Social changes and advances in technology and pedagogy during the last few years have produced an exponential increase in the demand for training and a revolution in the way education is understood. All the players involved in this process: students, teachers, contents and tools, need to adapt to this new situation. This fact has increased the complexity of the educational environment.
Models, that have always played an important role in the understanding of the teaching-learning processes, are now a requirement to monitor and control the educational practice. One of the main problems faced by modeling is the integration of the pre-existent models and the ability of obtain quantitative results.
In this dissertation, the Educational Practice Model (EPM) is proposed. EPM is a mathematical model for characterization and diagnosis of educational processes. This model arises from an attempt to resolve the problem of modeling education as a particular case of a more general modeling problem: representation of dynamical systems in interaction with their environments. This change of approach to a higher level of abstraction is inspired by two fundamental ideas: the abstraction process followed by Physics to unify the representation of the fundamental interactions, and the concept of meta-representation proposed by Heylighen to represent dynamical systems.
Based on these two ideas, a meta-representation is proposed that allows different representations to be generated in order to describe different elements of educational practice: teachers, students or educational resources. In this thesis, the mathematical development to represent one of this elements is proposed: description of the evolution of the degree of knowledge of a student during a course.
The representation developed here characterizes the elements involved in the educational practice for very practical purposes: detecting problems, diagnosis, and even proposing solutions. The detection process warns about problems appearing and indicates about their magnitude (quantification of their importance), and location (discrimination of objectives involved). The diagnosis and proposal of solutions can distinguish if the problems of effectiveness are related to heterogeneity of the group of students, inherent difficulty of the objectives involved, design of the didactic materials, or the way they are used.
The proposed model not only makes it easier to reuse and compare educational resources (teaching actions, didactic units and mechanisms of evaluation), but also provides ways to reuse and compare the information obtained during the course itself, the effectiveness of the resources, or the results of the evaluation.