The leading research technologies are metacognitive technologies of a reflexive character with the means of information and communication technologies. The following methods were used in the study: theoretical (analysis of philosophical, psychological and pedagogical literature on the problem of research, study of mass and generalization of advanced pedagogical experience, pedagogical modeling), empirical (pedagogical observation, conversation, questionnaire, interviewing, testing). The materials of the article can be useful to future mathematics teachers, graduate students, teachers of higher educational institutions interested in the formation of teacher's pedagogical culture, and professional training of subject specialists.

Nowadays in a new Paralympic kind of sport taekwondo WTF LMAI in Russia there is no Federal State Educational Standard (FSES). Athletes-invalids train in terms of standard for people with LMAI (locomotor apparatus injury) or taekwondo standard in the groups with healthy athletes. For the detailed study of the educational-training process with Paralympic taekwondo-athletes it is necessary to create effective technologies, define the methods of work. The aim of the work is to substantiate educational-training process in taekwondo for people with locomotor apparatus injury. The introduced practice of inclusive methods of teaching on the scientific base helped to achieve high stable result. We proved the necessity to realize cooperative lessons of taekwondo-athletes with LMAI and healthy, specially trained for them, taekwondo-athletes. We defined prospective directions in inclusive teaching Paralympic kind of sport taekwondo WTF LMAI.

The interests of clients of the railway industry and Russian Railways in matters of recovery and compensation for “lost profits” and “lost opportunities” are not considered and regulated in laws and by-laws regarding railway transportation. Claim work is based on compensation for real damage both from users of railway transport services and from the Russian Railways holding.An algorithm for the formation, submission and resolution of claims in the provision of rail transportation services is considered. The functionality of the personal account for the clients of JSC “Russian Railways” of the project “Electronic Claimant” was analyzed. The importance of developing a basic formula that takes into account the factors affecting the amount of lost profits is indicated. The existing scheme for conducting recourse work to recover losses of Russian Railways JSC is given and a scheme for conducting claim work to compensate for lost profits of Russian Railways JSC on the basis of a unified automated system of act and claim work is presented. It is proposed as a basis for further elaboration of this issue, a mechanism for rebilling in the event of final losses from a failed transportation for clients of the Russian Railways holding. The expediency of applying a possible replacement transaction when the company finds another counterparty is also considered. The application of these measures will make it possible to create equal competitive conditions in the market for all customers and the Russian Railways holding.

In the article discusses some approaches to the problem of pedagogical design of educational activities of students taking into account their individual characteristics. Features of the design of individual educational routes in mathematics are revealed.

The article discusses the psychological and pedagogical problems of using computer games in school education. Graphic and animation capabilities of visual programming language Scratch, as well as computer games for educational purposes as a means of increasing cognitive interest and educational motivation of students to study informatics and mathematics are demonstrated.