초등 영재 교수․학습을 위한 평면에서의 등주문제 내용구성 연구 - 기하적인 방법을 중심으로 -
A Study on the Teaching Design of the Isoperimetric Problem on a Plane for Mathematically gifted students in the Elementary School - focused on the geometric methods -
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In this article, we study on the teaching design, focused on the geometric methods, of 2-D isoperimetric problem for the elementary mathematically gifted students. For our teaching design, we discussed the ideals of Zenodorus's polygon proof, Steiner's four-hinge proof, Steiner's mean boundary proof, Steiner's snowball-packing proof, Edler's finite existence proof and Lawlor's dissection proof, and then the ideals achieved were modified with the theoretical backgrounds-the theory of Freudenthal's mathematisation, the method of analysis-synthesis. We expect that this article would contribute to the elementary mathematically gifted students to acquire and to improve spatial sense.
Abstract
In this article, we study on the teaching design, focused on the geometric methods, of 2-D isoperimetric problem for the elementary mathematically gifted students. For our teaching design, we discussed the ideals of Zenodorus's polygon proof, Steiner's four-hinge proof, Steiner's mean boundary proof, Steiner's snowball-packing proof, Edler's finite existence proof and Lawlor's dissection proof, and then the ideals achieved were modified with the theoretical backgrounds-the theory of Freudenthal's mathematisation, the method of analysis-synthesis. We expect that this article would contribute to the elementary mathematically gifted students to acquire and to improve spatial sense.
참고문헌 (15)
- 정영옥, "초등수학교육의 이해" (2005), 경문사
- 강문봉, "Lakatos 방법론을 초등수학에 적용하기 위한 연구", 수학교육학연구, 14(2), pp.143~156 (2004), 대한수학교육학회
- 강문봉, "분석법에 관한 고찰", 대한수학교육학회 논문집, 2(2), pp.81~93 (1992)
- 우정호, "Lakatos의 수리철학의 교육적 연구", 대한수학교육학회 논문집, 3(2), pp.1~16 (1993)
- 우정호, "수학학습-지도 원리와 방법" (2006), 서울대학교 출판부
- 최근배, "초등수학 영재를 위한 평면에서의 등주문제 고찰 -게슈탈트 관점을 중심으로", 학교수학, 11(2), pp.227~241 (2009), 대한수학교육학회
- Blasjo, V., "The Evolution of the Isoperimetric Problem", The American Mathematical Monthly, 112, pp.526~566 (2005)
- "The Isoperimetric Inequality: A History of the Problem, Proofs and Applications"[URL]
- Freudenthal, H., "Mathematics as an educational task" (1973), Reidel
- Hildebrandt, S., "The Parsimonious Universe: Shape and Form in the Natural World" (1996), Springer-Verlag New York, Inc
- Polya, G., "How to Solve It: A new Aspect of Mathematical Method, 2nd ed" (1957), Princeton University Press
- Polya, G., "Induction and Analogy in Mathematics" (1973), Princeton University Press
- "Historical Review of the Isoperimetric Theorem in 2-D, and its place in Elementary Plane Geometry"[URL]
- "The Remarkable Life of the Isoperimetric Problem: The World's Most Influential Mathematics Problem"[URL]
- "Steiner Symmetrization and Applications"[URL]