Observing in school geometry

Observing is an important process in learning geometry. In the first part of the thesis observing is considered from a psychological perspective: the Gestalt theory, its history, the distribution of gestalt qualities, as well as various studies and theories of templates. The observing process is considered also from the didactic point of view by means of the van Hiele’s theory of levels of geometric reasoning. Since colours also influence observing, a list of advices for teachers about using colours is included. In the thesis we consider also the concepts of angle and triangle, as examples of objects which students observe in geometry. Different didactic tips on how to present these topics to students are also included, as well as some exercise tasks aimed at improving observing skills. Finally, we present how observing geometric shapes is treated in selected textbooks. In the empirical part of the thesis we present a simple research, in which we investigated how various visual elements in the representation of a geometric configuration facilitate or hinder the recognition of geometric objects and geometric properties. As part of the research a test was taken by students of grade seven of a lower secondary school. The tasks of the test required only visual observation, thus the students made no use of measuring or construction aids as they worked them out. Regarding the influence of colours, proximity, and position of images of geometric objects we found that students find difficult to recognise a shape in ‘non-standard’ positions and find difficult to identify congruent objects if one of them is rotated. We also investigated how the emphasis of specific elements (vertices, sides, surfaces) as well as the choice of foreground/background colours of the shape affects its recognition by the students. We found that in this respect the choice of colour combinations plays an important role