This thesis presents a research about solving problem tasks of students of Teacher Education in the Republic of Croatia and in the Czech Republic. The term of a problem task is also explained, as well as their importance in shaping students' mathematical competencies. Problem tasks are classified within the Word problems category, as well as within the QUASAR and TTML projects. The context of mathematics and problem tasks is presented in a historical context, as the problem task has evolved throughout the history of mathematics. The results of PISA and TIMSS external evaluations in the last few years for the Republic of Croatia and the Czech Republic are also presented. Some problem-solving methods are also listed, including Georg Polya's four steps and Descartse's attempt to find a universal problemsolving method. The methods are presented as just one example, guideline that can help with general design, they are not universal for every task. The framework program of schooling in Croatia and the Czech Republic was also presented, as well as mathematics as a subject in school. In addition, the Hejny problem-solving method specific to students at Charles University in the Czech Republic was presented. The conducted research did not show that there are any big differences in solving problem tasks for students in Croatia and the Czech Republic. Most of the respondents chose the same or similar methods in solving problem tasks.