The contemporary way of teaching mathematics places the most importance on the independence and activity of its students and therefore today’s schooling is increasingly based on inquiry-based learning. This paper describes what we mean by inquiry-based learning, as well as what lays in its basis and which particular form of task encourages research. We put emphasis on the role of teachers as leaders, moderators and organizers of the research process in teaching. As an initiative of the research process, asking questions is crucial, so it is important that teachers wisely choose questions that would guide students through research and allow them to come up with solutions. Depending on the amount of support provided by the teachers we distinguish three types of student research, which are also listed in this paper. Not unlike other forms of teaching, inquiry-based learning also has its positive and negative sides. The paper presents the positive aspects of inquirybased learning, as well as the obstacles that teachers encounter in implementing such a form teaching. In addition, we provided a comparison between inquiry-based learning and traditional teaching, with which most students and teachers are accustomed to.