Divergence and convergence of mental forces of children in open and closed mathematical problems

In this study we investigated relationships between convergent and divergent thinking with an emphasis on fluency, originality, flexibility and elaboration in the mathematical domain. A related purpose was to examine relationships between problem types in mathematical tasks. The math section of a performance-based assessment was used to assess 857 Grade 1 to 6 students' performance in the mathematical domain. Statistically significant correlations were found between divergent and convergent thinking, and between convergent thinking and the components of divergent thinking. Also, this study provided evidence for the construct validity of the Problem Continuum Matrix (Schiever and Maker, 1991, 1997). Correlations between problem types varied according to the proximity of the types to each other.