• East Asian mathematical journal
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• v.33 no.2
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• pp.199-216
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• 2017

A rational number as operator is eventually that it is considered a mapping. Depending on how selecting domain (the target of operation by rational number) and codomain (including the results of operations by rational number), it is possible to see the rational in two aspects. First, rational numbers can be deal with functions if we choose the target of operation by rational number as a number field containing rationals. On the other hand, if we choose the target of operation by rational number as integral domain $\mathbb{Z}$, then rational numbers can be regarded as partial functions on $\mathbb{Z}$. In this paper, we regard the rational numbers with a view of partial functions, we investigate the theoretical background of the relationship between the multiplication of rational numbers and the composition of rational numbers as operators.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.353-372
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• 2015

This study investigated how to utilize number line related number concept learning and analyzed problems related utilization of number line focused on natural number and rational number(fraction, decimal), in elementary school mathematics textbook. The purpose of this study is to identify desirable direction about the utilization of number line, based on analysis of the introduction of time, introduction contents and utilization method in elementary school mathematics textbook.

• The Mathematical Education
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• v.50 no.1
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• pp.61-67
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• 2011

There may be two methods defining the rational exponent $a^{\frac{m}{n}}$ for any positive real number a. The one which is used in all korean highschool mathematics textbooks is to define it as $\sqrt[n]{a^m}$, that is $(a^m)^{\frac{1}{n}}$. The other is to define it as $(\sqrt[n]a)^m}$, that is $(a^{\frac{1}{n}})^m$. In this paper, we insist that the latter is more appropriate and universal, and that the contents of current textbooks on the definition of the rational exponent should be corrected.

• Proceedings of the KAIS Fall Conference
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• 2009.05a
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• pp.307-310
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• 2009

임의의 입력 해상도와 출력 해상도의 비율로 주어지는 영상 축소 스케일러를 구현하려면 축소된 영상에 대한 화소의 좌표를 계산하기 위해서 범용 제산기의 사용이 요구된다. 이 범용 제산기는 매 화소마다 동작해야하기 때문에 처리속도를 높이기 위하여 LUT로 구현되나, LUT의 정밀도에 따라서 하드웨어의 규모가 비대해지는 문제가 야기된다. 본 논문에서는 제산기나 LUT 기반의 제산 연산을 수반하지 않는 영상 축소 알고리즘을 제안한다. 제안한 알고리즘은 비교기와 가산기 만으로 구성되어 있으며, 임의의 유리수로 표현되는 축소 비율을 허용함에도 불구하고, 기존 방식에 비해서 1/10 이하로 하드웨어 규모를 줄이는 것이 가능하다.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.517-534
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• 2012

As observing the learning of middle school mathematics students for three years, I examined the relationship between students' procedural knowledge and their conceptual knowledge as they develop those knowledges in the rational number domain. In particular, I explored the implications of an unbalanced development in a student's conceptual knowledge and procedural knowledge by considering two conditions: (a) the case of a student who has relatively strong conceptual knowledge and weak procedural knowledge, and (b) the case of a student who has relatively weak conceptual knowledge and strong procedural knowledge. Results suggest that conceptual knowledge and procedural knowledge are most productive when they develop in a balanced fashion (i.e., closely iterative or simultaneously), which calls into question the assumption that one has primacy over the other.

• Journal of Educational Research in Mathematics
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• v.23 no.1
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• pp.17-35
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• 2013

The purpose of this study was to analyze the extendibility of division algorithm and Euclid algorithm for integers to algorithms for rational numbers based on word problems of fraction division. This study serviced to upgrade professional development of elementary and secondary mathematics teachers. In this paper, fractions were used as expressions of rational numbers, and they also represent rational numbers. According to discrete context and continuous context, and measurement division and partition division etc, divisibility was classified into two types; one is an abstract algebraic point of view and the other is a generalizing view which preserves division algorithms for integers. In the second view, we raised some contextual problems that can be used in school mathematics and then we discussed division algorithm, the greatest common divisor and the least common multiple, and Euclid algorithm for fractions.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.6 no.3_4
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• pp.101-111
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• 1973

To study the effect of freezing rate on the duality of frozen abalone(Haliotis gigantea, GMELIN) liquid nitrogen spray freezing, air blast freezing, semi-air blast freezing, and still air freezing were carried out. The rheological change, protein denaturation, and free water content of frozen and thawed abalone were examined at the period of 0, 1, 2, and 3 month during cold Storage at $-20^{\circ}C$. The results are summarized as follows : 1. The onset and duration of rigor mortis of fresh abalone was faster and shorter as compared to that of fishes. 2. There was no difference in compression value and shear value between freezing methods but they varied with a slight decrease in storage period. 3. Gradual decrease in extractibility of salt soluble protein was observed in all samples except those frozen with liquid nitrogen. 4. The free water of the foot muscle remained constant during the storage while that of the adductor muscle tended to increase. 5. A significant correlation was observed among the changes of panel texture and free water (P< 0.01), protein denaturation (P<0.05), and compression value (P<0.01).

• Education of Primary School Mathematics
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• v.21 no.4
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• pp.375-395
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• 2018

This study examines the influence of the bodily interaction with digital technology on meaning-making process in a mathematical activity. Increasing interest in the use of multi-touch dynamic digital technology has brought the movement of the body to the center of research focus in recent mathematics education literature. Thereby, we investigate the process in which the meaning of the density of rational numbers emerges around the bodily interaction on the multi-touch dynamic digital technology. We analyze a case of a small group of primary school students with microethnography. In the result, the students formed the higher level of meaning of the density, where the finger movement of zooming in-and-out played a crucial role throughout the meaning-maknig process.

• Communications of Mathematical Education
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• v.25 no.2
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• pp.323-339
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• 2011

The expansion of exponential law as the law of calculation of integer numbers can be a good material for the students to experience an extended configuration which is based on an algebraic principle of the performance of equivalent forms. While current textbooks described that exponential law can be expanded from natural number to integer, rational number and real number, most teachers force students to accept intuitively that the exponential law is valid although exponent is expanded into real number. However most teachers overlook explaining the value of exponent of rational number or exponent of irrational number so most students have a lot of questions whether this value is a rational number or a irrational number. Related to students' questions, most teacher said that it is out of the current curriculum and students will learn it after going to college instead of detailed answers. In this paper, we will present several examples and the values about irrational exponents of a positive rational and irrational exponents of a positive irrational number, and study the recognition and fallacy of would-be teachers about the cases of irrational exponents of a positive rational and irrational exponents of a positive irrational number at the expansion of exponential law.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.1-17
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• 2004

According to the 7-th curriculum, irrational number should be introduced using repeating decimals in 8-th grade mathematics. To do so, the relation between rational numbers and repeating decimals such that a number is rational number if and only if it can be represented by a repeating decimal, should be examined closely Since this relation lacks clarity in some text books, irrational numbers have only slight relation with repeating decimals in those books. Furthermore, some text books introduce irrational numbers showing that $\sqrt{2}$ is not rational number, which is out of 7-th curriculum. On the other hand, if we use numeral 0 as a repetend, many results related to repeating decimals can be represented concisely. In particular, the treatments of order relation with repeating decimals in 8-th grade text books must be reconsidered.