Interdisciplinary approaches in education play a crucial role in developing students’ real-world mathematical problem-solving (MPS) skills and critical thinking (CT) skills. One such approach, the Harezmi Education Model (HEM), integrates mathematics, science, computer technologies, social sciences, the arts, and sports through data-driven, technology-supported learning environments. This research sought to explore how the HEM can be incorporated into primary mathematics teaching and to determine its effect on learners’ MPS and CT skills. The study was designed according to an explanatory sequential mixed-methods approach. During the quantitative stage, a quasi-experimental pretest–posttest model was implemented with fourth-grade students, who were separated into an experimental group (n = 26) and a control group (n = 26). In the subsequent qualitative stage, semi-structured interviews were carried out with 15 primary school teachers. The quantitative data were examined through multivariate analysis of variance (MANOVA), whereas the qualitative data were interpreted using content analysis. The results demonstrated that instruction grounded in HEM produced statistically significant improvements in students’ MPS and CT skills. Teacher perspectives further indicated that HEM supports interdisciplinary learning and real-world connections, although challenges related to resources, time management, and teacher preparedness were noted. Overall, the results suggest that HEM offers a promising interdisciplinary framework for enhancing mathematics instruction and 21st-century skills in primary education.