Students field independent-dependent solving surface area of square pyramid: Commognitive perspective

Understanding students' cognitive processes in solving mathematical problems is crucial for improving instructional strategies and learning outcomes. However, limited studies have examined students' commognitive aspects in the context of geometric problem-solving, particularly in relation to cognitive styles such as Field-Independent (FI) and Field-Dependent (FD) tendencies. This study addresses this gap by analyzing the four aspects of commognition word use, visual mediators, narratives, and routines demonstrated by students when solving story problems on the surface area of a square pyramid. The study also explores the patterns of thinking and solution strategies employed by FI and FD students in approaching these problems. Conducted in Class VIII A at SMP Negeri 1 Sigi, the study involved two male students, one representing each cognitive style, to highlight differences in problem-solving approaches while controlling for gender. Data collection involved the Group Embedded Figures Test (GEFT) to determine cognitive style, validated problem-solving task sheets, and semi-structured interviews conducted in parallel with the written tasks. Data were analyzed using data condensation, data display, and conclusion drawing techniques. The findings indicate that FI students approach problem-solving with greater detail, clarity, efficiency, and accuracy, explicitly demonstrating all four aspects of commognition. In contrast, FD students exhibit clarity, efficiency, and accuracy but lack detail and thoroughness in their written responses. Both cognitive styles demonstrate all four commognitive aspects, with notable differences in the narrative component FI students explicitly write formulas, whereas FD students understand the formulas but do not record them in writing. These findings provide valuable insights into how cognitive styles influence mathematical problem-solving and commognitive development, offering implications for differentiated instructional strategies in mathematics education.