Abstract: 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.

Abstract: The article is devoted to one of the urgent problems of modern mathematical education: the formation of educational and research skills of students in the process of solving problems in the subject area “Mathematics”. The levels of formation of educational and research skills of students are described, based on a set of criteria identified by N.A. Menshikova. It is shown that for the formation of educational and research skills of students it is advisable to use blocks of interrelated educational and research tasks that allow students with a low level of formation of educational institutions to participate in solving problems of a higher level of complexity.

Abstract: The problem of the formation of personality activity in teaching mathematics is very complex. The question remains for the teacher of mathematics: what methods to apply so that teaching mathematics is effective and practice-oriented, develops personality activity in collective mathematical activity? The paper describes the specifics of the use of case technology in teaching mathematics.

Abstract: 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.

Abstract: The article the role and place of the course «Elementary mathematics» in the subject-methodical preparation of the future teacher of mathematics at the present stage of higher pedagogical education.

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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.

Abstract: In the article presents the classification of problems by differential geometry, which is based on the nature of the relationship between the elements of the problem and the relationship between the reproducing and creative activity of students in their decision. It is shown that an important source for the choice of texts of problems and methods of their solution are the works of scientists – creators of classical differential geometry. Work with the corresponding scientific text allows the student to master such an educational strategy as methodological reduction.

Abstract: The article briefly describes the changes in the main types of professional activity of future mathematics teachers, describes the experience of organizing research activities of future mathematics teachers at the undergraduate and graduate levels.

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The article identifies four categories of goals for studying mathematics at school: mastering theoretical positions at the evidentiary level, mastering algorithms for solving mathematical problems that illustrate the provisions of the theory, using the studied algorithms to solve applied and research problems, using mathematical methods and algorithms for teaching programming. Such a selection makes it possible to substantiate and specify the use of digital technologies in the course of mathematics, as well as to ensure their continuity, including with subsequent higher education courses. The importance of using mobile and cloud technologies and applications in independent (home) work of students in mathematics is emphasized.

Abstract: The article describes the main difficulties that students face in the initial period of study at a higher educational institution as part of the study of mathematical disciplines. Possible ways of overcoming these difficulties for students in the field of training Pedagogical education – future teachers of mathematics – on the example of the discipline «Mathematical Analysis» are given.

Abstract: The translation of the school system of knowledge into a formal language to create an ontology of school educational mathematics showed that there are gaps indicating significant shortcomings in the design of the contents of the geometry course. A study among students of N.I. Lobachevsky Institute of mathematics and mechanics of KFU to determine the quality of understanding of generic concepts, graphic representations of geometric figures, the results of which showed the relationship between the problems in the presentation of the content of the school course of Plane geometry and the quality of students' knowledge.

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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.

Abstract: The article analyzes the relationship of the national project «Education» of the state program of the Russian Federation «Development of education» with the training of teachers of mathematics and computer science at the university. The paper identifies the main directions of the national project, which should be the basis for the modernization of educational programs aimed at training specialists in the field of mathematics and computer science, teachers of the subject areas.

Abstract: The purpose of mathematical training of bachelors of technical specialties in the framework of the competence approach is the formation of mathematical competence of the specialist, which is expressed in the ability of graduates to apply mathematical methods in professional activities. Competences are acquired by students in the process of mastering the content of education fixed in educational standards and curricula of disciplines. Using new methods and forms of organization of the educational process, using new teaching tools, competencies are formed in lectures and practical classes in higher mathematics.

Abstract: The problems of teaching elementary mathematics for foreign citizens at Perm National Research Polytechnic University are considered.

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The developed educational projections, levels and prerequisites of the mathematical educational multilingual ontology OntoMath^Edu are presented. Educational projection is viewed as the formalization of a certain system of subject training in mathematics. It is a subset of OntoMathEdu ontology concepts, which are structured at this stage of ontology development using two didactic relationships – educational level and prerequisites.

Educational levels are allocated on the basis of the teaching standards of the corresponding education system, the relation of prerequisites is determined by the sequence of the studied concepts in a particular education system.

The OntoMath^Edu ontology defines two projections representing the educational systems of Russia and Great Britain. The algorithm for constructing an ontology through linking various projections allows it to be further replenished with new educational projections, which can later be used in the system of multilingual teaching of mathematics.

Abstract: Experience of designing different variants for web-based development environment (IDE) for Optimizing parallelizing system and compiler for reconfigurable architecture is described. Designed system is based on existing tools and frameworks such as Jupyter Notebook and Eclipse Che. Set of requirements for Optimizing parallelizing system components is developed to make it possible to integrate them into web-based development environment accessible through the Internet. Designing portable environment for compiler development, compiler technology demonstration and teaching parallel program development is also described. Examples of performing newly developed program transformations are shown to be used during program optimizations for FPGA inside the designed web environment. Means of program transformation visualization are described for use with Jupyter Notebook. The work shown demonstrates possibility to organize remote access to library of instruments and tools for program optimizations currently under development that would be convenient for application developers.

Abstract: The article describes the experience of organizing joint activities of undergraduate and graduate students in analyzing the forming of professional activities during the period of teaching practice.

Abstract: 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.

Abstract: In the article proposes a set of methods for teaching algebra at school, which contributes to the adaptation and development of the personality of the student, to increase the efficiency and scientific nature of teaching mathematics.

Abstract: Actual problem of modern theory and methods of teaching mathematics – teaching methods of self-regulation in the process of solving mathematical tasks.

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The article proposes a methodology related to the use of integrated project tasks in teaching mathematics, based on the practical application of the acquired knowledge in mathematical disciplines in conjunction with computer modeling and programming. Examples of specific integrated project tasks are presented.

Abstract: 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.

Abstract: There were identified problems that arise in the teaching of mathematics a medical university. We considered the ways of organizing independent work at each stage of studying a subject by using an electronic training course implemented on the Moodle platform. We studied the students' attitude to the components of the course, which allows to assess which resources are the most demanded.

Abstract: 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.