This thesis entitled "Learning Mathematical Modelling the interactions of the elements of an activity system from the perspective of the Engeström activity theory" aimed at understanding effects on learning by interactions evidenced in Mathematical Modeling environment, from the perspective of Engeström activity theory. To accomplish this, I developed in the Mathematical Modeling Experimental Laboratory (LEMM), at the University Campus of Castanhal (UFPA), modeling activities with groups of Math Course students in graduating, graduate or post graduate students to obtain data through observation and interview. Based on the principles of the Engeström activity theory, Mathematical Modeling developed by the students were understood as an activity system that involves the elements (subject, object and community artifacts mediators, rules and division of labor) that relate to a result, that are mediated by interactions for achieving a result. Research has shown that the collective work, the historicity and multivocality of subjects acting in overcoming contradictions to reach expansive transformations have repercussions on learning in Mathematical Modeling, configured as an activity system, the interactions of the elements of the system itself.
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