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# Mathematical Model for CBT Exam Malpractice Detection System (CEMDS)

Franklin Ouvolelolo Okorodudu, Omede Gracious C.

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## To cite this version:

Franklin Ouvolelolo Okorodudu, Omede Gracious C.. Mathematical Model for CBT Exam Malpractice Detection System (CEMDS). International Journal of Computer Applications, 2024, 186 (21), pp.1-3. hal-04678290

HAL Id: hal-04678290

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Submitted on 27 Aug 2024

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# Mathematical Model for CBT Exam Malpractice Detection System (CEMDS)

Franklin O. Okorodudu
Delta State University,
Department of Computer Science, Abraka.
Delta State Nigeria

Gracious C. Omede
Delta State University,
Department of Computer Science, Abraka.
Delta State Nigeria

## ABSTRACT

As we know it now, technology has come a long way in transforming several aspects of people's lives, assisting in human efficiency and precision. Educators increasingly demand to investigate alternative methods of assessing pupils utilizing various mediums to assist students. Examination is the most common and commonly acknowledged method of assessing student aptitude and comprehension. Information and communication technology would have effectively achieved an error-free and efficient result during calculation when registering and conducting tests. However, there are specific problems in monitoring computer-based testing (CBT) examinations. One method in which wealth disparity reveals itself is Because of the enormous variety of systems utilized in CBT tests, examiners frequently regard space as a difficulty between students, making communication easier amongst students, and having fewer invigilators (examination supervisors) in larger exam halls makes handling this scenario difficult. A system can multitask using CBT-based exam monitoring tools; the same system used to write the test can also monitor the student utilizing it. It may be accomplished by automatically activating the system's webcam after a student has logged in for an exam.

## General Terms

Model for CBT monitoring

## Keywords

CBT, ICT Tools, Examination, Monitoring, Detention, Model

## 1. INTRODUCTION

Examination misconduct is the most severe academic blight plaguing the Nigerian education system, particularly in the secondary school sector. According to studies, many failures and abnormalities occur in people's lives due to the plague of test misconduct at the secondary school level of education [1]. Numerous attempts have been made by government agencies, school administrations, and examination bodies to divert Nigerian students away from the scourge of test malpractice, but all have failed. As a result, this study assessed whether the computer-based Testing (CBT) modality will minimize testing in Nigerian public examinations.

The process of assisting learning or developing information, skills, attitudes, beliefs, and habits is called education (World Bank Education, 2019). The primary goal of education is to give the student information to make him or her accountable in society. The extent to which the stated goal can be realized is measured by assessment, which determines the degree to which the learner has learned the planned information. The monster known as misconduct has plagued the educational industry.

## 2. LITERATURE REVIEW

Online examinations, also known as electronic examinations

and earlier as computer-based assessments, can be described as a method that incorporates examinations using the web or the Internet, according to [2], as referenced in [3]. [4] also, online assessments are practical in evaluating students' knowledge utilizing contemporary computer technology while not influencing traditional university course exams involving pencils, papers, and invigilators. They also stated that online examinations can increase student examination standards compared to the traditional examination method of pen and paper, which involves more work on the side of students and invigilators. According to researchers [5, 6], the advantages of online tests include their convenience in terms of saving time, effort, and money. They stated that its usage speeds testing by removing paper-based operations like printing. It saves staff time and effort that would otherwise be required to grade hundreds of questions, giving them more time to provide relevant feedback [5]. Additional advantages of online tests include dependability, authenticity, and convenience.

Even with the benefits of an online assessment system for students and instructors, they have different perspectives. It has piqued the interest of scholars, who are now conducting studies targeted at evaluating online examinations. Several researchers [7, 3] attempted to analyze students' impressions and perceptions of online assessments and discovered intriguing findings. According to the studies, students judged online examinations to have significant advantages over traditional, paper-based exams, such as scoring reliability and long-term efficiency in terms of time, effort, and expenses. However, his studies also suggested that fairness, validity, and security are the primary barriers to the effective deployment of online tests. Such metrics must be accurate and reliable to make relevant and fair comparisons between individuals, groups, and organizations [8]. According to [9], exams will reveal which parts of the class each student appears to have taken the most interest in and remembered (2020).

Moreover, [9] stated that the test procedure benefits the school by determining which faculties and courses require greater attention regarding resources. Schools need to ensure that they are offering students the best they can, and tests are an excellent way to track how well that specific course is doing.

### 2.1 Concept of Online Examination

Considerable attention has been paid to online examination procedures in the twenty-first century since the expanding population and education demands require connected technologies to meet nations' intended educational goals. [10] State that an online examination system is a software solution that allows any company or institute to plan, organize, and manage tests online. They said it may be done over the Internet, intranet, or local area network.

Furthermore, [11] defined an online examination system as a web-based examination system in which exams are
administered online via the Internet or an intranet using a computer system. They stated that the primary purpose of this online test system is to comprehensively evaluate the student using a completely automated approach that not only reduces the needed time but also produces fast and accurate results.[12], As quoted in [11], an Exam Management System, a web-based online examination system (EMS), was suggested. EMS controls the examination and auto-grading for students' tests, facilitates exam administration, gathers responses, auto-marks submissions, and generates test results. EMS provides secure login, multi-instructor support, and portability. Nevertheless, they claimed that the following characteristics are missing: resuming capability, random question selection, random question distribution, and random choice distribution. It may cause academics to wonder about the impartiality and dependability of online testing processes established by instructors, lecturers, and examiners for other institutions. Rashad, Kandil, Hassan, and Zaher explained that the Web-Based Exam Management System was created to provide automated online grading, test archiving, and exam administration. Most of the most often used questions conform to the Intended Learning Outcome (ILO) for the courses, and they should be appraised and evaluated online by comparing with the correct responses. According to them, common questions include yes/no, multiple-choice/single-answer, multiple-choice/multiple-answer, matching, numeric, and essay questions.

Based on our experiences as students at the University of Cape Coast, it is clear that online examination techniques primarily remove essay-type questions as a method of grading students over the Internet. The online examinations mentioned above might focus on objectively measuring students' knowledge level regarding a particular course rather than the subjective or essay evaluation style commonly connected with paper and pencil or pen exams. Why are online examination procedures used? Is it possible that ordinary paper has outlived its usefulness?

[3] also researched Online Examination Procedures in Higher Education Institutions: Learners' Views. Online tests, often known as electronic examinations (e-exams), are rapidly being used in Palestinian higher education institutions. [13] believes computers are the most valuable and adaptable technologies ever created. They are used to make several sorts of tasks more convenient and practical. According to [14], ICT technologies can dramatically minimize the energy test administrators require to monitor an examination system. Minimize the amount of work needed by exam administrators. In all the above proposer by researcher there was no mathematical model used in examination monitoring and how resources are allocated to the OS for optimal result

# 3. MATERIALS AND METHODS

## 3.1 Mathematical Model For CBT Exam Malpractice Detection System (CEMDS)

Key Parameters:

i. System's Operating System (OS)

ii. System's Processor

iii. System's Memory (RAM)

iv. All Programs (software) installed on the system

Let the OS, Processor, RAM and Installed software of the system be represented with O, P, R and Y, respectively. I assume that P is a multitasking processor and O is responsible for assigning tasks (program to be executed) to P and operational space R.

IF O can assign multiple tasks at a given time (t) with corresponding memory space for each task, Then, ∀ time (t) multiple tasks (operations) are assigned to P to perform with R spaces as well.

Since Y is installed software, Let Y be a universal set of tasks that P processes and are performed concurrently. Thus, P is a set of processes; p1, p2, p3, ..., pn for n tasks assigned to it by O.

$$ \Rightarrow P \ni \{p_1, p_2, p_3, \dots, p_n\} \dots (1) \\ \forall n \text{ tasks} $$

$$ \therefore P = p_1 \cap p_2 \cap p_3 \cap \dots \cap p_n \dots (2) \\ \forall n \text{ tasks performed concurrently} $$

On the other hand, Y is a set of tasks (installed programs) from which O assigns P and R at time t. Thus, Y is a set of y₁, y₂, y₃, ..., yₘ tasks for m software installed on the system.

$$ \Rightarrow Y \ni \{y_1, y_2, y_3, \dots, y_m\} \dots (3) \\ \forall m \ni \text{ tasks that can be performed by P} $$

$$ \therefore Y = y_1 \cap y_2 \cap y_3 \cap \dots \cap y_m \dots (4) \\ \forall m \text{ tasks that can be performed concurrently} $$

Also, for n tasks to be performed by P,

$$ \exists R = r_1 \cap r_2 \cap r_3 \cap \dots \cap r_n \dots (5) \forall \text{ tasks} $$

If m is all installed programs, n is the assigned programs to be executed at a given time t.

$$ \Rightarrow m > n \\ \therefore \text{ all installed programs cannot be executed simultaneously t.} $$

$$ \therefore \forall Y = y_1 \cap y_2 \cap y_3 \cap \dots \cap y_m, \\ \text{only } Y = y_1 \cap y_2 \cap y_3 \cap \dots \cap y_n \\ \text{is performed at } t(m > n) $$

Any P process requires a Y in union with an R.

Thus, $P = Y \cup R$,

$$ \therefore P = p_1 \cap p_2 \cap p_3 \cap \dots \cap p_n \\ \equiv (y_1 \cup r_1) \cap (y_2 \cup r_2) \cap (y_3 \cup r_3) \cap \dots \cap (y_n \cup r_n) \dots (6) \\ \text{Then,} $$

$$ p_1 = y_1 \cup r_1; p_2 = y_2 \cup r_2; p_3 = y_3 \cup r_3 \dots p_n \\ = y_n \cup r_n $$

Which can be represented with the Venn diagrams below;

<figure><img src="image_3.png" /><figcaption>Fig.1: Venn diagram of the operating system</figcaption></figure>
The fig.1 above set can be expressed as a quadratic equation of the form,

$$P = \sum_{i=1}^{n} y_i r_i \dots vii$$

For i =CBTEMDS program, let O assign it to P and R, and keep every other task on hold until completed.

$$\therefore P = p_i = \sum_{i=1}^{n} y_i r_i \approx y_1 r_1 \text{ where } n = 1$$

∀ tasks to be performed is CBTEMDS ... ... viii

$$\therefore P = y_1 r_1 \text{ for CBTEMDS task only } \dots \dots (ix)$$

It implies that,

$$P = y_1 \cup r_1 \dots \dots (x)@ time t_1$$

∀ CBTEMDS task processing

## 4. DISCUSSION

The above model orchestrates the overall functioning of a computing device, managing resources, processes, files, and devices and providing a user interface. On the other hand, the CPU performs the actual processing of data and instructions by executing arithmetic, logic, and control operations as directed by the OS and software applications. Both work in tandem to ensure computing devices' efficient and effective operation.

The relationship between the functionalities of the Operating System (OS) and the Central Processing Unit (CPU) in computing is intricate and symbiotic, influencing a computer system's overall performance and functionality.

It has resumption capability, random question generation and random choice distribution, multi-level security measures, and intelligence to detect impersonation.

The new system is taking a different dimension, whereby every ICT tool will be activated, and the database will be linked to every student who has keyed in their details during the examination period for record keeping and analysis for feedback; if this system is implemented, then our institution will be saved from examination malpractices.

## 5. CONCLUSION

In conclusion, the use of Information and Communication Technology (ICT) tools in Computer-Based Testing (CBT) examinations has shown great potential in enhancing the efficiency and accuracy of the assessment process. However, there are specific challenges that need to be addressed, such as the issue of wealth disparity in access to technology and the difficulty in monitoring exams conducted on multiple systems. The development of a model for CBT monitoring, using tools such as webcams, can provide a solution to these challenges and improve the overall examination process. Further research and collaboration between educators and technology experts are needed to optimize the use of ICT tools in assessments and ensure fair and effective examination practices.

## 6. ACKNOWLEDGMENTS

Our thanks to the experts who have contributed towards this work.

## 7. REFERENCES

[1] Zakka, J. (2014). Innovative strategies for curbing examination malpractices in public examinations in Nigeria. University of Nigeria. Unpublished M.Ed Thesis.

[2] Ayo, C. K., Akinyemi, I. O., Adebiyi, A. A., &Ekong, U. O. (2007). The prospects of e-examination implementation in Nigeria. *Turkish Online Journal of Distance Education*, 5(4), 125-134.

[3] Shraim, K. (2019). Online Examination Practices in Higher Education Institutions: Learners' Perspectives. Turkish Online Journal of Distance Education, 20(4), 185-196.

[4] Sarrayrih, M. A., &Ilyas, M. (2013). Challenges of online exam, performances and problems for online university exam. International Journal of Computer Science Issues (IJCSI), 10(1), 439.

[5] Dreher C., Reiners T., &Dreher H. (2011). Investigating Factors Affecting the Uptake of Automated Assessment Technology. Journal of Information Technology Education, 10, 161-181.

[6] Baleni Z. (2015). Online formative assessment in higher education: Its pros and cons. The Electronic Journal of e-Learning, 13(4), 228-236

[7] IsauAdewole A., Olugbenga A., Olusegun A., & Susan K. (2018). Students' Perception of Computer-Based Examinations: A Case Study of LadokeAkintola University of Technology, Ogbomoso Oyo State, Nigeria. Journal of Humanities and Social Science. 23(5), 1-7.

[8] James, R. (2019). Tertiary student attitudes to invigilated, online summative examinations. International Journal of Educational Technology in Higher Education, 13(1), 19.

[9] Hurd, M. (2020). Purpose of Exams. Edu - quip Blog. https://www.eduquip.co.uk/ blog/the-purpose-of-exams.

[10] Kotwal, D. V., Bhadke, S. R., Gunjal, A. S., & Biswas, P. (2016). Online examination system; international research Journal of Engineering and Technology, 3(1), 115-117.

[11] Hameed, M. R., & Abdullatif, F. A. (2017). Online examination system. International Advanced Research Journal in Science. Engineering and Technology, 4(3), 106-110.

[12] Rashad MZ, Kandil MS, Hassan AE, Zaher MA. An Arabic web-based exam management system. International Journal of Electrical & Computer Sciences. 2010; 10(1):35-41.

[13] Edono, K. P., (2016). ICTs for learning: An overview of systemic initiatives in the Australian states and territories. Australian Educational Computing, 17(2), 3-14.

[14] Franklin.O.Okorodudu&Getty.Elzakpa (2023). ICT - TOOLS-BASED EXAMINATION MONITORING SYSTEM; THE DELTA STATE UNIVERSITY EXAMPLE. ciência e técnicavitivinícola journalISSN: 2416-3953 38(1) pp 45-69