**5. Modern mathematics approaches for students**

It is known that the main concepts related to the assimilation of knowledge in the discipline of stereometry are: axioms, definitions, theorems and their proofs, and, most importantly, the solution of tasks [9]. The role of the functions is as follows:


Today, with the development of information technology, it can be said that the learning process is a function of objects: student, mathematical knowledge, teacher, and "virtual reality", with the teacher managing the learning process with the help of a computer. It is expected that with the developed StereoMV stereoscopic system, the efficiency of the learning process will increase. The material and applied tasks included in the system will be ordered by difficulty and complexity, starting from easier ones and ending with more complex tasks. Lessons can be solved both individually, and students can be divided into separate groups [9]. The course on the discipline of stereometry is a continuation of the course on planimetry. Very often, in the study of stereometry it is necessary to use various definitions and theorems of planimetry to clarify stereometric concepts, i.e., the solution of some stereometric problems is reduced to the solution of planimetry problems. The developed new stereo system makes it possible to build a spatial model of the studied object. At the same time, in the traditional way of learning, the drawings are mainly presented in a plane, which can make it difficult for the students and lead to confusion. The basic knowledge related to the study of stereometry in the middle course uses knowledge obtained already in the second school grade (8-year old students). This knowledge is related to planimetry and algebra, and students get to know them before the specific study of spatial objects. In the second grade, students study the types of triangles, measure the lengths of the sides of a triangle, square, and rectangle with a ruler, as well as study units of measurement (cm, dm, m). The teaching material of the third grade is related to the introduction of basic geometric knowledge, as students learn to use drawing tools (ruler and protractor), study-specific definitions, and the

concept of an angle (straight, acute, and obtuse). Students learn to use the square grid, which is a propaedeutic of the Cartesian coordinate system introduced in the upper course. By measuring, they learn to distinguish which shape is a square and which is a rectangle. The fourth-grade learning material is all about learning and drawing a square and a rectangle on the square grid. The concept of the area of a geometric figure and the units of area measurement are introduced. After the fourth grade, the area of the studied figures from geometry is expanded, the properties of the figures are examined, and conclusions are formulated based on experience and observation. A habit of deductive thinking is formulated. The new geometric concepts of students at this age are: straight parallelepiped, cube, vertex, edge, wall, etc. The formula for volume and units of volume measurement are derived experimentally. One of the essential concepts in planimetry, which is the basis of stereometry in the study of a regular pyramid, is similar triangles and similar polygons. The system provides an opportunity to form initial knowledge of stereometry, implementing the material laid out in the textbook for the fifth grade. In connection with the teaching of geometry in IX–X grades, the problem of improving the methodology to develop spatial thinking takes on great importance. The development of this type of thinking in students is carried out through a unique system of tasks that meet the regularity of forming logical thinking. In the tenth-grade geometry course, students use cabinet projection and ways to depict polyhedra such as prisms and pyramids. Among the stereometric tasks of particular importance are the tasks of constructing a section of a polyhedron with a plane. In reality, these sections represent a polygon, which students are familiar with from the sixth-grade course and it is an essential element of the stereo system. The necessary knowledge related to areas are regular/irregular polygon and polyhedra. In the developed module of the system, there is a partial presentation of the material related to the above course on introductory sections of geometric bodies. In studying the topics associated with the cylinder and cone, the questions of depicting a circle and regular inscribed and circumscribed polygons are considered. The necessary propaedeutics for an upper course in stereometry are carried out through the course from I–III and IV–V classes, respectively. Up to this point, the measurement of sections in the planimetry course has been approached inductively. In this way, one goes outside the confines of the classroom by measuring objects with a meter. It is shown that there exists a mutual, unambiguous and reversible correspondence between the objects and the set of positive numbers [9]. The upper course students have the knowledge obtained from the elementary and intermediate courses about the volumes of geometric figures. and this knowledge should be expanded, ie. raised to a higher level. In Bulgarian schools, similar triangles and the signs of their similarity are first examined, then similar polygons are introduced. As it is known, two triangles are similar when there is a correspondence between their vertices, i.e., their angles are equal, and their sides are proportional. The Similar Polygon Theorem states, "If two polygons are divided by their diagonals into similar triangles, then they are also similar." Here the theorem of dependence between the perimeters and their corresponding sides is introduced. The formula for the volume of a pyramid can be obtained by the method of indivisibles of the Italian mathematician Cavalieri [9]. The pyramid's height is divided into a number of proportional parts, after which sections parallel to the base are drawn. There is a dependence between the area of the base and its parallel section. A polyhedron's section with a plane, is a polygon with sides intersecting the walls of the polyhedron with a plane.
