Search results for: collaborative problem solving

Authors: Tessa Berg, Emma Guion Akdag

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Summative feedback forms are used in academia for gathering data on course quality and student understanding. Students answer a series of questions based on the course they are soon to finish in these forms. Feedback forms are notorious for being homogenised and limiting and thus the data captured is often neutral and lacking in tacit emotional responses. This paper contrasts student feedback forms with collaborative drawing. We analyse 19 pictures drawn by international students on a pre-sessional course. Through visuals we present an approach to enable a holistic level of student understanding. Visuals communicate irrespective of possible language, cultural and educational barriers. This paper sought to discover if the pictures mirrored the feedback given on a typical feedback form. Findings indicate a considerable difference in the two approaches and thus we highlight the value of collaborative drawing as a complimentary resource to aid the understanding of student experience.

Keywords: feedback forms, visualisation, student experience, collaborative drawing

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Authors: Ivy Jessen Galvan

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Over the past decade, a phenomenon has emerged at the frontier of the digital economy: a wave of ‘disruptive’ technologies that offer digital solutions to variety of everyday problems, challenging the way traditional industries operate. Most of these disruptive technologies are applications ('apps') that rely on the Internet to connect people to people for sharing, selling, renting, or lending, creating a unique economic model wherein users provide for other users’ demand – called 'collaborative economy.' Although collaborative economy is spreading in every part of the world, there may be different ways in which this phenomenon is unfolding throughout the developing countries. In this study, the characteristics of collaborative economy in the Philippines are highlighted and compared from observations in the developed world. The paper looks at two leading collaborative economy ventures in the Philippines – Grab and Shopee – probing into how these smartphone-based platforms place technology into the 'micro-frictions' of the Philippine developing context. Using framing analysis on interviews conducted among Grab and Shopee users in Metro Manila, three frames have been identified: 1) metropolitan solution; 2) financial inclusion and; 3) formalization of labor. This research contextualizes the Fourth Industrial Revolution in ASEAN by analyzing the effect of a digital economy in everyday life.

Keywords: ASEAN Unicorns, collaborative economy, developing countries, fourth industrial revolution

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Authors: Asia Majeed

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The learning of mathematics in science, engineering and social science programs can be enhanced through practical problem-solving techniques. The instructors can design their lessons with some strategies to improve students’ educational needs and accomplishments in mathematics classrooms. The use of technology in class problem solving and application sessions can enhance deep understanding of mathematics among students. As mathematician, we believe in subject specific and content-driven teaching methods. Through technology the relationship between the physical problems and the mathematical models can be analyzed. This paper is about selective use of technology in mathematics classrooms and helpful to others mathematics instructors who wishes to improve their traditional teaching techniques to improve students’ attitude in learning mathematics. These techniques corpus can be used in teaching large mathematics classes in science, technology, engineering, and social science.

Keywords: attitude in learning mathematics, mathematics, non-mathematics undergraduate students, technology

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Authors: Bachir Bentouati, Lakhdar Chaib, Saliha Chettih, Gai-Ge Wang

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The problem of economic dispatch (ED) is the basic problem of power framework, its main goal is to find the most favorable generation dispatch to generate each unit, reduce the whole power generation cost, and meet all system limitations. A heuristic algorithm, recently developed called Stud Krill Herd (SKH), has been employed in this paper to treat non-convex ED problems. The proposed KH has been modified using Stud selection and crossover (SSC) operator, to enhance the solution quality and avoid local optima. We are demonstrated SKH effects in two case study systems composed of 13-unit and 40-unit test systems to verify its performance and applicability in solving the ED problems. In the above systems, SKH can successfully obtain the best fuel generator and distribute the load requirements for the online generators. The results showed that the use of the proposed SKH method could reduce the total cost of generation and optimize the fulfillment of the load requirements.

Keywords: stud krill herd, economic dispatch, crossover, stud selection, valve-point effect

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Authors: N. F. Jamaluddin, N. A. H. Aizam

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This paper explains the educational timetabling problem, a type of scheduling problem that is considered as one of the most challenging problem in optimization and operational research. The university examination timetabling problem (UETP), which involves assigning a set number of exams into a set number of timeslots whilst fulfilling all required conditions, has been widely investigated. The limitation of available timeslots and resources with the increasing number of examinations are the main reasons in the difficulty of solving this problem. Dynamical change in the examination scheduling system adds up the complication particularly in coping up with the demand and new requirements by the communities. Our objective is to investigate these demands and requirements with subjects taken from Universiti Malaysia Terengganu (UMT), through questionnaires. Integer linear programming model which reflects the preferences obtained to produce an effective examination timetabling was formed.

Keywords: demands, educational timetabling, integer linear programming, scheduling, university examination timetabling problem (UETP)

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Authors: Liliana O. Martínez, Juan E González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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A serious game category mobile application called Math Dominoes is presented. The main objective of this applications is to strengthen the teaching-learning process of solving algebraic equations and is based on the board game "Double 6" dominoes. Math Dominoes allows the practice of solving first, second-, and third-degree algebraic equations. This application is aimed to students who seek to strengthen their skills in solving algebraic equations in a dynamic, interactive, and fun way, to reduce the risk of failure in subsequent courses that require mastery of this algebraic tool.

Keywords: algebra, equations, dominoes, serious games

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Authors: Wera Supa, Panita Wannapiroon

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This paper is a report on the designing of the social collaborative learning model based on proactive involvement to Promote the global merit principle in cultivating youths’ morality. The research procedures into two phases, the first phase is to design the social collaborative learning model based on proactive involvement to promote the global merit principle in cultivating youths’ morality, and the second is to evaluate the social collaborative learning model based on proactive involvement. The sample group in this study consists of 15 experts who are dominant in proactive participation, moral merit principle and youths’ morality cultivation from executive level, lecturers and the professionals in information and communication technology expertise selected using the purposive sampling method. Data analyzed by arithmetic mean and standard deviation. This study has explored that there are four significant factors in promoting the hands-on collaboration of global merit scheme in order to implant virtues to adolescences which are: 1) information and communication Technology Usage; 2) proactive involvement; 3) morality cultivation policy, and 4) global merit principle. The experts agree that the social collaborative learning model based on proactive involvement is highly appropriate.

Keywords: social collaborative learning, proactive involvement, global merit principle, morality

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Authors: Z. Tasir, S. N. Kew, D. West, Z. Abdullah, D. Toohey

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Research on Learning Analytics is progressively developing in the higher education field by concentrating on the process of students' learning. Therefore, a research project between Malaysian and Australian Universities was initiated in 2015 to look at the use of Learning Analytics to support the development of teaching practice. The focal point of this article is to discuss and share the experiences of Malaysian and Australian universities in the process of developing the collaborative research on Learning Analytics. Three aspects of this will be discussed: 1) Establishing an international research project and team members, 2) cross-cultural understandings, and 3) ways of working in relation to the practicalities of the project. This article is intended to benefit other researchers by highlighting the challenges as well as the strategies used in this project to ensure such collaborative research succeeds.

Keywords: academic research project, collaborative research, cross-cultural understanding, international research project

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Authors: Thien Van Ngo

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The engineering design process is a systematic approach to solving problems. It involves identifying a problem, brainstorming solutions, prototyping and testing solutions, and evaluating the results. The engineering design process can be used to teach students how to solve problems in a creative and innovative way. The research aim of this study was to investigate the effectiveness of using the engineering design process to enhance student learning outcomes in a physics course. A mixed research method was used in this study. The quantitative data were collected using a pretest-posttest control group design. The qualitative data were collected using semi-structured interviews. The sample was 150 first-year students in the Department of Mechanical Engineering Technology at Cao Thang Technical College in Vietnam in the 2022-2023 school year. The quantitative data were collected using a pretest-posttest control group design. The pretest was administered to both groups at the beginning of the study. The posttest was administered to both groups at the end of the study. The qualitative data were collected using semi-structured interviews with a sample of eight students in the experimental group. The interviews were conducted after the posttest. The quantitative data were analyzed using independent sample T-tests. The qualitative data were analyzed using thematic analysis. The quantitative data showed that students in the experimental group, who were taught using the engineering design process, had significantly higher post-test scores on physics problem-solving than students in the control group, who were taught using the conventional method. The qualitative data showed that students in the experimental group were more motivated and engaged in the learning process than students in the control group. Students in the experimental group also reported that they found the engineering design process to be a more effective way of learning physics. The findings of this study suggest that the engineering design process can be an effective way of enhancing student learning outcomes in physics courses. The engineering design process engages students in the learning process and helps them to develop problem-solving skills.

Keywords: engineering design process, problem-solving, learning outcome of physics, students’ physics competencies, deep learning

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Authors: Takahiro Hino, Michiharu Maeda

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Particle swarm optimization (PSO) is an optimization approach that achieves the social model of bird flocking and fish schooling. PSO works in continuous space and can solve continuous optimization problem with high quality. Set-based particle swarm optimization (SPSO) functions in discrete space by using a set. SPSO can solve combinatorial optimization problem with high quality and is successful to apply to the large-scale problem. In this paper, we present an algorithm of SPSO with status memory to decide the position based on the previous position for solving traveling salesman problem (TSP). In order to show the effectiveness of our approach. We examine SPSOSM for TSP compared to the existing algorithms.

Keywords: combinatorial optimization problems, particle swarm optimization, set-based particle swarm optimization, traveling salesman problem

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Authors: Harshit Garg, Shakshi Gupta

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One of the major problems in today’s world is the growing pollution. The cause for all environmental problems is the increasing pollution rate. Looking upon the statistics, one can find out that most of the pollution is caused by the vehicular pollution which is more than 70 % of the total pollution, effecting the environment as well as human health proportionally. One is aware of the fact that vehicles run on roads so why not having the roads which could adsorb that pollution, not only once but a number of times. Every problem has a solution which can be solved by the state of art of technology, that is one can use the innovative ideas and thoughts to make technology as a solution to the problem of vehicular pollution on roads. Solving the problem up to a certain limit/ percentage can be formulated into a new term called ECO ROADS.

Keywords: environment, pollution, roads, sustainibility

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Authors: Razwan Ahmed Tanvir, Greg Speegle

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Collaborative blockchain ecosystems allow diverse groups to cooperate on tasks while providing properties such as decentralization and transaction security. We provide a model that uses a repository blockchain to manage hard forks within a collaborative system such that a single process (assuming that it has knowledge of the requirements of each fork) can access all of the blocks within the system. The repository blockchain replaces the need for Inter Blockchain Communication (IBC) within the ecosystem by navigating the networks. The resulting construction resembles a tree instead of a chain. A proof-of-concept implementation performs a depth-first search on the new structure.

Keywords: hard fork, shared governance, inter blockchain communication, blockchain ecosystem, regular research paper

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

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In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg 4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. This solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: embedded Runge-Kutta-Fehlberg method, initial value problem, EULR problem, integration step

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Authors: Slava Kalyuga

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There are two opposing major points of view on the optimal degree of initial instructional guidance that is usually discussed in the literature by the advocates of the corresponding learning approaches. Using unguided or minimally guided problem-solving tasks prior to explicit instruction has been suggested by productive failure and several other instructional theories, whereas an alternative approach - using fully guided worked examples followed by problem solving - has been demonstrated as the most effective strategy within the framework of cognitive load theory. An integrated approach discussed in this paper could combine the above frameworks within a broader theoretical perspective which would allow bringing together their best features and advantages in the design of learning tasks for STEM education. This paper represents a systematic review of the available empirical studies comparing the above alternative sequences of instructional methods to explore effects of several possible moderating factors. The paper concludes that different approaches and instructional sequences should coexist within complex learning environments. Selecting optimal sequences depends on such factors as specific goals of learner activities, types of knowledge to learn, levels of element interactivity (task complexity), and levels of learner prior knowledge. This paper offers an outline of a theoretical framework for the design of complex learning tasks in STEM education that would integrate explicit instruction and inquiry (exploratory, discovery) learning approaches in ways that depend on a set of defined specific factors.

Keywords: cognitive load, explicit instruction, exploratory learning, worked examples

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Authors: Can Zhang, Qun Li, Yonglin Lei, Zhi Zhu, Dong Guo

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Aiming at the problem of factor screen in distributed collaborative navigation of dense UAV swarm, an efficient distributed collaborative navigation factor screen method is proposed. The method considered the balance between computing load and positioning accuracy. The proposed algorithm utilized the factor graph model to implement a distributed collaborative navigation algorithm. The GNSS information of the UAV itself and the ranging information between the UAVs are used as the positioning factors. In this distributed scheme, a local factor graph is established for each UAV. The positioning factors of nodes with good geometric position distribution and small variance are selected to participate in the navigation calculation. To demonstrate and verify the proposed methods, the simulation and experiments in different scenarios are performed in this research. Simulation results show that the proposed scheme achieves a good balance between the computing load and positioning accuracy in the distributed cooperative navigation calculation of UAV swarm. This proposed algorithm has important theoretical and practical value for both industry and academic areas.

Keywords: screen method, cooperative positioning system, UAV swarm, factor graph, cooperative navigation

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Authors: Wang Zhanquan, Yang Zeping, Gu Chunhua, Zhu Fazhi, Guo Weibin

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Recently, Massive Open Online Courses (MOOCs) are becoming the new trend of education. There are many problems under the environment of Database Principle curriculum teaching process in MOOCs, such as teaching ideas and theories which are out of touch with the reality, how to carry out the technical teaching and interactive practice in the MOOCs environment, thus the methods of database course under the environment of MOOCs are proposed. There are three processes to deal with problem solving in the research, which are problems proposed, problems solved, and inductive analysis. The present research includes the design of teaching contents, teaching methods in classroom, flipped classroom teaching mode under the environment of MOOCs, learning flow method and large practice homework. The database designing ability is systematically improved based on the researching methods.

Keywords: problem solving-driven, MOOCs, teaching art, learning flow;

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Authors: Charalambous-Darden Nefi, Antoniou Phivi

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This study presents drawing as an alternative tool for facilitating interaction and communication among the members of a class (teachers and students) in an inclusive school setting. It applies elements of the Collaborative Drawing Method (CDM), an interactive method of drawing where two individuals draw together on the same surface. For the past ten years, the facilitators of this study have been researching the effects of spontaneous and non-spontaneous drawing upon elementary school students with Autism Spectrum Conditions (ASC). This research eventually led them to the application of elements of the CDM. The method was applied to both adults and children and children with one another. The astonishing outcomes of these applications indicate that collaborative drawing, with its inclusive nature, has the potential to help individuals develop interaction and communication among themselves, making it suitable for everyone. This workshop aims to allow the participants to become familiar with the CDM by applying it during the workshop, with the ultimate goal of enhancing their educational approaches by adding the CDM to their teaching methods.

Keywords: autism, collaborative drawing, autism spectrum condition, ASC

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Authors: Leszek Chybowski, Artur Bejger, Katarzyna Gawdzińska

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Subversion analysis is a tool used in the TRIZ (Theory of Inventive Problem Solving) methodology. This article introduces the history and describes the process of subversion analysis, as well as function analysis and analysis of the resources, used at the design stage when generating possible undesirable situations. The article charts the course of subversion analysis when applied to a fuel injection nozzle of a marine engine. The work describes the fuel injector nozzle as a technological system and presents principles of analysis for the causes of a cracked tip of the nozzle body. The system is modelled with functional analysis. A search for potential causes of the damage is undertaken and a cause-and-effect analysis for various hypotheses concerning the damage is drawn up. The importance of particular hypotheses is evaluated and the most likely causes of damage identified.

Keywords: complex technical system, fuel injector, function analysis, importance analysis, resource analysis, sabotage analysis, subversion analysis, TRIZ (Theory of Inventive Problem Solving)

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Authors: Kian Jon Chua, Islam Md Raisul

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Findings on a research study conducted for a group of year-2 engineering students participating in a flipped classroom (FC) experience that is judiciously incorporated into project-based learning (PBL) module are presented. The chief purpose of the research is to identify whether if the incorporation of flipped classroom approach to project-based learning indeed yields a positive learning experience for engineering students. Results are presented and compared from the two classes of students – one is subjected to a traditional PBL learning mode while the other undergoes a hybrid PBL-FC learning format. Some themes related to active learning, problem-solving ability, teacher as facilitator, and degree of self-efficacy are also discussed. This paper hopes to provide new knowledge and insights relating to the introduction of flipped classroom learning to a project-based engineering module. Some potential study limitations and future directions to address them are also presented.

Keywords: hybrid project-based learning, flipped classroom, problem-solving, active learning

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Authors: Akumeyam Elvis Akum, Njanjo Thecla Anyongo Mukete, Fonkeng George Epah

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Globally, the goal of higher education is to enhance graduate employability skills. Paradoxically, Cameroon’s graduate employability rate is far below the graduation rate. This worrisome situation caused the researcher to hypothesize that the teaching and learning experiences account for this increasing disparity. The study sought to investigate the effect on graduate employability of the teaching of organizational, problem-solving, innovation, and risk management skills on graduate employability. The study adopted a descriptive survey design with a quantitative approach. Data was collected by quantitative techniques from a random sample of 385 graduates using closed-ended structured questionnaire. Generally, findings revealed that entrepreneurship education does not sufficiently enhance graduate employability in the University of Buea. Specifically, the teaching of organizational skills does not significantly enhance their employability, as an average of 55% of graduates indicated that the course did not sufficiently help them develop skills for planning, management of limited resources, collaboration, and the setting of priorities. Also, 60% of the respondents indicated that the teaching of problem-solving skills does not significantly enhance graduate employability at the University of Buea. Contrarily, 57% of the respondents agreed that through their experiences in entrepreneurship education, their innovation skills were improved. The study recommended that a practical approach to teaching should be adopted, with attention to societal needs. A framework to ensure the teaching of entrepreneurship to students at the undergraduate level is recommended, such that those who do not continue with university studies after their Bachelor’s degree would have acquired the needed skills for employability.

Keywords: employability, entrepreneurship education, graduate, innovative skills, organizational skills, problem-solving skills, risk management skills

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Authors: Lulu Sun

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In Addition is an after-school mathematics program in which students and their parents build mathematical confidence and competence by solving problems they curious about. It is a program consists of mix-grade from 4th to 6th grade of 10 to 20 students, including math problem solving and other activities. This partnership will focus on the relationship between the In-Addition and the parents’ engagement; in this kind of partnership, it has the In-Addition program teaching and the family engagement. This partnership is purpose to building cooperation between the program and parents, strengthening the links between the program and families.

Keywords: program-family, family engagement, positive bias, partnership

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Authors: D. K. Rao, M. G. M. Khan, K. G. Reddy

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The focus of this paper is to develop a technique of solving a combined problem of determining Optimum Strata Boundaries (OSB) and Optimum Sample Size (OSS) of each stratum, when the population understudy is skewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB is formulated as a Mathematical Programming Problem (MPP) which is then solved by dynamic programming technique. A numerical example is presented to illustrate the computational details of the proposed method. The proposed technique is useful to obtain OSB and OSS for a Pareto type skewed population, which minimizes the variance of the estimate of population mean.

Keywords: stratified sampling, optimum strata boundaries, optimum sample size, pareto distribution, mathematical programming problem, dynamic programming technique

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Authors: Kikuo Asai, Yuji Sugimoto

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We developed a prototype system for multiplayer RC-car driving in a collaborative Augmented Reality (AR) environment. The tele-existence environment is constructed by superimposing digital data onto images captured by a camera on an RC-car, enabling players to experience an augmented coexistence of the digital content and the real world. Marker-based tracking was used for estimating position and orientation of the camera. The plural RC-cars can be operated in a field where square markers are arranged. The video images captured by the camera are transmitted to a PC for visual tracking. The RC-cars are also tracked by using an infrared camera attached to the ceiling, so that the instability is reduced in the visual tracking. Multimedia data such as texts and graphics are visualized to be overlaid onto the video images in the geometrically correct manner. The prototype system allows a tele-existence sensation to be augmented in a collaborative AR environment.

Keywords: multiplayer, RC-car, collaborative environment, augmented reality

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Authors: Rex C. Apillanes, Ana Rubi L. Sereño, Ellen Joy L. Palangan

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The main objective of this action research is to know the effectiveness of the compendium on Contextualized Story Word Problem in Mathematics used as an intervention material to enhance the comprehension and problem-solving skills of Grade 4 pupils. This also addresses the competencies outlined in the curriculum guide while, at the same time, providing instructional material which the pupils can work on and practice solving word problems. The twelve randomly selected grade four pupils of Mantuyom Elementary School have been chosen as respondents for this action research in consideration of their consent and approval. A Pre-Test and a Post-test have been given to the pupils to determine their baseline proficiency level in four fundamental operations. The data has been statistically treated using a T-test to determine their difference. At a mean score of 13.42 and 16.83 for pre and post-tests, respectively, the p-value of 0.000620816 reflects a highly significant difference for the pre-test and post-test. This is lesser than the 0.05 level of significance (p≤0.05). Therefore, it is found that the compendium of contextualized story word problems is an efficient instructional material for Mathematics 4, yet; it is recommended that a Parents’ User Guide shall be developed to assist the parents in the conduct of the Remediation, Reinforcement and Enhancement (RRE).

Keywords: action research, compendium, contextualized, story, word problem, research, intervention

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Authors: Hamzeh Awad

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Disability is considered to be a worldwide complex phenomenon which rising at a phenomenal rate and caused by many different factors. Chronic diseases such as cardiovascular disease and diabetes can lead to mobility disability in particular and disability in general. The ICF is an integrative bio-psycho-social model of functioning and disability and considered by the World Health Organization (WHO) to be a reference for disability classification using its categories and core set to classify disorder’s functional limitations. Specialist programs at Sultan Bin Abdul Aziz Humanitarian City (SBAHC) are providing both inpatient and outpatient services have started to implement the ICF and use it as a problem solving tool in Rehab. Diabetes is leading contributing factor for disability and considered epidemic in several Gulf countries including the Kingdom of Saudi Arabia (KSA), where its prevalence continues to increase dramatically. Metabolic disorders, mainly diabetes are not well covered in Rehab field. The purpose of this study is present to research and clinical rehabilitation field of DREAM and ICF as a framework in clinical and research setting in Rehab service. Also, shed the light on using the ICF as problem solving tool at SBAHC. There are synergies between disability causes and wider public health priorities in relation to both chronic disease and disability prevention. Therefore, there is a need for strong advocacy and understanding of the role of ICF as a reference in Rehab settings in Middle East if we wish to seize the opportunity to reverse current trends of acquired disability in the region.

Keywords: international classification of functioning, disability and health (ICF), prototype, rehabilitation and diabetes

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Authors: Sara J. Mills, Sally Howell

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The field of special education has long struggled to bridge the research to practice gap. There is ample evidence from research of effective strategies for students with special needs, but these strategies are not routinely implemented in schools in ways that yield positive results for students. In recent years, the field of special education has turned its focus to implementation science. That is, discovering effective methods of implementing evidence-based practices in school settings. Teacher training is a critical factor in implementation. This study aimed to successfully implement Schema-Based Instruction (SBI) for math problem solving in four classrooms in a special primary school serving students with language deficits, including students with Autism Spectrum Disorders (ASD) and Intellectual Disabilities (ID). Using an action research design that allowed for adjustments and modification to be made over the year-long study, two cohorts of teachers across the school were trained and supported in six-week learning cycles to implement SBI in their classrooms. The learning cycles included a one-day training followed by six weeks of one-on-one or team coaching and three fortnightly cohort group meetings. After the first cohort of teachers completed the learning cycle, modifications and adjustments were made to lesson materials in an attempt to improve their effectiveness with the second cohort. Fourteen teachers participated in the study, including master special educators (n=3), special education instructors (n=5), and classroom assistants (n=6). Thirty-one students participated in the study (21 boys and 10 girls), ranging in age from 5 to 12 years (M = 9 years). Twenty-one students had a diagnosis of ASD, 20 had a diagnosis of mild or moderate ID, with 13 of these students having both ASD and ID. The remaining students had diagnosed language disorders. To evaluate the effectiveness of the implementation approach, both student and teacher data was collected. Student data included pre- and post-tests of math word problem solving. Teacher data included fidelity of treatment checklists and pre-post surveys of teacher attitudes and efficacy for teaching problem solving. Finally, artifacts were collected throughout the learning cycle. Results from cohort 1 and cohort 2 revealed similar outcomes. Students improved in the number of word problems they answered correctly and in the number of problem-solving steps completed independently. Fidelity of treatment data showed that teachers implemented SBI with acceptable levels of fidelity (M = 86%). Teachers also reported increases in the amount of time spent teaching problem solving, their confidence in teaching problem solving and their perception of students’ ability to solve math word problems. The artifacts collected during instruction indicated that teachers made modifications to allow their students to access the materials and to show what they knew. These findings are in line with research that shows student learning can improve when teacher professional development is provided over an extended period of time, actively involves teachers, and utilizes a variety of learning methods in classroom contexts. Further research is needed to evaluate whether these gains in teacher instruction and student achievement can be maintained over time once the professional development is completed.

Keywords: implementation science, mathematics problem solving, research-to-practice gap, schema based instruction

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Authors: Abbas Mirakhorli

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A hub covering problem is a type of hub location problem that tries to maximize the coverage area with the least amount of installed hubs. There have not been many studies in the literature about multi-objective hubs covering location problems. Thus, in this paper, a bi-objective model for the hub covering problem is presented. The two objectives that are considered in this paper are the minimization of total transportation costs and the maximization of coverage of origin-destination nodes. A genetic algorithm is presented to solve the model when the number of nodes is increased. The genetic algorithm is capable of solving the model when the number of nodes increases by more than 20. Moreover, the genetic algorithm solves the model in less amount of time.

Keywords: facility location, hub covering, multi-objective optimization, genetic algorithm

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Authors: Tien-Ling Yeh, Jo-Han Chan

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The percentage of dual-earner couples has become higher and higher each year. Family lifestyles in Taiwan have also been changing. This fact reflects the importance of family communication and parent-child relationship. This study aimed to explore the influences of family lifestyles and accompany forms on children’s capability to solve problems. The research process included two phases: (1) literature review, to explore the characteristics of children’s capability to solve problems and methods to measure this capability; and (2) questionnaire analyses, to explore the influences of lifestyles and accompany time and forms of modern families on their children’s capability to solve problems. The questionnaires were issued in October and November, 2016. A total of 300 questionnaires were retrieved, among which 250 were valid. The findings are summarized below: -The linguistic performances of the children from families of the busy and haggling lifestyle or the intermittent childcare lifestyle were rather good. Besides being interested in learning, these children could solve problems or difficulties independently. -The capability to ‘analyze problems’ of children from families with accompanying time during 19:00-19:30 (family dinner time) or 22:00-23:30 (before bedtime) was good. When facing a complex problem, these children could identify the most important factor in the problem. When seeing a problem, they would first look for the cause. If they encountered a bottleneck while solving a problem, they would review the context of the problem and related conditions to come up with another solution. -According to the literature, learning toys with numbers and symbols to learn to read can help develop children’s logic thinking, which is helpful to solve problems. Interestingly, some study suggested that children playing with fluid constructive toys are less likely to give up what they are doing and more likely to identify problems in their daily life. Some of them can even come up with creative and effective solutions.

Keywords: accompany, lifestyle, parent-child, problem-solving

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Authors: Daniel Kostrzewa, Henryk Josiński

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The expanded Invasive Weed Optimization algorithm (exIWO) is an optimization metaheuristic modelled on the original IWO version created by the researchers from the University of Tehran. The authors of the present paper have extended the exIWO algorithm introducing a set of both deterministic and non-deterministic strategies of individuals’ selection. The goal of the project was to evaluate the exIWO by testing its usefulness for solving some test instances of the traveling salesman problem (TSP) taken from the TSPLIB collection which allows comparing the experimental results with optimal values.

Keywords: expanded invasive weed optimization algorithm (exIWO), traveling salesman problem (TSP), heuristic approach, inversion operator

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem is to ask for fitting 3 circles into a right triangle such that they are tangent to each other, and each circle is also tangent to a pair of the triangle’s side. 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, we call it extended general Malfatti’s problem, these circles whose tangency graph, using the center of circles as vertices and the edge connect two circles center if these two circles tangent to each other, has the structure as Pascal’s triangle, and the exterior circles of these circles tangent to three sides of the triangle. In the extended general Malfatti’s problem, there are closed-form solutions for n=1, 2, and the problem becomes complex when n is greater than 2. In solving extended general Malfatti’s problem (n>2), we initially give values to the radii of all circles. From the tangency graph and current radii, we can compute angle value between two vectors. These vectors are from the center of the circle to the tangency points with surrounding elements, and these surrounding elements can be the boundary of the triangle or other circles. For each circle C, there are vectors from its center c to its tangency point with its neighbors (count clockwise) pi, i=0, 1,2,..,n. We add all angles between cpi to cp(i+1) mod (n+1), i=0,1,..,n, call it sumangle(C) for circle C. Using sumangle(C), we can reduce/enlarge the radii for all circles in next iteration, until sumangle(C) is equal to 2πfor all circles. With a similar idea, this paper proposed an algorithm to find the radii of circles whose tangency has the structure of Pascal’s triangle, and the exterior circles of these circles are tangent to the unit Realeaux Triangle.

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

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