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http://dx.doi.org/10.30807/ksms.2018.21.4.007

A Comparative Analysis of Pi and the Area of a Circle in Mathematics Textbooks of Korea, Japan, Singapore and The US  

Choi, Eunah (Woosuk University)
Publication Information
Journal of the Korean School Mathematics Society / v.21, no.4, 2018 , pp. 445-467 More about this Journal
Abstract
In this study, we analyzed the contents of pi and the area of a circle presented in Korean, Japanese, Singapore, and American mathematics textbooks, and drew implications for the teaching of pi and the area of a circle in school mathematics. We developed a textbook analysis framework by theoretical discussions on the concept of the pi based on the various properties of pi and the area of a circle based on the central ideas of measurement and the previous researches on pi and the area of a circle in elementary mathematics. We drew five suggestions for improving the teaching of pi and three suggestions for improving the teaching of the area of a circle in Korean elementary schools.
Keywords
pi; the area of a circle; the property of pi; central ideas of measurement; international comparison;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 강문봉 (2001). 초등학교에서 ${\pi}=3.14$의 사용에 대하여, 과학교육논총, 13, 51-62.
2 강완 (2001). 원의 넓이공식에 대한 교수학적 변환 분석, 과학과수학교육논문집, 27, 37-68.
3 교육과학기술부 (2012). 수학과 교육과정. 교육과학기술부 고시 제 2011-361호(별책 8).
4 교육부 (2015). 수학과 교육과정. 교육부 고시 제 2015-74호(별책 8).
5 교육부 (2017). 수학 6-1. 서울: 천재교육.
6 교육부 (2018), 수학 6-1. 세종: 교육부.
7 문교부 (1989). 산수 6-1. 서울: 국정교과서주식회사.
8 방정숙, 이지영, 이상미, 박영은, 김수경, 최인영, 선우진 (2015). 한국.중국.일본.미국의 초등학교 수학과 교육과정 비교.분석 - 도형 영역을 중심으로. 한국학교수학회논문집, 18(3), 311-334.
9 이승은, 이정은, 박교식 (2018). 우리나라와 일본의 초등학교 수학과 교육과정 측정 영역 비교.분석 : 외연량을 중심으로. 한국학교수학회논문집, 21(1), 19-37.
10 강향임, 최은아 (2015). 초등수학 영재교육 대상자의 원주율 개념에 대한 이해. 수학교육논문집, 29(1), 91-110.
11 최영기, 홍갑주 (2008). 원주율의 상수성과 아르키메데스의 계산법, 수학교육, 47(1), 1-10.
12 최은아, 강향임 (2014). 예비교사의 원의 넓이에 대한 내용지식 분석. 학교수학, 16(4), 763-708.
13 文部科學省(2008). 小學校學習指導要領解說算數編.
14 藤井齊亮 外(2015). 新編 新しい算數 5-下. 東京:東京書籍.
15 藤井齊亮 外(2015). 新編 新しい算數 6. 東京:東京書籍.
16 Baravalle, H. (1969). The number ${\pi}$, In J. K. Baumgart (Eds), Historical topics for the mathematics classroom, Reston, VA: NCTM.
17 Baturo, A., & Nason, R. (1996). Student teachers' subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31(3), 235-268.   DOI
18 Beckmann, P. (2002). 파이의 역사 (박영훈 역), 서울: 경문사. (원저 1971년 출판)
19 Boyer, C. B. (1968). A History of mathematics. John Wiley & Sons.
20 Cajori, F. (1905). History of mathematics, London: The Macmillan Company.
21 Cajori, F. (1917). History of elementary mathematics with hints on methods of teaching. London: The Macmillan Company.
22 Common Core State Standards Initiative(2010). Common Core State Standards for Mathematics(CCSSM). http://www.corestandards.org/ssets/CCSSI_Math%20Standards.pdf
23 Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: D. Reidel Publishing Company.
24 Kheong, F. H., Soon, G. K., & Ramakrishnan, C. (2017b). My pals are here! Maths 6B (2nd ed). Singapore: Marshall Cavendish Education.
25 Lehrer, R., Jaslow, L., & Curtis, C. (2003). Developing an understanding of measurement in the elementary grades. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement (pp. 100-121). Reston, VA: NCTM.
26 Lobato, J., & Ellis, A. B. (2010). Essential understandings: Ratios, proportions, and proportional reasoning. In R. M. Zbiek (Series Ed.), Essential understandings. Reston, VA: NCTM.
27 Linn, S. L. & Neal, D. K. (2006). Approximating Pi with the golden ratio. Mathematics teacher, 99(7), 472-477.
28 Burke, M. J., Taggart, D. L. (2002). So that's why 22/7 is used for ${\pi}$, Mathematics teacher, 95(3), 164-169.
29 Ofir, R. (1991). Historical happenings in the mathematical classroom, For the learning of mathematics, 11(2), 21-23.
30 Ministry of Education. (2012). Mathematics Syllabus Primary one to six. Singapore: Curriculum Planning & Development Division, Ministry of Education.
31 Outhred, L. N., & Mitchelmore, M. C. (2000). Young children's intuitive understanding of rectangular area measurement. Journal for Research in Mathematics Education, 31(2), 144-167.   DOI
32 Scott, P. (2008), ${\pi}$ The chronicle, Australian Mathematics Teacher, 64(4), 3-5.
33 Reynolds, A. & Wheatley, G. H. (1996). Elementary students construction and coordination of units in an area setting. Journal for Research in Mathematics Education 27, 564-581.   DOI
34 Santucci, L. C. (2011), Recreating history with Archimedes and Pi, Mathematics teacher, 105(4), 298-303.   DOI
35 Schepler, H. C. (1950), The Chronology of Pi, Mathematics Magazine, 23(4), 216-228.   DOI
36 Seitz, D. T. (1986), A geometric figure relating the golden ratio and pi, Mathematics teacher, 79(5), 340-341.
37 Smith, D. E. (1925). History of Mathematics vol. 2 special topics of elementary mathematics, NY: Dover Publications.
38 Stephan, M., & Clements, D. (2003). Linear and area measurement in prekindergarten to grade 2. In D. H. Clements, & G. Bright (Eds.), Learning and teaching measurement (pp.3-16). Reston, VA: NCTM.
39 Stephen, H. (2012). Saxon Math course 1. Orlando: Houghton Mifflin Harcourt Publishing Company.
40 Velasco, S., Roman, F. L., Gonzalez, A., & White, J. A. (2006). Statistical estimation of some irrational numbers using an extension of Buffon's needle experiment. International Journal of Mathematical Education in Science and Technology, 37(6), 735-740.   DOI