• School Mathematics
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• v.5 no.4
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• pp.401-420
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• 2003

We have many problems in the teaching and learning of proof, especially in the demonstrative geometry of middle school mathematics introducing the proof for the first time. Above all, it is the serious problem that many students do not understand the meaning of proof. In this paper we intend to show that teaching the meaning of proof in terms of historic-genetic approach will be a method to improve the way of teaching proof. We investigate the development of proof which goes through three stages such as experimental, intuitional, and scientific stage as well as the development of geometry up to the completion of Euclid's Elements as Bran-ford set out, and analyze the teaching process for the purpose of looking for the way of improving the way of teaching proof through the historic-genetic approach. We conducted lessons about the angle-sum property of triangle in accordance with these three stages to the students of seventh grade. We show that the students will understand the meaning of proof meaningfully and properly through the historic-genetic approach.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.57-65
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• 2011

The conceptions of definition and proof radically change in the transition from secondary to tertiary mathematics. Specifically this paper analyses the historical development of the axiomatic method from Greek to modern mathematics. To understand Greek and modern axiomatic method, it is important to know the different characteristics of the primitive terms, constant and variable. Especially this matter of primitive terms explains the change of conceptions of definition, proof and mathematics. This historical analysis is useful for introducing the meaning of formal definition and proof.

• Communications of Mathematical Education
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• v.13 no.1
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• pp.245-263
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• 2002

인류 문명의 발달과 함께 폭넓게 활용된 수학적 내용 중의 하나가 피타고라스 정리이다. 특히, 이집트, 메소포타미아, 그리고 중국과 같은 고대 문명의 발생지에서 발굴되는 많은 역사적 기록 속에서 피타고라스 정리에 대한 내용을 찾아볼 수 있다. 피타고라스 정리는 중등학교 수학교육에서 매우 중요한 정리로써, 정리 내용 자체뿐만 아니라 다양한 증명 방법과 증명 과정에 내재된 수학적 아이디어는 수학교육적 측면에서 큰 의미를 가지고 있다. 본 연구에서는 중학교 수학 교과 내용과 관련된 피타고라스 정리의 증명 방법들을 소개하고, 각 증명에 내재된 수학적 아이디어를 기술할 것이다.

• School Mathematics
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• v.18 no.4
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• pp.839-856
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• 2016

In 2009 revision and 2015 revision mathematics national curriculum, 'proof' was moved to high school from middle school in consideration of the cognitive development level of students, and 'proof by contradiction' was stated in the "success criteria of learning contents" of the first year high school subject while it had been not officially introduced in $7^{th}$ and 2007 revision national curriculum. Proof by contradiction is known that it induces a cognitive conflict due to the unique nature of rather assuming the opposite of the statement for proving it. In this article, based on the logical, mathematical and historical analysis of Proof by contradiction, we looked about the introductions and the applications of the current textbooks which had been revised recently, and searched for improvement measures from the viewpoint of discovery, explanation, and consilience. We suggested introducing Proof by contradiction after describing the discovery process earlier, separately but organically describing parts necessary to assume the opposite and parts not necessary, disclosing the relationships with proof by contrapositive, and using the viewpoint of consilience.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.887-921
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• 2009

Pythagorean theorem is one of mathematical contents which is widely used during human culture have developed. There are many historial records related to Pythagorean theorem made by Babylonian, Egyptian, and Mesopotamian. The theorem has the important meaning for mathematics education in secondary school education. Along with the importance of the proof itself, diverse proof methods and ideas included in their methods are also important since the methods improve students' ability to think mathematics. Hence, in this paper, we classify and analyze 390 proof methods published in the book "All that Pythagorean theorem" and other materials. Based on the results we derive educational meaning in mathematics with respect to main idea of the proof, the preliminaries of the study, and study skills used for proof.

• Communications of Mathematical Education
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• v.24 no.4
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• pp.891-907
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• 2010

This study analyzed the Fundamental Theorem of Calculus from the historical, mathematical, and instructional perspectives. Based on the in-depth analysis, this study suggested an alternative way of teaching the Fundamental Theorem of Calculus.

• 한국벤처창업학회:학술대회논문집
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• 2023.04a
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• pp.1-5
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• 2023

최근 정보통신기술의 발달로 인하여 디지털 전환의 발달이 활발하다. 특히나 이런 디지털 전환의 영향은 대기업에게만 주는 것이 아닌 소상공인들에게도 많은 영향을 주고 있다. 하지만 소상공인들을 대상으로 한 디지털 전환에 대한 연구는 적은 편이었기에 본 연구에서는 디지털 전환으로 인한 소상공인의 실질적인 성과가 있는가를 살펴보았다. 연구 방법으로는 보다 디지털 전환을 겪으며 소상공인들이 느꼈을 의사결정과 갈등의 현상을 파악하기 위하여 사례연구로 진행하였다. 연구 대상자로는 국내 대표 플랫폼인 N사에 디지털 전환 시스템인 스마트 스토어 개설과 라이브 커머스 등을 이용해 보고 싶었던 소상공인 여섯 팀을 섭외하여 진행하였다. 소상공인 디지털 전환을보다 면밀히 과정 기록 및 도움을 주기 위하여 경기도에 위치한 G학교 경영학 학부생들과의 협업으로 진행되었다. 연구는 총 12주 정도 소요되었고 프로그램이 끝난 후 각 소상공인 대표들과의 심층면담을 진행하였다. 본 연구에서는 소상공인들 스토어의 매출 및 고객 유입수가 모두 현저히 증가한 것으로 보여줌으로서 실질적인 성과가 있음을 보였다. 면담에서는 소상공인들이 디지털 전환은 새로운 고객 유입 및 홍보와 언제든 고객을 맞이할 수 있는 환경을 위해서는 선택이 아닌 필수라고 언급하여 정성적인 성과로 증명하였다.

• Journal of the Korean Geographical Society
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• v.39 no.4
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• pp.585-601
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• 2004

The purpose of this paper is to examine the change of Korean land transportation system and pattern during 1905-1911 concentrated on road construction so-caued ‘Sinjak-ro’. As conclusions, modem road or ‘Sinjak-ro’ started from modem port to inner hinterland where economic resource or regional center located. A trunk railroad running through Korea Peninsula from Busan to Sinuiju(border between China) is opened its complete operation in 1906 by Japanese investment, when no ‘Sinjak-ro’ road construction begun. Thus from the beginning, railroad station also became important starting point of ‘Sinjak-ro’ as seaports. Before the Japanese annexation of Korea, the ‘Sinjak-ro’ road was constructed mainly between seaport or station, where Japanese commercial settlement located, and hinterlands to help their economic invasion. This study could not deal with other modem transportation systems such as railroads and waterways. It is necessary to examine whole changes of modern transportation systems in this age so that we would comprehend modernization feature of Korea from the viewpoint of transportation history.

• 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 Korean Society of Law and Medicine
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• v.22 no.2
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• pp.49-79
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• 2021

Due to defendant's wrongful act by implant surgery, plaintiff has been suffered serious damages to his face and teeth, and pain caused by establishing implanted teeth. Jeonju Appellate Court sentenced to pay future medical expenses and alimony to the plaintiff in compensation for breach of duty or torts. The ruling is designed to relieve the burden of proof because it is extremely difficult for non-experts to determine whether dentists violated their 'duty of care' or whether there was a causal relationship between damages to medial treatment. It was judged that if symptoms that contributed to the patient's significant outcome occurred during or after surgery, such symptoms could be presumed to have been caused by medical negligence if indirect facts were proven to be other than medical negligence. Originally, the shifting of burden of proof in Germany, has already been developed in medical malpractice case since 1940s. In order to guarantee the patients' right, §630h German Civil Code (BGB) - presumption of negligence in the realization of controllable risk- has been also legislated. BGH (Bundesgerichtshof) has been interested in ensuring that the principle of equality between patients and doctors. So, in this study, we wanted to refer to German precedent cases to analyzing Korean medical malpractice lawsuit. In particular, the decision could be significant in that it approaches closer to allows the shifting burden of proof in drastically growing dental malpractice cases. This is clearly confirmed in the judgment of the dentist's "fault" that "if indirect facts about the symptom or occurrence are proven to be cause other than medical negligence, such symptoms can be presumed to be due to medical negligence."