Cognitive Backgrounds of Problem Solving: A Comparison of Open-ended vs. Closed Mathematics Problems
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Bahcesehir University
University of Arizona
Publication date: 2015-09-29
Corresponding author
Abdulkadir Bahar   

Bahcesehir University, Çırağan Caddesi, Osmanpaşa Mektebi Sokak No: 4, 34349 Beşiktaş/İstanbul, Turkey
EURASIA J. Math., Sci Tech. Ed 2015;11(6):1531-1546
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.

Materials and methods:
The author investigated this relationship by separating performance in open-ended and closed situations. Multiple regression analyses were performed to predict students’ problem solving performance. Intelligence, creativity, memory, knowledge, reading ability, verbal ability, spatial ability, and quantitative ability constituted independent variables whereas mathematical problem solving performance scores in closed and open-ended problems were the dependent variables.

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.

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