Abstract
The chapter consists of results of research aimed at lower secondary school pupils and their problems in solving tasks aimed at areas and volumes. The difficulties were identified via clinical interviews with pupils over solutions of selected diagnostic tasks.
The following problems were identified: pupils have problems with the distinction between the theoretical space and the space of representations (e.g., they infer features of the shape from its drawing); pupils have problems with the structuring of space (covering space and filling space); pupils tend to immediately use a formula without making an image of the problem situation and when it is mistaken, they tend to remedy it in a calculation way; pupils do not understand the geometric formula and have no image of the area of a triangle and its relationship to the area of the relevant parallelogram. The difficulties are described and illustrated by pupils' solutions and extracts from the interviews.
Their probable causes and re-education are outlined. Our research results are connected to results of related international research, international testing and results of our online survey among elementary and lower secondary teachers.