[논문]단위 조정 3단계 학생의 비례 문제 해결에서 나타나는 분수 지식

이진아; 이수진

doi:10.7468/mathedu.2022.61.1.1

단위 조정 3단계 학생의 비례 문제 해결에서 나타나는 분수 지식
Exploring fraction knowledge of the stage 3 students in proportion problem solving 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.61 no.1, 2022년, pp.1 - 28

이진아 (광교중학교) , 이수진 (한국교원대학교)

초록
AI-Helper

본 연구의 목적은 비례 문제 해결 과정에서 학생의 분수 지식이 어떻게 관련되어 나타나는지를 탐구하는 것이다. 이를 위해 단위 조정 3단계로 판단되는 중학교 1학년 학생 2명에 주목하여 분수 지식과 비례 문제 해결 과정에 대한 임상 면담 자료를 분석하였다. 분석 결과 자연수 맥락에서 단위 조정 3단계 학생으로 판단되었던 두 학생은 분수 맥락에서는 '활동을 통해' 3수준 단위를 조정하며 서로 다른 양적 조작 방식을 보여주었다. 특히 두 학생이 가분수가 포함된 곱셈 연산 과제에서 보여주었던 분할 조작과 단위 조정 활동에서 식별되었던 차이는 두 학생의 비례 문제에 대한 접근 방식에 있어서 중요한 차이로 나타났다. 이 과정에서 하나의 3수준 단위로부터 또 다른 3수준 단위 사이의 구조적 전환이 '재귀 분할의 내재화'와 관련이 되며, 합성 단위에 대한 스플리팅 조작에 중요한 근거가 됨을 시사하였다.

Abstract ▼ AI-Helper

The purpose of this study is to explore how students' fractional knowledge is related to their solving of proportion problems. To this end, 28 clinical interviews with four middle-grade students, each lasting about 30~50 minutes, were carried out from May 2021 to August 2021. The present study focuses on two 7th grade students who exhibited their ability to coordinate three levels of units prior to solving whole number problems. Although the students showed interiorization of three levels of units in solving whole number problems, how they coordinated three levels of units were different in solving proportion problems depending on whether the problems required reasoning with whole numbers or fractions. The students could coordinate three levels of units prior to solving the problems involving whole numbers, they coordinated three levels of units in activity for the problems involving fractions. In particular, the ways the two students employed partitioning operations and how they coordinated quantitative unit structures were different in solving proportion problems involving improper fractions. The study contributes to the field by adding empirical data corroborating the hypotheses that students' ability to transform one three levels of units structure into another one may not only be related to their interiorization of recursive partitioning operations, but it is an important foundation for their construction of splitting operations for composite units.

주제어

표/그림 (15)

표 Table 1. Stage of units coordination (Norton et al., 2015, p.212).
그림 Figure 1. Conducting a splitting operation for composite units to divide 3 by 5.
그림 Figure 2. Conducting a distributive partitioning operation to divide 3 by 5.
그림 Figure 3. A picture of the cookie problem drawn by Sangyeon (left) and Hyeji (right).
표 Table 2. Fractional Multiplication-related Interview Tasks.
표 Table 3. Proportion-related Interview Tasks.
그림 Figure 4. Partitioning picture the form of an m×n rectangle of Sangyeon.
그림 Figure 5. Partition picture of Hyeji drawn in slightly different forms depending on the Tasks.
그림 Figure 6. The trial and error of partitioning by Hyeji.
$Figure 7. Image about <TEX>$\frac{4}{3}$</TEX> of 11 that Hyeji has.$ 그림 Figure 7. Image about $\frac{4}{3}$ of 11 that Hyeji has.
그림 Figure 8. Partitioning from eye measurements¹⁵.
그림 Figure 9. The bars task picture drawn by Hyeji.
그림 Figure 10. The bars task picture that Sangyeon partitioned into 'eye measurements' at the beginning.
그림 Figure 11. The bars task picture drawn again by Sangyeon.
그림 Figure 12. A table of length and width expressed by Sangyeon.

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저자의 다른 논문 :

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