Markov Analysis of Students’ Performance and Academic Progress in Higher Education

Abstract

Background:The students' progression towards completing their higher education degrees possesses stochastic characteristics, and can therefore be modelled as an absorbing Markov chain. Such application would have a high practical value and offer great opportunities for implementation in practice. Objectives: The aim of the paper is to develop a stochastic model for estimation and continuous monitoring of various quality and effectiveness indicators of a given higher education study programme. Method: The study programme is modelled by a finite Markov chain with five transient and two absorbing states. The probability transition matrix is constructed. The quantitative characteristics of the absorbing Markov chain, like the expected time until absorption and the probabilities of absorption, are used to determine chosen indicators of the programme. Results:The model is applied to investigate the pattern of students' enrolment and their academic performance in a Slovenian higher education institution. Based on the students' intake records, the transition matrix was developed considering eight consecutive academic seasons from 2008/09 until 2016/17. The students' progression towards the next stage of the study programme was estimated. The expected time that a student spends at a particular stage as well as the expected duration of the study is determined. The graduation and withdrawal probabilities were obtained. Besides, a prediction on the students' enrolment for the next three academic years was made. The results were interpreted and discussed. Conclusion: The analysis presented is applicable for all higher education stakeholders. It is especially useful for a higher education institution's managers seeing that it provides useful information to plan improvements regarding the quality and effectiveness of their study programmes to achieve better position in the educational market.

Source of Knowledge Dynamics—Transition from High School to University

“…This is a typical example of reducible Markov chain, with the final grade seen as the absorbing state that cannot be anymore transitioned from. Academic performance in a Slovenian higher education institution is modeled by an absorbing Markov chain in [ 25 ]. Five transient and two absorbing states are identified, then students’ progression towards the next stage of the educational program is estimated in terms of expected duration of the study.…”

Methodology of monitoring key risk indicators

“…The Markov chain model is one of the most widely used probabilistic models, because of its simplicity and ability to model various types of phenomena (Skulj, 2009). An increasing number of implementations of Markov chains are recorded, such as student progress in the case of Alawadhi and Konsowa (2010), Adeleke, Oguntuase, and Ogunsakin (2014) and Brezavscek et al (2017). Gurning and Cahoon (2009) use it in marine transport, as do Faghih-Roohi, Xie, and Ng (2014), etc.…”

A Framework for Adaptive Personalized E-learning Recommender Systems

“…Markov Chain Model: Student model and progress is prone to stochastic characteristics. [11] developed a Markov model for Slovenian student's performance for monitoring and estimation based on student logs and records. iv.…”