Cognitive barriers in elementary students’ mathematical creative thinking on fraction problems: A hierarchical and multidimensional analysis - Yoani Mbipi; Tatang Herman (CV. FOUNDAE, 2026)
Background: Mathematical creative thinking is a crucial competency in contemporary mathematics education; however, elementary students often encounter difficulties in developing this ability, particularly in fraction learning. Previous studies have predominantly focused on measuring creative thinking performance, providing limited understanding of the cognitive barriers underlying students’ difficulties across different dimensions of creativity. Aims: This study aims to identify and describe cognitive barriers in sixth-grade students’ mathematical creative thinking when solving fraction problems across the dimensions of fluency, flexibility, originality, and elaboration. Method: A descriptive qualitative-dominant mixed-methods design was employed involving 30 sixth-grade students from an elementary school in Bandung, Indonesia. Data were collected through open-ended mathematical creative thinking tasks and semi-structured interviews. Students were categorized into low-, moderate-, and high-ability groups, and the data were analyzed using the Miles, Huberman, and Saldaña qualitative analysis framework. Results: The findings revealed that cognitive barriers were hierarchical and multidimensional. Low-ability students experienced representational barriers related to fraction concepts, moderate-ability students demonstrated transitional barriers characterized by dependence on visual representations, and high-ability students exhibited metacognitive barriers affecting precision and originality. Among the creative thinking dimensions, elaboration showed the lowest achievement (12.0%), followed by originality (13.1%), while fraction conceptual understanding remained relatively weak (28.0%). Conclusion: Mathematical creative thinking difficulties develop hierarchically across ability levels and are strongly interconnected across dimensions. The proposed hierarchical-multidimensional framework offers a foundation for diagnosis-based differentiated instruction in elementary mathematics learning.