An Analysis on the Repeated Error Patterns in Division of Fraction by Elementary Students

초등학생들이 분수의 나눗셈에서 보이는 반복적 오류 분석

  • Published : 2008.05.31

Abstract

This study analyzed the repeated error patterns in division of fraction by elementary students through observation of their test papers. The questions for this study were following. First, what is the most changable thing among the repeated error patterns appeared in division of fraction by elementary students? Second, what is the most frequent error patterns in division of fraction by elementary students? First of all, the ratios of incorrect answers in division of fraction by general students were researched. This research was the only one time. The purpose was to know what kind of compositions in the problems were appeared more errors. Total 554 6th grade students(300 boys and 254 girls) from 6 elementary schools in Seoul are participated in this research. On the basis of this, the study for analysis began in earnest. 5 tests made progress for about 4 months. Total 181 6th grade students(92 boys and 89 girls) from S elementary school in Seoul were participated in this. After each test, to confirm the errors and to classify them were done. Then the repeated error patterns were arranged into 4 types: alpha, beta, gamma and delta type. Consequently, conclusions can be derived as follows. First, most students modify their errors as time goes by even though they make errors about already learned contents. Second, most students who appeared errors make them continually caused a reciprocal of natural number in the divisor when they calculate computations about '(fraction) $\div$ (natural number)'. Third, most students recognize that the divisor have to change the reciprocal when they calculate division of fraction through they modify their errors repeatedly.

지금까지 분수의 나눗셈에 대한 오류 분석 연구는 대부분 단 1회의 검사를 통해 분석을 한 후 오류를 검증하였다. 즉, 학생들이 반복적으로 보이는 다양한 오류에 대한 분석한 선행연구는 없었다. 이에 본 연구에서는 수학의 연산 영역 중 초등학교 수학 교육과정의 마지막을 장식한다고도 볼 수 있는 '분수의 나눗셈'에 대한 학생들의 반복적 오류 유형을 살펴봄으로써 학생들의 사고를 엿봄과 동시에 학생들에게 좀 더 신중하고 정확하게 가르쳐야하는 정보를 얻는 것이 목적이다. 이를 위해 6학년 학생들이 분수의 나눗셈을 모두 학습한 후 시간의 흐름에 따라 나타나는 오류를 찾아내기 위해 학생들이 해결한 학습지를 바탕으로 관찰 분석 연구를 진행하였다.

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