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Abstract. The paper is aimed at current approaches toward using of information and communication technology in education. Firstly, nowadays usage of computers in education is introduced on the basis of an overview and survey of the researches presented on the recent conference Computers in Education organized by the Asia-Pacific Society for Computers in Education. Last research in the following areas is discussed here: computer-supported personalized and collaborative learning, seamless learning, level of attention and learning efficiency, learning analytics, application of innovative educational technologies in STEM education, and online game-based learning in school education. Despite the geographical orientation many issues may be inspirational for scholars from western countries. On the other hand, from research papers presented by researchers from Asia-Pacific region it is evident that they have been focusing on very similar topics in education as scientists in western countries do. Secondly, some observation concerning usage of information and communication technology in Egypt education as well as recent research works examined within the doctoral study program information and communication technology in Education provided by the University of Hradec Králové, Czech Republic, are presented in the paper in the light of the mentioned survey.

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Subjects dealing with graph theory and combinatorial optimization belong among the basic subjects of informatics study. Their aim is above all to develop and deepen students' capacity for logical and algorithmic thinking. Mathematical proofs that are inseparable part of these subjects do not belong to popular topics among students due to the difficulty to understand this field of mathematics. Within educational process we are searching for various tools to help students deal with this area of mathematics. Suitable visualization could become a very convenient instrument used to enhance understanding of theorems and their proofs. Using visualization and deep analysis of the topic together with discussion on mutual relationships between solutions to problems allows the teacher to enhance student's logical thinking and support their understanding to more complex proofs. In the paper we provide a justification for the importance of the mathematical proofs for students of informatics at first. Secondly, we introduce a research study examining an impact of visual applications on understanding of mathematical proofs; we implemented presentations instructed within the Discreet mathematics course, which are used to visualize proofs of mathematical theorems in the area of the graph theory, and we analysed students' approaches to proofs visualization and proofing in general.