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THE DUALISTIC PROPERTIES OF MATHEMATICS AND SOME FACTORS OF THEIR MODIFICATION
Abstract
Background: In the previous authors publications it was shown that modeling of fundamental properties of mathematics within the teaching process is very efficient. A group of fundamental properties consists of several so-called dualistic properties, which are inherent in all the branches of mathematics in all periods of its history. The purpose of this article is to bring to light some up-to-date factors, which generate a new appearance of the dualistic properties as well as their gradual modification. Methods: A method of the research can be described as follows. We consider mathematics in a general context and analyze some integration processes of different natures, i.e. the integration between mathematics and computer sciences, mathematics and technique, and so on. Results: At present, each of the dualistic properties under consideration is gaining some new appearance, which is an instrument to construct some new pedagogical scenarios. Conclusions: There exist two organizational forms of science, and both are actively developing. Their characteristic features are determined by the properties of the main data medium, i.e. paper or electronic medium. They do not compete with each other, but supplement with each other. Because of that, science as a whole becomes polymorphic and stable with respect to outside influence.
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