• Communications of Mathematical Education
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• v.29 no.1
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• pp.91-110
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• 2015

The purpose of this study is to investigate the understanding of pi of elementary gifted students and explore improvement direction of teaching pi. The results of this study are as follows. First, students understood insufficiently the property of approximation, constancy and infinity of pi from the fixation on 'pi = 3.14'. They mixed pi up with the approximation of pi as well. Second, they had a inclination to understand pi as algebraic formula, circumference by diameter. Third, few students understood the property of constancy and infinity of pi deeply. Lastly, the discussion activity provided the chance of finding the idea of the property of approximation of pi. In conclusion, we proposed several methods which improve the teaching of pi at elementary school.

• Communications of Mathematical Education
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• v.36 no.4
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• pp.589-610
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• 2022

This study aimed to derive pedagogical implications by comparing and analyzing how the concept of pi is taught in 10 different elementary mathematics textbooks, which are scheduled to be applied from 2023. We developed a textbook analysis framework by previous studies on the concept of pi and the teaching of pi, and analyzed in terms of three instructional elements (i.e. inferring conceptsof pi, understanding properties of pi, and applying relationships). We derived the need to emphasize various contexts for estimation of pi, presentation of problem situations that provide motivation to actually measure diameters and circumferences, providing an opportunity to explore the properties of measurement, and an experience the flexibility of selecting an approximate value of pi. Based on the above conclusions and pedagogical implications through the research results., we suggested ways to teach the concept of pi in elementary mathematics and improvement points for developing textbooks focusing on the context of introduction of pi and the use of technological tools.

• Journal of the Korean School Mathematics Society
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• v.21 no.4
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• pp.445-467
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• 2018

In this study, we analyzed the contents of pi and the area of a circle presented in Korean, Japanese, Singapore, and American mathematics textbooks, and drew implications for the teaching of pi and the area of a circle in school mathematics. We developed a textbook analysis framework by theoretical discussions on the concept of the pi based on the various properties of pi and the area of a circle based on the central ideas of measurement and the previous researches on pi and the area of a circle in elementary mathematics. We drew five suggestions for improving the teaching of pi and three suggestions for improving the teaching of the area of a circle in Korean elementary schools.

• Education of Primary School Mathematics
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• v.26 no.1
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• pp.65-82
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• 2023

The purpose of this study is to examine how pre-service teachers' digital capabilities and content knowledge for teaching pi appear and are strengthened in the process of developing digital-based teaching and learning materials of pi, and to derive implications for pre-service teacher education. To this end, the researchers analyzed the process of two pre-service teachers developing exploratory activity materials for teaching pi using block coding of AlgeoMath program. Through the analysis results, it was confirmed that AlgeoMath' block coding activities provided an experience of expressing and expanding the digital capabilities of pre-service teachers, an opportunity to deepen the content knowledge of pi, and to recognize the problems and limitations of the digital learning environment. It was also suggested that the development of digital materials using block coding needs to be used to strengthen digital capabilities of pre-service teachers, and that the curriculum knowledge needs to be emphasized as knowledge necessary for the development of digital teaching and learning materials in pre-service teacher education.

• Venture DIGEST
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• s.119
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• pp.44-45
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• 2008

참으로 다양한 것들이 존재 하는 나라. 아시아 속에서 또 하나의 독특한 문화를 가진 독립적인 대륙, 인도. 11억 인구의 거대 시장과 풍부한 자원을 보유한 인도는 엄청난 성장 잠재력을 보유한 나라로 손꼽힌다. 0의 개념, 십진법, 원주율, 피타고라스 정리, 지구의 태양 공전 주기, 체스까지 흥미로운 세계 최초를 만들어낸 기초학문의 강국 인도는 이제 선택이 아닌 필수교류 국가로 우리 앞으로 달려오고있다.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.833-855
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• 2017

This study aims to reinvestigate the reason for introducing radian as a new unit to express the size of angles, what is the meaning of radian measures to use arc lengths as angle measures, and why is the domain of trigonometric functions expanded to real numbers for expressing general angles. For this purpose, it was conducted historical, mathematical and applied mathematical analyzes in order to research at multidisciplinary analysis of the radian concept. As a result, the following were revealed. First, radian measure is intrinsic essence in angle measure. The radian is itself, and theoretical absolute unit. The radian makes trigonometric functions as real functions. Second, radians should be aware of invariance through covariance of ratios and proportions in concentric circles. The orthogonality between cosine and sine gives a crucial inevitability to the radian. It should be aware that radian is the simplest standards for measuring the length of arcs by the length of radius. It can find the connection with sexadecimal method using the division strategy. Third, I revealed the necessity by distinction between angle and angle measure. It needs justification for omission of radians and multiplication relationship strategy between arc and radius. The didactical suggestions derived by these can reveal the usefulness and value of the radian concept and can contribute to the substantive teaching of radian measure.

• 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.

• 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.