Integrating Problem-Based Learning and Flipped Classroom Models: Evaluating Their Impact on Mathematical Problem-Solving Skills

Integrating Problem-Based Learning (PBL) with the Flipped Classroom (FC) model has gained attention as a strategy to enhance students' mathematical problem-solving skills (MPSS). While multiple studies have examined this approach, their findings show considerable variation. A meta-analysis was conducted using Comprehensive Meta-Analysis (CMA) software to synthesize findings from previous studies. A random-effects model was applied to account for variability among studies. The pooled effect size was g = 1.06 with a p-value 0.01, indicating a strong and statistically significant positive impact of the PBL-FC model on MPSS. Moderator analysis showed that the effectiveness varied significantly by media platform used (Qb = 21.98, p = 0.01) and type of publication (Qb = 7.94, p = 0.01). However, no significant differences were found regarding educational level (Qb = 7.45, p = 0.06), experimental group size (Qb = 0.29, p = 0.62), or publication year (Qb = 0.21, p = 0.64). The forest plot indicated consistent positive effects across most studies, although variations in effect sizes suggest heterogeneity due to differences in methodology, populations, or contexts. This meta-analysis confirms that the PBL-FC model significantly improves students' MPSS. Differences in media platform and publication type should be considered in future implementations. These findings provide a foundation for best practices and further research into enhancing critical thinking through PBL-FC integration.