<![CDATA[This study investigates the role of self-efficacy in shaping elementary students’ mathematical problem-solving ability within a PBL–PMRI instructional model assisted by PhET Simulations. A mixed-methods concurrent embedded design was employed, with quantitative analysis as the primary approach and qualitative profiling as a complementary component. Participants were fourth-grade students from the Anggrek Cluster of primary schools in Semarang, Indonesia, assigned to experimental and control groups through cluster sampling. Data were collected using a self-efficacy questionnaire based on Bandura’s dimensions and a problem-solving test constructed according to NCTM indicators. Quantitative analyses included gain score analysis, mean difference testing, correlation, and interaction regression, while qualitative data were analyzed through interactive thematic procedures. The results show that the PBL–PMRI–PhET model significantly improves problem-solving performance and that self-efficacy is positively associated with strategic accuracy and persistence. Moreover, self-efficacy moderates instructional effectiveness, with high-efficacy students benefiting disproportionately from inquiry-oriented and technology-mediated learning. These findings indicate that instructional innovation and affective empowerment operate as an integrated system in developing mathematical problem-solving competence.]]>
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