KNOWLEDGE FOUNDATION IN THE SYSTEM OF PROFESSIONAL TRAINING OF PRE-SERVICE MATHEMATICS TEACHERS IN STUDYING THE MATHEMATICAL INDUCTION METHOD - Lukashova, Tetіana; Drushlyak, Marina; Khvorostina, Yurii (Physical and Mathematical Education, 2023)
Formulation of the problem. One of the fundamental didactic principles in the system of professional training of pre-service mathematics teachers is the foundation principle, which provides for the non-linear nature of the accumulation of mathematical knowledge and the creation of conditions for the gradual deepening and expansion of school knowledge in the direction of professionalization and the formation of a complete system of scientific and methodical knowledge. The study of the main content lines of various mathematics courses in pedagogical institutions of higher education has a spiral character and is based on the relevant basic concepts and methods studied in the school mathematics course.Materials and methods. To achieve the goal, methods of the theoretical level of scientific knowledge were used: analysis of scientific literature, synthesis, formalization of scientific sources, description, comparison, generalization of own experience.Results. The unfolding of the spiral of knowledge foundation of students of mathematical specialties of pedagogical institutions of higher education is illustrated by the example of studying the mathematical induction method, based on the educational programs "Secondary education (Mathematics. Informatics)" of the first (bachelor's) and second (master's) levels of higher education of Sumy State Pedagogical University named after A. S. Makarenko. At the first foundation level, students consider the classical scheme of the mathematical induction method and get acquainted with the schemes of the methods of generalized and generalized-enhanced induction. At the second level of foundation, there is a theoretical generalization of the knowledge obtained at the previous stage, students actively use various schemes of the method of mathematical induction both when proving mathematical statements (theorems, properties) and when solving problems. At the third foundation level, the induction method is studied in the context of methodological reasoning and applications in the school mathematics course. The fourth (applied) level of foundation involves the analysis of the development of the method of mathematical induction, its schemes, and modifications in the historical context, as well as the application of the method of mathematical induction and its modifications to solving applied problems.Conclusions. The example of the implementation of the principle of foundation when studying the method of mathematical induction confirms the importance of awareness by future teachers of mathematics of the importance of forming, accumulating, and deepening knowledge not only in the context of studying fundamental concepts but also mathematical methods for professional activity and understanding interdisciplinary connections. The design of educational disciplines taking into account the principle of the foundation of basic mathematical concepts and methods gives the student the opportunity to choose the trajectory of his future activity - this is not only working by profession but also the performance of fundamental and applied research, experimental development during graduate studies.
Keywords: knowledge foundation; pre-service mathematics teachers; professional training of pre-service mathematics teachers; mathematical induction method; foundation spiral