The task of plotting flat cross-sections of polyhedrons as a means of developing divergent and algorithmic thinking and spatial representation ability

Abstract

Relevance. In this work, we developed problems on plotting the flat sections of polyhedrons in the case when the prism section is defined by the trace which is located on the plane of the prism base and does not have common points with the base of the prism, and by point, which belongs to the side rib of the prism. Purpose. The purpose of the article is to establish that when solving problems on the construction of plane sections of polyhedra, students complete tasks; apply axioms and geometric properties; form and develop spatial representations; develop divergent and algorithmic thinking, the ability to reason logically, the ability to make correct arguments and conclusions. Methodology. Problems on plotting the flat sections of polyhedrons using the internal design method are developed. To solve these problems, two types of projections are used: parallel and central. A flat section of a pentagonal prism is constructed using a parallel projection method. The central projection is used to construct the flat section of the pyramid. Results. The designed tasks allow us to form and develop divergent and algorithmic thinking and form spatial representations. Conclusions. After researching this topic, we came to the conclusion that the ability to solve problems of this type contributes to the formation and development of divergent and algorithmic thinking, the ability of spatial representation in future mathematics teachers.