A mathematical model for reusing student learning skills across didactical units

In this paper, a mathematical model to capture information about learning capabilities of students for reusing across didactical units is presented. The model is based on the definition of a set of generic objectives related to the concepts, skills and attitudes the student is expected to assimilate by the end of a unit. Each objective is represented as an axis in a n-dimensional mathematical space. A relationship is established between the topics and each of the objectives. The grading process is modified to reflect how the student performs with respect to these objectives. The expected and obtained grades are then represented in this mathematical space. The proposed model provides support for diagnostics, facilitates the course characterization and comparison (even adaptive ones) and is suitable to be adopted in both new and on-going courses, because requires only the definition of the relationship between topics, evaluation and objectives.