Problem solving has beena core theme in education for several decades. Educators and policy makersagree on the importance of the role of problem solving skills for school andreal life success. A primary purpose of this study was to investigate theinfluence of cognitive abilities on mathematical problem solving performance ofelementary students. The author investigated this relationship by separatingperformance in open-ended and closed situations. Findings of the studyindicated that the cognitive abilities explained 32.3% (open-ended) and 48.2%(closed) of the variance in mathematical problem solving performance as awhole. Mathematical knowledge and general intelligence were found to be theonly variables that contributed significant variance to closed problem solvingperformance. General creativity and verbal ability were found to be the onlyvariables that contributed significant variance to open-ended problem solving performance.