20.500.12556/RUL-143265 Kombinatorične igre in njihova uporaba pri pouku matematike magistrsko delo Combinatorial games and their use in mathematical education Magistrsko delo obravnava osnove matematične teorije kombinatoričnih iger ter možnosti za uporabo takih iger pri pouku matematike v osnovni šoli. Prvi, teoretični del, predstavlja zaokrožen povzetek osnovne teorije z definicijami in izreki. V njem opredelimo osnovne pojme, kot so kombinatorična igra, drevo igre, strategija, pozicija, in jih ilustriramo s številnimi primeri. Nato dokažemo izrek Zermela o obstoju zmagovalne strategije za enega od igralcev ter izrek Sprague-Grundy o ekvivalenci med poljubno nepristransko igro normalnega tipa in igro NIM z eno kopico ustrezne velikosti. V drugem delu predstavimo 21 preprostih kombinatoričnih iger, ki bi jih lahko uporabili pri pouku matematike v osnovni šoli. Večina iger je izvirno delo, vsako predstavljeno igro pa spremlja razlaga zmagovalne strategije in vsebinska umestitev igre ob ustrezne matematične koncepte iz u nega na rta za osnovno šolo, kot so na primer števila, simetrija, delitelji, in podobno. Z občasno uporabo tovrstnih iger bi lahko popestrili običajen pouk matematike in pri učencih dodatno razvijali logi no sklepanje in analizo strategij. The Master's thesis deals with the basics of the mathematical theory of combinatorial games and the possibilities for using such games in mathematics lessons in primary school. The first, theoretical part, presents a rounded summary of the basic theory with definitions and theorems. In it, we define basic concepts such as combinatorial game, game tree, strategy, position, and illustrate them with many examples. Then we prove the Zermelo's theorem on the existence of a winning strategy for one of the players and the Sprague-Grundy theorem on the equivalence between an arbitrary unbiased game of normal type and a NIM game with one heap of appropriate size. In the second part, we present 21 simple combinatorial games that could be used in mathematics lessons in primary school. Most of the games are original work, and each featured game is accompanied by an explanation of the winning strategy and a content placement of the game alongside relevant math concepts from the primary school curriculum, such as numbers, symmetry, divisors, and the like. With the occasional use of these types of games, regular mathematics lessons could be enriched and students' logical reasoning and strategy analysis could be further developed. Kombinatorične igre igra normalnega tipa pristranske in nepristranske igre izrek Zermela izrek Sprague-Grundy razvijanje logičnega mišljenja Combinatorial games normal-play games impartial and partizan games Zermelo's theorem the Sprague-Grungy's theorem development of logical thinking true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2022-12-10 08:30:02 2022-12-10 08:30:15 2022-12-12 08:10:47 0000-00-00 00:00:00 2022 0 0 XV, 75 str. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 146260 133277955 16913.pdf 16913.pdf 1 21EF27C0BBFC255D9C72BA5DC088F8EA 28a5bd0533b41794928f3bee64a4a8d51191ca40ffbd4f2496fe9372d6181fe4 542bab3d-785c-11ed-9c94-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=164888 Pedagoška fakulteta 0 0 0