• Communications of Mathematical Education
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• v.14
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• pp.43-60
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• 2001

수학적 기호는 수학이라는 특수한 분야에 한정되어 사용되는 언어라고 할 수 있다. Usiskin(1996)은 수학을 쓰고 수학적 의미를 의사 소통하는 데에 기호가 그 수단이 되기 때문에 수학 또한, 수학적 기호로 만들어진 언어라고 말하였다. 그러나, 수학적 언어와 일상 언어사이의 이중성 때문에 언어로써 수학 기호는 학생들을 힘들게 만든다. 교사에게는 의미 있는 기호일지라도 학생들에게는 친숙하지 않을 수 있기 때문에, 많은 학생들이 자신들의 수학적 사고를 표현하거나 개념을 반영하거나 또는 아이디어를 확장하기 위해, 수학을 말하고, 읽고, 이해하고 쓰는 데에 어려움을 겪고 있다. 따라서, 본 연구는 학생들이 기호체계에 능숙해지도록 도와주고, 수학 학습과 문제 해결을 위해 수학 기호 언어가 의미 있고 접근하기 쉬운 의사소통 매체가 되게 하기 위하여 언어적 접근에 의하여 수학적기호의 교수-학습지도 방법에 대하여 살펴보고자 한다.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.461-481
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• 2009

The semiotic approach to the mathematics education has been studied in last 20 years by PME, ICME conferences. New cultural developments in multi-media, digital documents and digital arts and cultures may influence mathematical education and teaching and learning activities. Hence semiotical interest in the mathematics education research and practice will be increasing. In this paper the basic ideas of semiotics, such as Peirce triad and Saussure's dyad, are introduced with some mathematical applications. There is some similarities between traditional research topics for concept, representation and social construction in mathematics education research and semiotic approach topics for the same subjects. some semiotic applications for an arithmetic problem for work, induction, deduction and abduction syllogisms with respect to Peirce's triad, its meaning in scientific discoveries and learning in geometry and symmetry.

• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.165-180
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• 2011

Mathematical symbols concisely represent mathematical contents related to terms by describing their mathematical meanings implicitly. All symbols in elementary school mathematics textbooks are stated as to be read so that elementary school students could understand their mathematical meanings. The same is somewhat true as in middle school mathematics textbooks, however it is often the case that some symbols are difficult to be read and understood because their statements are unclear or different. In this study, we analyze problems and suggest implications on teaching and learning mathematics based on the statements and understanding of reading symbols in middle school mathematics textbooks.

• School Mathematics
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• v.7 no.1
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• pp.55-75
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• 2005

Mathematical symbolizing is an important part of mathematics learning. But many students have difficulties m symbolizing mathematical ideas formally. If students had experiences inventing their own mathematical symbols and developing them to conventional ones natural way, i.e. learning mathematical symbols via expressive approaches, they could understand and use formal mathematical symbols meaningfully. These experiences are especially valuable for students who meet mathematical symbols for the first time. Hence, there are needs to investigate how early elementary school students can and should experience meaningful mathematical symbolizing. The purpose of this study was to analyze students' mathematical symbolizing processes and characteristics of theses. We carried out teaching experiments that promoted meaningful mathematical symbolizing among eight first graders. And then we analyzed students' symbolizing processes and characteristics of expressive approaches to mathematical symbols in early elementary students. As a result, we could places mathematical symbolizing processes developed in the teaching experiments under five categories. And we extracted and discussed several characteristics of early elementary students' meaningful mathematical symbolizing processes.

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.463-483
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• 2003

In the learning of mathematics, students experience the semiotic activities of representing and interpreting mathematical signs. We called these activities as the representing and interpreting of mathematical signs. On the foundation of Peirce's three elements of the sign, we analysed that students constructed the representamen to interpret the concept of correlation as for the object, "as one is taller, one's size of foot is larger" 4 middle school students who participated the gifted center in Seoul, arranged the statistical data, constructed their own representamen, and then learned the conventional signs as a result of the whole class discussion. In the process, students performed the detailed representing and interpreting of signs, depended on the templates of the known signs, and interpreted the process voluntarily. As the semiotic activities were taken place in this way, it was needed that mathematics teacher guided the representing and interpreting of mathematical signs so that the representation and the meaning of the sign were constructed each other, and that students endeavored to get the negotiation of the interpretants and the representamens, and to reach the conventional representing.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.45-60
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• 2009

Mathematical thinking can be symbolized by the external signs, and these signs determine in reverse the form of mathematical thinking. Each symbol - a symbol in algebra, a symbol in analysis, and a diagram which verifies syllogism - reflects the diverse characteristic of cogitation in mathematics and perfirms a heuristic function.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.663-678
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• 2017

Semiotic studies in mathematical education have been based on Saussure, Peirce, and Frege and many prior researches have explored the concepts in a perspective of semiotics. However, the relationship among semiotical elements and the formation and the evolution of a conception are still ambiguous and veiled in many aspects. This thesis is intended to show how a conception was formed and evolved by expression, which is an element of semiotics. In this process, I sought to partially illuminate the relationship among expressions, concepts, and objects.

• School Mathematics
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• v.19 no.1
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• pp.189-208
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• 2017

The purpose of this study is to capture and explain the roles that signs and attention play in the fraction learning process, through a previous study that employs Deleuze's perspective on sign and the role of attention. From this case study of elementary school students, we found that signs are a prerequisite for learning and that learning takes place as different forms of attention shifts. The various types of semiotic resources used by teachers and students have been found to play an important role in coordinating collective attention between teachers and students.

• School Mathematics
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• v.18 no.3
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• pp.611-623
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• 2016

This study explored the problems of definitions and choices of terms and notations and proposed a few tasks for improvement of them included , , of high school mathematics based on 2009 revised mathematics curriculum and textbooks. We explored the problems on the features of the methods and contents of definitions of terms and notations in the viewpoint of the possibilities of difficulties on students' understanding, and proposed several criteria for choices of terms and notations in curriculum. And we proposed several tasks to improve the problems as follows: we need to implement much analyses and discussions on terms and notations and to open the results, to make the criteria for the examinations of mathematics textbooks in the viewpoint of therm and notation, to consider the differences of the methods of definitions among primary, middle, and high schools, and to consider the changes of terms and notations and the methods for introduction of them in textbooks.

• School Mathematics
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• v.5 no.1
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• pp.59-76
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• 2003

Algebraic signs are important on learning and problem solving of algebra. This study investigated the contents of letters and expressions in textbooks by syntactics, semantics and pragmatics, and considered the introduction and extension processes of algebraic signs didactically. We also categorized the signs, and looked into textbook problems in view of semiotic. The result is that textbook is constructed in syntactics and semantics. Finally, the assessment of 7th grade students' competence in syntactics, semantics, syntactics+- semantics, pragmatics, and problem solving shows that students' ability in syntactics and pragmatics Is a predictive variable for algebraic problem solving.