Search results for: problem solving skill

Authors: Felipe Azocar Simonet, Luis Acosta Espejo

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In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: coherent covering location problem, efficient frontier, lagragian relaxation, data envelopment analysis

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Authors: J. Van der Walt, N. A. Plastow, M. Unger

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Gross and fine motor skill difficulties among children affect their ability to learn and progress in school. Research indicates that children in low socio-economic areas are at a higher risk of motor skill difficulties, while therapy resources are limited. The Hopscotch motor skill programme is a well-researched accessible in-school intervention developed by occupational and physiotherapists through complex intervention development. The development stage of the complex intervention development model firstly included a prevalence study in a low-resourced area in the West Coast of South Africa, indicating a high prevalence with significant motor skill difficulties among pre-school children at 14.5% with fine motor skill difficulties at 24.6%. A scoping review identifies motor skill interventions for pre-school children and a proposed a framework of fundamental concepts to consider when developing a motor skill intervention. a Delphi-study considered the framework and encouraged collaboration between therapists and educators to make the programme accessible, resource and cost effective, specifically geared towards a rural, low resourced area. The results from the Delphi study, together with the proposed framework from the scoping review was used to develop the Hopscotch programme, adopting a task-shifting approach. The eight-week small-group programme is facilitated by teachers with the support of therapists. The programme aims to improve the motor skills of pre-school aged children with motor skill difficulties to promote academic readiness through obstacle courses, ball skill games and fine motor games and crafts. A randomised controlled trial is planned as a next stage to determine the preliminary effect of the programme on the motor and early academic skills of pre-school children.

Keywords: accesible learning, motor skill intervention, school readiness, task shifting

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Authors: Badr Alkahtani

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In this poster, numerical solutions of two-dimensional and three-dimensional lid driven cavity are presented by solving the steady Navier-Stokes equations at high Reynolds numbers where it becomes difficult. Lid driven cavity is where the a fluid contained in a cube and the upper wall is moving. In two dimensions, we use the streamfunction-vorticity formulation to solve the problem in a square domain. A numerical method is employed to discretize the problem in the x and y directions with a spectral collocation method. The problem is coded in the MATLAB programming environment. Solutions at high Reynolds numbers are obtained up to Re=20000 on a fine grid of 131 * 131. Also in this presentation, the numerical solutions for the three-dimensional lid-driven cavity problem are obtained by solving the velocity-vorticity formulation of the Navier-Stokes equations (which is the first time that this has been simulated with special boundary conditions) for various Reynolds numbers. A spectral collocation method is employed to discretize the y and z directions and a finite difference method is used to discretize the x direction. Numerical solutions are obtained for Reynolds number up to 200. , The work prepared here is to show the efficiency of methods used to simulate the physical problem where accurate simulations of lid driven cavity are obtained at high Reynolds number as mentioned above. The result for the two dimensional problem is far from the previous researcher result.

Keywords: lid driven cavity, navier-stokes, simulation, Reynolds number

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Authors: Tesfaye Basha

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The purpose of this study was to examine the sign language and academic achievement of deaf students in special and inclusive primary schools of Southern Ethiopia. The study used a mixed-method to collect varied data. The study contained Signed Amharic and English skill tasks, questionnaire, 8th-grade Primary School Leaving Certificate Examination results, classroom observation, and interviews. For quantitative (n=70) deaf students and for qualitative data collection, 16 participants were involved. The finding revealed that the limitation of sign language is a problem in signing and academic achievements. This displays that schools are not linguistically rich to enable sign language achievement for deaf students. Moreover, the finding revealed that the contribution of Total Communication in the growth of natural sign language for deaf students was unsatisfactory. The results also indicated that special schools of deaf students performed better sign language skills and academic achievement than inclusive schools. In addition, the findings revealed that high signed skill group showed higher academic achievement than the low skill group. This displayed that sign language skill is highly associated with academic achievement. In addition, to qualify deaf students in sign language and academics, teacher institutions must produce competent teachers on how to teach deaf students with sign language and literacy skills.

Keywords: academic achievement, inclusive school, sign language, signed Amharic, signed English, special school, total communication

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Authors: Ragea Alqahtani

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The purpose of the study was to measure the effectiveness of the Goldstein’s social skill streaming model based on the special and general pre-service teachers’ knowledge about controlling their emotions in conflict situations. A review of previous pieces of literature guided the design and measurement of the effectiveness of the approach to the control of emotions. The teachers were assessed using the coping strategy, adult anger, and Goldstein’s skill streaming inventories. Lastly, the paper provides various recommendations on the sensitization of the Goldstein’s Social Skill streaming model to both the special and pre-service teachers to promote their knowledge about controlling emotions in conflicts.

Keywords: emotional control, Goldstein social skill streaming model, modeling technique, self- as-a-model, self-efficacy, self-regulation

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Authors: Aydin Teymourifar, Gurkan Ozturk, Ozan Bahadir

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NSGA-II is one of the most well-known and most widely used evolutionary algorithms. In addition to its new versions, such as NSGA-III, there are several modified types of this algorithm in the literature. In this paper, a hybrid NSGA-II algorithm has been suggested for solving the multi-objective flexible job shop scheduling problem. For a better search, new neighborhood-based crossover and mutation operators are defined. To create new generations, the neighbors of the selected individuals by the tournament selection are constructed. Also, at the end of each iteration, before sorting, neighbors of a certain number of good solutions are derived, except for solutions protected by elitism. The neighbors are generated using a constraint-based neural network that uses various constructs. The non-dominated sorting and crowding distance operators are same as the classic NSGA-II. A comparison based on some multi-objective benchmarks from the literature shows the efficiency of the algorithm.

Keywords: flexible job shop scheduling problem, multi-objective optimization, NSGA-II algorithm, neighborhood structures

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Authors: Hong-Ming Chen

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This work considers the resolution of the Hull and White interest rate model with the jump process. A deterministic process is adopted to model the random behavior of interest rate variation as deterministic perturbations, which is depending on the time t. The Brownian motion and jumps uncertainty are denoted as the integral functions piecewise constant function w(t) and point function θ(t). It shows that the interest rate function and the yield function of the Hull and White interest rate model with jump process can be obtained by solving a nonlinear semi-infinite programming problem. A relaxed cutting plane algorithm is then proposed for solving the resulting optimization problem. The method is calibrated for the U.S. treasury securities at 3-month data and is used to analyze several effects on interest rate prices, including interest rate variability, and the negative correlation between stock returns and interest rates. The numerical results illustrate that our approach essentially generates the yield functions with minimal fitting errors and small oscillation.

Keywords: optimization, interest rate model, jump process, deterministic

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Authors: Rachid Ziteuni, Selt Omar

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In this paper, we propose a new polynomial metaheuristic elaboration (tabu search) for solving scheduling problems. This method allows us to solve the scheduling problem of n tasks on m identical parallel machines with unavailability periods. This problem is NP-complete in the strong sens and finding an optimal solution appears unlikely. Note that all data in this problem are integer and deterministic. The performance criterion to optimize in this problem which we denote Pm/N-c/summs of (wjCj) is the weighted sum of the end dates of tasks.

Keywords: scheduling, parallel identical machines, unavailability periods, metaheuristic, tabu search

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Authors: Alireza Alizadeh, Hossein Ghadimi, Oveis Abedinia, Noradin Ghadimi

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A Particle Swarm Optimization with Time Varying Acceleration Coefficients (PSO-TVAC) is proposed to determine optimal economic load dispatch (ELD) problem in this paper. The proposed methodology easily takes care of solving non-convex economic load dispatch problems along with different constraints like transmission losses, dynamic operation constraints and prohibited operating zones. The proposed approach has been implemented on the 3-machines 6-bus, IEEE 5-machines 14-bus, IEEE 6-machines 30-bus systems and 13 thermal units power system. The proposed technique is compared to solve the ELD problem with hybrid approach by using the valve-point effect. The comparison results prove the capability of the proposed method giving significant improvements in the generation cost for the economic load dispatch problem.

Keywords: PSO-TVAC, economic load dispatch, non-convex cost function, prohibited operating zone, transmission losses

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Authors: Yun Hang Stanley Cheung

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In recent years, many educators and entrepreneurs have often suggested that students’ and workers’ ability of the adversity response is very important, it would affect problem-solving strategies and ultimate success in their career or life. The meaning of resilience is discussed as the process of bouncing back and the ability to adapt well in adversity’s response, being resilient does not mean to live without any stress and difficulty, but to grow and thrive under pressure. The purpose of this study is to describe the process of resilience and adversity’s response. The use of the narrative inquiry aims for understanding the experiential process of adversity response, and the problem-solving strategies (such as emotion control, motivation, decisions making process), as well as making the experience become life story, which may be evaluated by its teller and its listeners. The narrative study describes the researcher’s self-experience of adversity’s response to the recovery of the seriously burnt injury from a hill fire at his 12 years old, as well as the adversities and obstacles related to the tragedy after the physical recovery. Sense-Making Theory and McCormack’s Lenses were used for constructive perspective and data analyzing. To conclude, this study has described the life story of fighting the adversities, also, those narratives come out some suggestions, which point out positive thinking is necessary to build up resilience and the ability of immediate adversity response. Also, some problem-solving strategies toward adversities are discussed, which are helpful for resilience education for youth and young adult.

Keywords: adversity response, life story, narrative inquiry, resilience

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Authors: M. Rodionov, Z. Dedovets

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The level and type of student academic motivation are the key factors in their development and determine the effectiveness of their education. Improving motivation is very important with regard to courses on middle school mathematics. This article examines the general position regarding the practice of academic motivation. It also examines the particular features of mathematical problem solving in a school setting.

Keywords: teaching strategy, mathematics, motivation, student

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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Authors: Derkaoui Orkia, Lehireche Ahmed

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The topic of this article is to exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for solving NP-hard problems. This approach provides tight relaxations of combinatorial and quadratic problems. In this work, we solve the maximum clique problem using this relaxation. The clique problem is the computational problem of finding cliques in a graph. It is widely acknowledged for its many applications in real-world problems. The numerical results show that it is possible to find a maximum clique in polynomial time, using an algorithm based on semidefinite programming. We implement a primal-dual interior points algorithm to solve this problem based on semidefinite programming. The semidefinite relaxation of this problem can be solved in polynomial time.

Keywords: semidefinite programming, maximum clique problem, primal-dual interior point method, relaxation

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Authors: R. Ouafi, F. Ouafi

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We study the problem of cutting a rectangular material entity into smaller sub-entities of trapezoidal forms with minimum waste of the material. This problem will be denoted TCP (Trapezoidal Cutting Problem). The TCP has many applications in manufacturing processes of various industries: pipe line design (petro chemistry), the design of airfoil (aeronautical) or cuts of the components of textile products. We introduce an orthogonal build to provide the optimal horizontal and vertical homogeneous strips. In this paper we develop a general heuristic search based upon orthogonal build. By solving two one-dimensional knapsack problems, we combine the horizontal and vertical homogeneous strips to give a non orthogonal cutting pattern.

Keywords: combinatorial optimization, cutting problem, heuristic

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Authors: Ismail El Gayar, Ossama Ismail, Yousri El Gamal

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This paper presented a technique to solve one of the transportation problems that faces us in real life which is the Bus Scheduling Problem. Most of the countries using buses in schools, companies and traveling offices as an example to transfer multiple passengers from many places to specific place and vice versa. This transferring process can cost time and money, so we build a decision support system that can solve this problem. In this paper, a genetic algorithm with the shortest path technique is used to generate a competitive solution to other well-known techniques. It also presents a comparison between our solution and other solutions for this problem.

Keywords: bus scheduling problem, decision support system, genetic algorithm, shortest path

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Authors: Sozan H. Omar, Luluah A. Al Jabr

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The current study aimed to identify critical thinking skills and its level of inclusion in all the activities (44) listed in 11th grade chemistry textbooks. The researcher used a descriptive analytical method by using the content analyzing design. An instrument was created for this purpose and tested for validity and reliability. Results showed that, all activities included critical thinking skills with different ratios as follow: conclusion skill was (87.72%), induction skill was (80.90%), interpretation skill was (77. 72%), discussion of evaluation skill was (68.64%), and assumption skill was (50.45%). Also, the study results indicated that, the level of inclusion of critical thinking skills in the scientific activities was more explicit than implicit with same order as the level of inclusions. In the light of the study's results, the researcher provided some recommendations including the need to provide and redistribute critical thinking skills in the activities listed the chemistry textbook, as well as the need to pay attention to the inclusion level of these skills more implicitly in the activities.

Keywords: critical thinking skills, chemistry textbooks, scientific activities

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Authors: A. A. Adekunle, A. M. Omoare, W. O. Oyediran

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This study was carried out to assess rural women’s skill acquisition in the processing of locust bean in Ipokia Local Government Area of Ogun State, Nigeria. Simple random sampling technique was used to select 90 women locust bean processors for this study. Data were analyzed with descriptive statistics and Pearson Product Moment Correlation. The result showed that the mean age of respondents was 40.72 years. Most (70.00%) of the respondents were married. The mean processing experience was 8.63 years. 93.30% of the respondents relied on information from fellow locust beans processors and friends. All (100%) the respondents did not acquire improved processing skill through trainings and workshops. It can be concluded that the rural women’s skill acquisition on modernized processing techniques was generally low. It is hereby recommend that the rural women processors should be trained by extension service providers through series of workshops and seminars on improved processing techniques.

Keywords: locust bean, processing, skill acquisition, rural women

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Authors: Karla Hrbackova, Irena Balaban Cakirpaloglu

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This paper is a report on self-regulation in socially rejected pupils. A certain form of social rejection can be found in almost every class within the school environment. Research shows that due to social rejection mechanisms supporting the individual´s effort of reintegration into the group are not triggered. Paradoxically the opposite tendency arises, i.e., an increase in selfish and defeating behaviour. The link between peer exposure and self-regulation is likely to vary as a function of a type and quality of peer interaction (e.g., rejection or acceptance). The paper aims to clarify the level of self-regulation related to interpersonal cognitive problem-solving within the process of social rejection in a school class. The research was done on a sample of 1,133 upper-primary school pupils using the Means-Ends Problem Solving technique (MEPS) and peer sociometric nomination. The results showed that the level of self-regulated skills is related to the status of social rejection. Socially rejected pupils achieve lower levels of self-regulation than other classmates. We found deficiency in the regulation of behaviour, emotions and the regulation of will in the peer rejected pupils with the exception of cognitive regulation in which no differences were detected between socially rejected pupils and other classmates. The results have implications for early prevention and intervention efforts to foster adaptive self-regulation and reduce the risk of later social rejection.

Keywords: interpersonal cognitive problem-solving, self-regulation, socially rejected pupils, upper-primary school pupils

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Authors: Thierno Diop, Michel Fortin, Jean Deteix

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Since the precise formulation of the elastic part is irrelevant for the description of the algorithm, we shall consider a generic case. In practice, however, we will have to deal with a non linear material (for instance a Mooney-Rivlin model). We are interested in solving a finite element approximation of the problem, leading to large-scale non linear discrete problems and, after linearization, to large linear systems and ultimately to calculations needing iterative methods. This also implies that penalty method, and therefore augmented Lagrangian method, are to be banned because of their negative effect on the condition number of the underlying discrete systems and thus on the convergence of iterative methods. This is in rupture to the mainstream of methods for contact in which augmented Lagrangian is the principal tool. We shall first present the problem and its discretization; this will lead us to describe a general solution algorithm relying on a preconditioner for saddle-point problems which we shall describe in some detail as it is not entirely standard. We will propose an iterative approach for solving three-dimensional frictional contact problems between elastic bodies, including contact with a rigid body, contact between two or more bodies and also self-contact.

Keywords: frictional contact, three-dimensional, large-scale, iterative method

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Authors: S. H. Borghei, E. Teymourian, M. Mobin, G. M. Komaki, S. Sheikh

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Imperialist competitive algorithm (ICA) is a recent meta-heuristic method that is inspired by the social evolutions for solving NP-Hard problems. The ICA is a population based algorithm which has achieved a great performance in comparison to other meta-heuristics. This study is about developing enhanced ICA approach to solve the cell formation problem (CFP) using sequence data. In addition to the conventional ICA, an enhanced version of ICA, namely EICA, applies local search techniques to add more intensification aptitude and embed the features of exploration and intensification more successfully. Suitable performance measures are used to compare the proposed algorithms with some other powerful solution approaches in the literature. In the same way, for checking the proficiency of algorithms, forty test problems are presented. Five benchmark problems have sequence data, and other ones are based on 0-1 matrices modified to sequence based problems. Computational results elucidate the efficiency of the EICA in solving CFP problems.

Keywords: cell formation problem, group technology, imperialist competitive algorithm, sequence data

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Authors: Nurul Nadrah

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As a result of the COVID-19 pandemic, a movement control order was implemented, leading to the adoption of online learning as a substitute for conventional classroom instruction. Thus, this study aims to determine the differences in skill performance between online learning and conventional methods among nursing students. We employed a quasi-experimental design with purposive sampling, involving a total of 59 nursing students, and used online learning as the intervention. As a result, the study found there was a significant difference in student skill performance between online learning and conventional methods. As a conclusion, in times of hardship, it is necessary to implement alternative pedagogical approaches, especially in critical fields like nursing, to ensure the uninterrupted progression of educational programs. This study suggests that online learning can be effectively employed as a means of imparting knowledge to nursing students during their training.

Keywords: nursing education, online learning, skill performance, conventional learning method

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Authors: William Chung

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This paper is to study the use of multiple subproblems in Dantzig-Wolfe decomposition of linear programming (DW-LP). Traditionally, the decomposed LP consists of one LP master problem and one LP subproblem. The master problem and the subproblem is solved alternatively by exchanging the dual prices of the master problem and the proposals of the subproblem until the LP is solved. It is well known that convergence is slow with a long tail of near-optimal solutions (asymptotic convergence). Hence, the performance of DW-LP highly depends upon the number of decomposition steps. If the decomposition steps can be greatly reduced, the performance of DW-LP can be improved significantly. To reduce the number of decomposition steps, one of the methods is to increase the number of proposals from the subproblem to the master problem. To do so, we propose to add a quadratic approximation function to the LP subproblem in order to develop a set of approximate-LP subproblems (multiple subproblems). Consequently, in each decomposition step, multiple subproblems are solved for providing multiple proposals to the master problem. The number of decomposition steps can be reduced greatly. Note that each approximate-LP subproblem is nonlinear programming, and solving the LP subproblem must faster than solving the nonlinear multiple subproblems. Hence, using multiple subproblems in DW-LP is the tradeoff between the number of approximate-LP subproblems being formed and the decomposition steps. In this paper, we derive the corresponding algorithms and provide some simple computational results. Some properties of the resulting algorithms are also given.

Keywords: approximate subproblem, Dantzig-Wolfe decomposition, large-scale models, multiple subproblems

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Authors: Alaa Sheta

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Economic Load Dispatch (ELD) is one of the vital optimization problems in power system planning. Solving the ELD problems mean finding the best mixture of power unit outputs of all members of the power system network such that the total fuel cost is minimized while sustaining operation requirements limits satisfied across the entire dispatch phases. Many optimization techniques were proposed to solve this problem. A famous one is the Quadratic Programming (QP). QP is a very simple and fast method but it still suffer many problem as gradient methods that might trapped at local minimum solutions and cannot handle complex nonlinear functions. Numbers of metaheuristic algorithms were used to solve this problem such as Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO). In this paper, another meta-heuristic search algorithm named Differential Evolution (DE) is used to solve the ELD problem in power systems planning. The practicality of the proposed DE based algorithm is verified for three and six power generator system test cases. The gained results are compared to existing results based on QP, GAs and PSO. The developed results show that differential evolution is superior in obtaining a combination of power loads that fulfill the problem constraints and minimize the total fuel cost. DE found to be fast in converging to the optimal power generation loads and capable of handling the non-linearity of ELD problem. The proposed DE solution is able to minimize the cost of generated power, minimize the total power loss in the transmission and maximize the reliability of the power provided to the customers.

Keywords: economic load dispatch, power systems, optimization, differential evolution

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Authors: Dhea Kothari

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There is an extensive amount of research that has examined the positive relationship between creativity and hypomania in terms of creative accomplishments, eminence, behaviors, occupations. Previous research had recruited participants based on creative occupations or stages of hypomania or bipolar disorder. This thesis focused on the relationship between hypomania and creative cognitive potential, such as divergent thinking and insight problem-solving. This was examined at an undergraduate educational level by recruiting students majoring in art, majoring in natural sciences (NSCI) and those double majoring in arts and NSCI. Participants were given a modified Alternate Uses Task (AUT) to measure divergent thinking and a set of rebus puzzles to measure insight problem-solving. Both tasks involved a level of overcoming functional fixedness. A negative association was observed between hypomania and originality of responses on the AUT when an object with low functional fixedness was given to all participants. On the other hand, a positive association was found between hypomania and originality of responses on the AUT when an object with high functional fixedness was given to the participants majoring in NSCI. Therefore, the research suggests that an increased ability to overcome functional fixedness might be central to individuals with hypomania and individuals with higher creative cognitive potential.

Keywords: creative cognition, convergent thinking, creativity, divergent thinking, insight, major type, problem-solving

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Authors: Talha A. Taj, Talha A. Khan, M. Imran Khalid

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Optimization techniques attract researchers to formulate a problem and determine its optimum solution. This paper presents an Enhanced Harmony Search (ENHS) algorithm for solving optimization problems. The proposed algorithm increases the convergence and is more efficient than the standard Harmony Search (HS) algorithm. The paper discusses the novel techniques in detail and also provides the strategy for tuning the decisive parameters that affects the efficiency of the ENHS algorithm. The algorithm is tested on various benchmark functions, a real world optimization problem and a constrained objective function. Also, the results of ENHS are compared to standard HS, and various other optimization algorithms. The ENHS algorithms prove to be significantly better and more efficient than other algorithms. The simulation and testing of the algorithms is performed in MATLAB.

Keywords: optimization, harmony search algorithm, MATLAB, electronic

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem solves the problem of fitting 3 circles into a right triangle such that these 3 circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles inside the triangle with special tangency properties among circles and triangle sides; we call it extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving Tri(Tn) problem, n>2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary Carc. We call these problems the Carc(Tn) problems. The CPU time it takes for Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties, is less than one second.

Keywords: circle packing, computer-aided geometric design, geometric constraint solver, Malfatti’s problem

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Authors: Abdul Halim Abdullah, Nur Liyana Zainal Abidin, Mahani Mokhtar

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Problem-solving is an activity which can encourage students to use Higher Order Thinking Skills (HOTS). Learning fractions can be challenging for students since empirical evidence shows that students experience difficulties in solving the fraction problems. However, visual methods can help students to overcome the difficulties since the methods help students to make meaningful visual representations and link abstract concepts in Mathematics. Therefore, the purpose of this study was to investigate whether there were any changes in students’ HOTS at the four highest levels when learning the fractions by using Thinking Blocks. 54 students participated in a quasi-experiment using pre-tests and post-tests. Students were divided into two groups. The experimental group (n=32) received a treatment to improve the students’ HOTS and the other group acted as the control group (n=22) which used a traditional method. Data were analysed by using Mann-Whitney test. The results indicated that during post-test, students who used Thinking Blocks showed significant improvement in their HOTS level (p=0.000). In addition, the results of post-test also showed that the students’ performance improved significantly at the four highest levels of HOTS; namely, application (p=0.001), analyse (p=0.000), evaluate (p=0.000), and create (p=0.000). Therefore, it can be concluded that Thinking Blocks can effectively encourage students to use the four highest levels of HOTS which consequently enable them to solve fractions problems successfully.

Keywords: Thinking Blocks, Higher Order Thinking Skills (HOTS), fractions, problem solving

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Authors: Ibrahim Abubakar Mikugi

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Nigerian graduates could only be self-employed and marketable if they acquire relevant skills and knowledge for successful establishment in various occupation and gainful employment. Research has shown that entrepreneurship education will be successful through developing individual entrepreneurial attitudes, raising awareness of career options by integrating and inculcating a positive attitude in the mind of students through skill acquisition. This paper examined the student- led entrepreneurship education through skill acquisition with specific emphasis on analysis of David Kolb experiential learning cycle. This Model allows individual to review their experience through reflection and converting ideas into action by doing. The methodology used was theoretical approach through journal, internet and Textbooks. Challenges to entrepreneurship education through skill acquisition were outlined. The paper concludes that entrepreneurship education is recognised by both policy makers and academics; entrepreneurship is more than mere encouraging business start-ups. Recommendations were given which include the need for authorities to have a clear vision towards entrepreneurship education and skill acquisition. Authorities should also emphasise a periodic and appropriate evaluation of entrepreneurship and to also integrate into schools academic curriculum to encourage practical learning by doing.

Keywords: entrepreneurship, entrepreneurship education, active learning, Cefe methodology

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Authors: Bolatbek Rysbaiuly, Aliya S. Azhibekova

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Problems concerning the interpretation of the well testing results belong to the class of inverse problems of subsurface hydromechanics. The distinctive feature of such problems is that additional information is depending on the capabilities of oilfield experiments. Another factor that should not be overlooked is the existence of errors in the test data. To determine reservoir properties, some inverse problems for parabolic equations were investigated. An approach to solving the inverse problems based on the method of regularization is proposed.

Keywords: iterative approach, inverse problem, parabolic equation, reservoir properties

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Authors: Radoslaw Pytlak, Damian Suski

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The aim of the paper is to provide a computational tool for planning a haemodialysis process. It is shown that optimization methods can be used to obtain the most effective treatment focused on removing both urea and phosphorus during the process. In order to achieve that, the IV–compartment model of phosphorus kinetics is applied. This kinetics model takes into account a rebound phenomenon that can occur during haemodialysis and results in a hybrid model of the process. Furthermore, vector fields associated with the model equations are such that it is very likely that using the most intuitive objective functions in the planning problem could lead to solutions which include sliding motions. Therefore, building computational tools for solving the problem of planning a haemodialysis process has required constructing numerical algorithms for solving optimal control problems with hybrid systems. The paper concentrates on minimum time control of hybrid systems since this control objective is the most suitable for the haemodialysis process considered in the paper. The presented approach to optimal control problems with hybrid systems is different from the others in several aspects. First of all, it is assumed that a hybrid system can exhibit sliding modes. Secondly, the system’s motion on the switching surface is described by index 2 differential–algebraic equations, and that guarantees accurate tracking of the sliding motion surface. Thirdly, the gradients of the problem’s functionals are evaluated with the help of adjoint equations. The adjoint equations presented in the paper take into account sliding motion and exhibit jump conditions at transition times. The optimality conditions in the form of the weak maximum principle for optimal control problems with hybrid systems exhibiting sliding modes and with piecewise constant controls are stated. The presented sensitivity analysis can be used to construct globally convergent algorithms for solving considered problems. The paper presents numerical results of solving the haemodialysis planning problem.

Keywords: haemodialysis planning process, hybrid systems, optimal control, sliding motion

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