평등 수렴의 역사에 대한 분석과 그 교육적 시사점에 대한 연구
A study on the analysis of history of uniform convergence and its educational implications
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This study analyses on the history of uniform convergence, and discusses its educational implications. First, this study inspects `overflowing of the Euclidean methodology' which was suggested by Lakatos as a cause of tardy appearance of uniform convergence, and reinterprets that cause in the perspective of `symbolization'. Second, this study looks into the emergence of uniform convergence of Seidel and Weierstrass in this viewpoint of symbolization. As a result, of analysis, we come to know that the definition of uniform convergence had been changed into the theory of `domain and graph' from that of `point and function value' by the location change of the quantifier. As these results, this study puts forward an educational suggestion from an angle of epistemological obstacle, concept definition and concept image.
Abstract
This study analyses on the history of uniform convergence, and discusses its educational implications. First, this study inspects `overflowing of the Euclidean methodology' which was suggested by Lakatos as a cause of tardy appearance of uniform convergence, and reinterprets that cause in the perspective of `symbolization'. Second, this study looks into the emergence of uniform convergence of Seidel and Weierstrass in this viewpoint of symbolization. As a result, of analysis, we come to know that the definition of uniform convergence had been changed into the theory of `domain and graph' from that of `point and function value' by the location change of the quantifier. As these results, this study puts forward an educational suggestion from an angle of epistemological obstacle, concept definition and concept image.
참고문헌 (12)
- U. Bottazzini, "The Higher calculus : A History of Real and Complex Analysis from Euler to Weierstrass" (1986), Springer-Verlag
- C. B. Boyer, "수학의 역사(하)" (2000), 경문사
- D. M. Bressoud, "실해석학 (2판)-전혀 새로운 접근-" (2009), 교우사
- C. H. Edwards, "The Historical Development of the Calculus" (1979), Springer-Verlag
- J. Fauvel, "The Use of history in Teaching Mathematics", For the Learning of Mathematics, 11(2), pp.3~6 (1991)
- J. W. Grabiner, "The Origins of Cauchy‘s Rigorous Calculus" (1981), MIT Press
- I. Grattan-Guinness, "The Development of the Foundations of Mathematical Analysis From Euler to Riemann" (1971), MIT Press
- I. Grattan-Guinness, "From the Calculus to Set Theory" (1980), Duckworth
- Jung, D. M., "실해석학 개론" (2016), 경문사
- M. Kitcher, "The Nature of Mathematical Knowledge" (1983), Oxford University Press
- I. Lakatos, "수학적 발견의 논리" (2001), 아르케
- Woo J. H., "수학 학습-지도 원리와 방법, 서울" (2000), 서울대학교 출판부