SYMMETRY PRINCIPLE AS A BASIS FOR INTEGRATION IN SCIENCE AND ITS VALUE FOR EDUCATION
Authors: Gapontsev V. L. , Fedorov V. A. , Gapontseva M. G. 
Published: May 2019

Introduction. In recent decades, the problem of the formation of a holistic perception in students’ minds of the surrounding reality in the field of education has become acute. The buildup of scientific knowledge, which is a determinant of the structure of the content of education, occurs impetuously. Students’ thinking and consciousness become fragmented due to the exorbitant, permanently increasing amount of information that is presented for learning, but cannot be fully mastered by students. The root cause is imbalance in the curriculum levels of integration and differentiation (with a roll in the direction of the latter). To compensate the current imbalance and reverse the dangerous situation that threatens society with extremely negative consequences, an audit of the structure of educational content and the search for its new conceptual models are required.

The aimof the publication was to show the importance of using the phenomenon of symmetry in the construction of structures of scientific knowledge and the content of education.Methodology and research methods. The study was based on the ideology of F. Klein “Erlangen programme”; E. Wigner’s scheme, showing the division of areas of scientific knowledge; generalised idea of symmetry by G. Weyl; the personal-activity approach to structuring the content of education, improved by V. S. Lednev; and also on the theoretical and methodological analysis of other scientific sources related to the topic under discussion.Results and scientific novelty. The general idea of symmetry, borrowed from geometry, but nonetheless having a general methodological rather than a particular character, is proposed as the basis for systematising sections of scientific knowledge and structuring foundation of the content of modern education. The ability of symmetry to combine the merits of the primary deductive concept and the general inductive concept reflects the tremendous work performed by mankind in the course of history to identify stable patterns, sets of invariants (the allocation of which is the basic condition for the development of intelligence) and the corresponding forms of symmetry. That is, the forms of generalised symmetry accumulate in a compact form all the available knowledge and serve as a tool developed by society for systematising the phenomena and laws of the surrounding reality. The examples convincingly demonstrated the integrative property of forms of symmetry, manifested in the relationship between its principles, the laws of nature and natural phenomena. The principles of symmetry set the structure to areas of the laws of nature and natural phenomena, which, in turn, in the form of cross-cutting lines (according to V. S. Lednev) can determine the content of education. In addition, it justifies the expediency of introducing a special cross-cutting Symmetry line, consisting of a course system – apical elements, supplemented by implicit elements scattered in courses of other cross-cutting lines. Such an approach will eliminate the narrow specialisation in the learning process and avoid fragmentary perception of educational information and the surrounding reality. Practical significance. The research materials presented in the publication can be useful both for scholars and educators, who study the content of education, as well as for practitioners involved in the selection of educational material in the development of educational programmes at various levels.