Abstract:

Studies from different countries prove that the definition and hierarchical classification of quadrilaterals play a crucial role in the development of geometric thinking. Our previous research in Slovakia shows that ninth graders in Slovakia have significant problems in classifying quadrilaterals. A quadrilateral is a polygon having four sides, four angles, and four vertices, such as square, rectangle, rhombus, trapezoid. In this paper we present the results of our research in which the main aim is to determine the connection between the classification of quadrilaterals and the level of geometric thinking according to van Hieles´ theory. The research was carried out in 29 elementary schools in 23 towns in Slovakia with a research sample comprising 781 ninth-grade pupils. For a deeper analysis of the dependencies and relations between the mentioned didactic variables the method of implicative statistical analysis was used, especially the C.H.I.C. (Classification Hiérarchique Implicative et Cohésitive) statistical software. One of the findings is that there is a relationship between students' hierarchical classification of quadrilaterals and geometric thinking. It appears that Slovakian pupils comprehend the properties of individual geometric shapes; however, they do not investigate the relationships between them. This may be problematic for pupils progressing to higher levels of geometric thinking. One of the possible reasons for this is that the pupils solve the tasks of an inductive and deductive nature relatively rarely, because such tasks are not to be found in the Slovak textbooks. For these reasons, our next goal is the proposal of materials for the support of the development of the classification of geometric shapes and thus the development of geometric thinking. We focus mainly on using Information and Communication Technologies in creating materials that are suitable for teaching geometry: Concept Map Makers, MathCityMap (math trails) and GeoGebra. The proposed materials are also presented in the paper.

Keywords:

Geometric thinking, concept map, math trails, GeoGebra, elementary school.