Botuzova Y. Theoretical and methodological principles of providing the continuity of teaching mathematical disciplines in the system «school – pedagogical university»

In the dissertation work the theoretical and methodological generalization of a scientific problem of providing the continuity of teaching mathematical disciplines in system «school – pedagogical university» is carried out. A new solution has been proposed. Attention is focused on the formation the readiness to provide continuity of teaching math as a base of the corresponding special professional competence of future teachers of mathematics. This readiness must form in the process of professional training of future math teacher. The problem of providing the continuity of teaching mathematical disciplines in normative-legal, scientific-pedagogical and methodological discourse was considered. A thorough content analysis of the concept of «continuity» was carried out, thanks to which it was possible to build a structural scheme of its semantic field and formulate the author's definitions of «continuity» and «continuity of teaching mathematical disciplines» as general pedagogical and didactic principles. The current state of school mathematics education in Ukraine is analyzed on the basis of the results of international monitoring researches and annual external independent assessment in mathematics. Possible ways to improve the level of mathematical training of school graduates are identified. One of these ways is to provide the continuity of teaching mathematical disciplines. The contingent of students-future mathematics teachers of the most popular pedagogical higher educational institutions has been investigated. It has been established that in recent years the number of applicants for specialty 014 Secondary education (Mathematics) remains insignificant, and their level of mathematical training is often insufficient to continue their studies on the specialty. The study suggested the introduction of a leveling course in mathematics for the first-year students. A factor analysis of the continuity of teaching mathematical disciplines in the system «school – pedagogical university» was conducted. As a result, four factors were identified. The interaction of these factors is reflected in the constructed factor basis for providing the continuity of teaching mathematical disciplines. The conceptual foundations of the problem of continuity of teaching mathematical disciplines in the system «school – pedagogical university» have been scientifically substantiated. These include the using of innovative directions in the development of education: competence approach, system approach, information and activity approach, STEM-oriented approach. The influence of the psychological and pedagogical characteristics the new generation of pupils and students on the process of teaching mathematical disciplines in educational institutions has been studied. Peculiarities of the organization of vocational guidance of senior pupils and the course of adaptation of students to study in the university at the decision of a problem of maintenance of continuity are analyzed. Such structural components of methodical system were defined: target, content, instrumental and evaluation. Each of them is described in detail. The expected result of the functioning of the methodical system is the readiness of the future teacher to provide the continuity of teaching mathematics as a base of the corresponding special professional competence. The criteria of this readiness were singled out and characterized: cognitive, motivational, technological and reflexive. Indicators and four levels of manifestation are defined for each criterion: creative, productive, reproductive, passive. The step-by-step model of formation of the specified readiness which realization is carried out in the course of professional training of future teachers of mathematics is constructed. Methodical recommendations for the formation of future mathematics teachers’ readiness to provide continuity of education in the study of mathematical disciplines, disciplines from the cycle of professional training and during pedagogical practice have been created and implemented in the educational process. Experimental implementation of the developed methodical system to provide the continuity of teaching mathematics in the system «school – pedagogical university» in the educational process confirms the possibility of creating favorable conditions for the formation of future mathematics teachers’ readiness to provide continuity of education. The results of the study can be used: to develop educational and professional training programs for future teachers of mathematics; for the preparation of curricula for mathematical disciplines and disciplines of the cycle of professional training by lectors of pedagogical and classical universities, which carrying out training of future teachers of mathematics; by lectors in preparation for classes, organization of independent work of students and conducting research; by specialists teaching mathematics teacher training courses; by teachers and students.