APPLICATION OF METHODS AND IDEAS OF NUMBER THEORY IN THE SCHOOL COURSE OF ALGEBRA: THE NEED FOR AWARENESS BY PRE-SERVICE TEACHERS MATHEMATICS - Lukashova Tetіana; Drushlyak, Marina; Shyshenko, Inna; Pokidko, Olena (Physical and Mathematical Education, 2022)
Formulation of the problem. The course of algebra and number theory has been at the forefront of pre-service mathematics teachers’ training for many decades. Given its importance and close relationship with the algebra school course and the content of several electives and math classes, it is important to focus on understanding the parallels between higher algebra ideas and categories and the math school course in the pre-service mathematics teachers’ training. Materials and methods. System analysis of scientific, educational, and methodical literature; comparison and synthesis of theoretical positions; generalization of own pedagogical experience. Results. The system of pre-service mathematics teachers’ training should focus on the use of ideas and methods of number theory in the school course algebra, and the content of school math classes. This problem can be solved in several ways: in the study of relevant topics and methods in the course of algebra and number theory; in the framework of elective courses ("Selected issues of Olympic mathematics", "Selected issues of number theory", etc.); in the classes of the mathematical circle in the study of relevant topics; in the implementation of interdisciplinary links (for example, with the course of discrete mathematics in the study of the rules of combinatorics, the method of inclusion and exclusion, etc.). A comparative analysis of the content of the curriculum of the course "Algebra and Number Theory" in the specialty 014 Secondary Education (Mathematics) and the curriculum for classes with in-depth study on issues of number theory, as well as the methods used. Some aspects of the application of congruence properties in solving problems of number theory are considered: proving divisibility, finding the remainder of the division, establishing conditions for simplicity of numbers, solving indefinite equations in integers, etc. Conclusions. The proposed system of exercises can be implemented both in classes on algebra and number theory in the study of numerical congruences and their properties, and in the course "Selected issues of Olympic mathematics" and meetings of the mathematical circle in the study of applications of number theory to solve heuristic problems, which helps pre-service mathematics teachers to understand the relations between the course of algebra and number theory and the school course of algebra.