Problem formulation. Research competence should be considered as one of the basic components of the training of masters of professional education, in connection with which it is necessary to implement the principle of double entry of the basic component into the system. The main emphasis should be placed on scientific research practice, the purpose of which is to acquire the skills of a teacher-researcher, to master the modern methods of working with scientific information, its analysis, synthesis, generalization, the ability to work with scientific literature, and the ability to solve pedagogical problems in order to use these abilities, skills, abilities, qualities in professional activity. Thus, during the course of scientific research practice, master’s students will develop research competence. The aim of the article is to study the role of scientific research practice of master’s students of pedagogical higher educational institutions in the formation of research competencies, which are most in demand in the master’s professional activity. Materials and methods. To conduct this research, the following methods were applied in a complex: analysis of psychological-pedagogical and methodical literature, systematization and generalization of different views on the formation of research competence in masters of pedagogical universities. Results. The article examines scientific research practice in the master’s degree, defines its goals and objectives, reveals the conditions of its organization and significance in the system of formation of students’ research competence. Attention is paid to the formation of students’ research competencies, first of all at the master’s level and then at the postgraduate level . Research competence is understood as an integrative characteristic of a person, which involves the possession of methodological knowledge, research technology, recognition of their value and readiness to use them in professional activities . Research practice is part of a complex multi-component system of formation of research competence of students in the master’s degree. In the study, the methodological features of conducting scientific-pedagogical practice at master’s degrees are given, and it is found that in the process of scientific-research practice, research competence will be formed in master’s students of pedagogical universities, which will reflect: the graduate’s ability to study, analyze, synthesize scientific literature in the field of professional activity; possessing the skills to optimally choose the methods of scientific research; ability to construct written and oral language in a logically correct, reasoned and clear manner; oratorical abilities, skills of public speaking and competent conversation with opponents; skills in identifying modern problems of professional education and ways to solve them; readiness to work with legislative and educational and regulatory documentation, which is constantly changing; skills of conducting a pedagogical experiment, evaluating and correcting its results; the ability to independently find creative ways to solve non-standard professional Conclusions. Formation of research competence of masters of pedagogical universities implies readiness for innovative professional activity in the field of education. A graduate of the second level of higher education can apply and develop the acquired skills of scientific activity by continuing his studies at the next level - the training of highly qualified personnel, where research competence plays a key role.
Problem formulation. On the basis of the State standard of basic general secondary education , the acquisition by children with special educational needs of high-quality, unified and professional education is considered one of the main and necessary conditions for their successful socialization, ensuring their participation in the life of society, which brings the results of self-realization in various types of professional and social activity. In fact, inclusive education allows to guarantee the socialization of children in a better way than training in correctional and developmental schools. In order to implement this direction to the full extent, updates are needed in teaching methods, in particular, in the teaching of mathematics. The aim of the article is to determine the methodological features of the implementation of level differentiation in the teaching of mathematics to students of primary and secondary schools in the conditions of inclusive education . Materials and methods. To conduct this research, the following methods were applied in a complex: analysis of psychological-pedagogical and methodical literature, systematization and generalization of different views on the methodology of teaching mathematics in conditions of inclusion. Results. On the basis of the analysis of questions regarding the methodical features of the implementation of level differentiation in the teaching of mathematics of secondary school students in the conditions of inclusive education, the main principles on which the organization of the inclusive education system is based were determined, the essence of the concept of «differentiation» in the process of teaching mathematics was examined in detail, and different types of differentiation were distinguished. It is indicated that for the correct application of different-level tasks, the teacher needs to take into account the composition of the contingent of students in inclusive classes, and a scheme for dividing students into groups is provided. Taking into account the composition of students in an inclusive class, the levels of knowledge acquisition are highlighted: advanced level (gifted children and children with a high degree of education); basic level (children of the age norm, children with OOP (with preserved intelligence)); minimally adaptive (children with intellectual disabilities and children with medium or low developmental potential). Depending on the features of students’ perception and processing of information, including those with special educational needs, the following categories are distinguished: audials , visual and kinesthetic . It is described by what signs the above categories can be recognized in the learning process. Methodological features are presented, which can be applied in the preparation of different level tasks of selected levels of knowledge acquisition, taking into account the peculiarities of perception of each level. Conclusions. The application of the presented methodological features in the preparation of tasks, in accordance with the types of information perception by students ( audials , visuals , kinesthetics ) , allows you to organize learning in an inclusive class, involving all students in the process, including children with special educational needs, this element of learning technology helps effectively teach diverse children in the existing
Problem formulation. Problem formulation. At the present stage of the educational system development, information and communication technologies (ICT) play one of the most important roles in the didactic system of the future teacher of mathematics. In the process of preparing a future mathematics teacher it is necessary from the very beginning to prepare students for future professional activities at the same time with professional competencies in terms of educational informatization. One of the effective ways of informatization of mathematics education can be the using of the Internet during the process of teaching mathematical disciplines. Because of the fact that every student cannot imagine his life without the Internet, it is possible to move from passive presentation of material to active through the tools of the Internet, which will significantly increase the interest in learning the discipline and improve learning outcomes. The aim of the article is to analyze the issues of didactic possibilities of ICT tools in mathematical education of future mathematics teachers. Materials and methods. The following methods were used to conduct this research: analysis of psychological and pedagogical and methodological literature, systematization and generalization of different views on determining the main ideas, types and methods of construction, as well as the use of Wiki technology in training future mathematics teachers. Results. Based on the analysis of the didactic possibilities of ICT tools in mathematics education of future mathematics teachers, it was determined that among the large number of Internet resources, the Web 2.0 service deserves special attention. This service is a block of social services (blogs and microblogs (Twitter, Blog, Live Jornal), social networks and social presentation systems (viber, Telegram, Instagram, Facebook), wiki projects (Wikipedia, Wikiversity, Wikibooks, Wiktionary) and management systems content (Moodle, Jomla, etc.); social media repositories (YouTube, etc.)), which allow students not only to receive but also to create information, information resources. For example, a blog in mathematics education can be used as a platform for information exchange, consultation, research and more. An equally interesting resource is the Wiki service, the use of which achieves the greatest effect in the independent work of students in the process of creating educational and research projects. Using Web 2.0 tools it is possible to create small training modules on a specific problem, illustrated with visualized examples with animation. The set of such modules can be a distance learning course that students can access at any time. The author also considers the directions and some possible types of use of Internet services in the training of mathematics teachers. Conclusions. An analysis of the didactic possibilities of ICT in mathematical education of future mathematics teachers showed that among all possible Internet services, Wiki has all main features and capabilities of Web 2.0 technology, and therefore is well suited for organizing an educational network of future maths teachers. Thus, the active use of various Internet services in the process of preparing future mathematics teachers turns the usual learning process into a joint creative activity in which all participants actively cooperate in the process of learning and acquiring new knowledge, which significantly increases the efficiency of education.
The article summarizes the experience of training masters of mathematics for organizing and conducting Mathematics Olympiads for schoolchildren. The purpose of the article is to characterize and summarize the methodological features of the training masters of mathematics for the organization of Mathematics Olympiads for schoolchildren. Among the research methods used, the following were decisive: analysis and generalization of scientific and methodical sources for the theoretical justification of the highlighted problem, modeling, and synthesis of the obtained data. Conclusions. Various possibilities of implementing such training have been analysed by the authors, taking into account the realities of the current state of the educational system of Ukraine. The methodical features of teaching master's students in mathematics to solving and creating mathematics olympiad problems and discrete subjects for schoolchildren are considered in the article. The benefit of the article is that the numerous examples of the implementation of the «to solve a problem – to replicate problems» approach proposed by the authors are presented, and the methodological expediency of its use in the educational process is substantiated. Conclusions. The authors have singled out the promising directions for further research in this field: the creation of appropriate educational and methodological support for the implementation of the approach «learning to solve a problem - learning to replicate problems» within the framework of other content lines of the course «Mathematics Olympiads problems: creation and solution» in the training of masters in mathematics (logical, stochastic, cryptographic, etc.) at pedagogical higher education institutions; the implementation of elements of this approach to the system of practicing teachers professional development the acquaintance high school students who study mathematics in depth with the relevant methods. The indisputable interest is in the creation of masters’ practice-oriented developments, as the part of their educational and research work, aimed at other aspects of the school mathematics education fundamentalization.
The article is devoted to the determination of the peculiarities of the study of mathematical analysis by master's students, future mathematics teachers, at a pedagogical university. The purpose of the article is to identify the main directions of practice-oriented teaching of mathematical analysis to masters of pedagogical higher education institution and to reveal the methods of implementing these directions in practice. In the course of the research such methods were used as an analysis of pedagogical and scientific-methodical literature, textbooks on mathematical analysis, school textbooks, materials of external independent evaluation (EIE), Internet sources; analysis of personal experience in teaching mathematical analysis at a pedagogical higher education institution; observations, conversations, experiment. Results. Currently, education at higher education institutions is based on a credit system, which gives students the prerogative to independently choose special elective courses for further study of subjects, but basic disciplines that are mandatory components, such as mathematical analysis, remain planned and unchanged. The study of mathematical analysis by masters should be oriented towards future professional activity, that is, it is necessary to focus on practice-oriented education when teaching this discipline. Practice-oriented training is considered as a process of assimilation of an educational program by masters with the aim of obtaining practical knowledge, abilities and skills necessary in a professional environment, that is, as a type of training in the process of which the formation and development of students' professional competencies takes place. The goal of practice-oriented training is to help the student «discover» and apply the acquired theoretical knowledge, learn to independently solve problems, adapt to the profession in modern conditions. The practice-oriented orientation of teaching mathematical analysis at pedagogical higher education institutions assumes the formation of students' methodical skills inseparable from subject skills. The article substantiates the role of mathematical analysis in the formation of mathematical competence and methodical literacy of the future teacher of mathematics. Conclusions. In the course of the study, based on the analysis of the content of the discipline «Selected issues of mathematical analysis» and the experience of teaching it at a pedagogical higher educational institution, the directions of master's students’ practice-oriented training this discipline at pedagogical higher educational institutions were highlighted. These include the following: 1) learning to analyse mathematical objects and the conditions in which they are specified; 2) creation of situations of new knowledge «discovery»; 3) organization of master's students' research activities and formation of their relevant skills; 4) organization of work with tests. Each direction is illustrated with examples from the mathematical analysis course.
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