Mapping Patterns in Analogical Reasoning: A Qualitative Study of Reflective Middle School Mathematics Students
Keywords:
mapping, analogical reasoning, qualitative study, reflective middle schoolAbstract
Analogical reasoning enhances mathematical problem-solving skills in middle school students by enabling knowledge transfer across different contexts. This study investigates how reflective middle school students map structural similarities between source and target mathematical problems and identifies patterns in their analogical reasoning. Through a qualitative case study, two Grade 7 students with reflective cognitive styles calculated 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 identified and mapped structural elements. Findings show that both participants effectively mapped structural elements from the rectangle to the parallelogram, integrating mapping throughout all problem-solving stages. Key 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 in mathematical problem-solving. Instructional strategies promoting analogical reasoning, structural understanding, metacognitive training, diverse learning styles, and thorough verification can substantially improve mathematical proficiency. However, the limited sample size and focus on reflective styles constrain generalizability, indicating the need for future research with larger, diverse samples and consideration of contextual factors.
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