Abstract
The article deals with pupils' understanding of concepts of the triangle and the rectangle at the beginning of lower secondary school. Through the test, tasks were assigned in which pupils had to decide whether the marked points (external, internal, on the sides, vertices) belong to a triangle or rectangle respectively.
Also investigated was how pupils determine the number of common points of the triangle and lines in different positions. In total, 505 pupils of the 6th grade of lower secondary schools took part in our testing.
The individual responses were coded and subjected to statistical analysis. Possible causes of pupils' responses were subsequently investigated in semi-structured interviews with another 20 pupils.
Testing was preceded by the analysis of several textbook series for the elementary school, which showed that the concept of the triangle and the rectangle proceeds from material models (cut out) through appropriate abstract patterns (coloured) to the reduction of figures to their boundary, which can support misconceptions of triangles and rectangles. We found that approximately only half of the pupils have an adequate concept of the triangle or rectangle; there are no significant differences between girls and boys.
The most common problem was that pupils reduced the triangle only to its boundary. In conclusion, we draw attention to the possible consequences of this misconception (area-perimeter, understanding polyhedra) and make some recommendations that could lead to correction.