Reform of General education and vocational schools set the task of improving the quality of education in all General subjects, including mathematics. It is well known that the assimilation of mathematical knowledge in many students have serious difficulties, the cause of which, as a rule, is insufficient mathematical training in preschool age.

Improvement of the content and methods of teaching mathematics in school involves a new attitude to the preparation of children in the period immediately preceding school. Currently, significant changes have already been made in the program of development of mathematical concepts in preschool children (increase in the volume of oral accounts, account groups of subjects, training in the measurement of individual values, expansion of geometric knowledge, etc.); found and tested more effective methods and means of training (modeling, problem problems and situations, developing and learning games, etc.).

The learning experience suggests that the development of logical thinking preschoolers to the greatest extent contributes to the study of elementary mathematics. Mathematical style of thinking is characterized by clarity, brevity, dissociation, accuracy and logic of thought, ability to use symbols. In this regard, the content of teaching mathematics at school and kindergarten is systematically reconstructed.

Naturally, the basis of cognition is sensory development, acquired through experience and observations. In the process of sensory cognition, representations are formed-images of objects, their properties, relations. Thus, operating a variety of sets (objects, toys, pictures, geometric figures), children learn to establish equality and inequality sets, call the number of words: "more", "less", "equally". The comparison of specific sets prepares children to assimilate in the following the concept of number. It is operations with sets that are the basis to which children apply not only in kindergarten, but also over the next years of schooling. The idea of the set forms the basis of children's understanding of the abstract number, the laws of the natural series of numbers. Although the concepts of natural number, as well as geometric shapes, sizes, parts and the whole are abstract, they still reflect the relationship and relationship of objects surrounding reality.

In the mathematical preparation of children, the development of elementary mathematical concepts plays an important role in teaching measurement as the initial method of learning the quantitative characteristics of the environment. This makes it possible for preschoolers to first of all use not generally accepted, but conditional measures in the measurement of bulk, liquid substances and lengths. At the same time, children develop an eye, which is very important for their sensory development.

In the process of systematic training in mathematics, children master a special terminology — names of numbers, geometric shapes (circle, square, triangle, rhombus, etc.), elements of figures (side, top, base), etc. However, it is not recommended to use such words in their work with children-terms as "natural glad", "totality", "structure", "elements of the set", etc. the work is not limited to classes. It should be borne in mind the use of all teaching space in terms of educational situation.

Methods of teaching mathematics to younger students is an applied field of knowledge (applied science). As a science, it was created to improve the practical activities of teachers working with children of primary school age. It has already been noted above that the methodology of mathematical development as a science actually makes its first steps, although the methodology of teaching mathematics has a thousand-year history. Today, there is no program elementary (and preschool) of education, which dispenses with mathematics. But until recently it was only about teaching younger children the elements of arithmetic, algebra and geometry. And only in the last twenty years of the XX century began to speak about the new methodical direction-the theory and practice of mathematical development of the child.

This direction became possible in connection with the formation of the theory of developmental education of a young child. This direction in the traditional method of teaching mathematics is still debatable. Not all teachers today are on the positions of the need to implement educational training in the process of learning mathematics, the purpose of which is not so much the formation of a child's specific list of knowledge, skills and subject-matter, as the development of higher mental functions, its abilities and the disclosure of the internal potential of the child.

For the progressive thinking teacher it is obvious that the practical results from the development of this methodological direction should become incommensurably more significant than the results of simple methods of teaching primary mathematical knowledge and skills of primary school children, in addition they should be qualitatively different. After all, to know something means to master it "something", to learn to manage it.