Representation, representational transformation and spatial reasoning hierarchical in spatial thinking

Abstract

The aim of this study is to find out the spatial thinking process of students in transforming 2-dimensional (2D) object image to 3-dimensional (3D) object image representation. Spatial thinking is needed to build how to transforming 2- dimensional (2D) object image to 3- dimensional (3D) object image. There is application of spatial thinking in our daily activities for examples in using maps, planning routes, designing floor plans, and creating art. The students of 5th grade have concrete operation level’s, it is critical period of concrete operation toward early abstract period. In preliminary study researcher found that they have problem to drawing 2-dimensional image object to 3-dimentional image object. They had said that side of cube is not square after they had drawn it but it was parallelogram. It is a problem and important thing, the researcher needs to explore how student using their spatial thinking. It is included how to student thinking process specially in case transforming 3dimensional (3D) object image to 2-dimensional (2D) object image in critical period. Spatial thinking in this study is identified through geometrical problems of transforming a 2dimensional object image into a 3-dimensional object image. Subject in this study are a boy and a girl who have visual learning style in middle level of mathematical ability. This is explorative descriptive study through qualitative approach. The result are: 1) there are different internal representations and spatial reasoning of spatial thinking between a boy and a girl, 2) there are different external representations and spatial reasoning of spatial thinking between a boy and a girl, 3) there are different representational transformation spatial objects between a boy and a girl.