• 한국수학교육학회지시리즈D:수학교육연구
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• 제12권1호
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• pp.1-26
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• 2008

The concept field is defined as the schema of all equivalent definitions of a mathematics concept. Concept system is defined as the schema of a group concept network where there are mathematics relations. Proposition field is defined as the schema of all equivalent proposition sets. Proposition system is defined as a schema of proposition sets where one mathematics proposition at least is "derived" from the other proposition. CPFS structure that consists of concept field, concept system proposition field, proposition system describes more precisely mathematics cognitive structure, and reveals the unique psychological phenomena and laws in mathematics learning.

• East Asian mathematical journal
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• 제23권3호
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• pp.313-326
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• 2007

The purpose of education of propositional logic is to understand the basic structure of the mathematics and to improve the logical thinking in normal life. But in the seventh curriculum, some basic terms, for examples $\wedge$ and $\vee$, are not introduced, the proposition $p{\\rightarrow}q$ is not defined properly, and use the wrong term $\Rightarrow$ so that it is difficult to understand the propositional logic. In this paper, we present a suitable content for the propositional logic in high-school mathematical class. We also present a proper definition of the proposition $p{x}{\Rightarrow}q{x}$ without using the notation $\rightarrow$. We finally give proper definitions of necessary conditions, sufficient conditions, and necessary and sufficient conditions.

• 대한수학회보
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• 제43권1호
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• pp.225-225
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• 2006

In this note a modification of Proposition 3.10 of [1] is given.

• East Asian mathematical journal
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• 제32권4호
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• pp.483-500
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• 2016

Ancient Greek mathematician Euclid left three books about mathematics. It's 'The elements', 'The data', 'On divisions of figure'. This study is based on the analysis of Euclid's 'On divisions of figure'. 'On divisions of figure' is a book about the construction of the shape. Because, there are thirty six proposition in 'On divisions of figure', among them 30 proposition are for the construction. In this study, based on the 'On divisions of figure' we explore the direction for construction education. The results were as follows. First, the proposition of 'On divisions of figure' shall include the following information. It is a 'proposition presented', 'heuristic approach to the construction process', 'specifically drawn presenting', 'proof process'. Therefore, the content of textbooks needs a qualitative improvement in this way. Second, a conceptual basis of 'On divisions of figure' is 'The elements'. 'The elements' includes the construction propositions 25%. However, the geometric constructions contents in middle school area is only 3%. Therefore, it is necessary to expand the learning of construction in the our country mathematics curriculum.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제30권3호
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• pp.393-418
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• 2016

명제를 반박하는 과정에서 생성되는 반례는 명제가 거짓이라는 추론의 타당성을 보이는 방법이자 수학교수 학습 측면에서도 수학적 사고력 향상에 중요한 역할을 기대하고 있다. 이에 본 연구에서는 현 교과서에서 다루어지고 있는 반례 활용에 대해 살펴보고, 학교 현장에서 교육학적 전략으로 활용할 수 있는 반례 활용 교육을 위한 자료를 개발하였다. 개발 자료는 거짓 명제 만들기와 참인명제 만들기로 구성하였고, 학생들에게 반례 활용 실험 수업을 통해 학생들의 반응을 살펴보았다. 연구 결과 정의적 영역의 측면에서는 명제에 관한 흥미를 높이고 자신감을 향상시키는 효과가 있었으며, 인지적 영역의 측면에서는 다양한 반례를 찾고 그 반례를 탐구하여 참인 명제를 만들어 보는 다양한 수학적 추론 활동을 통해 명제에 대한 유연한 사고와 함께 명제의 조건을 명확히 인지하면서 명제 개념을 학습하는데 도움이 되는 것으로 나타났다.

• 대한수학교육학회지:수학교육학연구
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• 제18권1호
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• pp.123-135
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• 2008

본 연구에서는 고등학교 과정에서 다루어지는 수학적 귀납법 증명의 대표적인 예제들을 이해하고 증명하는데 필요한 스키마를 분석하고, 그에 대한 학생들의 구성 여부를 조사하였다. 함수 스키마와 명제치 함수 스키마의 구성은 함의치 함수 스키마와 긍정 논리식 스키마의 구성에 선행하며 함의치 함수 스키마와 긍정 논리식 스키마는 수학적 귀납법 스키마를 위해 통합적으로 조절되어야 한다는 점도 확인하였다. 이를 바탕으로 하여 수학적 귀납법에 대한 학생들의 이해 수준은 $1{\sim}4$ 수준으로 설정될 수 있었다. 또한 이러한 이해 수준과 관련하여 수학적 귀납법을 학습하면서 겪는 학생들의 인지적 어려움이 분석되었다.

• 인문언어
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• 제2권2호
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• pp.301-319
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• 2002

In a recent paper, I have proposed an analysis concerning propositions and 'that'-clauses as a solution to Kripke's puzzle and other similar puzzles, which I now call 'the Indefinite Description Analysis of Belief Ascription Sentences.' I have listed some of the major advantages of this analysis besides its merit as a solution to the puzzles: it is amenable to the direct-reference theory of proper names; it does not nevertheless need to introduce Russellian (singular) propositions or any other new entities. David Lewis has constructed an interesting argument to refute this analysis. His argument seems to show that my analysis has an unwelcome consequence: if someone believes any proposition, then he or she should, ipso facto, believe any necessary (mathematical or logical) proposition (such as the proposition that 1 succeeds 0). In this paper, I argue that Lewis's argument does not pose a real threat to my analysis. All his argument shows is that we should not accept the assumption called 'the equivalence thesis': if two sentences are equivalent, then they express the same proposition. I argue that this thesis is already in trouble for independent reasons. Especially, I argue that if we accept the equivalence thesis then, even without my analysis, we can derive a sentence like 'Fred believes that 1 succeeds 0 and snow is white' from a sentence like 'Fred believes that snow is white.' The consequence mentioned above is not worse than this consequence.

• Korean Journal of Mathematics
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• 제17권1호
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• pp.43-52
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• 2009

The Galois ring is a finite extension of the ring of integers modulo a prime power. We consider characters on Galois rings. In analogy with finite fields, we investigate complete Gauss sums over Galois rings. In particular, we analyze [1, Proposition 3] and give some lemmas related to [1, Proposition 3].

• 한국수학교육학회지시리즈D:수학교육연구
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• 제16권2호
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• pp.107-123
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• 2012

A group of twenty-nine high school student-teachers were given a set of mathematical propositions focusing on shape-to-shape transformations. Their task was to determine through hands-on manipulation and use of dynamic software that each shape be transformed into an area equivalent rectangular region. This paper reports on a classroom-based research.

• 한국수학교육학회지시리즈A:수학교육
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• 제32권2호
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• pp.151-155
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• 1993

The purpose of this study is to point out and improve problems about proposition in the fifth curriculum and to present the direction of revision for the sixth curriculum. The method taken in this study was the analysis of written questions.