• Education of Primary School Mathematics
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• v.11 no.2
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• pp.141-159
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• 2008

The purpose of this study id to delve into how elementary mathematics textbook deal with the quadrilaterals from a view of Didactic Transposition Theory. Concerning the instruction period and order, we have concluded the following: First, the instruction period and order of quadrilaterals were systemized when the system of Euclidian geometry was introduced, and have been modified a little bit since then, considering the psychological condition of students. Concerning the definition and presentation methods of quadrangles, we have concluded the following: First, starting from a mere introduction of shape, the definition have gradually formed academic system, as the requirements and systemicity were taken into consideration. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Concerning the contents and methods of instruction, we have concluded the following: First, the subject of learning has changed from textbook and teachers to students. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Third, when instructing the characteristics and inclusive relation, students could build up their knowledge by themselves, by questions and concrete operational activities. Fourth, constructions were aimed at understanding of the definition and characteristics of the figures, rather than at itself.

• Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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• 2009.05a
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• pp.408-411
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• 2009

In this paper, conventional PI, fuzzy neural network(FNN) and adaptive teaming mechanism(ALM)-FNN for rotor field oriented controlled(RFOC) induction motor are studied comparatively. The widely used control theory based design of PI family controllers fails to perform satisfactorily under parameter variation nonlinear or load disturbance. In high performance applications, it is useful to automatically extract the complex relation that represent the drive behaviour. The use of learning through example algorithms can be a powerful tool for automatic modelling variable speed drives. They can automatically extract a functional relationship representative of the drive behavior. These methods present some advantages over the classical ones since they do not rely on the precise knowledge of mathematical models and parameters. Comparative study of PI, FNN and ALM-FNN are carried out from various aspects which is dynamic performance, steady-state accuracy, parameter robustness and complementation etc. To have a clear view of the three techniques, a RFOC system based on a three level neutral point clamped inverter-fed induction motor drive is established in this paper. Each of the three control technique: PI, FNN and ALM-FNN, are used in the outer loops for rotor speed. The merit and drawbacks of each method are summarized in the conclusion part, which may a guideline for industry application.

• Education of Primary School Mathematics
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• v.21 no.3
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• pp.261-272
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• 2018

In the current era of mathematics education, constructivism is a core theory of learning. For teachers, understanding and applying constructivism to their teaching practices are crucial for student centered teaching. However, some mathematics educators understand Constructivism in a different way. For example, some future teachers view Constructivism as making mathematics 'fun' by creating game without considering conceptual understanding. In this paper, the original articles of Constructivism were revisited and investigated to understand and to search for their meanings. Also several types and sources of Constructivism were identified; Radical Constructivism, Vygotsky's social-cultural theory of development, Social Constructionism, and Social Constructivism. This paper investigated arguments of the several types of Constructivism and discussed their implications for mathematics teaching.

• Journal for History of Mathematics
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• v.21 no.1
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• pp.109-120
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• 2008

Today linear algebra is one of compulsory courses for university mathematics by virtue of its theoretical fundamentals and fruitful applications. However, a mechanical computation-oriented instruction or a formal concept-oriented instruction is difficult and dull for most students. In this context, how to teach mathematical concepts successfully is a very serious problem. As a solution for this problem, we suggest establishing original concepts in linear algebra from the students' point of view. Any original concept means not only a practical beginning for the historical order and theoretical system but also plays a role of seed which can build most of all the important concepts. Indeed, linear algebra has exactly two original concepts : geometry of planes, spaces and linear equations. The former was investigated in [2], the latter in the present paper.

• Journal of Gifted/Talented Education
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• v.15 no.2
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• pp.35-57
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• 2005

As the results of studies based on the Russian Activities-Oriented Theory, the gifted students in many fields have common insights for the true nature of the problem, or the actual state. From Russian Activities-Oriented Theory of view, gifted students have the ability to discern the essential elements involved in each actual state and change of state of things, and to solve the problem, based on these elements. Enhancing these abilities of the students, the educator can develop the average student into a gifted one. This study result of the Russian specialist suggests the possibility of a stream of education that can develop gifted students. Hence, this paper discussed the points and processes of formation of the Russian Activities-Oriented Theory, and inquired on what is the true nature of the problem or the meaning of actual state and how it affects the studies of the student. The paper also investigated the actual conditions of wrong learning about some mathematical concepts and discussed the role of insights to the true nature of the problem in the learning process of the student.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.1
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• pp.115-140
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• 2009

Freudenthal has advocated the mathematisation theory. Mathematisation is an activity which endow the reality with order, through organizing phenomena. According to mathematisation theory, the departure of children's learning of mathematics is not ready-made formal mathematics, but reality which contains mathematical germination. In the first place, children mathematise reality through informal method, secondly this resulting reality is mathematised by new tool. Through survey, it turns out that area unit of Korea's seventh elementary mathematics textbook is not correspond to mathematisation theory. In that textbook, the area formular is hastily presented without sufficient real context, and the relational understanding of area concept is overwhelmed by the practice of the area formular. In this thesis, first of all, I will reconstruct area unit of seventh elementary textbook according to Freudenthal's mathematisation theory. Next, I will perform teaching experiment which is ruled by new lesson design. Lastly, I analysed the effects of teaching experiment. Through this study, I obtained the following results and suggestions. First, the mathematisation was effective on the understanding of area concept. Secondly, in both experimental and comparative class, rich-insight children more successfully achieved than poor-insight ones in the task which asked testee comparison of area from a view of number of unit square. This result show the importance of insight in mathematics education. Thirdly, in the task which asked testee computing area of figures given on lattice, experimental class handled more diverse informal strategy than comparative class. Fourthly, both experimental and comparative class showed low achievement in the task which asked testee computing area of figures by the use of Cavalieri's principle. Fifthly, Experiment class successfully achieved in the area computing task which resulting value was fraction or decimal fraction. Presently, Korea's seventh elementary mathematics textbook is excluding the area computing task which resulting value is fraction or decimal fraction. By the aid of this research, I suggest that we might progressively consider the introduction that case. Sixthly, both experimental and comparative class easily understood the relation between area and perimeter of plane figures. This result show that area and perimeter concept are integratively lessoned.

• Journal of Elementary Mathematics Education in Korea
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• v.7 no.1
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• pp.45-64
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• 2003

This study analyzes divisor and multiple in elementary school mathematics textbooks published according to the first to the 7th curriculum, in a view point of the didactic transposition theory. In the first and second textbooks, the divisor and the multiple are taught in the chapter whose subject is on the calculations of the fractions. In the third and fourth textbooks, divisor and multiple became an independent chapter but instructed with the concept of set theory. In the fifth, the sixth, and the seventh textbooks, not only divisor multiple was educated as an independent chapter but also began to be instructed without any conjunction with set theory or a fractions. Especially, in the seventh textbook, the understanding through activities of students itself are strongly emphasized. The analysis on the each curriculum periods shows that the divisor and the multiple and the reduction of a fractions to the lowest terms and to a common denominator are treated at the same period. Learning activity elements are increase steadily as the textbooks and the mathematical systems are revised. The following conclusion can be deduced based on the textbook analysis and discussion for each curriculum periods. First, loaming instruction method also developed systematically with time. Second, teaching method of the divisor and multiple has been sophisticated during the 1st to 7th curriculum textbooks. And the variation of the teaching sequences of the divisor and multiple is identified. Third, we must present concrete models in real life and construct textbooks for students to abstract the concepts by themselves. Fourth, it is necessary to develop some didactics for students' contextualization and personalization of the greatest common divisor and least common multiple. Fifth, the 7th curriculum textbooks emphasize inquiries in real life which teaming activities by the student himself or herself.

• The Mathematical Education
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• v.24 no.2
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• pp.48-73
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• 1986

Though the tradition of Korean mathematics since the ancient time up to the 'Enlightenment Period' in the late 19th century had been under the influence of the Chinese mathematics, it strove to develop its own independent of Chinese. However, the fact that it couldn't succeed to form the independent Korean mathematics in spite of many chances under the reign of Kings Sejong, Youngjo, and Joungjo was mainly due to the use of Chinese characters by Koreans. Han-gul (Korean characters) invented by King Sejong had not been used widely as it was called and despised Un-mun and Koreans still used Chinese characters as the only 'true letters' (Jin-suh). The correlation between characters and culture was such that, if Koreans used Han-gul as their official letters, we may have different picture of Korean mathematics. It is quite interesting to note that the mathematics in the 'Enlightenment Period' changed rather smoothly into the Western mathematics at the time when Han-gul was used officially with Chinese characters. In Koryo, the mathematics existed only as a part of the Confucian refinement, not as the object of sincere study. The mathematics in Koryo inherited that of the Unified Shilla without any remarkable development of its own, and the mathematicians were the Inner Officials isolated from the outside world who maintained their positions as specialists amid the turbulence of political changes. They formed a kind of Guild, their posts becoming patrimony. The mathematics in Koryo significant in that they paved the way for that of Chosun through a few books of mathematics such as 'Sanhak-Kyemong', 'Yanghwi-Sanpup' and 'Sangmyung-Sanpup'. King Sejong was quite phenomenal in his policy of promotion of mathematics. King himself was deeply interested in the study, createing an atmosphere in which all the high ranking officials and scholars highly valued mathematics. The sudden development of mathematic culture was mainly due to the personality and capacity of king who took anyone with the mathematic talent into government service regardless of his birth and against the strong opposition of the conservative officials. However, King's view of mathematics never resulted in the true development of mathematics perse and he used it only as an official technique in the tradition way. Korean mathematics in King Sejong's reign was based upon both the natural philosophy in China and the unique geo-political reality of Korean peninsula. The reason why the mathematic culture failed to develop continually against those social background was that the mathematicians were not allowed to play the vital role in that culture, they being only the instrument for the personality or politics of the king. While the learned scholar class sometimes played the important role for the development of the mathematic culture, they often as not became an adamant barrier to it. As the society in Chosun needed the function of mathematics acutely, the mathematicians formed the settled class called Jung-in (Middle-Man). Jung-in was a unique class in Chosun and we can't find its equivalent in China or Japan. These Jung-in mathematician officials lacked tendency to publish their study, since their society was strictly exclusive and their knowledge was very limited. Though they were relatively low class, these mathematicians played very important role in Chosun society. In 'Sil-Hak (the Practical Learning) period' which began in the late 16th century, especially in the reigns of Kings Youngjo and Jungjo, which was called the Renaissance of Chosun, the ambitious policy for the development of science and technology called for. the rapid increase of he number of such technocrats as mathematics, astronomy and medicine. Amid these social changes, the Jung-in mathematicians inevitably became quite ambitious and proud. They tried to explore deeply into mathematics perse beyond the narrow limit of knowledge required for their office. Thus, in this period the mathematics developed rapidly, undergoing very important changes. The characteristic features of the mathematics in this period were: Jung-in mathematicians' active study an publication, the mathematic studies by the renowned scholars of Sil-Hak, joint works by these two classes, their approach to the Western mathematics and their effort to develop Korean mathematics. Toward the 'Enlightenment Period' in the late 19th century, the Western mathematics experienced great difficulty to take its roots in the Peninsula which had been under the strong influence of Confucian ideology and traditional Korean mathematic system. However, with King Kojong's ordinance in 1895, the traditional Korean mathematics influenced by Chinese disappeared from the history of Korean mathematics, as the school system was hanged into the Western style and the Western mathematics was adopted as the only mathematics to be taught at the Schools of various levels. Thus the 'Enlightenment Period' is the period in which Korean mathematics shifted from Chinese into European.