Purpose of the study. Currently, the issues of informatization of education and the use of information technologies in the educational process are receiving new development. At the same time, high-quality training of future lecturers is possible only if innovative methods are used in the process of their training, reflecting modern, activity-based approaches to the organization of the educational process, forms of educational work, and also assessment methods. In this connection, the aim of the study was to find one of the solutions to the organization of independent work of students of a pedagogical institute using active and interactive learning technologies within the educational information environment of the university, as well as testing the identified innovative methods using distance learning technologies.Materials and methods. To resolve this problem, the authors of the article carried out the analysis of pedagogical literature, practical experience in organizing student learning, as well as self-analysis of the use of distance learning technologies in the process of teaching bachelors in the direction of preparation “Pedagogical Education”, followed by a generalization and systematization of the identified features. The study made it possible to distinguish three areas of educational and informational interaction within the framework of organizing and supporting students' independent work, namely, cloud technologies, social networks and distance learning technologies, as well as identify the strengths and weaknesses of each of the areas. At the same time, it is determined that the use of distance educational technologies has the greatest number of advantages. A questionnaire of 216 first-to-fifth year students of the Stavropol State Pedagogical Institute made it possible to establish the attitude and readiness of students to use distance learning technologies, to identify specific methods (namely, the project method and case method), which were later tested by us in the process of preparing bachelors using the distance learning system of the University, implemented on the basis of LMS Moodle.Results. The implementation of the project method based on the use of distance educational technologies allowed us to organize a comprehensive process of students' project work, which contributes to the manifestation of their independence in the planning, organization and control of their educational and cognitive activities. To implement the project method, the capabilities of such LMS Moodle elements were used and described as: “Hot Question”, “Checklist”, “Forum” or “Chat”, “Groupself-selection”, “Seminar”. It is concluded that the tools of the Moodle system are enough to ensure full-fledged extracurricular work of students on the project and evaluate the effectiveness of such work. LMS Moodle is also a convenient tool for organizing students to complete case studies. As a tool containing case materials and implementing an automatic or semi-automatic check of its solution, such Moodle elements as: “Task”, “Lecture”, “Questionnaire”, “Forum” were revealed and tested.Conclusion. Each of the presented directions for the implementation of active and interactive teaching methods using distance educational technologies has its own didactic and methodological advantages. The choice of this or that method or their integration depends on the goals and objectives facing a particular lecturer.

The paper substantiates the use of the method of graphic modeling, as one of the effective means of visualizing the solution of a text problem in accordance with the requirements of the federal state educational standards elementary general educationin the field of the formation of cognitive educational skills among students. Based on the analysis of educational and methodological complexes in mathematics for elementary school, a classification of graphic models used in solving text problems is compiled. The article also provides examples of solving tasks using the compilation of a graphical model "block diagram" and discusses the methodological features of working with a text task on a model of this type.

The article discusses the expediency of forming in elementary school the intellectual ability to recognize patterns in the surrounding world. Based on the analysis of the available literature, the article reveals the concepts of "regularity", "task for establishing patterns", characterizes the features of the methodology for teaching younger schoolchildren to establish graphic and numerical patterns. The subject of the article is primarily numerical patterns, in connection with which cyclic, increasing, decreasing, as well as mixed numerical patterns that underlie tasks for their identification are described. For some types of tasks, examples of the use of numerical patterns are given: when systematizing, generalizing the program material of the initial mathematics course; checking the level of formation of the corresponding computational skills; preparation for the development of new computational techniques.