20.500.12556/DKUM-17761 DOJEMANJE NESKONČNOSTI PREMICE PERCEPTION OF LINE'S INFINITY POVZETEK Diplomsko delo Dojemanje neskončnosti premice je sestavljeno iz dveh delov: teoretičnega in empiričnega. V teoretičnem delu so predstavljene Van Hielejeve stopnje geometrijskih predstav, definicije premice in neskončnosti, neskončnost števil, neskončnost premice, ponazorila neskončnosti premice, ponazoritvene vaje za izboljšanje predstav o premici in premica kot del učnega načrta. Namen diplomskega dela je bil ugotoviti, ali učenci dojemajo neskončnost premice ter analizirati stanje v osnovnih šolah. Pri raziskovanju so bile uporabljene deskriptivna, kavzalno-neeksperimentalna in kavzalna eksperimentalna metoda pedagoškega raziskovanja. Rezultati so pokazali, da učenci v četrtem razredu, ko se prvič srečajo s premico, še niso na stopnji razvoja, na kateri bi analitično razumeli neskončnost premice. Na deklarativnem nivoju sicer povedo, da je premica neskončno dolga oz. neomejena ravna črta, vendar pa si na konceptualnem nivoju premice ne predstavljajo kot take. Osnovni razlog je vizualna oz. delno analitična narava dojemanja geometrijskih pojmov na tej razvojni stopnji. Ugotovljeno je bilo, da bi bilo potrebno premico v višjih razredih, ko so učenci že sposobni dojeti in razumeti neskončnost premice, obravnavati na vizualnem in analitičnem nivoju in dosledno upoštevati spiralnost učnega načrta oz. izgradnje kognitivne mreže. V četrtem oz. petem razredu bi se torej le pridobivale izkušnje, ki so predpogoj za abstrahiranje pojma v višjih razredih. ABSTRACT The thesis Perception of Infinity of a Line consists of two parts: a theoretical and empirical part. The theoretical part presents Van Hiel’s levels of geometrical reasoning, definitions of a line and infinity, infinity of numbers, illustrative exercises for improving the perception of a line and a line as a part of curriculum. The aim of the thesis was to find out if students comprehend the infinity of the line, and to analyse the situation in elementary schools. A descriptive and experimental method were used in this research. The results have showed that the students of the 4th class, who get familiar with the line for the first time, are not on the development level which would enable them an analytical perception of the infinity of the line. They say that a line is unlimited and straight, but they cannot comprehend that on a conceptual level. The basic reason is visual and partly analytical way of perception of geometrical concepts at this stage of development. Consequently, line should be dealt with in higher classes of elementary school when students are able to perceive and comprehend the infinity of a line, and coverage on visual and analytical level is possible. At the same time the spiral of curriculum and construction of cognitive network should be taken in serious consideration. To sum up, work in 4th and 5th class should be focused on getting experience which would form a framework for abstraction of the concept in higher classes of elementary school. Ključne besede: pouk matematike osnovna šola geometrija neskončnost dojemanje neskončnosti premica. lessons of mathematics elementary school geometry infinity perception of infinity a line. true true false [M. Novak] Slovenski jezik Angleški jezik Diplomsko delo 2011-03-16 09:40:01 2011-04-11 12:58:41 2022-04-13 10:07:48 2023-12-22 03:32:57 2011 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 18266632 URN:SI:UM:DK:AGW5NMVC UNI_Novak_Martina_2011.pdf UNI_Novak_Martina_2011.pdf 1 2D7073FDE3989A1F40102D934EA5BF75 7320afb89e4a38a7d8547b15cb8ce1ab401826588bcf174d31d315a060e33e66 f79fd482-7c04-11eb-bb7a-00155d0001ca 20.500.12556/dkum/b0ebd843-9948-4ed6-9bec-7a285aeb98e9 https://dk.um.si/Dokument.php?lang=slv&id=20878 Pedagoška fakulteta 0 0 0