곱셈과 나눗셈 문장제 유형에 따른 문제해결능력 (An Analysis on Problem Solving Ability of 3rd Grade Types of Multiplication and Division Word Problem)

서지정보

· 발행기관 : 한국초등수학교육학회
· 수록지 정보 : 한국초등수학교육학회지 / 19권 / 4호 / 501 ~ 525페이지
· 저자명 : 임자선, 김성준

초록

본 논문은 2009 개정 교육과정 초등학교 3학년 수학 교과서와 익힘책에 제시된 곱셈과 나눗셈 문장제를 유형별로 분석하고, 초등학교 4학년 학생을 대상으로 문장제 유형에 따른 문제해결능력을 살펴봄으로써 곱셈과 나눗셈 문장제의 효율적인 지도방안을 생각해보기 위한 것이다. 이를 위해 먼저 초등학교 3학년 수학 교과서와 익힘책에 제시된 자연수의 곱셈 문장제를 동수누가, 비율, 비교, 정렬, 조합의 5가지 의미 유형으로, 나눗셈은 등분제와 포함제의 2가지 유형으로 구분하여 살펴보았다. 이와 함께 곱셈과 나눗셈 문장제에서 미지수의 위치에 따라 처음량, 변화량, 결과량을 묻는 문장제의 구문 유형에 대해서도 살펴보았다. 그런 다음 4학년 학생을 대상으로 문장제 문제해결능력 검사 도구를 개발하였는데, 앞서 분석한 곱셈과 나눗셈의 문장제 유형을 의미와 구문으로 나누어 2차례의 검사를 실시하여 정답률과 학생들의 오답 반응 등을 분석하였다. 분석 결과 곱셈은 동수누가에서의 정답률이 높게 나온 반면 나눗셈의 경우 포함제와 등분제에서 차이를 보이지 않았는데, 이는 교과서의 문제 유형 분포와 상관관계를 보임을 알 수 있다. 이러한 논의를 바탕으로 곱셈과 나눗셈 문장제의 효과적인 지도와 학생들의 문장제 문제해결능력을 향상시키기 위해 다양한 유형의 문장제를 제시할 필요가 있음을 제안하고 있다.

영어초록

This study analyzes arithmetic word problem of multiplication and division in the mathematics textbooks and workbooks of 3rd grade in elementary school according to 2009 revised curriculum. And we analyzes type of the problem solving ability which 4th graders prefer in the course of arithmetic word problem solving and the problem solving ability as per the type in order to seek efficient teaching methods on arithmetic word problem solving of students.
First, in the mathematics textbook and workbook of 3rd grade, arithmetic word problem of multiplication and division suggested various things such as thought opening, activities, finish, and let's check. As per the semantic element, multiplication was classified into 5 types of cumulated addition of same number, rate, comparison, arrayal and combination while division was classified into 2 types of division into equal parts and division by equal part. According to result of analysis, the type of cumulated addition of same number was the most one for multiplication while 2 types of division into equal parts and division by equal part were evenly spread in division.
Second, according to 1st test result of arithmetic word problem solving ability in the element of arithmetic operation meaning, 4th grade showed type of cumulated addition of same number as the highest correct answer ratio for multiplication. As for division, 4th grade showed 90% correct answer ratio in 4 questionnaires out of 5 questionnaires. And 2nd test showed arithmetic word problem solving ability in the element of arithmetic operation construction, as for multiplication and division, correct answer ratio was higher in the case that 4th grade students did not know the result than the case they did not know changed amount or initial amount. This was because the case of asking the result was suggested in the mathematics textbook and workbook and therefore, it was difficult for students to understand such questions as changed amount or initial amount which they did not see frequently. Therefore, it is required for students to experience more varied types of problems so that they can more easily recognize problems seen from a textbook and then, improve their understanding of problems and problem solving ability.

참고자료

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