(CZ) Didaktická transformace obsahu a školská praxe
(EN) Pedagogical Transformation of Content and Practice in School

Práce se zabývá otázkami didaktické transformace obsahu na příkladu elementární geometrie. Pojem logické struktury předmětu se konfrontuje s jeho strukturou didaktickou. Dále se uvádí pojem podnětné vyučování jako realizace konstruktivních přístupů v praxi školy. Hodnotí se role množin v poznávacím procesu, role definic a úloh.

By pedagogical transformation of the content (for example of the school subject mathematics) I understand its global trans-formation on the one hand its transforma-tion global and its partial transformation on the other handl. The global transformation means the conversion of a mathematical structure defined by a system of axioms into a so-called didactic, structure. In elementary geometry, for example, the didactic structure is represented by the application of teh following four priciples: 1. Partition of space. 2. Filling of space. 3. Motion in space. 4. Dimension of space.
The theoretical basis for partition of the plane is the Jordan curve theorem, and the practical stimuli connected with partition of space are familiar from everyday practice. The idea of partition of the plane enables the teacher to introduce many geometrical notions in a natural way (circle, polygon, halfplane, sphere, ...). The process of meas-urement is connected with paving or tes-selation of apart of plane (segment, space). Motion in space is well known to the pupils from their physical world, the results of recording motion leading to the drawing of some geometrical figures (constructing a segment, circle, polygon, ...). Our conception respects questions connected with dimension together with problems of mapping geometrical figures.
The partial didactical transformation of content is based on constructive approaches to education in the sense used in Investi-gating Mathematics Teaching by Barbara Jaworski and Jana Cachová. A very impor-tant part of the conception described is the attention given to the process of creation of mathematical notions. The suggestions pre-sented here are rooted in some ideas of Jan Amos Komenský, Jean Piaget and others and are connected with everyday school practice, especially the reality of school classes, the social environment and the teacher‘s beliefs. A good teacher solves all problems creatively and a in good way. It is important to put into practice the methodological approaches of Shulman‘s school in education through very good teachers.