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ACCOUNTING OF VARIOUS INFORMATION CODING METHODS AS THE CONDITIONS OF ORGANIZING ENHANCING REVIVAL // Pedagogical Review. 2018. Issue 4 (22). P. 27-38

The question of the professional preparation of the future mathematics teacher is current in modern conditions of the organization of school mathematical education. It allows him to implement a competence approach to solving the main problems of the school mathematics course. One of such problems is the organization of the educational material repetition. Future mathematics teachers should understand that not every repetition is productive and provides continuity links between different levels of learning. If the repetition is carried out in the same form as the study of the material, it becomes ineffective. Due to this fact, enriching repetition stands out among the various types of repetition. Studies show that future mathematics teachers should be ready for enriching repetition, which is that the material traversed is included in new connections, it is reconstructed and generalized. Тhe known signs of concepts and connections between concepts are subjects to revision. Future mathematics teachers’ psychological, didactic and subject knowledge about the problem needs to be integrated with the priority of using the psychological laws of personality development as the basis for organizing the learning process to prepare them for the organization of enriching repetition. In other words, it requires mastering the psycho-tactical approach to solving methodological problems. Future teachers must realize the need to organize enriching repetition, to understand what mathematical and psychological-pedagogical knowledge they need to be ready for the psychodynamic approach. Particular attention is paid to the consideration of the psychological patterns of the concepts and conditions formation that contribute to their formation. A key element of the methodological activity has been identified. It creates conditions for a competence approach to the organization of educational material enriching repetition - the development of various ways of information coding (verbal-symbolic, visual, subject-practical). Future teachers master text competence (by the example of the repetition of natural numbers) with the help of special integrated tasks, including the formulation of the problem, the psychological and pedagogical direction for learning activities, examples of solving the problem, an invitation to work. The result of this work is the creation of educational texts types and their examples that contribute to the development of encoding information methods on natural numbers and decimal fractions. In addition, they receive an example of a professional approach to solving the emerging problem in the teaching of mathematics.

Keywords: enriching repetition, information coding methods, continuity, positional number record

FORMATION OF RELATIONS BETWEEN CONCEPTS BY MEANS OF TEACHING TEXTS (ON THE EXAMPLE OF THE CONCEPT «FUNCTION») // Pedagogical Review. 2018. Issue 4 (22). P. 60-71

Fundamental importance for the development of thinking of a teenager, his intellectual education has the formation of concepts. Organization of training aimed at taking into account the laws of the process of formation of conceptual thinking is relevant in the methods of teaching natural sciences. Knowledge at the conceptual level is the knowledge of some sets of features of the concept (identification of features of the concept; establishment of the presence or absence of a certain feature in a given mathematical object; construction of objects with these features, etc.). The nature of each individual concept implies the existence of a certain system of concepts, beyond which it can not exist. Formation of the concept includes the construction of the content of education, aimed at establishing links between concepts. Establishment of a variety of relationships between concepts is especially important in the study of such a fundamental concept of mathematics as “function”, as this concept helps to identify the mutual connection and conditionality of different phenomena. Investigations show that this role of the concept of function is not always realized. Therefore, we need special educational texts that would create conditions for establishing links between concepts at each of the phases of the process of formation of the concept of “function”: motivation, categorization, enrichment, links. The motivation phase is “text – establishment of inter-subject relations”, motivating the search for a new concept that would allow to combine externally dissimilar, different situations, to find approaches to their study. Phase categorization – “text – encoding information, text – establishment of generic-specific relations, text - focus-example”, “text – relationships-mapping, analogy.” The phase of enrichment “text – establishing interdisciplinary connections, text –signs, concepts, text – systematization of concepts.” Transfer phase - “text – intra-subject links”, “text – concept application”. The knowledge of the typology of educational texts, contributing to the establishment of links between concepts in the study of “functions”, creates conditions for improving the quality of the study of this concept, for the formation of universal educational actions of various blocks.

Keywords: teaching text, function, phases of concept formation, genus-species relations, classification, operation of the recognitions, inter-subject links between concepts

Design features of the educational topic learning environment (on the example of mathematics) // Pedagogical Review. 2023. Issue 6 (52). P. 7-20

The relevance of the work is due to the fact that mathematics, as a special language of science and communication, is a cultural phenomenon of the modern digital society, and educational texts in mathematics, as a condition for the implementation of meaningful education for students, reflective selfdetermination of teachers and the design of a developmental learning environment, become the subject of research in various academic areas, including psychodidactics. The methodological base was a descriptive and systematic analysis of empirical facts in the study of the role of the educational text and the learning space of the educational topic in creating a developmental learning environment aimed at the meaningful mastering of mathematics by students. A comparative method was used in the analysis of educational texts from the standpoint of their features and properties that contribute to the creation of a developmental learning environment in the process of studying mathematics. The authors analyse and describe the modern educational text, the transformation of the education content and the crucial role of the learning environment in the process of mastering the educational topic. Having conducted the study and the analysis of the obtained data, the authors come to the conclusion that a specially designed educational topic learning environment is likely to become part of the developmental learning environment. Moreover, it seems to affect the achievement of a deep level of understanding the educational material by students and influences the system of concepts, facts, methods of action, thinking, perception of the world and the individual in the relevant environment.

Keywords: educational text, learning environment of the educational topic, developmental learning environment, conscious learning