메뉴 건너뛰기




Volumn 27, Issue 4, 2004, Pages 267-292

Gifted ninth graders' notions of proof: Investigating parallels in approaches of mathematically gifted students and professional mathematicians

Author keywords

[No Author keywords available]

Indexed keywords


EID: 13544250746     PISSN: 01623532     EISSN: None     Source Type: Journal    
DOI: 10.4219/jeg-2004-317     Document Type: Review
Times cited : (25)

References (60)
  • 1
    • 13544274460 scopus 로고    scopus 로고
    • Numerical and proof methods of Indian mathematics for the classroom
    • Almeida, D. (2003) Numerical and proof methods of Indian mathematics for the classroom. Mathematics in School, 32(2), 7-10.
    • (2003) Mathematics in School , vol.32 , Issue.2 , pp. 7-10
    • Almeida, D.1
  • 2
    • 0002122056 scopus 로고
    • A study of pupils' proof explanations in mathematical situations
    • Bell, A. W. (1976). A study of pupils' proof explanations in mathematical situations. Educational Studies in Mathematics, 7, 23-40.
    • (1976) Educational Studies in Mathematics , vol.7 , pp. 23-40
    • Bell, A.W.1
  • 3
    • 11644278069 scopus 로고
    • Mathematics and psychology
    • Birkhoff, G. (1969). Mathematics and psychology. SIAM Review, 11, 429-469.
    • (1969) SIAM Review , vol.11 , pp. 429-469
    • Birkhoff, G.1
  • 5
    • 54649084398 scopus 로고    scopus 로고
    • The practices of mathematicians: What do they tell us about coming to know mathematics?
    • Burton, L. (1999). The practices of mathematicians: What do they tell us about coming to know mathematics? Educational Studies in Mathematics, 37, 121-143.
    • (1999) Educational Studies in Mathematics , vol.37 , pp. 121-143
    • Burton, L.1
  • 7
    • 13544262695 scopus 로고
    • Who are the mathematically gifted elementary school children?
    • Chang, L. L. (1985). Who are the mathematically gifted elementary school children? Roeper Review, 8, 76-79.
    • (1985) Roeper Review , vol.8 , pp. 76-79
    • Chang, L.L.1
  • 8
    • 0000693952 scopus 로고
    • High school geometry students' justification for their views of empirical evidence and mathematical proof
    • Chazan, D. (1993). High school geometry students' justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24, 359-387.
    • (1993) Educational Studies in Mathematics , vol.24 , pp. 359-387
    • Chazan, D.1
  • 11
    • 13544273537 scopus 로고    scopus 로고
    • The importance of challenging tasks for mathematically gifted students
    • Diezmann, C., & Watters, J. (2003). The importance of challenging tasks for mathematically gifted students. Gifted and Talented International, 17, 2, 76-84.
    • (2003) Gifted and Talented International , vol.17 , Issue.2 , pp. 76-84
    • Diezmann, C.1    Watters, J.2
  • 12
    • 0002263487 scopus 로고
    • Constructive aspects of reflective abstraction in advanced mathematics
    • L. P. Steffe (Ed.), New York: Springer-Verlag
    • Dubinsky, E. (1991). Constructive aspects of reflective abstraction in advanced mathematics. In L. P. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 160-187). New York: Springer-Verlag.
    • (1991) Epistemological Foundations of Mathematical Experience , pp. 160-187
    • Dubinsky, E.1
  • 13
    • 0347410479 scopus 로고
    • The role of proof in problem solving
    • A. Schoenfeld (Ed.), Hillsdale, NJ: Erlbaum
    • Epp, S. S. (1990). The role of proof in problem solving. In A. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 257-269). Hillsdale, NJ: Erlbaum.
    • (1990) Mathematical Thinking and Problem Solving , pp. 257-269
    • Epp, S.S.1
  • 15
    • 13544262696 scopus 로고
    • Mathematical creativity
    • D. Tall (Ed.), Dordrecht, The Netherlands: Kluwer Academic Publishers
    • Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42-53). Dordrecht, The Netherlands: Kluwer Academic Publishers.
    • (1991) Advanced Mathematical Thinking , pp. 42-53
    • Ervynck, G.1
  • 20
    • 0005810124 scopus 로고
    • A computer assisted instruction program for exercises on finding axioms
    • Goldberg, A., & Suppes, P. (1972). A computer assisted instruction program for exercises on finding axioms. Educational Studies in Mathematics, 4, 429-449.
    • (1972) Educational Studies in Mathematics , vol.4 , pp. 429-449
    • Goldberg, A.1    Suppes, P.2
  • 21
    • 13544264781 scopus 로고
    • Identifying the gifted student in mathematics
    • Greenes, C. (1981). Identifying the gifted student in mathematics. Arithmetic Teacher, 28(6), 14-17.
    • (1981) Arithmetic Teacher , vol.28 , Issue.6 , pp. 14-17
    • Greenes, C.1
  • 23
    • 1542568453 scopus 로고
    • Characteristics and special needs of the gifted student in mathematics
    • Heid, M. K. (1983). Characteristics and special needs of the gifted student in mathematics. The Mathematics Teacher, 76, 221-226.
    • (1983) The Mathematics Teacher , vol.76 , pp. 221-226
    • Heid, M.K.1
  • 24
    • 0012012692 scopus 로고
    • Proof is convincing and explaining
    • Hersh, R. (1993). Proof is convincing and explaining. Educational Studies in Mathematics, 24, 389-399.
    • (1993) Educational Studies in Mathematics , vol.24 , pp. 389-399
    • Hersh, R.1
  • 26
    • 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
  • 28
    • 13544257485 scopus 로고
    • Achieving skill in solving geometry problems
    • J. Kilpatrick & I. Wirszup (Eds.), Stanford, CA: School Mathematics Study Group
    • Ivanitsyna, E. N. (1970). Achieving skill in solving geometry problems. In J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and teaching mathematics (Vol. 4). Stanford, CA: School Mathematics Study Group.
    • (1970) Soviet Studies in the Psychology of Learning and Teaching Mathematics , vol.4
    • Ivanitsyna, E.N.1
  • 29
    • 0842266967 scopus 로고
    • Identifying and teaching mathematically gifted elementary school children
    • Johnson, M. L. (1983). Identifying and teaching mathematically gifted elementary school children. Arithmetic Teacher, 30(5), 25-26, 55-56.
    • (1983) Arithmetic Teacher , vol.30 , Issue.5 , pp. 25-26
    • Johnson, M.L.1
  • 31
    • 84970741494 scopus 로고
    • Pursuing qualitative differences in the flexible use of a problem solving strategy by young children
    • Kanevsky, L. S. (1990). Pursuing qualitative differences in the flexible use of a problem solving strategy by young children. Journal for the Education of the Gifted, 13, 115-140.
    • (1990) Journal for the Education of the Gifted , vol.13 , pp. 115-140
    • Kanevsky, L.S.1
  • 33
    • 13544252815 scopus 로고
    • NACOME: Implications for curriculum design
    • Kline, M. (1976). NACOME: Implications for curriculum design. Mathematics Teacher, 69, 449-454.
    • (1976) Mathematics Teacher , vol.69 , pp. 449-454
    • Kline, M.1
  • 35
    • 0004229474 scopus 로고
    • Cambridge, England: Cambridge University Press
    • Lakatos, I. (1976). Proofs and refutations. Cambridge, England: Cambridge University Press.
    • (1976) Proofs and Refutations
    • Lakatos, I.1
  • 36
    • 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
  • 37
    • 0002885248 scopus 로고
    • Problem-solving or knowledge centered: The influence of philosophy on mathematics teaching
    • Lerman, S. (1983). Problem-solving or knowledge centered: The influence of philosophy on mathematics teaching. International Journal of Mathematics Education, 14(1), 59-66.
    • (1983) International Journal of Mathematics Education , vol.14 , Issue.1 , pp. 59-66
    • Lerman, S.1
  • 39
    • 3843109453 scopus 로고    scopus 로고
    • Expressing generality and roots of algebra
    • N. Bednarz, C. Kieran, & L. Lee (Eds.), Dordrecht, The Netherlands: Kluwer
    • Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra (pp. 65-86). Dordrecht, The Netherlands: Kluwer.
    • (1996) Approaches to Algebra , pp. 65-86
    • Mason, J.1
  • 46
    • 0037860124 scopus 로고
    • Visualization and mathematical giftedness
    • Presmeg, N. C. (1986). Visualization and mathematical giftedness. Educational Studies in Mathematics, 17, 297-311.
    • (1986) Educational Studies in Mathematics , vol.17 , pp. 297-311
    • Presmeg, N.C.1
  • 48
    • 0012003521 scopus 로고
    • How well do students write geometry proofs?
    • Senk, S. (1985). How well do students write geometry proofs? Mathematics Teacher, 78, 448-456.
    • (1985) Mathematics Teacher , vol.78 , pp. 448-456
    • Senk, S.1
  • 49
    • 13544272933 scopus 로고
    • A study of pupils' individual characteristics in processing mathematical information
    • Shapiro, S. I. (1965). A study of pupils' individual characteristics in processing mathematical information. Voprosy Psikhologii, 2.
    • (1965) Voprosy Psikhologii , vol.2
    • Shapiro, S.I.1
  • 51
    • 13544275927 scopus 로고    scopus 로고
    • How do mathematically gifted students abstract and generalize mathematical concepts?
    • Sriraman, B. (2002). How do mathematically gifted students abstract and generalize mathematical concepts? NAGC 2002 Research Briefs, 16, 83-87.
    • (2002) NAGC 2002 Research Briefs , vol.16 , pp. 83-87
    • Sriraman, B.1
  • 52
    • 2942591342 scopus 로고    scopus 로고
    • Mathematical giftedness, problem solving, and the ability to formulate generalizations
    • Sriraman, B. (2003a). Mathematical giftedness, problem solving, and the ability to formulate generalizations. Journal of Secondary Gifted Education, 14, 151-165.
    • (2003) Journal of Secondary Gifted Education , vol.14 , pp. 151-165
    • Sriraman, B.1
  • 53
    • 13544254629 scopus 로고    scopus 로고
    • The characteristics of mathematical creativity
    • Sriraman, B. (2003b). The characteristics of mathematical creativity. The Mathematics Educator, 14, 19-34.
    • (2003) The Mathematics Educator , vol.14 , pp. 19-34
    • Sriraman, B.1
  • 55
    • 13544259013 scopus 로고
    • Experimental teaching of mathematical logic in the elementary school
    • Suppes, P., 61 Binford, F. (1965). Experimental teaching of mathematical logic in the elementary school. The Arithmetic Teacher, 12, 187-195.
    • (1965) The Arithmetic Teacher , vol.12 , pp. 187-195
    • Suppes, P.1    Binford, F.2
  • 56
    • 0040155408 scopus 로고
    • Resolving the continuing dilemmas in school geometry
    • M. M. Lindquist & A. P. Shulte (Eds.). Reston, VA: National Council of Teachers of Mathematics
    • Usiskin, Z. P. (1987). Resolving the continuing dilemmas in school geometry. In M. M. Lindquist & A. P. Shulte (Eds.), Learning and teaching geometry, K-12: 1987 yearbook (pp. 17-31). Reston, VA: National Council of Teachers of Mathematics.
    • (1987) Learning and Teaching Geometry, K-12: 1987 Yearbook , pp. 17-31
    • Usiskin, Z.P.1
  • 60
    • 13544270264 scopus 로고
    • Individual differences in solving geometry problems on proof
    • J. Kilpatrick & I. Wirszup (Eds.), Stanford, CA: School Mathematics Study Group
    • Yakimanskaya, I. S. (1970). Individual differences in solving geometry problems on proof. In J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and teaching mathematics (Vol. 4). Stanford, CA: School Mathematics Study Group
    • (1970) Soviet Studies in the Psychology of Learning and Teaching Mathematics , vol.4
    • Yakimanskaya, I.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.