• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.179-225
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• 2003

The purpose of this study is to revise the previous mathematics glossary Since the last mathematics glossary was published by MOE in 1937, there have been two curriculum revisions. As a result, many terms which are newly included in the curriculum are not specified in the mathematics glossary. Moreover, part of mathematics terms and the informations about mathematicians and mathematics educators in mathematics glossary are not correct. Thus the revision of the mathematics glossary is definitely necessary. To collect the opinions about mathematics terms, a large scale survey targeting mathematics education researchers and mathematics teachers was conducted and the subsequent meetings were held. Also, the studies regarding mathematics terminology were thoroughly reviewed to provide the direction of desirable mathematics terms. Reflecting all these informations, the draft of the new mathematics glossary was completed.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.57-73
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• 2010

Transcendental numbers are important in the history of mathematics because their study provided that circle squaring, one of the geometric problems of antiquity that had baffled mathematicians for more than 2000 years was insoluble. Liouville established in 1844 that transcendental numbers exist. In 1874, Cantor published his first proof of the existence of transcendentals in article [10]. Louville's theorem basically can be used to prove the existence of Transcendental number as well as produce a class of transcendental numbers. The number e was proved to be transcendental by Hermite in 1873, and $\pi$ by Lindemann in 1882. In 1934, Gelfond published a complete solution to the entire seventh problem of Hilbert. Within six weeks, Schneider found another independent solution. In 1966, A. Baker established the generalization of the Gelfond-Schneider theorem. He proved that any non-vanishing linear combination of logarithms of algebraic numbers with algebraic coefficients is transcendental. This study aims to examine the concept and development of transcendental numbers and to present students with its open problems promoting a research on it any further.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.253-270
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• 2007

by A.C. Clairaut was written based on the historico-genetic principle such as his . In this paper, by analyzing his we can induce six principles that Clairaut adopted to teach algebra: necessity and curiosity as a motive of studying algebra, harmony of discovery and proof, complementarity of generalization and specialization, connection of knowledge to be learned with already known facts, semantic approaches to procedural knowledge of mathematics, reversible approach. These can be considered as strategies for teaching algebra accorded with beginner's mind. Some of them correspond with characteristics of , but the others are unique in the domain of algebra. And by comparing Clairaut's approaches with school algebra, we discuss about some mathematical subjects: setting equations in relation to problem situations, operations and signs of letters, rule of signs in multiplication, solving quadratic equations, and general relationship between roots and coefficients of equations.

• Korean Journal of Logic
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• v.8 no.2
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• pp.3-32
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• 2005

Hilbert's rational ambition to establish consistency in Number theory and mathematics in general was frustrated by the fact that the statement itself claiming consistency is undecidable within its formal system by $G\ddot{o}del's$ second theorem. Hilbert's optimism that a mathematician should not say "Ignorabimus" ("We don't know") in any mathematical problem also collapses, due to the presence of a undecidable statement that is neither provable nor refutable. The failure of his program receives more shock, because his system excludes any ambiguity and is based on only mechanical operations concerning signs and strings of signs. Above all, $G\ddot{o}del's$ theorem demonstrates the limits of formalization. Now, the notion of provability in the dimension of syntax comes to have priority over that of semantic truth in mathematics. In spite of his failure, the notion of algorithm(mechanical processe) made a direct contribution to the emergence of programming languages. Consequently, we believe that his program is failure, but a great one.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.487-498
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• 2013

Sang-Seol Lee(1870-1917) wrote a manuscript BaekSeungHoCho(百勝胡艸) in the late 19th century. BaekSeungHoCho was transcribed in classical Chinese from the 1879 Japanese book Physics(物理學) by Teizo Ihimori (1851-1916). Sang-Seol Lee, a famous independence activist, is also called Father of the Modern Mathematics Education of Korea, because of his early contribution to the modern mathematics education in the 19th century. In this paper, we introduce contents of his manuscript BaekSeungHoCho for the first time and discuss the significance of this book. Also, we show his contribution on the introduction to modern physics in the late 19th century Korea.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.27-51
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• 2012

This paper analyzed the pedagogical content knowledge (PCK) presented in three novice teachers' mathematics instruction. PCK was analyzed in terms of the knowledge of mathematics content, the knowledge of students' understanding, and the knowledge of teaching methods. Teacher A executed a concept-oriented instruction with manipulative materials because she had difficulties in learning mathematics during her childhood. Teacher B attempted to implement an inquiry-centered instruction in the lesson of looking for the area of a trapezoid. Teacher C focused on the real-life connection to mathematics instruction. There were substantial differences among the teachers' PCK revealed in mathematics teaching, depending on their instructional goals. The detailed analyses of three teachers' teaching in terms of their PCK will give rise to the issues and suggestions of professional development for beginning elementary school teachers in mathematics teaching.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.2
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• pp.89-103
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• 2018

A genius "Prince of Mathematician" Gaussian and "Father of Communication" Shannon comes up with the creative idea of motivation to meet each other? The answer is a coin leaf. Gaussian found some creative ideas in the matter of obtaining a sum of 1 to 100. This is the same as the probability distribution curve when a coin leaf is thrown. Shannon extended the Gaussian probability distribution to define the entropy, taking the source symbol and the reciprocal logarithm to obtain the weighted average. These where the genius Gaussian and Shannon meet in the same coin leaf. This paper focuses on this point, and easily proves Gaussian distribution and Shannon entropy. As an application example, we have obtained the capacity and transition probability of Jeongju seminal vesicle, and the Shannon channel capacity is 1 when the equivalent transition probability is 1/2.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.167-180
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• 2007

In this study, we explored the role of analysis in the algebra development. For this, we classified ancient geometric analysis into an analysis by reduction and a Pappusian problematic analysis. this shows that both analyses have the function of reduction. Pappus' analysis consists of four steps; transformation, resolution, construction, demonstration. The transformation, by which conditions of given problem is transformed into other conditions which suggest a problem-solving, seems to be a kind of reduction. Mathematicians created new problems as a result of the reductional function of analysis, and became to see mathematics in the different view. An analytical thinking was a background at the birth of symbolic algebra, the reductional function of analysis played an important role in the development of symbolic algebra.

• Journal for History of Mathematics
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• v.24 no.2
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• pp.1-15
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• 2011

Approximation is a very useful approach in mathematics research. It was the same in traditional Chinese and Chosun mathematics. This study derived five characteristics from approximation approaches which were found in Chinese and Chosun mathematical books: improvement of approximate values, common and inevitable use of approximate values, recognition of approximate values and their reasons, comparison of their exactness, application of approximate principles. Through these characteristics, we can infer what Chinese and Chosun mathematicians recognized approximate values and how they manipulated them. They took approximate approaches by necessity or for the sake of convenience in mathematical study and its applications. Also, they tried to improve the degree of exactness of approximate values and use the inverse calculations to check them.

• School Mathematics
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• v.8 no.2
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• pp.161-176
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• 2006

Some adequate programs for mathematising are necessary to pre-service mathematics teachers, if they can guide their prospective students in secondary school to make a mathematising. They should be used to mathematising. In this paper, mathematising teaching units for the inquiry into number partition models with constant differences are designed for this purpose. They guide a series of process to make nooumenon for organizing phainomenon which is organized already through number partition model. Especially the new nooumenon and the process of obtaining it are discussed. But it is restricted when the numbers for partitioning are natural numbers, and elements and their differences are integers. Through these teaching units, pre-service mathematics teachers can experience and practice secondary mathematising, as they go through the procedures which are similar with those of mathematicians making theorems.