• Education of Primary School Mathematics
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• v.16 no.2
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• pp.93-106
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• 2013

A large part of students' difficulties with fractional division algorithms in the current algorithm textbooks, seem to be due to self-induction methods. Through concrete analysis of surveys and interviews, we confirmed the educational value of fractional algorithms used to elicit alternative ways of context of determination of a unit rate. In addition, we suggested alternative methods based on the results of the teaching methods and curriculum configuration.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.91-110
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• 2024

The purpose of this study is to explore visual models for deriving the fractional division algorithm, to see how students understand this integrated model, the rectangular partition model, when taught in elementary school classrooms, and how they structure relationships between fractional division situations. The conclusions obtained through this study are as follows. First, in order to remind the reason for multiplying the reciprocal of the divisor or the meaning of the reciprocal, it is necessary to explain the calculation process by interpreting the fraction division formula as the context of a measurement division or the context of the determination of a unit rate. Second, the rectangular partition model can complement the detour or inappropriate parts that appear in the existing model when interpreting the fraction division formula as the context of a measurement division, and can be said to be an appropriate model for deriving the standard algorithm from the problem of the context of the inverse of a Cartesian product. Third, in the context the inverse of a Cartesian product, the rectangular partition model can naturally reveal the calculation process in the context of a measurement division and the context of the determination of a unit rate, and can show why one division formula can have two interpretations, so it can be used as an integrated model.

• 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.

• School Mathematics
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• v.7 no.2
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• pp.103-121
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• 2005

This article compares and analyzes mathematics textbooks of North Korea, South Korea, China and Japan and draws meaningful ways for introducing the division algorithm of fractions. The analysis is based on the five contexts: 'measurement division', 'determination of a unit rate', 'reduction of the quantities in the same measure', 'division as the inverse of multiplication or Cartesian product', 'analogy with multiplication algorithm of fractions'. The main focus of the analysis is what context is used to introduce the algorithm and how much it can appeal to students. This analysis supports that there is a few differences of introducing methods the division algorithm of fractions among those countries and more meaningful way can be considered than ours. It finally suggests that we teach the algorithm in a way which can have students easily see the reason of multiplying the reciprocal of a divisor when they divide with fractions. For this, we need to teach the meaning of a reciprocal of fraction and consider to use the context of determination of a unit rate.

• Journal of the Korean School Mathematics Society
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• v.23 no.2
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• pp.203-222
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• 2020

Because the role of the teacher is important for the education to actualize the goals of the curriculum, the interest about the teacher's knowledges has been addressed as an important research topic. Among them, the pedagogical content knowledge is the knowledge that can emphasize the professionalism of the teacher. In this study, I analyzed the elementary pre-service teachers' the problem solving strategies that they imagined the methods that elementary school students can think about fraction division. Pre-service teachers who participated in this study were completed all of the mathematics education courses in the pre-service teachers' education courses. The research was conducted using the four type-problems of fraction division. The results showed that elementary pre-service teachers responded in the order of equal sharing problem-measurement division-partitive division-context of determination of a unit rate problem. They presented significant responses not only with typical algorithms but also with pictures or expressions. On the basis of this research, we have to take an interest in the necessity of sharing and recognizing various methods of fraction division in pre-service teachers education.