A theoretical framework that provides a foundation for understanding the process of forming geometric concepts is the van Hiele’s model of the development of geometric thinking, which follows the students’ progress with a hierarchically arranged series of levels characterized by an increase in abstractness. The model is aligned with the development of children's cognitive structures from an early age, when they can see objects only as a whole, and until the age when they are capable of formal, axiomatic geometric thinking. The paper presents the results of the research of student achievements in relation to the first three levels of development of geometric thinking according to van Hiele’s model in primary school mathematics classes. The research was conducted on a sample of 118 primary school students in the Pčinja district. Using the theoretical analysis method, based on the description of the level (visualization, analysis and informal deduction) and the curriculum of the primary geometry lessons, appropriate criteria were set as indicators to measure if a level was reached. A knowledge test was created that contained tasks corresponding to each of the abovementioned levels, and it was used as an instrument. The results obtained indicate that students' geometric thinking, in relation to their educational stage, develops in accordance with van Hiele's levels. Thus, first-grade students reached the visualization level, a third of the second-grade students and half of the third-grade students reached the analysis level, while 16.1% of the fourth-grade students reached the informal deduction level, which was expected for children of this age.