My research topic is the development of mathematical competences with ICT tools. I proceed according to my research plan. I compare the efficiency of the learning and teaching process of mathematics in different – based on traditional and supported by ICT tools – teaching environments. In doing so, I try to get to know and review the ICT tools. I search those Mathematics lesson activities that can be supported by ICT tools (computers, interactive boards, internet). I want to learn about the impact of ever-expanding touch-screen devices (smart phones, tablets, ...) on learning habits. I would like to use some topics and methods from the Hungarian teaching tradition, which are unusual in Transcarpathia, where I am teaching. One of the traditional Hungarian topics is the dissection, which is in the international literature connected with the name of Farkas Bolyai. I review the dissection used to determine the area of the plane figures and look for these types of competition tasks.