• School Mathematics
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• v.13 no.3
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• pp.501-524
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• 2011

The purpose of this study was to develop teaching-learning materials for informal activities geared toward teaching the nature and structure of proof, to make a case analysis of the application of the developed instructional materials to students in an elementary gifted class, to discuss the feasibility of proof education for gifted elementary students and to give some suggestions on that proof education. It's ultimately meant to help improve the proof abilities of elementary gifted students. After the characteristics of the eight selected gifted elementary students were analyzed, instructional materials of nine sessions were developed to let them learn about the nature and structure of proof by utilizing informal activities. And then they took a lesson two times by using the instructional materials, and how they responded to that education was checked. An analysis framework was produced to assess how they solved the given proof problems, and another analysis framework was made to evaluate their understanding of the structure and nature of proof. In order to see whether they showed any improvement in proof abilities, their proof abilities and proof attitude were tested after they took lessons. And then they were asked to write how they felt, and there appeared seven kinds of significant responses when their writings were analyzed. Their responses proved the possibility of proof education for gifted elementary students, and seven suggestions were given on that education.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2002.06a
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• pp.209-218
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• 2002

보안의 형식검증은 시스템의 초기 상태를 정의하고 트랜잭션을 통해 그 상태를 추적하며 보안을 위해 각 상태를 체크하는 과정이다. 보안 증명이 잘못될 수 있는 경우는 시스템의 초기상태를 정의할 때와 상태가 안전하기 위한 조건을 정의할 때인데, 본 논문에서는 상태 트랜잭션을 위해 BAN 논리를 이용하여 대표적인 지불프로토콜인 NetBill 프로토콜에 대한 형식기법을 제안하였으며, 보안 프로토콜의 증명을 위해 BAN 논리의 확장을 제시했다. 이러한 확장된 연구결과는 원자성, 익명성 및 프라이버시와 같은 다른 중요한 보안의 특성을 증명하기 위해 이용될 수 있다.

• Aerospace Engineering and Technology
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• v.1 no.2
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• pp.155-172
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• 2002

Airship technical regulations for certification system of each countries are reviewed to assist the development of medium size airship that can be applied observation and communication relay with the ability of holding position at high altitude.

• The Mathematical Education
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• v.43 no.4
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• pp.381-390
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• 2004

In this study, we conceptualized the ‘preformal proof’, which is a transitive level of proof from the experimental and inductive justification to the formalized mathematical proof. We investigated concrete features of the preformal proof in the historico-genetic and the didactical situations. The preformal proof can get the generality of the contents of proof, which makes a distinction from the experimental proof. And we can draw a distinction between the preformal and formal proof, in point that the preformal proof heads for the reality-oriented objects and does not use the formal language.

• 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.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.359-374
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• 2014

Students' difficulties and errors in relation to mathematical proofs are worth while to say one of the dilemmas in mathematics education. The potential elements of their difficulty are scattered over the process of proving in geometry as well as algebra. This study aims to investigate whether middle school students understand the context of algebraic proof including literal expressions. We applied 24 third-grade middle school students a test item which shows a proof including a literal expression and missing the conclusion. Over the half of them responded wrong answers based on only the literal expression without considering its context. Three of them were interviewed individually to show their thinking. As a result, we could find some characteristics of their thinking including the perspective on proof as checking the validity of algebraic expression and the gap between proving and understanding of proof etc. From these, we also discussed about several didactical implications.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.371-392
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• 2009

A lot of researches state mathematical justification is important. Specially, NCTM (2000) mentions that mathematical reasoning and proof should be taught every student from pre-primary school to 12 grades. Some of researches say elementary school students are also able to prove and justify their own solution(Lester, 1975; King, 1970, 1973; Reid, 2002). Balacheff(1987), Tall(1995), Harel & Sowder(1998, 2007), Simon & Blume(1996) categorize the level or the types of mathematical justification. We re-categorize the 4 types of mathematical justification basis on their studies; external conviction justification, empirical-inductive justification, generic justification, deductive justification. External conviction justification consists of authoritarian justification, ritual justification, non-referential symbolic justification. empirical-inductive justification consists of naive examples justification and crucial example justification. Generic justification consists of generic example and visual example. The results of this research are following. First, elementary school teachers in Korea respectively understand mathematical justification well. Second, elementary school teachers in Korea prefer deductive justification when they justify by themselves, while they prefer empirical-inductive justification when they teach students.

• Communications of Mathematical Education
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• v.14
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• pp.197-215
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• 2001

최근 수학적 사고력 연구가 구체적 수학내용에 기반한 활동과 조작에 대한 연구보다는 활동이나 조작을 통한 결과로 수학적 사고력에 접근하는 일회성 연구로 이루어지는 경향이 있다. 본고에서는 교육 내용을 선정하기 위해 학교수학에서 아동들이 어떤 수학적 사고를 하는데 장애을 겪는지에 주목하여, 이러한 장애를 극복하는 것을 통해 수학적 사고력의 신장을 생각해보고자 하였다. 이에 대수에서는 문자도입에 따른 추상적 상징의 수용과 이용부분에서, 기하에서는 논증기하의 증명도입과정에서 형식적, 연역적 사고 시작으로 아동이 수학적 사고에 어려움을 겪는다는 사살에 주목하였다. 특히 논증 기하의 연역적, 형식적 증명은 논리와 추론이 바탕이 되어야 한다. 그런데 논리와 추론은 고등학교 1학년과정 집합과 명제부분에 들어있어 아동은 논리와 추론에 대한 어떤 경험도, 교육도 받지 않은 상태에서 증명을 하게 된다. 이에 교육 내용으로 수학적 사고력을 신장을 위해 가장 필요한 내용이 논증 기하가 도입되기 이전에 초등학교 5,6학년 아동을 대상으로한 논리와 추론교육이라고 본다. 또한 교육 방법으로는 컴퓨터를 이용한 교육공학적 접근을 하고자 하였다. 교육공학적 접근이 적극 권장되는 교육적 현실과 정규교육과정에서 이를 받아들일만한 시간적 여유가 없음을 감안하여, 교과 내용과 연계된 컴퓨터 교육을 제안하는 바이다. 이에 논리 및 추론 교육은 컴퓨터 교육으로 초등학교의 특기적성 시간이나 정규수업 시간에 이용할 것을 제안한다. 논리와 추론교육을 위해 무엇을 어떻게 가르칠 것인가에 대한 답으로 논리와 추론교육에 적합한 수학적 내용으로 크게 이산수학과 중등 기하의 초등화하여 탐구하도록 하는 내용을, 교육 방법 측면에서는 논리와 추론 교육을 위한 LOGO 기반 마이크로월드를 설계, 이용하여 수학적 사고력을 신장시키고자 한다. 여기까지가 수학적 사고력을 위한 가능성을 모색한 것이라면 후속연구로 이러한 가능성을 실험연구로 검증하고자 한다.

• Journal of the Korea Society of Computer and Information
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• v.27 no.7
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• pp.35-48
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• 2022

In this study, it propose a proof theory method for expressing and reasoning knowledge in a multiagent environment. Since this method determines logical results in a mechanical way, it has developed as a core field from early AI research. However, since the proposition cannot always be proved in any set of closed sentences, in order for the logical result to be determinable, the range of expression is limited to the sentence in the form of a clause. In addition, the resolution principle, a simple and strong reasoning rule applicable only to clause-type sentences, is applied. Also, since the proof theory can be expressed as a meta predicate, it can be extended to the metalogic of the proof theory. Metalogic can be superior in terms of practicality and efficiency based on improved expressive power over epistemic logic of model theory. To prove this, the semantic method of epistemic logic and the metalogic method of proof theory are applied to the Muddy Children problem, respectively. As a result, it prove that the method of expressing and reasoning knowledge and common knowledge using metalogic in a cooperative multiagent environment is more efficient.

• Journal of Korean Philosophical Society
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• v.147
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• pp.215-237
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• 2018

The purpose of this study is to illuminate the precise nature and the central line of Kant's proof of the causal principle stated in the Second Analogy of the 2nd. edition of the Critique of Pure Reason. The study argues for the following thesis: 1. The proof of the Second Analogy concerns only the causal principle called the "every-event-some-cause" principle, and not the causal law(s) called the "same-cause-same-event" principle. 2. The goal of the proof is to establish the possibility of knowledge of an temporal order of successive states of an object. 3. The proof is broadly an single transcendental argument in two steps. The 1st. step is an analytic argument that infers from the given perceptions of an oder of successive states of an objects to the conclusion that the causal principle is the necessary condition for the objectivity of dies perceived order. The 2nd. step is a synthetic argument that infers from the formal nature of time to the conclusion that the causal principle is a necessary condition for die possibility of objective alterations and of empirical knowledge of these alterations. 4. The poof involves not the 'non sequitur' assumed by P. F. Strawson, that is, Kant infers not directly from a feature of our perceptions to a conclusion regarding the causal relations of distinct states of affairs that supposedly correspond to these perceptions.