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This study explores the impact of the Collaborative Problem-Solving (CPS) methodology on first-year engineering students in a leading Latin American engineering school. Using a quasi-experimental design, 523 students were assigned to either CPS or traditional teaching methods for the Mathematics I course. The CPS approach involved collaborative problem-solving activities and a flipped classroom model. Results showed that students in the CPS group had higher academic passing rates and reported a denser network of social and academic connections compared to their peers in the control group. The CPS students also demonstrated more diversified and frequent study groups. These findings suggest that CPS enhances students' collaborative problem-solving skills, academic performance, and social networks, providing valuable insights for engineering education practices.