Logical thinking represents an important process of reasoning and a basic skill in building students' knowledge and experience which should accompany the learning process and develop students' potential at all levels of education. The program of teaching and learning mathematics in primary education in Serbia contains a large number of topics that support the goal of learning mathematics, but there is also room for improvement. The paper deals with the possibility of propaedeutics of logic and the encouragement of logical thinking, the application of open-ended tasks in the initial teaching of mathematics. Respectively to the program contents of the mathematics class, examples of open-ended tasks are presented, as support and analog to teachers in creating teaching practice, in order to promote the development of students' logical thinking, as an important component of mathematics learning outcomes.