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 basic branch of both discrete and continuous mathematics is Set theory, the study of which is a difficult task. Designed and developed in the Maple computer algebra system, the Maplets package–the set theory application–enables to provide assistance both in teaching (by demonstrating the performance of operations on sets, testing knowledge and skills in using operations), and in studying set theory and solving the simplest combinatorial tasks (can be used as a simulator for students). By using interactive worksheets and animated images in Maple, students are given the opportunity for numerous experiments that will contribute to the development of their math education as well as computational skills. The application will form a sustainable need for the use of computer systems by students in the study of various branches of mathematics.
The paper outlines ways in which the Maple computer algebra system can be used to master one of the branches of discrete mathematics – set theory. Computer algebra systems (CAS) expand the possibilities of creating, applying and using mathematical models on a daily basis by engineers, researchers, and foster the improved training of students in a wide range of disciplines. In addition, computer technology can help implement such methods as genetic approach and the use of various techniques to representing target objects in education. The most suitable for teaching discrete mathematics and mathematics at large are computer algebra systems such as Maple and Mathematica. The paper provides a Maple framework designed for the initial stages of mastering discrete mathematics within university curriculum, in particular, for working with the basic concepts and laws of set theory.
The article describes the continuity in teaching the elements of the set theory on the levels of preschool, primary general and basic general education. The relevance of studying the theme "Set" is grounded. The result of the analysis of educational and methodical literature on this theme is described, showing that in the basic school at the proper level neither the definifions nor the ideas of the set theory are stated, which entails the students' difficulties in mastering this theme. In this regard, to improve the efficiency of the study, it is proposed to use the Maplet-applications developed by us using Maplets library of the system of computer algebra Maple: "Union of two sets", "Intersection of two sets", "Difference of two sets", "Symmetric difference of two sets", "Addition of one set to another". These Maplet applications allow to interactively perform basic operations on sets, control students' knowledge of the order in which these operations are performed, and can be the starting point for solving more complex set theory problems.
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