Pavel Gorev

The key learning outcome of the main educational program of preschool education is the development of cognitive abilities of the pupil. The work for the development of cognition of a preschooler should be considered as a purposeful activity aimed at cognition of the surrounding reality on the basis of the formation of cognitive functions, such as perception, thinking, memory, attention, speech. Therefore, cognitive activity is the main one in cognitive classes in kindergarten. The result of all the system of cognitive activities should be the formation of cognitive functions in a preschooler. At the same time, we must take into consideration the requirements for the structure of a cognitive lesson and the choice of the main technology for this structure design. Reasoned discourse can be considered as the main technology of a cognitive lesson. The discourse allows organizing the student's active mental work both in the process of perceiving the teacher's argumentation and in the process of building his/her own reasoning strategy and forming arguments. On the other hand, the standard of preschool education and the successive standard of primary school education distinguish the task of mastering educational sign-symbolic means by students. The minimum set of these means is defined by the standards (substitution, modeling, encoding and decoding of information, logical operations, including general problem-solving techniques) and allows them to be included as a mandatory component in the lesson structure. That is why the purpose of the article is to describe the structure of a cognitive lesson based on the technology of reasoned discourse in preschool education. The authors of the article highlight the methodological aspects of formulating the tasks of cognitive activity, describe the content of cognitive actions in older preschoolers and characterize the significance of reasoned discourse in this process. The theoretical significance of the article lies in the identification of the structure of a cognitive lesson based on the technology of reasoned discourse in preschool education. The practical implementation of this structure will create favorable conditions for the development of the pupil's knowledge on the basis of the formation of the child's cognitive functions in the system of pre-school education. It can be assumed that this structure of a cognitive lesson can be considered in relation to the study of any topic in the educational process of a preschool educational organization.

In accordance with the current Federal State Standard of Primary General Education, the organization of project and research activities of primary school children is one of the most important and necessary conditions for the full development and socialization of the child’s personality, carried out through activities aimed at successfully mastering universal learning activities, which is supposed by the fundamental methodology of a system and activity-based approach. The project and research-based learning of primary school children, being insufficiently studied from the point of view of practical implementation, is an alloy of various activities in which the child participates to achieve meta-subject results. However, the potential of this kind of work for primary school students still requires a comprehensive study and practical implementation in schools. Thus, the purpose of the presented article is to describe the content and forms of project and research-based learning of primary school students through activities of "Children's University", justification of the effectiveness of the technology for managing the relevant educational project. The leading approach in this case is the modeling of the project activity system in primary school education with the inclusion of a system and activity-based approach, the project-based and developing education methods. As a result of the study, the practical component of the work is presented: detailed description of all the events taking place on the educational platform, specification of the main classes for primary school students. In the course of the study, the authors carried out work on testing the project management technology for the “Children's University” project, analyzing the data obtained during the ascertaining and control experiments. The theoretical significance of the article is due to the contribution to the development of scientific ideas about the project- and research-based learning of primary school children within the activities complex "Children's University" aimed at harmonizing new knowledge with the level of the student’s abilities development. The practical use of this technology allows us to organize the work of step-by-step introduction of project- and research-based learning into the practice of an educational organization. The article may be interesting to primary school teachers, students of pedagogical areas of training, researchers studying the project- and research-based learning of younger students.

Pedagogical science has always faced an issue of finding effective means to achieve the educational results of students. This problem is especially urgent today, when the world is changing rapidly, and those tools, that yesterday could keep pupils interested in studying mathematics and provided an opportunity to develop their mathematical abilities, quickly become out-of-date. Today, the search for a new toolkit that contributes to the development of students by means of mathematics, as well as mechanisms for incorporating it into the educational process, is highly relevant. Thus, the purpose of the article is to study the possibilities of using a new learning tool - puzzles in all their diversity in the process of teaching mathematics to children and teenagers, both in class and in extracurricular activities. The leading method here is the modeling of the methodological system of training in basic and additional mathematical education of children and teenagers, with the inclusion of a new didactic toolkit in it, which will contribute to the increase of students' interest in the subject, as well as to the development of certain mathematical abilities: logical thinking, abstraction, combining, operating with spatial images, critical thinking, mathematical memory. As a result of the research, the author of the article determined the place, opportunities and methodological aspects of including puzzles in the process of learning mathematics, both in the system of classical and nontraditional (creative) lessons of mathematics, and in the structure of extracurricular activities of students: mathematical circle, system of mathematical competitions, mathematical summer camp, etc. Practical use of this system makes it possible to reduce the disadvantage of tools deficiency for the development of mathematical abilities of students in the pedagogical practice, which gives us an opportunity to speak of high academic results in mathematical activity of children and teenagers.

The article is devoted to the issues of introducing into the modern school education certain creative lessons and courses that contribute to the actualization of the creative beginning of the student's personality. Theoretical information on a paired creative lesson in the NFTM-TRIZ system and the structure of a creative mono-science based on it are given. Describes two of the brightest stages of such a lesson and didactic tools for them “Surprise by a miracle” and “Puzzle”. The article also describes the individual courses of creative development of students, which make up the structure of the continuous formation of creative thinking from preschool education to 10–11th grades of secondary school.

One of the most important aspects of the education system development is the ability to make informed conclusions about the need to change the approaches or actions taken. The educational system continuously generates and accumulates significant amount of data, and the issue of systemic work with these data by a wide range of education subjects today may be called one of the significant ones. Big Data can become a powerful tool which would help to transform learning, rethink approaches, reduce long-standing gaps and adapt experience to improve the effectiveness of the educational system. Very important is the task of describing the technology of operating big data, aimed at the development of educational systems through the identification of formed patterns in the education system. The authors of the article determine the methodological aspects of implementing big data operating technology in education. The leading approach in this case is the modeling of the educational system development including regulatory measures based on the results of the identified patterns analysis. As a result of the research carried out by the authors of the article, Big Data technology was described as a means of developing educational systems, including identifying the distinguishing features of Big Data technology, structuring the system management processes, the direction of data mining in education, and the properties of mined Big Data in education. The theoretical significance of the article is due to the contribution to the development of scientific ideas about Big Data use in order to improve the efficiency of the educational systems development. Practical use of the research results allows to introduce Big Data into education management system by identifying and taking into account the patterns of the education system. The article may be interesting for persons involved in education system management.