Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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A Comparative Analysis of pi in Elementary School Mathematics Textbooks

초등학교 수학 교과서에 제시된 원주율의 지도방안 비교·분석

  • Received : 2022.12.02
  • Accepted : 2022.12.19
  • Published : 2022.12.31
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Abstract

This study aimed to derive pedagogical implications by comparing and analyzing how the concept of pi is taught in 10 different elementary mathematics textbooks, which are scheduled to be applied from 2023. We developed a textbook analysis framework by previous studies on the concept of pi and the teaching of pi, and analyzed in terms of three instructional elements (i.e. inferring conceptsof pi, understanding properties of pi, and applying relationships). We derived the need to emphasize various contexts for estimation of pi, presentation of problem situations that provide motivation to actually measure diameters and circumferences, providing an opportunity to explore the properties of measurement, and an experience the flexibility of selecting an approximate value of pi. Based on the above conclusions and pedagogical implications through the research results., we suggested ways to teach the concept of pi in elementary mathematics and improvement points for developing textbooks focusing on the context of introduction of pi and the use of technological tools.

본 연구는 2023년부터 적용 예정인 6학년 2학기 검정 교과서를 대상으로 초등 수학에서 원주율 개념을 어떻게 지도하고 있는지를 비교·분석하여 교수학적 시사점을 도출하고자 하였다. 이를 위해 원주율 개념과 원주율 지도에 관한 선행연구를 분석하여 분석 기준을 마련하였으며, 개념 추론하기, 속성 이해하기, 관계 적용하기의 교수·학습요소로 나누어 살펴보았다. 분석 결과를 통해, 어림 활동이 원주율 개념의 추론 활동으로 연결되기 위한 다양한 어림 맥락의 개발이 필요하다는 것과 지름과 원주를 실제로 측정을 해야 하는 동기를 제공하는 문제 상황의 제시, 지름을 단위로 하여 원주 위를 반복하여 세는 측도의 속성을 탐구할 수 있는 기회의 제공, 원주율의 상수 속성의 명시화, 상황에 따라 원주율의 근삿값 선택의 유연함을 경험하게 할 것을 시사점으로 제시하였다. 이상의 결론과 교수학적 시사점을 바탕으로 원주율의 도입 맥락과 공학 도구 활용에 초점을 맞추어 초등 수학에서 원주율 개념의 지도 방안과 향후 2022 개정 교육과정에 따른 교과서 개발에 개선점을 제안하였다.

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References

  1. Kang, W., Baek, S., Jeon, I., Lee, K., Kim, Y., ..., Lee, M. (2022). Mathematics 6-2. Daekyo. 
  2. Kang, H., & Choi, E. (2015). Elementary mathematically gifted students' understanding of Pi. Communications of Mathematical Education, 29(1), 91-110.  https://doi.org/10.7468/JKSMEE.2015.29.1.91
  3. Gu, K. & Na, B. (1997). The teaching of the area of figures in elementary school. Studies in mathematical and statistical. 21, 41-57. 
  4. Ministry of Education (2019). Notice of revision of classification of elementary school textbooks. Proclamation of the Ministry of Education #2019-195. Ministry of Education. 
  5. Ministry of Education (2020). Mathematics curriculum. Proclamation of the Ministry of Education #2020-236[Annex 8]. Ministry of Education. 
  6. Ministry of Education (2022). Mathematics curriculum. Proclamation of the Ministry of Education #2022-33[Annex 8]. Ministry of Education. 
  7. Ministry of Education (2021). Mathematics 6-2. Chunjae. 
  8. Kim, S., Kang, E., Kang, Y., Go, C., Kim, B., ..., Kim, Y. (2022). Mathematics 6-2. I-Scream. 
  9. Lew, H., Yu, H., Lee, C., Cho, Y., Tak, B., ..., Choi, I. (2022). Mathematics 6-2. Kumsung. 
  10. Park, K., Chong, Y., Ko, J., Kwon, S., Nam, J., ..., Prak, J. (2022). Mathematics 6-2. Bookdonga. 
  11. Park, M., Kang, K., Kim, D., Lim, D., Kim, S., ..., Kim E. (2022). Mathematics 6-2. Chunjae. 
  12. Park, S., Ryu, S., Kim, S., Kwon, S., Kim, N., ..., Kang, H. (2022)Mathematics 6-2. YBM. 
  13. Shin, D. (2009). A study on the influences on mathematics learning when π is taught as 3 [Master's thesis, Chucheon national university of education]. 
  14. Shin, H., Kim, T., Cho, B., Kim, L., Jeong, N,. ..., Choi, H. (2022). Mathematics 6-2. Visang. 
  15. Ahn, B., Na, G., Kim, M., Lee, K., Ryu, H., ..., Choi, J. (2022). Mathematics 6-2. Bookdonga. 
  16. Im, H., Ko, E., & Hwang, E. (2021). Analysis of instruction content and instruction method of circular constant by elementary mathematics curriculum: from the 1st curriculum to the 2015 revised curriculum. Journal of Learner-Centered Curriculum and Instruction. 22(2), 615-630. 
  17. Chang, H., Seo, D., Kim, M., Kim, S., Kim, J., ..., Kim, C. (2022). Mathematics 6-2. Mirae-n. 
  18. Jeong, D. (1998). Introduction to the history of mathematics for teachers. Incheon national university of education. 
  19. Cho, H. (2007). A study on the understanding of pi of middle school students [Master's thesis, Kongju national university]. 
  20. Choi, Y., & Hong, G. (2008). The nature of Pi as a constant and Archimedes' calculation method. The Mathematical Education, 47(1), 1-10. 
  21. Choi, E. (2018). A comparative analysis of Pi and the area of a circle in mathematics textbooks of Korea, Japan, Singapore and The US. Journal of the Korean School Mathematics, 21(4), 445-467.  https://doi.org/10.30807/KSMS.2018.21.4.007
  22. Choi, E., Joung, Y. (2021). Comparative research on teaching method for multiplication by 2-digit numbers in elementary mathematics textbooks of Korea, Japan, Singapore, and USA. Communications of Mathematical Education, 35(4), 505-525.  https://doi.org/10.7468/JKSMEE.2021.35.4.505
  23. Han, D., Ko, E., Lee, S., Cho, H., Han, S., ..., Shin, H. (2022). Mathematics 6-2. Chunjae. 
  24. Heo, S. (2019). A didactical analysis on the ratio of circumference, π [Master's thesis, Seoul national university].
  25. Baravalle, H. (1969). The number π, In J. K. Baumgart (Ed.), Historical topics for the mathematics classroom. NCTM.
  26. Beckmann, P. (1971). A history of pi. The Golem Press.
  27. Boyer, C. B. & Merzbach, U. C. (1968). A history of mathematics. John Wiley & Sons.
  28. Burke, M. J., Taggart, D. L. (2002). So that's why 22/7 is used for Pi!, The Mathematics teacher, 95(3), 164-169.
  29. Cajori, F. (1905). History of mathematics. The Macmillan Company.
  30. Linn, S. L. & Neal, D. K. (2006). Approximating Pi with the golden ratio. The Mathematics teacher, 99(7), 472-477. https://doi.org/10.5951/MT.99.7.0472
  31. Smith, D. E. (1925). History of Mathematics vol. 2 special topics of elementary mathematics. Dover Publications.