Abstract:

Van Hiele (1957) described the model in which geometric thinking is divided into five separate levels. Usiskin (1980) created a test for determining the level of geometric thinking following the van Hiele approach and this test is used all over the world. In the paper we focused on individual tasks in van Hiele test. Based on our experience, we assumed that Slovak pupils in the second level of elementary schools may have problems solving some tasks of the van Hiele geometric test. The aim of our research was thus to determine the problematic tasks of the van Hiele geometric test and to find the cause of these problems. The research sample consisted of 781 nine-graders and the research tool was the van Hiele geometric test. The research was carried out in 29 elementary schools in 23 cities in Slovakia. Qualitative and quantitative analysis were done in the research evaluation. 4PNL (4-Parameter Nested Logit) model was used to analyze the responses and distractors of the tasks. The statistical implicative analysis method, specifically the C.H.I.C. statistical software (Classification Hiérarchique Implicative et Cohésitive) was used for a deeper analysis of dependencies and relationships between stated didactical variables. We identified two most demanding tasks for the pupils that were focused on connecting logic and geometry. These tasks had a significantly lower success rate than the other tasks at the same level of geometric thinking and the characteristic curves in 4PNL were also different. These findings were also confirmed by a statistical implicative analysis that determines how the choice of task´s distractor depends on the level of geometric thinking. The cause of the problems in the identified tasks can also be traced to the methodology of teaching geometry in elementary schools in Slovakia. Pupils often do not see connections among the acquired pieces of knowledge and have only formal geometry knowledge. The research findings are presented in detail in the paper.

Keywords:

Van Hiele test, geometric thinking, 9th graders, misconceptions in geometry.