This article proposes a mathematical model of Intelligent Tutoring Systems (ITS), based on observations of the behaviour of these systems. One of the most important problems of pedagogical software is to establish a common language between the knowledge areas involved in their development, basically pedagogical, computing and domain areas. A mathematical model, like the one proposed here, can facilitate the integration of these different areas, as it defines the elements that constitute the system and defines the technological tools to implement it. The article presents an example demonstrating how the formalization was used to design the adaptive mechanism of an ITS to adapt its Interface Module to some student characteristics.