메뉴 건너뛰기




Volumn 36, Issue 4, 2005, Pages 317-346

Students' conceptions of a mathematical definition

Author keywords

Beliefs; Calculus analysis; Conceptual knowledge; Geometry; Higher order thinking; Reasoning; Secondary mathematics

Indexed keywords


EID: 22544445858     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review
Times cited : (109)

References (46)
  • 1
    • 0003272893 scopus 로고
    • Taxonomy of educational objectives: The classification of educational goals
    • New York: Longman
    • Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals, Handbook I : Cognitive domain. New York: Longman.
    • (1956) Handbook I : Cognitive Domain
    • Bloom, B.S.1
  • 2
    • 22544467094 scopus 로고
    • What is a circle?
    • Borasi, R. (1987). What is a circle? Mathematics Teaching, 118, 39-40.
    • (1987) Mathematics Teaching , vol.118 , pp. 39-40
    • Borasi, R.1
  • 4
    • 22544449680 scopus 로고
    • On humanistic alternatives in the practice of teacher education
    • Brown, S. I. (1982). On humanistic alternatives in the practice of teacher education. Journal of Research and Development in Education, 15(4), 1-12.
    • (1982) Journal of Research and Development in Education , vol.15 , Issue.4 , pp. 1-12
    • Brown, S.I.1
  • 5
    • 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
  • 6
    • 0012955770 scopus 로고    scopus 로고
    • To teach definitions in geometry or to teach to define?
    • A. Olivier & K. Newstead (Eds.). Stellenbosch, South Africa: University of Stellenbosch
    • de Villiers, M. (1998). To teach definitions in geometry or to teach to define? In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 248-255). Stellenbosch, South Africa: University of Stellenbosch.
    • (1998) Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education , vol.2 , pp. 248-255
    • De Villiers, M.1
  • 12
    • 0039194780 scopus 로고
    • Psychological aspects of learning geometry
    • P. Nesher and J. Kilpatrick (Eds.). New York: Cambridge University Press
    • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher and J. Kilpatrick (Eds.), Mathematics and cognition. New York: Cambridge University Press.
    • (1990) Mathematics and Cognition
    • Hershkowitz, R.1
  • 13
    • 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, 77(1), 7-16.
    • (1997) For the Learning of Mathematics , vol.77 , Issue.1 , pp. 7-16
    • Hoyles, C.1
  • 14
    • 22544446872 scopus 로고
    • Mathematics teaching: What is it?
    • Jaworski, B. (1992). Mathematics teaching: What is it? For the Learning of Mathematics, 12(1), 8-14.
    • (1992) For the Learning of Mathematics , vol.12 , Issue.1 , pp. 8-14
    • Jaworski, B.1
  • 15
    • 1542740771 scopus 로고
    • Effects of a definition and a varying number of examples and nonexamples on concept attainment
    • Klausmeier, H. J., & Feldman, K. V. (1975). Effects of a definition and a varying number of examples and nonexamples on concept attainment. Journal of Educational Psychology, 67, 174-178.
    • (1975) Journal of Educational Psychology , vol.67 , pp. 174-178
    • Klausmeier, H.J.1    Feldman, K.V.2
  • 16
    • 22544432953 scopus 로고
    • The relativity of mathematics
    • Kleiner, I., & Avital, S. (1984). The relativity of mathematics. Mathematics Teacher, 77, 554-558.
    • (1984) Mathematics Teacher , vol.77 , pp. 554-558
    • Kleiner, I.1    Avital, S.2
  • 17
    • 0011972194 scopus 로고    scopus 로고
    • Teachers' conceptions of proof in the context of secondary school mathematics
    • Knuth, E. (2002). Teachers' conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5, 61-88.
    • (2002) Journal of Mathematics Teacher Education , vol.5 , pp. 61-88
    • Knuth, E.1
  • 18
    • 0004229474 scopus 로고
    • Cambridge, UK: Cambridge University Press
    • Lakatos, I. (1976). Proofs and Refutations. Cambridge, UK: Cambridge University Press.
    • (1976) Proofs and Refutations
    • Lakatos, I.1
  • 19
    • 0002259262 scopus 로고
    • When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching
    • Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27, 29-63.
    • (1990) American Educational Research Journal , vol.27 , pp. 29-63
    • Lampert, M.1
  • 21
    • 0009321949 scopus 로고
    • On the mathematical nature of turtle programming
    • D. Pimm (Ed.). London: Hodder and Stoughton
    • Leron, U. (1988). On the mathematical nature of turtle programming. In D. Pimm (Ed.), Mathematics Teachers and Children (pp. 185-189). London: Hodder and Stoughton.
    • (1988) Mathematics Teachers and Children , pp. 185-189
    • Leron, U.1
  • 23
    • 0010854046 scopus 로고
    • The van Hiele levels of geometric thought in undergraduate preservice teachers
    • Mayberry, J. (1983). The van Hiele levels of geometric thought in undergraduate preservice teachers. Journal for Research in Mathematics Education, 14, 58-69.
    • (1983) Journal for Research in Mathematics Education , vol.14 , pp. 58-69
    • Mayberry, J.1
  • 24
    • 0000682797 scopus 로고
    • Making the transition to formal proof
    • Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27, 249-266.
    • (1994) Educational Studies in Mathematics , vol.27 , pp. 249-266
    • Moore, R.C.1
  • 26
    • 3843088853 scopus 로고    scopus 로고
    • Mathematical idea analysis: What embodied cognitive science can say about the human nature of mathematics
    • T. Nakahara & M. Koyama (Eds.). Hiroshima, Japan: Hiroshima University
    • Nunez, R. E. (2000). Mathematical idea analysis: What embodied cognitive science can say about the human nature of mathematics. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 3-22). Hiroshima, Japan: Hiroshima University.
    • (2000) Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education , vol.1 , pp. 3-22
    • Nunez, R.E.1
  • 27
    • 22544472816 scopus 로고    scopus 로고
    • Counter-examples that (only) prove and counter-examples that (also) explain
    • Peled, I., & Zaslavsky, O. (1997). Counter-examples that (only) prove and counter-examples that (also) explain. Focus on Learning Problems in Mathematics, 19(3), 49-61.
    • (1997) Focus on Learning Problems in Mathematics , vol.19 , Issue.3 , pp. 49-61
    • Peled, I.1    Zaslavsky, O.2
  • 28
    • 22544452822 scopus 로고
    • Just a matter of definition [Review of the book Learning mathematics through inquiry]
    • Pimm, D. (1993). Just a matter of definition [Review of the book Learning mathematics through inquiry]. Educational Studies in Mathematics, 25, 261-217.
    • (1993) Educational Studies in Mathematics , vol.25 , pp. 261-1217
    • Pimm, D.1
  • 29
    • 22544466239 scopus 로고    scopus 로고
    • Images and definitions for the concept of increasing/decreasing function
    • A. Olivier & K. Newstead (Eds.). Stellenbosch, South Africa: University of Stellenbosch
    • Rasslan, S., & Vinner, S. (1998). Images and definitions for the concept of increasing/decreasing function. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, 33-40). Stellenbosch, South Africa: University of Stellenbosch.
    • (1998) Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education , vol.4 , pp. 33-40
    • Rasslan, S.1    Vinner, S.2
  • 31
    • 0018217861 scopus 로고
    • Understanding understanding mathematics
    • Rissland, E. (1978). Understanding understanding mathematics. Cognitive Science, 2, 361-383.
    • (1978) Cognitive Science , vol.2 , pp. 361-383
    • Rissland, E.1
  • 32
    • 85068036857 scopus 로고
    • Example-based reasoning
    • J. F. Voss, D. N. Perkins, & J. W. Segal (Eds.). Hillsdale, NJ: Lawrence Erlbaum
    • Rissland, E. (1991). Example-based reasoning. In J. F. Voss, D. N. Perkins, & J. W. Segal (Eds.), Informal Reasoning and Education (pp. 187-208). Hillsdale, NJ: Lawrence Erlbaum.
    • (1991) Informal Reasoning and Education , pp. 187-208
    • Rissland, E.1
  • 33
  • 36
    • 22544485775 scopus 로고
    • Concept and principle learning
    • R. J. Shumway (Ed.). Reston, VA: National Council of Teachers of Mathematics
    • Sowder, L. (1980). Concept and principle learning. In R. J. Shumway (Ed.), Research in Mathematics Education (pp. 244-285). Reston, VA: National Council of Teachers of Mathematics.
    • (1980) Research in Mathematics Education , pp. 244-285
    • Sowder, L.1
  • 37
    • 0000213855 scopus 로고
    • Concept image and concept definition in mathematics with particular reference to limits and continuity
    • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169.
    • (1981) Educational Studies in Mathematics , vol.12 , pp. 151-169
    • Tall, D.1    Vinner, S.2
  • 39
    • 0001940478 scopus 로고
    • The role of definitions in the teaching and learning of mathematics
    • D. Tall (Ed.). Dordrecht: Kluwer
    • Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 65-81). Dordrecht: Kluwer.
    • (1991) Advanced Mathematical Thinking , pp. 65-81
    • Vinner, S.1
  • 40
    • 1842465710 scopus 로고
    • Traditional mathematics classrooms: Some seemingly unavoidable feature
    • J. P. de Ponte & J. F. Matos (Eds.). Portugal, Lisbon: University of Lisbon
    • Vinner, S. (1994). Traditional mathematics classrooms: Some seemingly unavoidable feature. In J. P. de Ponte & J. F. Matos (Eds.), Proceedings of the 18th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 353-360). Portugal, Lisbon: University of Lisbon.
    • (1994) Proceedings of the 18th Conference of the International Group for the Psychology of Mathematics Education , vol.4 , pp. 353-360
    • Vinner, S.1
  • 41
    • 2942593147 scopus 로고    scopus 로고
    • Beyond proving and explaining: Proofs that justify the use of definitions and axiomatic structures and proofs that illustrates technique
    • Weber, K. (2002). Beyond proving and explaining: Proofs that justify the use of definitions and axiomatic structures and proofs that illustrates technique. For the Learning of Mathematics, 22(3), 14-22.
    • (2002) For the Learning of Mathematics , vol.22 , Issue.3 , pp. 14-22
    • Weber, K.1
  • 42
    • 2442468774 scopus 로고
    • Inconsistent ideas related to definitions and examples
    • Wilson P. S. (1990). Inconsistent ideas related to definitions and examples. Focus on Learning Problems in Mathematics, 72(3-4), 31-47.
    • (1990) Focus on Learning Problems in Mathematics , vol.72 , Issue.3-4 , pp. 31-47
    • Wilson, P.S.1
  • 44
    • 21344474293 scopus 로고    scopus 로고
    • Sociomathematical norms, argumentation, and autonomy in mathematics
    • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458-477.
    • (1996) Journal for Research in Mathematics Education , vol.27 , pp. 458-477
    • Yackel, E.1    Cobb, P.2
  • 45
    • 0002356643 scopus 로고    scopus 로고
    • Explanation, justification and argumentation in mathematics classrooms
    • M. van den Heuvel-Panhuizen (Ed.). Utrecht, Netherlands: Utrecht University
    • Yackel, E. (2000). Explanation, justification and argumentation in mathematics classrooms. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 9-24). Utrecht, Netherlands: Utrecht University.
    • (2000) Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education , vol.1 , pp. 9-24
    • Yackel, E.1
  • 46
    • 22544458888 scopus 로고
    • Open-ended tasks as a trigger for mathematics teachers' professional development
    • Zaslavsky, O. (1995). Open-ended tasks as a trigger for mathematics teachers' professional development. For the Learning of Mathematics, 15(3), 15-20.
    • (1995) For the Learning of Mathematics , vol.15 , Issue.3 , pp. 15-20
    • Zaslavsky, O.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.