Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of elementary students. The author investigated this relationship by separating performance in open-ended and closed situations. Findings of the study indicated that the cognitive abilities explained 32.3% (open-ended) and 48.2% (closed) of the variance in mathematical problem solving performance as a whole. Mathematical knowledge and general intelligence were found to be the only variables that contributed significant variance to closed problem solving performance. General creativity and verbal ability were found to be the only variables that contributed significant variance to open-ended problem solving performance.