Tracing creative mathematical thinking trajectories of fifth-grade students in open ended geometry tasks: A phenomenographic study

This study aimed to explore the qualitatively different ways fifth-grade students conceptualize perimeter and area through open-ended geometric tasks. By analyzing written work and clinical interviews with five students, the study identified five conceptions ranging from procedural application to flexible spatial reasoning. Findings suggest that mathematical creativity emerges from the dynamic interaction between perceptual engagement, measurement conceptualization, and structural abstraction. The resulting outcome space organizes these conceptions along a continuum of increasing conceptual sophistication. This study offers important insights into task design and formative assessment in mathematics education. The results emphasize the role of open-ended tasks in fostering divergent mathematical thinking and going beyond mere procedural memorization in elementary school settings.