ON THE ROLE AND PLACE OF THE COURSE «ALGEBRA AND NUMBER THEORY» IN THE SYSTEM OF THE PRE-SERVICE MATHEMATICS TEACHER TRAINING

Abstract

Formulation of the problem. The following arguments support the implementation of the course "Algebra and Number Theory" in the system of professional training of pre-service mathematics teachers: this course provides the necessary theoretical and practical training of mathematics teachers and promotes understanding of the scientific basis of school mathematics course; some concepts and topics of the algebra course are presented in the mathematics curricula of general secondary education (prime and compound numbers, division with remainder, greatest common divisor and least common multiple, signs of divisibility, basic arithmetic theorem, polynomials and operations on them), as well as in the curricula for specialized classes (divisibility of integers, modular congruence, division of polynomials by remainder, roots of polynomials and Bezu theorem, rational roots of polynomials from one variable, etc.). Most of the topics of this course are the basis of elective curricula and math classes; and the problems of algebra and number theory are widely used in competitions and tournaments of various levels. In addition, the knowledge and skills that students acquire when studying this course, form the necessary basis for the study of other fundamental and applied mathematical disciplines (mathematical analysis, discrete mathematics, complex analysis, calculation methods, numerical systems), as well as elementary mathematics and methodology teaching mathematics.

Materials and methods. The study was based on scientific research of national and foreign scientists studying the training of pre-service mathematics and computer science teachers. To achieve this goal, the methods of the theoretical level of scientific knowledge were used: analysis of scientific literature, synthesis, formalization of scientific sources, description, and comparison.

Results. The article describes in detail the experience of teaching the course "Algebra and Number Theory" at the Department of Mathematics of Makarenko Sumy State Pedagogical University from the 90s of the last century to the present, based on modifications in the content of the course, changes in the number of hours devoted to mastering the course, on the transfer of certain topics to the content of other fundamental disciplines.

Conclusions. Based on our own experience, we believe that in the context of further reduction of classroom hours and the absence of the State Standard of Education, problems arising from the need for quality training of future mathematics teachers can and should be solved by implementing in the educational process elective courses that expand and deepen the content of the main course "Algebra and Number Theory" (in particular, on number theory or elements of modern algebra).