Mathematics is part of all curriculums of Russian educational establishments attended by children up to the age of 6.5 - 7 years. It is also a most important part of primary school education. Preschool and primary school period is the time when the foundation for mathematical education is built, which can bring value to the person not just through the gained mathematical knowledge and ways of doing things, but also through the overall positive influence on their development. It is at this time that the relevant educational systems can either establish or fail to establish the foundation to realize the great potential of positive influence of maths on the overall development of children.

Formation of this foundation is driven by the teachers' attitude to maths, their understanding of its nature as a field of knowledge and culture.

There are two main teachers' viewpoints on maths. The first one is: mathematics is a formal exact science where everything is predefined once and for all; maths carries no knowledge about the person and about the people, and therefore it is opposed to the humanities and is only indirectly related to the people, being used in cognition and creation of material values. The second viewpoint is: mathematics was invented by people. Maths has nothing outside of what has been invented, created by people. Mathematical objects, numbers, equations, geometrical figures, algorithms and formulas in the theory of combinations and the theory of probability represent essentially abstract, ideal notions. They were invented through the needs of people: material ones, and even to a greater degree, spiritual ones. Most important of those needs are the esthetic needs for beauty, simplicity, order, justice.

G. Sarantsev, after his review into various authors' opinions on the beauty of mathematical objects, stated that "the meaning of beauty is defined by ...: conformity of a mathematical object with its standard stereotype image; its order, coherence; its simplicity; universal use of this object in various mathematical fields; its singularity, unexpectedness" [2, p. 16].

An important characteristics of knowledge in education is its completeness. Any field of knowledge in the process of learning can be viewed as something established and something which is in the process of being established (F. Losev) [ ].

If mathematics is viewed as something established, then it is a complete sign system consisting of subsystems that constitute mathematical fields. If it is established, a learner cannot in principle make any changes to the existing mathematical structures. Something established can only be appropriated. The truth in something established is indisputable and absolute.

However, no matter how many thousands of years the mathematical fields and notions have existed, they can be seen as something which is in the process of being established. Even if notions were formulated a few thousand years ago, our mind transforms them in our perception process. In maths that is still in the process of being established, mathematical symbols, statements, texts are created here and now, they are born through person's own efforts using acquired cultural examples and the signs created by the person. Here not just the logical components of mathematical knowledge are implemented, but also social and cultural ones, which express and reflect the needs of the learner being a social person who enters social relations with other people and appropriates cultural examples, e.g. universal means of expressing quantitative relations, including mathematical ones, universal means of numeric designation and the rules of using numbers.

Formation of preschoolers' and primary schoolers' mathematical notions must represent preparation for their acquaintance and their first acquaintance with the world of maths which is wonderful, orderly, just and beautiful. Such preparation and acquaintance can be implemented by immersing the child into situations that prepare for the mathematical knowledge to be born, by creating and supporting the situations where mathematical knowledge is born through their cognition of the world in general, where the knowledge is first formed as a field of their native language, only to be transformed into the field of maths.

2. G. Sarantsev. How learning maths can become interesting. – Moscow: Prosvescheniye, 2011. 160 p.