Search results for: mathematics education research

Authors: Yasuhito Tanaka

Abstract:

In this paper we will constructively prove the existence of an equilibrium in a competitive economy with sequentially locally non-constant excess demand functions. And we will show that the existence of such an equilibrium in a competitive economy implies Sperner-s lemma. We follow the Bishop style constructive mathematics.

Keywords: Sequentially locally non-constant excess demand functions, Equilibrium in a competitive economy, Constructive mathematics

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Authors: Alba Barbarà Molinero, Rosalía Cascón Pereira

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We assert here that there might be some factors that influence professional identity construction at the university/higher education stage. In accord, we propose a conceptual framework of intervening factors in professional identity construction at university from a literature review and preliminary data from a qualitative pilot study using focus groups. This model identifies several factors that might influence university students- professional identity construction and group them into categories. In turn, we describe how these factors might contribute in strengthening or weakening their professional identity. Finally, we discuss the implications of strengthening students- PI for the university, individuals and organizations and we provide a roadmap for future empirical work in this area.

Keywords: Professional Identity, Higher education, influencing factors.

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Authors: G. Cossu, A. Esposito, G. Picco, C. Scrizzi, A. Tartaglia, E. Tresso

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A collaboration among the Hospital S. Giovanni Battista of Turin, the Politecnico of Turin, and the MUST company is described. The content of the collaboration has been and is the use of ICT-s, e-learning, and blended learning for the internal professional education, training, and keeping up to date of the personnel of the hospital. A platform for the delivery of the teaching materials has been built, including an evaluation and self-evaluation tool. The first on line courses have been developed and delivered and many more are in preparation. The first results of the monitoring of the efficacy of the online education have been positive.

Keywords: E-learning, blended learning, on line education, ICT.

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Authors: Chen Zhang, Wei Yaping

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With the rapid expansion of city scale and the excessive concentration of population, achieving relative equality of extracurricular education resources and improving spatial service performance of relevant facilities become necessary arduous tasks. In urban space, extracurricular education facilities should offer better service to its targeted area and promote the equality and efficiency of education, which is accomplished by the allocation of facilities. Based on questionnaire and survey for local students in Hangzhou City in 2009, this study classifies extracurricular education facilities in meg-city and defines the equalization of these facilities. Then it is suggested to establish extracurricular education facilities system according to the development level of city and demands of local students, and to introduce a spatial analysis method into urban planning through the aspects of spatial distribution, travel cost and spatial service scope. Finally, the practice of nine sub-districts of Hangzhou is studied.

Keywords: extracurricular education facilities, equalization, spatial service performance, meg-city

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Authors: Roelien Goede

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Information systems practitioners are frequently required to master new technology, often without the aid of formal training. They require the skill to manage their own learning and, when this skill is developed in their formal training, their adaptability to new technology may be improved. Self- directed learning is the ability of the learner to manage his or her own learning experience with some guidance from a facilitator. Self-directed learning skills are best improved when practiced. This paper reflects on a critical social research project to improve the self-directed learning skills of fourth year Information Systems students. Critical social research differs from other research paradigms in that the researcher is viewed as the agent of change to achieve the desired outcome in the problem situation.

Keywords: Action Research, Critical Social Research, Information Systems Education, Self-directed Learning.

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Authors: M. Nadeem, S. Nasir, K. A. Moazzam, R. Kashif

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The remarkable growth and evolution in information and communication technology (ICT) in the past few decades has transformed modern society in almost every aspect of life. The impact and application of ICT have been observed in almost all walks of life including science, arts, business, health, management, engineering, sports, and education. ICT in education is being used extensively for student learning, creativity, interaction, and knowledge sharing and as a valuable source of teaching instrument. Apart from the student’s perspective, it plays a vital role for teacher education, instructional methods and curriculum development. There is a significant difference in growth of ICT enabled education in developing countries compared to developed nations and according to research, this gap is widening. ICT gradually infiltrate in almost every aspect of life. It has a deep and profound impact on our social, economic, health, environment, development, work, learning, and education environments. ICT provides very effective and dominant tools for information and knowledge processing. It is firmly believed that the coming generation should be proficient and confident in the use of ICT to cope with the existing international standards. This is only possible if schools can provide basic ICT infrastructure to students and to develop an ICT-integrated curriculum which covers all aspects of learning and creativity in students. However, there is a digital divide and steps must be taken to reduce this digital divide considerably to have the profound impact of ICT in education all around the globe. This study is based on theoretical approach and an extensive literature review is being conducted to see the successful implementations of ICT integration in education and to identify technologies and models which have been used in education in developed countries. This paper deals with the modern applications of ICT in schools for both teachers and students to uplift the learning and creativity amongst the students. A brief history of technology in education is presented and discussed are some important ICT tools for both student and teacher’s perspective. Basic ICT-based infrastructure for academic institutions is presented. The overall conclusion leads to the positive impact of ICT in education by providing an interactive, collaborative and challenging environment to students and teachers for knowledge sharing, learning and critical thinking.

Keywords: Information and communication technology, ICT, education, ICT infrastructure, teacher education.

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Authors: Kumiko Aoki

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Japan is known to be a technological powerhouse, being noted for its automobiles, consumer electronics, laptop computers, portable gaming devices, and more recently healing animal robots. Japan is also noted for its popular culture; manga, anime, novels, films, character goods, game programs, cosplay cafes, karaoke and so on. It may be natural for people outside Japan to assume that e-learning in Japan must be well advanced and innovative. In reality, the application of technologies in education in Japan is far behind of other developed countries. Especially in higher education, apathy of students towards their study prevails and teachers continue ignoring such student attitudes. E-learning, which is supposed to revolutionalize the way people learn as it has potentials to enable more student-centered learning, has not been realized in Japan and mostly used to perpetuate the teachercentered teaching in a different format.

Keywords: e-learning, Higher Education, ICT in Education, Japan

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Authors: Ivana Šalinović

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The term gender emerged in the second half of the last century and since then a growing body of research dealing with the topic demonstrates its importance. Primarily, the research and the theories that were addressing the topic were focused on stating the differences between the terms sex and gender, where sex refers to the biological aspect of a person, while gender refers to the socially ascribed roles, attitudes, behaviors, and etc., and on gender discrimination whose visible and invisible repercussions are harming society and one of the agents of change should be educators on all educational levels since they are emotionally sculpting their students, that is why considerable effort should be put into implementing education about this topic into the standard curriculum. Not only educators, but it is also necessary to change the mindset of the younger generations because they will be important agents in the further elimination of gender discrimination, thus causing societal changes. Therefore, it is very important to hear their voices and their experiences and for these reasons, this research has been done, to see what the students of the second year at a private college university Aspira in Croatia have gone through in their educational ladder. The hypothesis was that the findings would most certainly show a huge difference between female and male students’ experiences and effects of gender discrimination, but the results have actually shown a very mixed picture and the original hypothesis was somewhat disapproved. Instead of finding out that girls experienced a lot of gender discrimination, it turned out that it was the boys who believed that in their previous and current education, there was no equal time distribution between genders, they noticed that the language was not gender-sensitive, teaching aids were not adopted to the genders. They were also the ones that pointed out that the discipline path was not the same for everyone, and they were the ones that the teacher’s gender had more influence on and were also the ones that experienced more gender discrimination.

Keywords: Gender, discrimination, elementary school, high school.

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Authors: Anjan Saikia

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600 schools going adolescents and 100 teachers from 16 schools of Dhemaji and Lakhimpur district of Assam, India were surveyed to assess and compare their awareness regarding AIDS and AIDS Education. An awareness test was administered containing 38 items for adolescents and 40 items for teachers in the test. Observations revealed that the majority of school-going adolescents are poor in their HIV/AIDS and AIDS education awareness. It shows that the school going adolescents of Dhemaji district are better in HIV/AIDS and AIDS education awareness than the school going adolescents of Lakhimpur district while comparing the gender, settlement, steam and district wise variables.

Keywords: Awareness, HIV, AIDS, AIDS education.

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Authors: G. Bago, P. Hedbávný

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This contribution was developed from a research within the doctoral thesis. Its object was to create multimedia materials for sport gymnastics. Consequently we surveyed the influence of its practical application on the efficiency of schooling at a university. We verified the prescribed hypothesis of the efficiency of the teaching process using the method of single-factor experiment, where the entrance independent variable was the change of system of tuition and the outgoing dependent variable was the change of level of acquired motor skills. The results confirmed the positive impact of using multimedia materials on the efficiency of the teaching process. Further, with the aid of questionnaires, we evaluated how the tested subjects perceive the innovative methods in sport gymnastics. The responses showed that the students rate the application of multimedia materials very positively.

Keywords: efficiency of education, means of education, multimedia materials, sports gymnastics

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Authors: Mahmoud Tarek Mohamed Hammad

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Despite the importance of the role and efforts made by the universities of the Kingdom of Saudi Arabia in reviving and preserving heritage architecture as an important cultural heritage in the Kingdom, The idea revolves around restoration and conservation processes and neglects the architectural heritage values, whose content can be used in sustainable contemporary architectural works. Educational values based on heritage architecture and how to integrate with the contemporary requirements were investigated in this research. For this purpose, by understanding the heritage architectural values as well as educational, academic process, the researcher presented an educational model of questionnaire forms for architecture students and the staff at the Architecture Department at Al-Baha University as a case study that serves the aims of the research. The results of the research show that heritage values especially those interview results are considered as a positive indicator of the importance of these values. The students and the staff need both to gain an understanding of heritage values as well as an understanding of theories of incorporating those values into the design process of contemporary local architecture. The research concludes that a correct understanding of the heritage values, its performance, and its reintegration with modern architecture technology should be focused on architectural education.

Keywords: Heritage architecture, academic work, heritage values, sustainable contemporary local architectural.

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Authors: Anita Kéri

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Satisfying foreign student needs has been in the center of research interest in the past several years. Higher education institutions have been exploring factors influencing foreign student satisfaction to stay competitive on the educational market. Even though foreign student satisfaction and loyalty are topics investigated deeply in the literature, the academic years of 2020 and 2021 have revealed challenges never experienced before. With the COVID-19 pandemic, new factors have emerged that might influence foreign student satisfaction and loyalty in higher education. The aim of the current research is to shed lights on what factors influence foreign student satisfaction and loyalty in the post-pandemic educational era, and to reveal if the effects of factors influencing satisfaction and loyalty have changed compared to previous findings. Initial results show that students are less willing to participate in online surveys during and after the pandemic. The return rate of the survey instrument is below 5%. Results also reveal that there is a slight difference in what factors students deem important during pandemic times regarding their satisfaction and loyalty. The results of the current study help us determine what factors higher education institutions need to consider, when planning the future service affordances for their foreign students, that might influence their satisfaction and loyalty.

Keywords: COVID-19, foreign students, loyalty, pandemic, satisfaction.

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Authors: N. Utaberta, B. Hassanpour, M. Surat, A. I. Che Ani, N.M. Tawil

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The concerns of education and practice of architecture do not necessarily overlap. Indeed the gap between them could be seen increasingly and less frequently bridged. We suggest that changing in architecture education and clarifying the relationship between these two can help to find and address the opportunities and unique positions to bridge this gulf.

Keywords: Architecture education, Learning, Practice, Teaching

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Authors: Volker Koch

Abstract:

This paper deals with the education of purchasing professionals in Austria. In this education, equivalent and measurable criteria are collected in order to create a comparison. The comparison shows the problem. To make the aforementioned comparison possible, methodologies such as KODE-Competence Atlas or presentations in a matrix form are used. The result shows the content taught and whether there are any similarities or interesting differences in the current Austrian purchasers’ formations. Purchasing professionals learning competencies are also illustrated in the study result.

Keywords: Competencies, education, purchasing professional, technological-oriented.

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Authors: Ana Mafalda Gonçalves, Neuza Pedro

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The evolution of ICT has changed all sections of society and these changes have been creating an irreversible impact on higher education institutions, which are expected to adopt innovative technologies in their teaching practices. As theorical framework this study select Rogers theory of innovation diffusion which is widely used to illustrate how technologies move from a localized invented to a widespread evolution on organizational practices. Based on descriptive statistical data collected in a European higher education institution three years longitudinal study was conducted for analyzing and discussion the different stages of a LMS adoption process. Results show that ICT integration in higher education is not progressively successful and a linear process and multiple aspects must be taken into account.

Keywords: e-learning, higher education, LMS, innovation, technologies

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Authors: Chaiwat Waree, Kalanyoo Petcharaporn

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This research aims to develop and evaluate a training course to promote learning activities of 2nd year, Suan Sunandha Rajabhat University, faculty of education students using multiple intelligences theory. The process is divided into two phases: Phase 1 development of training course to promote learning activities consisting of principles, objectives of the course, structure, training duration, content, training materials, training activities, media training, monitoring, measurement and evaluation quality of the course. Phase 2 evaluation efficiency of training course was to use the improved curriculum with experimental group which is 2nd year, Suan Sunandha Rajabhat University, faculty of education students was drawn randomly 152 students. The experimental pattern was randomized Control Group Pre-Test Post-Test Design, Analysis Data by t-Test with the software SPFSS for Windows. Research has shown that: 1). the ability of teaching and learning according to the theory of multiple intelligences after training is higher than before training significantly in statistic at .01 level, 2). The satisfaction of students to the training courses was overall at the highest level.

Keywords: A training course, learning activities, multiple intelligences.

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Authors: Essam Almuhsin, Ben Soh, Alice Li, Azmat Ullah

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It is widely accepted that university students must acquire new knowledge, skills, awareness, and understanding to increase opportunities for professional and personal growth. The study reveals a significant increase in users engaging in e-coaching activities and a growing need for it during the COVID-19 pandemic. The paper proposes an e-coaching methodology for higher education in Saudi Arabia to address the need for effective coaching in the current online learning environment.

Keywords: Role of e-coaching, e-coaching in higher education, Saudi higher education environment, e-coaching methodology, importance of e-coaching.

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Authors: Ruhugül Özge Ocak, Banu Öztürk Kurtaslan

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Botanical gardens are very significant organizations which protect the environment against the increasing environmental problems, provide environmental education for people, offer recreation possibilities, etc. This article describes botanical gardens and their functions. The most important function of botanical garden is to provide environmental education for people and improve environmental awareness. Considering this function, some botanical gardens were examined and opinions were suggested about the subject.

Keywords: Botanical garden, environment, environmental education, recreation.

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Authors: Fan Yang

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With the development of social economy and the popularization of quality education, the Chinese government invests more and more funding in education. Campus constructions are experiencing a great development phase. Under the trend of sustainable development, modern green campus design needs to meet new requirements of contemporary, informational and diversified education means and adapt to future education development. Educators, designers and other participants of campus design are facing new challenges. By studying and analyzing the universal unsatisfied current situations and sustainable development requirements of Chinese campuses, this paper summarizes the strategies and intentions of the whole-life-cycle campus design. In addition, a Chinese high school in Zhejiang province is added to illustrate the design cycle in an actual case. It is aimed to make all participants of campus design, especially the designers, to realize the importance of whole-life-cycle campus design and cooperate better. Sustainable campus design is expected to come true in deed instead of becoming a slogan in this way.

Keywords: Campus design, green school, sustainable development, whole-life-cycle design.

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Authors: Ofelia A. Damag

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The study was focused on the development and assessment of the illustrated language activities of the 1996 Edition of the Portage Guide to Early Education. It determined the extent of appropriateness, applicability, time efficiency and aesthetics of the illustrated language activities to be used as instructional material not only by teachers, but parents and caregivers as well. The eclectic research design was applied in this study using qualitative and quantitative methods. To determine the applicability and time efficiency of the study, a try out was done. Since the eclectic research design was used, it made use of a researcher-made survey questionnaire and focus group discussion. Analysis of the data was done through weighted mean and ANOVA. The respondents of the study were representatives of Special Education (SPED) teachers, caregivers and parents of a special-needs child, particularly with difficulties in learning basic language skills. The results of the study show that a large number of respondents are SPED teachers and caregivers and are mostly college graduates. Many of them have earned units towards Master’s studies. Moreover, a majority of the respondents have not attended seminars or in-service training in early intervention for them to be more competent in the area of specialization. It is concluded that the illustrated language activities under review in this study are appropriate, applicable, time efficient and aesthetic for use as a tool in teaching. The recommendations are focused on the advocacy for SPED teachers, caregivers and parents of special-needs children to be more consistent in the implementation of the new instructional materials as an aid in an intervention program.

Keywords: Illustrated language activities, inclusion, portage guide to early education, special educational needs.

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Authors: Hersh C. Waxman, Yolanda N. Padrón, Jee-Young Shin, Héctor H. Rivera

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While many studies have conducted the achievement gap between groups of students in school districts, few studies have utilized resilience research to investigate achievement gaps within classrooms. This paper aims to summarize and discuss some recent studies Waxman, Padr├│n, and their colleagues conducted, in which they examined learning environment differences between resilient and nonresilient students in reading and mathematics classrooms. The classes consist of predominantly Hispanic elementary school students from low-income families. These studies all incorporated learning environment questionnaires and systematic observation methods. Significant differences were found between resilient and nonresilient students on their classroom learning environments and classroom behaviors. The observation results indicate that the amount and quality of teacher and student academic interaction are two of the most influential variables that promote student outcomes. This paper concludes by suggesting the following teacher practices to promote resiliency in schools: (a) using feedback from classroom observation and learning environment measures, (b) employing explicit teaching practices; and (c) understanding students on a social and personal level.

Keywords: achievement gap, classroom learning environments, educational resilience, systematic classroom observation

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Authors: Vesna Bosilj Vuksic, Mirjana Pejic Bach

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Business process management (BPM) has become widely accepted within business community as a means for improving business performance. However, it is of the highest importance to incorporate BPM as part of the curriculum at the university level education in order to achieve the appropriate acceptance of the method. Goal of the paper is to determine the current state of education in business process management (BPM) at the Croatian universities and abroad. It investigates the applied forms of instruction and teaching methods and gives several proposals for BPM courses improvement. Since majority of undergraduate and postgraduate students have limited understanding of business processes and lack of any practical experience, there is a need for introducing new teaching approaches. Therefore, we offer some suggestions for further improvement, among which the introduction of simulation games environment in BPM education is strongly recommended.

Keywords: business process management, simulation games, education

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Authors: Barbara A. Perry

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In 1996, the New Zealand government and the Ministry of Education announced that they were setting up a "world class system of inclusive education". As a parent of a son with high and complex needs, a teacher, school Principal and Disability studies Lecturer, this author will track the changes in the journey towards inclusive education over the last 20 years. Strategies for partnering with families to ensure educational success along with insights from one of those on the crest of the wave will be presented. Using a narrative methodology the author will illuminate how far New Zealand has come towards this world class system of inclusion promised and share from personal experience some of the highlights and risks in the system. This author has challenged the old structures and been part of the setting up of new structures particularly for providing parent voice and insight; this paper provides a unique view from an insider’s voice as well as a professional in the system.

Keywords: Disability studies, inclusive education, special education, working with families with children with disability.

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Authors: I. Benning

Abstract:

Using technology to expand the learning space is critical for a productive mathematical discourse. This is a case study of two teachers who developed and enacted GeoGebra-based mathematics lessons following their engagement in a two-year professional development. The didactical and semiotic affordance of GeoGebra in widening the learning space for a productive mathematical discourse was explored. The approach of thematic analysis was used for lesson artefact, lesson observation, and interview data. The results indicated that constructing tools in GeoGebra provided a didactical milieu where students used them to explore mathematical concepts with little or no support from their teacher. The prompt feedback from the GeoGebra motivated students to practice mathematical concepts repeatedly in which they privately rethink their solutions before comparing their answers with that of their colleagues. The constructing tools enhanced self-discovery, team spirit, and dialogue among students. With regards to the semiotic construct, the tools widened the physical and psychological atmosphere of the classroom by providing animations that served as virtual concrete to enhance the recording, manipulation, testing of a mathematical idea, construction, and interpretation of geometric objects. These findings advance the discussion of widening the classroom for a productive mathematical discourse within the context of the mathematics curriculum of Ghana and similar sub-Saharan African countries.

Keywords: GeoGebra, theory of didactical situation, semiotic mediation, mathematics laboratory, mathematical discussion.

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Authors: Bashaiar Alsanaa

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Never has a revolution affected all aspects of humanity as the communication revolution during the past two decades. This revolution, with all its advances and utilities, swept the world thus becoming an integral part of our lives, hence giving way to emerging applications at the social, economic, political, and educational levels. More specifically, such applications have changed the delivery system through which learning is acquired by students. Interaction with educators, accessibility to content, and creative delivery options are but a few facets of the new learning experience now being offered through the use of technology in the educational field. With different success rates, third world countries have tried to pace themselves with use of educational technology in advanced parts of the world. One such country is the small rich-oil state of Kuwait which has tried to adopt the e-educational model, however, an evaluation of such trial is yet to be done. This study aimed to fill the void of research conducted around that topic. The study explored students' acceptance of incorporating communication technologies in higher education in Kuwait. Students' responses to survey questions presented an overview of the e-learning experience in this country, and drew a framework through which implications and suggestions for future research were discussed to better serve the advancement of e-education in developing countries.

Keywords: Communication technologies, E-learning, Kuwait, Social media

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Authors: Serdar Öge, Alpay Karasoy, Özlem Kara

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Although women have merit in their jobs, they still are located very few in the top management in many sectors. There are many causes of such situation. Such a situation creates obstacles; especially invisible ones are called “glass ceiling syndrome”. Also, studies which handle this subject in academic community are very few. The aim of this research is to reach the results about glass ceiling obstacles in terms of female teaching staff (academics) working in higher education institutions. To this end, our study was performed on female academics working at Selcuk University, Konya / Turkey. Our study's main aim can be expressed as to determine whether there are glass ceiling obstacles for female academics working at the higher education institution in question, to measure their glass ceiling perceptions and, thus, to identify what the glass ceiling barrier components for them to promotion to senior management positions are.

Keywords: Career, Career Barriers, Glass ceiling syndrome.

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Authors: Amilia Hasbullah, Wan Zahari Wan Yussof, Maziah Ismail

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The primary education system in Indonesia involved the community recognized as the school committee, to take a part in the process of achieving the quality of education via the school facility performance, the low level of school committee involvement in the education system has become the issue in the development of education and reflected to the quality of education. This paper will discuss the conceptual framework and methodology for the performance of school committees within the management of school facilities in Batubara district of Indonesia. The concepts of Community based Facility Management (CbFM) and Logometrix are used as a basis to measure the school committee performance in order to address the needs of quality school management. The data will be taken from questionnaires distributed for those who work and use school facilities spread over seven sub district of Batubara, Indonesia. The result of this study is expected to provide a guide for evaluating the performance of existing school committee in improving the quality of education in Indonesia.

Keywords: community based facility management, School facility management, School committee performance.

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Authors: Sabine A. Zauchner-Studnicka

Abstract:

As the term indicates, reverse-mentoring flips the classical roles of mentoring: In school, students take over the role of mentors for adults, i.e. teachers or parents. Originally reverse-mentoring stems from US enterprises, which implemented this innovative method in order to benefit from the resources of skilled younger employees for the enhancement of IT competences of senior colleagues. However, reverse-mentoring in schools worldwide is rare. Based on empirical studies and theoretical approaches, in this article an implementation model for reverse-mentoring is developed in order to bring the significant potential reverse-mentoring has for education into practice.

Keywords: School education, reverse-mentoring, implementation model, innovation in education.

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Authors: Sumitra Nuanmeesri

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The research focus on study, analyze and design the model of the infrastructure and computer networks for distance education, online learning via new media, e-learning and blended learning. The collected information from study and analyze process that information was evaluated by the index of item objective congruence (IOC) by 9 specialists to design model. The results of evaluate the model with the mean and standard deviation by the sample of 9 specialists value is 3.85. The results showed that the infrastructure and computer networks are designed to be appropriate to a great extent appropriate to a great extent.

Keywords: Blended Learning, New Media, Infrastructure and Computer Network, Tele-Education, Online Learning.

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Authors: Francisco Ben, Tracey Price, Chad Morrison, Victoria Warren, Willy Gollan, Robyn Dunbar, Frank Davies, Mark Sorrell

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This paper focuses particularly on the educational aspects that contribute to the overall educational satisfaction rated by Tabor School of Education students who participated in the Australasian Survey of Student Engagement (AUSSE) conducted by the Australian Council for Educational Research (ACER) in 2010, 2012 and 2013. In all three years of participation, Tabor ranked first especially in the area of overall student satisfaction. By using a single level path analysis in relation to the AUSSE datasets collected using the Student Engagement Questionnaire (SEQ) for Tabor School of Education, seven aspects that contribute to overall student satisfaction have been identified. There appears to be a direct causal link between aspects of the Supportive Learning Environment, Work Integrated Learning, Career Readiness, Academic Challenge, and overall educational satisfaction levels. A further three aspects, being Student and Staff Interactions, Active Learning, and Enriching Educational Experiences, indirectly influence overall educational satisfaction levels.

Keywords: Tertiary student satisfaction, tertiary educational experience, pre-service teacher education, path analysis.

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