Misconceptions of third and fifth graders about geometrical shapes and bodies

Namen magistrskega dela je obravnava zmotnih predstav tretješolcev in petošolcev pri učenju in poučevanju matematične teme geometrijskih likov in teles. Avtorja Clements in Battista (1992) v svojem delu opisujeta številne raziskave, ki kažejo na to, da tema geometrijskih likov in teles učencem povzroča težave. Ker so bile raziskave, ki potrjujejo omenjeno dejstvo, po večini izvedene le v tujini, sem se odločila, da problematiko poznavanja in razumevanja geometrijskih likov in teles raziščem v eni izmed slovenskih osnovnih šol. V teoretičnem delu sem opisala operativne cilje in vsebine, ki jih učenci spoznajo od 1. do 5. razreda v okviru tematskih sklopov »Geometrijske oblike in uporaba geometrijskega orodja«, »Geometrijski elementi« ter »Liki in telesa«. Predstavila sem pomen poznavanja učnih težav pri matematiki za uspešno poučevanje geometrije in osnovnošolski pristop poučevanja geometrije »od telesa k točki«, v okviru katerega sem predlagala tudi didaktična priporočila za poučevanje geometrije v osnovni šoli. Geometrijsko mišljenje so do sedaj raziskovali že številni avtorji, zato sem v teoretičnem delu predstavila še izsledke tujih raziskav o težavah pri geometriji in o razvoju geometrijskih pojmov in predstav s poudarkom na avtorjih van Hielu in Piagetu. Ker geometrija pogosto temelji na abstraktnem znanju in ker je reševanje geometrijskih problemov za učence zahtevno, sem se osredinila še na učenčeve strategije reševanja problemov in najpogostejše vrste napak, s katerimi se pri tem srečujejo. Osnovna raziskovalna metoda empiričnega dela je bila deskriptivna neeksperimentalna, glede na raziskovalni pristop pa je bila raziskava kvantitativna in kvalitativna. Na podlagi preizkusa znanja sem ugotavljala, na kateri stopnji geometrijskega mišljenja po van Hielu so tretješolci in petošolci, raziskala pa sem tudi najpogostejše zmotne predstave učencev o geometrijskih likih in telesih ter razlike v uspešnosti reševanja nalog glede na spol in glede na starost učencev. S pomočjo anketnega vprašalnika sem ugotavljala še, kakšna je povprečna ocena učencev pri matematiki, kakšen odnos imajo do nje, kakšen pomen pripisujejo poznavanju geometrijskih likov in teles v vsakdanjem življenju ter kakšno težavnost pripisujejo obravnavi teme geometrijskih likov in teles v šoli. Rezultati raziskave so pokazali kar nekaj težav tretješolcev in petošolcev pri razumevanju, uporabi in predstavi geometrijskih likov in teles. Učenci so imeli težave s prepoznavanjem oblik, ki so posebne, malokrat videne. Bolj kot so bile oblike razvejane in netipične, več težav so imeli tretješolci in petošolci z njihovim prepoznavanjem. Raziskava o zmotnih predstavah na področju geometrije je pomembna za razvoj področja didaktike matematike. Na podlagi ugotovljenega se bo v prihodnje lahko opredelilo, kako izboljšati težavna geometrijska področja, in sicer z vidika ustreznih didaktičnih pripomočkov, metod in oblik dela ter načina dela za preprečevanje zmotnih predstav o geometrijskih likih in telesih.The purpose of the master\u27s thesis is to deal with the misconceptions of third and fifth graders in teaching and learning mathematical topics on geometric shapes and bodies. The authors Clements and Battista (1992) describe in their work a number of studies showing that the topic on geometric shapes and bodies causes problems to students. Since the studies, which confirm this fact were mostly carried out only abroad, I decided to explore the problem of knowing and understanding geometric shapes and bodies in one of the Slovene primary schools. In the theoretical part I described the operational objectives and the content that students learn from the first to the fifth grade within the thematic frames »Geometrical forms and the use of geometrical tools«, »Geometric elements« and »Geometric shapes and bodies«. I presented the importance of understanding learning difficulties in mathematics for successful teaching of geometry and a primary school approach of teaching geometry »from the body to the point«, in which I also suggested didactic recommendations for teaching geometry in primary school. Until now geometric thinking has been studied by many authors, so in the theoretical part I presented also the findings of other studies on problems in geometry and on the development of geometric concepts focusing on authors van Hiele and Piaget. Because geometry is often based on abstract knowledge and because for students solving geometry problems is challenging, I focused on pupils\u27 problem-solving strategies and the most common types of errors that they encounter. The basic research method of the empirical part was the descriptive non-experimental, and according to the research approach the study was quantitative and qualitative. Based on the school test, I determined, at which stage of geometric thinking are the third and fifth graders according to van Hiele. I also explored the most common pupils\u27 misconceptions about geometrical shapes and bodies, as well as differences in the successfulness of solving problems considering gender and age of the pupils. With the help of a questionnaire I observed, what was the average grade of pupils in mathematics, their attitude towards mathematics, what significance they attribute to the knowledge of geometric shapes and bodies in everyday life and what difficulty they attribute to the topic of geometric shapes and bodies in school. The results showed that third and fifth grades have quite a lot of problems in understanding, using and recognizing geometric shapes and bodies. Pupils had difficulties in recognizing shapes that are special, rarely seen. The more the shapes were branched and atypical, more problems the third and fifth graders had with their identification. The study on misconceptions in the field of geometry is important for the development of the didactics of mathematics. Based on the findings, in future it will be possible to define, how to improve difficult geometric areas, viewed from the perspective of appropriate teaching materials, methods and forms of work and approaches to prevent misconceptions of geometrical shapes and bodies