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(예비)교사를 위한 완비성의 학습과 지도에 관한 소고

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주제분류수학

초록

In this paper, the author focuses on the teaching-level and learning-level of the completeness axiom and its applications on [0,1] and R, RxR, RxRxR by (expected) teachers in the school mathematics, which is usually introduced in the class of real analysis of university mathematics. Firstly the author considers the properties of the completeness axiom and its 19 equivalent theorems, next he deals with its importances in the school mathematics and finally he suggests the teaching and learning of the concepts on the completeness axiom and its applications on [0,1] and R, RxR, RxRxR by (expected) teachers in the school mathematics.

Abstract

In this paper, the author focuses on the teaching-level and learning-level of the completeness axiom and its applications on [0,1] and R, RxR, RxRxR by (expected) teachers in the school mathematics, which is usually introduced in the class of real analysis of university mathematics. Firstly the author considers the properties of the completeness axiom and its 19 equivalent theorems, next he deals with its importances in the school mathematics and finally he suggests the teaching and learning of the concepts on the completeness axiom and its applications on [0,1] and R, RxR, RxRxR by (expected) teachers in the school mathematics.

참고문헌 (21)

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  10. 최용준, "중학교 수학 2 교과서" (2010), (주) 천재문화
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  16. Prediger Susanne, "How to develop mathematics-for- teaching and for understanding: the case of meanings of the equal sign", J. Math. Teacher Educ., 13, pp.73~93 (2010)
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  19. Trench, William F., "Introduction To Real Analysis" (2003), Pearson Education
  20. Usiskin, Z., "Teachers' mathematics: A collection of content deserving to be a field. Paper presented at the National Summit on the Mathematical Education of Teachers", ~ (2001)
  21. Wilhelmi Miguel R., "Didactic effectiveness of mathematical definitions, the case of the absolute value", int'l Electronic J. of Mathematics ed, 2(2), pp.72~90 (2007)

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