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A general philosophical analysis of the situation created at the beginning of the XXI century leads to the conclusion that at present the planet is experiencing a catastrophic antropo-social-ecoplanetary crisis. According to the authors, to resolve the created situation, it is necessary to recognize that the task of the human being and humanity, preserving the harmony of the soul is the formation of a bio-friendly culture, protecting and creating rather than destroying the life of natural landscapes. Adoption a bio-friendly spiritual paradigm presupposes another kind of upbringing, education and value orientation of people.Only the full-value upbringing-education with the formation of a holistic, practical, predictive consciousness and conscious practical creative activity in balance with nature is able to create the necessary foundation for solving the most complex anthropo-social-natural problems. Education is the foundation of culture, a unique over-biological system of transferring social experience, a mechanism of social continuity, by which it is possible to realize the essential human forces. The modern technogenic-informational civilization has developed into a global civilization of lies and global parasitism; the main cause of the antropo-social-ecoplanetary crisis is the global catastrophic anthropic crisis. The main deformations have occurred in the person him/herself, who has turned into an anthropo-system of accumulating type; we should not forget that the humanity, mainly represented by the egocentric anthropo-systems (of the accumulation type), is transforming into a planetary parasite, consisting of a collection of anthropo-microbes destroying the surface of the living cosmic organism of the Earth-Gaia. As a result, the cosmic macro-organism, sick from anthropo-parasites, is able to produce such a defensive reaction that will destroy the parasites and sanitize the Earth-Gaia; the key goal is the restoration of a harmonious whole human being as a transforming anthropo-system. There is a vital need in the human being who has reason, spirituality and morality, who is balanced, creative as a being able to enter into a state of symbiosis with the maternal nature of the planet; the main way to restore the whole person and normal anthropo-social and socio-natural life is a ban on the destruction of education in the form and content, on the zombieing of population; restoring Russian upbringing-education on the principles of creation of an integral person and the god-and-man; restoration of the Russian Institute of Philosophy of the Human Being. The authors have determined that it is exactly as a result of the deformation of humanity that the local problems have been transformed into the global ones. The antropo-social-ecoplanetary catastrophe provoked by the deformed human being is moving around the planet and can be stopped only by the human being him/herself by means of his/her qualitative transformation, with the restoration of the intellectual moral-spiritual potential and a creative harmonizing force in the world.

The author of the article shows that the economy of the global world requires a special methodology for its study, which should take into account the interests not only of the elite, the so-called civilized countries, but also the specificities of the regional world, the prevailing socio-economic traditions, mentality, and so on. The article analyzes the situation that has arisen in modern economics education. The author shows that many of the problems of the educational sphere are determined by the general uncertainty that exists in the economy of not only Russia but also of the entire world. At the heart of this policy, which is aimed at destatization (education is positioned as a private affair of the student), there are the liberal concepts of «free market». The educational reform has the anti-state character and sets the tone of anti-social economics education. The idea, on which all the educational changes of the last three decades are based, presupposes the positioning of the state, society and the individual as self-sufficient antipodes. When designing a new system of economics education, it is also important to take into consideration that the former opposition between state and market in the developed countries no longer makes sense: both the state and the market occupy a certain place in the socio-economic system, perform their unique functions and exist in inseparable unity. The author substantiates a social need for development of a new economics education due to intensification of the globalization processes in the modern world, which involve the Russian Federation too. However, the Russian scientists have to take into account as much as possible the domestic experience of economic management, as well as to revive the unique theoretical works of Russian thinkers.

A defining subsystem of the society is its economic sphere, which creates the material-financial conditions for the functioning of education. Here there are also formed the main risks arising from the state of economy. The specific sources of risk are sharp polarization of the population, differences between regions in terms of economic development, underfunding of education, exchange rate fluctuations, uncontrolled inflation, a sharp change in the rate of technological development, instability in the level of supply and demand in the labor market, and others. In the article, there are considered from the standpoint of social philosophy (in the aspect of security issues of domestic education) the economic factors, the direction of influence of the economy on the state of education and the causes of economic risks. The present state of the Russian economy is analyzed, as well as its development trends in terms of the main performance parameters, including the implementation of social programs. The article also highlights the main internal and external risks in education due to the state of economy, and the ways are justified of their neutralization by means of educational policy of the state and the possibilities of educational institutions.

In the perspective of post-nonclassical scientific paradigm, there arises in the methodology of modern social-humanitarian knowledge the desire to include into the explanatory schemes the category of the human being, which makes it possible to analyze such interdisciplinary phenomena as subjectness, individuality, personality, «spiritual Self», consciousness, conscience, morality. Explanation of the nature of these definitions requires philosophical reflection, reinterpretation of methodological approaches in modern social-humanitarian knowledge in general. The article discusses the relationship of fractal resonance and quantum approaches that could serve as an explanatory principle of phenomena related to acquiring the social and cultural experience in the educational process. Describing the characteristics of the person as a multidimensional phenomenon, the authors present him/her as an informational self-similar structure that permeates the physical body and is a source of non-linear fractals, interacting with the world and itself according to the resonance principle. Based on this conceptual position, they first formulate the essential characteristics of the fractal-resonance and quantum approaches in relation to the field of social-humanitarian knowledge. Turning to the methodology of the above approaches, the authors present and describe a system of principles on which their implementation in modern education is based. The study summarizes and systematizes the experience of domestic and foreign scientists, which allows creating a holistic view of the methodological possibilities of fractal-resonance and quantum approaches in education. A special attention can be paid to the formulated and theoretically substantiated by the authors system of principles of fractal-resonance and quantum approaches, which allows translating the sociocultural experience in the educational process, and which is based on the laws of quantum mechanics and the theory of fractals. An apparent merit of this article is conceptualization of the ideas of quantum psychology and fractal pedagogy and the rationale for their use in the field of modern education. In the comparative analysis, the author suggests that the «reality» of the classical world includes a number of alternative worlds, which bear the traits of self-similarity, whereas most of them have fully fractal, scale-invariant forms. In the context of principles of the fractal-resonance approach, it is justified that the reality and consciousness are a single whole, where the consciousness can be seen as the relationship between the fractal structures of internal and external worlds of the human being, whereas the quantum approach makes it possible to fully identify how the mental, the ideal are related to the material, the physical, the bodily.

The article reveals the ontological and gnoseological relationship between the categories of «creativity» and «education» in the historical-philosophical context. We study the essence of the concept of «image» in education and creativity. The main problem areas of the modern educational process are touched upon and the ways to resolve them through a heuristic model of training and a creative approach in education are outlined. A general line of development of the modern education system is the creation of necessary conditions for the full realization of a broad and flexible creative thinking of the individual in the context of integration of educational realities. Only a creatively oriented education can bring up unconventionally thinking people in the diverse fields of knowledge. The author shows that a creative approach to education is determined by a holistic perception of the creative subject, where the unconscious personality characteristics, being a prerequisite for creative activity, are no less important than rational thinking, which in turn causes blurring of the boundaries between training and upbringing. It is only through creative activity as a generalizing element of educational paradigm that it becomes possible a comprehensive understanding and nonstandard solution of educational and everyday problems of different complexity, the development of cognitive independence and search activity of the person.

The article is devoted to the problem of adequacy of mathematics. This problem is a significant and interdisciplinary one; it covers pure mathematics, applied mathematics, philosophy and methodology of science, pedagogics and etc. There exist purely philosophical approaches to the problem of adequacy of mathematics, which are primarily based on the thesis of indispensability of mathematics in the best and successful natural science theories. However, in our opinion, they have no value for real applications. Firstly, the vast majority of scientific disciplines are not formalized ones. Secondly, less than one percent of all scientific problems are solved on the basis of theories. Thirdly, even in physics the role of theories is restricted only to theoretical problems, while the explanation of concrete physical phenomena requires the use of empirical laws and models of physical theories. The work objective consists in carrying out a methodological analysis of real applications of applied mathematical statistics. The fact is that, in spite of massive application of mathematics in practically all branches of knowledge, modern formal apparatus does not fully conform to the correct application of mathematics. The known conditions of application of mathematics are not stringent, and the correct use of mathematics is rather an art than a science. The problems of correct and effective use of mathematics are topical, because they are important for scientific practice; however, they have not received sufficient attention in the philosophical and methodological literature. The basic idea of the work consists in the demonstration of effectiveness of methodological analysis in the context of real applications of mathematics. In the article, the requirements to application of a mathematical discipline are formulated on the basis of a suggested notion of a basic property of the mathematical discipline. Since the set of the requirements is not complete, a strategy is proposed directed on widening and refinement of the requirements of using mathematics. The strategy consists in defining properties of mathematical objects facilitating or preventing the usage of mathematical apparatus. As a result of this work, the notion of adequacy of mathematical discipline, in particular, of applied statistics is made more precise. The difficulties of application of applied statistics cause the appearance of new promising directions in statistics. All known potentials of applied mathematical statistics is, in some way, connected with the development of general and applied statistical ideas. However, the advancement of the statistical science in general requires improving the methodology of teaching the statistical disciplines and realizing the organizational modification of statistical bodies.

The author of the article notes that presently, in connection with the introduction of distant education in domestic higher education institutions, a necessity has appeared of widespread usage of standardized testing. Tests, together with some advantages (assessment of erudition, the ability to update the knowledge, training of mechanical memory, etc.), have significant shortcomings: formal and not always information-essential and significant questions or tasks and formalized variants of answers that do not touch the essence of the question (task), are weakly connected with its content and reflect only the formal side of it. In addition, according to the author, the main danger of using such variants is «guessing» of the correct answers or their selection by eliminating absurd or random variants. These tests do not focus on the development of cognitive abilities of pupils and simultaneous complementary implementation of element-wise and operation-wise analysis and control of knowledge and skills, multiplying its didactic function. According to the author, the right combination of questions and possible responses to them, which go beyond the topic (including the applied-type questions), allows using programmed exercises to make the contents of control tests meet the challenges of the thinking development. The programmed response options constitute a system of «reference points», which are outlined in the preparation of a task and through which the student’s thinking moves. Such variants of answers determined a program of their mental activity. The programmed variants of answers define the boundaries of the area of mental actions, point to objects or certain aspects of the same object, on which the thought should be focused, set the direction and sequence of transition of thought from one object to another in the initial phase, promote the penetration of thought into the essence of the object (into the concept of it). The article highlights the general requirements for the preparation of programmed exercises, their questions and answers. An example of programmed exercise is given, devoted to the problematic study, develop and control of the mastering by future social workers, teachers and methodologists of an integrative concept of professional-pedagogical thinking.

The authors note that at the basis of training in the academic drawing at the art departments of pedagogical higher education institutions there is an organized process of scientific cognition, and also mastering the methodological knowledge of academic drawing. An instrument of control of the process of training in drawing is a pedagogical mindset, which allows awakening students’ purposeful vision of nature dictated by specific educational objectives, and also the personal-evaluative attitude to the depicting process. The pedagogical mindset helps to form consistently and gradually the professional competences of the drawing artist, since it is obvious that every time the process of image creation is followed by certain purposes and tasks of visual perception. It is exactly the purpose mindset that creates a certain form of mental organization of activity, causing mobility of perception and activity of formation of graphic representations, which allows finding the basic direction for the solution of graphic tasks. Moreover, the number of mindsets is determined by the quantity of stages of work on the image and methodical sequence of complication of training material. In the article the statement is substantiated that the basic method of training in the academic drawing and comprehension of the graphic literacy is a research method. Its essence is conditioned by its functions: on the basis of purposeful observation, the professional art perception is formed; the consecutive assimilation of knowledge is organized, that is the known knowledge, acquired at the early stages of training, is applied to the solution of more complex problems; and, as a result of such solution, new knowledge is obtained, and also mastering the methods of scientific and art cognition in the process of graphic activity is provided, that is, the initial conception in the academic drawing is realized. In the art-pedagogical education this process traditionally begins with the depicting of a still life, which is an especially valuable object for cognition of the foundations of the graphic literacy, visually and lucidly demonstrating various regularities of forms in space and their composite interaction. The authors suggest training in still life drawing, using a complex of consistently complicating tasks: the search, short-term-training and long-term-creative tasks. As a result, each academic task will be presented by one complete work and a series of brief sketches and exercises, the stages of studying of theoretical and practical questions of the graphic literacy.

The authors analyze the ways of graphic representation, which are developing in the course of evolution of fine arts, changing the character, contents, principles and organizational forms. Modern scientists, on the basis of analysis of the specificities of perception of form in the course of drawing, offer the following classification of the systems of depiction: a conditional- schematic, contour-schematic, constructive- spatial, spatial-plastic, and associative-tone ones. It is noted in the article that the process of training in drawing is based on development of the graphic representation systems and in accordance with them. Historically first was the system of conditional-schematic image based on perception of the main features of natural object and reproduction of these features in drawing (rock paintings of ancient people, canons of Ancient Egypt, Medieval art, Old Russian art); whereas schematism of the image is a manifestation of the process of consecutive simplification of form. The system of the contour-schematic depiction which was developed in the art of Ancient Greece assumes the differentiated mastering of elementary regularities of the image. At that, a vision of interrelation of reference points is formed at the planar perception of a volume form, the ability to analysis and comparison of proportions develops, there appears accuracy of reproduction in the depiction of contour of a form by means of linear perspective. The artists of Renaissance identified as the main task of the drawing artist the scientific- analytical work which is focused on cognition of construction, the essence of form-creation, and is a process of cognition of the images of natural objects. The authors note that even today the scientific-methodical ideas of the artists of Renaissance are the necessary base for the design of modern innovative techniques and give a possibility to develop new systems of depiction. The task of modern teacher in the course of training in drawing is to direct the attention of the student from live observation to abstraction, from the external form of nature to its design, proportions, the internal rhythmic organization, directing the academic drawing to the development of spatial-rhythmic system of depiction which manifests itself in harmonious creation of a drawing on the basis of rhythm.

The article raises the problem of forming a creative approach to compositional knowledge, based on emotionally-shaped perception, the formation of the original plan, which determines the general direction of the depictive actions of the artist. A competent composition is to be based on the time-proved fundamental laws of composition, drawing and painting, which have been formulated by artists during centuries-old history of development of fine arts. The authors focus attention on the fact that the composition process is characterized, first of all, by a creative beginning which cannot be regulated only by the knowledge of objective rules of realistic depiction. The creative beginning of any composition starts with the birth of a subjective plan which is in many respects caused by the emotional-image-bearing factor forming an esthetic component of the composition and its expressiveness. It is the emotional-image-bearing component that intensifies the cognitive and creative processes. The following major principles are considered as indisputable compositional components: commensuration and proportionality, integrity and hierarchy, balance and rhythm, unity and analogy, contrast and nuance, symmetry and asymmetry, wholeness and harmony. The authors note that for the professional artist the knowledge of laws, rules, as well as mastering of techniques and means of composition is connected, at the subconscious level, with the realization of an art-figurative plan in dialectic unity of the content and the graphic form. At the same time, the compositional work of students is often defined only by the logic of the teacher’s directions and depends on the formal signs connected with existence of initial skills of depiction and also with the level of the formed perception for the image. And here it is important to pay attention to the fact that carrying out a specific compositional task in the educational process does not presuppose the existence of a unique correct solution, because to fulfill the task, each trainee is required to produce his/her own original versions of solution. This is what determines a creative nature of this activity. Composition in the fine arts is a two-in-one process of formation of a mental image and the process of material realization of this image on the graphic plane; thus, any image needs to be perceived in two aspects: the semantic and spatial-plastic ones. In the educational process it is expressed in revealing the semantic content of a subject of future composition, formation of an artistic conception on its basis and designing a methodical sequence of performing the work on composition taking into account application of the composition laws, methods of image construction and artistic image creation.