The task of geometry teaching in regular schools cannot be the supplying of scientifical knowledge of the preparation for the study of a special subject like mathematics. That is why I will begin with the explanation of general objectives of geometry teaching at school. After that I will talk about methods of teaching geometry which fit together with these objectives. With this it will come out that no axiomatic way will be suitable the main point of the method should be rather working on problems. With such a conception a computer presents a good help. On one hand it can spare drawing work during experimentations with figures and on the other hand it animates to look out for new questions. In the second part then I will present and discuss several problems as illustration of the before presented conception. Three examples have to do with polygons (shapes of triangles, angles in regular polygons, combinatoric with polygones) and concern mostly the junior secondary school while two examples about curves concern the senior secondary school.