • C. Mammana and V. Villani (eds.), Kluwer, Dordrecht
    • Duval, R.: 1998, 'Geometry from a cognitive point of view', in C. Mammana and V. Villani (eds.) Perspectives on the Teaching of Geometry for the 21st Century, Kluwer, Dordrecht, pp. 37-51.
    • (1998) Perspectives on the Teaching of Geometry for the 21st Century , pp. 37-51
    • Duval, R.1
  • 17
    • 0031358414 scopus 로고    scopus 로고
    • Exploring the territory before proof: Students' generalizations in a computer microworld for transformation geometry
    • Edwards, L.D.: 1997, 'Exploring the territory before proof: students' generalizations in a computer microworld for transformation geometry', International Journal of Computers for Mathematical Learning 2(3), 187-215.
    • (1997) International Journal of Computers for Mathematical Learning , vol.2 , Issue.3 , pp. 187-215
    • Edwards, L.D.1
  • 19
    • 52849114569 scopus 로고
    • Educational Solutions (also available as chapters 10-12 of Science of Education, part 2B), New York
    • Gattegno, C: 1988, The Awareness of Mathematization, Educational Solutions (also available as chapters 10-12 of Science of Education, part 2B), New York.
    • (1988) The Awareness of Mathematization
    • Gattegno, C.1
  • 22
    • 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
  • 26
    • 0039194780 scopus 로고
    • Psychological aspects of learning geometry
    • P. Nesher and J. Kilpatrick (eds.), CUP, Cambridge
    • Hershkowitz, R.: 1990, 'Psychological aspects of learning geometry', in P. Nesher and J. Kilpatrick (eds.), Mathematics and Cognition, CUP, Cambridge, pp. 70-95.
    • (1990) Mathematics and Cognition , pp. 70-95
    • Hershkowitz, R.1
  • 27
    • 0003276234 scopus 로고
    • Exploratory software, exploratory cultures?
    • A.A. DiSessa, C. Hoyles and R. Noss with L.D. Edwards (eds.), Springer, Berlin
    • Hoyles, C: 1995, 'Exploratory software, exploratory cultures?', in A.A. DiSessa, C. Hoyles and R. Noss with L.D. Edwards (eds.), Computers and Exploratory Learning, Springer, Berlin, pp. 199-219.
    • (1995) Computers and Exploratory Learning , pp. 199-219
    • Hoyles, C.1
  • 28
    • 0009576203 scopus 로고    scopus 로고
    • The curricular shaping of students' approaches to proof
    • Hoyles, C: 1997, 'The curricular shaping of students' approaches to proof', For the Learning of Mathematics 17(1), 7-16.
    • (1997) For the Learning of Mathematics , vol.17 , Issue.1 , pp. 7-16
    • Hoyles, C.1
  • 29
  • 30
    • 0003431211 scopus 로고
    • Hoyles, C. and Noss, R. (eds.), MIT Press, Cambridge, Mass.
    • Hoyles, C. and Noss, R. (eds.): 1992, Learning Mathematics and Logo, MIT Press, Cambridge, Mass.
    • (1992) Learning Mathematics and Logo
  • 33
    • 0008108041 scopus 로고
    • Geometrical relationships and dependencies in Cabri
    • Hölzl, R., Healy, L., Hoyles, C. and Noss, R.: 1994, 'Geometrical relationships and dependencies in Cabri', Micromath 10(3), 8-11.
    • (1994) Micromath , vol.10 , Issue.3 , pp. 8-11
    • Hölzl, R.1    Healy, L.2    Hoyles, C.3    Noss, R.4
  • 37
    • 33646327520 scopus 로고
    • Solving problems in computer-based geometry environment: The influence of the features of the software
    • Laborde, C.: 1992, 'Solving problems in computer-based geometry environment: the influence of the features of the software', Zentralblatt für Didaktik der Mathematik 24(4), 128-135.
    • (1992) Zentralblatt für Didaktik der Mathematik , vol.24 , Issue.4 , pp. 128-135
    • Laborde, C.1
  • 38
    • 0002129346 scopus 로고
    • The computer as part of the learning environment; the case of geometry
    • C. Keitel and K. Ruthven (eds.), Springer-Verlag, Berlin
    • Laborde, C.: 1993a, 'The computer as part of the learning environment; The case of geometry', in C. Keitel and K. Ruthven (eds.), Learning from Computers: Mathematics Education and Technology, Springer-Verlag, Berlin.
    • (1993) Learning from Computers: Mathematics Education and Technology
    • Laborde, C.1
  • 39
    • 26444440885 scopus 로고
    • Do the pupils learn and what do they learn in a computer based environment? The case of Cabri-géomètre
    • B. Jaworski (ed.), University of Birmingham, UK
    • Laborde, C.: 1993b, 'Do the pupils learn and what do they learn in a computer based environment? The case of Cabri-géomètre', in B. Jaworski (ed.) Proceedings of the 1993 Technology in Mathematics Teaching Conference, University of Birmingham, UK, pp. 39-52.
    • (1993) Proceedings of the 1993 Technology in Mathematics Teaching Conference , pp. 39-52
    • Laborde, C.1
  • 40
    • 0001380274 scopus 로고
    • What about a learning environment where Euclidean concepts are manipulated with a mouse?
    • A.A. DiSessa, C. Hoyles and R. Noss with L.D. Edwards (eds.), Springer, Berlin
    • Laborde, C. and Laborde, J.-M.: 1995, 'What about a learning environment where Euclidean concepts are manipulated with a mouse?', in A.A. DiSessa, C. Hoyles and R. Noss with L.D. Edwards (eds.), Computers and Exploratory Learning, Springer, Berlin.
    • (1995) Computers and Exploratory Learning
    • Laborde, C.1    Laborde, J.-M.2
  • 41
    • 21344463746 scopus 로고    scopus 로고
    • The development of the idea of mathematical proof: A 5-year case study
    • Maher, C.A. and Martino, A.M.: 1996, 'The development of the idea of mathematical proof: a 5-year case study', Journal for Research in Mathematics Education 27(2), 194-214.
    • (1996) Journal for Research in Mathematics Education , vol.27 , Issue.2 , pp. 194-214
    • Maher, C.A.1    Martino, A.M.2
  • 46
    • 85068027972 scopus 로고
    • Cognitive technologies for mathematics education
    • A.H. Schoenfeld (ed.), Lawrence Erlbaum Associates, Hillsdale, N.J.
    • Pea, R.D.: 1987, 'Cognitive technologies for mathematics education', in A.H. Schoenfeld (ed.), Cognitive Science and Mathematics Education, Lawrence Erlbaum Associates, Hillsdale, N.J., pp. 89-122.
    • (1987) Cognitive Science and Mathematics Education , pp. 89-122
    • Pea, R.D.1
  • 47
    • 0002921383 scopus 로고
    • Practices of distributed intelligence and designs for education
    • G. Salomon (ed.), CUP, Cambridge
    • Pea, R.D.: 1993, 'Practices of distributed intelligence and designs for education', in G. Salomon (ed.), Distributed Cognitions: psychological and educational considerations, CUP, Cambridge, pp. 47-87.
    • (1993) Distributed Cognitions: Psychological and Educational Considerations , pp. 47-87
    • Pea, R.D.1
  • 48
    • 26444535782 scopus 로고    scopus 로고
    • The construction of meaning for geometrical constructions: Two contrasting cases
    • Pratt, D. and Ainley, J.: 1996, 'The construction of meaning for geometrical constructions: two contrasting cases', International Journal of Computers for Mathematical Learning 1(3), 293-322.
    • (1996) International Journal of Computers for Mathematical Learning , vol.1 , Issue.3 , pp. 293-322
    • Pratt, D.1    Ainley, J.2
  • 49
    • 0000545757 scopus 로고
    • Van Hiele levels and achievement in writing geometry proofs
    • Senk, S.L.: 1989, 'Van Hiele levels and achievement in writing geometry proofs', Journal for Research in Mathematics Education, 20(3), 309-321.
    • (1989) Journal for Research in Mathematics Education , vol.20 , Issue.3 , pp. 309-321
    • Senk, S.L.1
  • 54
    • 84940033546 scopus 로고    scopus 로고
    • Oxford University Press, New York
    • Wertsch, J.V.: 1998, Mind as Action, Oxford University Press, New York.
    • (1998) Mind as Action
    • Wertsch, J.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.