The review article examines the field of scientific research devoted to the analysis of errors in mathematics. The problem of mastering mathematical concepts by younger schoolchildren continues to be relevant in pedagogical psychology. Systematic work with students' mistakes is an important stage in the teacher's work. The review shows the significance of the analysis of mathematical errors. The importance of not only detecting systematic mistakes of students, but also the misconceptions about concepts behind them is substantiated. The reasons for the typology of errors are revealed in the context of a discussion about the relationship between conceptual and procedural knowledge. Various approaches to the typology of mathematical errors are described. The typology of errors based on the identification of error patterns, which has become widespread in research, is considered in detail. In this typology, three large groups of mathematical errors are distinguished: factual, procedural and conceptual. Examples of these errors are given on the material studied by younger schoolchildren.

The article presents the results of testing an innovative product, developed in MSUPE, simulation teaching activities of the mathematics teacher of the first class. Discusses the possibility of using simulation for the formation of the labour features of the future teachers. The analysis of the place of use of the simulator in the context of the modular principle of teacher education that combines learning of the theoretical knowledge with their practical application. Are obtained in the course of the study, data on changes in the ability to carry out meaningful reflection, reducing external learning motivation in the experimental group of students. On the basis of the observations given the qualitative analysis of students ' attitudes toward a new software product and its role in the development of the content of the training module. A number of conclusions about the effects and prospects of the use of simulation teaching.

<p><span lang="EN-US">The article discusses one of the aspects of the training of a teacher of primary general education &ndash; the ability to analyze the causes of students' mistakes made by them when mastering mathematical concepts. The special importance in the competence of the primary school teacher of understanding the value of the initial, initial representations of the child as a result of his own mental activity is noted.</span><span lang="EN-US"> An overview of the concept of mathematical thinking in the psychological and pedagogical literature is given. The understanding of mathematical thinking as theoretical, carried out on mathematical material, is highlighted. The levels of development of mathematical thinking and its main components &ndash; analysis, planning and reflection &ndash; are recorded. The modules of the educational program for the training of primary school teachers are described, aimed at developing students' competencies that allow them to adequately assess the manifestations of mathematical thinking in younger schoolchildren on mathematical material traditionally studied in primary school. The sequence of actions aimed at identifying the error pattern is presented. Examples of tasks for students are given, showing ways of developing the educational action of control; determining patterns of mathematical errors.</span></p>

At the present time, the development of dexterity, the development of normative indicators that characterize the level of development of dexterity in preschoolers, remains an urgent problem. The paper analyzes the level of physical fitness of children aged 5–6 in the process of physical education using specially selected physical exercises and gives recommendations for the development of sets of exercises for the development of dexterity in preschool educational institutions.

The article provides an assessment of the psychological compatibility of those who go in for sports acrobatics at the stage of improving sportsmanship. The results of the study confirmed the influence of the level of harmony and compatibility on the achieved result in the course of competitive wrestling.