• 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.

• International Journal of Computer Science & Network Security
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• v.22 no.9
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• pp.31-34
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• 2022

The concept of locating chromatic number of graph is a development of the concept of vertex coloring and partition dimension of graph. The locating-chromatic number of G, denoted by χ_L(G) is the smallest number such that G has a locating k-coloring. In this paper we will discussed about the procedure for determine the locating chromatic number of Origami graph using Python Programming.

• 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.

• 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.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.

• 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.

• International Journal of Contents
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• v.2 no.1
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• pp.17-21
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• 2006

In this paper, we describe a concept-based question-answering system in which concept rather than keyword itself makes an important role on both question analysis and answer extraction. Our idea is that concepts occurred in same type of questions are similar, and if a question is analyzed according to those concepts then we can extract more accurate answer because we know the semantic role of each word or phrase in question. Concept frame is defined for each type of question, and it is composed of important concepts in that question type. Currently the number of question type is 79 including 34 types for person, 14 types for location, and so on. We experiment this concept-based approach about questions which require person s name as their answer. Experimental results show that our system has high accuracy in answer extraction. Also, this concept-based approach can be used in combination with conventional approaches.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.165.2-165
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• 2001

A number of previous researches in evolutionary algorithm are based on the study of facets we observe in natural evolution. The individuals of species in natural evolution occupy their own niche that is a subdivision of the habitat. This means that two species with the similar requirements cannot live together in the same niche. This is known as the competitive exclusion principle, i.e., complete competitors cannot coexist. In this paper, a new evolutionary programming algorithm adopting this concept is presented. Similarly in the case of natural evolution , the algorithm Includes the concept of niche obtained by partitioning a search space and the competitive exclusion principle performed by migrating individuals. Cell partition and individual migration strategies are used to preserve search diversity as well as to speed up convergence of an ...

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.3
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• pp.425-439
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• 2014

The concept of a fraction as division is a core idea which serves as a axiom in the process of a extension of the natural number system to rational number system. Also, it has necessary position in elementary mathematics. Nevertheless, the timing and method of the introduction of this concept in Korean elementary math textbooks is not well established. In this thesis, I suggested a solution of a various topics which is related to this problem, that is, transforming improper fraction to mixed number, the usage of quotient as a term, explaining the algorithm of division of fraction, transforming fraction to decimal.