The effect of case-based collaborative learning and number sense on students' mathematical critical thinking skills

This study aimed to investigate the effects of the Case-Based Collaborative Learning (CBCL) model and students’ number sense on mathematical critical thinking skills. Grounded in collaborative learning theory and numerical cognition frameworks, the study examined whether structured case-based collaboration enhances higher-order thinking and whether its effectiveness depends on students’ cognitive readiness. A quasi-experimental pretest–posttest control group design was employed involving 120 vocational high school students enrolled in a numeracy course. Participants were assigned to an experimental group (n = 60) receiving CBCL instruction and a control group (n = 60) receiving Case-Based Learning (CBL). The intervention was conducted over two instructional sessions within a two-week period. Data were collected using validated essay-type assessments measuring critical thinking and number sense. After testing assumptions of normality and homogeneity, the data were analyzed using two-way factorial ANOVA to examine main and interaction effects. The findings revealed a significant main effect of instructional model, with CBCL outperforming CBL (η²p = 0.040), indicating a small-to-moderate practical effect. A larger main effect was found for number sense (η²p = 0.195), demonstrating that students with higher number sense exhibited substantially stronger critical thinking performance. Furthermore, a significant interaction effect was identified (η²p = 0.187), suggesting that the effectiveness of CBCL was strongly conditioned by students’ number sense level. These results underscore the importance of aligning collaborative case-based instructional strategies with students’ cognitive competencies to meaningfully enhance critical thinking in numeracy education.