Departures from the formal of actual students' university careers: an application of non-homogeneous fuzzy Markov chains

Abstract

As in most higher education (HE) systems, the Italian university organisation draws paths of credit progression in formal curricula, which aim at framing the acquisition of knowledge and competencies within each specific major. The resulting yearly syllabi therefore develop in a sequence of examinations that are to be successfully passed, and formal administrative registration allows access to the following academic year. In general, there is a divergence between formal and actual career progression because each university student can proceed at her/his own pace, sketching her/his own trajectories, free to depart from the formal progression. Even if applied to various HE settings, Markov chain models do not fit the aforementioned situation. A methodological extension has been introduced, whereby progression levels are considered as fuzzy states. Markov chains with fuzzy states identify the latter with specified academic years and express each student's situation as a relational link to present and past academic attainments. This link is operationalised by means of a membership function, which is here discussed with reference to the Italian HE system.

Keywords:

• students' progression
• non-homogeneous Markov system
• fuzzy states
• membership function
• Italian higher education system

Disclosure Statement

No potential conflict of interest was reported by the authors.

Notes

1. In the Italian university system, the values 30 cum laude and 18 are the highest and the lowest pass marks, respectively. In this analysis, we decided to transform the value 30 cum laude into 33. The increase, from 30 cum laude to 33, reflects the procedure at the time, currently abandoned.

2. In the Italian academic system, the amount of training activities for a full-time student in each academic year must be worth 60 credits. The first cycle degree is awarded with 180 credits.

3. For the first two academic years, dropout is the absorbing state, while from the third academic year on, the absorbing states are graduation and dropout.

4. The p-value is equal to .562.