The first discussions and articles on pedagogy as a science in Serbia appeared in the second half of the XIX century. At that time, there was no consensus among the leading European and world educators on the basic issues and problems of pedagogical science. Serbian pedagogues who lived and worked in the period when pedagogy was constituted as a science in this region, were supporters of different pedagogical directions. Accordingly, there were differences between them in understanding and interpreting the most important pedagogical issues, which included the issue of determining the purpose and tasks of education. A significant contribution to the constitution of pedagogical science in our country, and therefore to the development of understanding of the purpose and tasks of education, were made by pedagogues who belonged to Herbart's pedagogical school. For this reason, the main attention in the paper is focused on descriptive-historical study and analysis and on the purpose and tasks of educating the most famous Serbian Herbartians - Vojislav Bakić, Ljubomir Protić and Stevan Okanović.