doktorska disertacija
Manja Podgoršek (Author), Alenka Lipovec (Mentor)

Abstract

Vizualne reprezentacije imajo pomembno vlogo v izgradnji razumevanja matematičnih konceptov učencev, še posebej pomembne so pri izgradnji razumevanja zgodnjih aritmetičnih pojmov. V doktorski nalogi zato obravnavamo omenjeno tematiko, ki jo na podlagi teoretičnih spoznanj preverjamo tudi empirično. Izbrani zgodnji aritmetični pojmi so odštevanje, zakon o združevanju, ulomek kot operator in potenca. Izvedena sta bila dva dela raziskave, v katerih so sodelovali učenci šestega razreda osnovne šole. Zanimalo nas je, kakšne so risbe podanih matematičnih pojmov z vidika ustreznosti, usmerjenosti in pravilnosti ter kakšne načine prikaza podanih pojmov je mogoče zaznati iz risb. Dodatno nas je zanimalo, kakšna je povezanost učenčevega opisa risbe s prikazanim matematičnim pojmom na risbi. Risbe so bile v raziskavi uporabljene kot raziskovalno sredstvo, kar predstavlja novost na področju aritmetike. S kombinacijo deskriptivne in kavzalno-neeksperimentalne metode empiričnega pedagoškega raziskovanja smo ugotovili, da abstraktnost matematičnih pojmov vpliva tako na ustreznost kot tudi na pravilnost ustvarjene risbe, kar pomeni, da sta odštevanje in zakon o združevanju pogosteje ustrezno oz. pravilno reprezentirana matematična pojma. Iz risbe prepoznana konceptualna usmerjenost risb pa izstopa v primeru ulomka kot operatorja in potence. Konceptualna usmerjenost pri teh dveh pojmih v najvišjem deležu vodi do prikaza pravilnega rezultata. Verbalno podani opisi risb, pridobljeni v drugem delu, predstavljajo dodano vrednost z vidika učenčeve interpretacije prikazanega ter hkrati ponujajo dodaten vpogled v učenčevo razumevanje matematičnih pojmov.

Keywords

disertacije;matematika;vizualizacija;reprezentacije;učenci;aritmetika;

Data

Language: Slovenian
Year of publishing:
Typology: 2.08 - Doctoral Dissertation
Organization: UM PEF - Faculty of Education
Publisher: [M. Podgoršek Mesarec]
UDC: 37.091.3:51(043.3)
COBISS: 198922755 Link will open in a new window
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Other data

Secondary language: English
Secondary title: Visual representations of selected early arithmetics concepts
Secondary abstract: The visual representations play a significant role in constructing the understanding of mathematical concepts among students, particularly in building comprehension of early arithmetic notions. In this doctoral thesis, we address this topic and empirically validate it based on theoretical insights. The selected early arithmetic concepts include subtraction, the associative property, fraction as an operator, and exponentiation. The research comprises two parts involving sixth-grade elementary school students. We aimed to analyze the drawings of the given mathematical concepts in terms of appropriateness, orientation, and correctness, as well as identify the ways in which the concepts are portrayed in the drawings. Additionally, we explored the correlation between the student's description of the drawing and the represented mathematical concept. Drawings were utilized as a research tool, representing a novelty in the field of arithmetic. Through a combination of descriptive and causal-nonexperimental methods of empirical pedagogical research, we found that the abstract nature of mathematical concepts influences both the appropriateness and correctness of the created drawings. This implies that subtraction and the associative property are more frequently represented appropriately or correctly. The conceptual orientation of drawings stands out in the case of the fraction as an operator and exponentiation. A high percentage of conceptual orientation in these two concepts leads to the representation of the correct result. Verbal descriptions of the drawings obtained in the second part add value in terms of the student's interpretation of the depiction and simultaneously provide additional insight into the student's understanding of mathematical concepts. 
Secondary keywords: dissertations;mathematics;visualization;representations;students;arithmetics;Osnovnošolsko učenje in poučevanje;Matematika;Univerzitetna in visokošolska dela;
Type (COBISS): Doctoral dissertation
Thesis comment: Univ. v Mariboru, Pedagoška fak.
Pages: 1 spletni vir (1 datoteka PDF (XXIV, 242 str.))
ID: 21863345