Conditions under which group work leads to learning have been studied in collaborative settings. Little is known, however, about whether and how the interplay between collaboration and cooperation impinges on group learning. In this paper, we study this interplay in the context of mathematical problem-solving. We focus on how training students to learn together influences this interplay, and on the relations of this interplay with mathematical problem-solving. Five groups of Grade 8 students participated in a course aimed at fostering learning to solve mathematical problems in small groups. Before and after the course, they solved a mathematical problem. An increase in the ratio of cooperation episodes out of total group work time was observed, as well as advancements in mathematical problem-solving. In addition, we found a mid-high correlation between instances of cooperation and mathematical activity: up to a certain threshold, cooperating more in a group yielded an increase in the individual generation of mathematical claims and arguments. We identified the critical role of coordination: for group learning to be productive, students should continuously negotiate and adjust their goals through communication before or while they cooperate on different tasks. We conclude that teachers aiming at fostering group work should encourage the diversification of modes of group work, for the advancement of mathematical problem-solving or of any case in which individual settings are too challenging.