Argumentation in elementary school geometry

V diplomskem delu obravnavam utemeljevanje v osnovnošolski geometriji. Utemeljevanje v matematiki je pomembno za razvoj razmišljanja, sporočanja, povezovanja in utrjevanja matematičnega znanja. Kljub vsem pomembnim funkcijam dokazovanja in utemeljevanja, ki presegajo potrjevanje oziroma verifikacija veljavnosti trditev, je utemeljevanje v šolskem okolju pogosto odrinjeno na stranski tir. V teoretičnem delu naloge najprej predstavljam načine utemeljevanja glede na njihovo raven formalnosti. Za razvoj argumentativnega govora je pomembna vloga učitelja kot spodbujevalca, zato v nadaljevanju povzemam študijo primera o spodbujanju produktivnega argumentativnega pogovora pri bodočih učiteljih matematike. V nadaljevanju obravnavam še odnos med raziskovanjem, razumevanjem in utemeljevanjem pri reševanju matematičnih problemov. V empiričnem delu analiziram pet izbranih osnovnošolskih učbenikov in ugotavljam, da se razlikujejo v mnogih vidikih utemeljevanja geometrijskih trditev. V vseh učbenikih je prisotno utemeljevanje geometrijskih trditev, različno pa je število teh utemeljitev in nivo strogosti utemeljevanja. V analizi pozitivno izstopa najnovejši učbenik Tangram 7 (2013), ki edini predvideva, da učenci samostojno ugotavljajo dejstva in jih samostojno utemeljujejo. V mnogih vidikih utemeljevanja dejstev v geometriji pa negativno izstopa učbenik Svet matematičnih čudes 7 (2005).This thesis is about argumentation in elementary school geometry. Argumentation in mathematics is essential for the development of thinking, reporting, connecting and consolidating mathematical knowledge. Despite all these relevant functions, which exceed the pure verification of the validity of propositions, in elementary school mathematics argumentation is often regarded as a matter of minor importance. The theoretical part of the thesis begins with the presentation of several modes of argumentation of different level of formality. Since in the development of argumentative speech the teacher plays an important role as a motivator, a case study is presented on how to encourage productive argumentative speech among prospective mathematics teachers. This is followed by discussion of the relationship between discovery, comprehension and argumentation in the process of solving mathematical problems. The empirical part of the thesis deals with the analysis of argumentation in five elementary school textbooks. In the analysis various aspects of argumentation of geometrical propositions were considered. All five textbooks contain some sort of substantiation of geometry related propositions, however they differ in the number of argumentations and the formality level of substantiation. The analysis reveals that one of the textbooks, Tangram 7 (2013), stands out in a positive way as it is the only one that explicitly demands that pupils independently discover and substantiate facts, whereas another textbook, Svet matematičnih čudes 7 (2005), stands out in a negative way in many aspects related to the substantiation in geometry