고등학교 수학 교과서에서의 반례에 대한 학습가능성 탐색

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참고문헌 (68)

1. 교육과학기술부, (2011), 교육과학기술부
2. 김수미, "범례 제시를 통한 도형 개념 지도 방안", 수학교육학연구, 15(4), pp.401~417 (2005), 대한수학교육학회
3. 김수환, "고등학교 수학 I" (2009), 교학사
4. 김수환, "고등학교 수학 Ⅱ" (2009), 교학사
5. 김해경, "고등학교 수학 Ⅰ" (2009), 더 텍스트
6. 김해경, "고등학교 수학 Ⅱ" (2009), 더 텍스트
7. 양승갑, "고등학교 수학 I" (2009), 금성출판사
8. 양승갑, "고등학교 수학 Ⅱ" (2009), 금성출판사
9. 우무하, "고등학교 수학 I" (2009), 박영사
10. 우무하, "고등학교 수학 Ⅱ" (2009), 박영사
11. 우정호, "고등학교 수학 Ⅰ" (2009), 두산동아
12. 우정호, "고등학교 수학 Ⅱ" (2009), 두산동아
13. 류희찬, "고등학교 수학 I" (2009), 미래엔컬처그룹
14. 류희찬, "고등학교 수학 Ⅱ" (2009), 미래엔컬처그룹
15. 윤재한, "고등학교 수학 Ⅰ" (2009), 더 텍스트
16. 윤재한, "고등학교 수학 Ⅱ" (2009), 더 텍스트
17. 이강섭, "고등학교 수학 I" (2009), 지학사
18. 이강섭, "고등학교 수학 Ⅱ" (2009), 지학사
19. 이동원, "고등학교 수학 I" (2009), 법문사
20. 이동원, "고등학교 수학 Ⅱ" (2009), 법문사
21. 이만근, "고등학교 수학 I" (2009), 고려출판
22. 이만근, "고등학교 수학 Ⅱ" (2009), 고려출판
23. 이정곤, "예비교사들을 대상으로 한 증명활동과 반례생성 수행결과 분석 : 수열의 극한을 중심으로", 수학교육학연구, 21(4), pp.379~398 (2011), 대한수학교육학회
24. 이종희, "상위권 고등학생들의 수학적 정당화와 반증의 유형에 대한 사례연구", 교과교육학연구, 13(3), pp.633~652 (2009), 교과교육연구소
25. 이준열, "고등학교 수학 I" (2009), 천재교육
26. 이준열, "고등학교 수학 Ⅱ" (2009), 천재교육
27. 정상권, "고등학교 수학 I" (2009), 금성출판사
28. 정상권, "고등학교 수학 Ⅱ" (2009), 금성출판사
29. 최용준, "고등학교 수학 I" (2009), 천재교육
30. 최용준, "고등학교 수학 Ⅱ" (2009), 천재교육
31. 황석근, "고등학교 수학 I" (2009), 교학사
32. 황석근, "고등학교 수학 Ⅱ" (2009), 교학사
33. 황선욱, "고등학교 수학 Ⅰ" (2009), 좋은책신사고
34. 황선욱, "고등학교 수학 Ⅱ" (2009), 좋은책신사고
35. Alcock, L., "Using warranted implications to read and understand proofs", For the Learning of Mathematics, 25(1), pp.34~38 (2005)
36. Balacheff, N., "Radical constructivism in mathematics education", pp.89~110 (1991), Kluwer Academic Publishers
37. Ball, D. L., "The Teaching of Proof", Paper presented at the International Congress of Mathematicians, pp.907~920 (2002)
38. Carpenter, T., "Proceedings of the Twelfth International Commission on Mathematical Instruction", pp.155~162 (2001), University of Melbourne
39. ": Preparing America’s students for college and career" (2011)[URL]
40. Epp, S., "A unified framework for proof and disproof", Mathematics Teacher, 91(8), pp.708~713 (1998)
41. Hanna, G., "Advanced mathematical thinking", pp.54~61 (1991), Kluwer Academic Publishers
42. Hanna, G., "Challenges to the importance of proof", For the Learning of Mathematics, 15(3), pp.42~49 (1995)
43. Hersh, R., "Proving is convincing and explaining", Educational Studies in Mathematics, 24, pp.389~399 (1993)
44. Knuth, E., "Teachers’ conceptions of proof in the context of secondary school mathematics", Journal of Mathematics Teacher Education, 5(1), pp.61~88 (2002)
45. Ko, Y., "Proofs and Counterexamples: undergraduate students' strategies for validating arguments, evaluating statements, and constructing productions", 박사, pp.2010
46. Ko, Y., "Validating proofs and counterexamples across content domains: Practices of importance for mathematic majors", Journal for Mathematical Behavior, 32, pp.20~35 (2013)
47. Komatsu, K., "Counter-examples for refinement of conjectures and proofs in primary school mathematics", Journal of Mathematical Behavior, 29, pp.1~10 (2010)
48. Lakatos, I., "Proofs and refutations : The logic of mathematical discovery" (1976), Cambridge University Press
49. Lampert, M., "When the problem is not the question and the solution is not the answer : Mathematical knowing and teaching", American Educational Research Journal, 27(1), pp.29~63 (1990)
50. Lin, F. L., "Modeling students' learning on mathematical proof and refutation", Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 1, pp.3~18 (2005), University of Melbourne
51. Lithner, J., "Mathematical reasoning in calculus textbooks exercises", The Journal of Mathematical Behavior, 23, pp.405~427 (2004)
52. Mason, J., "Using counter-examples in calculus" (2009), Imperial College Press
53. Mesa, V., "Strategies for controlling the work in mathematics textbooks for introductory calculus", Research in Collegiate Mathematics Education, 16, pp.235~265 (2010)
54. Mesa, V., "Textbook mediation of teaching : an example from tertiary mathematics instructors", Educational Studies in Mathematics, 79(1), pp.85~107 (2012)
55. National Council of Teachers of Mathematics., "Curriculum and evaluation standards for school mathematics" (1989), National Council of Teachers of Mathematics
56. National Council of Teachers of Mathematics., "Principles and standards for school mathematics" (2000), National Council of Teachers of Mathematics
57. Peled, I., "Counter-examples that(only)prove and counter-examples that(also)explain", FOCUS on Learning Problems in Mathematics, 19(3), pp.49~61 (1997)
58. Polya, G., "How to solve it" (1973), Princeton University Press
59. Schmidt, W. H., "Many visions, many aims, 1 : A cross-national investigation of curricular intentions in school mathematics" (1996), Kluwer
60. Schoenfeld, A. H., "Teaching and Learning proof across the grades: A K-16 perspective", pp.12~16 (2009), Routledge
61. Selden, A., "Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem?", Journal for Research in Mathematics Education, 34(1), pp.4~36 (2003)
62. Thurston, W. P., "On proof and progress in mathematics", For the Learning of Mathematics, 15(1), pp.29~37 (1995)
63. Travers, K. J., "The IEA Study of mathematics I : Analusis of mathematics curricula" (1989), Pergamon Press
64. Watson, A., "Mathematics as a constructive activity: learners generating examples" (2005), Lawrence Erlbaum Associates
65. Weber, K., "Mathematics majors’ perceptions of conviction, validity, and proof", Mathematical Thinking and Learning, 12, pp.306~336 (2010)
66. Yackel, E., "A research companion to principles and standards for school mathematics", pp.227~236 (2003), National Council of Teachers of Mathematics
67. Zaslavsky, O., "Students’ understanding of the role of counter-examples", Proceedings of the 22nd conference of the international group for the psychology of mathematics education, 4, pp.225~232 (1998), University of Stellenbosch
68. Zazkis, R., "What makes a counterexample exemplary?", Educational Studies in Mathematics, 68(3), pp.195~208 (2008)

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