Vloga konkretnih ponazoril pri razumevanju algoritma pisnega deljenja v javni in Montessori osnovni šoli

Simončič, Metka (avtor), Manfreda Kolar, Vida (mentor)

Konkretna ponazorila so pri pouku matematike nepogrešljiva, saj učencem pomagajo pri razvijanju številskih predstav ter razumevanju abstraktnih matematičnih pojmov in postopkov. Številni strokovnjaki se strinjajo glede pomembnosti ponazoril pri pridobivanju znanja, kljub temu pa njihova mnenja glede uporabe ponazoril niso enotna. Večinoma se strinjajo, da so konkretna ponazorila v prvih treh razredih osnovne šole nujna, redki pa utemeljujejo njihovo uporabo tudi v višjih razredih. Pisno deljenje je ena izmed učnih vsebin pri matematiki na razredni stopnji, za katero se predpostavlja visoka zmožnost abstrakcije mišljenja. Način poučevanja te vsebine v montessori osnovni šoli se precej razlikuje od poučevanja v javni osnovni šoli. Glavna razlika je v tem, da v montessori osnovni šoli to vsebino obravnavajo zelo konkretno, z rokovanjem s konkretnimi materiali, v javni osnovni šoli pa večinoma le na simbolni ravni. V tem magistrskem delu smo primerjali razumevanje algoritma pisnega deljenja med učenci obeh šol, pri čemer smo se osredotočili na vpliv uporabe konkretnih ponazoril. Izvedli smo kvalitativno raziskavo, v kateri smo individualno opazovali učence javne in montessori osnovne šole med reševanjem nalog pisnega deljenja. Pozneje smo analizirali njihove izdelke in opažanja glede uporabe konkretnih ponazoril. Analiza rezultatov je pokazala, da učenci montessori osnovne šole pogosteje uporabljajo konkretna ponazorila in dosegajo boljše rezultate pri reševanju nalog pisnega deljenja kot učenci javne osnovne šole. V vzorcu so konkretna ponazorila uporabili le učenci z učnimi težavami. Nadarjeni učenci ponazoril niso uporabljali, saj so najverjetneje že dosegli abstraktno stopnjo mišljenja. Učenci z učnimi težavami pri matematiki, ki so pri računanju uporabili konkretna ponazorila, so v povprečju dosegli boljši rezultat od ostalih učencev z učnimi težavami, ki ponazoril niso uporabljali, kar kaže na pozitiven vpliv ponazoril za to skupino učencev. Analiza napak, ki so se pojavile med reševanjem nalog, je pokazala, da pri učencih z učnimi težavami prevladujeta dve vrsti napak, ki se pri nadarjenih ne pojavita, in sicer napake, povezane s priklicem aritmetičnih dejstev in ničlo v rezultatu. Z rezultati raziskave želimo učitelje spodbuditi k pogostejši uporabi konkretnih materialov pri poučevanju proceduralno zahtevnejših matematičnih vsebin, kot je na primer pisno deljenje.

• Jezik: Slovenski jezik
• Ključne besede: konkretna ponazorila
• Vrsta gradiva: Magistrsko delo/naloga
• Tipologija: 2.09 - Magistrsko delo
• Organizacija: PEF - Pedagoška fakulteta
• Leto izida: 2022
• PID: 20.500.12556/RUL-137182
• COBISS.SI-ID: 110048771
• Datum objave v RUL: 16.06.2022

SIMONČIČ, Metka, 2022, Vloga konkretnih ponazoril pri razumevanju algoritma pisnega deljenja v javni in Montessori osnovni šoli [na spletu]. Magistrsko delo. [Dostopano 21 april 2025]. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=137182

Sekundarni jezik

• Jezik: Angleški jezik
• Naslov: Role of concrete visual representations for understanding of the long division algorithm in public and Montessori primary schools

Izvleček

Concrete visual representations are indispensable in mathematics lessons, as they help students to develop their numerical ideas and understanding of abstract mathematical concepts and procedures. Many experts agree on the importance of concrete visual representations in knowledge acquisition, but their opinions on their use are not unanimous. Most agree that concrete visual representations are necessary in the first three years of primary school, but few emphasize their use in the higher grades. The long division is one of the subjects taught in mathematics at grade level, which requires a high level of abstract thinking. The way this content is taught in a Montessori primary school is quite different from the way it is taught in a public primary school. The main difference is that in a Montessori environment, this content is dealt with in a very concrete way, with the handling of concrete materials, whereas in a public primary school, it is mostly dealt with on a symbolic level. In this master's thesis, we compared the understanding of the long division algorithm between students in the two schools, focusing on the impact of the use of concrete visual representations. We conducted a qualitative study in which we individually observed students in public and Montessori primary school while they were solving long division tasks. We subsequently analysed their products and observations on the use of concrete visual representations. Analysis of the results shows that Montessori primary school students use concrete materials more often and perform better on long division tasks than students in public primary school. In the sample, only students with learning difficulties used concrete visual representations. Gifted students did not use them, as they had probably already reached an abstract level of thinking. Students with learning difficulties in mathematics who used concrete visual representations in their calculations scored on average better than other students with learning difficulties who did not use representations, indicating the positive impact of representations for this group of students. An analysis of the errors that occurred during the problem-solving tasks showed that two types of errors that do not occur in the gifted group are prevalent in the case of students with learning difficulties, namely errors related to the recall of arithmetic facts and zero in the result. The results of the survey are intended to encourage teachers to use concrete representations more often when teaching procedurally demanding mathematical content, such as long division.

• Ključne besede: concrete representations