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The article discusses the possibilities of using electronic educational resources in mathematics lessons in elementary school for the implementation of an activity-based approach to education. On the example of one of the video lessons, methods of organizing an active search activity of younger schoolchildren in teaching mathematics are demonstrated. One of the regularities is the following: "The development of a student occurs only in activity, and the more active the activity, the more successful it is to move forward in development." Coordination of the organization of the educational process with the above regularity presupposes the role of the student in it not so much as an object, but as a subject of activity. Thus, the concept of an activity-based approach to education consists in organizing subject-subject relations, in rethinking the role of a student as a subject of education and the role of a teacher as an organizer of student activities. Currently, a lot of electronic educational resources (EER) have been developed that have the ability to organize active educational activities of younger schoolchildren in the classroom: video lessons, electronic games, tests for self-examination. However, teachers do not always realize such opportunities. Observations show that often, both in face-to-face and distance learning, the use of EER is limited only to their demonstration, without further analysis. At best, students perform the proposed tasks according to the model given, for example, in the video lesson. This significantly reduces the effectiveness of the implementation of the activity approach to learning.

The article discusses the possibilities of organizing continuity in solving problems between the initial and basic secondary levels of education, only two lines of organizing succession are touched upon - this is a unified approach to compiling a brief record of the problem (content analysis) and a unified approach to finding a way to solve the problem. The generalized ability to solve problems is the most important cognitive universal action, since it allows you to solve not only objective problems (mathematical, linguistic, physical, etc.), but also to solve problems that arise in life. Modeling the process of solving a problem allowed us to establish that the discovery by students of the relationship between different ways of solving one problem, structures of different types of problems is possible if conditions are created in which students will be forced to perform comparison, analysis, modeling, generalization, that is, to actively use thinking, not memory. Therefore, we offer our own way of maintaining continuity in learning to solve problems at the primary and secondary levels of education. The proposed unified approach to the analysis of the content of the problem, the result of which will be a compiled short note, allows students to form a generalized ability to analyze the content of the problem and find a way to solve it.

The article reveals the essential characteristics of the concepts of "self-organization of the system", "self-organization of personality" from the standpoint of synergetic, activity, personal, competence approaches. Self-organization is possible only in systems with a complex structure, a large number of elements and interconnections. In such systems, self-organization becomes purposeful. Self-organization can be carried out with the aim of forming a complex system arising from a set of separate subsystems; in order to maintain the life of the system, its adaptation to constantly changing internal and external conditions; for the purpose of self-development of the system, taking into account past experience. One characteristic feature of self-organization is that this process is carried out only on the basis of internal resources. The most important condition for the formation of students' ability to carry out self-organization and self-education is mastering the essence of these concepts. Therefore, it is advisable to consider different approaches to their definitions of the relationship between them. The expediency of the interpretation of personality self-organization as a competence, which includes personal, cognitive, activity, value-motivational components, is substantiated. The analysis of the essence of self-organization of the individual made it possible to identify all the named components. It is advisable to consider the ability to self-organize as the competence and the most important educational result of higher education