• 논리연구
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• 제18권1호
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• pp.39-64
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• 2015

수학적 플라톤주의자가 해결해야 할 가장 큰 문제는 바로 베나세라프가 제기하고 필드가 재정식화한 인식론적 문제라고 할 수 있다. 최근에 밸러궈는 자신의 독특한 형태의 수학적 플라톤주의인 FBP 즉 "혈기 왕성한 플라톤주의"는 이 인식론적 문제를 해결할 수 있다는 논의를 전개했다. 필자는 이 논문에서 그런 논의가 얼마나 성공적인가를 평가하면서 그의 논변이 지닌 문제점들을 살핀다. 우선 필자는 밸러궈 특유의 수학적 플라톤주의가 인식론적 문제를 해결한다는 논변을 형식적 측면에서 비판적으로 분석한다. 그리고 밸러궈의 논변과 전략에 대해 마녀주의의 사례를 통해 보다 본격적 반론을 전개한다. 마지막으로 밸러궈가 유비 논변에 기초해 자기 입장을 옹호하려는 대응을 무력화시키기 위한 논의를 펼친다.

• Educational Technology International
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• 제16권2호
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• pp.183-200
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• 2015

This study investigated the effect of learning achievements and cognitive load according to different types of presenting learning materials and epistemological beliefs (EB). Learning achievements in this study were composed by retention and transfer of ill-structured problem. A total of 80 college students participated in the study. Prior to the learning, students were guided to fill out a questionnaire regarding epistemological beliefs and a prior knowledge test. The students of each group studied with a different type of reading material: full text (FT), full text including key questions (KeyFT) and full text including a concept map (CmFT). After a session of study was finished, they were asked to complete the posttest: retention and transfer. The results showed that there was a significant difference in transfer achievements. CmFT outperformed higher scores than the other types. There was no significant difference in retention among the groups. It is strongly believed that the types of presenting learning materials may have affected the understanding of ill-structured problem solving skills. Students with sophisticated EB showed higher achievements on retention and transfer than naive-EB and mixed-EB. Even though the data showed decrease of the cognitive load on the type of materials and EB, there were no significant differences on the cognitive load. We should consider a positive effect of types of presenting learning materials and EB enhancing capabilities of solving ill-structured problems in real life.

• 대한수학교육학회지:수학교육학연구
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• 제11권2호
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• pp.341-349
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• 2001

Infinity is one of the important concept in mathematics, science, philosophy etc. In history of mathematics, potential infinity concept conflicts with actual infinity concept. Reason that mathematicians refuse actual infinity concept during long period is because that actual infinity concept causes difficulty in our perceptions. This phenomenon is called epistemological obstacle by Brousseau. Potential infinity concept causes difficulty like history of development of infinity concept in mathematics learning. Even though students team about actual infinity concept, they use potential infinity concept in problem solving process. Therefore, we must make clear epistemological obstacles of infinity concept and must overcome them in learning of infinity concept. For this, it is useful to experience visualization about infinity concept. Also, it is to develop meta-cognition ability that students analyze and control their problem solving process. Conclusively, students must adjust potential infinity concept, and understand actual infinity concept that is defined in formal mathematics system.

• 한국과학교육학회지
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• 제40권4호
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• pp.359-374
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• 2020

본 연구는 조사연구와 자기연구의 복합 형태로 구성되었다. 조사연구로서 초등 교사의 융합 수업 및 융합 지식에 대한 인식론적 신념을 조사하였다. 그 결과를 대표하는 사례로서 교사이자 연구자인 "나"를 연구 참여자로 하여 융합 수업을 실행하는 교사로서 나의 융합 수업과 융합 지식에 대한 인식론적 신념을 살펴보고, 속력을 주제로 수학-과학-체육의 가족 유사성에 근거한 융합 과학수업 프로그램을 지도한 양상을 자기연구로 실행하였다. 초등 교사들의 융합 수업과 융합 지식에 대한 인식론적 신념에 대한 개방형 검사 문항을 초등 교사 28명에게 서면 질의 방법으로 조사하였다. 연구에 참여했던 초등 교사들은 융합 수업을 교과 활용적 접근 또는 다학문적 접근의 융합으로 생각하였다. 융합 지식을 개별 교과의 집합체로 인식하고 있었으며, 융합된 지식은 학생 스스로 문제를 해결하는 과정에서 습득할 수 있다는 인식론적 신념을 가지고 있었다. 교사이자 연구자인 나 역시 비슷한 신념을 지니고 있었다. 자기연구를 수행하는 동안 나는 가족유사성의 범주별 분석 결과와 그것에 근거한 융합 지식 체계를 반영하기 위해 노력하였으나, 간학문적 접근의 융합 활동을 구현하는데 어려움이 있었다. 수학의 단위, 비와 비율의 개념은 과학의 속력 개념과 연계되어 있어서 두 교과의 개념을 융합적으로 이해하는데 효과가 있었으며, 체육 활동은 수학과 과학 개념을 융합적으로 학습하기 위한 맥락을 제공하여 간학문적 접근의 융합 수업을 촉진시킬 수 있었다. 가족유사성에 근거한 간학문적 융합 지식 체계와 교사인 나의 인식론적 신념 간의 간극과 해결 양상에 대한 논의가 제시되었다.

• 대한수학교육학회지:수학교육학연구
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• 제12권2호
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• pp.181-192
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• 2002

There are various methods of proving a proposition. Among these, 'mathematical induction' is treated in school mathematics weightly. But many students have difficulty with the proof by 'mathematical induction'. To solve this problem, analysis needs to be attempted in various aspects This study attempts to compare the teaching methods of 'mathematical induction' in South and North Korea and to acquire the implication. In fact, many differences between South and North Korea are found. These differences are caused by epistemological and psychological premise. Therefore this study investigates the epistemological and psychological aspects in North Korea and compares the textbooks in South and North Korea. Through this study, some implications are found. First, the sequence of introducing the 'mathematical Induction' needs to be considered. Second, the rich context of applying the 'mathematical induction' is needed. Finally, disagreement between curriculum and textbook in South Korea needs to be reconsidered.

• 건축역사연구
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• 제12권2호
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• pp.61-69
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• 2003

Manfredo Tafuri's Ideological criticism in architecture has opened a new horizon to interpreting architecture in modern capitalist architecture for it views architecture not just as a style or formal invention, but in terms of socio-economical process. It offered a comprehensive understanding of a chaotic situation of contemporary architecture and historical meaning modern architectural movements in relation with capitalistic development. However, it has been criticized as architectural pessimism which does not allow any possibility for progressive architectural practice. It was also criticized of epistemological problem of how one could be outside ideology without assuming true consciousness against false consciousness of ideology. Tafuri solves this problem by assuming Althusserian activist concept of knowledge and suggest the concept of labor of writing history of critical historians, instead of a design for utopian society, as a possible critical architectural practice. However, I argue that ultimately ideological criticism does not deny architectural practice itself, nor researches on formal characteristics of architecture. The problem lies rather in the architectural Intellectuals' attachment to the traditional concept of architect as a form giver to the society. By rejecting this myth and broadening the concept of architectural practice from design to production, we can find that Ideological problem is not architectural pessimism, but rather it opens up a new way of approaching to the problem of architectural practice in modern capitalist society.

• 한국수학사학회지
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• 제26권5_6호
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• pp.389-400
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• 2013

The article makes a discussion to conceptualize a histo-genetic principle in the real historical view point. The classical histo-genetic principle appeared in 19th century was founded by the recapitulation law suggested by biologist Haeckel, but recently it was shown that the theory on it is no longer true. To establish the alternative rationale, several metaphoric characterizations from the history of mathematics are suggested: among them, problem solving, transition of conceptual knowledge to procedural knowledge, generalization, abstraction, circulation from phenomenon to substance, encapsulation to algebraic representation, change of epistemological view, formation of algorithm, conjecture-proof-refutation, swing between theory and application, and so on.

• 영어영문학
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• 제64권3호
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• pp.361-381
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• 2018

Shakespeare reflects/refracts the controversial spirit of his age in the epistemological and political skepticism of his Roman plays: Titus Andronicus, Julius Caesar, Coriolanus, and Antony and Cleopatra. Skepticism doubts all received truth and suspends judgment, and it often takes the form of mental jousting on both sides of a question. Renaissance skepticism was strengthened by rhetorical education. Arguing on both sides of the question (in utramquem partem) was a practice taught in Shakespeare's grammar school in order to enhance students' mental abilities in logic and dialectic. This rhetorical exercise seldom leads to a third-term resolution: it just reveals all the apparent and hidden aspects of a problem at issue. Shakespeare's Roman plays, especially his Julius Caesar, demonstrate this skeptical attitude, leaving the judgment to the audience.

• 건축역사연구
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• 제11권4호
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• pp.7-19
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• 2002

If we compare socio-cultural aspects of the two historical periods known as 'pre-modern' 'modern,' it would seem that the Aristotelian understanding of technology has difficulty explaining techno-cultural phenomenon of modern society. The problems are first that the discourse of scientific technology in the modern period has proceeded without a metaphysical base, and second that nothing in present culture regulates the limitations of scientific technology. The clear distinction between means and ends in the traditional approach is no longer valid in the jumble of interrelationships. Such complexity forces us to acknowledge that means and ends are relative and interchangeable, and that neither has a clear moral superiority over the other. Technology in modern society is no more a neutral means. The products of science do not always exist to serve human ends. In modem architecture and urban design, both its productive and destructive tendencies leave man and his society in an endless confusion of complexity and opposition. These problems of technology still result in unsolved question today. On this point, the discussion another currently prevalent attitude to technology, especially Heideggerian thinking in the below could give a somewhat clearer answer to the problem of modem architecture and technology, although it also comprises limited contemplation in itself.

• 대한수학교육학회지:수학교육학연구
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• 제11권2호
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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.