An academic value-added mathematical model for higher education in Colombia

The concept of academic added-value can be associated with a variation in the cognitive development of students who complete an educational cycle at a given institution belonging to a reference universe, related to the tendency shown by all students in the aforementioned universe. Certain knowledge at the beginning and end of the cycle must be evaluated to estimate such variation. The pertinent literature states that learning is the result of students, teachers, and classmates' intellectual capacity, mainly within the family and an institution. This article proposes an academic value-added linear mathematical model representing a single student and sets of students in Colombia, grouped by institution, in terms of two vectors: learning outcome, regarding standardised national exams at the beginning and end of higher education programmes, and context, estimated as socioeconomic strata.