• Journal for History of Mathematics
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• v.31 no.6
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• pp.273-289
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• 2018

The KaiFangFa開方法 of traditional mathematics was completed in ${\ll}$JiuZhang SuanShu九章算術${\gg}$ originally, and further organized in Song宋 $Yu{\acute{a}}n$元 dinasities. The former is the ShiSuoKaiFangFa釋鎖開方法 using the coefficients of the polynomial expansion, and the latter is the ZengChengKaiFangFa增乘開方法 obtaining the solution only by some mechanical numerical manipulations. ${\ll}$SanHak JeongEui算學正義${\gg}$ basically used the latter and improved the estimate-value array by referring to the written-calculation in ${\ll}$ShuLi JingYun數理精蘊${\gg}$. As a result, ZengChengKaiFangFa was more refined so that the KaiFangFa algorithm is more consistent.

• The Journal of Korean Philosophical History
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• no.35
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• pp.385-413
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• 2012

This thesis is a study on the relation of between Xiangshu Zhouyi Theory and mathematics, Zhouyi Theory as the one of the study of Chinese classics, was formed by Zhouyi' Eight Diagrams, the theory of Yinyangwuxing and the knowledge of natural science in Han dynasty. 'Xiangshu' had been regarded as the important concept and theory in the history of Zhouyi Theory From the beginning of Han dynasty to the end of Qing dynasty. At this developing of this Periodical Change, 'Xiangshu' had been endoded in the expression system of mathematics. This thesis considers binary system and surplus nembers, multiple and progression, magic square and circular constant, a proportional expression from Zhouyi Theory point of view. Xiangshu Zhouyi theory got the answer of these questions like the origin of Zhouyi, interpreting Guayao-word and Cosmology by using those expression systems of mathematics. Besides mathematics, Xiangshu Zhouyi theory was also related to astronomy, medicine, etc. Xiangshu Zhouyi theory had kept the pace with the general development of natural science. This thesis from the premise that Xiangshu Zhouyi theory kept the pace with natural science, summing up the mathematical expression system in the history of Zhouyi theory, proves that Xiangshu Zhouyi theory had developed according as the conditions of natural science.

• Journal for History of Mathematics
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• v.27 no.3
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• pp.165-182
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• 2014

After algebraic expressions for the roots of 3rd and 4th degree polynomial equations were given in the mid 16th century, seeking such a formula for the 5th and greater degree equations had been one main problem for algebraists for almost 200 years. Lagrange made careful and thorough investigation of various solving methods for equations with the purpose of finding a principle which could be applicable to general equations. In the process of doing this, he found a relation between the roots of the original equation and its auxiliary equation using permutations of the roots. Lagrange's ingenious idea of using permutations of roots of the original equation is regarded as the key factor of the Abel's proof of unsolvability by radicals of general 5th degree equations and of Galois' theory as well. This paper intends to examine Lagrange's contribution in the theory of polynomial equations, providing a detailed analysis of various solving methods of Lagrange and others before him.

• Journal for History of Mathematics
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• v.27 no.3
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• pp.197-210
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• 2014

Species like insects and fishes have, in many cases, non-overlapping time intervals of one generation and their descendant one. So the population dynamics of such species can be formulated as discrete models. In this paper various discrete population models are introduced in chronological order. The author's investigation starts with the Malthusian model suggested in 1798, and continues through Verhulst model(the discrete logistic model), Ricker model, the Beverton-Holt stock-recruitment model, Shep-herd model, Hassell model and Sigmoid type Beverton-Holt model. We discuss the mathematical and practical significance of each model and analyze its properties. Also the stability properties of stationary solutions of the models are studied analytically and illustratively using GSP, a computer software. The visual outputs generated by GSP are compared with the analytical stability results.

• East Asian mathematical journal
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• v.29 no.4
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• pp.355-392
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• 2013

Generally school algebra is to start with introducing variables and algebraic expressions, which have major cognitive obstacles to students in the transfer from arithmetic to algebra. But the recent studies in the teaching school algebra argue the algebraic thinking from an early algebraic point of view. We compare the Korean elementary mathematics textbooks with Americans from this perspective. First, we discuss the history of school algebra in the school curriculum. And Second, we investigate the recent studies in relation to early algebra. We clarify the goals of this study(the importance of early algebra in the elementary school) through these discussions. Next we examine closely the number sense in the arithmetic and the symbol sense in the algebra. And we conclude that the operation sense can connect these senses within early algebra using the algebraic thinking. Finally, we compare the elementary mathematics books between Korean and American according to the components of the operation sense. In this comparative study, we identify a possibility of teaching algebraic thinking in the elementary mathematics and early algebra can be introduced to the elementary mathematics textbooks from aspects of the operation sense.

• Education of Primary School Mathematics
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• v.21 no.1
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• pp.19-37
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• 2018

The purpose of this study was to analyze the multicultural mathematics education factor shown in mathematics textbook. For this purpose, 2015 revised curriculum, mathematics textbook and teacher's guide book of first and second grade were analyzed using framework for multicultural mathematics education factor. The results of this study revealed that the general guideline of the national curriculum included 'culture identity', 'diversity of knowledge' and 'social problem solving' but the curriculum of mathematics excluded 'culture identity'. Nevertheless, mathematics textbook showed various multicultural mathematics education factor except 'social problem solving'. But there are several kinds of problem. Fist, application level of multicultural mathematics education factor was mostly low. Second, history of mathematics and culture aspects were Europocentric. Thirds, characters in mathematics text book were excessively standard. there weren't other ethnicity, the disabled, multicultural students. On the basis of these results, this paper includes several implications for the future multicultural mathematics education in elementary school.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.183-197
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• 2012

Geometry having long history of mathematics have important role for thinking power and creativity progress in middle school. The regular polygon included in plane geometry was mainly taught convex regular polygon in elementary school and middle school. In this study, we investigated the denotation's extension of regular polygon by mathematical basic knowledge included in school curriculum. For this research, first, school mathematical knowledge about regular polygon was analyzed. And then, basic direction of research was established for inquiry. Second, based on this analysis inductive inquiry activity was performed with research using geometry software(Cabri Geometry II). Through this study the development of enriched learning material and showing the direction of geometry research is expected.

• Research in Mathematical Education
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• v.3 no.1
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• pp.9-21
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• 1999

In mid 1980s, open education arrived in Korea. It was influenced by the educational reforms implemented in American primary schools. Currently, the Ministry of Education is appealing to teachers for their active involvement in educational reform by using open education methodology. Often teachers in Korea complain that they do not know what to do or how to change in order to practice the open education. It is time to review the state of open education in Korea and the United States. This paper contains the following segments: 0) Introduction, 1) Beginning of open education, 2) A brief history of open education in Korea, 3) The current status of open education in the United States, 4) A glance at open mathematics classroom in Korea, 5) Lessons from the review, and 6) Conclusion.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.483-495
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• 2023

In his book "Exercitationum Mathematicalarum," a 17th-century mathematician van Schooten proposed linkages for drawing parabola, ellipse, and hyperbola. The linkages proposed by van Schooten can be used in action-based mathematics education and as a material for using mathematical history in school mathematics. In particular, students are not provided with the opportunity to learn by manipulating the quadratic curves in the high school curriculum, so van Schooten's linkages can be used for school mathematics. To this end, a method of implementing van Schooten's linkage in a dynamic geometry environment was presented, and proved that the traces of the figure drawn using van Schooten's linkage were parabola, ellipse, and hyperbola.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.97-118
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• 2011

This study aimed finding effective models for the teaching the concept of function. We selected two models. One is discrete model which focuses on the 'corresponding relation of the elements of the sets(domain and range). The other is continuous model which focuses on the dependent relationship of the two variables connected in variable phenomenon. A vending machine model was used as a discrete model, and a water bucket model was used as a continuous model in our study. We taught 2 times about the concept of function using two models to the 60 students (7th grade, 2 classes) living in Taebak city, and tested it twice, after class and about 3 months later. A vending machine model was helpful in understanding the definition of function in the 7th grade math textbook. Also, it was helpful to making concept image and to recalling it. On the other hand, students who used the water bucket model had a difficultly in understanding the all independent variables of the domain corresponding to the dependent variables. But they excelled in tasks making formula expression and understanding changing situations.