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함수의 합성∘이 가지는 의미에 대한 고찰

A Study on Meaning of Composition of Functions

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Composition of functions are important tool for producing associativity in mathematical model. However it is not properly treated in dealing together with the other operation, the addition , of functions defined on real numbers. In this note, we will study mathematization of the construction of nearring axiom from relationships between the addition and the composition of functions, comparing with those between the addition and the multiplication of functions. Furthermore, we will suggest some helpful teaching methods of these mathematization in the secondary school mathematics.

Abstract

Composition of functions are important tool for producing associativity in mathematical model. However it is not properly treated in dealing together with the other operation, the addition , of functions defined on real numbers. In this note, we will study mathematization of the construction of nearring axiom from relationships between the addition and the composition of functions, comparing with those between the addition and the multiplication of functions. Furthermore, we will suggest some helpful teaching methods of these mathematization in the secondary school mathematics.

참고문헌 (12)

  1. 김부윤, "Byproduct Mathematization에 관한 연구" (2010)
  2. 김응태, "현대대수학" (2003), 경문사
  3. 교육과학기술부, "고등학교 교육과정 해설 5-수학" (2008), 한국보훈복지의료공단 신생인쇄조합
  4. 류희찬, "고등학교 수학" (2009), 대한교과서(주)
  5. 우정호, "수학교육학 연구방법론" (2007), 경문사
  6. 이재학, "고등학교 수학" (2009), (주)금성출판사
  7. 이준열, "고등학교 수학" (2009), (주)천재교육
  8. 이현정, "분배법칙의 지도", 석사, pp.2003
  9. 황선욱, "고등학교 수학" (2009), (주)좋은책 신사고
  10. 황우형, "고등학교 수학" (2009), 대한교과서(주)
  11. B. Baumslag, "Group Theory" (1968), McGraw-Hill
  12. James R. Clay, "Nearrings:Geneses and Appli-cations" (1992), Oxford University Press

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