Search results for: optimal learning.

Authors: Ivan Traina, Luigi Sangalli, Fabio Tognon, Angelo Lascioli

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Currently, challenges regarding preschooler children are mainly focused on a sedentary lifestyle. Also, motor activity in infancy is seen as a tool for the separate acquisition of cognitive and socio-emotional skills rather than considering neuromotor development as a tool for improving learning abilities. The paper utilized an observational research method to shed light on the results of practicing neuromotor exercises in preschool children with disability as well as provide implications for practice.

Keywords: Children with disability, learning abilities, inclusion, neuromotor development.

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Authors: Yongxin Yuan, Jiashang Jiang

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A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.

Keywords: Finite element model, model updating, modal data, optimal approximation.

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Authors: Eatedal A. Alabdulkreem, Hamed S. Al-Raweshidy, Maysam F. Abbod

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Border Gateway Protocol (BGP) is the standard routing protocol between various autonomous systems (AS) in the internet. In the event of failure, a considerable delay in the BGP convergence has been shown by empirical measurements. During the convergence time the BGP will repeatedly advertise new routes to some destination and withdraw old ones until it reach a stable state. It has been found that the KEEPALIVE message timer and the HOLD time are tow parameters affecting the convergence speed. This paper aims to find the optimum value for the KEEPALIVE timer and the HOLD time that maximally reduces the convergence time without increasing the traffic. The KEEPALIVE message timer optimal value founded by this paper is 30 second instead of 60 seconds, and the optimal value for the HOLD time is 90 seconds instead of 180 seconds.

Keywords: BGP, Convergence Time, HOLD time, Keep alive.

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Authors: Enrique Barra, Aldo Gordillo, Juan Quemada

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This paper presents the Virtual Science Hub platform. It is an open source platform that combines a social network, an e-learning authoring tool, a videoconference service and a learning object repository for science teaching enrichment. These four main functionalities fit very well together. The platform was released in April 2012 and since then it has not stopped growing. Finally we present the results of the surveys conducted and the statistics gathered to validate this approach.

Keywords: E-learning, platform, authoring tool, science teaching.

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Authors: N. Rugthaicharoencheep, T. Langtharthong

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This paper presents the optimal placement and sizing of distributed generation (DG) in a distribution system. The problem is to reliability improvement of distribution system with distributed generations. The technique employed to solve the minimization problem is based on a developed Tabu search algorithm and reliability worth analysis. The developed methodology is tested with a distribution system of Roy Billinton Test System (RBTS) bus 2. It can be seen from the case study that distributed generation can reduce the customer interruption cost and therefore improve the reliability of the system. It is expected that our proposed method will be utilized effectively for distribution system operator.

Keywords: Distributed generation Optimization technique Reliability improvement, Distribution system.

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Authors: Masao Okabe

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Nowadays, in Japan, variety of students get into a university and one of the main roles of introductory courses for freshmen is to make such students well prepared for subsequent intermediate courses. For that purpose, the flipped-mastery model is not enough because videos usually used in a flipped classroom is not adaptive and does not fit all freshmen with different academic performances. This paper proposes an ontology-navigated tutoring system called EduGraph. Using EduGraph, students can prepare for and review a class, in a more flexibly personalizable way than by videos. Structuralizing learning materials by its ontology, EduGraph also helps students integrate what they learn as knowledge, and makes learning materials sharable. EduGraph was used for an introductory course for freshmen. This application suggests that EduGraph is effective.

Keywords: Adaptive e-learning, flipped classroom, mastery learning, ontology.

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Authors: M. H. Imam, Imran A. Tasadduq, Abdul-Rahim Ahmad, Fahd M. Aldosari

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Learning outcomes of a course (CLOs) and the abilities at the time of graduation referred to as Student Outcomes (SOs) are required to be assessed for ABET accreditation. A question in an assessment must target a CLO as well as an SO and must represent a required level of competence. This paper presents the idea of an Expert System (ES) to select a proper question to satisfy ABET accreditation requirements. For ES implementation, seven attributes of a question are considered including the learning outcomes and Bloom’s Taxonomy level. A database contains all the data about a course including course content topics, course learning outcomes and the CLO-SO relationship matrix. The knowledge base of the presented ES contains a pool of questions each with tags of the specified attributes. Questions and the attributes represent expert opinions. With implicit rule base the inference engine finds the best possible question satisfying the required attributes. It is shown that the novel idea of such an ES can be implemented and applied to a course with success. An application example is presented to demonstrate the working of the proposed ES.

Keywords: Expert system, student outcomes, course learning outcomes, question attributes.

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Authors: Karen Armstrong

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Online discussions are an important component of both blended and online courses. This paper examines the varieties of online discussions and the perils, pitfalls and possibilities of this rather new technological tool for enhanced learning. The discussion begins with possible perils and pitfalls inherent in this educational tool and moves to a consideration of the advantages of the varieties of online discussions feasible for use in teacher education programs.

Keywords: online discussions, computer-mediatedcommunication (CMC), computer-supported collaborative learning(CSCL), e-learning, teacher education

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Authors: Serena Alvino, Paola Forcheri, Maria Grazia Ierardi, Luigi Sarti

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One of the main advantages of the LO paradigm is to allow the availability of good quality, shareable learning material through the Web. The effectiveness of the retrieval process requires a formal description of the resources (metadata) that closely fits the user-s search criteria; in spite of the huge international efforts in this field, educational metadata schemata often fail to fulfil this requirement. This work aims to improve the situation, by the definition of a metadata model capturing specific didactic features of shareable learning resources. It classifies LOs into “teacher-oriented" and “student-oriented" categories, in order to describe the role a LO is to play when it is integrated into the educational process. This article describes the model and a first experimental validation process that has been carried out in a controlled environment.

Keywords: Learning object, pedagogical metadata, experimental validation.

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Authors: Zahra Hatami, Hesham Ali, David Volkman

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Selecting a portfolio for investing is a crucial decision for individuals and legal entities. In the last two decades, with economic globalization, a stream of financial innovations has rushed to the aid of financial institutions. The importance of selecting stocks for the portfolio is always a challenging task for investors. This study aims to create a financial network to identify optimal portfolios using network centralities metrics. This research presents a community detection technique of superior stocks that can be described as an optimal stock portfolio to be used by investors. By using the advantages of a network and its property in extracted communities, a group of stocks was selected for each of the various time periods. The performance of the optimal portfolios was compared to the famous index. Their Sharpe ratio was calculated in a timely manner to evaluate their profit for making decisions. The analysis shows that the selected potential portfolio from stocks with low centrality measurement can outperform the market; however, they have a lower Sharpe ratio than stocks with high centrality scores. In other words, stocks with low centralities could outperform the S&P500 yet have a lower Sharpe ratio than high central stocks.

Keywords: Portfolio management performance, network analysis, centrality measurements, Sharpe ratio.

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Authors: Alawode Kehinde O., Jubril Abimbola M. Komolafe Olusola A.

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This paper solves the environmental/ economic dispatch power system problem using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and its hybrid with a Convergence Accelerator Operator (CAO), called the NSGA-II/CAO. These multiobjective evolutionary algorithms were applied to the standard IEEE 30-bus six-generator test system. Several optimization runs were carried out on different cases of problem complexity. Different quality measure which compare the performance of the two solution techniques were considered. The results demonstrated that the inclusion of the CAO in the original NSGA-II improves its convergence while preserving the diversity properties of the solution set.

Keywords: optimal power flow, multiobjective power dispatch, evolutionary algorithm

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Authors: Thapanee Seechaliao

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This research paper presents guiding on how to design social media into higher education courses. The research methodology used a survey approach. The research instrument was a questionnaire about guiding on how to design social media into higher education courses. Thirty-one lecturers completed the questionnaire. The data were scored by frequency and percentage. The research results were the lecturers’ opinions concerning the designing social media into higher education courses as follows: 1) Lecturers deem that the most suitable learning theory is Collaborative Learning. 2) Lecturers consider that the most important learning and innovation Skill in the 21st century is communication and collaboration skills. 3) Lecturers think that the most suitable evaluation technique is authentic assessment. 4) Lecturers consider that the most appropriate portion used as blended learning should be 70% in the classroom setting and 30% online.

Keywords: Instructional design, social media, courses, higher education.

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Authors: M. Mazhar Manzoor, Nasar.A, A. Sattar

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In the open space of decision support system the mental impression of a manager-s decision has been the subject of large importance than the ordinary famous one, when helped by decision support system. Much of this study is an attempt to realize the relation of decision support system usage and decision outcomes that governs the system. For example, several researchers have proposed so many different models to analyze the linkage between decision support system processes and results of decision making. This study draws the important relation of manager-s mental approach with the use of decision support system. The findings of this paper are theoretical attempts to provide Decision Support System (DSS) in a way to exhibit and promote the learning in semi structured area. The proposed model shows the points of one-s learning improvements and maintains a theoretical approach in order to explore the DSS contribution in enhancing the decision forming and governing the system.

Keywords: Decision Support System , Learning Organization,

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Authors: A. O. Oladele

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The purpose of this study was to find out the effectiveness of neurological impress method and repeated reading technique on reading fluency of children with learning disabilities. Thirty primary four pupils in three public primary schools participated in the study. There were two experimental groups and a control. This research employed a 3 by 2 factorial matrix and the participants were taught for one session. Two hypotheses were formulated to guide the research. T-test was used to analyse the data gathered, and data analysis revealed that pupils exposed to the two treatment strategies had improvement in their reading fluency. It was recommended that the two strategies used in the study can be used to intervene in reading fluency problems in children with learning disabilities.

Keywords: Learning disabilities, neurological impress method, repeated reading, reading fluency.

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Authors: Hadi Firouzi, Majid Nili Ahmadabadi, Babak N. Araabi

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Conceptualization strengthens intelligent systems in generalization skill, effective knowledge representation, real-time inference, and managing uncertain and indefinite situations in addition to facilitating knowledge communication for learning agents situated in real world. Concept learning introduces a way of abstraction by which the continuous state is formed as entities called concepts which are connected to the action space and thus, they illustrate somehow the complex action space. Of computational concept learning approaches, action-based conceptualization is favored because of its simplicity and mirror neuron foundations in neuroscience. In this paper, a new biologically inspired concept learning approach based on the probabilistic framework is proposed. This approach exploits and extends the mirror neuron-s role in conceptualization for a reinforcement learning agent in nondeterministic environments. In the proposed method, instead of building a huge numerical knowledge, the concepts are learnt gradually from rewards through interaction with the environment. Moreover the probabilistic formation of the concepts is employed to deal with uncertain and dynamic nature of real problems in addition to the ability of generalization. These characteristics as a whole distinguish the proposed learning algorithm from both a pure classification algorithm and typical reinforcement learning. Simulation results show advantages of the proposed framework in terms of convergence speed as well as generalization and asymptotic behavior because of utilizing both success and failures attempts through received rewards. Experimental results, on the other hand, show the applicability and effectiveness of the proposed method in continuous and noisy environments for a real robotic task such as maze as well as the benefits of implementing an incremental learning scenario in artificial agents.

Keywords: Concept learning, probabilistic decision making, reinforcement learning.

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Authors: Somayeh Alizadeh, Mehdi Ghazanfari, Mohammad Fathian

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Fuzzy Cognitive Maps (FCMs) have successfully been applied in numerous domains to show relations between essential components. In some FCM, there are more nodes, which related to each other and more nodes means more complex in system behaviors and analysis. In this paper, a novel learning method used to construct FCMs based on historical data and by using data mining and DEMATEL method, a new method defined to reduce nodes number. This method cluster nodes in FCM based on their cause and effect behaviors.

Keywords: Clustering, Data Mining, Fuzzy Cognitive Map(FCM), Learning.

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Authors: Stuart Palmer, Dale Holt

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Based on 276 responses from academic staff in an evaluation of an online learning environment (OLE), this paper identifies those elements of the OLE that were most used and valued by staff, those elements of the OLE that staff most wanted to see improved, and those factors that most contributed to staff perceptions that the use of the OLE enhanced their teaching. The most used and valued elements were core functions, including accessing unit information, accessing lecture/tutorial/lab notes, and reading online discussions. The elements identified as most needing attention related to online assessment: submitting assignments, managing assessment items, and receiving feedback on assignments. Staff felt that using the OLE enhanced their teaching when they were satisfied that their students were able to access and use their learning materials, and when they were satisfied with the professional development they received and were confident with their ability to teach with the OLE.

Keywords: Academic staff, Distance education, Evaluation, Online learning environment.

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Authors: Muhammed Yousoof, Mohd Sapiyan, Khaja Kamaluddin

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Learning programming is difficult for many learners. Some researches have found that the main difficulty relates to cognitive load. Cognitive overload happens in programming due to the nature of the subject which is intrinisicly over-bearing on the working memory. It happens due to the complexity of the subject itself. The problem is made worse by the poor instructional design methodology used in the teaching and learning process. Various efforts have been proposed to reduce the cognitive load, e.g. visualization softwares, part-program method etc. Use of many computer based systems have also been tried to tackle the problem. However, little success has been made to alleviate the problem. More has to be done to overcome this hurdle. This research attempts at understanding how cognitive load can be managed so as to reduce the problem of overloading. We propose a mechanism to measure the cognitive load during pre instruction, post instruction and in instructional stages of learning. This mechanism is used to help the instruction. As the load changes the instruction is made to adapt itself to ensure cognitive viability. This mechanism could be incorporated as a sub domain in the student model of various computer based instructional systems to facilitate the learning of programming.

Keywords: Cognitive load, Working memory, Cognitive Loadmeasurement.

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Authors: Wen-Chao Tang, Tang-Yi Liu, Ming Gao, Gang Xu, Hua-Yuan Yang

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This study developed a method for teaching acupuncture manipulation in small groups optimized with the theory of motor learning. Sixty acupuncture students and their teacher participated in our research. Motion videos were recorded of their manipulations using the lifting-thrusting method. These videos were analyzed using Simi Motion software to acquire the movement parameters of the thumb tip. The parameter velocity curves along Y axis was used to generate small teaching groups clustered by a self-organized map (SOM) and K-means. Ten groups were generated. All the targeted instruction based on the comparative results groups as well as the videos of teacher and student was provided to the members of each group respectively. According to the theory and research of motor learning, the factors or technologies such as video instruction, observational learning, external focus and summary feedback were integrated into this teaching method. Such efforts were desired to improve and enhance the effectiveness of current acupuncture teaching methods in limited classroom teaching time and extracurricular training.

Keywords: Acupuncture, group teaching, video instruction, observational learning, external focus, summary feedback.

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Authors: Francisca Grimón, Marylin Giugni, Josep Monguet F., Joaquín Fernández, Luis León G.

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In blended learning environments, the Internet can be combined with other technologies. The aim of this research was to design, introduce and validate a model to support synchronous and asynchronous activities by managing content domains in an Adaptive Hypermedia System (AHS). The application is based on information recovery techniques, clustering algorithms and adaptation rules to adjust the user's model to contents and objects of study. This system was applied to blended learning in higher education. The research strategy used was the case study method. Empirical studies were carried out on courses at two universities to validate the model. The results of this research show that the model had a positive effect on the learning process. The students indicated that the synchronous and asynchronous scenario is a good option, as it involves a combination of work with the lecturer and the AHS. In addition, they gave positive ratings to the system and stated that the contents were adapted to each user profile.

Keywords: Blended Learning, System Adaptive, Model, Clustering Algorithms.

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Authors: Rosaline Govender

Abstract:

This research study is an exploration of the selfdirected professional development of teachers who teach in public schools in an era of democracy and educational change in South Africa. Amidst an ever-changing educational system, the teachers in this study position themselves as self-directed teacher-learners where they adopt particular learning practices which enable change within the broader discourses of public schooling. Life-story interviews were used to enter into the private and public spaces of five teachers which offer glimpses of how particular systems shaped their identities, and how the meanings of self-directed teacher-learner shaped their learning practices. Through the Multidimensional Framework of Analysis and Interpretation the teachers’ stories were analysed through three lenses: restorying the field texts - the self through story; the teacher-learner in relation to social contexts, and practices of self-directed learning. This study shows that as teacherlearners learn for change through self-directed learning practices, they develop their agency as transformative intellectuals, which is necessary for the reworking of South African public schools.

Keywords: Professional development, professionality, professionalism, self-directed learning.

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Authors: Estevan B. Costa, Armando M. Toda, Marcell A. A. Mesquita, Jacques D. Brancher

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The advances in technology in the last five years allowed an improvement in the educational area, as the increasing in the development of educational software. One of the techniques that emerged in this lapse is called Gamification, which is the utilization of video game mechanics outside its bounds. Recent studies involving this technique provided positive results in the application of these concepts in many areas as marketing, health and education. In the last area there are studies that covers from elementary to higher education, with many variations to adequate to the educators methodologies. Among higher education, focusing on IT courses, data structures are an important subject taught in many of these courses, as they are base for many systems. Based on the exposed this paper exposes the development of an interactive web learning environment, called DSLEP (Data Structure Learning Platform), to aid students in higher education IT courses. The system includes basic concepts seen on this subject such as stacks, queues, lists, arrays, trees and was implemented to ease the insertion of new structures. It was also implemented with gamification concepts, such as points, levels, and leader boards, to engage students in the search for knowledge and stimulate self-learning.

Keywords: Gamification, Interactive learning environment, Data structures, e-learning.

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Authors: Glenda A. Gunter

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Current research has explored the impact of instructional immediacy, defined as those behaviors that help build close relationships or feelings of closeness, both on cognition and motivation in the traditional classroom and online classroom; however, online courses continue to suffer from higher dropout rates. Based on Albert Bandura-s Social Cognitive Theory, four primary relationships or interactions in an online course will be explored in light of how they can provide immediacy thereby reducing student attrition and improving cognitive learning. The four relationships are teacher-student, student-student, and student-content, and studentcomputer. Results of a study conducted with inservice teachers completing a 14-week online professional development technology course will be examined to demonstrate immediacy strategies that improve cognitive learning and reduce student attrition. Results of the study reveal that students can be motivated through various interactions and instructional immediacy behaviors which lead to higher completion rates, improved self-efficacy, and cognitive learning.

Keywords: Distance Learning, Self-Efficacy, Instructional immediacy, Student achievement.

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Authors: Promise A. Azor, Avievie Igodo, Esabai M. Ase

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The paper merged the return of premium clause and voluntary contributions to investigate retirees’ investment plan in a defined contributory (DC) pension scheme with a portfolio comprising of a risk-free asset and a risky asset whose price process is described by geometric Brownian motion (GBM). The paper considers additional voluntary contributions paid by members, charge on balance by pension fund administrators and the mortality risk of members of the scheme during the accumulation period by introducing return of premium clause. To achieve this, the Weilbull mortality force function is used to establish the mortality rate of members during accumulation phase. Furthermore, an optimization problem from the Hamilton Jacobi Bellman (HJB) equation is obtained using dynamic programming approach. Also, the Legendre transformation method is used to transform the HJB equation which is a nonlinear partial differential equation to a linear partial differential equation and solves the resultant equation for the value function and the optimal distribution plan under logarithm utility function. Finally, numerical simulations of the impact of some important parameters on the optimal distribution plan were obtained and it was observed that the optimal distribution plan is inversely proportional to the initial fund size, predetermined interest rate, additional voluntary contributions, charge on balance and instantaneous volatility.

Keywords: Legendre transform, logarithm utility, optimal distribution plan, return clause of premium, charge on balance, Weibull mortality function.

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Authors: Laura Zizka, Gaby Probst

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The COVID-19 pandemic has affected the way Higher Education Institutions (HEIs) have given their courses. From emergency remote where all students and faculty were immediately confined to home teaching and learning, the continuing evolving sanitary situation obliged HEIs to adopt other methods of teaching and learning from blended courses that included both synchronous and asynchronous courses and activities to HyFlex models where some students were on campus while others followed the course simultaneously online. Each semester brought new challenges for HEIs and, subsequently, additional emotional reactions. This paper investigates the affective side of teaching and learning in various online modalities and its toll on students and faculty members over the past three semesters. The findings confirm that students and faculty who have more self-efficacy, flexibility, and resilience reported positive emotions and embraced the opportunities that these past semesters have offered. While HEIs have begun a new semester in an attempt to return to ‘normal’ face-to-face courses, this paper posits that there are lessons to be learned from these past three semesters. The opportunities that arose from the challenge of the pandemic should be considered when moving forward by focusing on a greater emphasis on the affective aspect of teaching and learning in HEIs worldwide. 

Keywords: affective teaching and learning, engagement, interaction, motivation, social presence

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Authors: S. Alfalah, J. Falah, T. Alfalah, M. Elfalah, O. Falah

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The field of education is an ever-evolving area constantly enriched by newly discovered techniques provided by active research in all areas of technologies. The recent years have witnessed the introduction of a number of promising technologies and applications to enhance the teaching and learning experience. Virtual Reality (VR) applications are considered one of the evolving methods that have contributed to enhancing education in many fields. VR creates an artificial environment, using computer hardware and software, which is similar to the real world. This simulation provides a solution to improve the delivery of materials, which facilitates the teaching process by providing a useful aid to instructors, and enhances the learning experience by providing a beneficial learning aid. In order to assure future utilization of such systems, students’ perceptions were examined toward utilizing VR as an educational tool in the Faculty of Information Technology (IT) in The University of Jordan. A questionnaire was administered to IT undergraduates investigating students’ opinions about the potential opportunities that VR technology could offer and its implications as learning and teaching aid. The results confirmed the end users’ willingness to adopt VR systems as a learning aid. The result of this research forms a solid base for investing in a VR system for IT education.

Keywords: Education, information, technology, virtual reality.

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Authors: Maricar G. Misola, Bryan B. Navarro

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Facility Layout Problem (FLP) is one of the essential problems of several types of manufacturing and service sector. It is an optimization problem on which the main objective is to obtain the efficient locations, arrangement and order of the facilities. In the literature, there are numerous facility layout problem research presented and have used meta-heuristic approaches to achieve optimal facility layout design. This paper presented genetic algorithm to solve facility layout problem; to minimize total cost function. The performance of the proposed approach was verified and compared using problems in the literature.

Keywords: Facility Layout Problem, Genetic Algorithm, Material Handling Cost, Meta-heuristic Approach.

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Authors: Aisha Tarek Noour, Nick Hubbard

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Learner motivation is considered to be an important component for the Blended e-Learning (BL) Method. BL is an effective learning method in multiple domains, which opens several opportunities for its participants to engage in the learning environment. This research explores the learners’ perspective of BL according to the Self-Determination Theory (SDT). It identifies the opportunities and challenges for using the BL in Logistics Education (LE) in Egyptian Higher Education (HE). SDT is approached from different perspectives within the relationship between Intrinsic Motivation (IM), Extrinsic Motivation (EM) and Amotivation (AM). A self-administered face-to-face questionnaire was used to collect data from learners who were geographically widely spread around three colleges of International Transport and Logistics (CILTs) at the Arab Academy for Science, Technology and Maritime Transport (AAST&MT) in Egypt. Six hundred and sixteen undergraduates responded to a questionnaire survey. Respondents were drawn from three branches in Greater Cairo, Alexandria, and Port Said. The data analysis used was SPSS 22 and AMOS 18.

Keywords: Intrinsic Motivation, Extrinsic Motivation, Amotivation, Blended e-Learning, Self Determination Theory.

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Authors: Jeff Clarine, Chang-Shyh Peng, Daisy Sang

Abstract:

Bioassay is the measurement of the potency of a chemical substance by its effect on a living animal or plant tissue. Bioassay data and chemical structures from pharmacokinetic and drug metabolism screening are mined from and housed in multiple databases. Bioassay prediction is calculated accordingly to determine further advancement. This paper proposes a four-step preprocessing of datasets for improving the bioassay predictions. The first step is instance selection in which dataset is categorized into training, testing, and validation sets. The second step is discretization that partitions the data in consideration of accuracy vs. precision. The third step is normalization where data are normalized between 0 and 1 for subsequent machine learning processing. The fourth step is feature selection where key chemical properties and attributes are generated. The streamlined results are then analyzed for the prediction of effectiveness by various machine learning algorithms including Pipeline Pilot, R, Weka, and Excel. Experiments and evaluations reveal the effectiveness of various combination of preprocessing steps and machine learning algorithms in more consistent and accurate prediction.

Keywords: Bioassay, machine learning, preprocessing, virtual screen.

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Authors: S. Hamid Mirmohammadi, Shahrazad Tamjidzad

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This paper is concerned with the single-item continuous review inventory system in which demand is stochastic and discrete. The budget consumed for purchasing the ordered items is not restricted but it incurs extra cost when exceeding specific value. The unit purchasing price depends on the quantity ordered under the all-units discounts cost structure. In many actual systems, the budget as a resource which is occupied by the purchased items is limited and the system is able to confront the resource shortage by charging more costs. Thus, considering the resource shortage costs as a part of system costs, especially when the amount of resource occupied by the purchased item is influenced by quantity discounts, is well motivated by practical concerns. In this paper, an optimization problem is formulated for finding the optimal (r, Q) policy, when the system is influenced by the budget limitation and a discount pricing simultaneously. Properties of the cost function are investigated and then an algorithm based on a one-dimensional search procedure is proposed for finding an optimal (r, Q) policy which minimizes the expected system costs.

Keywords: (r, Q) policy, Stochastic demand, backorders, limited resource, quantity discounts.

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