Napačne predstave o ulomkih pri petošolcih in vloga modelov pri njihovem razumevanju : magistrsko delo

Berdajs, Nuša (author), Manfreda Kolar, Vida (mentor)

V magistrskem delu smo raziskovali, katere napačne predstave o ulomkih se pojavljajo pri učencih 5. razreda ter kako uporaba različnih modelov vpliva na njihovo razumevanje. V teoretičnem delu so predstavljeni ključni vidiki pojma ulomek, pogoste napačne predstave učencev ter pomen uporabe različnih vizualnih modelov pri poučevanju. Poseben poudarek je namenjen modelom množice, ploskovnim in dolžinskim modelom ter njihovemu vplivu na oblikovanje konceptualnega razumevanja ulomkov. Raziskava je temeljila na diagnostičnem testu in polstrukturiranih intervjujih, podatki pa so bili analizirani z deskriptivno statistiko in vsebinsko analizo. Cilj raziskave je bil ugotoviti, kako izbira vrste modela (ploskovni, dolžinski, model množice) vpliva na razumevanje različnih vidikov koncepta ulomek in odpravo napačnih predstav ter kako učenci utemeljujejo svoje strategije in pojasnjujejo napake pri reševanju nalog z ulomki. Zanimalo nas je, ali imajo petošolci težave pri razumevanju pomena števca in imenovalca, prepoznavanju enakovrednih ulomkov, prepoznavanju in ponazarjanju ulomkov, ki so večji ali enaki 1 ter prepoznavanju analogije med dvema različicama dolžinskega modela – številskim in pravokotnim trakom. Prav tako smo preverili vlogo preširokega posploševanja pri prenosu pravil, ki veljajo za množico naravnih števil, na množico racionalnih števil. Ugotovitve kažejo, da imajo učenci 5. razreda pogoste težave pri razumevanju pomena števca in imenovalca ter prepoznavanju enakovrednih ulomkov. Pri primerjanju in urejanju ulomkov pogosto prenašajo pravila iz množice naravnih števil (npr. sklepajo, da večji imenovalec pomeni večji ulomek) in se pri modelih osredotočajo na štetje delov namesto na razmerje med delom in celoto. Rezultati potrjujejo, da lahko vizualni modeli pomembno podprejo razumevanje, vendar njihova učinkovitost ni enaka (npr. dolžinski modeli pomagajo pri primerjanju velikosti ulomkov, medtem ko modeli množice v tem primeru napačne predstave pogosto le še okrepijo). Ugotovitve bodo prispevale k učinkovitejšemu poučevanju ulomkov in načrtovanju didaktičnih pristopov, prilagojenih učenčevemu razumevanju. Spremembe, predvidene v novem učnem načrtu, dodatno utemeljujejo aktualnost obravnavane tematike.

• Language: Slovenian
• Keywords: ulomki, napačne predstave, ploskovni model, dolžinski model, model množice, 5. razred
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: PEF - Faculty of Education
• Place of publishing: Ljubljana
• Publisher: N. Berdajs
• Year: 2026
• Number of pages: 100 str.
• PID: 20.500.12556/RUL-180613
• UDC: 51:37(043.2)
• COBISS.SI-ID: 271553283
• Publication date in RUL: 12.03.2026

Secondary language

• Language: English
• Title: Fifth-Grade Pupils’ Misconceptions About Fractions and the Role of Representational Models in Their Understanding

Abstract

In this master thesis, we investigated which misconceptions about fractions occur in 5th grade students and how the use of different models affects their understanding. The theoretical part presents key aspects of the concept of fractions, common misconceptions of students and the importance of using different visual models in teaching. Particular emphasis is given to surface, length and set models and their influence on the formation of conceptual understanding of fractions. The survey was based on a diagnostic test and semi-structured interviews, and the data were analysed using descriptive statistics and content analysis. The aim of the study was to find out how the choice of model type (surface, length, set model) affects the understanding of different aspects of the fraction concept and the elimination of misconceptions, as well as how students justify their strategies and explain their mistakes when solving fraction problems. We were interested in whether Grade 5 pupils have difficulties in understanding the meaning of numerator and denominator, in identifying equivalent fractions, in identifying and representing fractions greater than or equal to 1, and in recognising the analogy between the two versions of the length model - the number strip and the rectangular strip. We also tested the role of overgeneralisation in transferring rules that apply to the set of natural numbers to the set of rational numbers. The findings show that Grade 5 pupils often have difficulty understanding the meaning of numerators and denominators and identifying equivalent fractions. When comparing and ordering fractions, they often transpose rules from the set of natural numbers (e.g. inferring that a larger denominator means a larger fraction) and focus on counting parts rather than the relationship between the part and the whole in models. The results confirm that visual models can significantly support understanding, but their performance is not equal (e.g. length models help to compare the size of fractions, whereas set models often reinforce misconceptions in this case). The findings will contribute to more effective teaching of fractions and to the design of didactical approaches tailored to students' understanding. The changes foreseen in the new curriculum further substantiate the relevance of the topic.

• Keywords: fractions, misconceptions, surface model, length model, set model, 5th grade