• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.329-349
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• 2003

Mathematics education is accomplished by systems such as mathematical curriculum and tools such as a textbook which reflects such systems. Human beings make such systems and tools. Therefore, a viewpoint of mathematics of those who make them is an important factor. The view point of mathematics is formed during doing and learning mathematics, but the already formed viewpoint of mathematics affects doing and teaching mathematics. Hence, it will be a factor which affects basically that those who employ themselves on mathematics education have a certain viewpoint of mathematics. This article presents dialectical materialistic viewpoint as the viewpoint of mathematics which affects fundamentally on mathematical teaching-learning practice. The dialectical materialism is carried through the process and result of mathematics development. This shows that mathematical knowledge is objective. Mathematical knowledge has developed according to three basic rules of dialectical materialism i.e. the transformation of quantity into quality, the unification of antagonistic objects, and the negation of negation. This viewpoint of mathematics should offer the viewpoint of mathematics education which is different from the view point of absolutism, relativism or formal logic. In this article I considered mathematics separating standpoint of mathematics into materialistic viewpoint and dialectical viewpoint. 1 did so for the convenience of analysis, but you will be able to look at the unified viewpoint of dialectical materialism. 1 will make mention of teaching-learning method on another occasion.

• School Mathematics
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• v.5 no.4
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• pp.521-540
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• 2003

The processes of mathematics development and the results of it are always those of making a conquest of the circumscription by historical inevitability within the historical circumscription. It is in this article that I try to show this processes through the history of calculus. This article develops on the basis of the dialectical materialism. It views the change and development as the facts that take place not by individual subjective judgments but by social-historical material conditions as the first conditions. The dialectical materialism is appropriate for explaining calculus treated in full-scale during the 17th century, passing over ahistorical vacuum after Archimedes about B.C. 4th century. It is also appropriate for explaining such facts as frequent simultaneous discoveries observed in the process of the development of calculus. 1 try to show that mathematics is social-historical products, neither the development of the logically formal symbols nor the invention by subjectivity. By this, I hope to furnish philosophical bases on the discussion that mathematics teaching-learning must start from the real world.

• Journal of Korean Philosophical Society
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• no.93
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• pp.231-260
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• 2011

Simondon's theory of individuation and methodology of transduction presents a possibility of contemporary natural philosophy and a new perspective about the relation between philosophy and sciences. According to Simondon's anti-substantial viewpoint, being, as a metastable system charged with potential energy, complicates itself with quantum leaps transversing successive equilibriums. Individuation is the becoming of phases of being which transits from preindividual state to individuated states. Physical individuation as a paradigmatic model of individuation in general demonstrates not only insufficiency of form-oriented hylomorphism, but also spontaneous formational capacity of matter and reality of energetic relational operation immanent in matter. Genesis of a individual (structure or form) occurs as a resolution of the disparation between orders of magnitude, that is, the difference of potentials immanent in nature through the internal resonance, communication by information, transductive relation between the opposites. I'm trying to show that Simondon revives 'physis' of ancient natural philosophy by his own transductive applications of contemporary physics' conceptions, and therefore suggest a new non-reductive materialism. Especially Simondon's 'transduction' which is neither induction, deduction, nor dialectic, but an original ontological process and a peculiar method of thinking, I think, is worthy of note in order to construct network of knowledge and inter-relation between various sciences.