The inclusion of the author’s course of studying the functionality of the “Electronic Perm Educational System” (EPES) in the university training of a pedagogical sphere specialist contributes to the development of the ability to work in a digital environment in basic and additional education. The teaching of this course is focused on the use of technologies related to the implementation of educational engineering, which has now gone beyond the scope of technical specialties and has spread to the field of training specialists in the field of pedagogical design, design of educational programs and trajectories. Particular attention in this course is paid to the formation of ICT competencies of future teachers in the development of digital products in the process of studying specialized disciplines and elective courses, in particular, such as “Probability theory and mathematical statistics”, “Electronic Perm Educational System”, implemented on the basis of competence oriented, design and engineering approaches. The possibility of accumulation of these approaches in the work of student design workshops in the EPES Library cluster is demonstrated. As a result of the activities of such workshops, a digital educational product (DEP) is supposed to be needed in real learning practice and has prospects for further use by the student already in the role of a teacher after graduation: a lesson script, an electronic test or other educational content. Special tasks for students are characterized, aimed at developing and diagnosing the ICT competence of future mathematics teachers at the Perm Pedagogical University. Usually, the solving of the task includes the following stages: development of annotations, creation of a passport and subject content of the DEP, organization of approbation, presentation, defense and publication of the developed materials in EPES. The description of diagnostics of ICT competence of a future mathematics teacher in three of its components is given: general user, general pedagogical and subject-pedagogical.

The article is devoted to the description of methodological approaches to teaching schoolchildren the basics of artificial intelligence based on the technology of organizing project and educational and research activities to achieve meta-subject results of education, the formation of systemic representations and the experience of their application in real life. The experience of organizing courses within the framework of additional education for students of 10–11th grades of secondary school on the use of neural networks in solving practice-oriented problems is presented. The block structure of the content of the courses is given, which is based on the phased implementation of the idea of the future project. A detailed description of the content of each block is given with a demonstration of a presentation of complex theoretical material that is accessible to the understanding of schoolchildren. In particular, recommendations are given for the study of sequential and recurrent models of artificial neural networks, fully connected and convolutional layers, object detectors, as well as an algorithm for training neural networks by backpropagation of errors. Data acquisition tools for training artificial neural networks are described. An algorithm for writing a program for training a neural network to recognize handwritten digits of the MNIST set is characterized. Examples of projects for the use of neural networks, carried out by students together with the teacher as part of the study of the proposed courses, are given.The article is addressed to teachers of additional education, informatics teachers, teachers and students of universities — everyone who is interested in the use of artificial neural networks in solving practical problems and methods of teaching schoolchildren in project activity.

The article describes the experience of implementing lifelong pedagogical education and suggests the characteristics of the training features of future mathematics teachers at the Perm State Humanitarian Pedagogical University, as well as teachers of the Perm Krai using the information and educational environment in the context of the digital transformation of education. Based on the ideas of the psychological and pedagogical concept related to the description of the creation of conditions for the gradual deepening and expansion of knowledge, skills and abilities of the future teacher in the direction of professionalization, special attention is paid to the founding of the participants in the educational process of the ability to work in a digital environment. The stages of founding such a skill are illustrated by examples of projects completed by students at certain stages of university education. As one of the examples, the structure of a digital teacher’s room, implemented in one of the schools in the city of Perm, is given. In general, the presented content allows us to state that the advantage of the ideas of translating into practice the continuous training of mathematics teachers in the context of the digital transformation of education, noted by the features described by the authors, is their multiplicativity, which implies the possibility of implementation in any region of Russia and in neighboring countries, as well as replication not only in the educational sphere, but also in other areas of human activity. The article can be useful both for students enrolled in the direction of “Pedagogical education” and for specialists in the field of teaching staff training.