Search results for: mathematics and science education

Authors: Gang Chen, Ruimin Shen

Abstract:

This paper presented a collaborative education model, which consists four parts: collaborative teaching, collaborative working, collaborative training and interaction. Supported by an e-learning platform, collaborative education was practiced in a data structure e-learning course. Data collected shows that most of students accept collaborative education. This paper goes one step attempting to determine which aspects appear to be most important or helpful in collaborative education.

Keywords: Collaborative work, education, data structures.

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Authors: Ali Kartal

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According to the new developments in the field of information and communication technologies, the necessity arises for active use of these new technologies in education. It is clear that the integration of technology in education system will be different for primary-higher education or traditional- distance education. In this study, the subject of the integration of technology for distance education was discussed. The subject was taken from the viewpoint of students. With using the information of student feedback about education program in which new technological medias are used, how can survey variables can be separated into the factors as positive, negative and supporter and how can be redesigned education strategy of the higher education associations with the examining the variables of each determinated factor is explained. The paper concludes with the recommendations about the necessitity of working as a group of different area experts and using of numerical methods in establishing of education strategy to be successful.

Keywords: Distance education, student feedback, working as a group, numerical methods.

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Authors: M. Rodionov, Z. Dedovets

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This article discusses plausible reasoning use for solution to practical problems. Such reasoning is the major driver of motivation and implementation of mathematical, scientific and educational research activity. A general, practical problem solving algorithm is presented which includes an analysis of specific problem content to build, solve and interpret the underlying mathematical model. The author explores the role of practical problems such as the stimulation of students' interest, the development of their world outlook and their orientation in the modern world at the different stages of learning mathematics in secondary school. Particular attention is paid to the characteristics of those problems which were systematized and presented in the conclusions.

Keywords: Mathematics, motivation, secondary school, student, practical problem.

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Authors: Yasuhito Tanaka

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We examine the maximum theorem by Berge from the point of view of Bishop style constructive mathematics. We will show an approximate version of the maximum theorem and the maximum theorem for functions with sequentially locally at most one maximum.

Keywords: Maximum theorem, Constructive mathematics, Sequentially locally at most one maximum.

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Authors: Leandro Marcos Alves Vaz

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The teaching of physics in Brazilian public schools emphasizes strongly the theoretical aspects of this science, showing its philosophical and mathematical basis, but neglecting its experimental character. Perhaps the lack of science laboratories explains this practice. In this work, we present a method of teaching physics using the computer. As alternatives to real experiments, we have the trials through simulators, many of which are free software available on the internet. In order to develop a study on the use of simulators in teaching, knowing the impossibility of simulations on all topics in a given subject, we combined these programs with phenomenological and/or experimental texts in order to mitigate this limitation. This study proposes the use of simulators and the debate using phenomenological/experimental texts on electrostatic theme in groups of the 3rd year of EJA (Adult and Youth Education) in order to verify the advantages of this methodology. Some benefits of the hybridization of the traditional method with the tools used were: Greater motivation of the students in learning, development of experimental notions, proactive socialization to learning, greater easiness to understand some concepts and the creation of collaborative activities that can reduce timidity of part of the students.

Keywords: Physics teaching, simulators, youth and adult education, experimentation, electrostatic.

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Authors: Yasar Guneri Sahin, Mehmet Cudi Okur

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In this presentation, we discuss the use of information technologies in the area of special education for teaching individuals with learning disabilities. Application software which was developed for this purpose is used to demonstrate the applicability of a database integrated information processing system to alleviate the burden of educators. The software allows the preparation of individualized education programs based on the predefined objectives, goals and behaviors.

Keywords: Special education, disabled individual, informationtechnology, individual education programs.

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Authors: Bilgehan Gültekin, Tuba Gültekin

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Universities have an important role in social education in many aspects. In terms of creating awareness and convincing public about social issues, universities take a leading position for public. The best way to provide public support for social education is to develop public communication campaigns. The aim of this study is to present a public communication model which will be guided in social education practices. The study titled “Importance of public communication campaigns and art activities in Social Education “is based on the following topics: Effects of public communication campaigns on social education, Public relations techniques for education, communication strategies, Steps of public relations campaigns in social education, making persuasive messages for public communication campaigns, developing artistic messages and organizing art activities in social education. In addition to these topics, media planning for social education, forming a team as campaign managers, dialogues with opinion leaders in education and preparing creative communication models for social education will be taken into consideration. This study also aims to criticize social education Case studies in Turkey. At the same time, some communicative methods and principles will be given in the light of communication campaigns within the context of this notice.

Keywords: Art activities in social education, Persuasive communication, Public communication campaigns, Public relations techniques for education

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Authors: Xun Ge

Abstract:

Recently, X. Ge and J. Qian investigated some relations between higher mathematics scores and calculus scores (resp. linear algebra scores, probability statistics scores) for Chinese university students. Based on rough-set theory, they established an information system S = (U,CuD,V, f). In this information system, higher mathematics score was taken as a decision attribute and calculus score, linear algebra score, probability statistics score were taken as condition attributes. They investigated importance of each condition attribute with respective to decision attribute and strength of each condition attribute supporting decision attribute. In this paper, we give further investigations for this issue. Based on the above information system S = (U, CU D, V, f), we analyze the decision rules between condition and decision granules. For each x E U, we obtain support (resp. strength, certainty factor, coverage factor) of the decision rule C —>x D, where C —>x D is the decision rule induced by x in S = (U, CU D, V, f). Results of this paper gives new analysis of on higher mathematics scores for Chinese university students, which can further lead Chinese university students to raise higher mathematics scores in Chinese graduate student entrance examination.

Keywords: Rough set, support, strength, certainty factor, coverage factor.

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Authors: Lee Bih Ni, Nurul Asyikin Binti Hassan

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This paper discusses the use of mnemonic and mathematical methods in enhancing the understanding of history. Mnemonics can help students from all levels including high school and in various disciplines including language, math and history. At the secondary level, students are exposed to various courses that require them to remember many facts that can be mastered through the application of mnemonic techniques. Researchers use narrative literature studies to illustrate the current state of art and science in the field of research focused. Researchers used narrative literature reviews to build a scientific base of knowledge. Researchers gather all the key points in the discussion, and put it here by referring to the specific field where the paper is essentially based. The findings suggest that the use of mnemonic techniques can improve the individual's memory by adding little effort. In implementing mnemonic techniques, it is important to integrate mathematics and history in the course as both are interconnected as mathematics has shaped our history and vice versa. This study shows that memory skills can actually be improved; the human mind can remember something more than expected.

Keywords: Cognitive strategy, mnemonic technique, secondary school level study, mathematical mnemonic.

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Authors: Elham Shirvani–Ghadikolaei, Seyed Mahdi Sajjadi

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State of the art technology has the tremendous impact on our life, in this situation education system have been influenced as well as. In this paper, tried to compare two space of learning text and hypertext with each other, and some challenges of using hypertext in religious education. Regarding the fact that, hypertext is an undeniable part of learning in this world and it has highly beneficial for the education process from class to office and home. In this paper tried to solve this question: the consequences and challenges of applying hypertext in religious education. Also, the consequences of this survey demonstrate the role of curriculum designer and planner of education to solve this problem.

Keywords: Hyper-textual, education, religious text, religious education.

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Authors: Fatimah Alsaleh, Glenda Anthony

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The practicum experience is a critical component of any initial teacher education (ITE) course. As well as providing a near authentic setting for pre-service teachers (PSTs) to practice in, it also plays a key role in shaping their perceptions and sense of preparedness. Nevertheless, merely including a practicum period as a compulsory part of ITE may not in itself be enough to induce feelings of preparedness and efficacy; the quality of the classroom experience must also be considered. Drawing on findings of a larger study of secondary and intermediate level mathematics PSTs’ sense of preparedness to teach, this paper examines the influence of the practicum experience in particular. The study sample comprised female mathematics PSTs who had almost completed their teaching methods course in their fourth year of ITE across 16 teacher education programs in Saudi Arabia. The impact of the practicum experience on PSTs’ sense of preparedness was investigated via a mixed-methods approach combining a survey (N = 105) and in-depth interviews with survey volunteers (N = 16). Statistical analysis in SPSS was used to explore the quantitative data, and thematic analysis was applied to the qualitative interviews data. The results revealed that the PSTs perceived the practicum experience to have played a dominant role in shaping their feelings of preparedness and efficacy. However, despite the generally positive influence of practicum, the PSTs also reported numerous challenges that lessened their feelings of preparedness. These challenges were often related to the classroom environment and the school culture. For example, about half of the PSTs indicated that the practicum schools did not have the resources available or the support necessary to help them learn the work of teaching. In particular, the PSTs expressed concerns about translating the theoretical knowledge learned at the university into practice in authentic classrooms. These challenges engendered PSTs feeling less prepared and suggest that more support from both the university and the school is needed to help PSTs develop a stronger sense of preparedness. The area in which PSTs felt least prepared was that of classroom and behavior management, although the results also indicated that PSTs only felt a moderate level of general teaching efficacy and were less confident about how to support students as learners. Again, feelings of lower efficacy were related to the dissonance between the theory presented at university and real-world classroom practice. In order to close this gap between theory and practice, PSTs expressed the wish to have more time in the practicum, and more accountability for support from school-based mentors. In highlighting the challenges of the practicum in shaping PSTs’ sense of preparedness and efficacy, the study argues that better communication between the ITE providers and the practicum schools is necessary in order to maximize the benefit of the practicum experience.

Keywords: Mathematics, practicum experience, pre-service teachers, sense of preparedness.

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Authors: Kew-Cheol Shim, Sung-Hwan Moon, Ji-Hyon Kil, Kyoungho Kim

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The purpose of this paper was to examine views of secondary school science teachers about purposes to use practical works in school science. The instrument to survey consisted eighteen items, which were categorized into four components as follows: ‘Scientific inquiry’, ‘Scientific knowledge’, ‘Science-related attitude’, and ‘STS (science-technology-society)’. Subjects were 152 secondary school science teachers (male 70 and female 82; middle school 50 and high school 102), who are teaching in 42 schools of 8 provinces. On the survey, science teachers were asked to answer on 5-point Lickert scale (from 1 to 5) how they thought of using practical works on purposes with domains of science objectives in school. They had positive views about using practical works for improving scientific inquiry process skills, science-related attitudes, and perceptions about STS literacy, and acquiring scientific knowledge. They would have the most willingness of using practical works for ‘Scientific Inquiry’ among domains of science objectives in school.

Keywords: Secondary school, science teacher, practical work, scientific inquiry, scientific knowledge, science-related attitude, STS.

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Authors: M. D. Nghiteke, A. Mji, G. T. Molepo

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Inclusive education stems from a philosophy and vision, which argues that all children should learn together at school. It is not only about treating all pupils in the same way. It is also about allowing all children to attend school without any restrictions. Ten primary school teachers in a circuit in Namibia volunteered to participate in face-to-face interviews about inclusive education. The teachers responded to three questions about their (i) understanding of inclusive education; (ii) whether inclusive education was implemented in primary schools; and (iii) whether they were able to work with learners with special needs. Findings indicated that teachers understood what inclusive education entailed; felt that inclusive education was not implemented in their primary schools, and they were unable to work with learners with special needs in their classrooms. Further, the teachers identified training and resources as important components of inclusive education. It is recommended that education authorities should perhaps verify the findings reported here as well as ensure that the concerns raised by the teachers are addressed.

Keywords: Classrooms and schools, inclusive education, resources, training.

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Authors: Alexandra M. Kriofske Mainella

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This paper will examine the need for more aggressive public policies around bodily, reproductive and sexual health education for young people with disabilities in the United States. This paper will consider the policies around sexuality education for students in the United States and the recommendation for national standards around sexuality education. We will investigate the intersection of these policies and recommendations for students with disabilities and the Individuals with Disabilities Education Act (IDEA): what this means for students with disabilities’ access to comprehensive sexuality education and how it affects their behaviors and outcomes.

Keywords: Disability, sexuality, education, policy.

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Authors: A. Meydanlioglu, F. Arikan

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In recent years, thanks to the development of information and communication technologies, the computer and internet have been used widely in higher education. Internet-based education is impacting traditional higher education as online components increasingly become integrated into face- to- face (FTF) courses. The goal of combined internet-based and traditional education is to take full advantage of the benefits of each platform in order to provide an educational opportunity that can promote student learning better than can either platform alone. Research results show that the use of hybrid learning is more effective than online or FTF models in higher education. Due to the potential benefits, an increasing number of institutions are interested in developing hybrid courses, programs, and degrees. Future research should evaluate the effectiveness of hybrid learning. This paper is designed to determine the impact of hybrid learning on higher education.

Keywords: E-learning, higher education, hybrid learning, online education.

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Authors: Jayson G. Balansag

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An integrated biology and chemistry (iBC) course for freshmen college students was developed in University of Delaware. This course will prepare students to (1) become interdisciplinary thinkers in the field of biology and (2) collaboratively work with others from multiple disciplines in the future. This paper documents and describes the implementation of the course. The information gathered from reading literature, classroom observations, and interviews were used to carry out the purpose of this paper. The major goal of the iBC course is to align the concepts between Biology and Chemistry, so that students can draw science concepts from both disciplines which they can apply in their interdisciplinary researches. This course is offered every fall and spring semesters of each school year. Students enrolled in Biology are also enrolled in Chemistry during the same semester. The iBC is composed of lectures, laboratories, studio sessions, and workshops and is taught by the faculty from the biology and chemistry departments. In addition, the preceptors, graduate teaching assistants, and studio fellows facilitate the laboratory and studio sessions. These roles are interdependent with each other. The iBC can be used as a model for higher education institutions who wish to implement an integrated biology course.

Keywords: Integrated biology and chemistry, integration, interdisciplinary research, new biology, undergraduate science education.

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Authors: Takatoshi Ishii, Koji Kimita, Keiichi Muramatsu, Yoshiki Shimomura

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To increase the quality of learning, teacher and learner need mutual effort for realization of educational value. For this purpose, we need to manage the co-creational education among teacher and learners. In this research, we try to find a feature of co-creational education. To be more precise, we analyzed learners’ reports by natural language processing, and extract some features that describe the state of the co-creational education.

Keywords: Co-creational education, e-portfolios, ICT integration, labeled Latent Dirichlet allocation.

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Authors: Altynai Zhaitapova, Aizhan Satyvaldiyeva

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In this article the authors investigate the main tendencies of development of the management in the education system of the Republic of Kazakhstan: problems, solutions and development of the education system of Kazakhstan in the realities of globalization.

Keywords: Change management, education, globalization, innovations management systems, quality of education.

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Authors: Herruzo E., Espejo R.A., Moreno R., González C., Benavides J.I., Plata, O.

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This paper aims to explain the project carried out at the University of Cordoba, specifically at the High Polytechnic School in collaboration with two other organizations belonging to the Andalusian Ministry of Innovation, Science and Business: Andalusian Innovation and Development Agency (IDEA agency) [1] and the Territorial Net of Entrepreneurship Support (in Spanish Red Territorial de Apoyo al Emprendedor) [11]. The project is being developed in several stages of which only the first one has already been completed. However, several important preliminary results derive from it, based mainly in the description of the nature of entrepreneurship in the field of university education and its impact on student-s competency as recommended by the European Higher Education Area. Some problems holding back the correct future development will also be shown as derived from the specific context of application of the project.

Keywords: EHEA, Entrepreneurship, Innovation, TransversalCompetence.

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Authors: Shivangi Agrawal, Hsiu-I Ting

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Entrepreneurship is an essential source of economic growth and a prominent factor influencing socio-economic development. Entrepreneurship education educates and enhances entrepreneurial activity. This study aims to understand current trends in entrepreneurship education and evaluate the effectiveness of diverse entrepreneurship education programs. An increasing number of universities offer entrepreneurship education courses to create and successfully continue entrepreneurial ventures. Despite the prevalence of entrepreneurship education, research studies lack inconsistency about the effectiveness of entrepreneurship education to promote and develop entrepreneurship. Strategies to develop entrepreneurial attitudes and intentions among individuals are hindered by a lack of understanding of entrepreneurs' educational purposes, components, methodology, and resources required. Lack of adequate entrepreneurship education has been linked with low self-efficacy and lack of entrepreneurial intent. Moreover, in the age of digitisation and during the COVID-19 pandemic, digital learning platforms (e.g. online entrepreneurship education courses and programs) and other digital tools (e.g. digital game-based entrepreneurship education) have become more relevant to entrepreneurship education. This paper contributes to the continuation of academic literature in entrepreneurship education by evaluating and assessing current trends in entrepreneurship education programs, leading to better understanding to reduce gaps between entrepreneurial development requirements and higher education institutions.

Keywords: entrepreneurship education, digital technologies, academic entrepreneurship, COVID-19

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Authors: Hassan Attahiru Gwandu

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This study aims at surveying and analyzing the contribution of Sokoto scholars or Sokoto Caliphate in the development of science and technology in West Africa. Today, it is generally accepted that the 19^th century Islamic revivalism in Hausaland was a very important revolution in the history of Hausa society and beyond. It is therefore, as a result of this movement or Jihad; the Hausaland (West Africa in general) witnessed several changes and transformations. These changes were in different sectors of life from politics, economy to social and religious aspect. It is these changes especially on religion that will be given considerations in this paper. The jihad resulted is the establishment of an Islamic state of Sokoto Caliphate, the revival Islam and development of learning and scholarship. During the existence of this Caliphate, a great deal of scholarship on Islamic laws were revived, written and documented by mostly, the three Jihad leaders; Usmanu Danfodiyo, his brother Abdullahi Fodiyo and his son Muhammad Bello. The trio had written more than one thousand books and made several verdicts on Islamic medicine. This study therefore, seeks to find out the contributions of these scholars or the Sokoto caliphate in the development of science in West Africa.

Keywords: Sokoto Caliphate, scholarship, science and technology, West Africa.

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Authors: Sophie Huck, Knut Linke

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This study will examine how IT practitioners can be motivated for IT studies and which kind of support they need during their occupational studies. Within this research project, the challenge of supporting students being engaged in business for several years arose. Here, it is especially important to successfully guide them through their studies. The problem of this group is that they finished their school education years ago. In order to gather first experiences, preliminary e-learning courses were introduced and tested with a group of users studying General Management. They had to work with these courses and have been questioned later on about their approach to the different methods. Moreover, a second group of potential students was interviewed with the help of online questionnaires to give information about their expectations regarding extra occupational studies. We also want to present best practices and cases in e-education in the subarea of mathematics and distance learning. Within these cases and practices, we use state of the art systems and technologies in e-education to find a way to increase teaching quality and the success of students. Our research indicated that the first group of enrolled students appreciated the new preliminary e-learning courses. The second group of potential students was convinced of this way of learning as a significant component of extra occupational studies. It can be concluded that this part of the project clarified the acceptance of the e-learning strategy by both groups and led to satisfactory results with the enrolled students.

Keywords: E-learning evaluation, self-learning, virtual classroom, virtual learning environments.

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Authors: L. Vujičić, Ž. Ivković, Ž. Boneta

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There is a widespread belief in everyday discourse that science subjects (physics, chemistry and biology) are, along with math, the most difficult school subjects in the education of an individual. This assumption is usually justified by the following facts: low GPA in these subjects, the number of pupils who fail these subjects is high in comparison to other subjects, and the number of pupils interested in continuing their studies in the fields with a focus on science subjects is lower compared to non-science-oriented fields. From that perspective, the project: “Could it be different? How do children explore it?” becomes extremely interesting because it is focused on young children and on the introduction of new methods, with aim of arousing interest in scientific literacy development in 10 kindergartens by applying the methodology of an action research, with an ethnographic approach. We define scientific literacy as a process of encouraging and nurturing the research and explorative spirit in children, as well as their natural potential and abilities that represent an object of scientific research: to learn about exploration by conducting exploration. Upon project completion, an evaluation questionnaire was created for the parents of the children who had participated in the project, as well as for those whose children had not been involved in the project. The purpose of the first questionnaire was to examine the level of satisfaction with the project implementation and its outcomes among those parents whose children had been involved in the project (N=142), while the aim of the second questionnaire was to find out how much the parents of the children not involved (N=154) in this activity were interested in this topic.

Keywords: Documenting, early childhood education, evaluation questionnaire for parents, scientific literacy development.

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Authors: Correa Arias, César

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Today, Higher Education in a global scope is subordinated to the greater institutional controls through the policies of the Quality of Education. These include processes of over evaluation of all the academic activities: students- and professors- performance, educational logistics, managerial standards for the administration of institutions of higher education, as well as the establishment of the imaginaries of excellence and prestige as the foundations on which universities of the XXI century will focus their present and future goals and interests. But at the same time higher education systems worldwide are facing the most profound crisis of sense and meaning and attending enormous mutations in their identity. Based in a qualitative research approach, this paper shows the social configurations that the scholars at the Universities in Mexico build around the discourse of the Quality of Education, and how these policies put in risk the social recognition of these individuals.

Keywords: Higher education, quality of education, social recognition, social configurations.

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Authors: Anita Kéri

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With the outbreak of the global pandemic of COVID-19, online education characterizes today’s higher education. For some higher education institutions (HEIs), the shift from classroom education to online solutions was swift and smooth, and students are continuously asked about their experience regarding online education. Therefore, there is a growing emphasis on student satisfaction with online education, a field that had emerged previously, but has become the center of higher education and research interest today. The aim of the current paper is to give a brief overview of the tools used in the online education of marketing-related classes at the examined university and to investigate student satisfaction with the applied teaching methodologies with the tool of a questionnaire. Results show that students are most satisfied with their teachers’ competences and preparedness, while they are least satisfied with online class quality, where it seems that further steps are needed to be taken.

Keywords: Online teaching, pandemic, satisfaction, students.

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Authors: C. Ardil

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This paper presents the open science philosophy and paradigm of scientific research on how to transform classical research and innovation approaches. Open science is the practice of providing free and unrestricted online access to the products of scholarly research. Open science advocates for the immediate and unrestricted online access to published, peer-reviewed research in digital format. Open science research is made available for free in perpetuity and includes guidelines and/or licenses that communicate how researchers and readers can share and re-use the digital content. The emergence of open science has changed the scholarly research and publishing landscape, making research more broadly accessible to academic and non-academic audiences alike. Consequently, open science philosophy and its practice are discussed to cover all aspects of cyberscience in the context of research and innovation excellence for the benefit of global society.

Keywords: Open science, open data, open access, cyberscience , cybertechnology.

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Authors: Mehmet Durnali

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The main purpose of this study is to find out, analyze and discuss basic principles of education and training in the constitutions, including the latest amendment, of France, Indonesia, Japan, South Africa, the United States of America, and Turkey. This research specifically aims at establishing a framework in order to compare educational values such as right of education, responsibilities of states and those of people, and other issues pertaining to education in the Constitution of Turkey to others. Additionally, it emphasizes the meaning of education in constitution, the reasons for references to education in constitutions and why it is important for people, states or nations and state organs. Qualitative analysis technique is performed to accomplish the aim of this study. Maximum variation sampling is used. The main data source of the analysis is official organic laws of those countries. The data is examined by using descriptive and content analysis method.

Keywords: Education in the constitution, education law, legal principles of education, right to education.

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Authors: S. Rawashdi, D. Bshouty

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This paper aimed at discussing how to urge middle and high school Arab students in Israel to be aware of the importance of and investing in learning mathematics. In the first phase of the study, three questionnaires were passed to two nine-grade classes, one on Awareness, one on Awakeness and one on Learning. One of the two classes was an outstanding class from a public school (PUBS) of 31 students, and the other a heterogeneous class from a private school (PRIS) with 31 students. The Learning questionnaire which was administrated to the Awareness and Awareness topics was passed to PRIS and the Awareness and Awareness Questionnaires were passed to the PUBS class After two months we passed the post-questionnaire to both classes to validate the long-term impact of the study. The findings of the study show that awakeness and awareness processes have an effect on the math learning process, on its context in students' daily lives and their growing interest in learning math.

Keywords: Awakeness, awareness, learning mathematics, pupils.

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Authors: Pelin Yildiz

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The term interactive education indicates the meaning related with multidisciplinary aspects of distance education following contemporary means around a common basis with different functional requirements. The aim of this paper is to reflect the new techniques in education with the new methods and inventions. These methods are better supplied by interactivity. The integration of interactive facilities in the discipline of education with distance learning is not a new concept but in addition the usage of these methods on design issue is newly being adapted to design education. In this paper the general approach of this method and after the analysis of different samples, the advantages and disadvantages of these approaches are being identified. The method of this paper is to evaluate the related samples and then analyzing the main hypothesis. The main focus is to mention the formation processes of this education. Technological developments in education should be filtered around the necessities of the design education and the structure of the system could then be formed or renewed. The conclusion indicates that interactive methods of education in design issue is a meaning capturing not only technical and computational intelligence aspects but also aesthetical and artistic approaches coming together around the same purpose.

Keywords: Interactive education, distance learning, designeducation, computational intelligence.

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Authors: Belkacem Meziane

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The original 3D Lorenz-Haken equations -which describe laser dynamics- are converted into 2-second-order differential equations out of which the so far missing mathematics is extracted. Leaning on high-order trigonometry, important outcomes are pulled out: A fundamental result attributes chaos to forbidden periodic solutions, inside some precisely delimited region of the control parameter space that governs self-pulsing.

Keywords: chaos, Lorenz-Haken equations, laser dynamics, nonlinearities

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