The article considers the matter of realization the competence approach while preparing the 9-th form pupils for solving equitations and inequalities during the state final certification in Maths. In the context of reform of mathematical education, building a personality oriented mathematical training systems is important to the implementation of competence approach to training. The need to implement the competency approach has declared a common criteria evaluation of academic achievements of the pupils in secondary education, which were approved by the Ministry of Education, Science, Youth and Sports of Ukraine. At the same time, the deficiencies remain contradiction between having a solid theoretical scientific achievements of the problems and the lack of the competence approach ways of its implementation in school practice; between the goals and objectives of mathematics education aimed at forming system knowledge, intellectual development, cognitive activity of the pupils on formation of their key and mathematical competencies and inadequate methodological support, the lack of specific guidelines necessary for solving these problems. This causes the relevance of scientific evidence means to implement the competency approach in the school mathematical education. State final certification (STC) in mathematics has become an inherent part of the process of graduation in primary school. At various times the collections of tasks for DPA included only the task of algebra or with algebra and geometry. One of the main lines of content of school course of algebra is a line equations and inequalities, which has an extensive system of interdiscipline connections with other lines of course. So traditionally equations and inequalities are well represented in the state final certification tasks in mathematics. But the results of these tasks in recent years has significantly deteriorated, making the actual problem definition and justification opportunities to improve the methods of studying equations and inequalities in the course of algebra competency-based approach. The analysis of the tasks of STC indicates that each of the four parts of the collection has tasks that are directly related to the content line equations and inequalities (resolve or investigate equation (inequality) or system plot the equation (inequality, systems of equations) to solve word problems, reduced to equations or systems of equations. An urgent and important is the development of the guidelines for the preparation of the pupilts for solving the problems of state final certification from all lines of the mathematics content of basic school.
In the article on basis of the systems analysis and generalization of the data on the study the principles of formation of the future mathematics teacher’s readiness to the pedagogical innovative activities are disclosed and their meaning and essence highlighted. These are the principles of innovative learning, integrity and systemic character, continuity and succession, personally oriented activities, partnership and cooperation, integration, context activity, problematic and creativity, individualization and differentiation of learning, feedback. The principle of innovative teaching directs learning to develop readiness of the individual to work in a new environment, adapt to changes in the society (including the change in the quantity of hours to study mathematics, changes in regard to mathematics education, priorities in studying mathematics), set new, unusual for its task, use new ways to solve problems, take a new experience, develop and improve. The principle of problematic and creativity in teaching future teachers and their preparation for innovative pedagogical activities is based on creating and solving problem situations and tasks. The principle of partnership and cooperation is reflected in the content of teachers and students work at all stages of preparation of the future mathematics teachers to implement the main directions of innovative educational activities. The principle of individualization and differentiation of education is reflected in the choice of innovative methods and forms of training – the optimal combination of general, group and individual forms and corresponding to them methods coupled with orientation to self-actualization and self-development of future teachers. The principle of feedback orients to creating a positive and effective feedback as a prerequisite for diagnosis preparedness of the future teacher of mathematics to pedagogical innovation and the implementation of the effective remedial changes. The implementation of this principle involves neutralizing the fear of rating, the ability to respond positively to constructive criticism, the formation of the students’ attitude to mistakes as integral and even useful elements of the training activities from the first weeks of learning. There is an urgent importance of the issue of formation of the regularities of the future mathematics teacher’s readiness to innovative educational activities.
The article analyzes the views of native and foreign scientists on the concept «innovation competence of the teacher», the concept «innovation competence of the mathematics teacher» is defined, the conceptual provisions concerning the analysis of the structure and content of this concept are described, the components of the innovation competence of the mathematics teacher are outlined and the directions of their formation in the teaching disciplines of mathematical cycle are proposed. The formation of future teachers of mathematics readiness to innovative pedagogical activity is an objective process of purposeful preparation for the creation, implementation and dissemination of educational innovations, which is based on: 1) the adaptation of students to higher education, the implementation of the principle of continuity between the older and the higher school, the formation of motivation of the students for professional activities; 2) maximum use of innovative techniques in the study of the disciplines of mathematical cycle, giving the educational process of students the creative, innovative character; 3) deepening integration of psycho-pedagogical and professional knowledge of future teachers of mathematics; application of innovative information technologies in the educational process; 4) the use of the system principle of training of future specialists in the design, development and partial validation of models of mathematics teacher’s work in the form of a common scheme or plan activities in the implementation of the educational process, based on the predominant activity of students, organized and created by the teacher; 5) the development and application of «prognostic acmeological training» of future teachers of mathematics to innovative pedagogical activity. The predictability of this preparation means its orientation to the school of the future taking into account the main trends in the development of technologies for teaching mathematics. Its implementation on a contextual basis provides a consistent use of all types of preparation of future teachers of mathematics. The innovative competence of teachers of mathematics is seen as part of general professional competence and the necessary condition for the formation of mathematical competence, the content of which is determined by the peculiarities of innovative activity, its social significance, creative nature and focus on continuous creation of something new, development of personal and professional potential of the teacher.
The article analyzes the views of domestic and foreign scholars on the basic concepts of educational innovation, which include the concept of innovation, innovation process, innovation capabilities. During innovations in pedagogy we mean new (or improved) product pedagogical implemented in the educational process and promotes its development. in the context of innovation in mathematical education innovation process should be considered as a set of procedures and tools that allow pedagogical innovation digested educational company and effectively used in practice on a scientific basis. Innovative capacity is understood as the capacity of the teacher, which is defined as a set of cultural and creative individual teacher characteristics, expressing willingness to improve teaching activities and the availability of internal tools and techniques that provide this alert. To most essential characteristics of innovation processes that must be considered in the preparation of future mathematics teachers for innovative teaching activities include advisable stages (awareness forecasting of social needs, finding ways and means of conceptual solution to the problem, the birth of a new idea, of a new concept of innovation, invention, innovation implementation , spreading innovation saturation in a competitive industry, recession irradiation innovation) and patterns of flow (irreversible destabilization of pedagogical innovation environment; the final of the innovation process; stereotyping pedagogical innovations; loop, repayment of pedagogical innovations). In order to fruitful innovation in mathematics education should be organized targeted training of future and current teachers of mathematics to innovative educational activities. It should not only inform students (teachers) in teaching methodology courses and (or) the basic concepts of pedagogy pedagogical innovation, flow patterns and stages of innovation processes, but they form a conscious commitment to creative overcome these potential difficulties inherently accompany the work of teachers of mathematics-oriented production, analysis and innovation in their daily work, to promote their innovative potential. The prospect of future research is to clarify the concept and components of readiness of the future teachers of mathematics to innovative teaching.
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