International studies on the knowledge of mathematics at the generalist-class teaching level have indicated that Slovene students are quite skilled at computations, but have difficulties solving mathematical problems. This finding stimulated us to create a problem-based instruction model. We wanted to find out whether the students in the experimental group, who received problem-based instruction, would display greater ability in solving difficult mathematical problems compared to the group receiving conventional instruction. We were also interested in the students' attitude towards mathematics. We formulated the experimental factor--problem posing and solving as the key math-teaching activity--broadened the conventional mathematical problem by introducing into it several other types of problems and strategies of their solving. The efficiency of the model created was tested on a sample of 179 nine-year-old students. The results of the study are useful for the preparation of mathematics curriculum reform and important for the authors of maths materials for teachers and students. The research findings are of great value in the undergraduate education of teachers, as well as for qualified and practicing teachers and their further and regular professional training. (Contains 6 tables.)