• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.717-735
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• 2016

For teaching division-with-remainder(DWR) problems, it is necessary to know students' strategies and errors about DWR problems. The purpose of this study is to investigate and analyze students' strategies and errors of DWR problems and to make some meaningful suggestions for teaching various methods of solving DWR problems. We constructed a test which consists of fifteen DWR problems to investigate students' solving strategies and errors. These problems include mathematical as well as syntactic structures. To apply this test, we selected 177 students from eight elementary schools in various districts of Seoul. The results were analyzed both qualitatively and quantitatively. The sixth graders' strategies can be classified as follows : Single strategies, Multi strategies and Assistant strategies. They used Division(D) strategy, Multiplication(M) strategy, and Additive Approach(A) strategy as sub-strategies. We noticed that frequently used strategies do not coincide with strategies for their success. While students in middle group used Assistant strategies frequently, students in higher group used Single strategies frequently. The sixth graders' errors can be classified as follows : Formula error(F error), Calculation error(C error), Calculation Product error(P error) and Interpretation error(I error). In this study, there were 4 elements for syntaxes in problems : large number, location of divisor and dividend, divisor size, vocabularies. When students in lower group were solving the problems, F errors appeared most frequently. However, in case of higher group, I errors appeared most frequently. Based on these results, we made some didactical suggestions.

• Journal of Educational Research in Mathematics
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• v.23 no.1
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• pp.17-35
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• 2013

The purpose of this study was to analyze the extendibility of division algorithm and Euclid algorithm for integers to algorithms for rational numbers based on word problems of fraction division. This study serviced to upgrade professional development of elementary and secondary mathematics teachers. In this paper, fractions were used as expressions of rational numbers, and they also represent rational numbers. According to discrete context and continuous context, and measurement division and partition division etc, divisibility was classified into two types; one is an abstract algebraic point of view and the other is a generalizing view which preserves division algorithms for integers. In the second view, we raised some contextual problems that can be used in school mathematics and then we discussed division algorithm, the greatest common divisor and the least common multiple, and Euclid algorithm for fractions.