An Analysis on the Concept and Measuring Activities of the Height of Figures in Elementary School Mathematics Textbooks2

Title & Authors
An Analysis on the Concept and Measuring Activities of the Height of Figures in Elementary School Mathematics Textbooks2
Paek, Dae Hyun;

Abstract
The concept and measuring activities of the height of figures are essential to find the areas or volumes of the corresponding figures. For plane figures, the height of a triangle is defined to be the line segment from a vertex that is perpendicular to the opposite side of the triangle, whereas the height of a parallelogram(trapezoid) is defined to be the distance between two parallel sides. For the solid figures, the height of a prism is defined to be the distance of two parallel bases, whereas the height of a pyramid is defined to be the perpendicular distance from the apex to the base. In addition, the height of a cone is defined to be the length of the line segment from the apex that is perpendicular to the base and the height of a cylinder is defined to be the length of the line segment that is perpendicular to two parallel bases. In this study, we discuss some pedagogical problems on the concepts and measuring activities of the height of figures to provide alternative activities and suggest their educational implications from a teaching and learning point of view.
Keywords
height;area;volume;measurement;learning activities;
Language
Korean
Cited by
References
1.
교육과학기술부 (2011). 수학 6-1. 두산동아(주). (Ministry of Education, Science & Technology (2011). Elementary school mathematics 6-1. Doosandonga(Inc.).)

2.
교육부 (2014). 수학 4-2. (주)천재교육. (Ministry of Education (2014). Elementary school mathematics 4-2. Chunjae Education(Inc.).)

3.
교육부 (2015a). 수학 5-1. (주)천재교육. (Ministry of Education (2015a). Elementary school mathematics 5-1. Chunjae Education(Inc.).)

4.
교육부 (2015b). 수학 6-1. (주)천재교육. (Ministry of Education (2015b). Elementary school mathematics 6-1. Chunjae Education(Inc.).)

5.
교육부 (2015c). 수학 6-2. (주)천재교육. (Ministry of Education (2015c). Elementary school mathematics 6-2. Chunjae Education(Inc.).)

6.
교육부 (2015d). 수학 익힘책 5-1. (주)천재교육. (Ministry of Education (2015d). Elementary school mathematics workbook 5-1. Chunjae Education (Inc.).)

7.
교육부 (2015e). 수학 5-1 교사용 지도서. (주)천재교육. (Ministry of Education (2015e). Teacher's guide for elementary school mathematics 5-1. Chunjae Education(Inc.))

8.
교육부 (2015f). 수학 6-1 교사용 지도서. (주)천재교육. (Ministry of Education (2015f). Teacher's guide for elementary school mathematics 6-1. Chunjae Education(Inc.))

9.
교육부 (2015g). 수학 6-2 교사용 지도서. (주)천재교육. (Ministry of Education (2015g). Teacher's guide for elementary school mathematics 6-2. Chunjae Education(Inc.).)

10.
국립국어원 (2016). 표준국어대사전. http://stdweb2.korean.go.kr. 에서 2016년 1월 인출. (National Institute of Korean Language (2016). Basic Korean Dictionary, Extracted from http://stdweb2. korean.go.kr in January, 2016.)

11.
권석일․박교식 (2011). 초등학교 수학 교과서에서의 용어 사용과 정의 방식에 대한 비판적 분석: 몇 가지 예를 중심으로. 한국초등수학교육학회지, 15(2), 301-316. (Kwon, S. and Park, K. (2011). A critical analysis on usage and defining methods of terms in elementary mathematics textbooks in Korea centered in some examples. Journal of Elemen-tary Mathematics Education, 15(2), 301-316.)

12.
김원경․조민식․방금성․김수미․배수경․오혜정 외 (2014). 중학교 수학 1. 비상교육. (Kim, W.., Cho, M., Bang, K., Kim, S., Bae, S., Oh, H. et al. (2014). Middle school mathematics 1. Visang (Inc.).)

13.
나귀수 (2012). 초등학교 학생들의 넓이 개념 이해도 조사-초등학교 6학년 학생들을 중심으로-. 한국 초등수학교육학회지, 16(3), 451-469. (Na, G. (2012). Examining students' conceptions about the area of geometric figures. Journal of Elementary Mathematics Education, 16(3), 451-469.)

14.
류희찬․류성림․이경화, 신보미, 강순모, 윤옥교 외 (2014). 중학교 수학 1. 천재교과서. (Lew, H., Ryu, S., Lee, K., Shin, B., Kang, S., Yoon, O. et al. (2014). Middle school mathemat-ics 1. Chanjae.)

15.
박교식 (2013). 우리나라 초등학교 수학용어의 분석과 비판: 몇 가지 예를 중심으로. 한국초등수학교육학회지, 17(1), 1-17. (Park, K. (2013). An analysis and criticism on mathematics terminologies used in elementary school mathematics: Focused on some examples, Journal of Elementary Mathematics Education, 17(1), 1-17.)

16.
박교식․임재훈 (2005). 초등학고 수학 교과서에서 사용되는 무정의 용어 연구. 수학교육학연구, 15(2), 197-213. (Park, K. and Yim, J. (2005). A critical examination of undefined mathematical terms used in elementary school mathematics textbooks of Korea. Journal of Educational Research in Mathematics, 15(2), 197-213.)

17.
백대현 (2011). 제7차와 2007년 개정 교육과정의 초등 학교 수학 교과서에 제시된 '약속'의 내용과 서술 방식의 비교 분석. 수학교육학연구, 21(3), 261-278. (Paek, D. H. (2011). A comparative analysis on the contents and statements of definitions in elementary school mathematics textbooks on the 7th and the revised 2007 curricula. Journal of Educational Research in Mathematics, 21(3), 197-213.)

18.
우정호․박교식․이종희․박경미․김남희․임재훈 외 (2014). 중학교 수학 1. 두산동아. (Woo, J., Park, K., Lee, J., Park, K., Kim, N., Yim, J. et al. (2014). Middle school mathematics 1. Doosandonga.)

19.
이강섭․최상기․왕규채․이강희․송교식․안인숙 외 (2014). 중학교 수학 1. (주)미래엔. (Lee, K., Choi, S., Wang, K., Lee, K., Song, K., Ahn, I. et al. (2014). Middle school mathematics 1. Mirae-n.)

20.
임승현․박영희 (2011). 초등학교 6학년 학생들의 도형의 높이에 대한 이해 연구. 한국초등수학교육학회지, 15(1), 141-159. (Im, S. H. and Park, Y. H. (2011). A study on the understanding of height concept of figures of sixth grade students of elementary schools. Journal of Elementary Mathematics Education in Korea, 15(1), 143-159.)

21.
황선욱․강병개․한길준․한철형, 권혁천, 김의석 외 (2014). 중학교 수학 1. 좋은책 신사고. (Hwang, S., Kang, B., Han, K., Han, C., Kwon, H., Kim, E. et al. (2014). Middle school mathematics 1. Sinsago.)

22.
Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Flanders, J., Hartfield, R et al. (2007). Everyday mathematics. Wright Group/McGraw Hill.

23.
Charles, R. I., Crown, W., & Fennel, F. (2005). Mathematics, grade 6. Pearson Education.

24.
Clements, D. H., Malloy, C. E., Moseley, L. G., Orihuela, Y., & Silbey, R. R. (2005). Math, grade 6. McGraw Hill.

25.
Norwood, K. S., Roby, T., Mendoza Epperson, J. A. Dixon, J. K., Scheer, J. K., Wright, D. G et al. (2009). HSP math grade 6. Harcourt School Publishers.

26.
Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2012). Helping children learn mathematics (10th edition). John Wiley & Sons, Inc.

27.
Serra, M. (2008). Discovering geometry, Fourth ed., Key Curriculum Press.