• Communications of Mathematical Education
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• v.21 no.4
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• pp.575-596
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• 2007

This study investigates preservice teachers' development of subject-matter knowledge and pedagogical content knowledge in teaching function concept. This development takes place in the pedagogical mathematics courses in which the theory of constructivism and cooperative learning theory are aligned. Pre and post courses test were administered to examine the development and the follow-up interviews were conducted to gain more details. Analysis of the written questionnaire results and interview transcripts reveal that their limited concept image can be extended and developed in depth through pedagogical mathematics courses that apply reformed teaching methods.

• International Journal of Computer Science & Network Security
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• v.21 no.9
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• pp.173-178
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• 2021

The article reveals the essence of the concept of "pedagogical innovation" and identifies trends in the development of a modern educational institution. A qualitative analysis of the scientific literature in the field of innovation science has been carried out. The essence of the concept of "pedagogical innovation" is revealed. The modern classification of pedagogical innovations is given. The factors of the success of the introduction of pedagogical innovations are determined. The main trends in the development of modern educational institutions are outlined.

• International Journal of Computer Science & Network Security
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• v.22 no.10
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• pp.107-112
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• 2022

Nowadays clusters are recognized as an important instrument for promoting industrial development, innovation, competitiveness and growth. An educational cluster is a set of interrelated vocational educational institutions of various levels that are united by industry with each other and are connected by partnership with industry enterprises. This article attempts to develop and describe cluster model of university students' multilingual training. The purpose of this study is to describe multilingual training of university students and their polycultural competencies formation and to define the process of multilingual training in form of a cluster. The authors consider clusters as an integral part of the educational campus within the concept framework of Shadrinsk State Pedagogical University. To determine the essence of the concept of a cluster model of university students' multilingual training, theoretical, empirical, observational, and diagnostic methods were implemented, such as a review of scientific literature, a compilation of best practices, observation, statistical methods, etc. The authors analyzed the programs of partner universities and organized international webinars and internships for bachelors and masters abroad and developed online courses "Foreign language for undergraduate students and masters". Experimental data obtained during the implementation of cluster training show the effectiveness of the formation of students' polycultural competencies.

• International Journal of Computer Science & Network Security
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• v.21 no.12
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• pp.117-122
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• 2021

The article considers the position of scientists on the concept of "pedagogical technology", identifies the signs of pedagogical technology and existing classifications, considers non-traditional (innovative) learning technologies, as well as their practical forms of application in the educational process, summarizes the results, makes recommendations for the practical application of the studied material. The article considered the basic concepts of pedagogical technology, as well as some types of non-traditional (innovative) teaching technologies. Also, examples of the use of some elements of innovative technologies in practical educational activities are given. The choice of specific non-traditional pedagogical technologies is determined by the target orientation, content specificity, individualization of training, technical equipment of the educational institution, etc.

• Journal of The Korean Association For Science Education
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• v.27 no.8
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• pp.699-710
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• 2007

During the last two decades, many researchers have attempted to understand pedagogical content knowledge (PCK). Now it is time to think about how to apply the theoretical aspects of PCK to practice. In an attempt to address this issue, it is indispensable to review the existing literature on teachers' knowledge bases and PCK. Therefore, the purposes of this paper are to look at how the concept of PCK has been developed and extended over the past two decades as well as to provide a shared understanding of PCK for the practical use of this concept in teacher education programs. The paper begins with a discussion of various models of teachers' knowledge as conceptualized by several renowned researchers, moves on to a review of existing research focusing on the knowledge of science teachers, then examines the literature on PCK as a critical part of teachers' professional knowledge, and finally concludes with an integrated operational definition of PCK that can be employed into designing teacher education programs.

• International Journal of Computer Science & Network Security
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• v.21 no.3
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• pp.21-30
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• 2021

Economic transformations have led to an increase in the role of creative assets and their central role in public life. Changes in creative activity have led to a change in the organization of the work of institutes engaged in the training of specialists, in particular teachers of labor education. Methods and approaches to training determine the development of creative industries, being the basis for models of professional training of future teachers of labor training. The purpose of an article was to develop a modern model of professional training of future teachers of labor training based on the concept of creative economy. The methodology is based on the concepts of holistic craft and creative economy. Based on the integration of pedagogical learning models "Craft as design and problem-solving", "Craft as skill and knowledge building", "Craft as product-making" and "Craft as self-expression" developed and experimentally confirmed the conceptual model of professional training of future teachers of labor training. The proposed model forms a practitioner with professional, technical, digital and creative skills who is able to transfer the experience to students. The training course "Creativity and creative thinking" has been developed. The model provided for the development of a course based on the strategy of developing professional creativity, flexibility, improvisation, openness, student activity, joint practice, student-oriented approach. The practical value implies the adaptation of the developed model of professional training of future teachers of labor education during the training of teachers in higher education, which is confirmed in the experiment.

• International Journal of Computer Science & Network Security
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• v.21 no.6
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• pp.7-10
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• 2021

The article analyzes and concretizes the understanding of the differences between the concepts of competence / competence according to the criterion general - personal. Based on the identified characteristics of competence (completed personal quality, activity character, educational result, successful implementation of professional and educational activities), the concept of competence as an integrative dynamic quality of a person, manifested in effective activity in a specific area, is defined. The structure of the IC has been substantiated, including motivational and value; information technology; communicative and reflective components. The content of the named IC components is disclosed. The article analyzes the essence of the characteristics of basic concepts (competence / competence), consideration of information competence in the research of famous scientists in order to concretize the studied phenomenon; concretization of the identified pedagogical conditions in educational process.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.255-273
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• 2019

In order to help students to understand the essence of prime concepts, this study looked at the history of prime concept development and analyzed how to introduce the concept of textbooks. In ancient Greece, primes were multiplicative atoms. At that time, the unit was not a number, but the development of decimal representations led to the integration of the unit into the number, which raised the issue of primality of 1. Based on the uniqueness of factorization into prime factor, 1 was excluded from the prime, and after that, the concept of prime of the atomic context and the irreducible concept of the divisor context are established. The history of the development of prime concepts clearly reveals that the fact that prime is the multiplicative atom is the essence of the concept. As a result of analyzing the textbooks, the textbook has problems of not introducing the concept essence by introducing the concept of prime into a shaped perspectives or using game, and the problem that the transition to analytic concept definition is radical after the introduction of the concept. Based on the results of the analysis, we have provided several pedagogical implications for helping to focus on a conceptual aspect of prime number.

• Research in Mathematical Education
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• v.3 no.1
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• pp.35-56
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• 1999

The evolution of the function concept was delineated in terms of the 17th and 18th Centuries' dependent nature of function, and the 19th and 20th Centuries' arbitrary and univalent nature of function. According to mathematics educators' beliefs about the value of the function concept in school mathematics, certain definitions of the concept tend to be emphasized. This study discusses three types - genetical (dependence), logical (settheoretical), analogical (machine/equations) - of definition of function and their values.

• International Journal of Computer Science & Network Security
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• v.22 no.11
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• pp.192-198
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• 2022

The article is devoted to current problems of the concept leadership. The essence of the concept of "leadership" is considered and leadership theories. The authors of the article conducted a multifaceted analysis of leadership theories, analyzed the factors of their formation and identified their relationship. Also, the reasons for the difference and connection between leadership and leadership. Styles were presented leadership and their role in building effective leadership. To form the basis of effective leadership was compared to the main criteria inherent in this theories. The following research methods were used in the work: theoretical (analysis of regulatory documents and scientific literature on the problem under study, comparison, generalization, modeling), empirical (diagnostics of the level of formation of managerial competencies of students of the system, questioning, observation, peer review, comparative qualitative and quantitative analysis of diagnostic results the level of formation of managerial competencies).