Students’ Progress throughout Examination Process as a Markov Chain

Robert Hlavatý,Ludmila Dömeová

doi:10.5539/ies.v7n12p20

Robert Hlavatý, Ludmila Dömeová

Open Access

https://doi.org/10.5539/ies.v7n12p20

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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.

Highlights

The evaluation of students’ progress is a very important part of any educational system
The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague
We show how students’ achievements during the semester affect the final result of the exam in terms of the final grade

Summary

Introduction

The evaluation of students’ progress is a very important part of any educational system. Making the decision to let a student pass or fail is difficult especially if the teacher is supposed to decide only by the final exam results. To make a final grade decision is even more complicated if the teacher does not know the student personally and does not have enough information about the student’s progress during the course. To support the decision making process at the final exam, the partial evaluation during the semester can be introduced. This was the case of the investigated course with about a thousand of students and ten teachers. It is generally supposed that the final grade is a measure of the students learning in the particular course but there are many more influential factors. Their variation arises from three sources: the student, the teacher, and ‘‘nature’’, which reflects random and unmeasured factors (Grant, 2007)

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