Failures of Mathematical Creative Thinking in Solving Three-Variable Linear Equation Systems Viewed from Self-Regulation

Abstract

This study aims to analyze the failure of students’ mathematical creative thinking abilities in solving systems of linear equations in three variables (SPLTV) problems based on their level of self-regulation. Mathematical creative thinking is an essential higher-order skill, yet many students struggle to generate ideas, apply flexible strategies, and elaborate solutions when solving complex problems. This research employed a qualitative descriptive approach involving students categorized into high, medium, and low self-regulation levels. Data were collected through creative thinking tests, self-regulation questionnaires, and semi-structured interviews. The analysis focused on identifying patterns of failure across indicators of creative thinking, including fluency, flexibility, originality, and elaboration. The results indicate that students with low self-regulation tend to fail at planning problem-solving strategies, monitoring solution steps, and evaluating results, leading to incomplete or incorrect solutions. Students with moderate self-regulation partially fulfill creative thinking indicators, while those with high self-regulation demonstrate better control of their thinking processes, though some difficulties remain in originality and elaboration. These findings highlight the critical role of self-regulation in supporting students’ mathematical creative thinking and provide implications for designing instructional interventions to reduce learning failure in SPLTV topics.