Uporaba grafičnih reprezentacij pri matematiki na razredni stopnji

Primožič, Katja (author), Manfreda Kolar, Vida (mentor)

V diplomskem delu so predstavljene različne zunanje reprezentacije pri pouku matematike. Osredotočili smo se predvsem na grafične reprezentacije. Opredelili smo jih kot grafične reprezentacije v vsakdanjem življenju, pri šolskih predmetih in grafične reprezentacije pri matematiki. Predstavili smo vpeljavo matematičnih pojmov, računskih operacij, odnosov in relacij s pomočjo uporabe grafičnih reprezentacij. Teoretični del zajema tudi klasifikacijo grafičnih reprezentacij glede na stopnjo njihove uporabnosti: uporabne, neuporabne, zavajajoče in neustrezne grafične reprezentacije. V empiričnem delu so predstavljeni rezultati raziskave, s katero smo ugotavljali uporabo grafičnih reprezentacij pri reševanju besedilnih nalog, uporabnost grafičnih reprezentacij za rešitev nalog in načine ponazoritev, ki jih učenci uporabljajo pri reševanju problemskih nalog. V raziskavi je sodelovalo 17 učencev četrtega razreda osnovne šole. Podatke smo zbrali s pomočjo učnega lista, ki je vseboval 5 besedilnih oz. problemskih nalog, jih analizirali in prikazali v obliki tabel in grafov. Rezultati raziskave so pokazali, da večina učencev uporabi grafične reprezentacije pri nalogah, ki to posebej zahtevajo. Delež teh učencev se zmanjša pri zahtevnejši nalogi, pri kateri imajo težave z računanjem. Pri nalogah, ki navodila za risanje nimajo, pa je odstotek grafičnih reprezentacij zelo majhen. Prav tako smo ugotovili, da grafične reprezentacije pri večini nalog niso uporabne, kljub temu da so naloge pravilno rešene. Kot najmanj uporabne so se izkazale pri nalogi, kjer so imeli učenci težave z razumevanjem koncepta naloge. Pri prvi problemski nalogi je bil delež posameznih ponazoritev približno enak, pri drugi pa je prevladovala simbolna ponazoritev naloge. Pokazalo se je, da je uporaba grafičnih reprezentacij pri učencih na zelo nizki ravni, učenci se jih neradi poslužujejo, prav tako si v večini primerov z lastnimi reprezentacijami ne znajo pomagati.

• Language: Slovenian
• Keywords: reprezentacija
• Work type: Undergraduate thesis
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Year: 2016
• PID: 20.500.12556/RUL-84831
• COBISS.SI-ID: 11135049
• Publication date in RUL: 09.09.2016

Secondary language

• Language: English
• Title: The use of graphic representations in mathematics at primary level

Abstract

This diploma thesis presents various external representations in maths lessons. We focus primarily on graphic representations, which we define as graphic representations in daily life, in school subjects and in mathematics. We present the introduction of maths terms, mathematical operations and relations with the help of graphic representations. Additionally, the theoretical part encompasses the classification of graphic representations according to their level of usefulness: useful, useless, fallacious and unsuitable graphic representations. In the empirical part, we present the results of the study aimed at evaluating the usage of graphic representations in solving mathematical word problems, the usefulness of graphic representations in key to exercises, as well as different ways of depiction the students use when doing problem-solving exercises. The research included 17 fourth-grade primary school students. The data, which was obtained from a handout containing 5 word/problem-based exercises, was analysed and displayed in table and graph form. The results of the survey indicate that the majority of students use graphic representations in exercises that specifically demand that. The percentage of such students decreases when students face counting obstacles while solving more challenging tasks. The share of graphic representations reduces dramatically in exercises which lack instructions that require drawing. Furthermore, the results show graphic representations happen to be useless in greater number of exercises, even though the exercises are carried out correctly. They prove to be least efficient in exercises, in which students experience difficulties understanding the concept of a particular exercise. The proportion of certain representations is almost the same in the first exercise, while the symbolic representation prevails upon others in the second exercise. The research reveals the students use graphic representation extremely inefficiently, they make use of them with considerable reluctance, they regularly cannot even help themselves using their own representations.

• Keywords: representation