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Introduction. The authors show the necessity for preschool teachers to know how to develop the ideas of square, its measurement and the comparison of subject squares in preschoolers. The main preschool curriculums and a large body of literature on the problem were analyzed, which revealed the lack of methodological sources for the development of ideas about square. As a result, the authors have designed and described the appropriate methodology.

Methods. The section describes four stages of getting familiar with square for preschool-age children: 1) the development of an idea of the square of objects and their comparison through the method of imposition; 2) measuring and comparing square of figures using conditional measurements; 3) the determination of the dependence of the measurement results of the square on the size of the measurement; 4) familiarization with the generally accepted standard measures of measuring square in centimeters. At each stage, the features of introducing the new material are considered, and examples of tasks and exercises are given. The conditions for the effective development of ideas about the area of objects in preschoolers are described. Positive aspects of the development of preschool children are revealed when they get familiar with the mathematical concept of “square”.

Conclusions. The authors note that the designed methodology has been successfully applied by educators of preschoolers and senior preschool groups for schools in kindergartens in Stavropol. It is shown that the fulfillment by preschoolers of the relevant thematic tasks and exercises contributes to the development of their sensory abilities, logical thinking, coherent speech, attention, and memory, which will favorably influence further education in primary school and will be useful in practical activities.

This article deals with the implementation of the federal state educational standard as guarantee of psychological safety in the learning environment of a post-conflict area. The optimal ways of implementing the federal state educational standard for all participants in the learning process are distinguished, with the goal of increasing the level of psychological safety in respect to difficulties connected with the particularities of the post-conflict area. The sources of the threats that should be taken into account for guarantee of psychological safety are pinpointed. The psychological follow-up of the implementation of the federal state educational standard is discussed.

The author notes that the most important international initiative in education quality assessing including pre-schools is to determine “sustainable development goals until 2030”. As part of this initiative, national experts, UNESCO and Brookings Institute experts have been engaged in elaborating an initiative to measure the quality of education - Learning Metrics Task Force (LMTF). The author emphasizes the similarities between the areas of quality preschool education development in the LMTF initiative and those contained in the pre-school education FSES. The article deals with the evaluation of Russia’s pre-school education quality using the ECERS scales. It is noted that the ECERS Scales are already being used by two regions in Russia - the Republic of Sakha (Yakutia) and Moscow. According to the author, the experience of using the ECERS in Russia has shown these international tools to be highly relevant to Russian pre-school education, comprehensible to teachers and experts, and to offer a great potential for developing the Russian system in terms of interaction between kindergarten teachers and preschoolers. The toolkit is of interest to researchers and specialists in regional education systems, heads of pedagogical universities alike because it enables them to get a comprehensive picture of quality both in individual establishments and in the preschool education system as a whole.

The correct behavior in extreme situations is often a key to salvation. The article describes the content of the educational field “Security”, the value of outdoor games for physical development and consolidation of ideas about the basics of the fire safety. Outdoor games designed to strengthen the knowledge of the fire safety among children of preschool age are described.

The purpose of the article is to show the results of a study on the diagnosis and development of historical memory among future teachers of preschool organizations studying in Russian regions with state national-Russian bilingualism. The empirical basis of the study was the pedagogical departments of the universities of Tatarstan, Chuvashia, and Mari El. In the course of diagnosing the level of development of historical memory among future teachers, it was found that more than half of them do not have historical memory, a third of students admit that they are not ready to form historical memory in their future students in educational institutions, many have a poor understanding of events that have historical significance for the country are lost in the concepts of a large and small Motherland characteristic of a bilingual environment.

The problem is that universities practically do not conduct diagnostic monitoring of the development of historical memory; many teachers ignore these issues when students master worldview and communication modules; there is no effective strategy for the formation of historical memory as a basic basis for the education of patriotism and citizenship in classes in the disciplines of the general cultural block. In total, 1886 students and 12 university teachers took part in experiments (diagnostic and formative) over 5 years (2019–2023).

The research methods used were questionnaires, testing, pedagogical observation, pedagogical experiment, generalization of research results at interregional scientific and practical conferences, and mathematical data processing.

The main results of the study were problem areas in the formation (unformation) of students’ historical memory in the conditions of state national-Russian bilingualism, a pedagogical strategy for the development of historical memory in the process of mastering the disciplines of the general cultural block, and methodological recommendations for the formation of historical memory in bilingual regions.

Conclusions. In universities with state national-Russian bilingualism, it is necessary to carry out diagnostic monitoring of the development of students’ historical memory, identify problem areas of this development, and design pedagogical strategies for patriotic education based on the data obtained. Promising areas of pedagogical research can be models, technologies, means of forming historical memory when mastering disciplines of both general cultural and professional blocks, as well as the formation of historical memory in the conditions of scientific research or teaching practice.