Browse > Article
http://dx.doi.org/10.7858/eamj.2021.024

A Study on the Plane Figure of Elementary School Mathematics in the View of Classification  

Kim, Hae Gyu (Department of Mathematics Education, Teachers College Jeju National University)
Lee, Hosoo (Department of Mathematics Education, Teachers College (Elementary Education Research Institute) Jeju National University)
Choi, Keunbae (Department of Mathematics Education, Teachers College Jeju National University)
Publication Information
East Asian mathematical journal / v.37, no.4, 2021 , pp. 355-379 More about this Journal
Abstract
In this article, we investigated plane figures introduced in elementary school mathematics in the perspective of traditional classification, and also analyzed plane figures focused on the invariance of plane figures out of traditional classification. In the view of traditional classification, how to treat trapezoids was a key argument. In the current mathematics curriculum of the elementary school mathematics, the concept of sliding, flipping, and turning are introduced as part of development activities of spatial sense, but it is rare to apply them directly to figures. For example, how are squares and rectangles different in terms of symmetry? One of the main purposes of geometry learning is the classification of figures. Thus, the activity of classifying plane figures from a symmetrical point of view has sufficiently educational significance from Klein's point of view.
Keywords
line symmetry; rotational symmetry; symmetric group;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Gutierez, A. (1996). Children's ability for using different plane representations of space figures. New Directions in Geometry Education, 33-42.
2 Kennedy, L. M., Tipps, S., & Johnson, A. (2004). Guiding children's learning of mathematics. Belmont: Wadsworth.
3 Klein, F. (1872). A comparative review of recent researches in geometry". Complete English Translation is here https://arxiv.org/abs/0807.3161
4 Lockwood, E. H. & Macmillan, R. H. (1978). Geometric Symmetry, London: Cambridge Press.
5 Mainzer, K. (2005). Symmetry And Complexity: The Spirit and Beauty of Nonlinear Science. World Scientific. ISBN 981-256-192-7.
6 Maletsky, Evan M. et al. (2002). Harcourt Math (Math-Grade 4), Harcourt, Inc.
7 McGee, M. G. (1979). Human spatial abilities: Psychometric studies and environmental, genetic, hormonal, and neurological influences. Psychological Bulletin, 86(5), 889-918.   DOI
8 Harris, L. J. (1981). Sex-related variations in spatial skill. In L. S. Liben, A. H. Patterson, & N. Newcombe (Eds.), Spatial representation and behavior across the life span (pp.83-125). NewYork: AcademicPress.
9 Tartre, L. A. (1990a). Spatial orientation skill and mathematics problem solving. Journal for Research in Mathematics Education, 21(3), 216-229.   DOI
10 National Council of Teachers of Mathematics (2000). Principal and standards for school mathematics. Reston, VA: The Author
11 Weyl, H. (1969). Symmetry, Princeton University Press.
12 교육부 (2018). 수학 4-2, (주)천재교육: 서울.
13 김유경.방정숙(2007). 초등학교 6학년 학생들의 공간 감각과 공간추론 능력실태 조사. 대한수학교육학회지 학교수학, 9(3), 353-373.
14 박상욱, 박교식, 김지원. (2014). 미국 초등학교 수학 교과서 Everyday Mathematics의 확률 영역 분석. 한국초등수학교육학회지, 18(3), 475-492.
15 우정호(2006). 수학 학습-지도 원리와 방법. 서울대학교 출판부: 서울
16 정영옥 (2017). 초등학교 수학에서 공간 방향에 대한 교육과정과 교과서 비교. 대한수학교육학회지 학교수학, 19(4), 663-690.
17 이성미.방정숙 (2007). 초등학생들의 공간감각 이해능력 실태조사. 수학교육, 46(3), 273-292.
18 이종영(2005). 초등학교에서 지도하는 공간 감각 내용에 관한 고찰. 대한수학교육학회지 학교수학, 7(3), 269-286.
19 조영선.정영옥(2012). 초등학생들의 공간 감각 실태 조사-4, 5, 6학년을 중심으로. 한국초등수학교육학회지, 16(3), 359-388.
20 Bishop, A. J. (1980). Spatial abilities and mathematics education - A review. Educational Studies in Mathematics, 11, 257-269.   DOI
21 하혜진 (2018). 대칭성을 이용한 사각형 학습지도 방안 연구, 서울대학교 대학원 교육학 석사학위 논문
22 National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: The Author
23 DeLanda, M. (2009). 강도의 과학과 잠재성의 철학 (이정우, 김영범 역). 서울: 그린비. (원저 2002년 출판)
24 Baroody, A. J. & Coslick, R. T. (1998). Fostering children's mathematical power: An investigative approach to k-8 mathematics instruction. Mahwah, NJ: Lawrence Erlbaum Associates. 권성룡 외 11인 공역(2005). 수학의 힘을 길러주자. 왜? 어떻게? 서울: 경문사.
25 Hershkowitz, R. (1990). Psychological aspect of learning geometry. In P. Nesher, & J. Kilpatrick (Eds), Mathematics and Cognition (pp. 70-95). Cambridge, UK: University Press.
26 Clements, D. H. (1999). Geometric and spatial thinking in young children. In V. C. Juanita(Ed.), Mathematics in the Early Years (pp. 66-79). Reston, VA: National Council of Teachers of Mathematics.
27 Clements, D. H. & Battista, M. B. (1992). Geometry and spatial reasoning. In A. G. Douglas (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). New York: Macmillan Publishing Company.
28 Del Grande, J. J. (1990). Spatial sense. Arithmetic teacher, 37, 14-20.   DOI