The article deals with the problems of organizing programming practice for schoolchildren aged 13–17, as well as the problems of their motivation. A methodology and a software platform are proposed that provide such students with a workshop on algorithmization and programming by implementing algorithms written in various programming languages on this competition platform.

The article describes the experience of digital transformation of mathematical disciplines based on author's digital educational platform Mirera. The Mirera DEP is optimized for the Russian system of organization of higher education, focused on the development and delivery of courses that combine online and offline technologies for conducting the educational process. The Mirera DEP provides course authors with tools for developing computerized courses with automated verification of the correctness and independence of current and control tasks performed by students using artificial intelligence methods. Various original types of tests are built into the platform, supporting both in the description of tasks and in answer options, content in various formats, including TeX, sequences of elements (for automated testing of student knowledge of the structure of proof of course theorems or schemes for solving typical problems), semantic analysis of text responses, etc.

This article discusses the application of vector models for the preliminary analysis of students' free-form answers. Vector representations of words and documents were obtained using word2vec, doc2vec, and BERT models. The similarity between the answer given by the student and the correct answer was determined using the cosine measure. It was found that vector models allow identifying obviously incorrect answers with sufficient accuracy. For answers that are close in wording, an additional verification step is proposed. Using word2vec, binary classification of answers to certain questions was performed, and accuracy, precision, recall and F1-measure estimates were given.

Cognitive abilities cover all higher human intellectual functions, including oral and written speech. The use of ellipses in writing is associated with the ability to clearly formulate a thought, avoiding the redundancy of its expression. Testing the ability to use ellipses can be the basis, on the one hand, for assessing the cognitive operation of generating ellipses in writing and detecting violations of this operation. This can serve as the basis for the early detection of dementia in medicine. On the other hand, such testing can be used to teach speech technologies, including in foreign languages. From a scientific point of view, it is important to determine the influence degree of training on the performance of text tasks. The article describes the development of a computer system for remote on-line testing the operation of converting a complete sentence into a sentence with an ellipsis of a certain type, the principles of evaluating the results of testing the subjects. The concept of the system is discussed. The structure of system and software development environment are described. A feature of the system is the creation of a new type of tasks related to natural language processing. The complexity of the development is determined by the need for automated formation of a bank of sentences’ pairs in natural language without ellipses and with ellipses of a certain type, which entails the inclusion, in the software environment, of text parsing tools and algorithms for automated formation of ellipses and / or restoration of complete sentences from elliptical ones. In conclusion, the prospects for the development and application of the proposed system are discussed.

A service for generating and visualizing educational cards of mathematical concepts based on the ontology of school mathematics OntoMathEdu is presented. The main stages of collecting information for displaying the concept card are given. The developed service is used as a recommendation system in the distance education course of KFU "Technology for solving planimetric problems". Mathematical concepts located in the texts of lecture materials are enriched with links to the corresponding concept card on the service.

The article discusses the possible use of LMS Moodle in the development of the course “The use of computer modeling in education”. The course is based on the introduction of interdisciplinary integration of higher mathematics, computer modeling, programming into the educational process and involves the use of computer mathematics systems and software environments. Examples of specific integrated tasks are presented.

When designing the training course “Using Computer Simulation in Education” in LMS Moodle, the following set of elements was used: “lecture”, “task”, “test”, “forum”, “resource”, “wiki”, “chat”, “glossary”.

The use of the methodology for compiling integrated tasks based on LMS Moodle showed that: integrated tasks using information technology help to increase the level of mastering the material of complex sections of higher mathematics; the content of the course of higher mathematics is the fundamental basis of the material studied in the proposed course, and contributes to a deep understanding of mathematical disciplines; integrated design tasks form practical skills and abilities of computer modeling using programming in various software environments.