DOI QR코드

DOI QR Code

Rethinking the Name and Use of Pythagorean Theorem from the Perspectives of History of Mathematics and Mathematics Education

'피타고라스 정리'의 명칭과 활용에 대한 비판적 고찰

  • Chang, Hyewon (Dept. of Math. Edu., Seoul National Univ. of Edu.)
  • Received : 2021.10.19
  • Accepted : 2021.12.10
  • Published : 2021.12.31

Abstract

It has been argued that as for the origin of the Pythagorean theorem, the theorem had already been discovered and proved before Pythagoras, and the historical records of ancient mathematics have confirmed various uses of this theorem. The purpose of this study is to examine the relevance of its name caused by Eurocentrism and the weakness of its use in Korean school mathematics and to seek improvements from a critical point of view. To this end, the Pythagorean theorem was reviewed from the perspectives of the history of mathematics and mathematics education. In addition, its name in relation to objective mathematical contents regardless of any specific civilization and its use as a starting point for teaching the theorem in school mathematics were suggested.

Keywords

Acknowledgement

This work was supported by the 2021 Research Fund of Seoul National University of Education.

References

  1. S. D. A. Aish, A Greek mathematical papyrus from the Cairo Museum, Archiv fur Papyrusforschung und Verwandte Gebiete 62(1) (2016), 43-56. https://doi.org/10.1515/apf-2016-0004
  2. S. E. Anderson, Worldmath curriculum: Fighting Eurocentrism in mathematics, The Journal of Negro Education 59(3) (1990), 348-359. https://doi.org/10.2307/2295569
  3. Chinese Bookstore, Zhou bi suan jing, Shanghai: Chinese Bookstore. 中華書局, 周髀算經, 上海: 中華書局.
  4. Chung D. K., A great legacy-Pythagorean theorem, Annual Report of Science and Mathematics 10 (1994), 41-51.
  5. Chung E. T., New education middle school mathematics II, Seoul: Minjoong, 1952.
  6. A. C. Clairaut, Elemens de geometrie, Gauthier-Billars et Cle, Editeurs, 1741/1920. (translated by CHANG, H. 2018).
  7. Common Core State Standards Initiative, Common core state standards for mathematics, 2010.
  8. C. Cullen, Astronomy and mathematics in ancient China: the Zhou bi suan jing, Cambridge university press, 1996.
  9. J. W. Dauben, Chinese mathematics, In V. J. Katz(Ed.) The mathematics of Egypt, Mesopotamia, China, India, and Islam - a sourcebook, (pp. 187-384). Princeton: Princeton University Press, 2007.
  10. Encyclopedia, "The Mathematics of Ancient Egypt." Complete dictionary of scientific biography, Retrieved in August 16, 2021 from Encyclopedia.com:https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and\-press-releases/mathematics-ancient-egypt.
  11. D. Fowler, E. Robson, Square root approximations in old Babylonian mathematics: YBC 7289 in context, Historia Mathematica 25(4) (1998), 366-378. https://doi.org/10.1006/hmat.1998.2209
  12. S. Guo, Jiuzhang Suanshu, Shanghai publication, 2007. 郭书春 释注, 九章算術 释注, 上海古籍出版社, 2007.
  13. R. Gustafson, Was Pythagoras Chinese-revisiting an old debate, The Mathematics Enthusiast 9(1) (2012), 207-220. https://doi.org/10.54870/1551-3440.1241
  14. Han D. H., A study on the rediscovery of the Pythagorean theorem, School Mathematics 4(3) (2002), 401-413.
  15. T. L. Heath, The thirteen books of Euclid's Elements, vol. I. Cambridge university press, 1908.
  16. T. L. Heath, A history of Greek mathematics, vol 1. Oxford university press, 1921.
  17. Her M., A note for improving mathematical terms in Korea, Communications of Mathematical Education 27(4) (2013), 391-406. https://doi.org/10.7468/JKSMEE.2013.27.4.391
  18. H. D. Hirschy, The Pythagorean theorem, In NCTM (Ed.), Historical topics for the mathematics classroom (pp. 215-218), Reston: NCTM, 1969.
  19. Hwang S. W., et al. Middle school mathematics 2, Seoul: MiraeN, 2019.
  20. N. Ichimatsu, Middle school mathematics grade 3, School Books Co., 2014. 一松 信 外 30, 中学校數学3, 学校図書株式會社, 2014.
  21. A. Imhausen, Ancient Egyptian mathematics: New perspectives on old sources, The Mathematical Intelligencer 28 (2006), 19-27. https://doi.org/10.1007/BF02986998
  22. A. Imhausen, Egyptian mathematics, In V. J. Katz(Ed.) The mathematics of Egypt, Mesopotamia, China, India, and Islam - a sourcebook, (pp. 7-56), Princeton: Princeton University Press, 2007.
  23. G. G. Joseph, Foundations of Eurocentrism in mathematics, Race & Class 28(3) (1987), 13-28. https://doi.org/10.1177/030639688702800302
  24. C. W. Keung, Discovering mathematics 2B, Singapore: Star Publishing, 2014.
  25. Kim Y. S., Park K. S., Rethinking about terminology in school mathematics, Proceedings of 1994 Conference of the Mathematics Education 4(2) (1994), 1-10.
  26. Lee K. et al, Middle school mathematics 3, Seoul: MiraeN, 2019.
  27. E. S. Loomis, The Pythagorean proposition, Washington, D.C.: National Council of Teachers of Mathematics, 1968.
  28. J. C. Martzloff, A history of Chinese mathematics, Germany: Springer, 1997.
  29. Ministry of education, Mathematics syllabuses-secondary one to four: express course, normal (academic) course, Singapore: Curriculum Planning and Development Division, 2019.
  30. Ministry of education, Mathematics curriculum standards (1946-1997), Seoul: Seonmyoung publication, 2000.
  31. Ministry of education, science, and technology, Mathematics curriculum, 2011-361, Separate book 8, 2007.
  32. M. Nanda, Who discovered the Pythagorean theorem? Science in saffron: Skeptical essays on history of science, Gurgaon, India: Three Essays Collective, 2016.
  33. J. Needham, Science and civilisation in China, Cambridge university press, 1959.
  34. Park K. M., et al., The 2015 revised mathematics curriculum development study II, Research report of ministry of education, BD 15120005, 2015.
  35. Park K. S., A semantic investigation on high school mathematics terms in Korea - centered on terms of Chinese characters, Journal of Educational Research in Mathematics 13(3) (2003), 227-246.
  36. Park K. S., A study on characteristics of actual state of school mathematics terms in North Korea, School Mathematics 7(1) (2005), 1-15.
  37. Park M. H., Comparative study on teaching of Pythagorean theorem in South and North Korea, School Mathematics 4(2) (2002), 223-236.
  38. People's Education Press Research Institute, Mathematics grade 8, Beijing: People's Education Press, 2017. 人民敎育出版社 課程敎材硏究所, 數學 八年級 下册, 北京: 人民敎育出版社, 2017.
  39. People's Education Press Research Institute, Mathematics grade 9, Beijing: People's Education Press, 2017. 人民敎育出版社 課程敎材硏究所, 數學 九年級 下册, 北京: 人民敎育出版社, 2017.
  40. K. Plofker, Mathematics in India, In V. J. Katz(Ed.), The mathematics of Egypt, Mesopotamia, China, India, and Islam - a sourcebook, (pp. 385-514). Princeton: Princeton University Press, 2007.
  41. B. Ratner, Pythagoras: Everyone knows his famous theorem, but not who discovered it 1000 years before him, Journal of Targeting, Measurement and Analysis for Marketing 17(3) (2009), 229-242. https://doi.org/10.1057/jt.2009.16
  42. E. Robson, Mesopotamian mathematics, In V. J. Katz(Ed.), The mathematics of Egypt, Mesopotamia, China, India, and Islam - a sourcebook, (pp. 57-186), Princeton: Princeton University Press, 2007.
  43. R. Roy, Babylonian Pythagoras' theorem, the early history of zero and a polemic on the study of the history of science, Resonance January (2003), 30-40.
  44. T. Sawada, Middle school mathematics grade 3, Educational Publishing Co., 2014. 澤田利夫 外 23, 中学數学3, 敎育出版株式會社, 2014.
  45. A. Seidenberg, On the volume of a sphere, Archive for History of Exact Sciences 39(2) (1988), 97-119. https://doi.org/10.1007/BF00348438
  46. K. Shigematsu, Middle school mathematics grade 3, Nippon Bunshi Publishing Co., 2014. 重松敬一 外 24, 中学數学3, 日本文敎出版株式會社, 2014.
  47. K. Soma, Worlds of mathematics, grade 3 Dainippon Book Co., 2014. 相馬一彦 外 17, 數学の世界 3年, 大日本図書株式會社, 2014.
  48. Song R., Ju M., Development research of multicultural mathematics teacher education model: Exploring preliminary model based on situational analysis, The Journal of Educational Research in Mathematics 24(2) (2014), 227-251.
  49. J. Stedall, Mathematics emerging: a sourcebook 1540-1900, NY: Oxford university press, 2008.
  50. Suh B. E., A study on reorganization of 'Pythagorean theorem' in school mathematics, The Mathematical Education 57(2) (2018), 93-110. https://doi.org/10.7468/MATHEDU.2018.57.2.93
  51. F. J. Swetz, Trigonometry comes out of the shadows, In F. Swetz et al. (Eds.), Learn from the masters, The mathematical association of America, (pp. 57-71), 1995.
  52. E. C. Wittmann, Connecting mathematics and mathematics education, Cham: Springer, 2020.