• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.467-480
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• 2014

Concepts related to the fraction should be taught with formative thinking activities as well as concrete operational activities. Teaching improper fraction should follow the concept of fraction as a relation of two natural numbers. This concept is also important not to be skipped before teaching the fraction such as "4 is a third of 12". Mixed number should be taught as a sum of a natural number and a proper fraction. Fraction as a quotient of a division is a hard concept to be taught since it requires very high abstractive thinking process. Learning the transformation of division into multiplication of fractions should precede that of fraction as a quotient of a division.

• 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 Elementary Mathematics Education in Korea
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• v.19 no.1
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• pp.17-37
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• 2015

In this paper, we compared and analyzed the Korean National Mathematics textbooks of the 2007 amendment curriculum and the Harcourt Math in America focused on fractions and decimals. To summarize the results of the analysis are as follows. First, both textbooks introduce fractions to the meaning of parts-whole concept, but the Harcourt Math is stronger than that of Korean Mathematics textbooks in the concept of unit fractions as a generator of fractions. Second, the fractions can be considered trivial materials - a fraction representing 1 whole, a fraction with it's denominator is 1 - were more clearly represented in our US textbooks than those of our Korean textbooks. Third, in the introduction of the term relating to the fractions, Korea is a strong point of view of the classification of fractions than the point of view of representation in comparison with the case of the United States. Fourth, the equivalent fraction and equivalent decimal concepts were described more detail in the United States of textbooks than those of the case of Korean textbooks. Finally, the approaches of fraction and decimal concepts were introduced more mathematically in the case of the United States than those of the case of Korean textbooks.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.151-170
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• 2009

The purpose of the study is to analyze the sixth graders' understanding of concepts and operation about fraction. The test was administered and analyzed to 707 sixth graders' performance on fractions after the fraction instructions in elementary schools in Seoul, Korea. The participants are asked to answer two sets of questions for 40 minutes. First, they are asked to answer to 16 problems about the concepts of fraction with respect to part-whole, ratio, operator, measure, quotient, equivalent, and operations. Second, specially, to investigate sixth graders' ability of drawing and describing the situation of division including fraction, the descriptive problem asked students (1) to describe $3\;{\div}\;\frac{1}{2}$ into pictorial representation and (2) to write the solving process. The participants of this study didn't show deep understandings about the concepts and operation of fraction. The degree of understanding of subconstructs of fraction shows that their knowledge of ratio concept with respect to fraction was highest while their understanding of measure with respect to fraction was lowest. Considering their wrong answers, about 59% of participants showed misconception to the question of naming one fraction that appears between $\frac{1}{5}$ and $\frac{1}{6}$. Further, they didn't explain their understanding with drawing about the division of fraction ($3\;{\div}\;\frac{1}{2}$).

• Education of Primary School Mathematics
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• v.25 no.3
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• pp.213-232
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• 2022

With the importance of number line in learning fractions, this study investigated how 4th grade students understand fractions and its operations in number line. The questionnaire consisted 22 items which were related to representing fractions, comparing the size of fractions, and operating addition and subtraction of fractions. Both structured number line and sub-structured number line were presented in the items. As results of the study, the overall success rates were not high and even some items showed higher incorrect answer rates than the success rates. Also, the students showed a difficulty in solving non-structured number line tasks. It was also noticeable that students showed several types of incorrect answers, which means that students had incomplete understanding of both fractions and number line. This paper is expected to shed light on elementary students' understanding of fractions and number line and to provide implications of how to deal with number line in teaching and learning fractions in the elementary school.

• Korean Journal of Optics and Photonics
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• v.8 no.2
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• pp.154-160
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• 1997

On the base of the fractional Fourier transform(FRT) which is known as a generalized form of the conventional Fourier transform, the fractional correlation has been implemented. Shift-variance property of the fraction correlation has been evaluated and compared with the shift-invariance of the conventional correlation. The fractional correlation operation has been implemented by using a planar optics configuration which integrates all of the optical components on a single glass substrate. A good agreement between the experimental and calculated results has been obtained.

• School Mathematics
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• v.17 no.4
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• pp.571-591
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• 2015

Even though fractions make up one of the most important concepts in the domain of numbers in elementary math, it is difficult to teach or learn them due to their different quantity concepts and notation methods from natural numbers and their various concepts. The didactic transposition of fractions is thus important, and there is a need to examine the didactic concepts of fractions used in the South Korean textbooks for its research. This study compared elementary math textbooks among South Korea, Taiwan, and China and investigated differences in the instructional time and order of fraction concepts in the textbooks according to their didactic concepts and also differences in the instructional methods according to quantitative concepts.

• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.49-55
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• 2009

A cooperative game often arises from domination problem on graphs and the core in a cooperative game could be the optimal solution of a linear programming of a given game. In this paper, we define a {k}-fractional domination game which is a specific type of fractional domination games and find the core of a {k}-fractional domination game. Moreover, we may investigate the balancedness of a {k}-fractional domination game using a concept of a linear programming and duality. We also conjecture the concavity for {k}-fractional dominations game which is important problem to find the elements of the core.

• School Mathematics
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• v.14 no.1
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• pp.135-150
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• 2012

This paper analyzes the activities for (fraction) ${\times}$(fraction) in Korean elementary textbooks focusing on the connection between visual models and the algorithm. New Korean textbook attempts a new approach to use length model (as well as rectangular area model) for developing the standard algorithm for the multiplication of fractions, $\frac{a}{b}{\times}\frac{d}{c}=\frac{a{\times}d}{b{\times}c}$. However, activities with visual models in the textbook are not well connected to the algorithm. To bridge the gap between activities with models and the algorithm, distributive strategy should be emphasized. A wealth of experience of solving problems of fraction multiplication using the distributive strategy with visual models can serve as a strong basis for developing the algorithm for the multiplication of fractions.

• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.147-162
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• 2007

This paper reports an analysis of 19 Chinese and Korean middles school mathematics teachers' understanding of division by fractions. The study analyzes the teachers' responses to the teaching task of generating a real-world situation representing the meaning of division by fractions. The findings of this study suggests that the teachers' conceptual models of division are dominated by the partitive model of division with whole numbers as equal sharing. The dominance of partitive model of division constraints the teachers' ability to generate real-world representations of the meaning of division by fractions, such that they are able to teach only the rule-based algorithm (invert-and-multiply) for handling division by fractions.