In this study, from a cognitive perspective, we present the structures necessary for a student to construct the concept of the mean value theorem. The theoretical framework used for this research is based on the action-process-object-scheme theory. We propose, as a result, two genetic decompositions that describe two possible ways to construct the concept: a graphical path and an analytical path. Generic decompositions become a point of reference for the design of teaching strategies; in that sense, the results of this research are presented as a theoretical proposal for teaching and learning the model of the mean value theorem to undergraduate students of mathematics, physics, engineering or in whichever area this particular subject is studied, with the purpose of contributing to the strengthening of educational practices and student learning.