Vpliv reprezentiranja matematičnih vzorcev na učenčevo uspešnost v 1. razredu osnovne šole : diplomsko delo

Kuhelj, Katja (author), Hodnik, Tatjana (mentor)

Diplomsko delo obravnava vpliv reprezentiranja matematičnih vzorcev na učenčevo uspešnost v 1. razredu osnovne šole. V teoretičnem delu predstavljamo pojem vzorec z matematičnega vidika. Vzorce je mogoče najti povsod okoli nas v različnih pojavnih oblikah. V ospredju so trije mogoči načini prikazovanja vzorcev, najprimernejši za predšolske otroke konkretni material in pozneje v šolanju grafične in simbolne reprezentacije. V navezavi na to se naloga osredotoča na tri raziskave s tega področja. Prva je raziskovala nadaljevanje petih vzorcev v petih različnih reprezentacijah, druga se je osredotočala na rastoči in padajoči vzorec, tretja pa je ugotavljala, kako se je znanje o vzorcih skozi čas spreminjalo, katera znanja o vzorcih imajo predšolski otroci in kako razlaga vpliva na ta razvoj. Teoretični del poudarja, da Kurikulum za vrtce (1999) zelo skopo zajema področje vzorcev, medtem ko sta v Učnem načrtu za matematiko v osnovni šoli (2011) zapisana dva cilja. V empiričnem delu smo ugotavljali, kateri vzorci glede na kompleksnost gradnika učencem povzročajo težave ter kako vrsta reprezentacije, torej konkretna, grafična ali simbolna, vpliva na uspešnost nadaljevanja vzorca. Hkrati so v ospredju tudi najpogostejše napake, ki jih v nadaljevanju naredijo učenci. Učencem, vključenim v vzorec, je bilo najlažje nadaljevati vzorec z gradnikom AABBAABB, najtežje pa vzorec z gradnikom AAABAAAB. Izkazalo se je, da je dolžina gradnika bistveno vplivala na uspešnost nadaljevanja, večje število različnih elementov pa učencem ni predstavljalo dodatne otežitve. Učenci so bili najuspešnejši pri nadaljevanju vzorcev, ki so bili predstavljeni s konkretno reprezentacijo in najmanj uspešni z grafično reprezentacijo. Najpogostejše napake učencev so se kazale v nedokončanih ali izpuščenih gradnikih ter neustreznem prepoznavanju elementov posameznih gradnikov.

• Language: Slovenian
• Keywords: Osnovnošolsko učenje in poučevanje, vzorec, reprezentacija, gradnik vzorca, učenci 1. razreda, nadaljevanje vzorca
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Place of publishing: Ljubljana
• Publisher: K. Kuhelj
• Year: 2025
• Number of pages: 41 str.
• PID: 20.500.12556/RUL-173138
• UDC: 373.3(043.2)
• COBISS.SI-ID: 250062083
• Publication date in RUL: 13.09.2025

Secondary language

• Language: English
• Title: Impact of mathematical pattern representation on student achievement in the first grade of primary school

Abstract

The thesis discusses the impact of representing mathematical patterns on learners' performance in the 1st grade of primary. In the theoretical part, we present the concept of a pattern from a mathematical perspective. Patterns can be found everywhere around us in various forms. The focus is on three possible ways of representing patterns, the most suitable for preschool children being concrete materials and, later in schooling, graphic and symbolic representations. In connection with this, the thesis focuses on three studies in this field. The first investigated the continuation of five patterns in five different representations, the second focused on ascending and descending patterns, and the third examined how knowledge of patterns has changed over time, what knowledge of patterns preschool children have, and how interpretation influences this development. The theoretical part emphasizes that the Curriculum for Kindergartens (1999) covers the field of patterns very sparsely, while the Curriculum for Mathematics in Primary Schools (2011) sets out two objectives. In the empirical part, we determined which patterns cause difficulties for students in terms of the complexity of the building block and how the type of representation, i.e., concrete, graphic, or symbolic, affects the success of continuing the pattern. At the same time, the most common mistakes made by students in continuing the pattern are also highlighted. The students involved in the pattern found it easiest to continue the pattern with the building block AABBAABB and most difficult with the building block AAABAAAB. It turned out that the length of the building block had a significant impact on the success of the continuation, while a larger number of different elements did not pose an additional difficulty for the students. Students were most successful in continuing patterns that were presented with concrete representations and least successful with graphic representations. The most common mistakes made by students were incomplete or omitted building blocks and incorrect recognition of the elements of individual building blocks.

• Keywords: pattren, representation, pattren component, first-grade students, pattern continuation