Alfa Charisma Sardjono Pello, I. Ketut Budayasa, Agung Lukito
Analogical reasoning plays a crucial role in mathematical problem-solving by facilitating knowledge transfer across different contexts. This study explores how reflective middle school students identify structural similarities between source and target mathematical problems, focusing on patterns in their analogical reasoning. Using a qualitative case study approach, two Grade 7 students with reflective cognitive styles solved problems involving the area of a rectangle (source problem) and a parallelogram (target problem). Their problem-solving processes were analyzed using the Structuring, Applying, and Verifying (S-A-V) framework to examine how they mapped structural elements. The findings reveal that both participants successfully transferred structural concepts from the rectangle to the parallelogram, integrating mapping throughout all problem-solving stages. Key observed patterns include deep structural understanding, high metacognitive engagement, distinct modality preferences (verbal-linguistic and visual-spatial), adaptability in strategy transfer, and rigorous verification practices. These results suggest that reflective cognitive styles significantly enhance analogical reasoning and problem-solving proficiency in mathematics. Instructional strategies that emphasize analogical reasoning, metacognitive training, structural understanding, and diverse learning modalities can further support students’ mathematical development. However, the study’s limited sample size and focus on reflective cognitive styles constrain its generalizability, highlighting the need for further research with larger, more diverse participant groups. By fostering these cognitive and instructional approaches, educators can enhance students’ problem-solving abilities across STEM disciplines, equipping them with the adaptability and reasoning skills necessary for success in an increasingly technology-driven world. © 2026 Author(s)
Universitas Negeri Surabaya, Jawa Timur, Surabaya, Indonesia
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