• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.351-373
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• 2017

The meanings of division don't change and rather are connected from whole numbers to rational numbers. In this respect, connecting division of natural numbers, division of fractions, and division of decimal numbers could help for students to study division in meaningful ways. Against this background, the units of division of fractions and division of decimal numbers in fifth grade were redesigned in a way for students to connect meanings of division and procedures of division. The results showed that most students were able to understand the division meanings and build correct expressions. In addition, the students were able to make appropriate division situations when given only division expressions. On the other hand, some students had difficulties in understanding division situations with fractions or decimal numbers and tended to use specific procedures without applying diverse principles. This study is expected to suggest implications for how to connect division throughout mathematics in elementary school.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.3
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• pp.395-411
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• 2013

There are two concepts of division: measurement division and partitive or fair-sharing division. Students are expected to understand comprehensively division algorithm in both contexts. Contents of textbooks and teachers' guidebooks should be suitable for helping students develop comprehensive understanding of algorithm for whole-number division in both contexts. The results of the analysis of textbooks and teachers' guidebooks shows that they fail to connect two division contexts with division algorithm comprehensively. Their expedient and improper use of two division contexts would keep students from developing comprehensive understanding of algorithm for whole-number division. Based on the results of analysis, some ways of improving textbooks and teachers' guidebooks are suggested.

• School Mathematics
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• v.11 no.4
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• pp.685-706
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• 2009

This dissertation is aimed to investigate the reason why a contextualization is needed to help the meaningful teaching-learning concerning multiplications and divisions of fractions, the way to make the contextualization possible, and the methods which enable us to use it effectively. For this reason, this study intends to examine the differences of situations multiplying or dividing of fractions comparing to that of natural numbers, to recognize the changes in units by contextualization of multiplication of fractions, the context is set which helps to understand the role of operator that is a multiplier. As for the contextualization of division of fractions, the measurement division would have the left quantity if the quotient is discrete quantity, while the quotient of the measurement division should be presented as fractions if it is continuous quantity. The context of partitive division is connected with partitive division of natural number and 3 effective learning steps of formalization from division of natural number to division of fraction are presented. This research is expected to help teachers and students to acquire meaningful algorithm in the process of teaching and learning.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.445-458
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• 2012

Current textbooks may provide students and teachers with three improper notions related to the quotient and the remainder in division for decimal numbers as in the following. First, only the calculated results in (natural numbers)${\div}$(natural numbers) is the quotient. Second, when the quotient and the remainder are obtained in division for decimal numbers, the quotient is natural number and the remainder is unique. Third, only when the quotient cannot be divided exactly, the quotient can be rounded off. These can affect students and teachers on their notions of division for decimal numbers, so improvements are needed for to break it. For these improvements, the following measures are required. First, in the curriculum guidebook, the meaning of the quotient and the remainder in division for decimal numbers should be presented clearly, for preventing the possibility of the construction of such improper notions. Second, examples, problems, and the like should be presented in the textbooks enough to break such improper notions. Third, the didactical intention should be presented clearly with respect to the quotient and the remainder in division for decimal numbers in teacher's manual.

• Education of Primary School Mathematics
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• v.22 no.2
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• pp.113-127
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• 2019

The purpose of this study is to justify the fraction division algorithm in elementary mathematics by applying the definition of natural number division to fraction division. First, we studied the contents which need to be taken into consideration in teaching fraction division in elementary mathematics and suggested the criteria. Based on this research, we examined whether the previous methods which are used to derive the standard algorithm are appropriate for the course of introducing the fraction division. Next, we defined division in fraction and suggested the unit-circle partition model and the square partition model which can visualize the definition. Finally, we confirmed that the standard algorithm of fraction division in both partition and measurement is naturally derived through these models.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.1-16
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• 2011

This study is to review division of whole numbers which is dealt in the revised elementary mathematics textbook and manual for teacher. The textbook and manual for teachers are most important documents to teach mathematics. And they are important to the would-be teachers who study the elementary mathematics with such documents. Therefore the textbook and manual for teachers should have no errors. But I found they have some errors and problems regarding division of whole numbers. In this paper, I discuss the problems and suggest the alternative plans.

• School Mathematics
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• v.14 no.2
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• pp.191-212
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• 2012

In the field of arithmetic in mathematics education, there has been lack of fine-grained investigations addressing the relationship between students' construction of division knowledge with fractional quantities and their whole number division knowledge. This study, through the analysis of part of collected data from a year-long teaching experiment, presents a possible constructive itinerary as to how a student could modify her unit-segmenting scheme to deal with various fraction measurement division situations: 1) unit-segmenting scheme with a remainder, 2) fractional unit-segmenting scheme. Thus, this study provides a clue for curing a fragmentary approach to teaching whole number division and fraction division and preventing students' fragmentary understanding of the same arithmetical operation in different number systems.

• Education of Primary School Mathematics
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• v.14 no.3
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• pp.317-328
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• 2011

We analyzed errors committed by Korean prospective elementary teachers in finding and interpreting quotient and remainder within measurement division of fractions. 65 prospective elementary teachers were participated in this study. They solved a word problem about measurement division of fractions. We analyzed solutions of all participants, and interviewed 5 participants of them. The results reveal many of these prospective teachers could not tell what fractional part of division result means. Thses results suggest that teacher preparation program should emphasize interpreting calculation results within given situations.

• Education of Primary School Mathematics
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• v.20 no.1
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• pp.69-84
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• 2017

The purpose of this study is to review how to introduce a division algorithm in mathematics textbooks which were applied 2009 revised curriculum. As a result, the textbooks do not introduce the algorithm in the context of division by equal part. The standardized division algorithm was introduced apart from the stepwise division algorithms and there is no explanation in between them. And there is a lack connectivity between activities and algorithms. This study is expected to help new curriculum and textbook to introduce division algorithm in proper way.

• Journal of Elementary Mathematics Education in Korea
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• v.10 no.2
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• pp.221-242
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• 2006

For teaching division more effectively, it is necessary to know students' informal knowledge before they learned formal knowledge about division. The purpose of this study is to research students' informal knowledge of division and to analyze meaningful suggestions to link formal knowledge of division in elementary school mathematics. According to this purpose, two research questions were set up as follows: (1) What is the students' informal knowledge before they learned formal knowledge about division in elementary school mathematics? (2) What is the difference of thinking strategies between students who have learned formal knowledge and students who have not learned formal knowledge? The conclusions are as follows: First, informal knowledge of division of natural numbers used by grade 1 and 2 varies from using concrete materials to formal operations. Second, students learning formal knowledge do not use so various strategies because of limited problem solving methods by formal knowledge. Third, acquisition of algorithm is not a prior condition for solving problems. Fourth, it is necessary that formal knowledge is connected to informal knowledge when teaching mathematics. Fifth, it is necessary to teach not only algorithms but also various strategies in the area of number and operation.