In this paper the application of problem teaching mathematics and respect its characteristics was investigated in the lower grades of primary school, in order to demystify its role and importance in enhancing the educational and functional effect. The research was done in the period from September to December 2015, by testing students of fourth grade in five elementary schools. Statistical analysis of the selected groups has shown there is no statistically significant difference between groups, and the test normality of distribution was done using the Kolmogorov-Smirnov and Shapiro-Wilk test. Analysis and comparison of results before and after the experimental program, indicates a significant improvement in students' knowledge and mathematical competencies applying the methodology that has been implemented.

In this paper, the research on the application of mathematical modeling in the problem teaching mathematics in analyzed schools was carried out in the form of an experiment, with the aim of demystifying its role and importance in increasing the educational and functional effect. In the period of one school semester, in five primary schools it has been shown that mathematical modeling can be implemented and can achieve significant effects. The statistical overview of selected groups demonstrated the application of mathematical modeling in experimental classes, but gave an overview of the results of applying mathematics and modeling in control groups. Tests were performed using Kolmogorov-Smirnov, Shapiro-Wilkov, Mann-Whitney and Wilcoxon test. The analysis and comparison of the results before and after the experimental program indicates a significant improvement in student knowledge and mathematical competences using the methodology of mathematical modeling which was carried out using the experiment.

In this paper we observed the global dynamics and the occurrence of a certain bifurcation for the corresponding values of a certain rational difference equation of the second order with analyzed quadratic terms. The analysis of the local stability of the unique equilibrium point, as well as the unique periodic solution of period two, was performed in detail. The constraint of the equations on both sides for the corresponding values of the parameters is proved and on this basis the global stability is analyzed. The existence of Neimark-Sacker bifurcation with respect to the arrangement of equilibrium points has been proven. Thus, the basins of attraction have been determined in full for all the positive values of the parameters and all the positive initial conditions.

In this paper we give a representation of Stirling numbers of the second kind, we obtain explicit formulas for some cases of Stirling numbers of the second kind and illustrate a method for founding other such formulas. 2010 Mathematics Subject Classification. 11B73, 05A10.

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