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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.