The paper discusses basic implementation aspects of the Mathematical Education Development Concept, adopted by the Russian Government in 2013. According to the above document, the main problems of mathematical education include: low motivation of secondary and higher school students for studying the discipline, resulted from underestimation of mathematical knowledge; and outdated educational content, overloaded by technical elements. In the author’s opinion, a number of important new mathematical fields, developed over the last years, - the graph theory, discrete mathematics, encoding theory, fractal geometry, etc – have a large methodological and applied educational potential. However, these new subdisciplines have very little representation both in the secondary and higher school mathematical curricula. As a solution for overcoming the gap between the latest scientific achievements and pedagogical practices, the author recommends integration of the above mentioned mathematical disciplines in educational curricula instead of some outdated technical issues. In conclusion, the paper emphasizes the need for qualified mathematical teachers’ training for solving the problems of students’ motivation development and content updates.

The paper is devoted to fostering the innovative thinking of secondary school students in the light of widespread introduction and development of high-technologies, and growing demand for innovative specialists, particularly in technical and scientific spheres. The research, aimed at finding the ways for fostering the students’ innovative thinking, incorporates the definition and analysis of innovative mentality, including its cognitive and instrumental components, and various characteristics such as creative, theoretical, social, constructive, transformative, and pragmatic ones, which constitute a complex structure of innovative thinking. Based on the specified characteristics of innovative thinking, the authors define the main educational tasks for activating the innovative mentality, and demonstrate the ways for their fulfillment in the context of additional education. The authors believe that the above recommendations can reinforce the readiness of the young generation for innovative professional activity in different spheres, and develop their professional self-determination in accordance with the state demands for the advanced economy.

span style='font-size:10.0pt;line-height: 115%;font-family:"BookmanOldStyle","serif";mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;color:black;mso-ansi-language:RU;mso-fareast-language: EN-US;mso-bidi-language:AR-SA'>ии наук педагогического образования, Екатеринбург

The paper is devoted to innovative activities of educational institutions regarded as the platform for fostering the students’ innovative potential and intellectual capacity. The authors consider the risks of innovative projects carried out in Russian universities; they analyze the biggest external challenges in the given sphere, including the fast obsolescence of knowledge, abrupt social changes, low competitiveness of Russian education in the global market, as well as the internal challenges related to insufficient qualification and advanced age of most academic staff, lack of necessary infrastructure, outdated educational paradigm, poor motivation for innovations, etc. Referring to the external and internal spheres, the author demonstrates possible risks of innovation activity in educational institutions both on the micro- and macro-level. The paper emphasizes the need for identification and classification of innovative project risks as a basis for effective prognostication and risk management. The risk classification model, developed by the author, can be used for estimating the prospects of innovative projects, and effort coordination in overcoming the adverse impact of risks зы развитию системы образования (недостаточная квалификация и преклонный возраст большинства преподавателей, отсутствие необходимой инфраструктуры и устаревшая парадигма управления, слабая нацеленность на производство инноваций и инноваторов и т. д.). В зависимости от сегмента внутренней и внешней среды представлены возможные риски инновационной деятельности вуза на микро- и макроуровнях. Очевидно, что имеющие практическую значимость прогнозирование и эффективное управление рисками инновационных проектов в вузе требуют идентификации и классификации этих рисков. Предлагаемый авторами вариант классификации позволит, по их мнению, определять перспективы развития инновационных проектов и направить усилия на разработку мер по защите от негативного воздействия рисков.

The paper reveals the research findings concerning a complicated process of academic staff formation in the secondary school. The main determinants of the process include the discrepancy between the actual development level of academic staff and the existing requirements of pedagogic society. The author denotes the main motives for academic staff development: moral and financial incentives for professional growth, new educational tasks, unsatisfactory social status of educational institution, etc; and identifies the complex of objective and subjective conditions positively affecting the given process. According to the author, the main priority should be given to the methodological provision of academic staff, integration of their activity, and stimulation of informational, methodical, and organizational channels of school activity. In conclusion, the paper considers the principles of life-long teacher training, corporate cooperation, partnership and solidarity, and discusses the technological structure of academic staff development, based on the competence model of education. 

The paper deals with one of the urgent problems of the postindustrial society – rational consumption of energy resources. The authors point out the objective and subjective energy-saving factors, as well as the reasons behind the neutral and indifferent attitude to the energy saving. The given concept is specified as the complex of actions designed for decreasing the futile energy losses. The energy saving policy requires the adequate competence that should be developed from the pre-school age and maintained through the system of life-long learning. The crucial role in developing the competence in question belongs to the teachers fully endowed with the necessary psychological and pedagogical knowledge. The paper defines the concept of energy saving competence, and analyzes its axiological, motivational, cognitive, and reflexive components, along with the energy related ecological qualities in order to single out the adequate criteria of rational energy utilization. In conclusion, the authors come out with the structural content model designed for fostering the energy-saving competence, including the objective, operational, organizational, and reflexive blocks. Additionally, the paper contains the approximate list of general cultural and professional competences, as well as the ways of their acquisition by vocational school students and teachers. 

The paper discusses the results and prospects of experimental development of didactic multidimensional technology; the demand for such a technology results from the increasing complication of educational content and rising education quality requirements. Further improvements of educational process are closely related to implementing the information technologies – i.e. mental cards, information graphics, frames, structural schemes and other visualization forms. The research is aimed at finding the effective instruments of didactic modeling of knowledge. Based on several functional approaches, the authors have formulated the concept of personified informational educational system, and developed a courseware – DMT DESIGN (SA).1. The program is based on the subagent approach and macro- and micronavigation technologies, applied to the functional structure and educational content. In the conclusion, the authors outline the main trends of forthcoming experimental research, aimed at identifying the opportunities of didactic multidimensional tools implementation in educational processes.

The paper considers one of the main theoretical and practical pedagogical problems of education quality assessment. The quality measurement depends on successful identification of genuine (scientific) and false diagnostic methods; the process becomes even more complicated in case of latent variables. As a solution, the authors recommend the Rasch measurement model for identifying an integral indicator of education quality. The method in question involves development, approbation and analysis of diagnostic materials, as well as mathematical and statistical data processing based on specialized computer software. The paper describes the advantages and theoretical potential of the Rasch method, and emphasizes its capacity for solving the key problem of quality modeling – i.e. suitability and utility of indicator variables for the given research.

The research is devoted to teaching one of the basic mathematical concepts – the function – in the secondary school. Regarded as the key instrument of mathematics and experimental modeling, the notion of function including its perception, interpretation and application have always been under the scrutiny of Russian and foreign scientists. The authors focus their attention on specificity of students’ perception of the above concept, integrated in teaching process, and provide several examples of functions, applied in different spheres of everyday life, in order to develop students’ operational skills and competences related to mathematical functions. All the interrelated aspects of teaching methods and practices are considered on the basis of activity approach and information technologies. The paper recommends a series of particular exercises, based on the APOS theory (Action – Process – Object – Scheme), along with the Geogebra courseware to help students master their conceptual understanding of mathematical function, and its operational options in various mathematical contexts (e.g. calculating the roots, estimating the limits and derivatives, changing the parameters, solving practical problems, etc). The assignment samples demonstrate visibility of the courseware and effectiveness of its application in practical teaching.

The paper considers educational practices in the closed-type institutions for teenagers with deviations in legal, intellectual and psychoemotional behavior, and reveals a social rehabilitation model for this category of teenagers. The model is based on A. V. Petrovsky’s concept of the three phases of personality development in adolescence – adaptation, individualization and integration. The author presumes that any deviation in a teenager’s behavior increases as the result of negative experience, developed and retained in asocial surroundings. The goal of teaching staff in closed-type institutions is to transform the trend of deviant behavior into the normal attitude of social adaptation. The author emphasizes a need for positive experience of passing the above phases in friendly atmosphere with adequate behavior patterns. Preventive work implies the priority changes – i.e. the prevalence of the future over the past, self-determination (revision of goals, meanings, and attitudes to a free choice), reorientation from ≪I don’t want, I can’t, I don’t have to≫ to the positive connotations of ≪I have to, I can, I want≫. The paper denotes the methods and ways of pedagogical facilitation, relating to different phases of educational process, and provides a technique for regular monitoring of personal behavior changes, including the key evaluation positions and scales. The paper is addressed to the teaching staff involved in rehabilitation of teenagers with deviant behavior.

The paper analyzes characteristics of the postindustrial educational system, including the credit competence assessment, academic loads, and module-rating discipline structure. The employers’ judgments, reflected in the survey outcomes, make it possible to single out the most significant competencies for students to master. Such findings are regarded as a foundation for developing the assignment modules, integrating the problematic, testing and projecting tasks, designed to master necessary competences; their effectiveness is estimated by using the criteria of behavioral psychology. The paper demonstrates the sequences of monitoring assessment of students’ academic achievements, and recommends the batching principle of rating point accrual, based on criterion-oriented evaluation standards, reflecting students’ competence levels. The authors identify the basic competence indicators: interest in the subject, reflections on the test results, and inner motivation for project activities. The complex of batching equations is given for developing the training cards of academic disciplines, and guaranteeing the effectiveness of education system.