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| 1 | In the present paper methods of formation of critical thinking abilities when one passes through a solution of special developed system tasks in mathematical analysis are suggested. Mentioned abilities are a means to raise the quality of professional training of future teachers for mathematics within of every described indicators. Keywords: mentality, critical thinking, professional training, quality of professional training, training of teachers for mathematics | 1316 | ||||
| 2 | The article demonstrates the experience of work for the student training for the unified state exam on mathematics at the institutions of post-secondary education as one of the directions of realization of the continuous mathematical education in the system «school – pre-university education – university – postgraduate education, self-education». The basic recommendations for the student training for the unified state exam on mathematics in view of the features of the exam in the test form are proposed. Keywords: continuous mathematical education, training for the unified state exam, quality improvement of school education | 1112 | ||||
| 3 | The paper presents the results of research on the study of the course of ordinary differential equations and partial differential equations in the context of the competency approach to training future math teachers. As is known, models of real processes can be described in the language of mathematics, including by means of ordinary differential equations and partial differential equations. Ability to create such mathematical models and work with them is an integral part of the human culture. Thereby it is necessary to search for new approaches to the training of maths teachers, aimed at the formation of ideas about the role of models and modeling. In this connection the course of differential equations is essential means in attracting students to research work and for the formation of professional competence of the future teacher of mathematics. The course of differential equations plays a fundamental role in the professional training of mathematics teacher in terms of understanding the gist of the application and the practical orientation of teaching mathematics, mastery of the method of mathematical modeling. The course of differential equations and its methods give another tool for knowledge of the world, which allows to create a scientific understanding of the real physical space. The results presented in the paper allow us to conclude, that the involvement of students in research work in the framework of the course of differential equations not only promotes the overall development and professional training of the future teacher of mathematics, but also getting completely new results are important in the modern theory of differential equations and theoretical physics. Keywords: professional training of future maths teacher, professional competence, differential equations | 1240 | ||||
| 4 | The paper presents the results of involvement of future mathematics and physics teachers in independent scientific research activity in conditions of realization of competence approach. In the case of such approach the competence is a general capability which is checked and created in activities. It is based on knowledge and allows the person to establish connection between the system of actions for successful problem solution. During the educational process, the formation of elements of competencies at implementation of curriculum is carried out by means of maintenance of the studied subject. The course of the differential equations has great opportunities for forming of professional competencies of future teachers of mathematics and physics, however the existing education guidance, according to the theory of differential equations, are obviously not oriented to form the competencies. Besides modern development of technology, chemistry, biology, ecology, geography, economics and other sciences is impossible without the use of differential equations. The solutions of Clairaut-type equations with a special right-hand part found in the paper are a new result in the theory of partial differential equations. In turn the organization of independent scientific research in the framework of the course of differential equations promotes the main goal of professional competencies of future mathematics and physics teachers, namely forming the professional competencies being ready to use theoretical and practical knowledge in science and education. Keywords: differential equations, professional competencies | 1241 | ||||