In this paper, ordinary differential equations (ODEs), whose solutions are the probability functions such as cumulative distribution function (CDF), probability density function (PDF), quantile function (QF), survival function (SF), hazard function (HF), and reversed hazard function (RHF) of extended Rayleigh distributions, that are obtained by applying differential calculus and quantile mechanics along with sufficient algebraic interpretations. New extended Rayleigh distribution to higher dimensions, extended Rayleigh-Rayleigh distribution, and Power Rayleigh distribution are of interest. The necessary conditions required for the existence of the ODEs and the initial (or boundary) conditions consistent with the various parameters that defined the distributions are also included. Furthermore, the particular ODEs solved by each probability function of the selected distributions are derived and displayed for specific parameter values. The method employed can serve as a new technique for approximating and estimating solutions of ordinary differential equations, which can be used in modelling various dynamical systems that are difficult to solve with many available methods by manipulating the rich body of knowledge in probability distribution theory as a valuable tool, thereby strengthening the interdisciplinary connection between mathematics and probability theory, statistics.
Considering the continuous attempts to enhance preschool provision in Ethiopia, the teacher's competencies have gained significance in ensuring high-quality education for every preschool learner. In this review paper, an analytical and theoretical comparison will be made on three competence models, namely ADDIE, PCK (Pedagogical Content Knowledge), and the 7C - 21 model, in the Ethiopian preschool setting. Using the guidelines of the systematic literature review, the 70 papers published from 2000 to 2024 were coded in a dual way. A comparison matrix was prepared to assess the models based on their relevance to preschool teaching, research backing, contextual adaptation, and incorporation of 21st century competencies. Instead of making a comparison across countries and proposing a framework as universally suitable, the paper strives to find out the best framework among the three for designing preschool teachers' pedagogic competence in Ethiopia. Based on results of the review, the 7C - 21 model that identifies seven competencies, including logical mathematical thinking, verbal reasoning, elementary scientific culture, critical reading writing, global culture and environment, metacognitive and creative thinking, and vocational guidance proved to be the most adaptable in a multilingual and varied resource preschool context. Intentionally infusing such competencies in preschool teacher training programs, the 7C - 21 framework may help preschool teachers become reflective practitioners, collaborative peers, and strong advocates for holistic child development.
The study was intended to assess the effect of a BL educational model on secondary school students' mathematics motivation in Ethiopia. A non-equivalent quasi-experimental study using a pre-test and post-test design was conducted. Two intact classes from different schools were randomly selected and assigned to experimental (n=38) and comparison group (n=45). From the previous semester students’ record book, both groups have almost an equivalent in their mathematics performance. Data collected from the respondents were analysed using ANOVA test with a significance level of P<0.05. The study shows the students learning using the BL model are more motivated than those learning using the conventional learning model, with an average score of 4.17. The data revealed that there is a significant difference between groups with an effect size of η2=. 094. Moreover, a paired t-tests shows that there is a medium effect size for the experimental group (d=.58) when compared with the comparison group (d=.09). Thus, the study indicates that BL was more effective in enhancing grade ten students’ mathematics motivation when compared with conventional method of teaching. Based on the finding, the researcher recommends BL educational model in mathematics education and suggests stakeholders and policymakers to incorporate the model into the curriculum.
This study provides a comparative analysis of educational quality for internally displaced children in Ethiopia's Oromia and Amhara regions, employing a convergent parallel mixed methods design with 624 participants. Through systematic integration of quantitative data (analyzed via t tests, ANOVA, and regression) and qualitative thematic analysis, the research reveals striking regional disparities. Oromia demonstrated significantly superior outcomes across all measured domains: academic performance, learning space quality, TLS functionality, and mental health service access. Critically, the same interventions showed vividly different effectiveness between regions, with TLS and ALP interventions demonstrating 50 - 71% greater predictive power in Oromia. The analysis identifies distinct implementation approaches as the key differentiator: Oromia's contextually integrated, community owned model contrasted fundamentally with Amhara's standardized, externally dependent approach. These divergent pathways resulted in substantially stronger sustainability prospects in Oromia. The findings challenge standardized approaches to education in emergencies, demonstrating that educational resilience emerges from community agency, cultural integration, and historical institutional patterns rather than technical intervention design alone. The study recommends a twin track strategic approach: building foundational systems and ownership capacity in Amhara, while strengthening and scaling existing resilience factors in Oromia.
As the global economy evolves, there is a growing emphasis on aligning educational curricula with industry needs to ensure graduates are employable and equipped with relevant skills. In Nigeria, this alignment between undergraduate curricula and industry requirements is critical for addressing unemployment, enhancing national development, and achieving Sustainable Development Goal 4 (SDG 4), which focuses on ensuring inclusive and equitable quality education and, promoting lifelong learning opportunities for all. As a result, increasing attention is being directed toward aligning education towards industry skill sets, and, Sustainable Development Goal 4 (SDG 4) has been identified as a key driver for this social and economic development. The study adopted a mixed methods research design to investigate the degree of alignment between the curricula and industry requirements. Fresh graduates serving in Ibadan North formed the population for this study. Course content, skill acquisition, and preparedness for employment questionnaire (r=0.86) and interview guide were used to collect data which were analysed both descriptively and with Pearson Product - Moment Correlation Coefficient (PPMC). The study found out that the curriculum contents were not adequate enough to enhance preparedness for the world of work (1.66) which is far below the acceptance criterion of 2.5. There was a mild relationship between curriculum related factors and the preparedness for either entrepreneurial or paid employment(r=0.311; p<0.05) and it is statistically significant. The study concluded that aligning the Nigerian undergraduate curriculum with industry skills requirements is essential for achieving SDG 4. Therefore, NUC should tailor the Nigerian undergraduate curriculum with industry skills requirements and the individual university should strive to equip their students with industry ready skills.
This study investigates how Indigenous Knowledge (IK) is being revitalized and integrated into public pre primary education (PPE) for the Borena Oromo community in southern Ethiopia (Borena Zone) and northern Kenya (Marsabit County). Using a qualitative approach — including document analysis, interviews with policymakers and curriculum experts, focus group discussions with teachers, parents, and elders, and classroom observations, the research explores the practices of integrating IK into PPE in both countries. The findings reveal distinct approaches: Ethiopia emphasizes regional contextualization but lacks structured implementation guidelines, while Kenya’s Competency-Based Curriculum mandates localized content but faces gaps in teacher preparedness and linguistic tensions. Common challenges across both contexts include a lack of detailed implementation guidelines, insufficient teacher training in Indigenous pedagogies, resource constraints, donor dependency, urbanization, and the erosion of knowledge between generations. Furthermore, sociocultural factors such as limited parental engagement in curriculum design and the dominance of global languages hinder effective integration. The study underscores the vital role of community elders in co designing curricula and advocating for de colonial, ecological, and Indigenous Knowledge Systems (IKS) approaches to close the gap between policy and practice. Institutionalizing elders’ participation, establishing cross border IK hubs, co designing curricula with communities, and strengthening ecological resilience are recommended. In conclusion, centering IK as a dynamic and foundational element of PPE is essential for fostering holistic and identity affirming learning and development for Borena children.
This systematic review synthesizes the role of leaders’ accountability in addressing student academic achievement setbacks across diverse country contexts. Leaders’ accountability is recognized as a critical factor in educational performance, second only to classroom teaching, yet its impact remains underexplored in certain regions such as Africa, and particularly in Ethiopia. The study employed a systematic review guided by predefined objectives and the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA, 2020) guidelines. A total of 54 articles were extracted from databases, including Google Scholar, Cross Reference, Taylor & Francis, and Sage. Eligibility criteria were applied to ensure thematic relevance. Data were analyzed using SPSS Version 25 for descriptive statistics and presented through tables, pie charts, and bar charts. The country-context analysis revealed that the majority of studies were Western-dominated, with limited contributions from Africa and nearly no publications from Ethiopia. Findings emphasized that accountability, when properly implemented, serves as a low-hanging fruit for optimizing performance and accelerating organizational change. Leader’s accountability was identified as the second most influential factor after classroom teaching in enhancing student academic achievement. Establishing measurable outcome-based accountability frameworks for leaders help submit their responsibilities. The study underscores the potential of leaders’ accountability as a strategic tool to mitigate academic achievement setbacks. By shifting focus from blame to structured responsibility, accountability frameworks can drive meaningful improvements in student outcomes and support systemic educational change, offering a constructive alternative to the prevailing tendency of finger-pointing in the Ethiopian education system.
This narrative systematic review synthesizes existing research on teacher pedagogical and technological knowledge models in Ethiopia to identify prevailing frameworks, conceptual developments, and gaps. Following PRISMA guidelines, twenty-five empirical studies identified via structured searches in Google Scholar, ERIC, Scopus, Web of Science, and accredited local journals (2005 – 2024). Search terms included teacher knowledge, pedagogical content knowledge (PCK), general pedagogical knowledge (GPK), and TPACK. Thematic analysis was applied to extract patterns and categorize findings; full search strings, inclusion/exclusion criteria, and a PRISMA flow diagram are reported. A formal quality appraisal using the Mixed Methods Appraisal Tool (MMAT) informed interpretation. Coding was inductive, conducted by two independent reviewers, with inter-rater reliability Cohen’s k = 0.82. Thematic analysis reveals a growing focus on TPACK and PCK frameworks in Ethiopian research, while GPK remains underexplored. Teacher knowledge in Ethiopia is emergent, characterized by limited integration of established pedagogical theories into classroom practice. Comparative synthesis highlights contradictions: ICT-assisted training improved pedagogical knowledge in some contexts, yet theoretical coherence and classroom enactment remain inconsistent. Contextual factors-infrastructure limitations, policy emphasis on technology, and uneven teacher preparation-help explain why TPACK receives more attention than GPK. As the first systematic review of in the country, this study provides novel insights into local research trends and theoretical gaps and underscores the need for curricula and professional development that integrate both foundational (GPK) and technology-enhanced (TPACK) frameworks. Findings inform policy, practice, and future research.
Reduced visual acuity (RVA) is a frequently overlooked barrier to learning in early primary grades, despite its welldocumented impact on children’s reading performance and overall academic development. This study assessed the prevalence of RVA among Standard Three pupils aged 8 – 10 years in a public primary school in Dodoma City, Tanzania, where evidence on visual health in early primary learners is limited. A quantitative, cross-sectional, school-based vision screening design was employed. All 200 pupils present during data collection were screened using the standardized LEA Symbols Chart under controlled classroom lighting conditions. Visual acuity below 6/12 was classified as reduced in accordance with international vision screening guidelines. The findings revealed that 35 pupils (17.5%) had reduced visual acuity, indicating that nearly one in six pupils may experience vision-related learning challenges. Boys showed a slightly higher prevalence (54.3%) than girls (45.7%), and the highest proportion occurred among eight-year-old pupils (42.9%). These results suggest a relatively higher burden of RVA compared with findings from several African and highincome settings, highlighting the vulnerability of primary school learners in urban Tanzanian contexts. The study concludes that unaddressed RVA poses a significant challenge to equitable learning opportunities and recommends integrating routine vision screening into school health programs, strengthening referral mechanisms, raising teacher awareness, and improving access to corrective interventions to support inclusive and effective primary education.
This study examines the potential of holy water treatment to help control the spread of cholera in Ethiopia. A mathematical model was developed to understand how holy water could influence cholera transmission. The model was carefully analyzed to ensure that its solutions are realistic and biologically meaningful. To better understand the disease's spread, we calculated the basic reproduction number (𝑅0) using the next-generation matrix method. This number is crucial in determining whether cholera will spread or be controlled. Our findings show that when the basic reproduction number (𝑅0) is less than one, the disease-free state is stable, meaning cholera could eventually be eliminated or reduced. However, if the basic reproduction number (𝑅0) is greater than one, the disease-free state becomes unstable, suggesting that cholera will continue to spread. Numerical simulations conducted in MATLAB demonstrated a significant reduction in cholera transmission following holy water treatment, indicating its potential as an effective tool for disease control. This reduction is not only due to the direct effects on water quality but also stems from the psychological and spiritual impact on the population. The belief in the purifying and healing power of holy water can lead to a reduction in mental stress, tension, and confusion, which are often linked to the fear and anxiety surrounding cholera outbreaks. This spiritual and psychological peace may contribute to better health behaviors, such as improved hygiene practices and adherence to treatment, further helping to control the disease. These results could guide public health strategies and offer new insights into cholera prevention in Ethiopia.
Honeybees (Apis mellifera) play a vital role as pollinators of key crops in agriculture. They produce honey and beeswax for nutritional and industrial uses. Infectious diseases caused by viruses pose a significant threat to their colonies and biodiversity, which requires investigation. In this paper, we develop and present a deterministic SIRS mathematical model that effectively captures the population dynamics of honeybee colonies impacted by viral infections, incorporating new assumptions and parameters into established models. The qualitative behavior of honeybee-pathogen interactions shows that whenever the survivability of a newly hatched egg is guaranteed, both the disease-free and endemic equilibria of the model are locally asymptotically stable with some conditions on parameters. According to the analysis of the model qualitative behavior of honeybee-virus interactions shows that whenever the survivability of newly hatched eggs is maintained, the disease-free and endemic equilibria of the model are locally asymptotically stable with some conditions on parameters. Disease-free and endemic equilibria are globally asymptotically stable. The basic reproduction number ℛ0 is determined using the next-generation matrix method, and sensitivity analysis shows that virus transmission rates are the most influential parameters. Numerical simulations for different scenarios are performed using MATLAB software and the outcomes describe the significance of model parameters, such as the net growth rate of brood and rate of maturation.
Fruits are naturally perishable commodity due to their high moisture content, affecting their postharvest quality and shelf life. Bananas and tomatoes are among the widely cultivated and consumed horticultural crops worldwide, yet, they are prone to huge postharvest loss. Thus, this study aimed at evaluating the preservative potential of nanosilver coatings biosynthesized from selected plant extracts in improving the shelf life of banana and tomato. Accordingly, four Silver nanoparticles (AgNPs) biosynthesized from aqueous extracts of ginger rhizomes (GAgNPs), turmeric rhizomes (TAgNPs), banana peel (BPAgNPs), and orange peel (OPAgNPs) were used. The AgNPs-based coating solutions were then prepared from the AgNPs at concentrations of 30 and 40 μg/mL, in which the fruits were dip-coated. Finally, the disease incidence and changes in physico-chemical composition of the fruits were measured once every 7 days for 28 days. Banana and tomato fruits treated with AgNPs-coatings were observed to have better quality and extended shelf time at least by 7 days, compared to the untreated control. The AgNPs coatings also maintained the physico-chemical properties of the fruits: improved fruit firmness, moisture content, total soluble solid, stable pH and titratable acidity, and ascorbic acid contents throughout the storage time. Generally, study revealed that surface application of biosynthesized AgNPs with very low concentration (endorsed by WHO), is an effective technique to extend the postharvest shelf life and quality of stored fruits. Therefore, the use of biosynthesized AgNPs based coatings to extend the shelf life of fruits and vegetables could be suggested as one of the most successful methods.
Internally displaced children in conflict-affected regions face severe educational disruptions, yet comprehensive evidence on their academic challenges and support mechanisms remains limited. This mixed-methods study addresses the gap by examining the educational barriers, learning outcomes, and support strategies for Grade 1–4 IDP students in Ethiopia's Oromia and Amhara regions. Using a convergent parallel design, the research integrated quantitative data from standardized assessments and structural equation modeling with qualitative insights from focus group discussions and interviews involving 384 students, 96 teachers, 120 parents, and 24 officials and NGOs. Key findings reveal that IDP children experience substantial academic deficits, scoring significantly lower in mathematics (9.2-point gap) and reading (29% proficiency gap) compared to host-community peers. These disparities were driven by multiple barriers: overcrowded classrooms (76:1 student-teacher ratio), resource shortages (8:1 textbook ratio), psychological distress (62% reached clinical thresholds), and social exclusion. The study identified support mechanisms particularly teacher mentoring, catch-up programs, and resource provision that significantly mitigated these negative impacts, though their effectiveness varied regionally. The findings underscore that effective educational interventions must integrate psychosocial support with academic remediation while adapting to local contexts. This research provides evidence-based strategies for policymakers and practitioners working to safeguard education in emergencies and promote learning continuity for vulnerable children affected by displacement.
This research explored the practices, challenges and possibilities associated with utilization of Technology in teaching and learning in some Higher Education Institutions. . Using a mixed-methods approach, quantitative and qualitative data were collected from 164 students, 143 academic staff, and 90 administrative workers. The findings identified a number of critical barriers to the effective integration of digital technologies in teaching and learning, including limited access to subscription-based academic resources, insufficient technological infrastructure, limited internet availability, and inconsistent connectivity. Furthermore, the survey found that the majority of participants used digital technology largely for enjoyment reasons, such as watching movies online and listening to music, rather than to improve instructional methods or conduct academic research. A concerning outcome highlighted by the study was the prevalence of cyberbullying, with female students disproportionately affected. . In light of these findings, the study suggests that higher education institutions prioritize digital infrastructure improvement, broaden access to academic digital resources, and promote ethical and responsible technology use in order to support educational excellence and protect the well-being of all stakeholders
The longer presence of early childhood education and care in Ethiopia and the notable milestones recorded in the process are remarkable and need to be appreciated. However, the system has equally been incarcerated with various challenges limiting its growth; yet amidst several opportunities that would have helped nurturing the system. Several research investigations were done to unearth these experiences and show directions for professionalizing the services. However, macro-level experiences that help understanding more decisive issues are yet to be examined. This article attempts to conduct critical analysis of these decisive issues employing a systems approach to early childhood development and education (ECDE) development and practice with the ‘Nurturing Care Framework’ and the ‘Integrated Multisectoral Approach for Low Income Countries’ embedded in it. The analysis unfolds that the current policy and legislative frameworks seem to provide an enabling condition for a multi-sectoral and integrated ECDE system in the country; but critical gaps were identified both in design and delivery of ECDE in the country. The need to ensuring a more enabling ECDE conditions, comprehensive ECDE implementation with reasonable fidelity, and monitoring experiences to unlock the system that operate in full force are needed. It concludes suggesting the need for a more inclusive, multisectoral, integrated and contextually relevant mechanism to address the critical gaps.
The study investigates the influence of the Cooperative Learning Approach (CLA) on sixth-grade students’ academic performance in English at primary schools in Dodoma Urban, Tanzania. CLA promotes active engagement, peer collaboration, and shared responsibility, contrasting sharply with traditional teacher-centered methods that often limit student interaction. The study employed an experimental research design involving four purposively selected private primary schools from a pool of 56 schools. A total of 300 students (150 in the experimental group and 150 in the control group) participated. Both groups completed a pre-test on the topic Comprehending Oral and Written Information. The experimental group then engaged in cooperative learning activities for one month, while the control group continued with conventional teaching methods. Post-tests were administered to evaluate performance changes. Results indicate a substantial improvement in the experimental group’s scores (with mean scores increased from 2.77 to 3.75) across speaking, listening, reading, and writing domains. Statistical analysis using paired-sample t-tests confirmed the significant impact of CLA on students’ performance, rejecting the null hypothesis. The study strongly advocates integrating CLA into primary education to enhance English proficiency, foster collaborative skills, and improve overall academic achievement. By introducing CLA, students are provided with opportunities to engage in collaborative problem-solving, peer discussion, and knowledge sharing, which may enhance comprehension, retention, and application of English language skills.
It has been argued that the current higher education institutions in Ethiopia have gaps in producing graduates that are well-equipped with the necessary knowledge and competences that fit into the actual job market. The purpose of this study was, thus, to investigate the challenges of higher institutions in Ethiopia in producing competent graduates. Descriptive mixed research design was used to describe the phenomenon, while pragmatic paradigm was employed to operate under the assumption that reality encompasses both subjective and objective elements. A multistage stratified random sampling technique was used to select research samples from different universities. Data were collected through questionnaires, interview and document review. The collected data were analyzed using content analysis and descriptive statistics including inferential analysis. Results reveal that higher institutions of Ethiopia are found to be limited to educating students to achieve minimum learning competences. Besides, the findings confirm that challenges related to curriculum alignment with the job market requirements, digitalizing the education system and instructors’ lecture-based pedagogical and instructional approaches are found to be at the top urgency to be acted on. It has been recommended that there is an urgent call for integrating the teaching-learning practices with the real world market, entrepreneurial needs, problem-solving skills and hands-on experiences.
Land use and land cover (LULC) changes can adversely affect livelihood assets/resources impacting rural communities. This study assessed the livelihood impacts of LULC changes on rural livelihoods in Bale Mountains Eco-Region (BMER), Southeast Ethiopia. A sustainable livelihood framework was employed to assess the impact. A cross-sectional survey of 339 households, combined with field observations, was conducted to gather data on the effects of LULC changes between 1973 and 2021. Household heads served as the unit of analysis, and quantitative data were analyzed using descriptive statistics, while qualitative data were analyzed through content analysis. Results showed that 62.8%, 62.2%, and 85.3% of respondents reported expansion of cultivation into marginal areas, increased overgrazing, and excessive tree cutting, respectively, as significant indicators of change during the study period. As a result, local communities have experienced reduced crop yields, loss of grazing lands, declining soil fertility, and increased vulnerability to environmental risks. Furthermore, 99.7% of respondents perceived LULC changes as having a direct impact on their livelihood adversely affecting their livelihood assets, primarily natural resources. Livelihood patterns have transformed significantly, shifting from traditional pastoralism to agro-pastoralism and crop-based systems, with households diversifying into various income-generating activities. Adverse livelihood outcomes, including reduced well-being and increased food insecurity, were commonly perceived among respondents. The findings highlight an urgent need for sustainable management of natural resources to improve livelihoods across different LULC types. Moreover, diversifying livelihood strategies and assessing the community’s coping and adaptive capacities are essential to mitigate the adverse impacts of LULC changes.
In this paper, discrete implicit linear multistep methods in block form for the solution of initial valueproblems was presented using the Chebyshev polynomials. The method is based on collocation of thedifferential equation and interpolation of the approximate solution of power series at the grid points.The procedure yields four consistent implicit linear multistep schemes which are combined assimultaneous numerical integrators to form block method. The basic properties of the method such asorder, error constant, zero stability, consistency and accuracy are investigated. The accuracy of themethod was tested with two stiff first order initial value problems. The results were compared with amethod reported in the literature. All numerical examples were solved with the aid of MATLABsoftware after the schemes are developed using MAPLE software and the results showed that ourproposed method produces better results.
This study explored the link between leadership style and academic staff's job satisfaction at Jimma University. A correlation research design was used to conduct the study. Data was collected from 291 academic staff selected using availability for leaders as their number was small, and proportionatestratified random sampling techniques for staff. Data was gathered using two standardized questionnaires: Multi-factor Leadership Questionnaire (MLQ-5x) and the Job Satisfaction Survey questionnaire (JSS) and analyzed using mean, Standard Deviation (SD), an independent-test and Pearson’s product-moment Correlation. Finally, the findings revealed a statistically significant (p < 0.05) and positive correlation between the transformational leadership style with all the dimensions of job satisfaction except supervision. Besides, there was a positive and significant correlation (p < 0.05) between transactional leadership style and staff’s job satisfaction. Nonetheless, there was a negative and statistically significant correlation between laissez-faire leadership style and job satisfaction. Thetransformational leadership style was the strongest predictor of job satisfaction (β = 025, P < 0.05). These findings may imply that academic job satisfaction would be improved in this university by enhancing the practice of transformational and transactional leadership styles. In this regard, better emphasis given to these two leadership styles in the university need to be encouraged. Hence, there is a need for leadership development training programs to advance the leadership skills of the leaders at the institution
