INNOVATIVE TECHNOLOGIES IN MATHEMATICS EDUCATION

The introduction of the competence model of Mathematics education involves the actualization of personal and activity factors of development of subjects of the educational process, development and scientific justification of innovative teaching technologies. The subject of the studyis innovative technologies of personality development in Mathematics education. Thepurpose of the study is to create, scientifically and theoretically substantiate as well as experimentally verify the innovative technologies of personality development in Mathematics education. Research methodology. To achieve the goal, the following research methods were used: survey, content-theoretical and structure-system analysis, abstraction and modeling, ranking, pedagogical experiment, statistical method as well as content generalization. Results obtained. In the presented work, the central idea pertains to the stance on the dual nature of mathematical competence. In the work at hand, on the dualistic nature of mathematical proficiency, in which its dual characteristics have external and internal manifestations. The external manifestations of mathematical competence include the socially recognized parameters and their attributes that enable society to assess individual’s proficiency in the realm of Mathematics. Instead, its internal manifestations are delineated by individual and psychological dimensions and personality characteristics, owing to which mathematical competence is an integral self-development system. Essential is the emphasis on mathematical proficiency as an inherent quality prevailing in the personal and psychological dimension of mathematical competence’s internal manifestation. Taking into consideration the spatial Cartesian realization, the role and place of mathematical abilities in the three-dimensional structure of the mathematical competence’s internal manifestation are substantiated, a content and systematic analysis of the studied phenomenon’s structural components is made. The existence of complex correlational relationships of four structural components of mathematical abilities (system-generating, coding-formalized, cognitive-generalizing, mnemonic-generalizing) with three dimensions of mathematical competence’s external manifestation (content-theoretic, process-active, personal-psychological) is established. The scientific idea that the development of students’ mathematical abilities is ensured by updating external dimensions of mathematical competence in educational and mathematical activities is introduced. Drawing upon the results of its implementation and introducing the principle of developmental continuity in education, a technology for the development of students’ mathematical abilities was elaborated. The foundation of this technology lies in the pedagogical approach known as the task-based method for instructing students in mathematics, in which the methods of mathematical and educational modeling are embodied, the transition from the abstract to the concrete. In such a way, the reflection of the process and the results of educational and mathematical activity is ensured. The instruction regarding the facets of students' current mathematical progression is delineated by their content, classification criteria, typological attributes, and cycle of developmental learning. Considering the advanced pedagogy in place, a theoretical-probabilistic methodological framework for developmental mathematics education was constructed, the content of its stages was revealed. It was established that innovative teaching technology involves the following stages: definition of areas of actual mathematical development; creation of zones of immediate mathematical development; transformation of zones of immediate mathematical development into the zones of actual mathematical development; designing the zones of students’ immediate mathematical development. The efficacy of the cutting-edge educational technology was evaluated based on the outcomes of the pedagogical trial. Practical value. In view of the problem raised in the work, the results of a pilot study on the manifestations of students’ mathematical abilities, significant factors of their development were examined. Validation of the constructed models and advanced technologies during hands-on Mathematics instruction enables us to argue about their impact on development, as well as about achieving the developmental function of education. It was found that all structural components of students’ mathematical abilities undergo positive changes. The obtained research results can be used by authors of mathematics programs and coursebooks, methodology teachers in the current system of Mathematics teachers professional training. The developed innovative technologies can be applied by teachers of higher education institutions, teachers-researchers, teachers-practitioners to realize the developmental function of teaching and self-development of pedagogical systems “teacher – learner”, “teacher – student”. The methodological developments presented in the paper will be useful in the system of further training of pedagogical staff in order to implement the concept of “New Ukrainian School”. Value / Originality. Examination of the outcomes stemming from the integration of the newly created cutting-edge technologies, the results of the pedagogical experiment made it possible to conclude about the possibility of resolving the contradictions of modern mathematical education related to the logic of educational cognition, associative-reflexive theory of learning, traditionally established technology of teaching Mathematics, which presuppose the elimination of empirical generalizations and the actualization of empirical thinking, the leveling of mathematical abilities and the neglect of the dual nature of students’ mathematical competence. The findings of the recent external independent evaluation, as well as the results of the national multi-subject testing serve as a manifestation of these discrepancies.