Spatial representations in mathematics in the 5th grade

V magistrskem delu z naslovom Prostorske predstave učencev pri matematiki v 5. razredu smo želeli predstaviti problematiko, s katero se učenci srečujejo pri geometriji. Ugotoviti smo želeli, kakšno prostorsko predstavo imajo učenci petih razredov in ali se med deklicami in dečki pojavljajo razlike na preizkusu znanja iz prostorskih predstav. V teoretičnem delu je predstavljen vsebinski sklop geometrije in njena umeščenost v učni načrt. Predstavili smo operativne cilje in vsebine, ki jih učenci spoznajo od 1. do 5. razreda. Poleg operativnih ciljev in vsebine smo omenili tudi splošne cilje, standarde znanja, ki jih mora učenec doseči, in didaktična priporočila, ki so v pomoč učitelju pri dosegi ciljev. Opisali smo pristop, s katerim učitelji seznanijo učence s tridimenzionalnimi in dvodimenzionalnimi oblikami pri geometriji in izpostavili vsebini, ki spodbujata prostorsko predstavo. Znotraj geometrije smo se osredinili na področje prostorskih predstav in njihovo kvalifikacijo na prostorsko vizualizacijo in prostorsko orientacijo. Primerjali smo ju med seboj in zapisali pomembne razlike med njima. Predstavili smo ugotovitve tujih raziskav avtorjev Piageta in zakoncev van Hiele. Piaget je raziskoval razvoj sposobnosti prostorskih predstav in razvoj prostorskih pojmov. Zakonca van Hiele pa sta raziskovala razvoj geometrijskih predstav. Teoriji smo med seboj tudi primerjali in zapisali najpomembnejše razlike. Na koncu smo se osredotočili še na napačne prostorske predstave in prikazali načine, kako bi učitelj lahko pripomogel k odpravi napak. V empiričnem delu smo kot metodo dela uporabili deskriptivno neeksperimentalno, glede na raziskovalno pristop pa smo izbrali kvantitativno raziskavo. Raziskava je temeljila na neslučajnostnem priložnostnem vzorcu. S pomočjo preizkusa znanja smo raziskali, kako uspešni so učenci pri reševanju nalog s poudarkom na prostorskih predstavah. Raziskali smo tudi, ali se med deklicami in dečki pojavljajo razlike na preizkusu znanja iz prostorskih predstav. Želeli smo tudi ugotoviti, katere so najpogostejše napačne prostorske predstave učencev in katere so najpogostejše težave pri prepoznavanju geometrijske mreže kocke. S pomočjo preizkusa znanja smo tudi raziskali, katera težava je pogosteje prisotna: prostorska vizualizacija ali prostorska orientacija. Rezultati raziskave so pokazali, da imajo učenci slabo prostorsko predstavo. Predvsem imajo težave z ločevanjem osnovnih matematičnih pojmov, kot so geometrijska telesa in geometrijski liki. Težave so imeli tudi s prepoznavanjem mreže kocke. Med deklicami in dečki se pojavljajo razlike pri preizkusu znanja iz prostorskih predstav, vendar pa te razlike niso statistično pomembne. Malo boljši rezultat so dosegli dečki. Več težav pri reševanju učencem povzroča prostorska vizualizacija, saj morajo učenci razumeti in si predstavljati mentalne premike dvo- in tridimenzionalnih predmetov. Pred tem pa si morajo ustvariti mentalno sliko in si jo predstavljati v svojih mislih. Tega vsi učenci 5. razreda še niso zmožni. Raziskava na področju prostorske predstave je pomembna za razvoj matematike, bolj natančno na področju geometrije. Rezultati raziskave nudijo vpogled v primanjkljaje učencev na področju prostorskih predstav in predstavljajo izhodišče za nadaljnje načrtovanje in izboljšave pouka geometrije na razredni stopnji.In the master\u27s thesis entitled Spatial representation in Mathematics in the 5th grade, we wanted to present the problems that pupils face in geometry. We wanted to find out what kind of spatial representation pupils of fifth grade have and whether there are differences between the sexes. In the theoretical part, we described the geometry and its placement in the curriculum. We presented the operational goals and contents that pupils learn from the 1st to the 5th grade. In addition to the operational goals and content, we also mentioned the general goals and standards of knowledge that a pupil must achieve and didactic recommendations that help the teacher achieve the goals. We have described the approach by which teachers acquaint students with three-dimensional and two-dimensional shapes in geometry and highlight the content that promotes a spatial representation. Within geometry, we focused on the field of spatial representation and its qualification to spatial visualization and spatial orientation. We compared each other and recorded important differences between them. We presented the findings of foreign research by Piaget and spouses van Hiele. Piaget explored the development of the ability of spatial representations and the development of spatial concepts. Spouses van Hiele investigated the development of geometric representations. We compared the theories and recorded the most important differences among themselves. In the end, we focused on the wrong spatial representations and presented the ways in which the teacher can help to correct mistakes. In the empirical part, we used the descriptive non-experimental method as a method of work, and according to the research approach we selected a quantitive study. The research was based on a random occasional sample. With the help of the exam, we studied how successful pupils are in solving tasks with an emphasis on a spatial representaion. We also explored whether there are differences in spatial representation between the sexes. We also wanted to find out which are the most common wrong spatial problems of pupils and which are the most common problems in identifying the geometric net of the cube. With the help of the exam we also invetigated which problem is more often presented-spatial visualization or spatial orientation. The results of the study showed that pupils have a poor spatial representation. They mainly have problems with the separation of basic mathematical concepts, such as geometric shapes and geometric bodies. Problems were also encountered by identifying a net of a cube. There are differences between girls and boys in the exam in spatial representation, but this differences are not statistically significiant. A little better result was achieved by boys. More problems in solving is caused by spatial visualization, as pupils must understand and imagine the mental move of two- and three-dimensional object. Before that they must create a mental picture and imagine it in their minds. Not all pupils in the 5th grade are not capable of this. The research of the spatial representaion is important for the development of mathematics, more precisely in the field of geometry. The results of the survey provide and insight into the pupil\u27s deficits in spatial representation and represent the starting point fort he further planning and improvement of geometry classes at the class level