The way the elementary school children learn geometry and acquire knowledge about space, makes its necessary to unite geometry learning and development of spatial representations and imagination during the first school years. However, the issue of an elementary geometry course remains questionable; the content and the sequence of learning of the geometric material are being disputed.

Children of elementary school develop spatial thinking abilities, and get basic skills and knowledge in geometry, drawing and measuring, only by chance, as the school does not address the issue enough.

In the elementary math program, geometric material can be found occasionally (only some small parts of it). It is a diminutive addition to arithmetic rather than a complete course, which in our opinion, a course of visual geometry should become.

The existing geometry introduction at school has a number of disadvantages:

1. There is no connection between the first geometric knowledge obtained at elementary school and geometry in the 5-6th grades. For example, notions «sphere» and «triangle», used in the first grade in such tasks as: «How many triangles, squares or spheres can you see in the figure?», are almost never used further at elementary school and the 5th grade. The only example of the space notion in the math book for the 5th grade, is a rectangular parallelepiped. So, a schoolchild learns only the definitions and primitive constructions in his elementary math, as the school program use neither the natural interest of pupils to geometry in this age, nor the rich geometric experience of children, which they gain in their everyday activities, it does not aim to develop their geometric intuition.
2. There is no proper system of introducing geometric facts of elementary and introductory geometry at middle school. According to our experience and observations, pupils cannot recognize segments on the rectangle sides (or other figures); they do not see the measuring of the length and width of a rectangle as measuring of the segment length; they do not find segments in the surrounding reality. While getting acquainted with the simple geometric facts, students narrow their educational chances, as they learn the spatial relations of the material world and geometry of objects only through measuring.
3. The teaching process is not dedicated and logical enough, though it is desirable and possible at both elementary and middle school.

Moreover, teaching geometry elements in a more integral form at elementary school would be rather useful, as it could solve the difficulties, which many pupils face when they first begin to learn geometry. These problems are:

1. the child must realize the most essential geometric facts;
2. it needs to master the unusual methodology (definitions, logic proof).

If a pupil already knows the basic geometry and his geometric imagination is more or less developed, then he can understand the material of a regular geometry course much better.

The recent debates concerning the content of the school geometry are definitely helpful: during the last decades geometry courses have become «more geometric», the course books, which used to be too boring, have become more visual, and the extreme illustrative ones - more logical.

However, the observed development of geometric education is scarce. We believe that the introduction of course «visual geometry» at schools and universities, will let the future teachers explain geometry to children (provide geometric propaedeutics) in a more integral, task-oriented and systemized way, using the child´s life experience and its rich imagination; and prepare for a better study of elementary geometry at the university.

In our opinion, the visual geometry course solves the following didactic tasks:

• provides a proper training for a regular geometry course (at school and university);
• helps develop spatial representations and imagination in school pupils (and students);
• gives students a practical knowledge, needed for learning of other school subjects: geography (for example, knowledge on angles, plan and scale), nature study (for example, configuration of leaves and flowers), physics (measuring areas, volumes), drawing (draw from nature);
• gives an opportunity to reason (inductive, realistic and etc.), assert hypotheses (their proof or disproof);
• develops artistic taste and esthetic culture in children (and students).

These are probably not all the educational goals that can be achieved by means of the visual geometry, but there have been mentioned enough to assure of its benefits.

We believe that teaching visual geometry will interest the teachers, who care about the further development of children, and are willing to help their students learn geometry. We are sure that visual geometry would be attractive for teachers with wide imagination, who search for new ideas in their profession. And hopefully, the course of visual geometry will find its place in the system of professional education for elementary school teachers.