SUBJECT ?NUMBER SYSTEMS? IN TWO-LEVELED FORMAT PREPARATION TEACHERS OF MATHEMATICS

The aim of this article is to analyze the format of a two-leveled training ? bachelor and master ? future teachers of mathematics from the point of view of the content of mathematical material, which is to develop prospective teachers of mathematics at those two levels, shaping their professional competence. Methods. The study involves the theoretical methods: the analysis of pedagogical and methodical literature, normative documents; historical, comparative and logical analysis of the content of pedagogical mathematical education; forecasting, planning and designing of two-leveled methodical system of training of future teachers of mathematics. Results and scientific novelty. The level differentiation of the higher education system requires developing the appropriate curricula for undergraduate and graduate programs. The fundamental principle must be the principle of continuity ? the magister must continue to deepen and broaden knowledge and skills, along with competences acquired, developed and formed on the undergraduate level. From these positions, this paper examines the course ?Number Systems? ? the most important in terms of methodology course for future mathematics teachers, and shows what content should be filled with this course at the undergraduate level and the graduate level. At the undergraduate level it is proposed to study classical number systems ? natural, integer, rational, real and complex. Further extensions of the number systems are studied at the graduate level. The theory of numeric systems is presented as a theory of algebraic systems, arising at the intersection of algebra and mathematical logic. Here we study algebras over a field, division algebra over a field, an alternative algebra with division over the field, Jordan algebra, Lie algebra. Comprehension of bases of the theory of algebras by the master of the ?mathematical education? profile will promote more conscious understanding of an axiomatic method, a structure of axiomatic theories in mathematics, development mechanisms of mathematical science; at the same time it will help to develop to complete vision of mathematics as a single science. As a result, the educational level of the master will be above the educational level of the bachelor of pedagogical mathematical education. Practical significance. The article can be useful to heads of departments and graduate programs, faculties of classical and pedagogical universities, carrying out preparation of masters in the direction ?Pedagogical Education (Mathematics)?.