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The presented paper is devoted to an innovative way of teaching mathematics, specifically the subject combinatorics in high schools. This is because combinatorics is closely connected with the beginnings of informatics and several other scientific disciplines such as graph theory and complexity theory. It is important in solving many practical tasks that require the compilation of an object with certain properties, proves the existence or non-existence of some properties, or specifies the number of objects of certain properties. This paper examines the basic combinatorial structures and presents their use and learning using relations through the Placemat method in teaching process. The effectiveness of the presented innovative way of teaching combinatorics was also verified experimentally at a selected high school in the Slovak Republic. Our experiment has confirmed that teaching combinatorics through relationships among talented children in mathematics is more effective than teaching by a standard algorithmic approach. [ABSTRACT FROM AUTHOR]

The paper acquaints the reader with the subject of social support and summarizes research in this field in the Czech Republic and Slovakia. Introducing the issues of gifted, twice-exceptional and underachieved children, the paper also points at the broad range of research possibilities in future. There is also a list of literature related to given phenomena. [ABSTRACT FROM AUTHOR]

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The study introduces unique research results on the topic of artistically gifted and talented children and young people, and their interactions with the environment and exhibitions of Slovak galleries. Artistically gifted teenagers (N = 32) from different regions of Slovakia participated in the research. Based on the research results, we consider the gallery environment stimulating for artistic talent of a person in a specific way. The authors of the study confirmed that in the observed group of artistically gifted teenagers, their artistic talent was positively impacted. Progress was captured in specific components of artistic expression (imagination, fantasy and creativity), which was identified as direct influence of visiting galleries. [ABSTRACT FROM AUTHOR]