Cognitive styles in posing geometry problems: implications for assessment of mathematical creativity

While a wide range of approaches and tools have been used to study children's creativity in school contexts, less emphasis has been placed on revealing students' creativity at university level. The present paper is focused on defining a tool that provides information about mathematical creativity of prospective mathematics teachers in problem- posing situations. To characterize individual differences, a method to determine the geometry-problem-posing cognitive style of a student was developed. This method consists of analyzing the student's products (i.e. the posed problems) based on three criteria. The first of these is concerned with the validity of the student's proposals, and two bi-polar criteria detect the student's personal manner in the heuristics of addressing the task: Geometric Nature (GN) of the posed problems (characterized by two opposite features: qualitative versus metric), and Conceptual Dispersion (CD) of the posed problems (characterized by two opposite features: structured versus entropic). Our data converge on the fact that cognitive flexibility-a basic indicator of creativity-inversely correlates with a style that has dominance in metric GN and structured CD, showing that the detected cognitive style may be a good predictor of students' mathematical creativity.