For several decades, scholars have studied cooperation and its outcomes in the educational context. Yet, we lack a complete understanding of how different instructional strategies impact the relationship between cooperation and learning. Here we studied how different instructional strategies led to different social configurations and their differences in individual academic performance in an experiment with 82 first-year students from an introductory physics course. Surprisingly, we found that students who actively seek out information on multiple peers are less likely to achieve good performance on well-structured (algebra-based) problems, whereas, for ill-structured (real-world-like) problems, this effect depended on the features of the learning environment. Besides, we observed that good performance on ill and well-structured problems responded to different social network configurations. In a highly clustered network (which contains redundant information), students performed well-structured problems better than ill-structured problems. In contrast, students with access to network structural holes (which enable access to more diverse information) performed ill-structured problems better than well-structured problems. Finally, ill-structured problems could promote creative thinking, provided that instructors guide the solving process and motivate students to engage in the appropriate cognitive demands these problems entail. Our results suggest that teaching and instructional strategies play an important role in cooperative learning; therefore, educators implementing cooperative learning methods have to accompany them with adequate instructional strategy.