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Currently relevant are the issues of improving the intellectual management of the educational process in the structure of subject mathematics teaching. The solution of this problem is aimed at ensuring the individual needs of each student in self-education and self-actualization, at the activation of cognitive, intellectual, motivational processes in the context of the new digital educational paradigm. The leading idea of the study is the development of an automated intelligent learning system in mathematics (ILS)...

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...