This paper is aimed at creating a model of a Personal e-Learning Environment (PLE) of a University Mathematics teacher. A special emphasis is put on the analysis of the approaches to understanding the notion Personal e-Learning Environment (PLE) and studies into creating a PLE model. The Deductive Content Analysis of the research papers and other academic sources in this article allowed defining the structure of the PLE model of University Mathematics teachers. The authors of the present paper see the bottom line of the modelling process as giving content to the PLE according to the types of teaching activities, which Mathematics teachers do to perform the Instructive, Cognitive, Designing, Planning, Social, Managerial roles. With the help of The Inductive Content Analysis Method the researchers in this paper analysed the data on ranking web-services. The data were taken from the web-resources and helped to select web 2.0 tools, which can be used to give content to the PLE. The conducted research made it possible to conclude that the idea to develop a PLE model of a teacher is based on such factors as the ranking of web-tools, IK competency of a teacher and his/her willingness to develop professionally. The authors of the present article assessed the answers of the academic staff at Ukrainian Universities concerning their level of awareness about using web-tools in teaching. The analysis of the results proved the insufficient level of such awareness and justified the relevance of designing an on-line course in order to support a Mathematics teacher in creating and using Personal e-Learning Environment.

This paper looks into the issue of implementing problem-based approach to developing creative thinking in students majoring in Mathematics at teacher training universities. The object of the study is the process of developing creative thinking in students, majoring in Mathematics at teacher training Universities, through task-based approach. The methods used in the present study are theoretical analysis of research papers and resources, as well as a survey, conducted among students and lecturers. This survey is aimed at determining distinctive features of the problems in Elementary Mathematics, which can help to develop creative thinking in students. The aim of this study is to introduce the syllabus of the online-course "Creative Thinking through Teaching Elementary Mathematics" and to design a system of Open-ended and Integrative Problems in order to develop the components of creative thinking in students, majoring in Mathematics at teacher training universities. The tasks of the present study: to determine what key components of creative thinking in students majoring in Mathematics can be developed, when teaching Elementary Mathematics to them; to determine distinctive features of the Rich Tasks that will contribute to developing creative thinking in students in the course of teaching Elementary Mathematics to them; to introduce the syllabus of the online-course "Creative Thinking through Teaching Elementary Mathematics"; to design a system of rich tasks for arranging the learning process.

This article considers the issue of implementing a model of blended learning to prepare master students majoring in Mathematics (speciality code in Ukrainian educational system “014 Secondary Education. Mathematics”). The research analyses the existing developments of the issue about the use of blended learning while training would-be mathematics teachers. The researchers determined and explained the stages of work on developing the online course “Methods for Teaching Mathematics to Students at Technical Universities”, that is used when students learn methodological subjects of the curriculum. The research describes the development of the theoretical online course model and methodological recommendations on the learning materials and preparing papers for the course. The article offers recommendations related to the course structure. The course developers defined the usability criteria of the educational platforms, determined the stages of course users’ activity, their content, and organization. The research describes the areas of online course activity management, the course tutors’ and moderators’ teamwork is defined as the main condition of its development and support. In order to prove the efficiency of implementing blended learning of the methodological subjects, an experiment was carried out during the assistant practice in technical universities that master students of the specialization “Mathematics” had. The results allowed confirming the efficiency of students’ practical training during blended learning of the methodological subjects that in its turn encouraged the improvement of the assistant practice results.

This article looks into the issue of online-training of master students, majoring in Mathematics for internship in technical universities. This study is focused on arranging students' learning activities with the help of an on-line course “Methods for teaching Mathematics to students in technical universities”. The study considers the issues that students face during the internship in technical universities and debates a possibility to factor in the students’ needs while designing the course content. The present study gives a description of the activities that students do while working with the course materials, requirements, and recommendations on facilitating the learning process through this course. Active participation of students and their contribution to discussing the course, its content and the facilitation of the learning process presume that introduction of the on-line course and its integration into the program of training master students enhances their readiness for internship.

The article looks into the issue of improving students' motivation during the study of Mathematics. This study focuses on the implementation of the С2 model within CLIL-approach while teaching Elementary Mathematics to students in higher technical educational institutions. The research analyzed the influence of teaching methods, modes, and resources, which can be used to support the teaching of mathematical discipline in English and improve students' motivation. The paper describes the types of students' activities in the course of the developed classes. The study presents the types of tasks, content support, and language support that contribute to student motivation, student-teacher interaction as well as the development of thinking, reasoning skills. The article shows consolidated activities of all the teachers engaged in teaching in experimental groups, and aimed at developing the syllabus and "bank" of learning support materials. This paper also discusses the requirements and recommendations, complying with which contributed to the positive dynamics in students' achievement motives, their cognitive motives, learning, and vocational motives. There was ground to conclude that the conducted course in Elementary Mathematics on the basis of the CLIL method had a positive effect on improving students' interest in mathematics as well as their motivation.

The present article considers the issue of developing motivational and value-orientated readiness of Math students at teacher training universities for implementing educational innovations. The method, chosen for the present research is the analysis of the scientists’ viewpoints, on-line resources and reports regarding the issue of designing and using Rich Tasks when teaching Mathematics, methods and means for developing students’ motivation for implementing educational innovations. This paper describes the methods, aimed at developing in students motivation and ability to systematize, devise, use Rich Tasks in their professional activity and to combine them with other innovational learning methods and means. The analysis of the teacher training internship results and the surveys in the experimental group give ground to make a conclusion about efficiency of the methods offered.

The article considers the development of the online educational model “Creative Thinking through Learning Elementary Maths” and the results of the effciency to implement this course for students of the specialization “Mathematics” while learning Elementary Mathematics. The research represents the development of learning materials for the online course posted in free access on the educational platform “Higher School Mathematics Teacher”. The course components (theoretical, practical, and feedback) are focused on the organization of motivated and consistent students’ activity; open and integrative Rich tasks of three levels of complexity. The course participants’ activity, focused on the recognition, classification, solution, creation of Rich tasks, encourages the formation of the main components of creative thinking that include a problem statement, fluency, flexibility, originality, and elaboration. The first version of the course materials was improved following course users’ wishes, and then the effciency of online course education was checked using an experiment. The analysis of results of the experiment allows concluding about the effciency of the developed model of learning an online course.

This paper is aimed at studying scientific communication as an integral part of a scientists activity. The authors of this article analysed the development of informational technologies, which gave rise to a new paradigm of scientific communication Research 2.0. In the present study the analysis of research papers, describing models of scientific communication is done. The findings allow to define the structure and content of a comprehensive program of activities, connected to scientific communication in compliance with the Scientific Communication Life Cycle Model. In order to implement the program, aimed at developing core skills through scientific communication of scientists, a target audience, comprising postgraduate students and young researchers in Mathematics and Teaching Methods was engaged. A five-stage program of activities, which was developed, prompted scientific activity of young researchers and gave them an opportunity to learn about means of presenting research results, elements of management, mechanisms for applying the findings. A constructive description of each module of the program is done, actions and a strategy are described, communication between participants and tutors through the platform Higher School Mathematics Teacher is arranged in this research. In order to assess the efficiency of implementing the program, Researcher Development Framework (RDF) is used. The study also presents the results of the activity of young researchers, who were engaged in the program. Following the change in the phase of the development of researchers characteristic features and in compliance with RDF, a conclusion is made about a positive impact of the program on the development of career skills of young scientists, their interaction skills, awareness of professional behavior procedure.