Students' analogical reasoning and creative thinking across mathematical ability levels

This study examines students' analogical reasoning and creative thinking in solving open-ended mathematical reflection problems across different levels of mathematical ability. Using a qualitative descriptive approach, data were collected from ninth-grade students through written tasks and interviews, with three participants representing high, medium, and low ability levels. The analysis focused on the stages of analogical reasoning: structuring, mapping, applying, and verifying based on Ruppert's model. The findings show apparent differences in students' reasoning processes. High-ability students demonstrated complete and systematic analogical reasoning across all stages and were able to justify their solutions logically. Medium-ability students demonstrated a partial understanding and relied mainly on procedural strategies, whereas low-ability students relied on intuitive visualization with limited mathematical justification. These differences suggest that creative thinking plays a crucial role in enhancing the completeness of analogical reasoning. The novelty of this study lies in its detailed analysis of how students with different mathematical ability levels progress through each stage of analogical reasoning when solving open-ended reflection problems. The results suggest that integrating analogical reasoning tasks into open-ended mathematics instruction can strengthen students' conceptual understanding and support the development of creative thinking.