• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.239-256
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• 2001

The notion of metaphor has been increasingly popular in research of mathematics education. In particular, metaphor becomes a useful unit for analysis to provide a profound insight into mathematical reasoning and problem solving. In this context, this paper takes metaphor as an analytic unit to examine the relationship between objectivity and subjectivity in mathematical reasoning. Specifically, the discourse analysis focuses on the code switching between literal language and metaphor in mathematical discourse. It is shown that the linguistic code switching is parallel with the switching between two different kinds of mathematical knowledge, that is, factual knowledge and mathematical imagination, which constitute objectivity and subjectivity in mathematical reasoning. Furthermore, the pattern of the linguistic code switching reveals the dialectical relationship between the two poles of mathematical reasoning. Based on the understanding of the dialectical relationship, this paper provides some educational implications. First, the code-switching highlights diverse aspects of mathematics learning. Learning mathematics is concerned with developing not only technicality but also mathematical creativity. Second, the dialectical relationship between objectivity and subjectivity suggests that teaching and teaming mathematics is socioculturally constructed. Indeed, it is shown that not all metaphors are mathematically appropriated. They should be consistent with the cultural model of a mathematical concept under discussion. In general, this sociocultural perspective on mathematical metaphor highlights the sociocultural organization of teaching and loaming mathematics and provides a theoretical viewpoint to understand epistemological diversities in mathematics classroom.

• Journal of Educational Research in Mathematics
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• v.13 no.1
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• pp.13-28
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• 2003

Practice of proof is considered in, the view of language and meta-mathematics, recognizing the role of proof that is the means of communication and development of mathematical understanding. Linguistic components in proof texts are symbol, verbal language and visual text, and contain the implicit knowledge in the meta-mathematics view. This study investigates the functions of linguistic elements according to Halliday's functional grammar and the rhetoric skills in proof texts in math textbook, teacher's note, and student's written text. We need to inquire into the aspects of language for mathematics learning process and the understanding and use of students' language.

• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.493-508
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• 2002

The purpose of this study is to compare the preferences of the school mathematical terms of South Korea and those of North Korea by administering a survey for learners, inservice teachers, and pre-service teachers, to establish the criteria of desirable school mathematical terms, and to evaluate the school mathematical terms of South Korea and those of North Korea based on the criteria. According to the result of the survey, the preferred mathematical terms are different from one group to the other, yet the mathematical terms of South Korea are more preferred. In general, terms written in pure Korean and concise terms which are easily understandable are favored. To discuss about the criteria of desirable school mathematical terms, four perspectives were set up, 1) the semantic perspective and the regulatory perspective, 2) terms written in pure Korean and Chinese letters, 3) terms from everyday language and technical terms, and 4) the consistency. Six criteria were followed from the aforementioned four perspectives. Finally, various school mathematical terms of South and North Korea were reviewed in the angles of the four perspectives and the six criteria.

• The Mathematical Education
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• v.41 no.3
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• pp.329-339
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• 2002

This study analyzes the epistemological meaning of‘social construction’in mathematical instruction. The perspective that consider the cognition of mathematical concept as a social construction is explained by a cyclic scheme of an academic context and a school context. Both of the contexts require a public procedure, social conversation. However, there is a considerable difference that in the academic context it is Lakatos' ‘logic of mathematical discovery’In the school context, it is Vygotsky's‘instructional and learning interaction’. In the situation of mathematics education, the‘society’which has an influence on learner's cognition does not only mean‘collective members’, but‘form of life’which is constituted by the activity with purposes, language, discourse, etc. Teachers have to play a central role that guide and coordinate the educational process involving interactions with learners in this context. We can get useful suggestions to mathematics education through this consideration of the social contexts and levels to form didactical situations of mathematics.

• Journal for History of Mathematics
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• v.29 no.2
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• pp.89-102
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• 2016

Lee Sang, one of the representative poets of Korean Modern Poetry, wrote poems which present the existentialistic modernism in the 1920s, the chaotic era of Korean history. The characteristics of his works have been shown by various points of view. This paper especially explored the meaning and feature of mathematical expressions by numbers, symbols and other signs of mathematics in Lee's poems. His poems are composed by scientific and abstract rules in mathematics which are expressed as mathematical symbols. The paper focuses on analyzing seven poems which maximizes mathematical expressions among his poetry. This kind of work would be the one of ways to figure out the features of mathematics through literature.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.45-55
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• 2014

Lacan gives an explanation on our real actual world by the concepts the "Real", the "Imaginary" and the "Symbolic". Although this three registers are not far from each other, they never can be unified. Among animals, only human has interest in the "truth". The concept of truth is discussed and debated in several contexts, including philosophy and religion. Many human activities depend upon the concept, which is assumed rather than a subject of discussion, including science, law, and everyday life. Language and words are a means by which humans convey information to one another, and the method used to determine what is a "truth" is termed a criterion of truth. Accepting then that "language is the basic social institution in the sense that all others presuppose language", Lacan found in Ferdinand de Saussure's linguistic division of the verbal sign between signifier and signified a new key to the Freudian understanding that "his therapeutic method was 'a talking cure'". The purpose of this paper is to understand Lacan's psychology and psychoanalysis by using the mathematical concepts and mathematical models, especially geometrical and topological models. And re-explanation of the symbolic model and symbols can help students understand new ideas and concepts in the educational scene.

• Journal of Elementary Mathematics Education in Korea
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• v.5 no.1
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• pp.77-98
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• 2001

This study has a purpose to find out how the problem posing activity by presenting the problem situation effects to the mathematical problem solving ability. It was applied in two classes(Experimental group-35, Controlled group-37) of the fourth grade at ‘D’ Elementary school in Bang Jin Chung nam and 40 Elementary school teachers working in Dang Jin. The presenting types of problem situation are the picture type, the language type, the complex type(picture type+ language type), the free type. And then let them have the problem posing activity. Also, We applied both the teaching-teaming plan and practice question designed by ourself. The results of teaching and learning activities according to the type of problem situation presentation are as follows; We found out that the learning activity of the mathematical problem posing was helpful to the students in the development of the mathematical problem solving ability. Also, We found out that the mathematical problem posing made the students positively change their attitude and their own methods for mathematical problem solving.

• The Mathematical Education
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• v.60 no.4
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• pp.529-542
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• 2021

The purpose of this research is to compare the mathematical beliefs that directly or indirectly affect the mathematics learning of Korean languge learners with those of non-Korean languge learners and identify the characteristics. To this end, an analytical comparative research was conducted through a questionnaire survey on perceptions of mathematics learning for 6th grade students of elementary school with different cultural and linguistic backgrounds in the same mathematics classroom. As a result of the analysis, Korean languge learners and non-Korean languge learners gave different meanings to learning mathematics, and they recognized various meanings of success in mathematics. In addition, the math learning ability of non-Korean learners was evaluated higher than that of Korean learners. Based on their positive beliefs, they decided how to resolve conflict situations with different problem-solving results. It will be necessary to prepare a teaching/learning plan that can fully implement multicultural mathematics education in the mathematics classroom where Korean language learners with different cultural and linguistic backgrounds belong. The results of this research can contribute to raising awareness of the need for follow-up researches to find ways to reduce the learning gap between Korean languge learners and non-Korean languge learners. It is expected that this research will contribute to understanding the perceptive characteristics of Korean language learners about learning mathematics and to prepare a plan to utilize them in mathematics lessons.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.21-38
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• 2006

Programmed grammars, one of the most important and well investigated classes of grammars with context-free rules and a mechanism controlling the application of the rules, can be described by graphs. We investigate whether or not the restriction to special classes of graphs restricts the generative power of programmed grammars with erasing rules and without appearance checking, too. We obtain that Eulerian, Hamiltonian, planar and bipartite graphs and regular graphs of degree at least three are pr-universal in that sense that any language which can be generated by programmed grammars (with erasing rules and without appearance checking) can be obtained by programmed grammars where the underlying graph belongs to the given special class of graphs, whereas complete graphs, regular graphs of degree 2 and backbone graphs lead to proper subfamilies of the family of programmed languages.

• The Mathematical Education
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• v.24 no.2
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• pp.35-47
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• 1986

As computer is diffused in society widely, it is desired that we investigate on computer uses in school education. In this paper, Possibility of Micro computer uses in mathematics education is investigated. Educational computing is classified roughly three categories they are CAI CMI and Computer iteracy education. CAI is discussed at this place. Firstly, programs of mathematics educational computing is introduced and they are classified into Practicing, Tutoring, Simulating, Gaming, Demonstration, Informing. Next, the problems that we must notice in mathematics educational computing are indicated. They are computer language, development of soft ware, effectiveness of CAI etc...