• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.495-515
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• 2012

This study is to diversely analyze teachers' Pedagogical Content Knowledge (PCK) regarding to the area of plane figures and discuss the consideration for the materialization of the effective class in learning the area of plane figures by identifying the improvements based on problems indicated in PCK. The subjects of inquiry are what the problems with teachers' PCK regarding to the area of plane figures are and how they can be improved. In which is the first domain of PCK, teachers need to fully understand the concept of the area and the properties and classification of the area and length, recognized the sequence structure as a subject of guidance and improve the direction which naturally connects the flow of measurement by using random units in guidance of the area. In which is the second domain of PCK, teachers need to establish understanding of the concept for the area and understanding of a formula as a subject matter object and improve the activity, discovery and research oriented class for students as a guidance method by escaping from teacher oriented expository class and calculation oriented repetitive learning. They also need to avoid the biased evaluation of using a formula and evenly evaluate whether students understand the concept of the area as a performance evaluation method. In which is the third domain of PCK, teachers need to fully understand the concept of the area rather than explanation oriented correction and fundamentally teach students about errors by suggesting the activity to explore the properties of the area and length. They also need to plan a method to reflect student's affective aspects besides a compliment and encouragement and apply this method to the class. In which is the fourth domain of PCK, teachers need to increase the use of random units by having an independent consciousness about textbooks and supplementing the activity of textbooks and restructure textbooks by suggesting problematic situations in a real life and teaching the sequence structure. Also, class groups will need to be divided into an entire group, individual group, partner group and normal group.

• The Mathematical Education
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• v.47 no.2
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• pp.155-168
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• 2008

The theory of representation, which has been an important topic of epistemology, has long history of study. But it has diverse meaning according to the fields of argument. In this paper the author set the meaning of mathematical representation as the interrelation of internal and external representations. With this concept, the following items were studied. 1. Survey on the concepts of mathematical representations. 2. Investigation of pedagogical significance of the mathematical representations, taking into account the characteristics of school mathematics. 3. Recommendation of principles for teaching representation to cope with the problems that are related with cause of disliking each domain of the secondary school mathematics. This study is expected to enable the development of teaching methods to help students strengthening their ability to comprehend mathematical sentences.

• International Journal of Computer Science & Network Security
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• v.21 no.5
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• pp.43-47
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• 2021

In the course of this article, the concept of "innovation" was considered and analyzed, which is considered not only as a subject, something new, but also as a process. The process of introducing something new into life, and in our case, into the educational process. Innovative educational technologies are varied and plentiful. In this article, the most commonly used. Among them: the use of ICT, game techniques, the portfolio method, personality-oriented, information support of the learning process, educational and health-saving technologies, and others.

• International Journal of Computer Science & Network Security
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• v.22 no.12
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• pp.91-97
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• 2022

Analyzing the psychological and pedagogical literature, we showed the interest of researchers in the problem posed. The concept of competence is considered, which is interpreted as giving the key to solving a wide range of educational and life tasks. Research competence implies the ability to cooperate, enter into contacts, readiness for changes, for self-determination and is an integral quality of the individual, expressed in the readiness and ability to independently search for solutions to new problems and creative transformation of reality based on a set of personal and meaningful knowledge, skills, methods of activity and value attitudes.The article offers conditions that certify the improvement of forms and methods of training students in the formation of research competence of future specialists. The use of innovative technologies contributes to improving the level of training of future specialists: students are better prepared for classes, take an active part in the assimilation of program material in laboratory classes. It is noted that this creates a subject-subject relationship between the student and the teacher, and changes the attitude of students to classes. In the process of such organization of educational activities, students are convinced of the need for knowledge and its effectiveness, learn to compare, generalize, classify, establish cause-and-effect relationships, express opinions, defend their point of view, they ensure success in their studies, and develop research competence. It is proved that in order to apply the latest technologies, the teacher himself must know them well, that is, constantly improve himself, master new methods, techniques, ideas, which will help him create new pedagogical technologies and implement them in the educational process.

• Communications of Mathematical Education
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• v.36 no.4
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• pp.589-610
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• 2022

This study aimed to derive pedagogical implications by comparing and analyzing how the concept of pi is taught in 10 different elementary mathematics textbooks, which are scheduled to be applied from 2023. We developed a textbook analysis framework by previous studies on the concept of pi and the teaching of pi, and analyzed in terms of three instructional elements (i.e. inferring conceptsof pi, understanding properties of pi, and applying relationships). We derived the need to emphasize various contexts for estimation of pi, presentation of problem situations that provide motivation to actually measure diameters and circumferences, providing an opportunity to explore the properties of measurement, and an experience the flexibility of selecting an approximate value of pi. Based on the above conclusions and pedagogical implications through the research results., we suggested ways to teach the concept of pi in elementary mathematics and improvement points for developing textbooks focusing on the context of introduction of pi and the use of technological tools.

• International Journal of Computer Science & Network Security
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• v.22 no.9
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• pp.75-82
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• 2022

Analyzing the psychological and pedagogical literature, we found the researchers' interest in the problem posed. The concept of "culture of professional communication» is considered, which is interpreted as the level of realization of creative abilities, exchange of messages, organization of mutual understanding, mutual knowledge in the process of professionally directed interaction between subjects, in which interpersonal relationships arise, manifest and form. The concept of "professional culture of communication of a teacher" is interpreted. The motives that are socially significant in the professional communication of the teacher are highlighted. The necessity of forming a culture of professional communication among students, in particular by means of information technologies in the present, is clarified. The interactive component of professional communication is considered. The types of interactions between people in everyday life (ritual and entertainment interaction, joint purposeful activity, no interaction, game and interpersonal interaction) are identified. Traditional and specific forms and methods of teaching are written out. All interactive technologies carried out by means of information technologies are conventionally divided into four groups, depending on the form of educational activity appropriate for their use (pair (work of the subject with the teacher or peers one on one by means of Information Technologies); frontal (the teacher simultaneously teaches a group of subjects by means of Information Technologies); group or cooperative (all subjects teach each other by means of Information Technologies); individual (independent work of the subject using Information Technologies)). In the higher education institution, future specialists should learn knowledge, acquire skills on the basic rules of the culture of professional communication and methods of interaction and their effective use, which is possible with the use of Information Technologies. Recommendations for optimal professional communication have been developed that help you express your thoughts easily and beautifully, and conduct a dialogue in a relaxed and harmonious way.

• East Asian mathematical journal
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• v.28 no.2
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• pp.135-158
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• 2012

The ideals of the rings of integers are used to induce rational number system as operators(=group homomorphisms). We modify this inducing method to be effective in teaching rational numbers in secondary school. Indeed, this modification provides a nice model for explaining the equality property to define addition and multiplication of rational numbers. Also this will give some explicit ideas for students to understand the concept of 'field' efficiently comparing with the integer number system.

• International Journal of Computer Science & Network Security
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• v.22 no.9
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• pp.123-130
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• 2022

Modernization of the educational sector requires globalization, democratization, and the transition to an information technology society. The main goal of education at the present stage is to solve the problem of ensuring the priority of the development of education and science. In modern conditions, the quality of training of qualified specialists is becoming particularly relevant. The great role of teacher education is emphasized by its main goal, which is to train specialists who can ensure the versatile and innovative development of a person as a person and the highest value of society, its mental, physical and aesthetic abilities, high moral qualities, and, consequently, the enrichment on this basis of the intellectual, creative and cultural potential of the people. Among the strategic tasks of modernizing higher education is to ensure informatization of the educational process and access to International Information Systems. The essence of the concept of multimedia is clarified. In the context of media education, multimedia lists a number of functions: informational, interpretive, cultural, entertainment, and educational. The need to meet the needs outlined in the article in the conditions of informatization of the educational process requires the teacher to have knowledge and skills in the field of multimedia pedagogical technologies, knowledge of advanced methods and means of modern science. It is considered what relevant concepts of media education have been developed and are being developed in Ukraine and form an important basis for the modernization of education, which will contribute to the construction of an information society in the country and the formation of civil society. Distance learning is considered - the most democratic form of education that allows broad segments of society to get an education. Distance learning methods are used in higher education institutions, in school education, in the system of advanced training of teachers, in the system of training managerial personnel.

• International Journal of Computer Science & Network Security
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• v.22 no.8
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• pp.97-104
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• 2022

European integration processes have acted as a catalyst for the emergence of a new type of educational environment, which is characterized by competent flexibility of specialists. Therefore, the article focuses on professional training of teachers in the context of European integration processes using information technology and the search for innovative methods of training specialists. One of the educational priorities in Europe is to create a new model of a teacher who has an academic education, knows innovative methods, is able to perform functions and tasks efficiently and professionally, adequately, quickly and correctly respond to changes and innovations. The tasks facing education in the European dimension are formulated. The main trends in the education of teachers in modern Europe are described: the need to deepen and expand subject training programs in pedagogical institutions of Higher Education, which will allow autonomy of activity, awareness of responsibility for independent creative decisions, create favorable conditions for the development of professionalism through the use of Information Technology and the search for innovative methods of training specialists. At the present stage, various models of teacher training are being developed based on the University and practical concept using information technology and searching for innovative methods of training specialists. On this basis, two different theories of perception of teacher education were formed: as preparation of teachers for work throughout their professional career; as preparation for the first years of professional work, which is periodically repeated in the process of continuous professional training and improvement. Among the advantages that the use of Information Technology and the search for innovative methods of training specialists to implement the learning process, it is worth mentioning the following: simultaneous use of several channels of perception of the student or student in the learning process, thanks to which the integration of information processed by different sensory organs is achieved; the ability to simulate complex real experiments; visualization of abstract information by dynamic representation of processes, etc.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.27-51
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• 2012

This paper analyzed the pedagogical content knowledge (PCK) presented in three novice teachers' mathematics instruction. PCK was analyzed in terms of the knowledge of mathematics content, the knowledge of students' understanding, and the knowledge of teaching methods. Teacher A executed a concept-oriented instruction with manipulative materials because she had difficulties in learning mathematics during her childhood. Teacher B attempted to implement an inquiry-centered instruction in the lesson of looking for the area of a trapezoid. Teacher C focused on the real-life connection to mathematics instruction. There were substantial differences among the teachers' PCK revealed in mathematics teaching, depending on their instructional goals. The detailed analyses of three teachers' teaching in terms of their PCK will give rise to the issues and suggestions of professional development for beginning elementary school teachers in mathematics teaching.