In the article, an analysis of solutions to six problems of geometrical character at the beginning of school attendance is shown. Problems were assigned to students individually and were evaluated from different points of view. The previous research was focused mainly on their arithmetical competence. But geometry also belongs in primary education. Therefore we prepared an analogous investigation which was focused on geometrical competence. The experiment confirms that our children have, at the beginning of school attendance, a good level of visual appreciation of their surrounding world. Our schools do not systematically develop further this skill.