# Spatial representations in mathematics in the 5th grade

Maja Zakrajšek (2018) Spatial representations in mathematics in the 5th grade. MSc thesis.

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## Abstract

In the master's 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's deficits in spatial representation and represent the starting point fort he further planning and improvement of geometry classes at the class level.

Item Type: Thesis (MSc thesis)
Keywords: spatial representation, geometry, geometric shapes, geometric bodies, curriculum
Number of Pages: 68
Language of Content: Slovenian
Mentor / Comentors:
Mentor / ComentorsIDFunction
doc. dr. Vida Manfreda KolarMentor
Institution: University of Ljubljana
Department: Faculty of Education
Item ID: 5281
Date Deposited: 04 Sep 2018 11:30