Pavel Gorev

Pedagogical science has recently undergone significant changes associated with the restructuring not only the education system, but the entire socio-economic system. If yesterday the educational process required only traditional tools, such as printed textbooks, a school board, today they are replaced by modern information and communication technologies. Modern learning technologies should allow students to use resources and educational experience anywhere in the world, starting with their own communities, including the Internet. These opportunities create conditions for all schoolchildren development, giving them a higher level of access to high-quality teaching materials, knowledge, personalized learning and planning tools for their future education. Such conditions may also give teachers the possibilities to use blended learning for their students, to rethink when, where and how students would deal with different components of the learning process. It is very important to test the interdisciplinary technologies of school education, improving the components of the educational process, taking into account the current educational standards and characterizing the features of the target audience, which now has access to various channels for acquiring knowledge. Blended learning is a combination of traditional forms of classroom learning with elements of online learning complementing and supporting the learning environment. Thus, the purpose of the article is to describe the interdisciplinary technology of blended learning in school education. The authors of the article determine the methodological aspects of blended technology implementation in school education programs. The leading approach in this case is modeling the methodological system of learning in general and additional school education with the inclusion of blended learning interdisciplinary technology in it. As a result of the study, the authors of the article differentiated the basic models of blended learning, the components of the blended learning environment (time, place, way or pace of learning), the types of blended learning integration, the key effects from the introduction of blended learning. The theoretical significance of the article is explained by the contribution to the development of scientific ideas about interdisciplinary learning technology aimed at matching new knowledge to the level of pupil's abilities development. Practical use of this technology makes it possible to organize the step-by-step introduction of the interdisciplinary technology of blended learning into the work of a general education organization.

In the conditions of modern economic development in our country, the revision of the basic paradigms of education and the radical transformation of the models and mechanisms of the school teachers’ work are required from pedagogical and methodological science. The dynamics of the current changes in professional methodological language reflects the unprecedented accelerated renewal of school teaching technology. It is very relevant to approbate intersubject technologies of school education, improving the content of training in a particular lesson in accordance with federal state educational standards, and characterizing the experience and methodological potential of the educational organization. Thus, the purpose of the article is to describe the intersubject technology of adaptive learning and testing in school education. The authors of the article determine the methodological aspects of implementing adaptivity in school educational programs. The leading approach in this case is the modeling of the methodological system of teaching in general and additional school education with the inclusion of intersubject technology of adaptive learning and testing. Intersubject technology contributes to the achievement of unified learning results for schoolchildren in shorter time due to the most relevant content for each student. As a result of the study, the authors of the article differentiated the main components of adaptive learning technology, the development and implementation technologies of adaptive testing. The theoretical significance of the article is due to the contribution to the development of scientific ideas about intersubject learning technologies aimed at matching new knowledge to the level of the student's abilities development. Practical use of the described technology makes it possible to organize the step-by-step introduction of intersubject technology of adaptive learning and testing into the work of an educational organization. The article may be interesting both for theorists of school educational system and for practicing teachers and students who are trained in the field of "Pedagogical education".

Pedagogical science has always faced an issue of searching for little time-consuming technologies of methodological support for teachers to achieve good educational results. This problem is especially urgent today, when those pedagogical methods and means which yesterday could maintain the interest of schoolchildren to study the subject, provide an opportunity for their development, become out-of-date in the rapidly changing world. Today, the approbation of new technologies for methodological support of teachers is very relevant. Thus, the purpose of the article is to describe one of the technologies of methodological support for teachers, namely the technology of developing boxed educational solutions. The authors of the article for the first time define the boxed educational solution as a package of program-methodological and subject-developing support that can be used by consumers of educational services (children, parents, teachers, administrators, employers) for independent use (turn-key project). The leading approach in this case is modeling the stages of development and phases of creating boxed educational solutions as a technology for developing boxed educational solutions for methodological support of teachers. As a result of the conducted research, the authors of the article differentiated the types of technologies for methodological support of teachers: customized and boxed solutions; the stages of educational solution development and the phases of a boxed educational solution creating are described. The theoretical importance of the article is due to the contribution to the development of scientific ideas about the technologies of methodological support for teachers. Practical use of this technology makes it possible to organize a step-by-step transition from the development of customized solutions to boxed educational solutions that help to reduce the time spent by teachers on the organization of educational activities of students. The practical value of the technology under consideration is justified by the project triangle, in which the important parameters of technology for methodological support of teachers are related: the amount of work, time and costs. Changing the values of one of these parameters causes the values of the other two to change. Boxed educational solutions allow you to balance the parameters and achieve the result of the planned quality.

The article is devoted to the use of non-standard problems in the supplementary mathematical education of pupils of the 5-6th grades of the secondary school. Technological approaches are proposed for the formation of didactic materials for students with different educational needs through the use of an electronic bank of non-standard mathematical problems that are structured both in complexity levels and conditionally divided into types: combinatorial and logical problems, as well as arithmetic tasks and tasks with geometric content.

The article is devoted to the questions of setting, approbation and introduction into the practice of the work of the educational institution of the course of additional mathematical education for students of the 5th and 6th grades "Developing Mathematics". The author points out the main aspects that influenced the selection of the content of the course, suggests a methodology for organizing classes in various forms based on modular structure of the course structure, as well as organizational and methodological recommendations for conducting the course in general education organizations.