ТHEORETICAL ASPECTS OF HIGHLIGHTING THE ESSENS OF THE THEORY OF IDENTICAL TRANSFORMATIONS OF MATHEMATICAL EXPRESSIONS IN MATH COURSES OF INSTITUTIONS OF GENERAL SECONDARY EDUCATION - Vasilioglo, Iryna; Drahanyuk, Sergey; Sinyukova, Helena (Physical and Mathematical Education, 2022)
Formulation of the problem. In math courses of institutions of general secondary education the content line of transformations of mathematical expressions, their so-called identical transformations directly follows the content line of a number, in fact is an integral part of the last one. According to position of practical-orientated training it is clear that carrying-out identical transformations of math expressions in training math courses mustn’t be an end in itself. For example, the theory of identical transformations of math expressions forms the first-hand basis for the theory of the solution of equations and inequalities, for the calculation of some indefinite and definite integrals, and so on. At the same time, any review of the present textbooks on algebra, algebra, and the elements of cultures for different classes of the institution of general secondary education undoubtedly indicates the lack of total mathematical accuracy and the unique determinacy according to the mentioned concepts. Thus, carrying out the necessary investigations of theoretical character, clearing up the expedient from mathematical and methodical points of view steps of their introduction into corresponding training courses seem rather actual to the authors. Materials and methods. The investigation is based on the author’s experience of a long time of practical work with students of institutions of general secondary education. It is also a result of processing different informational sources, conducting reasoning of deductive character, and formulating conclusions with the help of the synthesis of obtained inferences. Results. Expedient from the authors’ point of view theoretical principles of the up-to-date highlighting the theory of identical transformations of mathematical expressions in math courses of institutions of general secondary education are suggested in the article, the practical steps of their implementation to the corresponding training content are determined. Conclusions. Development of the up-to-date theory of absolute and comparative identical transformations of math expressions theoretical aspects of which the authors tried to highlight in the present paper seems to be expedient for math courses in institutions of general secondary education. Suggested ways of solving the arising problems need subsequent careful discussion.
Keywords: institution of general secondary education; mathematical courses; mathematical expression; identity; identical transformation