A Hybrid PBL-IGL Approach to Improving Algebraic Thinking and Self-Efficacy of High School Students

Algebraic thinking ability and self-efficacy are essential components in mathematics learning; however, many students still experience difficulties in both cognitive and affective aspects. Therefore, an instructional approach that integrates these two domains is needed. This study aims to examine the effectiveness of a hybrid Problem-Based Learning (PBL) model combined with an Individual Group Learning (IGL) strategy in improving students' algebraic thinking ability and self-efficacy. This study employed a quantitative approach using a one-group pretest–posttest design. The participants were 15 tenth-grade students of SMA Syarif Hidayatullah Grati in the 2024/2025 academic year. Data were collected through algebraic thinking tests and self-efficacy questionnaires and analyzed using paired-sample t-tests, N-Gain, and effect size (Cohen's d). The results showed a significant improvement in both variables (p < 0.001). The mean score of algebraic thinking increased from 65.40 to 86.10, with an N-Gain of 0.59 (moderate category) and a large effect size (d = 1.20). Similarly, students’ self-efficacy improved from 66.80 to 86.53, with an N-Gain of 0.60 (moderate) and a large effect size (d = 1.25). The greatest improvement in algebraic thinking was observed in modeling and solving contextual problems, indicating PBL's effectiveness in promoting higher-order thinking. These findings indicate that the PBL-IGL hybrid approach is effective in enhancing both cognitive and affective learning outcomes. The novelty of this study lies in integrating individual and collaborative learning within a problem-based framework, while simultaneously focusing on algebraic thinking and self-efficacy. This study contributes to mathematics education by providing empirical evidence that a balanced instructional design can improve students' understanding and confidence in learning mathematics.