This paper is about student oriented teaching and the application of a geometry themed project in primary education of mathematics. After a brief overview of the development of geometry as a science and as a school subject, this paper analyses its representation in The Curriculum and in the National curriculum for Croatian compulsory education. Van Hiele’s theory of geometrical thinking is used to give an insight into the structure and the ways of students’ understanding and comprehending geometry and its concepts. According to the Van Hiele’s theory, students develop their geometrical thinking and progressing through various stages by applied activities. Therefore, besides exhibiting the theory, this paper shows us different activities which are intended for developing geometrical thinking and which can be applied in class. Afterwards, the paper thoroughly reviews the cube and the square concept in geometry teaching, in the first four grades of elementary school. It gives guidelines for comprehending these concepts, same as circumference, surface and volume concepts. The central part of this paper revolves around student oriented mathematics teaching and project teaching as a form of student oriented teaching. Student oriented teaching represents a mutual student and teacher effort and implies the application of various activities. Paper exhibits its characteristics in relation to the traditional mathematics teaching. Then it describes the concept of project teaching. Project teaching is when a group of students work together in order to solve a more complicated problem. In its continuation, the paper gives a suggestion of a cube and square themed project in the primary teaching of mathematics and describes its implementation in one class.