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Counting is an important ingredient of mathematics education

조합수학의 수학교육 내용요소로서의 적합성과 필요성

  • Received : 2016.09.20
  • Accepted : 2016.10.26
  • Published : 2016.10.31

Abstract

Mathematics is a kind of language, and even a tool of cognition for human beings. Mathematics has been used to communicate and to develop the civilizations through the history. So mathematics is one of the most important subjects for human to teach and learn. Especially, developed countries believe that mathematics will play very important roles in the developments of future industries and so future society. In this article, we clarify that combinatorics which is mainly represented by counting is an important ingredient of future mathematics education. To do so, we investigate the characteristics of combinatorics from the educational and cognitive perspectives.

References

  1. Michael ATIYAH, Mind, Matter, and Mathematics. https://edoc.bbaw.de/files/23/09_Atiyah.pdf 이상욱, 고영미 번역, 생각과 물질 그리고 수학 - 아티야, Proceedings of the Korean Society for History of Mathematics 25(2) (2015), 81-91.
  2. William BYERS, How Mathematicians Think, Princeton University Press, 2007. http://press.princeton.edu/titles/8386.html
  3. Peter J. CAMERON, Combinatorics entering the third millennium, draft (2001). http://www.maths.qmul.ac.uk/-pjc/preprints/histcomb.pdf
  4. Jean-Pierre CHANGEUX, Alaine CONNES, Conversations on Mind, Matter, and Mathematics, Edited and Translated by M. B. DeBevoise, Princeton University Press, 1996. https://books.google.co.kr/books?isbn=0691004056
  5. Keith DEVLIN, What will count as mathematics in 2100? https://web.stanford.edu/-kdevlin/Papers/Math_in_2100.pdf
  6. ENGQUIST, BJORN, SCHMID (Eds.), Mathematics Unlimited - 2001 and Beyond, Springer, 2001. http://www.springer.com/la/book/9783642631146
  7. Timothy GOWERS (Ed.), The Princeton Companion to Mathematics, Princeton University Press, 2008.
  8. Paul R. HALMOS, Mathematics as a Creative Art, American Scientist 56 (1968), 375-389. http://math.slu.edu/-srivastava/Halmos.pdf 고영미, 이상욱 번역, 창조적인 예술로서의 수학 - 헐모시, Proceedings of the Korean Society for History of Mathematics 25(2) (2015), 93-103.
  9. Nicholas J. HIGHAM (Ed.), The Princeton Companion to Applied Mathematics, Princeton University Press, 2015.
  10. George LAKOFF, Rafael E. NUNEZ, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, Basic Books, 2000. http://www.cogsci.ucsd.edu/-nunez/web/FM.PDF, http://www.cogsci.ucsd.edu/-nunez/web/INTR-04.PDF
  11. LEE Man Keun, Dong-A Ilbo, Mathematical Odyssey of Professor Lee Man Keun, 21C Books, 2013.(이만근, 동아일보 지음, 이만근 교수의 수학 오디세이 1 & 2, 21세기북스, 2013.)
  12. Christian LENART, The Many Faces of Modern Combinatorics, preprint. http://www.albany.edu/-lenart/articles/combin1.pdf
  13. Laszlo LOVASZ, One Mathematics. http://www.cs.elte.hu/-lovasz/berlin.pdf
  14. KIM Jeong Hee, Mathematical Story, Beautiful as a Novel, The Dong-A Ilbo, 2013.(김정희 지음, 소설처럼 아름다운 수학이야기, 동아일보사, 2013.)
  15. KOH Youngmee, REE Sangwook, Educational Meaning of the Nine Chapters, The Korean Journal for History of Mathematics 23(1) (2010), 25-40.(고영미, 이상욱, 구장산술의 방정식론의 교육학적 의미, 한국수학사학회지 23(1) (2010), 25-40.)
  16. Yuri Ivanovitch MANIN, Ronald WENGENMAYR, The Tool of Knowledges, Max Planck Research 1 (2009), 52-57.
  17. David R. MAZUR, Combinatorics: A Guided Tour, MAA Textbooks, 2010. http://www.maa.org/publications/books/combinatorics-a-guided-tour
  18. National Research Council, The Mathematical Sciences in 2025, The National Academies Press, 2013.
  19. NOH Sun Sook, KIM Young Soo, KIM Min Kyung, Curriculum Development for Mathematics and Information Science in a Knowledge Based Society, Ewha Womans University Press, 2003.(노선숙, 김영수, 김민경 편저, 지식기반사회의 수학.정보과학 교육과정개발 기초 연구, 이화여자대학교 출판부, 2003. https://books.google.co.kr/books?isbn=8973005278)
  20. SIU Man Keung, Problem of Seven Light Bulbs - Some reflection on popularization of mathematics, entertainment versus the underlying mathematics, 2016, personal communication.
  21. Arne B. SLETSJOE, Abel Prize Laureate 2012: Endre Szemeredi, Combinatorics. http://www.abelprize.no/c54147/binfil/download.php?tid=54123
  22. Robert J. STERNBERG, Successful intelligence: finding a balance, Trends in Cognitive Sciences 3(11) (1999), 436-442. https://doi.org/10.1016/S1364-6613(99)01391-1
  23. Francis Edward SU, Teaching Research: Encouraging Discoveries, The American Mathematical Monthly 117(9) (2010), 759-769. https://www.math.hmc.edu/-su/leitzel/leitzel.pdf https://doi.org/10.4169/000298910x521634
  24. Rachel THOMAS, Millennium Mathematics Project: Bringing mathematics to life, MSOR Connections 4(3) (2004), 7-10. https://www.heacademy.ac.uk/system/files/msor.4.3g_1.pdf https://doi.org/10.11120/msor.2004.04030007
  25. Eugene WIGNER, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Pure and Applied Mathematics 13(1) (1960), 1-14. http://math.northwestern.edu/-theojf/FreshmanSeminar2014/Wigner1960.pdf https://doi.org/10.1002/cpa.3160130102
  26. Robin WILSON, Combinatorics, A Very Short Introduction, Oxford University Press, 2016.
  27. wikipedia, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. http://math.northwestern.edu/-theojf/FreshmanSeminar2014/Wigner1960.pdf