Education of Primary School Mathematics (한국수학교육학회지시리즈C:초등수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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Justifying the Fraction Division Algorithm in Mathematics of the Elementary School

초등학교 수학에서 분수 나눗셈의 알고리즘 정당화하기

  • Received : 2019.01.14
  • Accepted : 2019.04.18
  • Published : 2019.04.30
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Abstract

The purpose of this study is to justify the fraction division algorithm in elementary mathematics by applying the definition of natural number division to fraction division. First, we studied the contents which need to be taken into consideration in teaching fraction division in elementary mathematics and suggested the criteria. Based on this research, we examined whether the previous methods which are used to derive the standard algorithm are appropriate for the course of introducing the fraction division. Next, we defined division in fraction and suggested the unit-circle partition model and the square partition model which can visualize the definition. Finally, we confirmed that the standard algorithm of fraction division in both partition and measurement is naturally derived through these models.

본 연구의 목적은 자연수 나눗셈의 정의를 확장하여 분수 나눗셈에 적용함으로써 초등학교 수학에서 분수 나눗셈의 알고리즘을 정당화하는데 있다. 먼저 초등학교 수학에서 분수 나눗셈을 도입할 때 고려해야 할 준거들을 도출하여 제시하였다. 이를 바탕으로 분수 나눗셈의 표준 알고리즘을 유도하는 기존의 방식들이 분수 나눗셈 도입 과정에 적절한지를 고찰하였다. 또한 분수 나눗셈을 정의하였으며, 단위원 분할 모델과 정사각형 분할 모델을 통하여 구체적 조작 활동을 함으로써 등분제와 포함제 상황의 분수 나눗셈에서 표준 알고리즘을 자연스럽게 정당화하였다.

Keywords

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[그림 1] 분수 나눗셈의 이해(Sinicrope et al., 2002, p. 160) [Fig. 1] Interpretation of fraction division(Sinicrope et al., 2002, p. 160)

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[그림 2] 길이(m) 공간과 길이(u) 공간(임재훈,2016, p.530) [Fig. 2] Length(m) space and length(u) space(Lim, J. H., 2016, p.530)

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[그림 3] 쌓기나무 모델로 표현된 2차 단위 비율법 [Fig. 3] The method of scondary unit rate, expressed through building block model

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[그림 4] 쌓기나무 모델로 표현된 1차 단위 비율법 [Fig. 4] The method of primary unit rate, expressed through building block model

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[그림 5]$\frac{5}{7}{\div}\frac{2}{3}$ 의 단위원 분할 모델 [Fig. 5] The unit-circle partition model of $\frac{5}{7}{\div}\frac{2}{3}$

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[그림 6] $\frac{3}{2}{\times}\frac{2}{3}$ 의 정사각형 분할 모델 [Fig. 6] The square partition model of $\frac{3}{2}{\times}\frac{2}{3}$

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[그림 7] $\frac{4}{3}{\times}\frac{3}{4}$ 의 정사각형 분할모델 [Fig. 7] The square partition model of $\frac{4}{3}{\times}\frac{3}{4}$

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[그림 8] $\frac{d}{c}{\times}\frac{c}{d}$ 의 정사각형 분할모델 [Fig. 8] The square partition model of $\frac{d}{c}{\times}\frac{c}{d}$ (단, c

[표 1] 분수 나눗셈 알고리즘 접근 방식들의 한계점 [Table 1] The limitations of approach-methods for the fraction division algorithm

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