• Electronics and Telecommunications Trends
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• v.11 no.3 s.41
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• pp.71-84
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• 1996

Girard에 의해서 1987년에 처음 소개된 선형 논리(linear logic)는 컴퓨터 사이언스에 큰 관심을 불러 일으키며 빠르게 발전하고 있다. 선형 논리는 상태 및 자원을 논리적 수준에서 다루고 있는 특징이 있다. 본 고에서는 선형 논리의 의미, 동기 및 특성을 소개하며, Gentzen의 시퀀트 계산법과 Prawitz의 자연 연역법 사이의 연관성 및 여러 증명 사이의 '같음'에 대한 개념을 컷제거 정리 측면에서 논의하고, 이러한 개념에 의하여 선형 논리의 증명이 증명망으로서 표현될 수 있음을 보인다.

• Communications of Mathematical Education
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• v.28 no.4
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• pp.513-528
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• 2014

This study is intended to examine 36 in-service secondary school mathematics teachers' conceptions of proof in the context of mathematics and mathematics education. The results suggest that almost teachers recognize the role as justification well but have the insufficient conceptions about another various roles of proof in mathematics. The results further suggest that many of teachers have vague concept-images in relation with the requirement of proof and recognize the insufficiency about the actual teaching of proof. Based on the results, implications for revision of mathematics curriculum and mathematics teacher education are discussed.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.173-192
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• 2013

It may be replacement proofs with understanding and explaining geometrical properties that was a remarkable change in school geometry of 2009 revised national curriculum for mathematics. That comes from the difficulties which students have experienced in learning proofs. This study focuses on one of those difficulties which are caused by the forms of proofs: using letters for designating some sides or angles in writing proofs and understanding some long sentences of proofs. To overcome it, this study aims to investigate the applicability of Byrne's method which uses coloured diagrams instead of letters. For this purpose, the proofs of three geometrical properties were taught to middle school students by Byrne's visual method using the original source, dynamic representations, and the teacher's manual drawing, respectively. Consequently, the applicability of Byrne's method was discussed based on its strengths and its weaknesses by analysing the results of students' worksheets and interviews and their teacher's interview. This analysis shows that Byrne's method may be helpful for students' understanding of given geometrical proofs rather than writing proofs.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.123-135
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• 2008

This study analysed the schemata which are requisite to understand and prove examples of mathematical induction, and examined students' construction of the schemata. We verified that the construction of implication-valued function schema and modus ponens schema needs function schema and proposition-valued function schema, and needs synthetic coordination for successive mathematical induction schema. Given this background, we establish $1{\sim}4$ levels for students' understanding of the mathematical induction. Further, we analysed cognitive difficulties of students who studying mathematical induction in connection with these understanding levels.

• The Korean Society of Law and Medicine
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• v.17 no.2
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• pp.29-56
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• 2016

$F{\ddot{u}}r$ den Schadensersatzhaftung des Arztes, sog. die Arzthaftung, ist es vornehmlich vorauszusetzen: die $Sch{\ddot{a}}digungsbehandlung$ des Arztes, die Rechtswidrigkeit und das Verschulden. Zur Problematik der $Fahrl{\ddot{a}}ssigkeit$ in der Stufe des Verschuldens handelt sich es in dieser Beitrag um die Kritisierung der Rechtsprechung. $F{\ddot{u}}r$ die Entscheidung des Verschulden im medizinischen Fehler kommt es darauf an, ob die Sorgfaltspflicht des Arztes verletzt wird. $Daf{\ddot{u}}r$ wird der medizinische Standard rekurriert, den die Rechtsprechung nicht aus materieller, sondern aus normativer Sicht begreift. Erstaunlich $un{\ddot{u}}bereinstimmend$ mit deren Leitsatz wird der medizinische Standard als $Ma{\ss}stab$ der Sorgfaltspflicht materiell - zutreffend nur im Ergebnis - behandelt. Die Sorgfaltspflicht in der Medizin bedeutet nicht die natur-wissenschaftliche Erkenntnisse, sondern eine "Best-$M{\ddot{u}}ssen$" Pflicht. Demnach ist der Standpunkt der Rechtsprechung, wonach den med. Standard normativ bewertet und die Sorgfaltspflicht darduch wieder normativ entscheidet, nicht anders als eine $w{\ddot{o}}rtliche$ Wiederholung. Die Arzthaftung in der Rechtsprechung ist aufgrund mit der Verneinung von der Sorgfaltspflichtverletzung nicht angenommen, welche in der Tat jedoch aus verschiedenen $Gr{\ddot{u}}nden$, wie die Rechtswidrigkeit, die $Fahrl{\ddot{a}}ssigkeit$ oder $Kausalit{\ddot{a}}t$, nicht angenommen. Der $Fahrl{\ddot{a}}ssigkeitsbeweis$ in der Rechtsprechung entwickelt sich mit dem Beweis nach objektivem $Ma{\ss}stab$, der Vermutung nach Anschein-Beweis und der $Beschr{\ddot{a}}nkung$ mit der Wahrscheinlichkeit. Bei Letzterem $geh{\ddot{o}}rt$ es $schlie{\ss}lich$ zum medizinischen Bereich. Ein Eintritt in den fachliche Bereich im Rahmen der Beweislast stellt der Beweiserleichterung $gegen{\ddot{u}}ber$. Aus diesem Hintergrund ist ${\S}630$ h Abs. 5 BGB bemerkenswert, wonach das Vorliegen eines groben Behandlungsfehler $regelm{\ddot{a}}{\ss}ig$ zur Vermutung von der $Kausalit{\ddot{a}}tszusammenhang$ $f{\ddot{u}}hrt$. Dieser Paragraph ist inhaltlich als Beweislastumkehr angesehen. Damit ist es von Nutzen im Fall des groben Fehler, der beim - elementaren - kunstgerechten Verhalten nicht entstanden $h{\ddot{a}}tte$, wie $Hygienem{\ddot{a}}ngel$, ${\ddot{U}}berdosierung$ des Narkotikum.

• Journal of Educational Research in Mathematics
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• v.14 no.2
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• pp.143-156
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• 2004

Lakatos's mathematical philosophy implies that the mathematical knowledge is quasi-empirical and provides the context where mathematics grows and develops. So, it is educationally significant. But, it is not easy to apply Lakatos's methodology to teaching elementary mathematics, because Lakatos's logic of the mathematical discovery is based on the proofs and refutations but elementary mathematics does not contain any proof. This study is to develop the schemes that apply Lakatos's methodology to teaching elementary mathematics and to provide the teaching examples. I devised the teaching process and the curriculum development method. And I developed the teaching examples.

• School Mathematics
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• v.18 no.4
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• pp.749-771
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• 2016

The purpose of this study is to analyze mathematical tasks of Korea and the USA textbooks focused on conditions for parallelograms. In this study, structures of task, types of proof and reasoning, and levels of cognitive demand are investigated. The conclusion is as follows: First, with respect to structures of task, structures presented in the USA textbooks are more diverse. Second, with respect to types of proof and reasoning, Korea and the USA prefer IC task and DA task. And task types presented in the USA textbooks are more diverse. Third, with respect to levels of cognitive demand, in both Korea and the USA textbooks, PNC task and PWC task account most. And compared to the USA, Korea prefer algorithms. In addition, we find out implications for reconstruction of Korea textbook. It is as follows: First, with respect to structures of task and types of proof and reasoning, the diversity of composition needs to be raised. Second, with respect to levels of cognitive demand, the concentration in PNC task needs to be declined. And levels of cognitive demand on types of tasks need to be reconsidered. Third, with respect to tasks' topic and material, internal and external connectivities of mathematics need to be strengthened.

• The Mathematical Education
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• v.34 no.2
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• pp.141-202
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• 1995

van Hiele의 사고수준 이론에는 기초수존, 제1수준, 제2수준, 제3수준, 제4수준 등 5가지가 있고, 이 중에서 국민학교에 해당되는 것은 기초수준 (1학년), 제1수준(2, 3학년), 제2주순 (4, 5, 6학년) 등 세 가지 뿐이다. 그리고 기하학적의 구조 인식론에는 관제, 구성, 정의, 공리, 정리, 증명, 척도, 자호, 응용 등 9가지 단계가 있고, 이 9가지 단계를 기초수준, 제 1수준, 제 2수준의 각 수준에 대응시켜서 거기에 해당되는 기하도형 학습을 연구·분석하였다. 기하도형에 관한 학습은 주로 경험성과 창의성을 바탕으로 하는 보기문제를 제시하여 그 흐름을 해결함으로써 각 수준의 각 단계들을 스스로 인식하도록 하였다. 특히 여기에서 처음으로 등장하는 기하학의 구조 인식론이라는 것은 위에서 언급한 9가지 단계를 차례로 거쳐 가야만 아동들은 도형을 올바르게 빠짐없이 인식할 수 있다는 이론이다. 이 이론의 특징을 예를 하나 들어서 설명해 보면, 흔히들 정의를 단순히 무정의어와 정의어로 구분하고 있는데 반하여, 이 이론에서는 서로 역동적인 관계를 갖고 있는 기초정의, 상황정의, 포괄정의, 기본정의, 부수정의, 특수정의 등으로 나누었다는 점이다.

• Journal of Korea Fair Competition Federation
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• no.77
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• pp.26-32
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• 2002

단체수의계약은 중소기업의 경쟁력을 강화하는 기능을 갖고 있는 반면, 생산업체들은 경쟁을 하지 않고 일정 수준의 물량을 확보할 수 있기 때문에 중소기업들이 품질향상과 기술개발 노력을 등한시하는 요인으로 작용하기도 한다. 따라서 동 제도의 점진적인 축소에 이어 폐지시에는 그 대안으로 제한경쟁 및 지명경쟁 입찰자격 증명과 계약담당 공무원이 실시하는 이행능력평가를 협동조합이 담당하는 입찰자격증명 및 이행능력평가제도 도입도 검토해 볼 필요가 있다.

• Information and Communications Magazine
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• v.28 no.9
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• pp.84-95
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• 2011

2011년 IEEE 국제 정보 이론(ISIT) 심포지엄 (Symposium) 이 7월 31일부터 8월 5일까지 러시아 상트페테르부르크(St. Petersburg)에서 열렸다. 본 심포지엄에는 총 1,562편의 논문이 수락되어, 논문 수락율이 약 60%로 높지만, 최고 수준의 심포지엄으로, 1,500여명의 학자들이 참여했으며, 학문적으로 정보 이론의 핵심인 체비쇼프 다항식, 마코프 확률 연쇄, 콜모고로프 엔트로피, 페렐만의 푸앵카레 추측 증명 등, 학문의 원천 아이디어 발상에 대해 고찰하고, 최근 뜨거운 감자로 떠오른 극 부호(Po1ar code)를 간단히 소개했다. 또한, 우리 전통 문화 유산인 제주 정낭을 채널 부호의 관점에서 해석, 이에 따른 채널 용량을 구했고, 제주 정낭이 오늘날 중계망(Relay network)의 모태임을 증명했다.