Analysis of the Refractive Thinking of Students in Decision Making on Open Problems in Mathematics - Ardiana Ardiana (Lembaga Penerbitan dan Publikasi Ilmiah Program Pascasarjana IAI Sunan Giri Ponorogo, 2025)
This study aims to describe students’ decision-making processes in solving open mathematical problems based on refractive thinking. The research employed a qualitative approach with a descriptive design. The participants were undergraduate students of the Mathematics Education Study Program at the State University of Malang, selected purposively based on decision-making style, domicile, and understanding of the problem context. Research instruments included validated open-ended problem sets based on graph theory and semi-structured interview guides. Data were collected through problem-solving tasks and in-depth interviews, and then analyzed using Miles and Huberman’s interactive model, which consists of data reduction, data display, and conclusion drawing. The findings reveal that students experienced five stages of reflective thinking—perplexity, investigation, construction, evaluation, and decision—throughout the decision-making process. Students with a rational style demonstrated more systematic and consistent reasoning, while intuitive, dependent, and avoidant students tended to perform incomplete evaluations. These results highlight that refractive thinking plays a crucial role in forming logical and adaptive decisions. The study implies that open-ended, context-based mathematics learning can effectively enhance students’ higher-order thinking through reflective and evaluative reasoning. Future research should explore the development of instructional models and digital-based learning environments that systematically foster reflective thinking and decision-making skills across diverse cognitive styles and educational levels.