In recent years, changes in the Brazilian economic and social scenario have generated a growing demand for higher education in the country. In response to this new context, the federal government launched in 2007 a programme aiming at expansion of the enrolment to public higher education. In such environment of changes, several proposals have emerged to adapt the Brazilian federal universities to a new reality. Taking this context into account, the focus of our study is on proposals from the Mathematics Department of the Federal University of Minas Gerais. Their aim is to create a new model of teaching practices for the freshman lessons of the Exact Sciences area, which at first were being experimented in special classrooms of students attending their first course on differential and integral calculus. The data were collected from interviews with students and professors from the mathematics department. They were analyzed and systematized using an activity theory approach. We became instigated by a model developed by Engeström in his study on the changes in the Finnish public health system, considering it as a test (testbench) for activity theory in its application to a particular case. Following Engeström's footsteps when developing his research, we arrived at our own model showing the internal tensions in the activity of reformulation of the courses offered by the Department of Mathematics and in the conceptions of teachers that promote--and constraint--the proposals for change.