The Influence of Mathematical Problem-Solving and Critical Thinking Skills through Project-Based Flipped Classroom and Self-Regulated Learning

Introduction: In the field of mathematical education, enhancing problem-solving and critical thinking skills is essential for students to tackle complex mathematical challenges. Objectives: This study investigates the impact of Project-Based Flipped Classroom (PBFC) and Self-Regulated Learning (SRL) on improving these cognitive abilities within mathematics. A 2 x 2 factorial design with a nonequivalent control group pretest-posttest design was used to evaluate the effects. Methods: The participants included 64 seventh-grade students from SMP Negeri 2 Kedungpring Lamongan, divided into two groups using cluster random sampling. Data were collected through mathematical problem-solving tests and SRL-related questionnaires, with analysis performed using MANOVA. Results: The results revealed that (1) PBFC positively influenced students' mathematical problem-solving and critical thinking skills, (2) SRL contributed significantly to the improvement of these skills, (3) the interaction between PBFC and SRL enhanced both problem-solving and critical thinking outcomes in mathematics, and (4) students who exhibited high SRL and participated in PBFC demonstrated better performance in mathematical tasks. Conclusions: These findings highlight the effectiveness of integrating PBFC and fostering SRL to improve essential mathematical cognitive skills, with implications for teaching practices in mathematical education.