East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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A Study on the Theoretical Background of the Multiplication of Rational Numbers as Composition of Operators

두 조작의 합성으로서의 유리수 곱의 이론적 배경 고찰

  • Choi, Keunbae (Department of Mathematics Education, Teachers College Jeju National University)
  • Received : 2017.01.16
  • Accepted : 2017.02.19
  • Published : 2017.02.28
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Abstract

A rational number as operator is eventually that it is considered a mapping. Depending on how selecting domain (the target of operation by rational number) and codomain (including the results of operations by rational number), it is possible to see the rational in two aspects. First, rational numbers can be deal with functions if we choose the target of operation by rational number as a number field containing rationals. On the other hand, if we choose the target of operation by rational number as integral domain $\mathbb{Z}$, then rational numbers can be regarded as partial functions on $\mathbb{Z}$. In this paper, we regard the rational numbers with a view of partial functions, we investigate the theoretical background of the relationship between the multiplication of rational numbers and the composition of rational numbers as operators.

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References

  1. 이지영, 방정숙 (2014). 분수의 다양한 의미에서 단위에 대한 초등학교 6학년 학생들의 이해 실태 조사, 대한수학교육학회지 수학교육학연구, 24(1), 83-102.
  2. 정영우, 김부윤 (2012). 연산자로서의 유리수 체계의 구성에 관한 연구, East Asian Mathematical Journal, Vol. 28, pp. 135-158. https://doi.org/10.7858/eamj.2012.28.2.135
  3. 정은실 (2006). 분수 개념의 의미 분석과 교육적 시사점 탐구, 대한수학교육학회지 학교수학, 8(2), 123-138.
  4. 함혜림 (2014). 연산자 분수에 대한 고찰, 교육학 석사학위 논문, 경인교육대학교 교육전문대학원.
  5. Behr, M., Lesh, R., Post, T., & Silver E. (1983). Rational Number Concepts. In R. Lesh & M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes, (pp. 91-125). New York: Academic Press.
  6. Choi, K. & Lim, Y. (2000). Inverse monoids of Mobius type, J. Algebra, 223, 283-294. https://doi.org/10.1006/jabr.1999.8050
  7. Choi, K. & Lim, Y. (2002). Birget-Rhodes expansion of groups and inverse monoids of Mobius, Internat. J. Algebra Comput. 12, no. 4, 525-533. https://doi.org/10.1142/S0218196702001073
  8. Choi, K. & Lim, Y. (2008). Transitive Partial Actions of Groups, Periodica Mathematica Hungarica, Vol. 56(2), 169-181. https://doi.org/10.1007/s10998-008-6169-8
  9. Charalambous, C.Y. (2005) Revisiting theoritical model of fractions: Implications for teaching and research. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 2, pp. 233-240. Melbourne: PME.
  10. Howie, J. M. (1976). An Introduction to Semigroup Theory, Academic Press Inc.
  11. Kellendonk, J. and Lawson, Mark V. (2004). Partial Actions of Groups, Int. J . Algebra Comput. 14, 87. https://doi.org/10.1142/S0218196704001657
  12. Lamon, Susan J. (2008). Teaching Fractions and Ratios for understanding, Lawrence Erlbaum Associates, Inc.
  13. Lawson, Mark V. (1998). Inverse Semigroups: The Theory of Partial Symmetries, World Scientific Publishing Co. Pte. Ltd.
  14. Skemp R. R. (김판수.박성택 역) (1996). 초등수학교육, 서울: 교우사.
  15. Steffe, L. P. (2002). A new hypothesis concerning children's fractional knowledge, Journal of Mathematical Behavior, 20, 267-307.