20.500.12556/RUL-184474 Matematično in didaktično matematično znanje bodočih učiteljev matematike za poučevanje ulomkov magistrsko delo Mathematical and didactical knowledge of pre-service mathematics teachers for teaching fractions V magistrskem delu smo raziskovali matematično in didaktično matematično znanje bodočih učiteljev matematike pri poučevanju ulomkov v osnovni šoli. Ulomki sodijo med zahtevnejše matematične vsebine, saj zahtevajo razumevanje različnih pomenov ulomka ter predstavljajo pomembno osnovo za nadaljnje razumevanje racionalnih števil, decimalnih števil, odstotkov, razmerij in sorazmerij. V teoretičnem delu so predstavljeni ključni vidiki učiteljevega znanja o ulomkih po modelu Mathematical Knowledge for Teaching (MKT), s poudarkom na razlikovanju med matematičnim in didaktično matematičnim znanjem. Obravnavani so različni pomeni ulomka, najpogostejše napačne predstave učencev ter pomen različnih reprezentacij in modelov pri poučevanju ulomkov. Raziskava je temeljila na preizkusu znanja, podatki pa so bili analizirani s kombinacijo kvantitativnega in kvalitativnega pristopa. Cilj raziskave je bil ugotoviti, kako dobro imajo bodoči učitelji matematike razvito matematično in didaktično matematično znanje o ulomkih ter kako uspešni so pri prepoznavanju učenčevih napačnih predstav, pri razlagi napak in izbiri ustreznih didaktičnih pristopov. Ugotovitve kažejo, da imajo bodoči učitelji dobro razvito proceduralno znanje pri osnovnih operacijah z ulomki ter uspešno prepoznavajo napačne odgovore učencev. Več težav pa se pojavlja pri nalogah, ki zahtevajo globlje konceptualno razumevanje, predvsem pri manj intuitivnih pomenih ulomka, kot je ulomek kot razmerje, ter pri pojasnjevanju izvora napačnih predstav učencev. Razlage so pogosto usmerjene predvsem v pravilno izvajanje postopkov, manj pa v razvijanje matematičnega razumevanja. Rezultati potrjujejo, da dobro proceduralno znanje sámo po sebi še ne pomeni kakovostnega poučevanja matematike. Za uspešno poučevanje ulomkov je nujno razvijanje specializiranega matematičnega znanja, znanja o vsebini in učencih ter znanja o vsebini in poučevanju. Ugotovitve raziskave prispevajo k boljšemu razumevanju priprave bodočih učiteljev matematike ter k oblikovanju usmeritev za nadaljnje izboljšanje njihovega izobraževanja. This master's thesis examines the mathematical and pedagogical content knowledge of prospective mathematics teachers regarding the teaching of fractions in primary education. Fractions are among the more demanding mathematical topics, as they require an understanding of their multiple interpretations and provide an essential foundation for learning rational numbers, decimals, percentages, ratios, and proportions. The theoretical part presents the key aspects of teachers' knowledge of fractions based on the Mathematical Knowledge for Teaching (MKT) framework, with particular emphasis on the distinction between mathematical knowledge and pedagogical content knowledge. Different interpretations of fractions, common student misconceptions, and the role of various representations and models in teaching fractions are also discussed. The empirical study was based on a knowledge test, and the collected data were analysed using a combination of quantitative and qualitative research methods. The aim of the study was to examine the extent to which prospective mathematics teachers possess mathematical and pedagogical content knowledge of fractions, as well as their ability to identify students' misconceptions, explain students' misconceptions, explain students' errors, and select appropriate instructional approaches. The findings indicate that prospective mathematics teachers demonstrate well-developed procedural knowledge of basic fraction operations and are generally successful in identifying students' incorrect answers. However, greater difficultes arise in tasks requiring deeper conceptual understanding, particularly with less intuitive interpretations of fractions, such as fractions as ratios, and in explaining the underlying causes of students' misconceptions. Their explanations are often focused on the correct application of procedures rather than on developing students' conceptual understanding. The results confirm that well-developed procedural knowledge alone is not sufficient for highquality mathematics teaching. Effective teaching of fractions requires the development of specialized content knowledge, knowledge of content and students, and knowledge of content and teaching. The findings contribute to a better understanding of the preparation of prospective mathematics teachers and provide guidance for further improvements in teacher education. osnovnošolsko učenje in poučevanje matematika ulomki bodoči učitelji matematike matematično znanje didaktično matematično znanje model MKT napačne predstave učencev poučevanje ulomkov fractions prospective mathematics teachers mathematical knowledge pedagogical content knowledge Mathematical Knowledge for Teaching (MKT) students' misconceptions teaching fractions true false false S. Šaruga Slovenski jezik Angleški jezik Magistrsko delo/naloga 2026-07-08 08:31:26 2026-07-08 08:31:33 2026-07-09 13:11:43 0000-00-00 00:00:00 2026 0 Ljubljana 0 Ljubljana 121 str. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 511.13:373.3(043.2) 205885 284222979 52220.pdf 52220.pdf 1 D2B1347B6C1F58BD52EDDFFEDF2D9EE6 b6f49d03aa6f1fe75777872641252524779298f0a28535d54e0f632193c5b242 8b0d7e2b-7a96-11f1-9b0d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=237303 Pedagoška fakulteta 0 0 0