• 논리연구
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• 제22권1호
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• pp.151-182
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• 2019

연역 논증과 귀납 논증을 구분하는 실현 기준에 따르면, 전제와 결론 사이에 실현된 뒷받침 관계가 필연성일 경우에만 연역 논증이다. 이 경우 '부당한 연역 논증'은 형용모순을 저지르는 표현이 된다. 이와 달리 전제와 결론 사이에 의도된 뒷받침 관계를 구분 기준으로 삼는 것은 의도 기준인데, 이에 따르면 '부당한 연역 논증'은 형용모순이 아니다. 우리는 의도 기준을 옹호하는데, 실현 기준은 생략 논증을 연역 논증이나 귀납 논증 중 한 쪽으로 분류하기 위해서는 의도를 참조해야 한다는 난점, 또 나쁜 논증과 논증이 아닌 명제들의 집합을 구분하지 못한다는 난점을 지니기 때문이다. 의도 기준 역시 논증 제시 의도를 파악하기 어려운 경우가 있지만, 그것은 자비의 원리에 호소하면 해결할 수 있다. 나아가 결론에 대한 신념이나 논증 제시자의 성향을 나타내는 표현을 논증 제시 의도와 구분함으로써 우리는 의도 기준이 연역 논증과 귀납 논증을 구분하는 기준으로 제 역할을 할 수 있다고 결론짓는다.

• 한국실천공학교육학회논문지
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• 제5권1호
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• pp.1-13
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• 2013

이 연구의 본론에서 공학 교육에 적용되는 귀납법적 확증(confirmation)과 연역법적 검증(verification)을 다루고 이어서 귀납법 추리의 원리를 모형도를 통해 알아보았다. 그리고 이어서 공학교육에서 널리 쓰이는 확률론적 추론의 도입 배경과 보편적 명제에 대한 확률적 검정(test) )을 논의하였고 또한 실험에 대한 귀납법의 인정여부를 가지고 역사적으로 학계에서 끊임없이 논의 되어온 귀납법적 추론에 대한 정당성을 비교 분석하였다. 공학 교육에서 흔히 쓰이는 실험에 대한 철학적 명제를 가지고 실험에 대한 설명으로 선택된 귀납법의 승리와 반전, 그리고 확증에 대해 알아보았다. 이어서 실험에서의 전제, 절차, 및 통제에 대하여 논의 되어졌다. 마지막으로 귀납법적 추론 예제로써 Elliptical Trainer 실험 결과를 가지고 확률론적 추론이 어떻게 가능한지 보여 주었다. 그 결과 82%의 참 확률을 가지고 3개의 추론을 하였는데 이 연구에서는 보통 공학연구와 달리 추론(결론 법칙)에 대한 참 확률을 표기하여 공학에서 주로 적용하는 귀납법적 방법 자체가 확률추론임을 알린다.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2010년도 추계학술대회
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• pp.27-33
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• 2010

The paper proposes the guidelines of application and interpretation for quality and reliability methodologies using deductive or inductive reasoning. The research also reviews Bayesian quality and reliability tools by deductive prior function and inductive posterior function.

• 호남수학학술지
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• 제32권4호
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• pp.625-632
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• 2010

The notions of commutative pre-logics and terminal sections are introduced. Characterizations of a commutative prelogic are provided. Properties of deductive systems in pre-logics which are upper semilattices are considered.

• 한국수학교육학회지시리즈A:수학교육
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• 제37권1호
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• pp.73-85
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• 1998

The purpose of this study is to investigate the understanding of middle school students on the meaning of proof and to suggest a teaching method to improve their understanding based on three levels identified by Kunimune as follows: Level I to think that experimental method is enough for justifying proof, Level II to think that deductive method is necessary for justifying proof, Level III to understand the meaning of deductive system. The conclusions of this study are as follows: First, only 13% of 8th graders and 22% of 9th graders are on level II. Second, although about 50% students understand the meaning of hypothesis, conclusion, and proof, they can't understand the necessity of deductive proof. This conclusion implies that the necessity of deductive proof needs to be taught to the middle school students. One of the teaching methods on the necessity of proof is to compare the nature of experimental method and deductive proof method by providing their weak and strong points respectively.

• 대한수학교육학회지:수학교육학연구
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• 제9권2호
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• pp.419-438
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• 1999

This paper explored the impact of dynamic geometry software such as CabriII, GSP on student's understanding deductive justification, on the assumption that proof in school mathematics should be used in the broader, psychological sense of justification rather than in the narrow sense of deductive, formal proof. The following results have been drawn: Dynamic geometry provided positive impact on interacting between empirical justification and deductive justification, especially on understanding the necessity of deductive justification. And teacher in the computer environment played crucial role in reducing on difficulties in connecting empirical justification to deductive justification. At the beginning of the research, however, it was not the case. However, once students got intocul-de-sac in empirical justification and understood the need of deductive justification, they tried to justify deductively. Compared with current paper-and-pencil environment that many students fail to learn the basic knowledge on proof, dynamic geometry software will give more positive ffect for learning. Dynamic geometry software may promote interaction between empirical justification and edeductive justification and give a feedback to students about results of their own actions. At present, there is some very helpful computer software. However the presence of good dynamic geometry software can not be the solution in itself. Since learning on proof is a function of various factors such as curriculum organization, evaluation method, the role of teacher and student. Most of all, the meaning of proof need to be reconceptualized in the future research.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권2호
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• pp.325-344
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• 2010

본 연구는 중학생을 대상으로 학생들이 경험적 증명과 연역적 증명에 대한 선호를 결정할 때 영향을 미치는 요인을 분석하였다. 47명의 중학생에게 설문지를 통하여 자료를 수집하고 응답들을 분석한 결과, 경험적 증명과 연역적 증명의 선호에 영향을 미치는 요인들로 측정, 수학적 원리, 다양한 예를 통한 검증과정에 대한 인식들이 공통적으로 나타났다. 이 요소들은 경험적 증명과 연역적 증명의 선호와 비선호를 결정짓는 요인으로써, 선호하는 증명에 따라 상호 배타적으로 나타나지 않고 증명 선호에 영향을 미쳤다. 이를 통해 본 연구에서는 학생들이 특정 증명을 선호할 때, 한 증명에 대한 비선호와 다른 증명에 대한 선호가 동시에 작용할 수 있다는 결론과 함께 한 증명에 대한 선호요인을 보는 것만으로는 학생들의 증명 선호 이유를 정확히 파악할 수 없을 것이라는 가능성을 제언한다.

• East Asian mathematical journal
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• 제24권5호
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.

• 대한수학교육학회지:수학교육학연구
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• 제9권1호
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• pp.245-261
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• 1999

Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. But, teaching proof in school mathematics have been unsuccessful for many students. The traditional approach to proofs stresses formal logic and rigorous proof. Thus, most students have difficulties of the concept of proof and students' experiences with proof do not seem meaningful to them. However, different views of proof were asserted in the reassessment of the foundations of mathematics and the nature of mathematical truth. These different views of justification need to be reflected in demonstrative geometry classes. The purpose of this study is to characterize the types of students' justification in demonstrative geometry classes taught using dynamic software. The types of justification can be organized into three categories : empirical justification, deductive justification, and authoritarian justification. Empirical justification are based on evidence from examples, whereas deductive justification are based logical reasoning. If we assume that a strong understanding of demonstrative geometry is shown when empirical justification and deductive justification coexist and benefit from each other, then students' justification should not only some empirical basis but also use chains of deductive reasoning. Thus, interaction between empirical and deductive justification is important. Dynamic geometry software can be used to design the approach to justification that can be successful in moving students toward meaningful justification of ideas. Interactive geometry software can connect visual and empirical justification to higher levels of geometric justification with logical arguments in formal proof.

• 충청수학회지
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• 제27권1호
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• pp.57-64
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• 2014

It is known that the class of CI-algebras is a generalization of the class of BE-algebras [5]. Recently, K. H. Kim introduced the notion of a CS-algebra [4]. In this paper we discuss a closed deductive system of a CS-algebra, and we find some fundamental properties. Moreover, we study a CS-algebra homomorphism and a congruence relation.