Critical thinking of impulsive students in solving geometry problems

Abstract

Critical thinking is a higher-order thinking skill that plays a crucial role in mathematics education, particularly in geometry, which requires students to analyze relationships among objects, evaluate solution procedures, and construct logical arguments. However, students with an impulsive cognitive style tend to respond hastily, demonstrate insufficient accuracy, and frequently commit both procedural and conceptual errors in problem solving. This study aims to describe the critical thinking abilities of students with an impulsive cognitive style in solving geometry problem-solving tasks, especially those requiring reasoning about the properties of plane figures and the relationships among geometric elements. This study employed a descriptive qualitative approach involving two ninth-grade junior high school students as research participants. The participants were selected based on the results of the Matching Familiar Figures Test (MFFT), with fast response time and a high number of errors serving as the dominant indicators of an impulsive cognitive style. The research instruments consisted of a geometry problem-solving test and in-depth interview guidelines. Data analysis focused on Ennis’s critical thinking indicators, namely: (1) clarity of statements, (2) the basis for decision making, (3) procedural and computational accuracy, and (4) evaluation of solutions. The findings indicate that impulsive students exhibit dominant weaknesses in the indicators of clarity of reasoning, computational accuracy, and solution evaluation. They tend to determine solution steps hastily without re-examining the procedures used. Nevertheless, with respect to the indicator of identifying relevant information, impulsive students still demonstrate relatively adequate ability. They are also able to formulate problem-solving strategies; however, these strategies tend to be unsystematic and often fail to consider alternative approaches. These findings confirm that an impulsive cognitive style has a significant influence on the quality of students’ critical thinking in geometry problem solving. The pedagogical implications of this study highlight the need for teachers to design instructional strategies that better support the development of critical thinking among impulsive students, such as providing reasoning scaffolding, engaging students in reflective analysis of solution steps, and employing geometry tasks that promote carefulness, answer verification, and mathematical argumentation.