This paper briefly presents the van Hiele's theory of the development of student's geometric thinking at the beginning of the education. Below is a brief overview of the origin and development of geometry through history, its origins and how teaching geometry is perceived today. The contents of the geometry taught in elementary school are shown trough the Croatian The school plan and program (CNES, 2006). The objectives of teaching geometry from the Croatian National Curriculum (CNES, 2011) are also mentioned. Students develop their geometric thinking through respective activities. Pierre and Dina van Hiele set levels of geometric thinking to show that the development of recognition and visualization, through analysis, informal deduction and deduction can come up to a maximum level of stringency at which they become able to perform formal proof understanding of geometry in the full sense. Activities that can contribute to a faster understanding and acquiring knowledge of geometry in elementary school are displayed. We have applied van Hiele's theory in order to determine at which level our students are. A survey was conducted on a sample of 183 elementary school students, which was to determine whether the students really are at zero level and the first level in primary school. We started from the assumption that the students in the first grade of primary school are at the zero level and in the upper grades develop their geometric thinking to predicted levels. The hypothesis was partially confirmed.