Globalization of all spheres of activity of educational systems determines the need to create simple and accessible tools for monitoring and evaluating the quality of objects and resources. In particular, due to the need to intensify the processes of digital transformation of education, it is important to assess the quality of digital educational environments (DEE). The aim of the work is to substantiate the approach and describe the procedure for monitoring of DEE of educational institutions based on the available cloud services, providing convenient collection, accumulation, and processing of statistical and monitoring indicators.The projective criterial model of the system of assessment and monitoring of the quality of DEE, which is based on the results of self-assessment of the educational organization and external expert evaluation, was adopted. The main feature of the model is the participation of organizations and external experts in the process of designing criterion rubrics, conducting and analyzing the results of monitoring. Yandex Forms service is used for self-assessment of DEE and expert evaluation of the educational organization website which allows converting of the collected data into spreadsheets. By combining the data and their statistical processing it is possible to obtain indicators for different slices and ratings, to conduct a summary clustering of the DEE of the studied organizations by three levels: low, average, and high.The proposed model was implemented in the assessment of DEE practices of supplementary education for children. To determine the quantitative and qualitative indicators of the DLE and the official sites of additional education organizations we created questionnaires in Yandex Forms filled in by the representatives of the studied organizations. Pilot testing showed that the collection, processing, and delivery of monitoring data to users was technologically simple and easy.The projective criterial model for assessing the quality of the DEE of supplementary education organizations can be used for many other studies related to criterion-based assessment activities.

The relevance of the research under consideration is due to the need to improve the efficiency of the analysis of the quality, and completeness of the knowledge obtained by students when solving computational problems, the example problems in mathematics. The theoretical argumentation is proposed and the practical implementation of an intelligent automated analytical system for analyzing the quality and forecasting the content of educational material and the trajectories of the student's learning direction is described. The relevance of the research is the creation of neural network algorithms that allow analyzing the dynamics of changes in the student's level of formation of skills to solve arithmetic problems. The methods of analyzing the assimilation of educational information and methods of personalized construction of the curriculum for each student are substantiated.

Problem relevance. Due to the multi-departmental concepts and the different content of educational programs of schools and universities, a serious problem arises of the succession and continuity of the education system along the “vertical” in general and subject teaching in particular. Another didactic problem is the need to ensure interdisciplinary connections of basic courses in the traditional disciplinary model of the educational process for more effective and expedient formation of certain student’s competencies sets. In this regard, it is of interest to create new organizational and meaningful approaches to training specialists without a significant restructuring of the traditional educational process.The purpose of the article is to substantiate a collaborative model of subject training of students in a school-university cluster of disciplines, which ensures the succession and continuity of education at school and university.Methodological basis. On the example of three disciplines “Programming”, “Computanional Methods”, “Information Technologies in Education”, a cluster model of teaching schoolchildren and students in the direction of training “Mathematics and Computer Science” has been designed and implemented. A feature of the considered school-university cluster of disciplines is a unified methodological base of target, meaningful and didactic elements that form and develop the calculative-algorithmic component of the computational thinking of students. The basis of the means and methods of teaching in the cluster is made up of cognitive techniques and a platform of “computational and algorithmic primitives” — solving elementary task template. A recursive approach is used in the methods of cluster subject teaching of schoolchildren and students.Results and Conclusions. The model of the created disciplinary cluster “Programming — Computanional Methods — Information Technologies in Education” contributes to the formation and development of the calculative-algorithmic component of the computational thinking of schoolchildren and students, and also forms their assigned groups of competencies. The school-university cluster of disciplines ensures real succession and continuity of school and university education, without unnecessary, sometimes artificial, labor-intensive additional organizational and methodological means and techniques. The approach under consideration can be used to create clusters of disciplines in various educational areas, allowing their meaningful collaboration and forming given competencies sets and schoolchildren’s and student’s cognitive abilities.

The transformation of education, caused by the constantly changing demands of society and the avalanche growth of information, necessitates the search for new means of training future teachers, focused on the formation of universal qualities of a specialist. The creation of psycho-pedagogical classes requires expanded research into ways to improve pedagogical training with continuity at all levels, starting from school. Considering the focus on professional training, it is important to model the structure and content of educational tools that allow forming not only subject knowledge but also the readiness of future teachers to “learn to teach” adequately to the cognitive characteristics of modern students and the trends in the formation of digital content.The aim of the article is to substantiate the method of creating end-to-end inversion textbooks that allow forming and developing the readiness to learn to teach in students planning their future professional activities in the educational field (by the example of studying the topic of the informatics course “Information and information processes”).The literature analysis allowed us to identify three tools for modeling the format of presentation and structuring of the textbook content: the “inverted” or inversion (question-task) format of the structural composition of educational content; the end-to-end or vertical selection of educational content according to the principle of “vertical lever”, the principle of “transparent” box” based on structural mental diagrams for visualizing all components of educational material (theory, tasks, control methods). Using the example of the topic “Information and information processes”, the article shows the technology of applying these tools in compiling of innovative teaching resources is shown.An expert assessment of the created textbook confirmed the possibility and feasibility of its use in psycho-pedagogical classes and pedagogical universities for training, self-study, and self-control of students.

In the context of the global information boom, the question-and-answer form of teaching is the most preferable and effective for the digital generation, as it is oriented to maximize the activation of learners’ thought processes. Despite the fact that question-answer teaching is not new in pedagogy, practice shows the low readiness of teachers to design learning questions. The article is devoted to clarifying and describing the approach to constructing learning questions. In practice, this approach would allow the teacher to competently formulate learning questions to achieve better educational results, and students not only to search for answers to them, but also to learn how to compose questions themselves.The main idea of the approach to constructing learning questions is information modeling of objects and concepts of the subject area. The methodology of designing learning questions supposes the decomposition of the information model of educational material in accordance with its structure, presentation features, and educational effect. Educational material is usually classified by educational functions: theory, practice, control. Accordingly, three algorithms for composing questions are identified: on theoretical material, on practical material, and questions on understanding, which are control and measuring tools.The proposed approach to constructing learning questions for various types of educational material may be of interest to teachers, students of pedagogical universities, as well as students of psychological and pedagogical classes. The approach will also be useful for developers of electronic educational resources. Further research in this direction is planned to be expanded to the creation of a theory of learning questions from the perspective of the digital transformation of education.

The purpose of the study. Modern teaching tools and methods, as a rule, implicitly rely on the “black box” model. In contrast, the “white box” model has clear didactic advantages. Unfortunately, they are difficult to implement in the educational process due to the lack of available ways to construct this model. The purpose of the study is to develop a technology for constructing a “white box” model in the form of a structural and mental scheme of calculation tasks in the field of elementary physics. This technology involves the use of calculation primitives to design task schemes by superposition.Materials and methods. Development of technology for constructing the “white box” model in the form of a structural and mental scheme of calculation tasks in the field of elementary physics. The use of calculation primitives to construct task schemes by superposition. Determining the complexity of a specific task through the number of primitives involved in the “route” of the solution. Organization of students’ training according to the “white box” model with visualization of the process of forming skills to solve calculation tasks.Results. Schemes have the ability to ensure the strength and completeness of the formation of the ability to solve problems of the student. At the same time, the variety of routes and the set of weights of the paths make up the information model of learning. As an example, structural and mental schemes on the topic “thermal phenomena” are presented. They show the need to use several types of primitives, in particular, function primitives, sum primitives. Structural and mental schemes allow students to organize training according to the “white box” model, visualize the process of formation and development of students’ skills to solve calculation tasks, thereby ensuring control and self-control of educational activities.Conclusion. Based on the provisions of the mental approach, a technology for constructing structural and mental schemes representing a cognitive way of thinking in solving computational problems is proposed. The basic technology is computational primitives, with the help of which problem schemes are constructed by superposition. The complexity of a particular task is determined by the number of primitives involved in the “route” of the solution. The proposed technology is applicable to the construction of structural and mental schemes of computational problems in various subject areas.