한국수학교육학회지시리즈E:수학교육논문집 (Communications of Mathematical Education)

  • 제33권3호
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  • Pages.335-354
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  • 2019
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  • 1226-6663(pISSN)
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  • 2287-9935(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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직관을 강조한 미분 지도의 대안적 방안 탐색 : 싱가포르 교과서를 중심으로

Exploring Alternative Ways of Teaching derivatives

  • 투고 : 2019.08.22
  • 심사 : 2019.09.03
  • 발행 : 2019.09.30
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초록

본 연구는 직관을 강조하는 방식으로 우리나라 미분 지도의 대안적 방안을 탐색하는 것을 목표로 한다. 우리나라 교육과정과 교과서의 미분 지도에 관한 내용을 싱가포르를 포함한 국외 사례와 비교하여 분석하였다. 우리나라에 비해 비교적 이른 시기에 미분계수와 미분을 학습하게 되는 싱가포르의 경우, 순간변화율이 아닌 접선의 기울기로 미분 개념을 도입하며, 공학적 도구와 귀납적 외삽법을 이용해 형식적이기보다는 직관적으로 전개하는 것을 확인하였다. 또한, 다른 국외 사례들을 살펴본 결과 영국과 호주 또한 직관을 강조하는 방식으로 미분을 지도하고 있음을 확인하였다. 이상을 바탕으로, 직관을 강조하는 방식으로 미분을 도입하고 지도하는 것의 의의를 말하고, 우리나라 미분 지도에 대한 시사점을 제안하였다.

The purpose of this study is to explore alternative ways of teaching derivatives in a way that emphasizes intuition. For this purpose, the contents related to derivatives in Korean curriculum and textbooks were analyzed by comparing with contents in Singapore Curriculum and textbooks. Singapore, where the curriculum deals with derivatives relatively earlier than Korea, introduces the concept of derivatives and differentiation as the slope of tangent instead of the rate of instantaneous change in textbook. Also, Singapore use technology and inductive extrapolation to emphasize intuition rather than form and logic. Further, from the results of the exploration of other foreign cases, we confirm that the UK and Australia also emphasized intuition in teaching derivatives and differentiation. Based on the results, we discuss the meaning and implication of introducing derivatives and teaching differentiation in a way that emphasizes intuition. Finally, we propose the implications for the alternative way of teaching differentiation.

키워드

참고문헌

  1. Ku, J., Kim, S., Lee, H-W., Cho, S. & Park, H-Y (2016). OECD Programme for International Students Assessment: An analysis of PISA 2015 Results. Seoul: Korea Institute for Curriculum and Evaluation.
  2. Ministry of Education (2015). Mathematics curriculum. Seoul: Ministry of Education.
  3. Kim, W., Cho, M., Bang, K., Yun, J., Shin, J., Kim, K., Park, H., Shim, J., Oh, H., Lee, D., Lim, S., Kang, S., Lee, S. & Jung, J. (2018). Mathematics II. Seoul: Visang
  4. Kim, J. (2017). Highschool student's differential concept learning understanding concepts and step understanding the notion of differentiation Analysis. (Unpublished master's thesis). Ewha Womans University, Seoul, Korea.
  5. Lew, H., Sunwoo, H., Shin, B., Cho, J., Lee, B., Kim, Y., Lim, M., Han, M., Nam, S., Kim, M. & Jeong, S. (2018). Mathematics II. Seoul: Chunjae.
  6. Park, K., Lee, H., Park, S., Kang, E., Kim, S., Lim, H., Kim, S., Chang, H., Kang, T., Kwon, J., Kim, M., Pang, J., Lee, H., Lim, M., Lee, M., Kim, H., Yun, S., Lee, K., Lee, K., Jo, H., Kwon, Y., Kwon, O., Shin, D., Kang, H., Kim, J., Do, J., Park, J., Seo, B., An, H., Oh, T., Lee, K., Lee, K., Lee, M., Lee, S., Lee, E., Lee, J., Jeon, T., Choi, J., Hwang, S., Park, M., Kim, H., Kang, S., & Yeo, M.(2015). A development of a draft for 2015 revised mathematics curriculum. Seoul: Korea Foundation for the Advancement of Science & Creativity.
  7. Park, S. (2010). The New Interpretation of Archimedes' 'method'. The Korean journal for history of mathematics, 23(4), 47-58.
  8. Song, M-Y., Rim, H., Choi, H., Park, H. Y. & Son, S. (2013). OECE Programme for International Students Assessment: Analyzing PISA 2012 Results. Seoul: Korea Institute for Curriculum and Evaluation.
  9. Song, E. (2008). A Comparative study on the Mathematics textbooks of the Koran and the Singaporean highschools focused on the Equation units. (Unpublished master's thesis). Ewha Womans University, Seoul, Korea.
  10. Lee, Y. (2016). A Comparative Study on Middle School Mathematics Textbooks of Korea and Singapore - Focusing on functions. (Unpublished master's thesis). Kyung Hee University, Seoul, Korea.
  11. Lee, J. (2018). An Analysis of University Students' Representational Fluency About the Derivative Concept. The journal of educational research in mathematics, 28(4), 573-598. https://doi.org/10.29275/jerm.2018.11.28.4.573
  12. Lee, H. (2010). Both comparison and analysis about a mathematics textbook between Korea and Singapore. (Unpublished master's thesis). Kyungpook National University, Daegu, Korea.
  13. Chung, S. (2014). Mathematics for School Mathematics. Seoul: Kyowoo.
  14. Jeong, Y. (2010). An Investigation on the Historical Development of the Derivative Concept. School Mathematics, 12(2), 239-257.
  15. Jeong, E. (2010). A case study on The Connection between The Understanding of Limit Concept and The Acquisition Process of Differential Concept. (Unpublished master's thesis). Ewha Womans University, Seoul, Korea.
  16. Boyer, C. B. (1959). The history of the calculus and its conceptual development: (The concepts of the calculus). Courier Corporation.
  17. Boyer, C. B., & Merzbach, U, C. (2000). 수학의 역사, (양영오, 조윤동 역). 서울: 경문사.
  18. Amit, M., & Vinner, S. (1990). Some misconceptions in calculus: Anecdotes or the tip of an iceberg? In G. Booker, P. Cobb & T. N. de Mendicuti (Eds.), Proceedings of the 14th international conference for the psychology of mathematics education, 1(pp.3-10). Oaxtepec, Mexico: CINVESTAV.
  19. Bezuidenhout, J. (1998). First‐year university students' understanding of rate of change. International Journal of Mathematical Education in Science and Technology, 29(3), 389-399. https://doi.org/10.1080/0020739980290309
  20. Bostock, L., Chandler, F. S. (2015). Core maths for Advanced Level 3rd Edition. Oxford University Press.
  21. Duval, R.: 2000, 'Basic issues for research in mathematics education', in T. Nakahara and M. Koyama (eds.), Proceedings of the 24th International Conference for the Psychology of Mathematics Education, Japan, Nishiki Print Co., Ltd. I, pp. 55-69.
  22. Kant, I. (1956). Critique of Pure Reason. Translated by N. K. Smith. New York: St. Martin's Press.
  23. Neill, H., Quadling, D. (2002). Advanced level mathematics Pure Mathematics 1 (International). Cambridge University Press.
  24. Otte, M. (2003). Does mathematics have objects? In what sense?. Synthese, 134(1), 181-216. https://doi.org/10.1023/A:1022191731931
  25. Piaget, J., & Garcia, R. (1989). Psychogenesis and the history of science, (H. Feider, trans.), New York: Columbia University Press.
  26. Sakabe, M., Arihuku, K., Kurosaki, M., Nakasima, Y., & Makino, A. (2009). 칸트 사전. (이신철 역), 서울: 도서출판 b.
  27. Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press.
  28. Ministry of Education, Singapore. (2017). Education Statistics Digest 2017. Available online at: https://www.moe.gov.sg/docs/default-source/document/publications/education-statistics-digest/esd_2017.pdf
  29. Swift, S., Green, J., Kouris, T., Brodie, R., Grove, M., McMahon, A. (2014). Nelson Senior Maths Methods 11 for the Australian Curriculum. Toronto: Nelson.
  30. Yeo, J. et al. (2013). New Syllabus Additional Mathematics 9th Edition. Shinglee.

피인용 문헌

  1. 한국과 일본의 고등학교 수학과 교육과정 내용 비교 vol.23, pp.6, 2019, https://doi.org/10.24231/rici.2019.23.6.548