• Proceedings of the Korean Society for History of Mathematics Conference
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• 1999.11a
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• pp.8.2-8.2
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• 1999

• Proceedings of the Korean Society for History of Mathematics Conference
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• 2001.11a
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• pp.4-4
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• 2001

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.237-252
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• 2013

The philosophy of science of Bachelard is introduced mainly with epistemological obstacles in the discussions within mathematics education. In his philosophy, epistemological obstacles are connected with the dialectical developments of science. Science progresses through generalization of concepts and theories by negating things which were recognized as obvious. These processes start with ruptures against the existing knowledge. Epistemological obstacles are failure in keeping distance with the existing knowledge when reorganization is needed. This concept means that there are the inherent difficulties in the processes of concept formation. Finally I compare the view of Bachelard on the developments of science and the 'interiorization-condensation-objectification' scheme of reflexive abstraction in mathematics education and discuss the inherent difficulties in the learning mathematics.

• Journal for History of Mathematics
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• v.24 no.1
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• pp.45-61
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• 2011

The starting point of education is the ancient Greek philosophy. In this paper, we research the Hellenism culture: two famous poleis such as Sparta and Athens. Moreover, we investigate prominent philosopher Plato and Aristotle. In particular, we notice early childhood and female education through Hellenism culture. Finally, we study culture, politics and educations of the ancient Roman in order to compare those of our society.

• Journal of Educational Research in Mathematics
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• v.16 no.3
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• pp.179-198
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• 2006

In This Paper, I call Johnson & Lakoff (1980; 1999)'s Experientialism or Experiential Realism or, Embodied Realism, Nunez(1995; 1997)'s Ecological Naturalism as Experientialism and try to investigate the possibility of their Experientialism to be a philosophy of mathematical education. This possibility is approached in the respect with the problem of objectivism and relativism. I analyzed the epistemological background of embodied cognition first and then mathematical epistemology of experientialism. Experientialism shares its Philosophical position partly with Dewey and Merleau-Ponty. Experientialists deny the traditional hypothesis of philosophy as such separability of subject and object, and of body and rationality and also They have better position of epistemology than that of Hamlyn, and of Social Constructivism. Therefore, They guarantee wider range of mathematical universality than Hamlyn and Social constructivist. I conclude that the possibility of Experientialism to be a philosophy of mathematical education depends on the success of its supporting the practical study on mathematics education.

• Korean Journal of Logic
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• v.5 no.2
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• pp.67-91
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• 2002

모순에 대한 비트겐슈타인의 견해는 매우 특이할 뿐만 아니라 여러 논란을 불러일으키기에 충분하다. 예컨대 그에 따르면 모순이 수학체계에 존재한다 해도 해로울 것이 전혀 없다. 튜링은 이러한 비트겐슈타인의 견해에 대해서, 만일 수학체계에 모순이 있다면, "그 적용의 경우에 다리가 붕괴될 수도 있다"고 공격한다. 반면에 비트겐슈타인은 "모순 때문에 다리가 붕괴될 수도 있다고 말하는 것은 아주 옳은 소리로 들리지 않는다"라고 응수한다. 과연 유모순적인 계산체계로 건설된 다리는 무너질 것인가? 이 물음을 "튜링의 물음"이라고 부르고, 유모순적인 계산체계로 건설된 다리를 간단히 "튜링의 다리"라고 부르기로 하자. 이 글에서는 바로 이 튜링의 물음에 직접 대답하기 위해서 4개의 입론이 제시되고 있다. 우리는 이러한 입론을 토대로 해서 튜링의 물음에 대해 대답할 수 있고, 비트겐슈타인과 튜링의 논쟁을 조명할 수 있으며, 비트겐슈타인의 수학철학의 핵심적인 측면을 살펴볼 수 있다.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.175-190
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• 2007

In the nineteenth century was Augustus De Morgan, British mathematician, a great mathematics teacher. Although his name is well known to everybody who is interested in set theory, his major mathematical legacy would arise from his novel research in logic. In this article, we first investigate De Morgan's life briefly; we then consider his precious philosophy of mathematics education based on his students' remarks and his works. Finally, by considering his teaching style, we highlight some of the ingredients that go into making a great mathematics teacher.

• Communications of Mathematical Education
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• v.9
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• pp.327-333
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• 1999

21세기를 바로 앞두고, 우리 나라 수학 교육의 과거와 현재의 실태, 즉 수학교육의 목적, 교수 내용, 교수 방법, 평가 등을 철학적 관점과 심리학적 관점에서 역사적으로 재조명해 보는 것은 새로운 2000년대를 앞두고 의미 있는 일이 될 수 있다. 또한 이를 바탕으로 21세기에 우리 나라 수학 교육이 나아가야 할 방향을 세계적인 추세와 관련하여 제시해 보고자 한다.

• Korean Journal of Logic
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• v.22 no.3
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• pp.417-446
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• 2019

The operation theory of the Wittgenstein's Tractatus Logico-Philosophicus is the essential basis of the philosophy of mathematics of the Tractatus. Wittgenstein presents the definition of cardinal numbers on the basis of operation theory, and suggests the proof of "$2{\times}2=4$" by using the theory of operations in 6.241. Therefore, in order to explicate correctly the philosophy of mathematics, it is required to understand rigorously the theory of operations in the Tractatus. Accordingly in this paper, I will endeavor to explicate operation theory of the Tractatus as a preliminary study for explicating the philosophy of mathematics of the Tractatus. In this process, we can ascertain Frascolla's important contributions and fallacies in his reconstruction of 6.241. In particular, we can understand the background that in 6.241 Wittgenstein made mistakes and that there he dealt with the addition operation of the theory of operations, and on the basis of this, we can reconstruct correctly 6.241.

• Proceedings of the Korean Society for History of Mathematics Conference
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• 2000.11a
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• pp.9-10
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• 2000