Mathematical reflective thinking strategy in problem-solving viewed by cognitive style

Abstract

Mathematical reflective thinking is a mathematical thinking activity involving the persistent consideration process of the use of knowledge and decision making in solving a problem. This study aims to describe mathematical reflective thinking strategy of students based on impulsive and reflective cognitive styles in solving the mathematical problems. To do so, first, we developed three tasks about the linear programming problems. Next, 35 students of senior high school in the 11th grade (16-17 years-old), were given tasks and continued with the giving one set of Familiar Figures Figure Test (MFFT). Then four students were selected as representatives of the other students. In-depth interviews were conducted with students to confirm the findings of the task's answers. Finally, the data were analyzed to explain the mathematical reflective thinking strategy of students based on cognitive styles. We found that students with impulsive cognitive styles have a tendency to think reflectively on the stage of understanding and reflection, using inefficient strategies, not completing answers, and give up easily in the face of a difficult task. Whereas the students with reflective cognitive style have a tendency to think reflectively on the stage of reflection and critical reflection, using expert strategies, concluding answers, and solving difficult problems in accordance with logic; and trial and error.