Students’ Progress throughout Examination Process as a Markov Chain

Abstract

The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague. The idea is to create a model of students' progress throughout the whole course using the Markov chain approach. Each student has to go through various stages of the course requirements where his success depends on the completion of the previous duties. It makes the whole process ideal for usage of Markov chain theory in practice. We show how students' achievements during the semester affect the final result of the exam in terms of the final grade. The final grade can be understood as an absorbing state of a Markov chain that is terminal and cannot be transitioned from. With the help of Markov chains, the probability of success at the end of the course is shown regarding the students' behaviour and diligence during the course. This helps to identify weak or critical stages of the entire course and also supplies the planning of time capacity that will be needed to examine all students in the end. The mathematical model is constructed and consequently used in the case study at the second half of the paper.

Modelagem e Simulação do Progresso Estudantil no Ensino Superior com Sistemas de Eventos Discretos para Gerenciamento de Capacidade de Turmas Extras

“…O estudo de [Hlavatỳ and Dömeová 2014] criou um modelo de progresso do aluno em uma disciplina específica de um curso de graduac ¸ão, usando abordagens de cadeias de Markov. Para isso, o trabalho foi dividido em dois estágios, no primeiro, a modelagem foi realizada a partir das tentativas de aprovac ¸ão do aluno na disciplina, já no segundo estágio, criou-se um modelo de progresso do aluno dentro de uma avaliac ¸ão, dividindo-a entre parte escrita e parte oral, dando retornos ao aluno da situac ¸ão em que ele se encontrava no momento.…”

Source of Knowledge Dynamics—Transition from High School to University

“…One paper analyzes how students’ achievements during the semester affect the final outcome of the exam [ 24 ]. This is a typical example of reducible Markov chain, with the final grade seen as the absorbing state that cannot be anymore transitioned from.…”

Analysis of Students’ Academic Performance and Progression (Using Markov Chain Approach)

“…[2] have applied the Markov chain to analyze and predict the mathematical achievement gap between African American and white American students. [3] have presented the Markov chain model of students' progress throughout the particular course. [4] who used the theory of Non-Homogeneous Markov Systems (NHMS) with fuzzy states for describing students' educational progress in Greek Universities.…”