• Journal for History of Mathematics
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• v.15 no.2
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• pp.101-112
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• 2002

Gu-Jang-San-Sul is a book of Chinese ancient mathematics and has had an impact on Korean mathematics. The book is organized into nine chapters and each chapter is composed of problems, answers, and their computation algorithms. The contents reflect the practicality of Chinese mathematics. Especially the first chapter covers the computation of fractions for land surveying. This paper suggests how the computation methodology is used in teaching fractions for primary school students. Five strategies for fractions related to the reduction, addition, subtraction, multiplication, and division are followed by: 1) developing the ability to apply rules to problems by practicing the computation process according to the given algorithm; 2) developing the communication skill by comparing the differences of various computation algorithms; 3) setting computation problems; 4) understanding the characteristics of terminology in mathematics; and 5) being exposed to new ideas in mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.23-47
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• 2017

The purpose of this study is to analyze the types of errors that may occur in the four arithmetic operations of the fractions after classified according to the level of academic achievement for sixth-grade elementary school student who Learning of the four arithmetic operations of the fountain has been completed. The study was proceed to get the information how change teaching content and method in accordance with the level of academic achievement by looking at the types of errors that can occur in the four arithmetic operations of the fractions. The test paper for checking the type of errors caused by calculation of fractional was developed and gave it to students to test. And we saw the result by error rate and correct rate of fraction that is displayed in accordance with the level of academic achievement. We investigated the characteristics of the type of error in the calculation of the arithmetic operations of fractional that is displayed in accordance with the level of academic achievement. First, in the addition of the fractions, all levels of students showing the highest error rate in the calculation error. Specially, error rate in the calculation of different denominator was higher than the error rate in the calculation of same denominator Second, in the subtraction of the fractions, the high level of students have the highest rate in the calculation error and middle and low level of students have the highest rate in the conceptual error. Third, in the multiplication of the fractions, the high and middle level of students have the highest rate in the calculation error and low level of students have the highest rate in the a reciprocal error. Fourth, in the division of the fractions, all levels of students have the highest r rate in the calculation error.

• Communications of Mathematical Education
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• v.31 no.2
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• pp.153-166
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• 2017

164 preservice elementary teachers' decision and enactment of their knowledge of fraction multiplication were examined in a context where they were asked to write a story problem for a multiplication problem with two proper fractions. Participants were selected from an entry level course and an exit level course of their teacher preparation program to reveal any differences between the groups as well as any recognizable patterns within each group and overall. Patterns and tendencies in writing story problems were identified and analyzed. Implications of the findings for teaching and teacher education are discussed.

• School Mathematics
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• v.9 no.1
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• pp.13-28
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• 2007

Division of fractions can be categorized as measurement division, partitive or sharing division, the inverse of multiplication, and the inverse of Cartesian product. Division algorithm for fractions has been interpreted with manipulative aids or models mainly in the contexts of measurement division and partitive division. On the contrary, there are few interpretations for the context of the inverse of a Cartesian product. In this paper the significance and the limits of existing interpretations of division of fractions in the context of the inverse of a Cartesian product were discussed. And some new easier interpretations of division algorithm in the context of a Cartesian product are developed. The problem to determine the length of a rectangle where the area and the width of it are known can be solved by various approaches: making the width of a rectangle be equal to one, making the width of a rectangle be equal to some natural number, making the area of a rectangle be equal to 1. These approaches may help students to understand the meaning of division of fractions and the meaning of the inverse of the divisor. These approaches make the inverse of a Cartesian product have many merits as an introductory context of division algorithm for fractions.

• Education of Primary School Mathematics
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• v.22 no.2
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• pp.129-147
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• 2019

Because of the various concepts and meanings of fractions and the difficulty of learning, studies to improve the teaching methods of fraction have been carried out. Particularly, because there are various methods of teaching depending on the type of fractions or the models or methods used for problem solving in fraction operations, many researches have been implemented. In this study, I analyzed the fractional operations of CCSSM-CA and its U.S. textbooks. It was CCSSM-CA revised and presented in California and the textbooks of Houghton Mifflin Harcourt Publishing Co., which reflect the content and direction of CCSSM-CA. As a result of the analysis, although the grades presented in CCSSM-CA and Korean textbooks were consistent in the addition and subtraction of fractions, there are the features of expressing fractions by the sum of fractions with the same denominator or unit fraction and the evaluation of the appropriateness of the answer. In the multiplication and division of fractions, there is a difference in the presentation according to the grades. There are the features of the comparison the results of products based on the number of factor, presenting the division including the unit fractions at first, and suggesting the solving of division problems using various ways.

• 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 Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.105-122
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• 2014

In this paper, fraction division algorithms in Korean elementary mathematics textbooks are analyzed as a part of the groundwork to improve teaching methods for fraction division algorithms. There are seemingly six fraction division algorithms in ${\ll}Math\;5-2{\gg}$, ${\ll}Math\;6-1{\gg}$ textbooks according to the 2006 curriculum. Four of them are standard algorithms which show the multiplication by the reciprocal of the divisors modally. Two non-standard algorithms are independent algorithms, and they have weakness in that the integration to the algorithms 8 is not easy. There is a need to reconsider the introduction of the algorithm 4 in that it is difficult to think algorithm 4 is more efficient than algorithm 3. Because (natural number)${\div}$(natural number)=(natural number)${\times}$(the reciprocal of a natural number) is dealt with in algorithm 2, it can be considered to change algorithm 7 to algorithm 2 alike. In textbooks, by converting fraction division expressions into fraction multiplication expressions through indirect methods, the principles of calculation which guarantee the algorithms are explained. Method of using the transitivity, method of using the models such as number bars or rectangles, method of using the equivalence are those. Direct conversion from fraction division expression to fraction multiplication expression by handling the expression is possible, too, but this is beyond the scope of the curriculum. In textbook, when dealing with (natural number)${\div}$(proper fraction) and converting natural numbers to improper fractions, converting natural numbers to proper fractions is used, but it has been never treated officially.

• 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.

• Proceedings of the Korean Vacuum Society Conference
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• 2012.08a
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• pp.431-431
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• 2012

A compact tokamak reactor concept as a 14 MeV neutron source is desirable from an economic viewpoint for a fusion-driven transmutation reactor. LAR (Low Aspect Ratio) tokamak allows a potential of high "see full txt" operation with high bootstrap current fractions and can be used for a compact fusion neutron source. For the optimal design of a reactor, a radial build of reactor components has to be determined by considering the plasma physics and engineering constraints which inter-relate various reactor components and are constrained to use ITER physics and technology. In a transmutation reactor, the blanket should produce enough tritium for tritium self-sufficiency and the neutron multiplication factor, keff should be less than 0.95 to maintain sub-criticality. The shield should provide sufficient protection for the superconducting toroidal field (TF) coil against radiation damage and heating effects of the fusion neutrons, fission neutrons, and secondary gammas. In this work, characteristics of transmutation reactor based on LAR tokamak is investigated by using the coupled system analysis.

• Research in Mathematical Education
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• v.19 no.2
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• pp.89-100
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• 2015

The study investigated pre-service teachers' knowledge and computational skills by using Triangular Arithmagon. Participants included 90 pre-service teachers from two schools in the United States and Taiwan. The Triangular Arithmagons Test (TAT) was used to measure pre-service teachers' performance in whole number, fractions, and decimals operations (i.e., addition, subtraction, multiplication, and division), each of which included level-1 (basic) and level-2 (advanced) tests. MANOVA analysis was performed to compare the performance between teachers from the United States and Taiwan. Results indicated that overall, pre-service teachers in Taiwan outperformed those in the United States, especially on the advanced-level tests. Pre-service teachers in the United States were found to have poor ability of solving complex operation problems. Different curriculum plans and teaching methods may lead to the performance gap between the two countries.