• 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 Elementary Mathematics Education in Korea
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• v.23 no.2
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• pp.193-217
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• 2019

Researchers have observed one student who had difficulty in formulating a division equation. In the context of determination of a unit rate problem based on one student's case and previous research, we tried to examine in detail how students expressed the division formula, how to select the dividend and the divisor, and how they learned about those. First, a questionnaire was developed to analyze student's reactions and applied to the research participants. Interviews were conducted to discover how the participants choose the dividends and divisors derived from their cognitive characteristics corresponding to their selection method. The research exposed that the majority of the participants had difficulty in deciding the dividends and divisors. Moreover, the research indicated information that teaching methods need to be reformed. Finally, we obtained suggestions to place emphasis on how to decide a dividend and a divisor, why they made such selection and what the equation means. We proposed a learning method for the research above.