East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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유연한 수학적 사고에 의한 개념의 동치성 비교 - 사례 연구 -

  • Received : 2011.01.07
  • Accepted : 2011.08.31
  • Published : 2011.08.31
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Abstract

The flexible mathematical thinking - the ability to generate and connect various representations of concepts - is useful in understanding mathematical structure and variation in problem solving. In particular, the flexible mathematical thinking with the inventive mathematical thinking, the original mathematical problem solving ability and the mathematical invention is a core concept, which must be emphasized in all branches of mathematical education. In this paper, the author considered a case of flexible mathematical thinking with an inventive problem solving ability shown by his student via real analysis courses. The case is on the proofs of the equivalences of three different definitions on the concept of limit superior shown in three different real analysis books. Proving the equivalences of the three definitions, the student tried to keep the flexible mathematical thinking steadily.

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References

  1. 도종훈, 수학문제 해결과정에서 사고(발상)의 전환과 불변성의 인식, 한국수학교육학회지 시리즈 A <수학교육>, 2009, 5, 제 48권 제 2호, 183-190.
  2. 전평국, 정의적 특성이 수학적 문제 해결에 미치는 영향, 한국수학교육학회지 시리즈 A <수학교육> 제 30권 제 3호 (1991, 12), pp. 25-38.
  3. 정동명.조승제(2004), 실해석학 개론, 서울:경문사.
  4. 최영기, 도종훈, 수학적 사고의 유연성과 확산적 사고, 한국수학교육학회지 시리즈 A <수학교육>, 2005, 2, 제 44권 제 1호, 103-112.
  5. R. G. Bartle (1976), The Elements of Real Analysis. 2nd Ed., John Wiley & Sons Inc. New York.
  6. R. G. Bartle & D. R. Sherbert (2000). Introduction to Real Analysis, 3rd Ed., John Wiley & Sons Inc. New York.
  7. P. R. Halmos (1982), A Hilbert Space Problem Book, Springer-Verlag, New York.
  8. R. Johnsonbaugh & W. E. Pfaffenberger (1981), Foundations of Mathematical Analysis, Marcel Dekker, Inc., New York.
  9. NCTM, Focus in High School Mathematics: Reasoning and Sense Making, www.nctm.org/hsfocus (2009, pp. 9-10).
  10. A. Schoenfeld (1985), Mathematical Problem Solving, Academic Press, New York.
  11. L. B. Warner, L. J. Alock, J. Coppolo Jr. and G. E. Davis, How does flexible mathematical thinking contribute to the growth of understanding?, International Group for the Psychology of Mathematics Education, Paper presented at the 27th International Group for the Psychology of Mathematics Education Conference Held Jointly with the 25th PME-NA Conference (Honolulu, HI, Jul 13-18, 2003), v4 p371-378.