‘역 분수 문제’에 대한 5학년 학생들의 해결 방법 분석
An analysis of solution methods by fifth grade students about ‘reverse fraction problems’
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As the importance of algebraic thinking in elementary school has been emphasized, the links between fraction knowledge and algebraic thinking have been highlighted. In this study, we analyzed the solution methods and characteristics of thinking by fifth graders who have not yet learned fraction division when they solved ‘reverse fraction problems’ (Pearn & Stephens, 2018). In doing so, the contexts of problems were extended from the prior study to include the following cases: (a) the partial quantity with a natural number is discrete or continuous; (b) the partial quantity is a natural number or a fraction; (c) the equivalent fraction of partial quantity is a proper fraction or an improper fraction; and (d) the diagram is presented or not. The analytic framework was elaborated to look closely at students’ solution methods according to the different contexts of problems. The most prevalent method students used was a multiplicative method by which students divided the partial quantity by the numerator of the given fraction and then multiplied it by the denominator. Some students were able to use a multiplicative method regardless of the given problem contexts. The results of this study showed that students were able to understand equivalence, transform using equivalence, and use generalizable methods. This study is expected to highlight the close connection between fraction and algebraic thinking, and to suggest implications for developing algebraic thinking when to deal with fraction operations.
Abstract
As the importance of algebraic thinking in elementary school has been emphasized, the links between fraction knowledge and algebraic thinking have been highlighted. In this study, we analyzed the solution methods and characteristics of thinking by fifth graders who have not yet learned fraction division when they solved ‘reverse fraction problems’ (Pearn & Stephens, 2018). In doing so, the contexts of problems were extended from the prior study to include the following cases: (a) the partial quantity with a natural number is discrete or continuous; (b) the partial quantity is a natural number or a fraction; (c) the equivalent fraction of partial quantity is a proper fraction or an improper fraction; and (d) the diagram is presented or not. The analytic framework was elaborated to look closely at students’ solution methods according to the different contexts of problems. The most prevalent method students used was a multiplicative method by which students divided the partial quantity by the numerator of the given fraction and then multiplied it by the denominator. Some students were able to use a multiplicative method regardless of the given problem contexts. The results of this study showed that students were able to understand equivalence, transform using equivalence, and use generalizable methods. This study is expected to highlight the close connection between fraction and algebraic thinking, and to suggest implications for developing algebraic thinking when to deal with fraction operations.
참고문헌 (22)
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