This paper explores the ways in which problem-based learning is implemented and its effect on student performance. We conducted a parallel group study of primary school students in grades 5 to 8 to examine the effect of problem-based learning on students' scores on a math test. The assessment of the effect of problem-based learning using an experimental study is a reliable means of verifying the results of earlier research in this area, but also contributes to pedagogical research in terms of assessing the importance of the effect of this type of instruction on the development of various modern skills and competencies. In addition to the principal, experimental method and testing technique, we have employed the descriptive method and the technique of systematic observation in order to identify the manner in which problem-based learning is organized and implemented. The sample consisted of 480 students in grades 5-8 and 14 teachers in two primary schools in the municipality of Nikšić. The results indicate that the majority of teachers in the experimental groups (E-groups) adequately implemented problem-based learning. Differences between E-groups were identified with regard to the way in which students were incentivized, communication between the subjects, and the form of instruction, resulting in differences in performance between E-group students and control group (C-group) students on knowledge tests. Problem-based learning was found to be more effective when students worked on problems in a group format through cooperation and collaboration rather than working on problems individually. We therefore highlight the advantages of group work when implementing problem-based learning, which promotes the development of three areas of competencies in the modern age, as defined by the National Research Council committee in 2011: the cognitive, the interpersonal and the intrapersonal.