Introduction. The era of post-industrial society of knowledge differs from the previous socio-economic period in many important aspects: total digitalisation, automation and robotisation, and furthermore, cross-disciplinary integration of various scientific fields, among which mathematics is of particular relevance. Over the last decades, the language, tools and methods of the digital era have emerged as the basic universal research tools in physics, biology, chemistry, and engineering, organisation of production and in many other theoretical and applied spheres of activity. Against the background of progressively advanced mathematisation, which covers larger functional intellectual space, it is extremely important to provide the fundamental, advancing nature of mathematical training of students, including in the first place the students of the pedagogical directions. The graduates of pedagogical higher education institutions will have not only to convey certain academic educational information, but to coordinate educational trajectories according to a training maxim in their lifetime that is hardly possible without understanding of basic mathematics.The aim of the present publication is to discuss methodological, culturological and didactic aspects of mathematical training of students of the pedagogical directions.Methodology and research methods. In the course of the work, the authors used the provisions and requirements of the new Federal State Educational Standards (FSES). The psychological and pedagogical framework of the research is based on the concepts of developing learning and upbringing, vocational and pedagogical orientation of training of future teachers and the idea of lifelong education. The analytical review and synthesis of the content of philosophical, mathematical, pedagogical, methodological literature and normative documents was conducted. The state of mathematical components of pedagogical education and its ways of fundamentalisation were considered according to the theory of training, comparative, culturological and system-based types of analysis.Results and scientific novelty. The authors note the imbalance between the fundamental mathematical preparation, which is relevant for a modern person, and the competency-based approach, which currently dominates in education and constraints to students’ holistic understanding of mathematical area of knowledge, even within the boundaries of a particular discipline. The situation is exacerbated by an avalanche distribution of information technologies. One of the negative consequences of this situation is replacement of meaningful learning of mathematics with “coaching” of school students and university students for formal test performance. To address these challenges, culturological educational models, which form common cultural ideas of modern mathematics according to the principle of a cultural conformity, have to be the predominant in education, but not competency-based attitudes focused on narrow specialisation. Mathematical modelling, discrete mathematics and computation processes are identified as the most significant components of a new stage of universal mathematical culture evolution. As a result of a digital era, general-education concepts have already become the key concepts of various sections of mathematics, therefore, it is necessary to start a general introduction to the study of these concepts at the stages of school education.It is highlighted that fundamentalisation of mathematical preparation plays the leading role in the development of logical and professional innovative thinking of students through the understanding of multifunctional structures and schemes (as means and knowledge methods) similar to mathematical structures and schemes. It is appropriately useful to include special courses into a variable part of the master’s programmes (according to education directions), implying students’ research activities: “Mathematical Modelling in Professional Education”, “Bases of Modern Mathematical Culture”, “Discrete Mathematics”, “Mathematical Bases of the System Analysis”, etc.The authors are convinced that the introduction of the concept of mathematical preparation, based on the culturological and system-based approaches, will help to resolve an apparent contradiction between, on the one hand, the necessary integration and fundamentalisation of knowledge acquired by students, and, on the other hand, the disciplinary dissociations of educational material, shortcomings of competency-based training and formal use of information technologies.Practical significance. The materials of the publication can be useful for future and practicing teachers of mathematics, computer science and related academic disciplines. Moreover, the present publication can be used by education professionals interested in improving the education quality.

В исследовании рассматривается модель создания серии обучающих заданий, построенной с опорой на представления о трехкомпонентной структуре умственных действий (О-ориентировка, И-исполнение, К-контроль). С помощью задач динамического характера, ориентированных на управление учебно-познавательной деятельностью обучающихся, в работе раскрывается один из возможных подходов к совместному изучению формул полной вероятности и Байеса. Отмечается, что для эффективности управления учебно-познавательной деятельностью обучающихся, осуществляется пооперационная обратная связь, переходящая в промежуточную обратную связь и связь по конечному результату.В статье подчеркивается, что оптимальность процесса формирования элементов исследовательской деятельности осуществляется за счет повышения эффективности усвоения его по времени. Последнее достигается за счет приемов совместного усвоения обучающимися учебного материала, связанного с усвоением, например, формул полной вероятности и Байеса.В этом же ракурсе отмечается, что целесообразно использовать этапы информационной технологии решении задач, а использование ИКТ как процесс формирования инструментария в жизни и ИКТ-компетенций для профессиональной ориентации выпускника школы.В статье особо подчеркивается необходимость формирования ИКТ-компетенций учителя как требование федерального государственного образовательного стандарта в условиях в информационной образовательной среды, определены принципы построения методиче ской системы формирования ИКТ-компетенций в рамках педагогических вузов через решения задач с использованием компьютерных технологий.

The aim is to identify the degree of infl uence of methods and means of Informatics on the professional activities of the teachers. Research methodology. Methodological approaches are used: systemic, informational, sociocultural, personal. Methods. Analysis of psychological, pedagogical and special literature, materials of discussion platforms of conferences, systematization, generalization. Research problem. On the basis of the analysis of psychological and pedagogical literature to reveal the infl uence of information and communication technologies on the content of professional and pedagogical activity as a component of professional competence of the teacher. Results. The study noted a number of objective and subjective factors that have a significant impact on the ways of the teacher, the organization of training in the information and educational environment (IEE) and the content of the components of professional and pedagogical activity. Thus, the need to purposefully prepare future teachers to work in such an environment is not in doubt. Conclusion. In the article it is noted that the qualitative impact of information and communication technologies (ICT) in education, their role and importance to full-fl edged professional activity of the modern teacher will be meaningful only when ICTs are having a concrete impact on the content of the components of his professional and pedagogical activity, as ICT become key elements in improving the educational system.