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On concept patterns of the number system

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The present paper treats with the problem how we teach/learn mathematical concepts. Concept patterns suggested in [P-K-L] is an interesting approach to study this problem. It has been attacked various concepts in terms of three concept patterns, namely intuitive, logical, formal concepts. Following [Pa3] studied on real numbers, we mainly focus on concept patterns of the number system. In order to do this we revisit some criteria on concept patterns of real numbers for the purpose of coherence.

Abstract

The present paper treats with the problem how we teach/learn mathematical concepts. Concept patterns suggested in [P-K-L] is an interesting approach to study this problem. It has been attacked various concepts in terms of three concept patterns, namely intuitive, logical, formal concepts. Following [Pa3] studied on real numbers, we mainly focus on concept patterns of the number system. In order to do this we revisit some criteria on concept patterns of real numbers for the purpose of coherence.

참고문헌 (11)

  1. P. Ernest, "수학교육철학" (2006), 경문사
  2. H. Eves, "수학의 기초와 기본개념" (1995), 경문사
  3. S. MacLane, "Mathematics : form and function" (1986), Springer-Verlag
  4. 박홍경, "Pattern of concepts of determinant and matrix and effective concept learning", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 12(1), pp.101~108 (2009), 장전수학회
  5. 박홍경, "실수론의 근본적 개념", Proc. Jangjeon Math. Soc, 14, pp.387~393 (2011)
  6. 박홍경, "Three patterns of the concept of real numbers", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 15(1), pp.101~107 (2012), 장전수학회
  7. 박홍경, "On lecturing of the concept of real numbers", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 18(4), pp.609~617 (2015), 장전수학회
  8. 박홍경, "벡터개념의 강의적 체계순서에 관하여", 한국수학사학회지, 20(2), pp.59~72 (2007), 한국수학사학회
  9. 박홍경, "수학적 개념의 유형과 효과적인 개념학습- 벡터이론을 중심으로", 한국수학사학회지, 20(3), pp.105~126 (2007), 한국수학사학회
  10. 박홍경, "On teaching the concept of continuous functions in calculus", 한국데이터정보과학회지, 18(4), pp.859~868 (2007), 한국데이터정보과학회
  11. 박홍경, "An analysis on patterns of concepts in terms of lines and circles appeared in a textbook of secondary school mathematics", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 16(4), pp.575~585 (2013), 장전수학회

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