한국수학교육학회지시리즈A:수학교육 (The Mathematical Education)

  • 제50권4호
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  • Pages.429-440
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  • 2011
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  • 1225-1380(pISSN)
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  • 2287-9633(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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일상적 정의에서 수학적 정의로의 이행 - 영재 중학생들의 점과 선의 정의 인식 -

The Transition from Everyday Definitions to Mathematical Definitions - Gifted Middle School Students' Conceptions of Point and Line definitions -

  • 투고 : 2011.07.19
  • 심사 : 2011.11.18
  • 발행 : 2011.11.30
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초록

This paper analysed gifted middle students' conception of the definitions of point and line and the uses of definitions in proving. The findings of this paper suggest that the concept of mathematical definitions is very unnatural to students, therefore teachers and textbooks need to explain explicitly the characteristics of mathematical definitions which are different from dictionary definitions using common sense. Also introducing undefined terms in middle school geometry would give students a critical chance to deal with the transition from dictionary definitions to mathematical definitions.

키워드

참고문헌

  1. 강신덕 외 5인 (2010). 중학교 수학 2. 서울 : 교학사.
  2. 박영훈 외 5인 (2009). 중학교 수학 1. 서울 : 천재문화.
  3. 민중서림 편집국 (2001). 국어사전. 서울: 민중서림.
  4. 이준열 외 5인 (2010). 중학교 수학 2. 서울: 천재문화.
  5. 이지현 (2011). 학교수학에서 대학수학으로 공리적 방법의 이행에 관한 연구. 서울대학교 박사논문.
  6. 조영미 (2000). 직관기하의 정의 사용 양태 분석과 증명지도에 대한 시사점. 수학교육학연구, 10(2), 215-227.
  7. 조영미 (2001). 학교수학에 제시된 정의에 관한 연구. 서울대학교 박사논문.
  8. Alcock L., & Simpson A. (2002). Definitions: Dealing with categories mathematically. For the Learning of Mathematics, 22(2), 28-34.
  9. Edwards, B. S., & Ward, M. B. (2004). Surprises from mathematics education research: Student (mis)use of mathematical definitions. The American Mathematical Monthly, 111, 411-424. https://doi.org/10.2307/4145268
  10. Gray, E. M., Pitta, D., Pinto, M., & Tall, D. (1999). Knowledge construction and diverging thinking in elementary & advanced mathematics. Educational Studies in Mathematics, 38, 111-133. https://doi.org/10.1023/A:1003640204118
  11. Harel, G., & Tall, D. (1991). The General, the abstract, and the generic in advanced mathematics. For the Learning of Mathematics, 11(1), 38-42.
  12. Harel, G., Selden, A., & Selden, J. (2006). Advanced mathematical thinking: Some PME perspectives. In A. Gutierrez, P. Boero. (Eds), Handbook of research on the psychology of mathematics education: Past, present and future. Sense Publishers.
  13. Jacobs, H. R. (2003). Geometry seeing, doing, understanding(3rd ed.). New York : W. H. Freeman and Company.
  14. McClure, J. E. (2000). Start where they are: Geometry as an introduction to proof. American Mathematical Monthly, 107(1), 44-52. https://doi.org/10.2307/2589376
  15. Morgan, C. (2004). Word, definitions and concepts in discourses of mathematics. Teaching and Learning, 19(2). 103-117.
  16. Morgan, C. (2005). What is a definition for in school mathematics?. European Research in Mathematics Education IV.
  17. Raman, M. (2004). Epistemological messages conveyed by three high-school and college mathematics textbooks. Journal of Mathematical Behavior, 23, 389-404. https://doi.org/10.1016/j.jmathb.2004.09.002
  18. Robinson, R. (1954). Definition. Oxford University Press.
  19. Schultz, J. E., Hollowell, K. A., Ellis, W., & Kennedy, P. A. (2003). Geometry. Austin, Texas: Holt, Rinehart, and Winston.
  20. Tagliapietra, R., & Pilger, K. D. (2000). Geometry for christian school(2nd ed.). Bob Jones University Press.
  21. Tall, D. (1992a). The transition to advanced mathematical thinking: Functions, limits, infinity, and proof. In D. A. Grouws(Ed.), Handbook of research on mathematics teaching and learning(pp. 495-511). New York : Macmillan.
  22. Tall, D. (1992b). Construction of objects through definition and proof, PME Working Group on AMT, Durham, NH.
  23. Tall, D. (1997). From school to university: The transition from elementary to advanced mathematical thinking. In M. O. J. Thomas(Ed.), Proceedings of The Seventh Annual Australasian Bridging Network Mathematics Conference(pp.9-26). University of Auckland.
  24. Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall(Ed.), Advanced mathematical thinking(pp. 65-81). Dordrecht : Kluwer Academic Publishers.

피인용 문헌

  1. Exploring students' thinking in proof production in geometry vol.53, pp.3, 2014, https://doi.org/10.7468/mathedu.2014.53.3.383