• School Mathematics
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• v.18 no.1
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• pp.215-229
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• 2016

This study aims to identify Archimedes' idea used while proving proposition 23 in 'Quadrature of the Parabola' and to provide an alternative way for finding the sum of geometric series without applying the concept of limit by extending the idea though metaphor. This metaphorical model is characterized as static and thus can be complimentary to the dynamic aspect of limit concept adopted in Korean high school mathematics textbooks. In addition, middle school students can understand $0.999{\cdots}=1$ with this model in a structural way differently from the operative one suggested in Korean middle school mathematics textbooks. In this respect, I argue that the metaphorical model can be an useful educational tool for Korean secondary students to overcome epistemological obstacles inherent in the concepts of infinity and limit by making it possible to transfer from geometrical context to algebraic context.

• School Mathematics
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• v.5 no.1
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• pp.135-149
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• 2003

We present an understanding about students' conceptual model of differential equations, based on the discourse data that were collected in a differential equations course at a university in Korea. An interpretive approach is taken to analyze classroom discourse. This paper consists of three main parts. First, we completely analyze the students' use of conceptual metaphor in a university differential equations class. Secondly, we identify conceptual metaphors representing students' conceptual model of differential equations. Finally, we describe the mathematical characteristics of the conceptual metaphors identified in detail. Among other things, this paper reveals that there exists dual aspects of the students' conceptual model of differential equations. In other words, in the differential equations course observed we found that the students very often used two kinds of conceptual metaphor,“machine metaphor”and“fictive motion metaphor”, that have contrastingly different mathematical characteristics. In order to interpret the duality, we take a sociocultural perspective, and this perspective suggests and helps us to realize the significance of understanding of cognitive diversity in mathematics classroom.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.10
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• pp.4348-4353
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• 2011

This paper is based on the Cognitive Linguistics point of view on metaphor. Metaphors are not a matter of language use or rhetorics but of a conceptual frame, where thoughts work. The conceptual frames can highlight one aspect affecting our lives while hiding the other aspect of the facts. Politicians use metaphors to persuade people and justify their political decisions. Lakoff argues that the Republicans in the U.S. have their own conceptual framework based on the 'strict father model' of the conservatives, which can be found in important political speeches. Political metaphors supporting this view are found in the 'Attack on Iraq Speech' by G. H. Bush in 1991 and 'Operation Iraqi Freedom Address' by G. W. Bush in 2003.

• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.57-71
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• 2010

Similarity between concept and concept, principle and principle, theory and theory is known as a strong motivation to mathematical knowledge construction. Metaphor and analogy are reasoning skills based on similarity. These two reasoning skills have been introduced as useful not only for mathematicians but also for students to make meaningful conjectures, by which mathematical knowledge is constructed. However, there has been lack of researches connecting the two reasoning skills. In particular, no research focused on the interplay between the two in didactic transposition. This study investigated the process of knowledge construction by metaphor and analogy and their roles in didactic transposition. In conclusion, three kinds of models using metaphor and analogy in didactic transposition were elaborated.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.221-237
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• 2004

This research analyzed mathematical discourse of the students in an RME-based differential equations course at a university in order to investigate the social transformation of the students' conceptual model of differential equations. The analysis focused on the change in the students' use of conceptual metaphor for differential equations and pedagogical factors promoting the change. The analysis shows that discrete and quantitative conceptual model was prevalent in the beginning of the semester However, continuous and qualitative conceptual model emerged through the negotiation of mathematical meaning based on the inquiry of context problems. The participation in the project class has a positive impact on the extension of the students' conceptual model of differential equations and increases the fluency of the students' problem solving in differential equations. Moreover, this paper provides a discussion to identify the pedagogical factors Involved with the transformation of the students' conceptual model. The discussion highlights the sociocultural aspect of teaching and learning of mathematics and provides implications to improve teaching of mathematics in school.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.3
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• pp.431-456
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• 2016

The purpose of this study is to investigate the appropriate time of introduction and the usage of the number line, in order to suggest the right point of learning the number concept to the elementary school students. For the efficient achievement of this purpose, we investigated the mathematical models for constructing the number concept such as number line, empty number line and double number line, counting and development of number concept. Then, we conducted case study on the time of introduction and the usage of the number line. Finally, we analyzed the result. First, there is need for adjustment to conduct the introduction of the number line from the second year of elementary school, so to help the students understand the continuing number concept through the understanding on the metaphorical concept of the number line. Second, there is the need of positive introduction and the use on the mathematical models; empty number line which helps to draw various thinking strategy visually through the process of operations such as addition and subtraction; the division into equal part and division by equal part in which multiplicative comparative situation or division takes place; the double number line which helps to understand the rate or proportional distribution. Finally, when adopting the number line, the empty number line, or the double number line, we suggested the necessity of learning about elaborate guidance and the usage in order to fully understand the metaphorical concept of the number line.

• Cartoon and Animation Studies
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• s.5
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• pp.485-489
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• 2001

본 작품은 사실적 표현, 즉 실사에 근거한 분위기의 애니메이션에 관한 관점에서 시작한다. 물론 애니메이션에서는 생략과 과장이 자유로우며 풍자적이고 은유적인 분위기를 연출하는 것이 특징이다. 즉 사실성보다는 허구적이며 과장된 표현으로 왜곡을 가함으로써 관객들에게 극적 효과를 유발한다. 하지만 관객은 사실적이지 않은 허구인 것을 알면서도 자유로운 상상력의 오락적 분위기에 흥미를 갖는다. 아울러 본 작품은 애니메이션의 동인(動因)과 감성과의 관계를 전제로 한 애니메이션의 분석모형 작품이다. 이러한 모델 설계를 통해 대상물의 본질적인 면, 즉 사실성에 근거한 표현정도에 따라 인간의 감성이 달라질 수 있다는 가정 하에 애니메이션에 있어서 프레임 수와 대상물의 단순화 정도에 따라 감성이 어떻게 반응하고 변화하는가를 웹사이트 상에서 조사할 수 있도록 분석모형을 제작하였다. 연구작품을 위해 애니메이션의 동인이라고 할 수 있는 시간, 운동, 공간 중에서 움직임 지각에 영향을 줄 수 있는 타이밍, 즉 속도문제에 대해 프레임 수와 단순화 단계를 애니메이션의 Movement 동인에 대한 조작적 정의에 독립변수로 보았다. 분석모형의 설계는 객관적인 시각에서 대상물의 움직임을 파악할 수 있는 Duration이 짧은 유형의 대상물(말)과 중간정도의 대상물(사람), 그리고 긴 유형의 대상물(거북이)을 표본으로 선정하여 각 대상물마다 4단계의 프레임으로 나누어 좌표상의 Y축에 제작 배열하였다. 한편 단순화 단계는 대상물의 사실성에 선 드로잉에 이르기까지 4단계로 구분${\cdot}$제작하여 X축에 배열하여 각 클립별 감성언어 조사를 인터넷상에서 할 수 있도록 디자인하였다. 한편 각 클립에서 보여지는 표현향식에 대해 느끼는 감성조사는 디자인 관련 감성 형용사 중에서 본 연구에 적합한 감성언어들을 골라 조사 실시하고자 한다.

• Proceedings of the Korea Information Processing Society Conference
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• 2022.05a
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• pp.621-623
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• 2022

최근 코로나19로 인해 비대면으로 소통할 수 있는 플랫폼에 대한 관심이 증가하고 있으며, 가상 세계의 개념을 도입한 메타버스 플랫폼이 MZ세대의 새로운 SNS로 떠오르고 있다. 아바타를 통해 상호 교류가 가능한 메타버스는 텍스트 기반의 소통뿐만 아니라 음성과 동작 시선 등을 활용하여 변화된 의사소통 방식을 사용한다. 음성을 활용한 소통이 증가함에 따라 다른 이용자에게 불쾌감을 주는 혐오 발언에 대한 신고가 증가하고 있다. 그러나 기존 혐오 발언 탐지 시스템은 텍스트를 기반으로 하여 사전에 정의된 혐오 키워드만 특수문자로 대체하는 방식을 사용하기 때문에 음성 혐오 발언에 대해서는 탐지하지 못한다. 이에 본 논문에서는 인공지능을 활용한 음성 혐오 표현 탐지 시스템을 제안한다. 제안하는 시스템은 음성 데이터의 파형을 통해 은유적 혐오 표현과 혐오 발언에 대한 감정적 특징을 추출하고 음성 데이터를 텍스트 데이터로 변환하여 혐오 문장을 탐지한 결과와 결합한다. 향후, 제안하는 시스템의 현실적인 검증을 위해 시스템 구축을 통한 성능평가가 필요하다.

• Journal for History of Mathematics
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• v.30 no.4
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• pp.247-258
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• 2017

The goal of this essay is to examine metaphors for mathematics and to discuss philosophical problems related to them. Two metaphors for mathematics are well known. One is a tree and the other is a building. The former was proposed by Pasch, and the latter by Hilbert. The difference between these metaphors comes from different philosophies. Pasch's philosophy is a combination of empiricism and deductivism, and Hilbert's is formalism whose final task is to prove the consistency of mathematics. In this essay, I try to combine two metaphors from the standpoint that 'mathematics is a part of the ecosystem of science', because each of them is not good enough to reflect the holistic mathematics. In order to understand mathematics holistically, I suggest the criteria of the desirable philosophy of mathematics. The criteria consists of three categories: philosophy, history, and practice. According to the criteria, I argue that it is necessary to pay attention to Pasch's philosophy of mathematics as having more explanatory power than Hilbert's, though formalism is the dominant paradigm of modern mathematics. The reason why Pasch's philosophy is more explanatory is that it contains empirical nature. Modern philosophy of mathematics also tends to emphasize the empirical nature, and the synthesis of forms with contents agrees with the ecological analogy for mathematics.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.3
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• pp.193-200
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• 2021

This study was conducted to explore factors for evaluating creative problem-solving ability and to identify measurement items. After reviewing the previous study, a questionnaire was conducted, and from that, 7 factors and 26 preliminary questions were obtained. Regarding the creative problem-solving ability, problem-discovery ability, idea generation ability, idea evaluation ability, and idea execution ability were confirmed in the problem-solving process. In addition, the factors of interaction ability between problem solving practitioners and creative efficacy of problem solving practitioners were explored. Finally, in the above results, metaphors and figurative cognitive thinking ability and evaluation items for creative problem-solving ability of HTE creative education model were presented. Through subsequent studies, we hope to serve as the groundwork of the evaluation model of HTE creative education.