Pupils’ Concepts of the Triangle and the Rectangle at the Beginning of Lower Secondary School - Robová, Jarmila; Moravcová, Vlasta; Halas, Zdeněk; Hromadová, Jana (Scientia in educatione, 2019)
The article deals with pupils’ understanding of concepts of the triangle and the rectangle at the beginning of lower secondary school. The pupils were administered a test consisting of tasks asking them to decide whether the marked points (external, internal, on the sides, vertices) belonged to a triangle or rectangle, respectively. The assignment also sought to establish how pupils determined the number of common points which a triangle shared with differently positioned lines. A total of 505 pupils attending 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. The testing was preceded by an analysis of several textbook series designed for primary schools, which indicate that the pupils’ concept of the triangle and the rectangle tends to evolve from spatial models (cut out of paper) through appropriate geometric shapes (crayon coloured) which are eventually reduced to their bare boundaries, an evolution process which may generate misconceptions of triangles and rectangles on the part of the pupils. We found that approximately only half of the pupils had an adequate concept of the triangle or rectangle; there were no significant differences between girls and boys. The most common problem was that the 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.