Conceptions of Creativity in Elementary School Mathematical Problem Posing

Mathematical problem posing and creativity are important areas within mathematics education, and have been connected by mathematicians, mathematics educators, and creativity theorists. However, the relationship between the two remains unclear, which is complicated by the absence of a formal definition of creativity. For this study, the Consensual Assessment Technique (CAT) was used to investigate different raters' views of posed mathematical problems. The principal investigator recruited judges from three different groups: elementary school mathematics teachers, mathematicians who are professors or professors emeriti of mathematics, and psychologists who have conducted research in mathematics education. These judges were then asked to rate the creativity of mathematical problems posed by the principal investigator, all of which were based on the multiplication table. By using Cronbach's coefficient alpha and the intraclass correlation method, the investigator measured both within-group and among-group agreement for judges' ratings of creativity for the posed problems. Previous studies using CAT to measure judges' ratings of creativity in areas other than mathematics or mathematics education have generally found high levels of agreement; however, the main finding of this study is that agreement was high only when measured within-group for the psychologists. The study begins with a review of the literature on creativity and on mathematical problem posing, describes the procedure and results, provides points for further consideration, and concludes with implications of the study along with suggested avenues for future research.