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A Study on the Effective Use of Tangrams for the Mathematical Justification of the Gifted Elementary Students  

Hwang, Jinam (둔대초등학교 / 경인교육대학교 교육전문대학원)
Publication Information
Journal of Elementary Mathematics Education in Korea / v.19, no.4, 2015 , pp. 589-608 More about this Journal
Abstract
The inquiry subject of this paper is the number of convex polygons one can form by attaching the seven pieces of a tangram. This was identified by two mathematical proofs. One is by using Pick's Theorem and the other is 和々草's method, but they are difficult for elementary students because they are part of the middle school curriculum. This paper suggests new methods, by using unit area and the minimum area which can be applied at the elementary level. Development of programs for the mathematically gifted elementary students can be composed of 4 class times to see if they can prove it by using new methods. Five mathematically gifted 5th grade students, who belonged to the gifted class in an elementary school participated in this program. The research results showed that the students can justify the number of convex polygons by attaching edgewise seven pieces of tangrams.
Keywords
mathematical justification; tangram; convex polygon; development of programs for the mathematically gifted elementary students;
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  • Reference
1 교육부 (2015). 수학과 교육과정. 교육부 고시 제 2015-74호 [별책 8].
2 박교식 (2007). 정사각형 칠교판의 일곱 조각으로 만들 수 있는 볼록 다각형의 탐색. 수학교육학연구, 17(3), 221-232.
3 송상헌 (2004). 수학 영재 교수.학습 자료 개발을 위한 소재 발굴에 대한 연구. 과학교육논총, 16, 67-86. 경인교육대학교.
4 송상헌 (2008). 수학교육과정에 비추어 본 탱그램과 유사탱그램의 재조명. 수학교육학연구, 18(3), 391-405.
5 안주형, 송상헌 (2002). 탱그램과 모자이크 퍼즐의 활용에 대한 연구. 학교수학, 4(2), 283-296.
6 이윤우 (2014). 'Pick의 정리'문제 해결 과정에서 나타나는 수학영재 학생들의 사고특성과 정당화 분석. 한국교원대학교 석사학위논문.
7 최종현, 송상헌 (2005). 주제 탐구형 수학 영재 교수.학습자료 개발에 관한 연구. 학교수학, 7(2), 169-192.
8 Gardner, M. (1988). Time travel and other mathematical bewilderments. New York: W. H. Freeman and Company.
9 Grunbaum, B., & Shephard, G. C. (1993). Pick's theorem. The American Mathematical Monthly, 100(2), 150-161.   DOI
10 Lakatos, I. (1976). Proof and refutation: The logic of mathematical discovery. Cambridge, UK: Cambridge University Press.
11 Miyazaki, M. (2000). Levels of Proof in Lower Secondary School Mathematics. Educational Studies in Mathematics 27(3), 249-266.   DOI
12 Van Delft, P., & Botermans, J. (1995) Creative puzzles of the world. Berkeley, CA: Key Curriculum Press.
13 Wang, F. T., & Hsiung, C. C. (1942). A theorem on the tangram. The American Mathematical Montly, 49(9), 596-599.   DOI
14 和々草 (2007). http://www1.kamakuranet.ne.jp/usasan/에서 2015년 9월 인출.