• Korean Journal of Logic
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• v.2
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• pp.91-118
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• 1998

라이프니츠는 일반적으로 현대논리학의 선각자라고 부른다. 그래서 라이프니츠 논리학에서는 현대 논리학을 이해함에 있어서 중요한 단초들을 발견할 수 있다. 라이프니츠의 논리학을 대표하는 개념으로는 흔히 보편수학, 보편기호학 그리고 논리연산학을 들곤한다. 라이프니츠의 보편수학의 이념은 연대 논리학이 논리학과 수학의 통일에서 출발할 수 있는 결정적인 근거를 제공했다. 이러한 현대 논리학의 출발에 있어서는 상이한 두 입장을 발견할 수 있는데, 부울, 슈레더의 논리대수학과 프레게의 논리학주의가 바로 그것이다. 이 두 입장은 "논리학과 수학의 통일"에 있어서는 공통적인 관심을 보이지만, 논리학의 본질을 라이프니츠의 보편기호학에서 찾느냐 또는 라이프니츠의 논리연산학에서 찾느냐에 따라 상이한 입장을 취한다. 이외에도 보편과학이나 조합술을 이해하지 않고는 라이프니츠 논리학에 대한 총체적인 시각을 갖기 힘들다. 이 두 개념은 특히 타과학이나 과학적 방법론과 관련지어 논리학이란 과연 무엇인가라는 논리철학적인 조명에 있어서 중요한 실마리를 제공한다.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.77-94
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• 2011

This study aims to provide a teaching strategy accommodating the symbols of the definite integral and guiding students through the meaning of notations in area and volume calculations, based on characterization as to how students comprehend the symbols used in the Riemann sum formula and the definite integral, and their interrelationship. A survey was conducted on 70 high school students regarding the historical background of integral symbols and the textbook contents designated for the definite integral. In the following analysis, the comprehension was qualified by 5 levels; students in higher levels of comprehension demonstrated closer relation to the history of integral notations. A teaching strategy was developed accordingly, which suggested more desirable student understanding on the concept of definite integral symbols in area and volume calculations.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.459-475
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• 2012

Epistemology in which only subject and object of cognition exist can't play a role well in the society. In this paper we analyze structuralism which discusses linguistic and social conditions that make subject of cognition possible and semiologic epistemology's philosophical base with three keywords: subject, structure and discourse. Signification by the signs' relation not object of cognition and construct of subject make meaning of sign in network of signs. The construct exists before subject and subject can exist in the structural order. In understanding and analyzing learning of mathematics, this point of view makes you consider the other problems besides construction by subject.

• School Mathematics
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• v.10 no.2
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• pp.223-257
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• 2008

To understand terms and symbols correctly which is the basic factor of teaming mathematics is important for understanding and utilizing related mathematic contents. Since the definition of terms and symbols is the important starting point of learning mathematics, it has been studied a lot since the ancient times. This study investigates the transition of terms and symbols which was presented in our curriculum after Korea's independence and it also investigates terms and symbols which are used for the current middle school text books. As a result of studying the transition of the terms, more detailed and broader analysis should be done for the explanation, modification, deletion, and creation of the terms. And complements are needed for some of the terms and symbols. Also, some definition of the terms which are used in some of the current middle school text books should be explained in a way that is suitable for the students' capability. And some errors and omissions of the terms need to be corrected. Furthermore, we need to compare our definition of terms with that of the other countries and modify them if it is necessary. Also, It is better to put guidelines about the interpretation of terms and symbols in the curriculum to reduce the confusion which can be produced by the variety of explanation of the definition of terms and symbols.

• School Mathematics
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• v.16 no.2
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• pp.303-315
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• 2014

Even though the variety of expressions are dealt with in Korean elementary mathematics, the systematization of the subject matter of expressions is still insufficient. This is basically due to the failure of revealing clearly the identity of expressions dealt with in elementary mathematics. In this paper, as a groundwork to improve this situation, after the classification of signs as elements constituting expressions, in a position to consider elementary mathematics using transitional signs such as ${\square}$, ${\triangle}$, etc and words or phrases in expressions, expressions were defined and classified based on that classification of signs. It can be presented as the conclusion that the following four judgements which helps to promote the systematization of the subject matter of expressions are possible through this definition and classifications. First, by clarifying the identity of the expressions, any mathematical clauses or sentences can be determined whether those are expressions or not. Second, Forms of expressions can be identified. Third, the subject matter of expressions can be identified systematically. Fourth, the hierarchy of the subject matter of expressions can be identified.

• School Mathematics
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• v.11 no.2
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• pp.301-316
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• 2009

There are two distinct processes, definite integral and indefinite integral, in the integral calculus. And the term 'integral' has two meanings. Most students regard indefinite integrals as definite integrals with indefinite interval. One possible reason is that calculus textbooks do not concern the meaning in the relationship between definite integral and indefinite integral. In this paper we investigated the historical development of concepts of definite integral and indefinite integral, and the relationship between the two. We have drawn pedagogical implication from the result of analysis.

• The Mathematical Education
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• v.3 no.8
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• pp.11-12
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• 1965

• Proceedings of the Korea Society of Elementary Mathematics Education
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• 2010.08a
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• pp.105-124
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• 2010

• Journal for History of Mathematics
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• v.18 no.3
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• pp.91-106
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• 2005

History of mathematics must be analysed to discuss mathematical reality and thinking. Analysis of history of mathematics is the method of understanding mathematical activity, by these analysis can we know how historically mathematician' activity progress and mathematical concepts develop. In this respects, we investigate teaching algebra through historico-genetic analysis and propose historico-genetic analysis as alternative method to improve of teaching school algebra. First the necessity of historico-genetic analysis is discussed, and we think of epistemological obstacles through these analysis. Next we focus two concepts i.e. letters(unknowns) and negative numbers which is dealt with school algebra. To apply historico-genetic analysis to school algebra, some historical texts relating to letters and negative numbers is analysed, and mathematics educational discussions is followed with experimental researches.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.595-605
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• 2014

Infinite decimals have an infinite number of digits, chosen arbitrary and independently, to the right side of the decimal point. Since infinite decimals are ambiguous numbers impossible to write them down completely, the infinite decimal representation accompanies unavoidable opaqueness. This article focused the transparent aspect of infinite decimal representation with respect to the completeness axiom of real numbers. Long before the formalization of real number concept in $19^{th}$ century, many mathematicians were able to deal with real numbers relying on this transparency of infinite decimal representations. This analysis will contribute to overcome the double discontinuity caused by the different conceptualizations of real numbers in school and academic mathematics.