This paper is devoted to those readers who are professionally engaged in dealing with the questions of teaching and learning elementary school geometry. It consists of three lessons from a postgraduate course taught by this author at the Teacher's Training Faculty, University of Belgrade. Appearance of things in the surrounding world changes but some stable characteristic properties of their shapes stay unchanged. J. Piaget classifies these properties as topological projective and Euclidean and the spontaneous development of a child follows that order of ideas. It is a normal interest of a specialist in education to know how these ideas are mathematically established without wading through the books on these subjects which are often unapproachable to him or her. The aim of this paper is to make a direct approach to mathematical clarification of these ideas, based only on the reader's knowledge of the secondary school mathematics.