Opportunities are investigated and examples are provided of using Python libraries at the solution of the typical mathematical tasks. Features of interpretation of the received results are analyzed.

The paper presents the methodology of training students of mathematical specialty pedagogical University in the paradigm of mixed learning with elements of distance learning, combining classical didactics and didactics of e-learning.

Within the framework of this article, the content of applied mathematical training of an economist in the context of digitalization of economic education will be considered as one of the objects of pedagogical design. Traditionally, the content refers to one of the components of methodological systems, which acts as the main accumulator of the teacher’s pedagogical, didactic and methodological experience. The main directions for improving the applied mathematical training of an economist for working in the digital economy are given. Under the influence of the digitalization trend, basic and variable didactic modules are highlighted.

This article presents the results of a systematic literature review on the matter of universities’ experience with implementation of digital learning. The findings point out the advantages, disadvantages, discrepancies, problems, challenges, and possible solutions. The conclusion section contains general expectations in respect of the quality and effectiveness of digital education. Finally, the recommendations on how to minimize negative consequences are formulated.

The article presents using the van Hiele theory of geometric thinking for the organization of mixed training of students of the pedagogical Department of the N.I. Lobachevsky Institute of mathematics and mechanics KFU on the basis of SPOC course «Elementary mathematics: Plane geometry». Training includes the use of various IT-techniques and tools that can improve the quality of learning and form the necessary professional competence of the future teacher of mathematics. The course implements the technology of project-modular and inverted learning.

The article is devoted to dynamic adaptive testing of educational activity of high school students in Krasnoyarsk to solve mathematical problems of transformation of the graph of a quadratic function in electronic problem environments. Dynamic adaptive test simulator allowed to conduct: pre-test, diagnosing the level of residual knowledge of students; dynamic assessment of educational activities in the process of self-learning problem solving; post-test, diagnosing the level of training of students.

The paper identifies professional tasks that need to be solved by a computer science teacher in a digital educational environment. The author presents the experience of organizing and supporting research activities of students of pedagogical Universities related to the study of the application of digital technologies in education.

The article discusses the recursive ratios implementation in solving mathematical problems using instrumental software resources. It is emphasized that programs development for solving such problems contributes to a deeper understanding of the recursion process essence.

The article is devoted to the use of digital educational resources in the process of teaching mathematics in a primary school. The possibility of using the ”Living Mathematics” electronic educational-methodical set with teaching guidelines on the topic ”Remarkable points of a triangle. Euler's line”. The article is addressed to teachers and students of pedagogical universities, methodologists, teachers of mathematics.

The article shows the impact e-learning on modern approaches to the traditional educational process. Reveals the problems and contradictions of the use of e-learning in general education institutions.

Some results of implementation of the “soft” model of geometry teaching in schools of Nizhny Novgorod region are considered. The realization is based on the ideas of experimental mathematics, according to which the content of educational materials (open problems in geometry) is selected and developed. In addition, it is contributing to the development of students’ intelligence. Thus, student models the geometric situation using open-source software actively, is mobile in the selection of the software, understands geometric facts and regularities, acquires the ability to argue (to analyze, to compare, to generalize, to make conclusions). The experience of the using computer experiments at geometry lessons is examined form psychodidactic approach’s point of view. The advantages of special educational tasks are proved: open problems in geometry, which are based on the “soft” model of teaching geometry using the ideas of experimental mathematics. The peculiarity of the proposed open problems in geometry is that they, being a projection of traditional closed classical problems in geometry, at the same time, firstly, provide the formation of the main components of the mental (cognitive, conceptual, metacognitive, intentional) experience of the student and, secondly, create conditions for the manifestation of individual cognitive styles of students. Enrichment of metacognitive experience is carried out by means of chains of tasks, which create conditions for formation of abilities to plan, predict and control the mathematical activity.

The article is devoted to consideration of the services of the platform LEARNIS: web quests “Escape the room”, intellectual game “Your quiz”, terminology game “Explain me”. With their help, teachers of any subject area can conduct educational classes in a fun way. Considered services are elements of the system teaching methods proposed by the authors based on mobile technologies.

Рresents educational and research building model trajectory.

The issues of development of intersubject communications at the present stage of the formation of digital education in the preparation of student architects are discussed. The idea of strengthening intersubject communications, mathematics and architecture is defended by a new meaningful replenishment of educational programs, mastering digitalization skills when solving mathematical problems by mathematical methods, and involving elements of competition implemented using Web technologies in educational activities.

The main alternatives for the use of mobile devices in the educational process are highlighted. The alternative is the mobile device while it is a tool for a working with specialized and universal applications. In addition, the alternative is the mobile device helping to use augmented reality.

The article presents significant changes in the field of education, taking place in connection with the active and systematic application of digital information technologies. The main directions of development of informatization of domestic education in conditions of realization of opportunities of digital information technologies are justified and described. The high-level characteristics of the main components of traditional pedagogical science (including didactics) and pedagogical science in conditions of informatization of education of the period of digital technologies have been revealed. The definition of didactics of digital information technology period is presented.

In article the main requirements to development and deployment of the automated information systems at the Almetyevsk state oil institute on the basis of the analysis of operation of a control system of educational process of higher education institution are formulated.

The article describes the designer of electronic lessons in the platform "Electronic Game School", created by a creative group of teachers of the Sterlitamak branch of Bashkir State University.

The article focuses on the issues of modernizing the teaching of mathematical disciplines in the context of the digitalization of pedagogical objects: the educational process, methodological systems for teaching mathematical disciplines, educational paths for the development of key and subject competencies in the field of mathematics, mathematical and simulation modeling. The demand for digital technologies and digital products for the practice of mathematical preparation of the future bachelor is noted. From a methodological and research point of view, digital technologies are described that are essential for improving the quality of mathematical training.

The article defines the understanding of methodological approaches to the development of information competence of university students. It describes modern scientific concepts and methodological foundations that formed the basis for the selection of methodological approaches of the process under study. The combination of the content component, methods, means and forms of organizing the process of developing the information competence of university students is highlighted.

The need for schoolchildren to develop safe behavior skills in cyberspace is justified in the article. One way is to use web-quest technology. The article contains a brief description of this technology and an example of its use in teaching the basics of cybersecurity.

Modern terms set for the education new challenges and for mathematical education in particular. It must give possibility of achievement the necessary level of mathematical knowledge to every student. In this connection the content of mathematical education should be decisive in the transition from competencies to computer competencies and to computer competencies that significantly improve eastern requirements in the digital economy

This article discusses the project approach in the organization of educational activities. A brief description of educational and research projects in NArFU is given.

The article discusses the current problems of software development technology based on an object-oriented programming approach

We consider the construction of an internet site for students of technical university. We use the construction and management of the site program JOOMLA. The site can contain the materials for the students, results of an exam and so on.

In this paper, we consider ways of using systems of dynamic mathematics (Geogebra and others) in the project activities of secondary school students. The advantages of the approach under consideration are compared both with the use of computer programs in the framework of the standard educational process, and in comparison with traditional approaches in the organization of project activities.

The article discusses the main positions of using the methodological system of teaching the basics of mathematical informatics of future teachers of mathematics. Cloud technologies are considered as one of the means of learning and as an object of study.