• Journal for History of Mathematics
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• v.15 no.3
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• pp.49-58
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• 2002

The present paper aims to show basic substitution between metaphysics and mathematical abstraction in the philosophy of mathematics. The general troths of metaphysics and the truths particularly relevant to tile nature of mathematical abstraction serve as speculative guides in ordering the content and discussing the nature of the multiple questions which lie between the disputed frontiers of metaphysics and mathematical abstraction.

• Journal for History of Mathematics
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• v.15 no.1
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• pp.93-98
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• 2002

In this paper, we critically survey the mathematical Platonism in respect to its abstract, ahistorical, asocial and acultural character. The uncertainty of man's concepts is investigated with special attention to evolutionary theory, philosophical and epistemological developments regarding the cognitive unconsciousness and the embodied mind. We research into the implication of the Darwin machine theory for human consciousness and Wittegenstein's philosophy of mathematics.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.23-30
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• 2005

Intuition has played an important role in process of invention of mathematics and given understanding of mathematical truth and the direction of solution. So, I review about intuition in history of mathematical philosophy and mathematics because we need systematic research about intuition for search of the methods for enhancement of intuition in mathematics education. According to the research of scholars who emphasize intuitive education, intuition is common feature which everybody hold and is not special feature which particular person hold. In addition, intuition is universal ability that can enhance by proper instruction. So, we have to emphasize the importance of the development of intuition and education which emphasize creative thought via intuition.

• Korean Journal of Logic
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• v.23 no.2
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• pp.117-159
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• 2020

In the early Wittgenstein's Tractatus, both philosophy of logic and that of mathematics belong to the most crucial subjects of it. What is the philosophical view of the early Wittgenstein in the Tractatus? Did he, for example, accept Frege and Russell's logicism or reject it? How did he stipulate the relation between logic and mathematics? How should we, for example, interpretate "Mathematics is a method of logic."(6.234) and "The Logic of the world which the proposition of logic show in the tautologies, mathematics shows in equations."(6.22)? Furthermore, How did he grasp the relation between mathematical equations and tautologies? In this paper, I will endeavor to answer these questions.

• Research in Mathematical Education
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• v.8 no.2
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• pp.95-106
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• 2004

The purpose of this paper is to diagnose the problems of the revision process of the curriculum, and identify the issues in relation to the 7th mathematics curriculum. From the review on the curriculum revision process in Korea, three issues were identified; timing and scale of curriculum revision, research and curriculum revision, and the relationship between the revision of the overall curriculum and that of a subject curriculum. Regarding the mathematics curriculum, the three issues were raised for further discussion; lack of philosophy behind the mathematics curriculum, optimization of mathematics educational content, and differentiated curricula for students of different abilities.

• School Mathematics
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• v.5 no.2
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• pp.151-165
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• 2003

So far there have been intermittently quantitative and syntactic analyses of the past elementary mathematics curriculums to comprehend elementary mathematics education in Korea. However, we think we also need qualitative and semantic analyses to comprehend and examine the past elementary mathematics curriculums exactly and so to look out on our future elementary mathematics education. Generally, school mathematics curriculum reflects both the philosophical aspects of mathematics itself that form the background of the philosophy of mathematics education and the sociological aspects in real mathematics class that could be the output of the curriculum. With this view, the logic of the social constructivism can be an appropriate way that leads mathematical philosophical analysis and sociological analysis in mathematics education. With this kind of method of analysis we got the results that: the past Korean elementary mathematics curriculums mainly have the tendency from the ideology of the progressive educator(the 1st) to of the technological pragmatist(the 2nd), from that of the old humanist(the 3rd and 4th) to the progressive educator(the 5th and 6th) again, and lastly that of social constructivism(the 7th).

• School Mathematics
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• v.7 no.4
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• pp.375-389
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• 2005

Whitehead proposed that the education proceed through the rhythmic cycle on the basis of his metaphysical philosophy and educational philosophy. 'The Rhythm of Education' means that the intellectual levels of learners are elevated through the rhythmic cycles of stages of romance, precision, and generalization over and over again. As a result of these cyclic repetitions, the learners become truly free of inner prejudice. This study is to seek a method to apply Whitehead's proposition to mathematics education. I devise the curriculum constructing methods to experience Whitehead's three stages meaningfully, the teaching methods interplaying freedom and discipline rhythmically, and the teaching examples which adopt all these.

• Journal of Elementary Mathematics Education in Korea
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• v.4 no.1
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• pp.39-55
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• 2000

The purpose of this research is to analyse Korean elementary mathematics curriculum taking a philosophical view of mathematics education. In this research, 1 will analyze not only the current elementary mathematics curriculum but also the past ones. There have been intermittently quantitative and external analysis so far to comprehend the elementary mathematics curriculum. But, I thought we also need qualitative and internal comprehension and examined the curriculums through a philosophical analysis. Generally, mathematics curriculums at every period have their own mathematical philosophy consciously or tacitly. And, the school mathematics is the practice of mathematics curriculum based on that mathematical philosophy. Mathematical curriculum reflects both the philosophical aspect in mathematical philosophy that forms the background of the mathematical curriculum and the sociological aspect in real-class that is the output of the curriculum. With this view, the logic of social constructivism can be an appropriate way that leads mathematical philosophical analysis and sociological analysis in mathematics education. So, I comprehend the tendency of the Korean elementary mathematics curriculum from the first to the seventh through the philosophical views. In view of the results so far achieved, after the second half of the 20th century, the Korean mathematical curriculums mainly have the tendency from the Ideology of progressive educator (the first) to of technological pragmatist (the second), from that of old humanist (the third and forth) to progressive educator (the fifth and sixth), and lastly that of social constructivism (the seventh).

• The Mathematical Education
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• v.23 no.2
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• pp.17-34
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• 1985

• Journal for History of Mathematics
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• v.14 no.2
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• pp.55-60
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• 2001

In this paper we introduce three kinds of theory on the origin of the world, the formation theory, the emanation theory and the creation of nothing. Especially through Augustinus, great scholar of patristic philosophy in the Middle Ages, how the relationship between the God and the creature was shown with the concept of the infinity and the finite.