RELATIONAL REASONING IN MATHEMATICAL PROBLEM SOLVING: A STUDY OF HIGH SCHOOL STUDENTS WITH IMPULSIVE AND REFLECTIVE COGNITIVE STYLES
DOI:
https://doi.org/10.31000/yeheds69Abstract
Relational reasoning plays an important role in mathematical problem solving because it allows students to logically connect facts, concepts, principles, and operations to obtain meaningful solutions. However, students still tend to rely on memorized procedures without understanding the relationships between mathematical objects, thus experiencing difficulties in planning and justifying problem solving. This study aims to describe the relational reasoning of high school students with impulsive and reflective cognitive styles in solving mathematical problems on the topic of Three Variable Linear Equation Systems (TVLES). The study used a descriptive qualitative approach with a case study design. The research subjects consisted of two eleventh grade students who had average mathematical abilities and represented impulsive and reflective cognitive styles based onMatching Familiar Figures Test (MFFT). Data were collected through problem solving task (PST) based interviews, validated with time triangulation, and analyzed using the analysis model of Miles et al. (2014). The results showed that both subjects were able to build relationships between facts, concepts, principles, and operations at each stage of Polya's problem solving. However, the characteristics of the reasoning process shown were different. Reflective students understood the problem more carefully, considered alternative strategies, and implemented solutions systematically, while impulsive students worked faster, provided more concise justifications, and corrected errors through trial and error. The research findings indicate that cognitive style influences the characteristics of the relational reasoning process in building and explaining relationships between mathematical objects at each stage of problem solving. The results of this study provide an overview of the characteristics of students' relational reasoning that can be used as a basis for designing mathematics learning that is more appropriate to students' cognitive characteristics.
Keywords: Cognitive Style, Impulsive, Mathematical Problem Solving, Reflective, Relational Reasoning
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