• 한국수학교육학회지시리즈D:수학교육연구
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• 제24권3호
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• pp.255-278
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• 2021

Proof serves a critical role in mathematical practices as well as in fostering student's mathematical understanding. However, the research literature accumulates results that there are not many opportunities available for students to engage with proving-related activities and that students' understanding about proof is not promising. This unpromising state of instruction of proof calls for a novel approach to address the aforementioned issues. This study investigated an instruction of proof to explore a pedagogy to teach how to prove. The teacher utilized the way of problem posing to make proving a routine part of everyday lesson and changed the classroom culture to support student proving. The study identified the teacher's support for student proving, the key pedagogical changes that embraced proving as part of everyday lesson, and what changes the teacher made to cultivate the classroom culture to be better suited for establishing a supportive community for student proving. The results indicate that problem posing has a potential to embrace proof into everyday lesson.

• 한국수학교육학회지시리즈A:수학교육
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• 제50권4호
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• pp.441-466
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• 2011

In this article, we study on the teaching design, focused on the geometric methods, of 2-D isoperimetric problem for the elementary mathematically gifted students. For our teaching design, we discussed the ideals of Zenodorus's polygon proof, Steiner's four-hinge proof, Steiner's mean boundary proof, Steiner's snowball-packing proof, Edler's finite existence proof and Lawlor's dissection proof, and then the ideals achieved were modified with the theoretical backgrounds-the theory of Freudenthal's mathematisation, the method of analysis-synthesis. We expect that this article would contribute to the elementary mathematically gifted students to acquire and to improve spatial sense.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제20권3호
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• pp.373-389
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• 2006

본 연구에서는 조합등식의 증명에서 조합적 논증을 이용한 증명방법과 기존의 수학교과서에 제시된 증명방법을 비교하고 조합등식에서 조합적 논증을 이용한 문제해결 전략을 유형별로 분류하여 제시하고자 한다. 이를 통해서 조합적 논증을 이용한 조합등식의 탐구활동을 교수 학습과정에 활용하고, 심화 학습 자료를 개발하는데 기초 자료가 될 수 있을 것이다.

• 정보보호학회논문지
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• 제22권6호
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• pp.1265-1270
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• 2012

이 논문에서는 래티스(Lattice)의 CVP (Closest Vector Problem)에 기반한 영지식 증명 기반의 인증프로토콜을 제안한다. CVP를 이용해서 암호시스템을 설계할 때 흔히 사용하는 길이가 짧은 기저벡터를 트랩도어 또는 비밀키로 사용하지 않는 프로토콜로서 의의를 가지며, 프로토콜의 설계가 단순하고 안전성 증명도 쉬워진다. 제안한 프로토콜의 안전성을 completeness, soundness, simulatability로 증명한다.

• 펄프종이기술
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• 제33권4호
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• pp.15-20
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• 2001

The function of the moisture-proof paper is to prevent moisture from adsorbing into the packed goods. Water-vapor transmission rate of the moisture-proof paper should be less than 100g/$m^2$.24hr and the optimum rate would be less than 50g/$m^2$.24hr. In general the moisture-proof paper has been made by laminating polyethylene or polypropylene on top of the base paper. However this kind of moisture-proof paper has a problem in recycling so that it brings about environmental pollution. In general the moisture-proof paper has been made by laminating polyethylene or polypropylene on top of the base paper. However this kind of moisture-proof paper has a problem in recycling so that it brings about environmental pollution. The purpose of this paper was to make moisture-proof paper using the mixture of SB latex and wax emulsion which was recyclable and environmentally friendly. Water vapor transmission rate showed less than 50g/$m^2$.24hr in mixture ratio of 85:15, 87:13, 90:10. Especially the mixture ratio of 87:13 showed the most favorable water-vapor transmission rate. However, the moisture-proof layer was destroyed slightly by folding in packing. It has been observed that there was no close relationship between water-vapor transmission rate of the moisture-proof paper and grammage of the base paper, but the density of base paper had influenced on water vapor transmission rate. It was also observed that the moisture-proof paper could be recycled. The moisture-proof paper was similar to base paper in degree of the pulping, and there was no significant difference in dispersion between moisture-proof paper and base paper. Most of wax particles which caused the spots during drying process could be removed by flotation process. Tensile strength and tear strength of both moisture-proof paper and base paper after pulping were measured to examine the fiber bonding, and no significant difference in physical properties was observed.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제22권4호
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• pp.471-487
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• 2008

본 연구에서는 해석학 강좌를 운영하는 과정에서 얻어진 학생들의 수학적 발명의 사례를 제시하고 분석하여, 수학적 발명과 관련된 구체적인 교수-학습 과정, 얻어진 수학적 산출물들, 이들의 수학적 의의를 기술하였다.

• 한국수학사학회지
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• 제11권2호
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• pp.17-28
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• 1998

The problem of mathematical rigor is that of giving an objective definition of a rigorous proof. But standards of rigor have changed in mathematics and the notion of proof is not absolute. There are different versions of proof or rigor, depending on time, place, and other things. In this paper we will briefly trace that evolution.

• 대한수학교육학회지:수학교육학연구
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• 제8권1호
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• pp.291-298
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• 1998

This study deals with the problem of proof education in the middle school geometry bby examining van Hiele#s geometric thought level theory and Freudenthal#s mathematization teaching theory. The implications that have been revealed by examining the theory of van Hie이 and Freudenthal are as follows. First of all, the proof education at present that follows the order of #definition-theorem-proof#should be reconsidered. This order of proof-teaching may have the danger that fix the proof education poorly and formally by imposing the ready-made mathematics as the mere record of proof on students rather than suggesting the proof as the real thought activity. Hence we should encourage students in reinventing #proving#as the means of organization and mathematization. Second, proof-learning can not start by introducing the term of proof only. We should recognize proof-learning as a gradual process which forms with understanding the meaning of proof on the basic of the various activities, such as observation of geometric figures, analysis of the properties of geometric figures and construction of the relationship among those properties. Moreover students should be given this natural ground of proof.

• 논리연구
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• 제18권3호
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• pp.307-335
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• 2015

논증의 타당성에 대한 덤밋과 프라위츠의 증명론적 정의의 핵심사항 중의 하나는 열린 논증은 그 전제들에 대한 타당한 논증들을 그 결론에 대한 타당한 논증으로 전환하는 효과적인 방법이 있을 경우 타당하다는 조건이다. 그러나 그들의 정의에서 이 조건은 적절한 의미에서 결정 불가능한 전제들을 지니는 열린 논증들은 모두 사소하게 타당하게 된다는 부적절한 귀결을 지닌다. 필자는 프라위츠의 정의를 중심으로 증명론적 타당성 개념을 설명한 후, 이에 대한 사소성 문제를 제기하고 검토할 것이며, 이에 의거하여 프라위츠의 정의에 대한 수정안을 제시할 것이다.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.547-552
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• 2007

In this note, we extends some of the results of Liu [Fuzzy Sets and systems 157 (2006) 869-878]. This extension consists of a simple proof involving weighted functions and their preference index. We also give an elementary simple proof of the maximum entropy weighting function problem with a given preference index value without using any advanced theory like variational principles or without using Lagrangian multiplier methods.