The article describes the problem of preparing a modern teacher of mathematical disciplines for a higher technical educational institution in the system of higher pedagogical and classical education. The modern scientific research focusing on training a highly-qualified mathematics teacher has been analyzed. The results of the questionnaire for mathematics teachers at higher technical education institutions and students studying in 014 'Secondary Education (Mathematics)' specialties are presented. The current state of preparedness of master's degree holders to teach mathematicians at higher technical educational institutions is evaluated. One of the ways to solve the problem is to develop the 'For Higher School Mathematics Teacher' educational platform. The concept of developing this online environment and filling its components with content has been highlighted. The rationale for creating a community of practitioners consisting of teachers of higher technical and pedagogical educational institutions, the cooperation of which should contribute to solving the problem, is provided. The possibilities of using the platform for further training of both young and experienced teachers are considered.

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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.

The article looks into the issue of developing methodical requirements for the structure and content of online courses. The study is dedicated to the analysis of peculiarities of developing the content of online systems and developing methodical recommendations to educational materials for online courses of training higher school mathematics teachers. The research considers the experts' experience in preparing, structuring and developing the content for online courses and answers to volunteers who have agreed to test the educational materials of the course. The answers given by the participants have allowed estimating the quality of the developed course and detecting its insignificant drawbacks. The article discusses general requirements to the structure and content of the online course, means for the implementation of a testing subsystem, peculiarities of developing educational video content and educational materials in PDF format, issues of implementing forum and survey subsystems, as well as means of estimating learning outcomes. We have grounds to conclude that the quality of the course is determined by the range of factors, among which we point out the course organization based on weekly planning, implementation of a testing subsystem under conditions of extended functionality, creation of abilities to organize feedback.