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A Study on Experiments and Two Interpretations of Probability in 《Probability and Statistics》 and Its Educational Implications

《확률과 통계》의 시행과 두 가지 확률에 대한 고찰 및 교육적 시사점

  • Received : 2018.06.11
  • Accepted : 2018.10.15
  • Published : 2018.10.31

Abstract

Empirical probability and classical probability, which are two interpretations of Kolmogorov's axiom, are two ways to recognize the chances of events occurring in the real world. In this paper, I analyzed and suggested the contents of the high school textbooks ${\ll}$Probability and Statistics${\gg}$, associated with two interpretations of probability and experiments on which two interpretations are based. By presenting the cases required expressly stating what the experiment is for supporting students' understanding of some concepts, it was discussed that stating or not stating what the experiment is should be carefully determined by the educational intent. Especially, I suggested that in the textbooks we contrast the good idea of calculating the ratios of two possibilities in the imaginary world of the classical probability with the normal idea of grasping the chances of events through the frequencies in the real world of the empirical probability, with distinguishing the experiments in two interpretations of probability. I also suggested that in the textbooks we make it clear that the Weak Law of Large Numbers justifies our expectations of the frequencies' reflecting the chances of events occurring in the real world under ideal conditions. Teaching and learning about the aesthetic elements and the practicality of imaginary mathematical thinking supported by these textbooks statements could be one form of Humanities education in mathematics as STEAM education.

Keywords

References

  1. BAEK Y. S. et al, STEAM education in Korea, Journal of Learner-Centered Curriculum and Instruction 11(4) (2011), 149-171.
  2. C. BATANERO, M. HENRY and B. PARZYSZ, The nature of chance and probability, In Exploring probability in school: Challenges for teaching and learning (G. A. Jones, ed.), Springer Science & Business Media, 2005, 15-37.
  3. CHOI K. H., Basic probability theory, Freedom Academy INC., 2014.
  4. X. De SCHEEMAEKERE and A. SZAFARZ, The special status of mathematical probability: a historical sketch, Working Papers CEB 08-017.RS(2008), 1-14.
  5. H. FREUDENTHAL, Mathematics as an educational task, D. Reidel, 1973.
  6. G. A. JONES and C. A. THORNTON, An overview of research into the teaching and learning of probability In Exploring probability in school: Challenges for teaching and learning (G. A. Jones, ed.), Springer Science & Business Media, 2005, 65-92.
  7. KIM J. K., Probability theory, Freedom Academy INC., 2015.
  8. KIM T. S., Statistics, Freedom Academy INC., 2014.
  9. Korean Mathematical Society, Standard math glossary, Cheong Moon Gak Publisher, 2006.
  10. LEE G. D., A study on improvement of introductions and applications of 'Proof by Contradiction' in textbooks, School Mathematics 18(4) (2016), 839-856.
  11. LEE G. D., Mathematics of imagination, and education of imagining mathematics, Journal of Educational Research in Mathematics 26(1) (2016), 103-119.
  12. P. S. MANN, Introductory statistics, John Wiley & Sons Inc., 2007. 김영주 외 역, 통계학 개론, 자유아카데미, 2009.
  13. D. H. MELLOR, Probability: A philosophical introduction, Routledge, 2004.
  14. Ministry of Education, Announcement of key issues of the framework of 2015 Integrated Education Curriculum, Press release Sep. 24, 2014.
  15. Ministry of Education, Framework document of the national curriculum for the primary and secondary schools #2015-80 [Annex 1], 2015.
  16. D. S. MOORE, Uncertainty, In On the shoulders of giants: New approaches to numeracy(L. A. Steen, ed.), National Academy Press, 1990, 95-137.
  17. R. NETZ, Imagination and layered ontology in Greek mathematics, Configurations 17 (2009), 19-50. https://doi.org/10.1353/con.0.0066
  18. N. PAL and S. SARKAR, Statistics: concepts and applications, Prentice Hall of India, 2005. 오성환 외 역, 개념과 응용중심의 통계학, 자유아카데미, 2005.
  19. PARK H. et al, A study on the current status of STEAM education, Journal of the Korean Association for Science Education 36(4) (2016), 669-679. https://doi.org/10.14697/jkase.2016.36.4.0669
  20. K. POPPER, The open society and its enemies, Vol. 2, Routledge, 1945. 이명현 역, 열린사회와 그 적들 II, 민음사, 2015.
  21. P. SEDLMEIER, Improving statistical reasoning: Theoretical models and practical implications, Psychology Press, 1999.
  22. 苫米地英人, 數學嫌いの人のためのすべてを可能にする數學腦のつくり方, ビジネス社, 2016. 한진아 역, 숫자 없이 모든 문제가 풀리는 수학책, 북클라우드, 2017.