The aim of this final thesis is to present the contemporary trends in teaching, with an emphasis being on the modern approaches in Additional Mathematics in the third grade of primary school. The paper introduces the general characteristics of modern teaching whose primary goal is developing competences, along with the features of contemporary mathematics teaching where heuristic teaching, problem solving teaching method, project teaching and discovery learning are recognized as the main forms of modern teaching. Additional Mathematics and its function are also defined along with the most common types of tasks used in the classroom. Further on, the paper describes the characteristics of children gifted for math, as well as the importance of recognizing their talent. In addition, twenty school curricula were analysed for the purpose of this thesis with the special attention being given to planning and organizing Additional Mathematics in the third grade. Beside the analysis of curricula, the interviews were conducted with five primary teachers who were asked questions regarding their implementation of Additional Mathematics in the third grade of primary school. The results derived from the analysis of school curricula and interviews show the lack of modern trends represented in Additional Mathematics teaching. Despite the new forms of teaching being known, their use in schools is still rare, which results in the poor quality of teaching and the achievement of insufficiently good student outcomes. In order to avoid that, the changes in planning and implementing Additional Mathematics teaching are necessary.