• Korean Journal of Logic
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• v.12 no.2
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• pp.59-88
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• 2009

According to David Hume, a deductive demonstration for inductive inference is not possible, because inductive inference is not deductive; and an inductive demonstration for inductive inference is not possible either, because such a demonstration is circular. Thus, on his view, there is no way of justifying inductive inference. Ever since Hume raised this problem of induction, a fair number of philosophers have tried to solve it. Nevertheless there is still no solution which is plausible enough to receive wide endorsement. According to Wilfrid Sellars, we cannot justify inductive inference by any theoretical reasoning; we can vindicate it only by a certain sort of practical reasoning. In this paper, I defend this Sellarsian proposal by developing and explaining it.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.461-472
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• 2015

Korean students are taught area formulas of parallelogram and triangle by inductive reasoning in current curriculum. Inductive thinking is a crucial goal in mathematics education. There are, however, many problems to understand area formula inductively. In this study, those problems are illuminated theoretically and investigated in the class of 5th graders. One way to teach area formulas is suggested by means of process of problem solving with transforming figures.

• Journal of Korean Philosophical Society
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• v.141
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• pp.187-202
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• 2017

The aim of this paper is to clarify the difference between the concept of deduction-induction and Aristotle's concept of syllogismos-epagoge. First, Aristotle does not use the expression 'invalid syllogismos'. But a valid deduction is distinguished from a invalid deduction in modern logic. Second, from Aristotle's point of view syllogismos is paralleled by epagoge. Because syllogismos is equivalent to epagoge in logical form. But a disturbing lack of parallelism exists between deduction and induction by which the standards for establishing inductive conclusions are more demanding than those for deductive ones. Third, instructors in introductory logic courses ordinarily stress the need to evaluate arguments first in terms of the strength of the conclusion relative to the premises. Accordingly, students may be told to assume that premises are true. But Aristotle does not assume that premises are true. A syllogismos start from the conceptually true premise and a epagoge start from the empirically true premise.

• Journal of the Korean Society for Library and Information Science
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• v.28
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• pp.267-286
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• 1995

불리언 논리에 기초한 현재 정보검색 시스템은 두 가지 본질적인 문제점 - 1)부정확하거나 불완전한 질의 표현과 2)일관성 없는 색인 - 이 있다. 많은 연구자들이 신경망조직(neural network) 이 정보경색에 있어서 불완전한 질의표현 문제를 해결할 수 있다고 주장해 온 반면 일관성 없는 문제는 아직 해결하지 못한 채 남아있다. 본고에서는 이러한 두 가지 문제점을 해결하기 위해 신경망 조직과 귀납학습이 소개되고 있다. 또한 이 논문에서는 신경망 조직이 어떻게 귀납학습과 통합해서 효율적인 정보 검색시스템에 응용될 수 있는지를 보여주고 있다.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.23-48
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• 2007

This study begins from posing a problem, 'formal introduction of mathematical induction in school mathematics'. Most students may learn the mathematical induction at the level of instrumental understanding without meaningful understanding about its meaning and structure. To improve this didactical situation, we research on the historical progress of mathematical induction from implicit use in greek mathematics to formalization by Pascal and Fermat. And we identify various types of thinking included in the developmental process: recursion, regression, analytic thinking, synthetic thinking. In special, we focused on the role of regression in mathematical induction, and then from that role we induce the implications for teaching mathematical induction in school mathematics.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.109-124
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• 2004

대학수학에서 수학적귀납법의 원리를 소개하고 풍부한 예를 통해 이해를 돕는다. 특별히 교양수학을 수강하는 1학년 학생 수준에 맞게 매스매티카 프로그램을 이용하여 구체적인 예를 갖고 한단계 한단계 접근하여 수학적귀납법의 증명을 연습할 기회를 준다. 증명을 단계적으로 하는 것을 연습하여 학생들은 논리적인 사고능력을 개발하고 새로운 명제를 발견할 수 있는 기회를 맞보게 한다. 물론, 증명 연습은 1학년 신입생에게는 쉽지 않으나 여러 명제에 대해 연습을 하는 것은 수학적, 논리적 사고 능력을 개발하고 증명문제에 대한 인식을 바꾸는데 매우 중요한 역할을 할 것이다.

• Communications of Mathematical Education
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• v.15
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• pp.153-159
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• 2003

수학 학습의 목표를 수학적 사고력의 신장이라는 측면에서 보았을 때 이를 위하여 문제에 대한 다양한 해법을 찾는 활동은 중요하다. 문제에 대한 다양한 접근은 문제해결의 전략을 학습시키고 사고의 유연성을 길러줄 수 있는 방법이 된다. 문제에 대한 다양한 해법을 찾는 과정에서 이미 알고 있는 지식이 어떻게 응용되는지를 알게 된다. 특히 기하 문제에 대한 다양한 접근은 문제해결의 전략을 학습시킬 수 있는 좋은 예가 된다. 본고에서는 문제해결을 통한 수학적 일반성을 발견하기 위한 방법으로서 문제에 대한 다양한 해법을 연역과 귀납에 의하여 일반화하는 과정을 탐색하고자 한다. 특히 수학 문제에 대한 다양한 해법을 찾는 것은 문제해결 전략으로서 뿐만 아니라 창의적 사고의 신장 측면에서 시사점을 던져준다.

• 발명특허
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• v.5 no.7 s.53
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• pp.20-22
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• 1980

중세과학자가 크롬비(A.C Crombie)에 따르면 중세는 과학과 기술, 그리고 과학의 방법에서 모두 진전을 보였다. 먼저 합리적 설명의 개념, 특히 수학의 이용의 회복은 어떻게 이론을 세우고 검증 또는 반증하는 가의 문제를 제기했다. 이 문제는 스콜라적인 귀납이론과 실험적 방법에 의해 해결되었다. 그 예는 13, 14세기의 광학과 자기학에서 볼 수 있다.

• Journal of Educational Research in Mathematics
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• v.24 no.1
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• pp.1-27
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• 2014

In the present study, we analyze the four participating 9th grade students' mathematical reasoning processes in their dragging activities while solving open-ended geometry problems in terms of abduction, induction and deduction. The results of the analysis are as follows. First, the students utilized 'abduction' to adopt their hypotheses, 'induction' to generalize them by examining various cases and 'deduction' to provide warrants for the hypotheses. Secondly, in the abduction process, 'wandering dragging' and 'guided dragging' seemed to help the students formulate their hypotheses, and in the induction process, 'dragging test' was mainly used to confirm the hypotheses. Despite of the emerging mathematical reasoning via their dragging activities, several difficulties were identified in their solving processes such as misunderstanding shapes as fixed figures, not easily recognizing the concept of dependency or path, not smoothly proceeding from probabilistic reasoning to deduction, and trapping into circular logic.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.641-654
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• 2011

In order to grow students' rational and creative problem-solving ability which is one of the primary goals in mathematics education. students' proper understanding of mathematical concepts, principles, and rules must be backed up as its foundational basis. For the relevant teaching strategies. National Mathematics Curriculum advises that students should be allowed to discover and justify the concepts, principles, and rules by themselves not only through the concrete hands-on activities but also through inquiry-based activities based on the learning topics experienced from the diverse phenomena in their surroundings. Hereby, this paper, firstly, looks into both the meaning and the inductive reasoning process of mathematical principles and rules, secondly, suggest "learning through discovery teaching method" for the proper teaching of the mathematical principles and rules recommended by the National Curriculum, and, thirdly, examines the possible discovery-led teaching strategies using inductive methods with the related matters to be attended to.