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A Modern Reconstruction of the Problems on the Sums of Sequences in MukSaJipSanBup and its Pedagogical Applications

묵사집산법(?思集算法)에 수록된 퇴타개적문(堆?開積門)의 현대적 재구성 및 수학교육적 활용 방안

  • Received : 2019.12.18
  • Accepted : 2020.02.24
  • Published : 2020.02.28

Abstract

Under 2009 Revised Mathematics Curriculum and 2015 Revised Mathematics Curriculum, mathematics teachers can help students inductively express real life problems related to sequences but have difficulties in dealing with problems asking the general terms of the sequences defined inductively due to 'Guidelines for Teaching and Learning'. Because most of textbooks mainly deal with the simple calculation for the sums of sequences, students tend to follow them rather than developing their inductive and deductive reasoning through finding patterns in the sequences. In this study, we reconstruct 8 problems to find the sums of sequences in MukSaJipSanBup which is known as one of the oldest mathematics book of Chosun Dynasty, using the terminology and symbols of the current curriculum. Such kind of problems can be given in textbooks and used for teaching and learning. Using problems in mathematical books of Chosun Dynasty with suitable modifications for teaching and learning is a good method which not only help students feel the usefulness of mathematics but also learn the cultural value of our traditional mathematics and have the pride for it.

Keywords

References

  1. BAE J. S. et al, The Textbook of High School Mathematics I, Kumsung Publisher, Seoul, 2018.
  2. CHANG H. W., Analysis on Gu-il-jip, the mathematical book of Chosun dynasty and its pedagogical applications, The Journal of Educational Research in Mathematics 13(4) (2003), 429-446.
  3. CHANG M. H., A Study on Mathematics Education Teaching Method using History of Mathematics-Focused on the Second Grade of Middle School, The Korean Journal for History of Mathematics 1(1) (1984), 86-89.
  4. CHUNG D. G., A Study on the Use of History of Mathematics to Improve the Mathematics Instruction, Science Education Center Inchon National University of Education, The Bulletin of Science Education 10 (1998), 300-344.
  5. GIM C. C., KIM J. H., LEE K. H., An International Comparative Study on the Use of Illustrations of the Elementary Mathematics Textbooks in Korea, Japan, USA and Germany, The Journal of Curriculum & Evaluation 9(1) (2006), 299-319. https://doi.org/10.29221/jce.2006.9.1.299
  6. HER M., Mathematics Education through the Use of History of Mathematics, Research Institute of Basic Science Kwangwoon University, Journal of the Research Institute of Basic Science (1997), 21-32.
  7. HER M., A Study of Classical Problem Using Mathematics Education, The Korean Journal for History of Mathematics 13(1) (2000), 33-48.
  8. HER M., About the utility of mathematics, Journal for History of Mathematics 14(1) (2001), 61-72.
  9. HER M., The sequences of Muksa-jipsanbup, Journal for History of Mathematics 17(1) (2004), 15-32.
  10. HER M., A Comparison between Suanxue qimeng(Introduction to Mathematical Studies) and Muksa-jipsanbup, Journal for History of Mathematics 21(1) (2008), 1-16.
  11. HONG S. B. et al, The Textbook of High School Mathematics I, Jihaksa, Seoul, 2018.
  12. HWANG S. W. et al, The Textbook of High School Mathematics I, MiraeN, Seoul, 2018.
  13. KANG S. P., KIM S. J., LIM E. H., A study on the analysis of elementary mathematics textbook's illustrations: Focusing on the second grade, Journal of the Korean School Mathematics Society 8(2) (2005), 183-201.
  14. KIM K. W., CHO J. S., Development of teaching and learning materials using history of mathematics on numeration system in the middle school mathematics, Institute of Natural Science of The Silla University, Journal of The Natural Science 13 (2004), 1-14.
  15. KIM O. J., Muksa-jipsanbup and Mathematics of the 17th century Chosun Dynasty, Doctoral Dissertation of Korea University (2009).
  16. KIM W. K. et al, The Textbook of High School Mathematics I, Visang Education, Seoul, 2018.
  17. KIM R. Y., KIM H. Y., LEE H. H., Using Chosun Mathematics in Mathematics Education: Focusing on Similarity, Journal of Research in Curriculum & Instruction 21(2) (2017), 71-83. https://doi.org/10.24231/rici.2017.21.2.71
  18. KYONG S. J., Muksa-jipsanbup(YOO I. Y., HER M., Trans.), Seoul: Kyowoosa, 2006(Original work published 1616-?).
  19. KWON O. N. et al, The Textbook of High School Mathematics I, Kyohaksa, Seoul, 2018.
  20. Ministry of Education, Mathematics Curriculum, Bulletin of MOE No.2015-84 [Seperate Volume #8].
  21. Ministry of Education, Science and Technology, Mathematics Curriculum, No.2011-361 [Seperate Volume #8], 2011.
  22. Ministry Of Education & Human Resources Development, Mathematics Curriculum. No.2007-79 [Seperate Volume #8], 2007.
  23. Shmuel AVITAL, Learn from Masters; History of Mathematics Can Help Improve Instruction and Learning, The Mathematical Association of America (1995), 3-12. Shmuel Avital, 허민 옮김, 수학사는 교수와 학습을 증진시킬 수 있다, 한국수학사학회지 9(1) (1996), 58-69.
  24. YANG S. H., An Investigation of the Height Measurement of Island Recorded in Mathematics Books of the Late Chosun Dynasty and its Pedagogical Applications, Journal of Educational Research in Mathematics 28(1) (2018), 49-74. https://doi.org/10.29275/jerm.2018.02.28.1.49
  25. YANG S. H., A Survey of High School Students' Ideas for the Local Extrema, Journal of Korea Society Educational Studies in Mathematics 21(1) (2019), 155-172.
  26. YANG S. H., HER N., The Modern Explication of CheukRyangDoHae and its Pedagogical Applications, Journal for History of Mathematics 31(3) (2018), 127-150. https://doi.org/10.14477/jhm.2018.31.3.127
  27. YOON D. W., PARK S. J., The Effect of using Teaching-Learning Materials from Mathematical History of the Impact Students-Centered around Sequence Chapters of Mathematics, Communications of mathematical education 20(3) (2006), 343-359.