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Instructions of History of Mathematics with Mathematical Machines

수학기계를 활용한 수학사 수업

  • Received : 2013.06.30
  • Accepted : 2013.08.07
  • Published : 2013.08.31

Abstract

Although many people have recognized the importance of history of mathematics in mathematics education, there are few studies that history and mathematics educations are connected. In this paper, we present and discuss the ways of introducing the instruction with mathematics machines. This instruction use the history of mathematics as part of a class not as a tool to stimulate students' interest but as a goal that it can be targeted mathematical itself. To do this, we first analyze the characteristics of applying history of mathematics in mathematical education, second, describe the meaning and the educational value of mathematical machines, and finally explained the way of applying history of mathematics with mathematics machines. The Instruction of history of mathematics with mathematics machines has advantages that practice (manipulation and experiment) and theory (elaboration of definition, production of conjectures and constructions of proofs) are interlaced within a historic-cultural perspective.

Keywords

References

  1. S. Antonini, F. Martignone,"Pantographs for geometrical transformations: An explorative study on argumentation", Consultado el 14 de abril de 2011 en:, 2011, http: //www.cerme7.univ.rzeszow.pl/WG/1/CERME7_WG1_antonini_martignone.pdf
  2. M. G. Bartolini Bussi, Ancient instruments in the modern classroom, In J. Fauvel & J. van Maannen (Eds), History in mahtematics education: The ICMI Study, 2000, 343-351. Dordrecht: Kluwer
  3. G. W. Cathcart(ed), The mathematics laboratory: Readings from the arithmetic teacher, Reston, VA.: NCTM, 1977.
  4. Choi J. S.,"An Analysis and Criticism on the Definition of the Similarity Concept in Mathematical Texts by Investigating Mathematical History", The journal of educational research in mathematics 20(4) (2010), 529-546. 최지선,"수학사 고찰을 통한 교과서의 닮음 정 의에 대한 분석과 비판", 수학교육학연구 20(4) (2010), 529-546.
  5. F. H. van Eemeren, & R. Grootendorst, Argumentation, communication, and fallacies: A pragma-dialectical perspective, Hillsdale, NJ.: Lawrence Erlbaum Associates, 1992.
  6. J. Fauvel,"Using history in mathematics education", For the Learning of Mathematics 11(2) (1991), 3-6.
  7. J. Fauvel, J. van Maanen(Eds.), History in mathematics education, New ICMI study series: Vol. 6, Dordrecht, the Netherlands: Kluwer, 2000.
  8. F. Ferrara, M. Maschietto,"Are mathematics students thinking as Kepler? Conics and mathematical machines", Proceedings of the 8th Congress of European Research in Mathematics Education, Antaya, Turkey, 2013. http://cerme8.metu.edu.tr/wgpapers/WG4/WG4_ Maschietto.pdf
  9. I. Gulikers, K. Blom,"'A historical angle', a survey of recent literature on the use and value of the history in geometrical education", Educational Studies in Mathematics 47(2001), 223-258. https://doi.org/10.1023/A:1014539212782
  10. T. Heiede,"Why teach history of mathematics", The Mathematical Gazette 76(475) (1992), 151-157. https://doi.org/10.2307/3620388
  11. Heo D. H. and Oh Y. Y.,"The Influence of Mathematical History-Based Mathematics Teaching on Mathematical Communication and Attitudes of Elementary Students", Journal of Elementary Mathematics Education in Korea 15(2) (2011), 463-485. 허도하, 오영열,"의 사소통 중심의 수학사 기반 수업이 초등학생의 수학적 의사소통과 태도에 미치는 영향", 한국 초등수학교육학회지 15(2) (2011), 463-485.
  12. Jang M. R., and Kang S. J.,"How To Teach The Quadratic Curves Through Historical Overview", Communications of mathematical education 24(3) (2010), 731-744. 장미라, 강순 자,"역사적 고찰을 통한 이차곡선의 지도방안", 수학교육논문집 24(3) (2010), 731-744.
  13. U. T. Jankvist,"A categorization of the"whys"and"hows"of using history in mathematics education", Educational Studies in Mathematics 71(2009), 235-261. https://doi.org/10.1007/s10649-008-9174-9
  14. U. T. Jankvist,"Anchoring Students' metaperspective discussions of history in mathematics", Journal for Research in Mathematics 42(4) (2011), 346-385.
  15. Jin M. Y., Kim D. W., Song M. H. & Cho H. H.,"The history of conic sections and mathematics education", The Korean Journal for History of Mathematics 25(4) (2012), 83-99. 진만영 외,"원뿔곡선의 수학사와 수학교육", 한국수학사학회지 25(4) (2012), 83-99.
  16. V. J. Katz,"Ethnomathematics in the classroom", For the Learning of Mathematics 14(2) (1994), 26-30.
  17. V. J. Katz,"Some ideas on the use of history in the teaching of mathematics", For the Learning of Mathematics 17(1) (1997), 62-63.
  18. L. M. Kennedy,"A rationale", Arithmetic Teacher 33(6) (1986), 6-7.
  19. Kim K. W. and Kam H. S.,"The Application of the History of Mathematics to the Senior Mathematics Education in the Middle School", The Korean Journal for History of Mathematics, 16(2) (2003), 71-86. 김기원, 감혜성,"중학교 3학년 수학교육에서 수학사의 활용", 한국 수학사학회지 16(2) (2003), 71-86.
  20. Kim S. M.,"A Study on Manipulative Materials in Mathematics Education", Journal of the Korea Society of Educational Studies in Mathematics 2(2) (2000), 459-474. 김수미,"수학 교육에서의 조작교구에 관한 연구", 학교수학 2(2) (2000), 459-474.
  21. Kim W. K. et al., Middle School Mathematics 2, Seoul: Visang, 2013. 김원경 외,중학교 2 학년 수학, 서울 : 비상교육, 2013.
  22. Lee S. C. and Jeon S. P.,"The Methods of Mathematical Education used on History of Mathematics", The Journal of Namseoul University 10 (2) (2004), 163-176. 이성철, 전상표, "수학사를 이용한 수학교육의 방법", 남서울대학교 논문집 10(2) (2009), 163-176.
  23. Lew H. C. and Je S. Y.,"Construction of Quadratic Curves Using the Analysis Method on the Dynamic Geometry Environment", Korean Journal of Teacher Education 25(4) (2009), 168-189. 류희찬, 제수연,"역동적 기하 환경에서 파푸스의 분석법을 이용한 이차곡선의 작도 활동에서 나타난 학생들의 수학적 발견과 정당화", 교원교육 25(4) (2009), 168-189.
  24. M. Maschietto, M. G. Bartolini Bussi,"Mathematical machines: From history to the mathematics classroom", In P. Sullivan & O. Zavlasky (Eds.), Constructing knowledge for teaching secondary mathematics (vol. 6, 227-245), New York, USA: Springer, 2011.
  25. M. Maschietto, L. Trouche,"Mathematics learning and tools from theoretical, historical and practical points of view: the productive notion of mathematics laboratories", The International Journal on Mathematics Education 40(2010), 201-213.
  26. M. Maschietto,"The laboratory of mathematical machines of Modena", Newsletter of the European Mathematical Society 57(2005), 34-37.
  27. National Council of Teachers of Mathematics, Principles and standards for school mathematics, Reston, VA: National Council of Teachers of Mathematics, 2000.
  28. Ryu S. M. and Park Y. H.,"A Study on the Uses and the Activation Plan for the Manipulative Material in Elementary Mathematics", Journal of Research in Curriculum Instruction 11(1) (2007), 15-38. 류선미, 박영희,"초등학교 수학과 조작교구 활용실태 및 활성화 방안에 대한 조사 연구", 교과교육학연구 11(1) (2007), 15-38. https://doi.org/10.24231/rici.2007.11.1.15
  29. Shin J. Y. and Park J. S.,"An Effect on Mathematical Preference and Learning Attitude of the Application of Designing for Portfolio using Mathematical History", Journal of the Korean School Mathematics Society 7(2) (2004), 1-20. 신재용, 박준석,"수학사를 이용한 Portfolio 제작물 구안 적용이 수학적 성향 및 학습태도에 미치는 영향", 한국학교수학회논문집 7(2) (2004), 1-20.
  30. D. N. Walton, Begging the question: Circular reasoning as a tactic of argumentation, NY: Greenwood, 1991.
  31. Yim J. H. and Park K. S.,"A Critical Analysis of the Introduction of Similarity in Korean Mathematics Textbooks", The journal of educational research in mathematics 19(3) (2009), 393-407. 임재훈, 박교식,"우리나라 수학 교과서의 닮음 도입 및 정의에 관한 비판적 논의", 수학교육학연구 19(3) (2004), 393-407.
  32. S. L. Young,"How teacher educators can use manipulative materials with preservice teachers", Arithmetic Teacher 31(1983), 12-13.

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