GENERATOR SIGNS OF SCIENTIFIC AESTHETICS IN THE PROCESS OF TEACHING MATHEMATICS: THE ORDER

In the article [5] we addressed the issue of the manifestations of signs of the scientific aesthetics, prostate and logical rigor in mathematics and in the process of the teaching mathematics. In this paper, we consider the scientific aesthetics of the sign of order in mathematics and in the process of teaching mathematics. The order at all times was considered as one of the basic principles of nature, it was opposed to chaos and was seen as a source of beauty. The role of the order and its aesthetics in mathematics is great, which serves as the language of the golden book of nature, a way of expressing its laws. By Norbert Winner, the highest vocation of mathematics is to find order in the chaos around us. And not only mathematics, but also science as a whole has a purpose to recognize reality and seek to assert order in the chaos of the world. However, unlike other sciences, the order in mathematics is not only a research tool, but is also one of the main principles of formation. As the principle of formation, the order appears in many different areas of mathematics. Firstly, the order is determined in an arbitrary set in generalized form that puts the beginning of one of the fundamental ideas of modern mathematics - the theory of ordered sets. Then, one of the most interesting areas of modern algebra - theory of structures is creating based on the order. Another interesting chapter of modern algebra, theory of ordered algebraic systems (the theory of ordered groups, rings, ...) arises on the basis of the unity of order and algebraic operations. One of the most important concepts of mathematical analysis - sequence is determined with the order, which also underlies the induction, one of the basic mathematical methods to ascertain the truth. The order as a criterion of mathematical aesthetic was the object of research by G. Birkhoff, H. Eysenck, G. I. Sarantsev and others. In school mathematics teaching it also plays a key role and is an important source of aesthetic appeal of the respective constructions. Here the procedure is one of the main principles of formation of educational material. In the school course of mathematics, along with the relations of equality and inequality, the procedure acts as a ordering of the educational material, the relationship of concepts within the framework of the algebraic materials, implementation of consistent evidence and other forms. On the set of real numbers is also set "agreement" between the operations of addition and multiplication, and the inequalities that cannot be achieved for the field of complex numbers. The order, aesthetic approach also allows to make the right approach and solve a variety of methodological problems.