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All Journal Journal of Multidisciplinary Science: MIKAILALSYS International Journal of Education, Culture, and Society Mikailalsys Journal of Advanced Engineering International Mikailalsys Journal of Mathematics and Statistics International Journal of Education, Management, and Technology International Journal of Humanities, Education, and Social Sciences
Hassan Muhammad
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Religion Agriculture, Biological Sciences & Forestry Humanities Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Education Electrical & Electronics Engineering Engineering Environmental Science Languange, Linguistic, Communication & Media Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Social Sciences Other

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Mathematical Modeling of Typhoid Fever Transmission Dynamics: A Sensitivity Analysis and Implications for Public Health Strategies Hassan Muhammad; Auwal Abdullahi
Mikailalsys Journal of Advanced Engineering International Vol 3 No 2 (2026): Mikailalsys Journal of Advanced Engineering International
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjaei.v3i2.9377

Abstract

Typhoid fever remains an important public health concern, requiring robust analytical approaches to understand its transmission dynamics and support effective prevention and control strategies. This study develops a comprehensive mathematical model of typhoid fever transmission to examine the interactions among factors influencing disease spread and to provide evidence for improved control and eradication strategies. The model incorporates population replenishment through births and was validated using existing data to assess its ability to represent disease dynamics. Mathematical analysis was conducted to determine equilibrium states and the basic reproduction number, (R0), while sensitivity analysis was performed to identify parameters with substantial influence on typhoid transmission. Numerical solutions were obtained using the fourth-order Runge–Kutta method over a 40-year simulation period and implemented in MATLAB. The findings show that (R0) is a critical threshold governing the dynamics of typhoid fever. When (R0<1), the disease-free equilibrium is locally stable, indicating that disease transmission will eventually decline; conversely, when (R0>1), an endemic equilibrium exists, indicating the persistence of the disease within the population. Sensitivity analysis further demonstrates the relative influence of model parameters on disease transmission, providing insights into factors that may be prioritized in control interventions. These findings demonstrate the utility of mathematical modeling for understanding typhoid fever transmission and evaluating disease-control strategies. The study contributes a quantitative framework that can support policymakers and healthcare professionals in designing evidence-based interventions aimed at reducing typhoid transmission, strengthening prevention efforts, and improving public health outcomes.
Robust Integral Transform Methods for the Solution of Nonlinear Fractional Ordinary Differential Equations in Viscoelastic and Biological Systems Umar Mujahid Aliyu; David Opeoluwa Oyewola; Joel John Taura; Salisu Lukunti; Hassan Muhammad; Abubakar Yahya Adamu; Abdulhalim Isah Ibrahim; Mubarak Muhammad; Imafidor Hassan Ibrahim; Mohammed Abubakar Kolo; Isah Adamu; Wallen Juliet Piapna&#039;an; Mustapha Mohammed Mansur; Ibrahim Abubakar Adamu; Mohammed Yusuf Marafa; Abdulwasiu Umar; Sulaiman Ahmad; Nura Hashim
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 2 (2026): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v4i2.9237

Abstract

Nonlinear and fractional-order differential equations frequently arise in viscoelastic and biological systems; however, their solution remains challenging due to the presence of nonlocal operators, memory effects, and complex boundary conditions. Classical integral transforms, including the Laplace and Fourier transforms, often have limitations in addressing these features effectively. This study presents a robust hybrid methodology that combines the Mahgoub Transform with the Variational Iteration Method (VIM) to solve nonlinear and fractional-order ordinary differential equations (ODEs). The proposed approach was systematically applied to linear, nonlinear, and fractional-order ODEs to evaluate its convergence, accuracy, and capacity to handle memory-dependent effects. The findings demonstrate that the Mahgoub–VIM method achieves rapid convergence, high accuracy, and improved performance compared with traditional transforms such as the Sumudu Transform. These results indicate that the proposed method provides a reliable and efficient analytical framework for modeling complex viscoelastic and biological phenomena governed by nonlinear and fractional-order dynamics. This study contributes to the advancement of integral transform-based solution methods and offers practical implications for the mathematical modeling of systems characterized by memory-dependent behavior and nonlinear responses.
Assessing Differences in Student Motivation, Achievement, and Conceptual Understanding in a Gamified Mathematics Learning Environment Hassan Muhammad; Nura AY Musa; Danladi Biong&#039;ahu; Usman Garba
International Journal of Humanities, Education, and Social Sciences Vol 4 No 2 (2026): International Journal of Humanities, Education, and Social Sciences
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijhess.v4i2.9364

Abstract

Although gamified learning has received growing attention in mathematics education, empirical evidence on its simultaneous influence on students’ motivation, mathematics achievement, and conceptual understanding in developing educational contexts remains limited. This study examined differences in students’ motivation, mathematics achievement, and conceptual understanding associated with participation in a gamified mathematics learning environment. A quasi-experimental pretest–posttest control group design was employed, involving 700 secondary school students from 15 public schools in Northeast Nigeria. Using intact classes, students were assigned to an experimental group that received curriculum-aligned gamified mathematics instruction over a four-week period or to a control group that received conventional instruction covering the same content and duration. Data were collected using pretest and posttest measures of student motivation, mathematics achievement, and conceptual understanding. Motivation was assessed using an adapted questionnaire with established internal consistency, while achievement and conceptual understanding were measured using curriculum-aligned assessments validated through expert review. Data were analysed using descriptive statistics, paired-sample t-tests, and effect size estimates. The results showed statistically significant pretest–posttest gains in motivation, achievement, and conceptual understanding among students in the gamified instruction group, with moderate to large effect sizes, whereas students in the control group demonstrated minimal changes across the same measures. These findings indicate that curriculum-aligned gamified mathematics instruction is associated with enhanced student motivation, improved academic performance, and stronger conceptual understanding within the study context. The study contributes to mathematics education literature by providing large-sample quasi-experimental evidence on the concurrent affective and cognitive outcomes of gamified instruction in secondary mathematics classrooms in a developing educational setting.
Ability Performance Misalignment in WAEC Mathematics Examination Outcomes: A Quantitative Explanatory Study in North-East Nigeria Hassan Muhammad; Philip Issa Tsado; Ahmed Rufai Tete; Momozuku Umaru Salihu; Nura AY Musa
International Journal of Education, Culture, and Society Vol 4 No 3 (2026): International Journal of Education, Culture, and Society
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijecs.v4i3.9374

Abstract

This study investigates ability–performance misalignment in West African Examinations Council (WAEC) Mathematics examination outcomes in northeastern Nigeria. A quantitative explanatory cross-sectional design was employed using archival data from public senior secondary schools to examine discrepancies between classroom-based achievement and performance in a high-stakes external examination. The findings revealed that a substantial proportion of students exhibited ability–performance misalignment: some students with high classroom performance obtained low scores in the WAEC Mathematics examination, whereas some students with low classroom performance achieved comparatively high examination scores. Test anxiety, self-efficacy, and inconsistent assessment practices significantly contributed to this misalignment. These findings suggest that WAEC Mathematics examination results may not always accurately represent students’ mathematical achievement and highlight the need to reconsider how high-stakes assessment outcomes are interpreted and used in educational decision-making. The study contributes to the assessment literature by emphasizing the importance of integrating affective, instructional, and contextual factors when evaluating student performance and formulating assessment policies.
Comparing Mathematics Achievement across High-Stakes Examinations: Evidence from WAEC/NECO and JAMB in Nigeria Hassan Muhammad
International Journal of Education, Culture, and Society Vol 4 No 3 (2026): International Journal of Education, Culture, and Society
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijecs.v4i3.9375

Abstract

This study compares mathematics performance across essay-based secondary school examinations administered by the West African Examinations Council (WAEC) and the National Examinations Council (NECO) and the multiple-choice university entrance examination administered by the Joint Admissions and Matriculation Board (JAMB) in Nigeria. Using an ex post facto comparative design, archival mathematics examination records from 600 secondary school graduates were analyzed to determine the comparability of performance across the three examination systems. Mathematics performance in WAEC and NECO was operationalized using official grade classifications, whereas JAMB performance was assessed using subject-level aggregate score ranges. Data were analyzed through descriptive statistics, score standardization, and paired-samples t tests. The findings showed that a substantial proportion of candidates who attained credit-level grades in WAEC and NECO Mathematics obtained relatively low aggregate scores in JAMB Mathematics. Standardized mean comparisons further indicated that the same candidates performed better in WAEC and NECO than in JAMB, while the paired-samples analysis confirmed that the differences were statistically significant and associated with a large effect size. These results demonstrate systematic variation in mathematics performance between essay-based and multiple-choice high-stakes examinations. The study contributes empirical evidence to the mathematics education literature on assessment comparability in multi-examination contexts and underscores the need for cautious interpretation of examination outcomes generated by assessment systems with different formats and purposes, particularly when such results inform high-stakes educational decisions.
Hybrid Integral Transform Techniques for the Solution of Third-Order Nonlinear Ordinary Differential Equations Umar Mujahid Aliyu; David Opeoluwa Oyewola; Joel John Taura; Salisu Lukunti; Hassan Muhammad; Abubakar Yahya Adamu; Abdulhalim Isah Ibrahim; Mubarak Muhammad; Imafidor Hassan Ibrahim; Mohammed Abubakar Kolo; Isah Adamu; Wallen Juliet Piapna&#039;an; Mustapha Mohammed Mansur; Ibrahim Abubakar Adamu; Mohammed Yusuf Marafa; Abdulwasiu Umar; Sulaiman Ahmad; Nura Hashim
Mikailalsys Journal of Advanced Engineering International Vol 3 No 2 (2026): Mikailalsys Journal of Advanced Engineering International
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjaei.v3i2.9236

Abstract

Third-order nonlinear ordinary differential equations frequently arise in the mathematical modeling of complex engineering and physical phenomena; however, exact analytical solutions remain difficult to obtain because of strong nonlinearities and higher-order derivative effects. Classical integral transform techniques, including the Laplace and Fourier transforms, are widely used for solving differential equations but often have limitations when extended to nonlinear systems. Although modern integral transforms such as the Sumudu, Mahgoub, and Elzaki transforms offer computational advantages, their applicability is generally restricted to linear models. This study introduces a hybrid analytical approach that integrates the Mahgoub transform with the Variational Iteration Method (VIM) to solve third-order nonlinear ordinary differential equations more effectively. The proposed method converts the governing equation into the transform domain and applies an iterative correction functional to address nonlinear terms without linearization or discretization. The resulting solutions are expressed in rapidly convergent series form. Numerical validation demonstrates strong agreement with exact solutions, confirming the efficiency, accuracy, and stability of the hybrid Mahgoub–VIM approach. The study concludes that this hybrid semi-analytical method provides a reliable framework for solving higher-order nonlinear differential equations in applied mathematics and engineering analysis. These findings contribute to the development of transform-based analytical methods by extending the applicability of the Mahgoub transform to nonlinear differential equation models through variational iteration.
The Role of Augmented Reality (AR) in Enhancing Conceptual Understanding of Geometry in Mathematics Education: Systematic Review Hassan Muhammad; Nura Ay Musa; Auwal Ahmad; Nurudeen Adamu
International Journal of Education, Management, and Technology Vol 4 No 1 (2026): International Journal of Education, Management, and Technology
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijemt.v4i1.8073

Abstract

Geometry, a fundamental branch of mathematics, often challenges students due to its abstract nature and the demands it places on spatial reasoning and visualization, and traditional teaching methods frequently fail to convey complex geometric concepts effectively, leading to low engagement and poor understanding. This systematic review investigates the impact of Augmented Reality (AR) on enhancing students’ conceptual understanding of geometry in mathematics education by synthesizing existing empirical studies on AR-based geometry instruction. AR technology provides interactive, immersive learning environments that enable learners to manipulate three-dimensional geometric shapes and transformations in real time, thereby supporting deeper cognitive engagement with abstract content. The reviewed studies consistently report that AR interventions enhance spatial reasoning, improve visualization abilities, and foster deeper conceptual understanding of geometric ideas, while also increasing student motivation, engagement, and retention and supporting the development of critical problem-solving skills. At the same time, the review identifies key implementation challenges, including the high cost and limited availability of AR tools, as well as the need for targeted teacher training to design and facilitate AR-enhanced lessons. The review concludes that AR holds strong potential as a pedagogical innovation for geometry education, provided that infrastructural, financial, and professional development barriers are addressed, and recommends future research focusing on longitudinal designs, more affordable AR solutions, and the integration of AR into advanced geometric topics and diverse educational contexts.
Modeling Cholera Dynamics with Vaccination and Asymptomatic Transmission: A Mathematical Framework for Outbreak Control Hassan Muhammad; Alagbe S.O. Philip Issa Tsado; Angel Otse Ogbu
Journal of Multidisciplinary Science: MIKAILALSYS Vol 4 No 2 (2026): Journal of Multidisciplinary Science: MIKAILALSYS
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mikailalsys.v4i2.9368

Abstract

Cholera remains a persistent public health challenge in regions with limited access to clean water and adequate sanitation. Although mathematical models have substantially advanced understanding of cholera dynamics, the waning effectiveness of vaccination and the contribution of asymptomatic carriers to disease transmission have received comparatively limited attention. This study develops a mathematical model that incorporates these two epidemiologically important mechanisms to evaluate cholera transmission dynamics and outbreak-control strategies. The model stratifies the population into susceptible individuals (S), vaccinated individuals (V), asymptomatically infected individuals (A), symptomatically infected individuals (I), individuals receiving treatment in health centers (C), recovered individuals (R), and the concentration of bacteria in the aquatic environment (B). The basic reproduction number (R₀) was derived, indicating that cholera can be eliminated when R₀ < 1. Using data from cholera outbreaks reported between 2022 and 2025, numerical simulations were conducted to assess alternative intervention strategies. Sanitation measures alone reduced total cases by 43.1%, vaccination by 37.3%, and treatment by 28.0%, whereas the combined implementation of vaccination and sanitation produced a 69% reduction. Sensitivity analysis identified the human-to-human transmission rate (β₁), environment-to-human transmission rate (β₂), and vaccine effectiveness (σ) as the most influential parameters governing disease control. The findings demonstrate that integrated interventions are substantially more effective than single-control strategies and highlight the importance of combining vaccination campaigns with water, sanitation, and hygiene programs. This model contributes to cholera epidemiology by simultaneously accounting for asymptomatic transmission and waning vaccine effectiveness, thereby providing a quantitative framework for designing more effective outbreak-control policies.
Comparison of Item Parameters of WAEC, NECO and NABTEB Mathematics Multiple Choice Questions Obtained Using IRT in Anambra State Hassan Muhammad
International Journal of Education, Management, and Technology Vol 4 No 2 (2026): International Journal of Education, Management, and Technology
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijemt.v4i2.9347

Abstract

Nigeria’s senior school certificate examinations are administered by the West African Examinations Council (WAEC), National Examinations Council (NECO), and National Business and Technical Examinations Board (NABTEB); however, the psychometric comparability of their Mathematics items requires systematic evaluation. This study compared the mean difficulty, discrimination, and guessing parameters of the Mathematics multiple-choice items administered by the three examination bodies in 2022 and 2023. A descriptive survey design was employed, guided by six research questions and six corresponding hypotheses. The population comprised 57,150 Senior Secondary 3 students from public secondary schools, with reported registrations of 57,150 for WAEC, 44,853 for NECO, and 2,250 for NABTEB. A sample of 1,600 students was selected through a multistage sampling procedure. The instruments consisted of the 2022 and 2023 Mathematics multiple-choice examination items developed by WAEC, NECO, and NABTEB, which were administered by trained research assistants who were Mathematics teachers in the sampled schools. Responses were subjected to item analysis within an item response theory framework using Mplus Version 7.4. Mean parameter estimates were calculated to answer the research questions, while one-way analysis of variance was conducted at the .05 significance level to test the hypotheses. For both years, NABTEB items had the highest mean difficulty parameters, followed by WAEC and NECO. In 2022, NABTEB items had the highest mean discrimination parameter, followed by WAEC and NECO; in 2023, WAEC ranked highest, followed by NABTEB and NECO. For the guessing parameter, NABTEB ranked highest in 2022, followed by NECO and WAEC, whereas NECO ranked highest in 2023, followed by NABTEB and WAEC. Statistically significant differences were found among the examination bodies in the mean difficulty, discrimination, and guessing parameters during the period examined. These findings demonstrate variation in the psychometric characteristics of the three examinations and underscore the need for WAEC, NECO, and NABTEB to strengthen their item-analysis and test-development procedures.
Test-Taker Behaviour under Uncertainty: Joint Behavioural Modelling of Guessing, Risk Aversion, and Score Validity in Negatively Marked Multiple-Choice Mathematics Tests Hassan Muhammad; Mudassir Umar; Muhammad Abubakar Kole
International Journal of Education, Management, and Technology Vol 4 No 2 (2026): International Journal of Education, Management, and Technology
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijemt.v4i2.9365

Abstract

Although negative marking is intended to discourage random guessing in multiple-choice mathematics assessments, it may systematically influence test-takers’ decisions under uncertainty and thereby affect score interpretation. This study examines how guessing behaviour and risk aversion jointly relate to item-level decision-making and overall performance in negatively marked multiple-choice mathematics tests. Quantitative observational data were obtained from 885 senior secondary school students. Logistic regression models were used to estimate item-level guessing decisions, while linear regression models incorporating interaction terms examined cumulative performance outcomes. Higher expected score gains were significantly associated with an increased probability of guessing, whereas greater risk aversion was associated with reduced guessing and increased omission behaviour. A statistically significant guessing-by-risk-aversion interaction (reported as b = 0.29, p < .001) was interpreted as indicating that the performance benefits associated with guessing diminished as risk aversion increased. These findings demonstrate that scores from negatively marked multiple-choice mathematics assessments may reflect behavioural decision strategies in addition to mathematical competence, thereby introducing construct-irrelevant variance into score interpretation. The study contributes to assessment research by clarifying the joint role of guessing and risk aversion in testing behaviour and underscores the need for assessment designers and score users to evaluate cautiously the validity of negatively marked scores, particularly in high-stakes mathematics testing contexts.
Co-Authors Abdulhalim Isah Ibrahim Abdulwasiu Umar Abubakar Yahya Adamu Ahmed Rufai Tete Alagbe S.O. Philip Issa Tsado Angel Otse Ogbu Auwal Abdullahi Auwal Ahmad Danladi Biong&#039;ahu David Opeoluwa Oyewola Ibrahim Abubakar Adamu Imafidor Hassan Ibrahim Isah Adamu Joel John Taura Mohammed Abubakar Kolo Mohammed Yusuf Marafa Momozuku Umaru Salihu Mubarak Muhammad Mudassir Umar Muhammad Abubakar Kole Mustapha Mohammed Mansur Nura AY Musa Nura Hashim Nurudeen Adamu Philip Issa Tsado Salisu Lukunti Sulaiman Ahmad Umar Mujahid Aliyu Usman Garba Wallen Juliet Piapna&#039;an