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몫으로서의 분수와 분배전략

A Study on the Fraction as Quotient and Equal Sharing Strategies in Elementary Mathematics

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초록

In this paper, we investigate distribution strategies in the Egyptian fraction, and through this, we examine the distribution strategies of (fraction)÷(fraction) and then provide some educational implications. The (natural number)÷(natural number) of the sharing situation has the meaning of ‘share’ per unit, which can be seen as a situation where the unit ratio is determined. These concepts can also naturally be extended to the case of (fraction)÷(fraction) by some problem posing situations. That is to say, the case of (fraction)÷(fraction) can be deduced the case (natural number)÷(natural number) by the re-statement of the problem.

Abstract

In this paper, we investigate distribution strategies in the Egyptian fraction, and through this, we examine the distribution strategies of (fraction)÷(fraction) and then provide some educational implications. The (natural number)÷(natural number) of the sharing situation has the meaning of ‘share’ per unit, which can be seen as a situation where the unit ratio is determined. These concepts can also naturally be extended to the case of (fraction)÷(fraction) by some problem posing situations. That is to say, the case of (fraction)÷(fraction) can be deduced the case (natural number)÷(natural number) by the re-statement of the problem.

참고문헌 (19)

  1. 권성룡, "초등학생의 분수이해에 관한 연구", 학교수학, 5(2), pp.259~273 (2003), 대한수학교육학회
  2. 교육부, "수학 6-1" (2015), 천재교육
  3. 교육부, "수학 6-1 교사용 지도서" (2015), 천재교육
  4. 교육부, "수학 6-2" (2015), 천재교육
  5. 교육부, "수학 6-2 교사용 지도서" (2015), 천재교육
  6. 서동엽, "분수의 역사발생적 지도 방안", 수학교육학연구, 15(3), pp.233~249 (2005), 대한수학교육학회
  7. 우정호, "수학의 교육적 기초" (2006), 서울대학교 출판부
  8. 방정숙, "몫으로서의 분수에 관한 초등학교 수학과 교과용도서 분석", 수학교육학연구, 24(2), pp.165~180 (2014), 대한수학교육학회
  9. 최근배, "두 조작의 합성으로서의 유리수 곱의 이론적 배경 고찰", East Asian Mathematical Journal, 33(2), pp.199~216 (2017), 영남수학회
  10. Behr, M., "Acquisition of Mathematics Concepts and Processes", pp.91~125 (1983), Academic Press
  11. Brown, S. I., "The art of problem posing" (1983), Franklin Institute Press
  12. Charalambous, C. Y., "Drawing on theoretical to study students' understandings of fractions", Educational Studies in Mathematics, 64(3), pp.293~316 (2007)
  13. Kieren, T. E., "Rational Numbers: An Integration of Research", pp.49~84 (1993), Lawrence Erlbaum Associates
  14. Kim, A., "The development of four fifth grade students’ understanding and skill representing fractions as quotients", doctor, pp.2009
  15. 김아영, "The Construction of Children's Partitioning Strategy on the Equal Sharing Situation", 학교수학, 14(1), pp.29~43 (2012), 대한수학교육학회[DOI]
  16. 김아영, "The Type of Fractional Quotient and Consequential Development of Children's Quotient Subconcept of Rational Numbers", 수학교육학연구, 22(1), pp.53~68 (2012), 대한수학교육학회
  17. Lamon, S. J., "Teaching Fractions and Ratios for Understanding; Essential Content Knowledge and Instructional Strategies for Teachers" (2006), Lawrence Erlbaum Associates, Inc
  18. Silver, E. A., , For the Learning of Mathematics, 14(1), pp.19~28 (1994), FLM Publishing Association
  19. Toluk, Z., "Children’s conceptualizations of the quotient subconstruct of rational numbers", doctor, pp.1999

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