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The chapter deals with the model of the trajectory of training teachers and a new approach to constructing a smart learning environment. The authors present a scheme of the smart trajectory, which outlines new approaches towards teaching students. The role of using interactive activity-based smart components is shown. The chapter depicts the results of the approbation of the model. The approbation revealed that the use of the smart trajectory allows to develop analytical competences, the skills of problem solving, creativity, the capacity to communicate with teams, groups, and individuals. The result of building up the smart trajectory consists in the creation of multi-format and personified educational space in an interactive environment enabling a person to study at any time and anywhere getting free access to content around the world.

The article discusses the problems of using web technologies in the development of self-sufficiency of University students. We hypothesize that real professional situations in which he/she is obliged to work independently on the basis of web technologies contribute to the development of students' self-sufficiency. It is shown that the activity approach to learning, based on the use of project learning technologies in the process of preparing for lessons by learners and interactive technologies of blended learning, promotes the development of independence and self-reliance of students on the basis of web technologies. This article contains a matrix of integration of interactive technologies in the process of independent work of students. This will allow the teacher to select the tools for Moodle Leaning Management System in order to successfully implement the interactive forms and education methods in independent work of students in the conditions of turning down the monologue-based oral presentation of training material by the teacher. For assessment of the effectiveness results of research we carried out a survey of Bachelors of pedagogical education. The article presents the results of the survey of four-year students confirming the results of the study.

The paper presents the results of teaching mathematics to schoolchildren in a subject-based digital educational environment built according to the model proposed by the author. The aim of the study is to experimentally verify the effectiveness of the process of teaching mathematics to schoolchildren in a subject-based digital educational environment. The study required the use of a whole range of methods, such as observation, questioning, interpretation, tabular presentation of empirical data and their processing, static data processing and comparative analysis of the results. Two groups of students participated in the pedagogical experiment: the first group was an experimental group that studied mathematics in a subject-based digital educational environment, the second group was students who studied mathematics in a traditional form. In this study, the assumption was tested that the students of the experimental group show on average the same result of knowledge as the control group. To determine the absence of differences between the two experimental distributions, the students t-test was used. As a result, an alternative hypothesis was adopted that the students of the experimental group showed on average a higher level of knowledge than the participants of the control group. Therefore, it is possible to draw a conclusion about the effectiveness of the learning process based on the subject digital educational environment built according to the model proposed by the author. The value of this research lies in the fact that the author offers a theoretically sound model of the subject digital educational environment, the effectiveness of which has been experimentally tested. The instrumental approach of the model allows the teacher to build a digital educational environment taking into account the peculiarities of the taught subject according to his author's plan.

В данной статье обсуждается роль цифровой образовательной среды обучения программированию детей младшего школьного возраста в развитии у них алгоритмического мышления. Предлагаются педагогические условия, благодаря которым данная цифровая образовательная среда будет успешно внедрена в практику образовательных учреждений. Вводится понятие предметной цифровой образовательной среды педагога. Выдвинуто предположение, что развитие алгоритмического мышления у детей младшего возраста будет эффективным, если разработать предметную цифровую образовательную среду обучения программированию. В результате исследования была разработана цифровая образовательная среда педагога для обучения программированию детей младшего школьного возраста на основе среды ПиктоМир по авторскому учебно-методическому комплекту, состоящая из методического пособия для учителя, рабочей тетради для ученика, а также авторских цифровых образовательные ресурсов, онлайн-тренажеров, электронных презентаций и дидактических материалов. Разработанная цифровая образовательная среда обучения детей младшего школьного возраста программированию прошла апробацию на базе образовательной школы «Университетская» Елабужского института Казанского федерального университета в г. Елабуга Республики Татарстан. В рамках данного исследования сделан вывод о том, что предметная цифровая образовательная среда обеспечивает учителя возможностью конструирования среды по авторскому замыслу, позволяет ему выстраивать навигацию образовательной деятельности учеников. Ключевые слова: предметная цифровая образовательная среда, программирование, алгоритмизация, учебнометодический комплект.