A Study of the Sixth Graders' Knowledge of Concepts and Operations about Fraction

초등학생의 분수 이해 분석 - 6학년의 분수 개념 및 분수 나눗셈을 중심으로 -

The purpose of the study is to analyze the sixth graders' understanding of concepts and operation about fraction. The test was administered and analyzed to 707 sixth graders' performance on fractions after the fraction instructions in elementary schools in Seoul, Korea. The participants are asked to answer two sets of questions for 40 minutes. First, they are asked to answer to 16 problems about the concepts of fraction with respect to part-whole, ratio, operator, measure, quotient, equivalent, and operations. Second, specially, to investigate sixth graders' ability of drawing and describing the situation of division including fraction, the descriptive problem asked students (1) to describe $3\;{\div}\;\frac{1}{2}$ into pictorial representation and (2) to write the solving process. The participants of this study didn't show deep understandings about the concepts and operation of fraction. The degree of understanding of subconstructs of fraction shows that their knowledge of ratio concept with respect to fraction was highest while their understanding of measure with respect to fraction was lowest. Considering their wrong answers, about 59% of participants showed misconception to the question of naming one fraction that appears between $\frac{1}{5}$ and $\frac{1}{6}$. Further, they didn't explain their understanding with drawing about the division of fraction ($3\;{\div}\;\frac{1}{2}$).

초등학생에게 분수는 추상적인 개념이며 형식화된 이해를 요구하는, 핵심적인 수학적 기초 내용이다. 초등학교 수학에서 중학교 수학으로 연계되는 내용의 위계 구조상 적지 않은 영향력을 끼치는 내용 중 하나가 초등수학에서의 분수 학습일 것이다. 이에 본 연구에서는 초등학교 6학년생에게 나타난 분수 개념에 대한 이해와 오류를 분석하고 초등학교 학생이 가장 어려워하는 분수 나눗셈에 대한 표현 능력을 살펴봄으로써 초등수학에서의 시사점을 제공하고자 한다.