Information technologies and various innovative approaches to enhancement of school education mention processes of students personal development. In the CIS’s states and foreign countries essential experience of implementation of innovative technologies and means of informatization of educationin practice of school work is accumulated. In many cases such experience is interesting also from the point of view of a research of new approaches to school students upbringing.In article the international experience of use of innovative pedagogical technologies and information technologies in school education is analysed. Implementation of similar technologies allows to make a big contribution to forming at school students of creative capabilities. The available problems in school education in the training plan and education and a way of their overcoming are discussed.

For the last decades approach to mathematical calculations has changed radically. On change by the account, to arithmometers, slide rules and calculators computers have come. The expert not able to put into practice knowledge to make mathematical calculations by means of the computer can be hardly considered as a high quality. In order that it was possible to use the computer for the solution of mathematical tasks it is necessary to construct at first mathematical, and then and computer model of this task. In article the analysis of a concept of model is carried out the place of the substantial line “Formalization and modeling” in a school course of informatics are analyzed and methodical recommendations for increase in learning efficiency of the substantial line “Formalization and modeling in a school course of informatics” are offered.In article the analysis of the basic concept of the Formalization and modeling in a school course of informatics is carried out features of studying of the Formalization and Modeling line in a school course of informatics in different textbooks. The article will be useful to teachers of informatics and also the student studying mathematics to teachers, and also the experts as obliges facing need of mathematical data processing, creation of mathematical and computer models and interpretation of the received results.

The prospect of using distance learning on classes in mathematics and also requirements to ICT competence of mathematics teacher in the conditions information and education environments of educational organization are discussed in article. Requirements to ICT competence of a teacher are formulated in the professional standard for teacher and caused by the fact that the huge potential of information and education environment of educational organization remains unrealized mostly because there isn’t enough teachers capable and ready to use possibilities of new educational environment to increase efficiency of educational process. If today the all-user ICT- competence including knowledge of bases hardware and the software of the computer as the instrument of work in modern information space and necessary for the teacher to work with text editors, spreadsheets, e-mail and browsers, the multimedia equipment already is at the sufficient level at most of teachers, then all-pedagogical andsubject and pedagogical ICT-competence leaves is much to be desired, All-pedagogical and subject pedagogical ICT- competence are necessary for a teacher in particular for introduction electronic training and distance educational technologies. Implementation of distance learning allows to increase a share of independent work of pupils and to make active, develop ability of search, the analysis and synthesis of information.

In article attention to that fact that at students of higher educational institutions of the physical and mathematical and natural-science directions of preparation when training in the reverse tasks for differential equations the mathematical intuition which is an important component of their creative potential develops is paid. The mathematical intuition helps students to comprehend a physical sense of the researched application-oriented task, to select effective methods of mathematical physics for the decision of the reverse task for differential equations.The mathematical intuition of students develops in many respects in case of the decision of different educational jobs. Among such educational jobs: creation of system of integrable equations of the reverse task for differential equations, the proof of the conditional correctness of the decision of the reverse task for differential equations, creation of the difference analog of the reverse task for a differential equation; finding of the numerical decision of the reverse task, the proof of convergence of approximate solution of the reverse task to the exact decision, reasons for the idea of the proof of a correctness (the conditional correctness) of the decision of the reverse task for differential equations, a statement of logical outputs of application-oriented or humanitarian character on the basis of the conducted research of the reverse task and other educational jobs.In the course of such training students create system of fundamental knowledge in the field of the reverse and incorrect tasks, acquire new scientific knowledge in the field of applied and calculus mathematics, but, obviously, and develop a mathematical intuition.

The article deals with teachers and professional competence tyutorskoy, tutor support schools in the information space. The main requirements to the tutor support in the information space of schools, conditions of readiness of the teacher to tutor support schools in the information space. A theoretical analysis of the concept of information competence, tyutorskoy competence. It is noted that in thestructure of information competence must exist an element associated with the motivation, need and interest in the acquisition of knowledge and skills in the field of technical, software and information. Formulated key performance indicators definition of information competence of the tutor. The authors noted that information and work with it is in the modern educational and information space school mandatory components of pedagogical activity as a system.Analyzed and presented on the basis of the author’s experience of the possibility of using information and educational Moodle shell with tutor support positions in the information space of schools, sets out the basic elements and resources Moodle shell with a description of the implementation. In particular, the disclosed educational resources information and educational shell Moodle for remote support learning. The article describes a model developed by the author’s tutor support schools in the information space.

The article describes the possibilities of information and communication technologies and distance and offered them the use of the model in the educational process of the university.Today’s society moves to a fundamentally new level of access to quality education. Areas of education in Russia and trends shaping society require urgent solutions to the problems overtaking education system development on the basis of information technology organization in the country unified educational information environment. Informatization believes substantial transformation of content, methods and organizational forms of education. This should be resolved problem of educational content on the modern stage, the ratio of the traditional components of the educational process and new information technologies, new relationships of students, teachers and educational environment.Formation of new information technology pulls the formation of a new educational system that can ensure the provision of educational services to millions of people in reducing the unit cost of education. Actually to achieve these goals is directed Internet-education, which can be determined as the formation of large segments of the population obtains by using the information of educational resources on the Internet.Model integration of part-time and distance learning using information and communication technologies and the remote is used to provide educational services to students of distance and distance learning. An E-learning course on the basis of the distance learning platform is used to provide teaching materials and to check assignments, providing operational advice, advertisements and so on.

The paper discusses some problems of development of modern world education associated with the implementation of the competence approach (CA) in education on the example of the system of higher technical education of Mongolia. Discusses the training of national cadres for Mongolia in the system of the graduate school of the Russian Federation. Touches on some aspects of the international competition for the minds.The concepts of information - mathematical culture (IMC) and professional information - mathematical competence (PIMC), the definition of these concepts, a comparative analysis of the content of the IMC and PIMC in relation to the concepts of mathematical culture (MC) and the professional mathematical competence (PMC).The paper gives a justification of the importance of the proposed information - mathematical competences for the training of national engineering cadres of Mongolia. Addresses General questions relation of culture and professional competence. Emphasizes the importance of the fundamental principle of education when implementing CA in education.The description Problem-Oriented Information-Computational System (POICS) structure and shown their importance for the development of national educational systems.In the description of the conceptual structure of POICS allocated to its component parts, such as: system POICS, actually IP, analytical part, discussion part, and the computing system. Lists the functions performed by each component of POWS.

The main idea of modern education is intellectualization, globalization of the process of preparation of future specialists. The institutes of education can achieve this goal only through using innovative information and communication technologies. Application of ICT in the formation of professional communicative competence positively affect the quality of learning material, developing listening and speaking in real communicative level, develop writing and reading skills and promotes the development of various language skills of students of touristic specialties.When you create a specific ICT-based teaching-learning environment and use active learning techniques, you significantly improve the level of professional communicative competence of students: special professional and personal knowledge; possession of specialized terminology to the extent necessary and sufficient for a complete and accurate description of the object of the profession; information culture; linguistic knowledge and skills; verbal communication skills and behavior; skills to independently analyze and vocational training situation and find the best way out of it; cognitive activity; communication skills associated with the development of the profession; ability to organize relationships with others; creative approach to business; skills to critically analyze the information already developed and quickly master the new challenge.