Tasks of prepared drawings in training pupils to build the pyramid sections

An analysis of the results of the students performing the tasks of external independent testing in mathematics shows that in recent years, about 80% of test participants were not able to determine the type and cross-section of a given polygon plane, in particular the pyramid. Therefore, the problem of improving the method of teaching students to build cross sections of polyhedra is urgent.

The purpose of the article is to find out the peculiarities of constructing a system of tasks by ready drawings on the theme "Cross sections of the pyramid".

It is advisable to take into account the visual complexity of the task in order to construct a system of tasks according to the drawings. First, the visual complexity is determined by the number and volume of semantic units represented in the figure; second, the procedural component of the task has some influence. In addition, the process of solving the problems of cross-section construction of polyhedra is complicated by the need to make the transition from a visually distorted image to a visually plausible image and vice versa.

The article presents the tasks for forming the ability to construct cross sections of a pyramid, each of which offers nine tasks on ready-made drawings, arranged in 3 × 3 matrix tables. In the table, the type of pyramid is complicated horizontally, vertically, the locations of points belonging to the plane of cross section of the pyramid are complicated. This allows us to build a differential system of tasks according to the finished drawings.

In addition, both in-curricular and cross-curricular tasks should be taken into account when designing the system of tasks. It is effective to use the GeoGebra program, which allows to build images of polyhedra, their cross sections, rotate the obtained drawing, view it at different angles, which helps to shape students' ability to reproduce a complete spatial image, to view step-by-step section construction, to study the cross-sectional view of the polyhedron, including pyramids depending on the location of the points through which the section is made.