Algebraic thinking, combinatorial thinking and reasoning skills are considered as playing central roles within teaching and learning in the field of mathematics, particularly in solving complex open-ended mathematical problems Specific relations between these three abilities, manifested in the solving of an open-ended ill-structured problem aimed at mathematical modeling, were investigated. We analyzed solutions received from 33 groups totaling 131 students, who solved a complex assignment within the mathematical contest Mathematics B-day 2018. Such relations were more obvious when solving a complex problem, compared to more structured closed subtasks. Algebraic generalization is an important prerequisite to prove mathematically and to solve combinatorial problem at higher levels, i.e., using expressions and formulas, therefore a special focus should be put on this ability in upper-secondary mathematics education.

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The aspects of inquiry based learning (IBL) are vigorously and frequently in the focus of recent studies. With the use of inquiry in mathematics in the daily school practice, some further questions are arising there: What kind of problems can be useful for an analysis of students' competencies in the field of IBL and how to assess the performed level of competencies? In this paper, the Mathematics B-day contest assignment is introduced as a mean to assess the students' performance in mathematical inquiry skills. Some new rubrics with didactical variables were designed as a tool for assessing students' competencies. The statistical implicative analysis was used to investigate 29 solutions of Mathematics B-day 2017: Arrow clocks. We identified the key subtasks solutions directly related to the level of the IBL competencies performed in the final mathematical investigation. The subtask which required actually high level of algebraic thinking influenced the level of the final mathematical investigation the most.

The article elaborates on the characteristics and indicators of work life balance (WLB). The focus is on the selected criteria of WLB as well as social life and time spent off work. The WLB factors chosen and discussed are: the amount of stress, exhaustion and lack of time for family activities and responsibilities in the context of WLB. The results of the European survey conducted by the Eurofond are compared with the authors' questionnaire survey conducted in Slovakia in 2015. The survey results revealed stress and working hours to be statistically significant factors that can be seen as obstacles in the WLB and fulfilling family duties for many Slovaks. The survey also shows that the given sample of Slovak respondents performed much worse in the criteria of stress and lack of time results than the European average according to the Eurofond survey. The results could be partly influenced by the fact that the survey participants were mostly employed in the social sector.

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