Student retention is a significant challenge for higher education institutions (HEIs). The fact that a considerable number of dropouts from universities are primarily due to academic underperformance motivates universities to develop learning analytics tools based on models for predicting learning success. However, the scalability of such models is limited since students’ academic performance and engagement, as well as the factors influencing them, are largely determined by the educational environment. The article proposes a hybrid approach to forecasting success in completing an academic semester, which involves creating a set of predictive models. Some of the models use historical student data, while others are intended to refine the forecast using current data on student performance and engagement, which are regularly extracted from available sources. Based on this approach, we developed an ensemble of machine learning models and the Markov-process model that simultaneously address the tasks of forecasting success in mastering a course and success in completing a semester. The models utilize digital footprint data, digital educational history, and digital personality portraits of students extracted from the databases of Siberian Federal University, and the resulting ensemble demonstrates a high quality of the forecast. The proposed approach can be utilized by other HEIs as a framework for creating mutually complementary forecasting models based on different types of accessible educational data.

It is important for various participants of the educational process to be able to assess the quality of the educational program, its balance, and compliance with the stated educational results. One of the ways to analyze and evaluate the curriculum of an educational program of higher education can be the algorithm presented in the article, implemented in C++. It allows to calculate various statistical characteristics of the curriculum (for example, the number of educational units (disciplines) and their labor intensity in credits), as well as the relative contribution of an educational unit to the formation of competencies (learning outcomes).The comparative assessment of the main calculation indicators for several curricula of educational programs is implemented as a separate program module. The algorithm implements an approach that allows presenting the curriculum data in a convenient visualization form — as a weighted undirected graph, the vertices of which represent the disciplines of the curriculum, and the edges interdisciplinary links, demonstrating the participation of disciplines in the formation of the same competencies. Visualization of this representation was carried out using the Gephi software package.The program implementation of the algorithm proposed in the article may be of practical interest to scientific and pedagogical staff and administrative and managerial personnel of educational institutions of higher education

The article is devoted to the problems of learning success prediction. The aim of the work is to discuss current tasks and possible difficulties related to the development of services for predicting learning success in the digital environment of an educational institution. Among the variety of forecasting tasks arising in educational analytics, two main directions were identified and examined in detail: prediction of student dropout and prediction of academic performance for courses of the curriculum. The article discusses examples of creating and using predictive models in the educational process by secondary and higher education organizations. It is noted that despite the large number of studies in this problem field, there are only few examples of successfully implemented regional or at least organizational-level forecasting systems. The authors believe that the main obstacles to building a well-scalable system for supporting learning success based on predictive models are difficulties with data unification, lack of policy of using personal data in learning analytics, lack of feedback mechanisms and activities for correcting learning behavior. Solving each of these problems is a separate serious scientific task. The prospects for using the results of the research are indicated.

The paper deals with the problem of forming mathematical digital competency of engineering students. Authors suggest a comprehensive approach to solve the problem which is implemented in a course of applied mathematics for future engineers. The concept of mathematical digital competency of an engineering specialist, the formation of which is the aim of students' training, is articulated. The paper provides rationale for the use of professionally oriented task system for mastering methods of mathematical modelling, computer simulators as well as game simulation models for teaching applied mathematics with the use of +ACI-Teacher-Student+ACI-automated working space. It facilitates quick mastering of basic methods of applied mathematics, computer science, some elements of algorithmization and programming by engineering students. The contents of the virtual laboratory complex for the course of applied mathematics powered by AnyLogic platform for simulation model implementation is described. The description of the developed system for managing student individual work is given. Tools for diagnosing the formation of mathematical digital competency are also presented.

The work is devoted to the development of an approach to the analysis of curricula of educational programs of higher education in the context of the current federal state educational standards in terms of achieving the declared learning outcomes formulated in the form of a set of competencies. This approach may prove useful for developing automated tools for assessing the quality of educational programs, as well as their comparative analysis.We propose a model for representing the curriculum in the form of a simple weighted undirected graph based on the competence-based approach. We propose an approach to the visualization of the graph representation of the curriculum based on the use of a force-directed graph drawing algorithm, which ensures achieving maximum visibility. We propose an approach to determine the interdisciplinary links of educational units of the curriculum based on their total number of credits and the competencies they are involved in. The resulting visual representation of interdisciplinary connections helps to better understand the structure of the curriculum, identify disciplines with the maximum number of interdisciplinary connections, and also decompose the plan into clusters of the most interconnected disciplines. We propose options for defining integral characteristics of graph representations of curricula, based on which the curricula can be evaluated, as well as a comparative analysis of the corresponding educational programs can be performed. As examples, we consider the curricula for the of bachelor programs majoring in 09.03.01 "Computer Science and Computer Engineering" and 09.03.03 "Applied Computer Science ", implemented at the Institute of Space and Information Technology of Siberian Federal University.

Работа посвящена разработке подхода к анализу учебных планов образовательных программ высшего образования в условиях действующих федеральных государственных образовательных стандартов с точки зрения достижения заявленных образовательных результатов в виде набора компетенций. Данный подход может оказаться полезным для создания автоматизированных средств оценки качества и сравнительного анализа образовательных программ. На основе компетентностного подхода предложена модель представления учебного плана в виде простого взвешенного неориентированного графа. Предложен подход к визуализации графовового представления учебного плана на основе применения силового алгоритма визуализации, обеспечивающего достижение максимальной наглядности. Предложен подход к определению междисциплинарных связей образовательных единиц учебного плана через на основе их трудоемкости и формируемым компетенциям. Полученное визуальное представление междисциплинарных связей помогает лучше понять структуру учебного плана, выявить дисциплины с максимальным числом междисциплинарных связей, а также произвести декомпозицию плана на кластеры наиболее связанных между собой дисциплин. Предложены варианты интегральных характеристик графовых представлений учебных планов, на основе которых можно проводить их оценку, а также сравнительный анализ соответствующих образовательных программ. В качестве примеров рассмотрены учебные планы подготовки бакалавров по направлениям 09.03.01 «Информатика и вычислительная техника» и 09.03.03 «Прикладная информатика», реализуемых в институте космических и информационных технологий ФГАОУ ВО «Сибирский федеральный университет». The work is devoted to the development of an approach to the analysis of curricula of educational programs of higher education in the context of the current federal state educational standards in terms of achieving the declared learning outcomes formulated in the form of a set of competencies. This approach may prove useful for developing automated tools for assessing the quality of educational programs, as well as their comparative analysis.We propose a model for representing the curriculum in the form of a simple weighted undirected graph based on the competence-based approach. We propose an approach to the visualization of the graph representation of the curriculum based on the use of a force-directed graph drawing algorithm, which ensures achieving maximum visibility. We propose an approach to determine the interdisciplinary links of educational units of the curriculum based on their total number of credits and the competencies they are involved in. The resulting visual representation of interdisciplinary connections helps to better understand the structure of the curriculum, identify disciplines with the maximum number of interdisciplinary connections, and also decompose the plan into clusters of the most interconnected disciplines. We propose options for defining integral characteristics of graph representations of curricula, based on which the curricula can be evaluated, as well as a comparative analysis of the corresponding educational programs can be performed. As examples, we consider the curricula for the of bachelor programs majoring in 09.03.01 "Computer Science and Computer Engineering" and 09.03.03 "Applied Computer Science ", implemented at the Institute of Space and Information Technology of Siberian Federal University.

Problem statement. Learning analytics is an emerging scientific field, which studies learners and learning process based on data from digital environment. The aim of the study - to observe the development of learning analytics, its prospects and limitations and detecting the state of art of this scientific field in Russia. Methodology . The study is based on context analysis of scientific articles on the topic in the public domain. Special attention is given to reviewing scientific publications of Russian-speaking authors devoted to analytics of education data and the implementation of learning analytics tools in the educational process. Results . The research detects the global directions of learning analytics development and its problematic aspects. It provides the quantitative and qualitative analysis of scientific publications of Russian-speaking authors and identifiers the most popular research questions in the learning analytics field. It proposes the author’s vision of the hierarchy of directions for learning analytics development, consisting of the research aspect, the environment transformation aspect and the legal regulation aspect. The national initiatives in the digitalization of education are briefly discussed. Conclusion . A certain lag in the level of development of learning analytics in Russia from the global one is revealed. At the same time, there is a noticeable increase in interest to this area among individual researchers, educational institutions and at the state level, which allows us to count on positive changes.

Problem statement. One of the approaches to solving the problem of predicting the academic performance of students is displayed. Unlike existing studies in this area, which are mainly aimed at predicting the effectiveness of graduation, that is, based on the results of intermediate certifications that allow us to assess the chances of students to successfully graduate from a university, the results of this study are aimed at predicting the success of education in the early stages of the educational process. Methodology. A feature and novelty of the proposed prognostic model is the forecasting of student performance based on the Markov model, the data sources of which are universal predictors of an e-learning course that determine the success of subject education based on the personal characteristics of the student. Results. The authors present a description of a predictive model for assessing the success of subject education in the context of digitalization of education, reveal their experience of its approbation for students of the Siberian Federal University in the field of study “Informatics and Computer Engineering” and the results of a qualitative assessment of the model. Conclusion. The prospects for building a digital service for predicting the academic performance of students in the electronic information and educational environment of the university based on the results of the study are stated.

Student retention prediction is one of the most important problems of learning analytics. In the global scope research on the topic for higher education is rather extensive, there are cases of successful implementation of education support services in universities. The literature analysis shows of the growing interest in this problem in the Russian scientific and pedagogical community. At the same time, the specifics of Russian education does not allow direct transfer of foreign experience into the domestic educational system.The study reveals that a significant contribution to predicting student retention can be made by models for predicting academic performance in educational courses of the curriculum. The authors propose a structural model of a system for predicting academic performance, which includes a universal model based on generalized indicators of the digital footprint, a course-based model that takes into account the specifics of learning in a particular discipline, and a model based on the student’s educational profile.In the empirical study we trained 5 models for early prediction of interim assessment grades based on the universal indicators of the LMS Moodle student digital footprint. The most accurate model, especially in the first half of the semester, turned out to be ensemble-averaging models of logistic regression, random forest and gradient boosting. It was found that universal models are effective for detection of at-risk students in the discipline, the directions for further improvement of the universal model of performance prediction were determined and conditions for scaling the proposed approach to create a prognostic system for student retention to other educational institutions were formulated.

Long-term monitoring of the safety and reliability of large dams operation has been attracting increasing attention of researchers. Moreover, special consideration is given to the study of dam displacements that characterize its global behavior. The article discusses specifics of constructing predictive mathematical models for studying the deformation process associated with displacements of the high-head dam crest. The authors present the most successfully designed predictive mathematical models for various combinations of input effective factors, including the results of field observations and the calculated values of the component displacements. These models allow forecasting the control points of the dam body for various time stages of its operation. The advantages of using a mathematical model with separate introduction of the main effective factors into the model are shown, thereby eliminating the effect of their multicollinearity. Using the example of the Sayano-Shushenskaya hydro power plant for certain time stages of the dam operation and structures with different temperature conditions (average, warm and cold in respect to annual temperatures), the authors present the results of forecasting the dam displacements.

The article is focused on the problem of early prediction of students’ learning failures with the purpose of their possible prevention by timely introducing supportive measures. We propose an approach to designing a predictive model for an academic course or module taught in a blended learning format. We introduce certain requirements to predictive models concerning their applicability to the educational process such as interpretability, actionability, and adaptability to a course design. We test three types of classifiers meeting these requirements and choose the one that provides best performance starting from the early stages of the semester, and therefore provides various opportunities to timely support at-risk students. Our empirical studies confirm that the proposed approach is promising for the development of an early warning system in a higher education institution. Such systems can positively influence student retention rates and enhance learning and teaching experience for a long term.

A comparative analysis of the Bologna reforms dynamics in Russia and Germany is carried out in the paper. It is shown that extending the field of training Bachelors and developing newmaster programs in a flexibly way, considering the needs of innovation economy, filling education with the competence content, developing the strong constituents within Bologna process make it possible for Russian higher school to strengthen significantly its position in European educational space.

Long-term monitoring of the safety and reliability of large dams operation has been attracting increasing attention of researchers. Moreover, special consideration is given to the study of dam displacements that characterize its global behavior. The article discusses specifics of constructing predictive mathematical models for studying the deformation process associated with displacements of the high-head dam crest. The authors present the most successfully designed predictive mathematical models for various combinations of input effective factors, including the results of field observations and the calculated values of the component displacements. These models allow forecasting the control points of the dam body for various time stages of its operation. The advantages of using a mathematical model with separate introduction of the main effective factors into the model are shown, thereby eliminating the effect of their multicollinearity. Using the example of the Sayano-Shushenskaya hydro power plant for certain time stages of the dam operation and structures with different temperature conditions (average, warm and cold in respect to annual temperatures), the authors present the results of forecasting the dam displacements.

The world is going through a period of the rapid development of electronic learning systems. In addition, the creation of a digital educational environment and the formation of scientific ideas about using such systems in the educational process are currently taking place. This is of particular importance when teaching small-numbered indigenous peoples living in bilingual and multilingual regions. The article aims to develop an approach to organizing mathematics e-learning for students in a bilingual environment using mechanisms for adapting educational content to specific linguistic features. The study used scientific literature analysis and empirical methods. We suggest that adaptive e-learning courses be a means of e-learning in mathematics. They enable students to pursue an individual educational route and ensure content adaptation according to students’ language and the national peculiarities of their perception of learning materials. The result of the present study is an individual educational route created in an adaptive e-learning course in mathematics in a bilingual environment. In the future, the results of the research can become an element in the methodological system of personalized adaptive learning aimed at the preparation of a university student in a bilingual environment.

In modern systems, remote sensing widespread two-dimensional fast Fourier transform (FFT) for processing satellite images and the subsequent image filtering. In this paper we consider the possibility of using combinations of high and low frequency filters to improve global images terrestrial surface.

We construct a minimal cubature formula of degree $$2$$ for a torus in $${\mathbb R}^3$$ .

The article proposes a methodology for the formation of functional mathematical literacy of primary school students as a component of functional literacy. This methodology is based on mathematical models and their animation illustrations. Based on international research, it is shown that mathematical modeling is the most important universal action of a student in primary school. Examples of transformation of standard tasks for movement into tasks that are more close to reality are given, in solving which it is useful to use animation modeling, which involves the creation of children's animation for educational purposes. Animated videos illustrate the solution of non-standard mathematical problems, problems with unstructured, redundant or insufcient information. The activity of creating animation models allows students to increase the level of mathematical literacy, which is confrmed by the data of the pedagogical experiment.

. On the basis of the developed facet dynamic adaptive tests-simulators, there were obtained protocols of educational actions numerical evaluation on facet classification of English language tenses, for a random sample of 150 students. Testees are taught the facet classification of puzzles with sentences in English in a randomized puzzle electronic problem environment, in the conditions of numerical reinforcements of the actions of a testee: + 1 correct; - 1 incorrect actions. A self-consistent change in the relative frequency of reinforcements helps to adapt and increase the level of autonomy of testees. The qualification approach to the dynamic evaluation of the educational activity protocols made it possible to specify three groups of testees: those who have achieved the state of autonomous educational activity; approaching the state of autonomous educational activities; with insufficient training in foreign languages or with "trained" helplessness to bilingual activities