In the presented work, the concept of mathematical abilities is rational as both an essential internal characteristic of mathematical competence and an immanent attribute that prevails in its personal and psychological dimension. In view of the spatial Cartesian implementation the role and place of mathematical abilities in the three-dimensional structure of the internal manifestation of mathematical competence are substantiated. The semantic and system analysis of structural components of the studied phenomenon is made. It is established that complex correlations of four structural components of mathematical abilities (system-forming, coding-formalized, cognitive-generalizing, mnemonic-generalizing) can exist with three dimensions of the external manifestation of mathematical competence (semantic-theoretical, procedural-active, personal-psychological). It is introduced that the development of mathematical abilities is provided by updating the external dimensions of mathematical competence in educational and mathematical activities. The method of developing the mathematical abilities of students is presented according to the results of the implementation of this idea and the principle of developmental continuity. The basis of this technique is the developmental-problem method of teaching mathematics as a four-level problem structure which embodies the methods of mathematical and educational (educational-theoretical) modeling, the method of ascent from the abstract to the concrete, provides a reflection of the process and results of educational and mathematical activities. Due to the problem raised in the work the authors highlight the content and results of a pilot study on the development of mathematical abilities of future mathematics teachers (freshmen and graduates). The effectiveness of the created developmental methods of mathematical education was experimentally tested.
The article deals with theoretical fundamentals of the communicative-activity approach to mastering foreign languages as well as methods of its implementation under conditions of distance learning. Authors of the publication share the practical experience of distance work with freshmen of the Zhytomyr Polytechnic State University, foreign students studying the Ukrainian language. The publication considers problems that arise at the initial stage of learning a foreign language regardless of the language studied. The particular importance is attached to the following issues: the language divide, its types, reasons of its occurrence and ways to overcome it; typical mistakes made by students in the process of distance learning of reading and writing, as well as ways and methods for their prevention and elimination; the methodology for pronunciation training. The authors of the article tend to consider the usage of podcasts, mental maps and communicatively oriented authentic textbooks to be the most effective methods of distance work. The article provides the description of textbooks which are focused on the communicative-activity approach to the language learning and enable to essentially achieve the educational goal during the distance learning process. The publication emphasizes that of the four types of speech activity - speaking, writing, reading, listening – reaching the first one is especially challenging in the distance learning process. The joint use of exercises from the textbook and the students’ involvement in real speech situations is successful for developing speaking skills. The authors propose patterns of real speech situations, describe their content and methodology of their application. They also vividly prove the effectiveness of using podcasts, mental maps, and authentic textbooks in the language learning process.
The article reveals the main factors in the development of inclusive education in the Nordic countries. It is noted that society's attitude towards children with special educational needs can be both motivating and creating serious barriers to the implementation of inclusive education. It is determined that in order to remove the problem of segregation and intensify inclusion, it is necessary not only to have the appropriate tools to work, but also the opportunity to improve their professional knowledge and skills. The authors note that the development of education in the Scandinavian countries is a continuous process of reform, which began at the end of World War II and continues to this day. Analyzing the factors of development of inclusive education in different countries of the world, the authors claim that they have common conceptual and semantic characteristics. Based on the analysis of scientific sources and various experiences of the leading factors in the development of inclusion in the education system, such factors for the Scandinavian countries are identified as socio-economic, socio-political, socio-cultural and organizational. It is emphasized that the multidimensional definition of inclusive education, which combines school culture, policies, implementation practices, tangible and intangible resources, creates the basis for the quality of inclusive education. It is noted that a special place in the general concept of inclusive education is given to human resources, its training and retraining. It is established that another element of the success of inclusion is the involvement of families in the educational process. It is concluded that the path taken by the Nordic countries in the implementation of inclusive education is worthy of attention and imitation.
The article is devoted to the actual problem of studying the importance of online education resources for expanding the prospects of attracting future specialists to innovative activities in the field of social work. The necessity of using online courses in the context of self-educational activities of students as a characteristic feature of blended learning in the higher education system is proved. The expediency of mass open online courses for improval of the effectiveness of training social workers is determined. Attention is focused on the fact that online courses help to expand the opportunities for attracting students to provide innovative social services to various categories of clients, thereby acting as a factor of enriching their professional experience and increasing the resource potential for training social workers. The purpose of the article is to reveal the prospects of attracting students to provide innovative social services and opportunities to enrich their professional experience and increase the resource potential of training social workers through the use of mass open online courses. To achieve the goal and solve the problems of the study, theoretical, empirical and statistical methods of data synthesis and processing were used, the features of enriching professional experience in the field of social work were analyzed, and the possibilities of increasing the resource potential of training social workers through the use of mass open online courses were clarified. The importance of self-educational activities of students receiving education in the field of Social Work and the heterogeneity of online courses are confirmed. It is proved that expanding the resource potential of training social workers will help to attract future social workers to provide innovative social services to various categories of clients. The novelty of the study is to determine the prospects and opportunities of mass open online courses to expand the resource potential of training social workers for innovation and meet the self-educational needs of students.
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