This research was conducted during an online continuing education course for mathematics teachers, whose core focus was modeling and applications. We studied the interactions of one group of two teachers, who worked collectively in posing and solving a modeling problem through a closed group on the social network Facebook. The research question guiding this paper was how the development of mathematical modeling occurs from an Activity Theory perspective, recognizing tensions that occur, and its evolution in the process of posing and solving a modeling problem. The researchers took a qualitative approach, analyzing discursive manifestations in the modeling process. In the discussion, contradictions emerged in the group through events such as "dilemma" and "conflict". The results indicate that the modeling task acted as an artifact that brought to light inner contradictions, and thus, allowed teachers to move from a "conflict" to the formulation of an open problem, and from a "dilemma" to the construction of a model and a pedagogic strategy.