Evaluating Agile Neural Educational System for Effective Resource Management

The major challenge of most basic schools is inadequate educational resources despite a conscious effort to constantly provide. This is a result of inaccurate data management leading to inappropriate predictions for effective planning. The actual efficiency of a system is determined by its ability to predict real-life data with speed and accuracy. In this work, the neural educational expert system (ES) is evaluated using mathematical models for predicting the availability of resources for the growing school-aged population using a criteria-based formative evaluation to know resource life and its effect on availability. This will help in the decision to add more resources by knowing when and how the resources should be added. Technical mathematical model generation through differential equations is used to fuse the factors affecting the availability of educational resources. The real-life data is used in prediction regarding the actual enrollment of learners and the availability of resources. The model is evaluated and critically analyzed to know the degree of accuracy and the steady state. The findings revealed that the resources decay and attrite at an exponential rate in the long run and the constant number of resources provided cannot cater for the rate of decay, resulting in inadequacy. A proposed algorithm for managing the resources is presented. Plain Language Summary Purpose: The main aim of this work is to evaluate the agile neural educational system and find out the reasons behind the inadequate resources despite the effort to make resources adequate in schools. methods: methodology adopted is criteria-based formative evaluation using differential equations with initial value problem. conclusions: Inadequate educational resources affect the process of learning. Poor performance at the foundation affects higher levels of learning. Careful planning, provision, and management of educational resources can best be achieved by using the model to monitor the availability and provision of resources. This can be done through the careful control of two major factors; the addition of resources at regular intervals and good maintenance skills to reduce the decay of resources. This will minimize the cost of education which usually forms a major component of the budgets in countries. Going forward, it is prudent for the country to adopt this model to manage educational resources. implications: stakeholders of education will minimize the cost of education which usually forms a major component of the budgets in countries. Going forward, it is prudent for the country to adopt this model to manage educational resources. Limitations: this work is limited to resources in the form of physical quantities at the basic level of education.


Introduction
Despite stakeholders' efforts to constantly provide resources for schools, data available indicate that most countries lack adequate pedagogical tools for the school-going age population in school (Inusah et al., 2022).Evidence of school children without sitting places and writing places resulting in pupils lying on the floor using primitive tools is a common news item in the mass media (Inusah et al., 2023a;OECD, 2012).This negatively affects inclusivity and equity in education.In an initial exploration of educational data in Ghana, a detailed analysis of already existing data from the Educational Management Information System (EMIS) clearly shows the inaccuracies in the data and the repercussions on the quality of education in the country (Inusah et al., 2021).A subsequent classification of data and the use of technical tools to trace the challenges of basic education revealed the challenges of basic education as inadequate resources as a result of improper planning and projections for the growing population (Inusah et al., 2022).Stakeholder consultation to improve the management of data and enhance efficiency in decision-making received overwhelming support.Acceptance survey for the possible use of an expert system conducted as a follow-up for the views of the stakeholders of education using both interview and questionnaire survey shows massive zeal and readiness to use an expert system at the basic level of education (Inusah et al., 2023b).As an intervention for the challenges identified, an agile neural ES for managing basic education is proposed with a mathematical model (Inusah et al., 2023a).This system uses a mathematical model to predict the enrollment of learners for the coming years and the data is fed into the ES which is further analyzed through data mining to identify the challenges of various educational institutions and the appropriate interventions that should be carried out to help in addressing the challenges for the improvement of quality education.The main aim of this work is to evaluate the agile neural educational system and find out the reasons behind the inadequate resources despite the effort to make resources adequate in schools.With basic education as a foundation, improving quality at this level will also help in leveraging the achievement of education to the higher levels in a country (Tarabini et al., 2018).Interactive technological tools can help in achieving these by minimizing the cost of the provision of pedagogical tools such as textbooks (Conceic xa˜o, 2021).Many research works in Ghana including (MoE, 2018(MoE, , 2019) ) lament inadequate resources in basic schools which affects tuition.A report (Aheto-Tsegah, 2011) explicitly points to the problems facing basic education regarding the Key Performance Indicators (KPIs) for managing basic education.
Inadequate resources affect access to education at the basic level in Ghana (Akyeampong & Hunt, 2016).Special needs children suffer this more (Ametepee & Anastasiou, 2015).To improve the educational system's performance, urgent attention is necessary.This work aims to evaluate the agile neural educational system through a mathematical model by considering the factors that affect the availability of resources in education and the proposed system for the management of resources.Specifically, the paper seeks to identify the reason behind the inadequacy of the resources which affects the quality of education.This will help in enhancing inclusivity and equity for the growing school-age population.The following research questions guide the research; Why are resources inadequate despite the stakeholders' efforts to improve data management for adequate provision of resources?What should be done to improve the data and enhance resource availability for teaching and learning?
The remaining part of the work is structured in six areas comprising related work, methodology, presentation of results, discussion of findings, conclusion, and limitations.The related work looks at the structure of the educational system, system evaluation, and model evaluation.The methodology dwells on the application of differential equations in getting a solution to the problem by looking at the system structure and the educational system modeling.Results of the models using reallife data are presented and discussed based on the findings with a conclusion drawn.The limitation of the work is the final aspect.

Related Work
Relevant literature on neural system structure is a necessity to understand this work.This will help in knowing the appropriate methodology to handle the problem.Already existing works on how systems and models are evaluated will also be relevant.

Neural Systems
Understanding and presenting data in a meaningful form is a necessity for efficient management.The human brain reasons in the identification of problems and getting solutions to those problems.This is done by the basic unit of the human brain called the neuron (El-Dahshan et al., 2014).The applications of computerized reasoning in the solution of problems can be seen in neural networks (Raissi et al., 2019).This makes it possible to know the interrelationships that exist between and among components to produce results.As technology advances and the application of technology becomes inevitable, several research works in neural systems are cited.Specifically in education, Inusah et al. (2023a) used a neural system to manage basic education.Components of this system are the problems, interventions to educational challenges for quality education.The structure of the neural system is presented in the work which comprises solutions to the management of EMIS. Figure 1 is the framework of a neural ES to assist the human expert in managing the data.

Structure Educational System
The structure of education varies from country to country.However, a universal structure for all countries can be seen in the hierarchical structure and chronological grading.Every country recognizes early-grade learning which is the starting point for the educational system.This grade is usually for children between the ages of 3 and 5 years to prepare them for elementary education.By age 6, the child will be in grade 1 of primary education to go through the 6-year progressive learning which the child is expected to complete by age 11.After completing the primary level, the learner progresses to the Junior Secondary which is also known as Junior High School (JHS) at age 12 to start JHS1 and complete it by age 14 in JHS 3 if it is a 3-year JHS.In some counties, the learner progresses until age 17 for the combined junior High and Senior High School.Figure 2 shows the universal structure of basic education System Evaluation Understanding a complete system and evaluating it accurately is essential for enhancing the efficiency of that system (Tahar Djebbar et al., 2022).Interrelated components of a system must work together and be evaluated as a whole system.The criteria for a system as well as the factors that constitute the formation of a system should be taken into consideration (Chen et al., 2011).The paper (Liu, 2022), evaluates education using the K-means clustering method in data analysis.In Sdravopoulou et al. (2021), a naturalistic approach applied to technological systems across different aspects of life in augmented reality (AR) is critically evaluated.In Ghana, the school placement system which is computerized is evaluated using the fit and viability theory (Owusu & Nettey, 2022).This same methodology is applied in managing land records in Kenya, where Kwanya (2014) used the methodology to determine the effective management of land for enhanced production.In designing and evaluating a performance support system for electricity, Karakaya-Ozyer and Yildiz (2022) used a four-phase tendency to evaluate the system.A paper by Vandevelde et al. (2016) looks at the building of a robot and its evaluation using an expert evaluation and follow-up questionnaire.
The evaluation of a system to know the level of efficiency in handling a task is an essential step in system life.User acceptance of a system should be based on the ability of the system to solve the problem in the operation of works.As a requirement in system development, many developers devote much time to it.In the evaluation of the (Q)SARs system for predicting skin sensitization substances, balance accuracy is used as the main parameter in knowing the efficiency of the system (Fitzpatrick et al., 2018).In M. Radwan et al. (2016), the learning process of learners is enhanced through an expert system which is evaluated by neutrosophic logic.With this system, the percentage of unknown instances is handled accurately.

Model Evaluation
The evaluation of a model is a necessity to know the level of efficiency and the degree of accuracy to enhance the validity and reliability of the model (Contreras-Luja´n et al., 2022).Many research works on model evaluation show a variety of methodologies in evaluating a model to justify its usefulness.In Jena et al. (2015), a new adaptive model for the forecasting of the exchange rate is evaluated with a linear combiner and FLANN supplement.In a paper by Majhi et al. (2014), the prediction of stock indices using a neural network genetic algorithm with radial basis function was evaluated using a fuzzy set theory.The performance evaluation of staff in academia at a Sudanese university was done using a fuzzy logic model.This was for both qualitative and quantitative data (M.K. Yousif & Shaout, 2018) The text mining model is used for digitized textual data in Hindi (Rani & Lobiyal, 2022).The model and control experiment evaluating dust and heat energy effect on photovoltaics was evaluated using the solar performance photovoltaic (PV) (J.H. Yousif et al., 2022).In a related paper (Li & Cui, 2022), energy efficiency and utilization to combat the crisis in power supply revealed a boast in carbon neutrality.In a climate evaluation model, (Eyring et al., 2019) comprehensive and rapid evaluation of the model to enhance efficiency in climate assessment proves more successful through the Coupled Model Intercomparison Project (CMIP), which helps in sharing, comparing and analyzing global climate issues.In a paper by Tahar Djebbar et al. ( 2022), the potency of a vaccine is evaluated through an experimental model.

Resource Management
Efficient management of resources in institutions is a major factor in increasing productivity (Najam et al., 2020).This requires the use of innovative and sustainable ideas to link resources to where they are needed (Lee et al., 2021).Traditionally the importance of resource utilization for future growth and development is well recognized (Agatha, 2016).This enhances economic management in the utilization of limited available resources (Kim, 2021).A competent framework is therefore needed in the utilization of the resources (Midhat Ali et al., 2021).

Agile Learning and Efficient Resource Management
Evidence of agile neural learning systems in managing educational resources to improve efficiency is available in Yang et al. (2019).This deep-learning system helps in both the development and use of Computer Science courses in education.In Inusah et al. (2023a) an agile neural rule-based expert system is used in managing basic education to enhance more efficiency.The feature of deep learning strategically positions it to be the interconnections suitable for tracing a resource, its availability, adequacy and efficient usage (Mutlu & Yıldırım, 2019).The neural theory proves its efficiency over the traditional resource management in the aspect of accurate resource identification, ease in resource adaptability, and faster management of resources.

Methodology
The system evaluation methodology adopted is criteriabased formative evaluation (Chen et al., 2011) where real-life data is used in the evaluation.The essence of this methodology is to respect the culture of the educational system and help in constructing models regarding the factors considered in education.As physical quantities are involved, a differential equation with an initial value problem is used to formulate mathematical models by factoring in the necessary factors affecting resource availability.The steady state, half-life and doubling time of the system are used in determining the availability of resources with consideration of the lifespan.Real-life data is used in testing the accuracy of the models.The human resource evaluation model by Ozerov (2008) is adopted in a proposed model for the management of the resources for durability and availability

System Structure
Reasoning into the problems of education, poor quality education is considered a major nuisance.This is a result of the challenges of education and how these challenges contribute to poor quality.On a journey to quality education, interventions that can bring sustainable solutions are applied.When a positive result is received, an improvement in the quality of education is seen and both the rural and urban schools are endowed with quality outcomes.Figure 3 depicts the structure of a neuron.
Perceiving the challenges of education and the sustainable solutions to education, a neurological presentation associates the challenges to poor quality education and the journey to quality education is based on the solutions applied to the challenges.Major challenges of education are identified and the corresponding solutions for the challenges are presented below.
Educational institutions usually provide resources yearly to enable enrolled learners to have access.This is usually done by considering the deficit of resources needed after new entrants are enrolled.This, however, does not address resource inadequacy.Several factors affect the availability of resources in schools.A conscious effort to identify the challenge is seen below.

Educational System Modeling
Assuming K is the yearly provision of resources, R is the total available resources and t is any given time, R(t) denotes the total available resources with respect to time. Model Integrating R(t) = Kt + c with c as the integrating constant.
Putting c into Equation 1 Where there is no provision of the beginning resource, Let L be attrition or decay of resources in a year First case if K .L, higher retaining of resources than reduction, then R t ð Þ increases.Second case if K \ L, there is a faster reduction of resources than retaining, then R(t) decreases.

Model 3
Reduction of resources varies with total resources LaR )L = QR where Q is the constant of variation.
Model 3 solution Separation of variables will give dR KÀQR = dt integration will give l \ KÀQR j j ÀQ = t + c where c is the constant.
Putting in initial condition K Steady State.A dynamic system reaches a steady state if time does not bring any change in the results it produces.Mathematically, ) R is independent of t.Thus dR dt =0 Getting model 3 steady-state solution, is the solution for steady-state Available resources in school with time.R 0 are initial resource and K Q is the final resource with time.
) represents the increase in resources and R 0 e ÀQt is for the drease taking t 0 = 0 Sustainable Development Goal (SDG) 4.1 is to ensure that every learner completes free, equitable and quality basic education which will lead to relevant and effective learning outcomes (Johnston, 2016).For this to be successful, adequate provision of educational resources is necessary for more inclusivity and equity in education.The growing population of the country needs a corresponding growth in educational resources to enhance effective teaching and learning in schools.Therefore, educational resources at any time R(t) should be greater than or equal to enrollment in school at a time.

Model 4
Taking the total resources to be R.Total resources at any point in time should be in line with the resources available.From model 3, dR dt = K-QR where K is the yearly resources added, Q is the constant of variation and R is the total resources at any point in time.If there is no provision of resources yearly for the enrolled learners, K = 0.This implies dR dt = -QR as a total resource at the initial time R(t This is a decay which depicts a reduction in educational resources. The steady state of Model 4 R(t)= R 0 e ÀQt since Q .0, as t !', e ÀQt !0.If R 0 is the initial resource available and there are no additional resources added but with existing resources in use, R! 0 as t !'.This is a trivial steady state.
Half-Life of Resources.This is the time it takes a physical quantity to reduce to its half value.
Half-life depends on the rate of decay or attrition of resources.Interestingly, time is independent of resources but resource availability strongly depends on time.It will take some time for resources to deplete irrespective of the number of resources available.
Expected Life Span.Given the probability of a resource to deplete (decay) as a d/t unit, where Q/t units, then the life span of a resource will be 1/Q units' time.For the model R = R 0 e ÀQt , Q is the rate of decay per unit of time.The expected life-span of a resource (time of its survival) is 1=Q units of time (years) Model 5 From model 4, dR dt = -QR which is an exponential decay model.The exponential growth with the initial condition R(t 0 )= R 0 will be dR dt = QR.
Practically, this may not be possible as resources cannot be increased without being added.Moreover, resources will be used and depleted.Depreciation as well as limited finance in countries to constantly provide educational resources affects this result.

Doubling Time.
The doubling time rate is the time in which the value of a physical quantity gets twice its initial value.In the provision of educational resources, the time it will take for institutions to get twice the initial resources they were using will be the doubling time.Computing the doubling state for Model 6 For a more realistic representation of educational resources, combining models 4 and 5 is a necessity.In model 4, dR dt = -QR which is decay and in model 5 it is dR dt = QR which is growth.Integrating the two models, two controlling parameters will determine the total resource availability at any point.These parameters are the addition of resources and the decay of resources.As K is the yearly addition of resources and L is the decay or attrition of resources, model 6 will be dR dt = (K-L)R; the initial condition with R(t 0 )=R 0 .

Solving
Taking the difference between the addition of resources and the decay of resources as N (K-L = N) then R=R 0 e Nt .This is an exponential solution profile.
Case 1: if K .L, the addition of resources is more than the decay of resources.Then R 0 e (KÀD)t !' as t !'.This means R! ' as t !' which is a clear instance of a non-trivial steady state.
Case 2: if K \ L, R 0 e (KÀL)t !0 as t !' this means R! 0 as t !'.This is a trivial steady state.

Results and Findings
This section comprises two major parts; the experimental results from the models using real-life data and an analytical result in the model presented in the form of a flow chart for adoption in resource management and utilization.The experimental results are presented in Table 1.These results are from the mathematical models derived and the testing of the models with real-life information to know how time affects resource availability.The necessary cases or scenarios are presented under the models and the data shows the evidence.Carefully planned steps to ensure the control of attrition of resources as a major factor that affects resource availability are presented.This is to enhance the maximum use of resources by determining when to add more resources for effective teaching and learning.A system evaluation of the model for educational resource management is presented in the form of a flow chart.This model, if properly used, can help reduce attrition and improve the lifespan of already existing resources in schools.This will help in reducing the cost of providing more educational resources to cater for the growing population of school-going age.The choice of materials and the procurement process of the resources are also considered to enable the stakeholders to know the specifications and meet those requirements before those resources are accepted into the learning environment.Also, resources that are not in use but occupy space in the learning environment should be removed.
Starting from KG1 and progressing to JHS3, an initial enrollment of 45 learners for standard class size and an accumulation of 45 for a year to the last grade is presented as E in Table 1.The parameters for the models as well as the results for each of the models are presented.The average class size which determines the resources per year for a class is K and the attrition of resources per year which is L are the controlling parameters for the model results.The initial value of 45 is used to predict the base and the expected enrolled learners are E.This is checked to ensure that model 1 is dimensionally consistent before generalizing to model 2. Since model one does not consider attrition and other factors, model two is used to generalize model 1 and include the attrition of learners.Time(t) is an independent variable representing the different academic years for each class.The dependent variables are the results of the model.Linear models are noted for limitations such as the inability to present real-life data and withstand the test of time, hence an improvement of model 2 to exponential model 3.This model takes into consideration the necessary factors that affect resource availability in real-life.Model 4 tries to look at the failure to provide resources yearly for the learners while model 5 looks at the provision of resources without attrition of resources.From the results presented, it is clear that the expected enrollment of learners is always less than the total available learners for all models except model 1, which does not include the attrition of the resources.In addition, a reduction in resources as a result of depreciation and attrition is noticed at an exponential rate in the long run after a decade and a half in operation.This clearly shows the reason behind the inadequate resources in schools despite the intervention by stakeholders in education to constantly provide resources yearly.Figure 4 is a neuron of the system.

Proposed Model for Managing Resources
The inadequate resource calls for effective management of resources.In Jolita and Palmira (2013), a model for human resource evaluation and methods for improving the performance of the public sector are properly investigated to identify the problems and solutions.It adopted the model of Ozerov (2008).That model is adapted in this work as the educational system resource evaluation criteria to help in addressing the challenges of inadequate resources in schools.
Most countries including Ghana currently run free education.However, free education without adequate resources for effective teaching and learning cannot bring the needed outcome in education.This implies that it is the responsibility of the government through the Ministry of Education to provide educational resources to schools.A resource reserve is therefore necessary for the effective provision of resources.Educational institutions demand new resources evaluated by looking at the functions, descriptions and development.When it is established that the evaluation result is good, the resource provision is considered, else a specification of the demand will be necessary.In resource provision, an initial evaluation in selecting the resources should be done.If the result is positive, the resource will be used in school, else it should be returned to the provider.Regular evaluation of resources used in schools should be carried out to enable knowing the status and convenience of usage.If the result is good, an improvement in the convenience and usage of resources will be guaranteed to enhance adequate resources in school and proper utilization for the improvement of quality education.If the result is bad, the reason for the poor status of the resources, flaws, irrelevance, non-utilization and resources that can no longer be used in the school environment should be flagged out of the system.Where there are flaws in the resources, maintenance will be required, where the resource is not relevant for use, it should be moved away from the school environment, where a resource is not in use but still needed, it should be sent to the storage location and when the resource cannot longer be in the school environment, it should be removed completely from the school.Where resources are adequate for use in a school, they must be used for quality teaching and learning.Quality evaluation for convenience in use should therefore be considered.If it is good, a quality resource for efficient teaching and learning is guaranteed.If it is not good, the former status of the resource should be known and the cycle for maintenance considered.Where there are no adequate funds for the provision of resources, improvisation is necessary as an interim measure.The representation of the model for educational system management is in Appendix A.

Discussion
Managing educational data to improve data integrity for efficient management of resources is essential (Inusah et al., 2023b).In Figure 1, the integrity of educational data is enhanced using data mining techniques before the neural expert system (Inusah et al., 2023a).As presented in Figure 2, knowing the appropriate structure of the education system helps in following the appropriate criteria in evaluating the system to increase its efficiency (Chen et al., 2011).Computerized reasoning in the form of a neural network will help in representing the human understanding of data management and the interrelated components linked to the challenges of resource availability (Raissi et al., 2019).This is seen in Figure 3 in the human understandable and Figure 4 as the models depicted.
The pedagogical resources appear adequate in the early part of a new establishment if plans to provide yearly for the growing enrollment are implemented.As resources decay and attrite, an extension to more than a decade will lead to an increase in attrition as the lifespan of the resources diminishes.This will lead to higher resource inadequacy if a conscious effort is not made to increase the regular provision and maintenance of resources.Eventually, pedagogical tools will diminish and learners will be disadvantaged.This confirms the assertion of Inusah et al. (2022) that the teaching and learning resources are inadequate for effective teaching and learning in Ghanaian schools.It is the stage in most Ghanaian schools leading to inadequate pedagogical tools.
As indicated in Macias-Escobar et al. ( 2021) decisionmaking is a complex task which is usually underestimated leading to mismanagement and poor results.Resource availability in schools strongly affects effective pedagogy as inadequate resources compromise quality tuition (MoE, 2019).Accurate and effective planning which will lead to adequate provision and utilization of resources is, therefore, a necessity to enable schools to enhance inclusivity and equity for quality education (Inusah et al., 2023a).Unlimited demand coupled with scarce resources is a call for the effective allocation of resources for effective utilization (Hatami-Marbini et al., 2022).The rate of decay or attrition of resources affects the availability of resources if the rate of provision is not higher.For the total resources available on time to increase for the growing population to utilize, the massive provision of resources at regular intervals is key.As the population of school-going ages grow at an exponential rate, resource provision should be given priority in the education of learners.This confirms Sdravopoulou et al. (2021) statement on the use of a naturalistic approach in evaluating systems because resources degrade with time as they are used.As accuracy is essential in managing data and evaluating systems, the vital factors that affect the integrity of data for effective management should be considered (Fitzpatrick et al., 2018).Maintenance as well as careful usage affects the life span of resources.This should be enhanced in other to manage the limited resources for the growing population in schools.If the rate of degradation of resources is more than the provision of resources, the total available resources will reduce with time.Knowing the half-life of educational resources will help in planning for the provision of resources for effective teaching and learning.This, however, requires technical knowledge in determining the durability of a resource which is not captured in this paper.Accurate projections can help in knowing when the school-age population will reach the doubling stage for a corresponding doubling of resources to enhance effective pedagogy (Inusah et al., 2023a).The two major factors; the addition of resources and the decay of resources should be carefully managed.For better utilization of financial resources in countries, excess provision of resources should be monitored if the provision of resources is more than the degradation of resources in the country.A Steady-state of population growth of the school-going age will lead to a corresponding steady state for the provision of resources in schools.This should be strictly monitored.As indicated by Tahar Djebbar et al. (2022), system evaluation is essential for enhancing efficiency.The system model in Figure 3 is the proposed solution to the problem identified.

Conclusion
Inadequate educational resources affect the process of learning.Poor performance at the foundation affects higher levels of learning.Careful planning, provision, and management of educational resources can best be achieved by using the model to monitor the availability and provision of resources.This can be done through the careful control of two major factors; the addition of resources at regular intervals and good maintenance skills to reduce the decay of resources.This will minimize the cost of education which usually forms a major component of the budgets in countries.Going forward, it is prudent for the country to adopt this model to manage educational resources.

Limitations
This model is very good for the management of the same type of resources.Total resource availability here refers to the total available resources for an individual resource in the learning environment.It is not effective to sum different categories of learning resources together in using this model.The model is also good for single-user educational resources such as sitting places and writing places.Even though the model is accurate and can work on time, the provision of resources strongly depends on the need for resources by the population of school-going ages.If the population experiences an abnormal reduction or growth as a result of unpredicted events, the accuracy of the model may not be guaranteed.

Figure 2 .
Figure 2. International structure of educational system.

Figure 3 .
Figure 3.A neuron of the structure of education.

Figure 4 .
Figure 4. Resultant neuron of the educational system.
Proposed model for resource management.

Table 1 .
Parameters and Results for Models Over Time.