The Role of Mathematical Resilience in Critical Thinking Development Under PBL Models

This study investigates the impact of the Problem-Based Learning (PBL) model on elementary students' mathematical critical thinking skills and resilience. Employing a quasi-experimental design with a pretest-posttest control group, the research involved 45 fifth-grade students divided into experimental and control groups. Validated instruments, aligned with higher-order thinking and affective constructs, were used to assess critical thinking and mathematical resilience. Quantitative findings demonstrated that the PBL model led to statistically significant improvements in both constructs. Students in the experimental group outperformed their peers, with large effect sizes (Cohen’s d = 2.51 for critical thinking, 2.35 for resilience), and the Mann-Whitney U test confirmed significant intergroup differences. Furthermore, Spearman correlation analysis (r = 0.460, p < 0.05) revealed a moderate positive relationship between resilience and critical thinking. Qualitative analysis showed that students with higher resilience provided more reflective and elaborate responses. The study emphasizes the educational potential of integrating affective-cognitive instructional models. PBL not only enhances academic performance but also supports students’ emotional persistence and adaptability in learning mathematics. However, limitations such as small sample size and sampling method should be considered in interpreting the results. The study concludes that fostering mathematical resilience is essential to optimizing the cognitive benefits of PBL and recommends teacher training and curriculum strategies to implement this dual-focused approach effectively.