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Didactical Issues Related to Necessary Condition and Sufficient Condition

필요조건, 충분조건 개념의 학습과 관련한 문제들

  • Received : 2015.07.21
  • Accepted : 2015.08.20
  • Published : 2015.08.31

Abstract

The reason of the confusion of learners about the logic concepts such as implication, necessary condition and sufficient condition can be analyzed from the point of view of history of logic, discrepancy between ordinary language and formal logic, and reification which occurs in the process of cognition of discursive object and also indicates the necessity of a research. This study analysed the difficulties related to study and implication concept and attempted to the reflection of textbook and curriculum. Not that ordinary language makes the introduction of formal language easier, but that this study discussed the possibilities ordinary language intervenes the learning of formal language. This study additionally intended to understand learning difficulties of concrete subjects, abstract subjects and the gap between primary object and discursive object by understanding the process of sagging, encapsulating and reifying.

Keywords

References

  1. J. D. Carney, R. K.Scheer , Fundamental to Logic, New York: Macmillan, 1980. 논리학 입문, 전영삼 역, 간디서원.
  2. Sextus Empricus, Outlines of Pyrrhonism, Oxford University Press, 1996.
  3. H. Eves, The Foundations and Fundamental Concepts of Mathematics, 1997. 수학의 기초와 기본개념, 허민, 오혜영 역, 경문사.
  4. S. C. Kleene, Mathematical Logic, 1952. 수리논리학, 박한식 편역, 교학연구사.
  5. Kim Young Ok, First-year Undergraduate Students' Understanding about Statements, in School Mathematics 11(2) (2009), 261-280. 김영옥, 대학 신입생들의 명제에 대한 이해, 학교수학 11(2) (2009), 대한수학교육학회.
  6. Lee Young Ha, Jung Eun Ah, A Study of Middle and High School Set and Proposition Unit Analysis And Alternative, in Research of Curriculum and Instruction 7(2), 23-63, 2003. 이영하, 정은아, 중등학교 집합과 명제단원 분석 및 개선방안 연구, 교과교육학연구 7(2) (2003), 이화여자대학교 교과교육연구소.
  7. Lew Hee-Chan et al, Highschool Mathematics, Mirae N Co., 2009. 유희찬 외 8인, 고등학교수학, (주) 미래엔, 2009.
  8. Lew Hee-Chan et al, Highschool Mathematics Instruction Guide, Mirae N Co., 2009. 유희찬 외 8인, 고등학교 수학 교사용 지도서, (주) 미래엔, 2009.
  9. S. Pirie, Crossing the gulf between thought and symbol: language as (slippery) steppingstones, In H. Steinbring, M. Bartolini Bussi & A. Sierpinska(Eds.), Language and communication in the mathematics classroom, 7-29. Reston, VA: NCTM, 1998. 10.
  10. A. Sfard, Thinking as Communicating, Cambridge University Press, 2008.