[논문]대수적 사고를 강조한 분수 나눗셈 수업의 분석

조선미; 방정숙

doi:10.7468/mathedu.2021.60.4.409

대수적 사고를 강조한 분수 나눗셈 수업의 분석
An analysis of fractional division instruction emphasizing algebraic thinking 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.60 no.4, 2021년, pp.409 - 429

조선미 (서울영신초등학교) , 방정숙 (한국교원대학교)

초록
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본 연구는 초등학교 6학년 학생들을 대상으로 대수적 사고를 강조하여 분수 나눗셈을 지도하는 방안을 분석한 것이다. 문헌 연구에서 도출한 교수·학습 요소를 중심으로 분수 나눗셈 수업을 재구성하고, 실제 수업에서 주요 교수·학습요소가 어떻게 구현되는지 그 양상을 분석하였다. 특히 본 논문에서는 나누는 수 1에 대응하는 나누어지는 수의 양을 구하는 문제 맥락을 중심으로 분석하였다. 이를 토대로 초등학교 분수 나눗셈 수업에서 대수적 사고를 강조하여 지도하는 방안에 관한 구체적인 시사점을 도출하였다.

Abstract ▼ AI-Helper

This study investigated instructional methods for fractional division emphasizing algebraic thinking with sixth graders. Specifically, instructional elements for fractional division emphasizing algebraic thinking were derived from literature reviews, and the fractional division instruction was reorganized on the basis of key elements. The instructional elements were as follows: (a) exploring the relationship between a dividend and a divisor; (b) generalizing and representing solution methods; and (c) justifying solution methods. The instruction was analyzed in terms of how the key elements were implemented in the classroom. This paper focused on the fractional division instruction with problem contexts to calculate the quantity of a dividend corresponding to the divisor 1. The students in the study could explore the relationship between the two quantities that make the divisor 1 with different problem contexts: partitive division, determination of a unit rate, and inverse of multiplication. They also could generalize, represent, and justify the solution methods of dividing the dividend by the numerator of the divisor and multiplying it by the denominator. However, some students who did not explore the relationship between the two quantities and used only the algorithm of fraction division had difficulties in generalizing, representing, and justifying the solution methods. This study would provide detailed and substantive understandings in implementing the fractional division instruction emphasizing algebraic thinking and help promote the follow-up studies related to the instruction of fractional operations emphasizing algebraic thinking.

주제어

표/그림 (11)

$[Table 1] Problem contexts of fractional division used in this study$ 표 [Table 1] Problem contexts of fractional division used in this study
그림 [Fig. 1] The first example of using a visual model to explore the relationship between a dividend and a divisor
그림 [Fig. 2] The second example of using a visual model to explore the relationship between a dividend and a divisor
그림 [Fig. 3] The third example of using a visual model to explore the relationship between a dividend and a divisor
그림 [Fig. 4] An example of an expression of the equality between a dividend and a divisor
그림 [Fig. 5] An example of differentiating variables which represent different amounts
그림 [Fig. 6] An example of expressing an unspecified quantity in a variable expression
그림 [Fig. 7] An example of solving a problem using arrows in visual model
그림 [Fig. 8] An example of justifying the solution method by linking the expression and the visual model
그림 [Fig. 9] The first example exploring the meaning of an expression using variables
그림 [Fig. 10] The second example exploring the meaning of an expression using variables

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