• The Mathematical Education
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• v.49 no.4
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• pp.437-462
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• 2010

The purpose of this research is to analyze the textbook contents about the natural number concepts in the Korean National Elementary Mathematics Curriculum. Understanding a concept of natural number is crucial in school mathematics curriculum planning, since elementary students start their basic learning with natural number system. The concepts of natural number have various meaning from the perspectives of pedagogical research, and the philosophy of mathematics. The natural number concepts in the elementary math curriculum consist of four aspects; counting numbers, cardinal numbers, ordinal numbers, and measuring numbers. Two research questions are addressed; (1) How are the natural number concepts focusing on counting, cardinal, ordinal, measuring numbers are covered in the national math curriculum? ; (2) What suggestions can be made to enhance the teaching and learning about the natural number concepts? Findings reveal that (1) the national mathematics curriculum properly reflects four aspects of natural number concepts, as the curriculum covers 50% of the cardinal number system; (2) In the aspect of the counting number, we hope to add the meaning about 'one, two, three, ......, and so on' in the Korean Mathematics curriculum. In the ordinal number, we want to be rich the related meaning in a set. Further suggestions are made for future research to include them ensuing number in the curriculum.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.137-143
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• 2010

Category Fuz of fuzzy sets has a similar function to the Category Set. But it forms a weak topos. We study a natural number object and a weak natural number object in the weak topos Fuz. Also we study the weak natural number object in $Fuz^C$.

• School Mathematics
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• v.5 no.3
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• pp.385-399
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• 2003

In our present elementary mathematics curriculum, natural numbers are taught by using the a method of one-to-one correspondence or counting operation which are not related to measurement, and fractional numbers are taught by using a method which is partially related to measurement. The most serious limitation of these teaching methods is that natural numbers and fractional numbers are separated. To overcome this limitation, Dewey and Davydov insisted that the natural number and the fractional number should be taught by measurement of quantity. In this article, we suggested a method of teaching the natural number and the fractional number by measurement of quantity based on the claims of Dewey and Davydov, and compare it with our current method. In conclusion, we drew some educational implications of teaching the natural number and the fractional number by measurement of quantity as follows. First, the concepts of the natural number and the fractional number evolve from measurement of quantity. Second, the process of transition from the natural number to the fractional number became to continuous. Third, the natural number, the fractional number, and their lower categories are closely related.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.309-331
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• 2007

Mathematics education starts from learning the concept of number. How the children at the beginning of school age learn the concept of natural number is therefore important for their future mathematics education. Since ancient Greek period, the concept of natural number has reflected various mathematical-philosophical points of view at each period and has been discussed ceaselessly. The concept of natural number is hard to define. Since 19th century, it has also been widely discussed in psychology and education on how to teach the concept of natural number to the children at the beginning of school age. Most of the works, however, were focused on limited aspects of natural number concept. This study aims to show the best way to teach the children at the beginning of school age the various aspects of natural number concept based on activistic perspective, which played a crucial role in modern mathematics education. With this purpose, I investigated the theory of the activistic construction of knowledge and the construction of natural number concept through activity, and activistic approaches about instruction in natural number concept made by Kant, Dewey, Piaget, Davydov and Freudenthal. In addition, I also discussed various aspects of natural number concept in historical and mathematical-philosophical points of view. Based on this investigation, I tried to find out existing problems in instructing natural number to primary school children in the 7th National Curriculum and aimed to provide a new solution to improve present problems based on activistic approaches. And based on activistic perspective, I conducted an experiment using Cuisenaire colour rods and showed that even the children at the beginning of school age can acquire the various aspects of natural number concept efficiently. To sum up, in this thesis, I analyzed epistemological background on activistic construction of natural number concept and presented activistic approach method to teach various aspects of natural number concept to the children at the beginning of school age based on activism.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.9-22
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• 2005

Natural numbers have not yet been studied adequately on the aspect of its historical development in spite of its mathematical and educational importance. This article studied the historical development of natural number concept, that is, its historical meaning in the mathematical development process and influence of cultural and social element in relation with way of understanding number. From these examinations, we identified some characteristics in the history of natural number concept.

• East Asian mathematical journal
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• v.38 no.4
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• pp.379-396
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• 2022

In this paper, we investigate distribution strategies in the Egyptian fraction, and through this, we examine the distribution strategies of (fraction)÷(fraction) and then provide some educational implications. The (natural number)÷(natural number) of the sharing situation has the meaning of 'share' per unit, which can be seen as a situation where the unit ratio is determined. These concepts can also naturally be extended to the case of (fraction)÷(fraction) by some problem posing situations. That is to say, the case of (fraction)÷(fraction) can be deduced the case (natural number)÷(natural number) by the re-statement of the problem.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.58-64
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• 2011

The objective of this paper is to investigate the gravity effect on the shape characters of natural supercavity. A finite difference solver along with an implicit, dual time, preconditioned, three-dimensional algorithm has been used to solve the two-phase Navier Stokes equations. Numerical solutions were performed for natural supercavitating flow past a disk for different cavitation and Froud numbers. The numerical results were compared with corresponding analytical results in quantitative manner and it was found that the shape of supercavity was reasonably predicted Numerical results indicated that the gravity effect can induce the asymmetry of supercavity. The asymmetry was apparent when the froud number was smaller so that for constant cavitation number when we reduced the froud number the opt of the axis of supercavity increased. Moreover, for specific froud number a decrease in cavitation number resulted in an increase in the offset of the supercavity Numerical results revealed that for froud number greater than 25 the gravity effect is negligible.

• International Journal of Computer Science & Network Security
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• v.21 no.9
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• pp.79-85
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• 2021

The locating-chromatic number denote by 𝛘_𝐿(G), is the smallest t such that G has a locating t-coloring. In this research, we determined locating-chromatic number for subdivision of certain barbell operation of origami graphs.

• Journal for History of Mathematics
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• v.32 no.3
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• pp.109-134
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• 2019

In order to improve the educational situation in which the natural number e and the natural logarithm are dealt with somewhat perfunctorily, this study explores the genetic process in which the natural logarithm and its base e occurred, and has an educational discussion based on that analysed process. Specifically, the study inquires into how the natural logarithm happened in relation to the quadrature of the hyperbolic curves through analysis and thought experimentation in mathematics history. Particularly, it sheds light on the role of e and the naturalness of the natural logarithm in terms of the introduction of the real number exponent. Also, this study discusses what the findings suggest educationally.

• Fashion & Textile Research Journal
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• v.11 no.6
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• pp.942-946
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• 2009

The trends of patents related to natural dyeing were examined in order to guide the development of natural dyeing into a high value-added technology. Total 181 patents data provided from KISTI were analyzed and following results were drawn. Korea had the overwhelming number of patents related to natural dyeing over Japan or United States of America from 1970 to 2007. In case of domestic, the number of patent applications were heavily focused on the metropolitan area in 1990's, but started to increase in the Honam region and Youngnam region in the first half of the year 2000 which indicated that the researches and the developments of natural dyeing were very active. In the case of foreign countries, most of their patent applications comes from the corporation such as a company while the number of patents applications from individuals overwhelms that of corporation in South Korea. Also, more of individuals' patent applications were denied than corporations' patents applications. The vegetable dye, a type of dyestuff which is a research subject for patent application, had the most research done above all other dyestuff.