The European Parliament and the European Council propose to develop mathematical competence as one of the fundamental competencies for personal development and social progress. The national curriculum, adopted in 2011 as the fundamental document for educating students in primary and secondary schools in the Republic of Croatia, respects the recommended competencies. Mathematical area of the curriculum is organized in two domains: the mathematical concepts and mathematical processes. Mathematical processes involve the process of logical thinking, argumentation and reasoning, the subject of this study, which was conducted with a group of ten year olds with a special interest in mathematics. The aim of the study was to establish in which extend the selected tasks and learning act ivities are appropriate to students’ developmental age and if they contribute to developing the process of logical thinking, argumentation and reasoning. The results of the study show that students are able to II follow the sequence of logical reasoning, but they have difficulty communicating their own opinions; students have difficulties in interpreting the truth of complex mathematical statements; students are able to continue simple patterns, but have difficulty with complex patterns; students are able to apply their knowledge and skills in active learning using the strategy of guided discovery to identify regularity in geometry. Selected tasks and learning activities are appropriate and stimulating for students and contribute to the development of appropriate mathematical processes.