• School Mathematics
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• v.4 no.4
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• pp.539-554
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• 2002

Mathematics is constructed by many signs, and learning mathematics involves the understanding and uses of them. This study reflects mathematical signs and their meanings, and considers how they can be introduced in learning. For these, we first investigated epistemological positions as Piaget, Vygotsky, anthropology, and interactionism. And we investigated semiotic models that Saussure and Peirce built each. Among these we adopted Peirce' triadic model that is consisted of interpretant, object (referent), and represen tamen(sign). In mathematic learning process, representations are transformed by translations and meanings are growed to the representation of another sign. And the meaning of sign grows by learner's interpretation. In terms of theoretical grounds, we settled that the understanding of mathematical signs involved the understanding of their representations and their meanings. On the foundation of above contents, we searched how we introduced signs to students and there were methods that approached to students representationally or inquiringly.

• 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.