The relevance of the present research is defined by the necessity of improvement of methodical training of mathematics teacher in a higher educational institution on the basis of multi-component diagnostics of competencies which represent the multidimensional result of education. Such diagnostics is preferable to be carried out by means of multidimensional vectors which allow not only assessing the educational process from different points of view but also predicting correction of its problematic zones. Purpose of the article is to develop vector method for diagnostics of future mathematics teachers' methodic competencies. The proposed method of vector modeling promotes qualitative and quantitative assessment of the results of methodical training of future mathematics teacher from the point of view of intensity (by means of absolute characteristics) and orientation (in relation to cognitive, activity or value-based components). The article determines such directions of the model of mathematics teacher methodical training as cognitive, social and humanitarian, operational-activity-related, research and methodical. Each of them corresponds to certain competence: information-methodological, social interaction, individual cognitive activity, self-organization and self-management and also system-activityrelated. Criteria for assessment of competencies on the basis of performance of methodical oriented practice tasks and projects were developed.
The relevance of the research is due to additional opportunities to improve the quality of teaching mathematics in a digital school, support professional orientation and self-determination of young people through the inclusion of mobile services and platforms in mathematical activities. The research problem is determined by the following contradictions: 1) between the capabilities of modern digital technologies in terms of improving the quality of mathematical training, the formation of universal skills required by the economy of the future, and the model implemented by educational institutions; 2) between the need to provide resources for solving problems of a socioeconomic nature in the conditions of the fourth industrial revolution and the insufficient level of mathematical literacy of graduates. The purpose of this research is to study the didactic potential of mobile technologies to support mathematical education in a digital school while preparing specialists of the future. Moreover, the research offers a methodological approach to organize project activities of developing applications in terms of increasing the effectiveness of teaching mathematics and vocational guidance. The article clarifies the concepts "mathematical thinking", "mathematical literacy" for a digital school and describes the didactic principles of incorporating mobile resources into the educational space which increase the efficiency of training engineers of the future, support vocational guidance and self-determination. The author offers methodological methods and recommendations for organizing creative interdisciplinary project activities in order to develop mobile applications that contribute to the formation of qualities and skills forming the basis of mathematical thinking. The materials of the article can be used: firstly, to ensure the personalization of mathematical training in the course of creative, interdisciplinary, cognitive research activities of students while developing mobile applications, social integration and vocational guidance; secondly, to change the concept of mathematical education at school; thirdly, to improve the implemented model of education based on the traditional trajectory "preschool education-school-university-additional education" in the context of the new requirements of business, society, and the state for the training of highly qualified professionals in the professions of the future.
The relevance of the research problem is defined by practical and theoretical components. Evidence of theoretical and practical significance, reliability of scientific knowledge about the nature of learning activity contrasts with the real state of affairs in educational psychology denoting the insufficient number of studies on character of motives of adults' educational activity in the system of postgraduate education, "motivational conflict" between the basic high education and the following one acquired at the faculty of vocational retraining. The purpose of the article is to identify the content and professional nature of adults' learning activities during special vocational retraining, its dependence on a number of psychological factors, the most important of which is meaning-making. Meaning-making is the establishment of links between the results of learning and the motives stimulating this activity, i.e. between the objective of training activities and its motive. The leading method of study of this problem is the ascertaining experiment. In the result a quite close relationship between motives of educational activity and the fundamental needs and attitudes to learning are revealed. The factor of effectiveness of adults' learning in the period of additional vocational education is the relationship of motives of educational activity with the need for knowledge, affiliation, achievement and dominance, which determines the "strength" of perceived learning activities and obtaining of successful learning outcomes, attitude to learning as a whole. Article proceedings are valuable for organizers of vocational retraining of educational psychologists, academics, as well as valuable in the development of recommendations for policy-making in additional education in the area of "Practical Psychology in Education".
The actuality of the problem's research is caused by conditions of three kinds: firstly, the increasing demand for the profession and humanistic values of the practical psychologist in education; secondly, the special circumstances of the accelerated training of psychologists (from former teachers), who are actually taking possession of a new profession; thirdly, the lack of research, where the impact of training on professional identity is studied. The purpose of the article is to uncover the structure of future educational psychologists' professional notions, identifying the occurrence period of their basic elements ("standard frame") of professional-psychological picture of the world, establishing the peculiarities of professional outlook. The leading method of study of this problem is ascertaining experiment. As a result the structure and genesis of professional psychological image of the world of the future educational psychologists was revealed. The materials of the article are of great value to the organizers of professional retraining of educational psychologists, academics, as well as valuable in the development of recommendations regarding formation of policies in the sphere of additional education in "Practical Psychology in Education".Keywords: professional retraining of educational psychologists, professional competence, professional identity, structure and genesis of professional psychological image of the world
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