The topic of this thesis is Open-ended tasks in primary mathematics education. The thesis first deals with the notion of a mathematical problem and discusses its categorization depending on the prominent aspect of the problem. The characteristics of traditional and modern teaching are described as well, the main difference being that modern teaching does not emphasize what students already know but calls for the abandonment of such one-sided view of the problem. In modern teaching knowledge is perceived as an individual construct of each student resulting from their contact with the environment. The aim of that kind of a teaching process is to create, solve problems, develop student's innovation, entrepreneurship, and critical thinking. Open-ended tasks are ideal to fulfill these aims because there are many advantages which contribute to the teaching of mathematics. Open-ended task and its categorization are the focus of this thesis, and the strategies for creating an open-ended task are described, as well as the strategy for opening a closed type of task. The research part of this thesis refers to the analysis of the 4th grade mathematics textbooks. The research aimed to investigate the presence of open type tasks in comparison with closed type tasks. Domain C, referring to form and space, was observed in five different mathematical textbooks. Open-ended tasks found in the textbooks are classified according to a three-dimensional instrument which includes: the type of open-ended tasks, open-ended tasks with regard to a goal or a purpose, and open-ended tasks with regard to the main activity. The results of the research showed that open-ended tasks in the C domain are extremely poorly represented in the 4th grade textbooks which are written according to the mathematics curriculum. Consequently, at the end of the thesis, examples of open-ended tasks for the 4th grade of primary school are offered.