Description of the presentation on individual slides:

1 slide

Description of the slide:

2 slide

Description of the slide:

Levels of innovation in education Improvement is a change in one or more elements of the educational process; adaptation of the well-known methodology to the new conditions of educational activity (new ways of creating groups) Rationalization - the establishment of a new rule for using known pedagogical means to solve traditional problems (a different way of scheduling) Modernization - changing several elements of the current educational system (instead of 11 years of education, 12 years are assumed) Heuristic solution - finding a way to solve known pedagogical problems; creation and use of previously unknown pedagogical forms, methods, means for solving actual pedagogical problems (Shatalov's method of supporting notes) Pedagogical invention - a new tool, technology or a new combination of pedagogical means for the implementation of education (M.P. Shchetinin's immersion system) Pedagogical discovery - staging and the solution of a new pedagogical task, leading to a fundamental renewal of the educational system as a whole or a significant improvement in its constituent element (TRIZ pedagogy, competency-based approach, distance learning)

3 slide

Description of the slide:

Innovations and innovations Pedagogical innovation is an idea, method, means, technology or system. Innovation - the process of introducing and mastering innovation

4 slide

Description of the slide:

Problems generated by innovations Differences in the needs of students, their parents, schools; Existence in one school of supporters of different pedagogical concepts and approaches Non-compliance of the concepts of educational institutions with the requirements of the surrounding society, educational standards The problem of combining innovative programs with traditional ones Lack of educational and methodological support for working on new concepts Adaptation of innovations to existing conditions institutions Problems of interaction of innovations with administrative bodies, state monitoring systems.

5 slide

Description of the slide:

Types of innovations In the content of education In the methods, technologies, methods of the educational process Organization of the educational process In the management system of the school Innovations are radical or basic (fundamentally new technologies, management methods) addition of initial structures, principles, forms)

6 slide

Description of the slide:

Scale of innovations Local Modular (complex of private, interconnected, related, for example, to one group of subjects, one age group of students, etc.) Systemic (covering all educational institutions)

7 slide

Description of the slide:

The object and subject of pedagogical innovation Pedagogical innovation considers the education of a person, and not other processes - material, technical, economic, etc. (for example, the number of hours allocated for a subject, or providing schools with equipment) and the results of its implementation The subject of innovation is the relationship between the effectiveness of innovative processes and the factors that determine it, as well as ways to influence these factors in order to increase the effectiveness of changes (conditions, means, patterns, forms, methods, technologies) Pedagogy deals with educational processes, changing students and teachers.

8 slide

Description of the slide:

Three aspects of innovation processes Socio-economic Psychological-pedagogical Organizational and managerial

9 slide

Description of the slide:

The laws of pedagogical innovation The law of irreversible destabilization of the pedagogical innovation environment The law of the final implementation of the innovation process The law of stereotyping of pedagogical innovations The law of cyclical repetition, recurrence of pedagogical innovations

10 slide

Description of the slide:

5 meanings of innovation Changing the psychological climate in an educational institution, which is due to new goals and values ​​of education Implementation and dissemination of developed pedagogical systems Development of new design, management and teaching technologies in schools engaged in innovative activities, forced to constantly overcome emerging contradictions Innovative schools draw new ones into their orbit financial, informational, socio-cultural structures and mechanisms Pedagogical activity takes on the character of sustainable creative activity and has a positive impact on all components of the educational process

11 slide

Description of the slide:

8 ranks of innovations Zero-order innovations - reproduction of the traditional educational system or its element First-order innovations - quantitative changes with its unchanged quality Second-order innovations - regrouping of system elements and organizational changes Third-order innovations - adaptive changes in the educational system in new conditions without going beyond the old models of education Fourth-order innovations - the simplest qualitative changes in individual components of the educational system Fifth-order innovations - a change in all or most of the initial properties of the system Sixth-order innovations - the creation of educational systems of a "new type" with a qualitative change in the functional properties of the system while maintaining the system-forming functional principle Seventh-order innovations - a radical change in educational systems, the emergence of a "new kind" of educational systems

12 slide

Description of the slide:

Three components of the innovation process Creation Development Application of innovation

13 slide

Description of the slide:

The structure of the innovation process Creation of innovations: analysis of educational activities and identification of the need for changes; innovation design; experimental testing of innovations; innovation expertise. Dissemination of innovations: 1. preparation for distribution; 2. informing about innovations; 3. support for the development of innovations; 4. analysis of distribution and development of innovations

14 slide

Description of the slide:

Development of innovations: 1. analysis of educational activities and identification of the need for changes: 2. search for innovations; 3. evaluation and selection of innovations; 4. designing the desired future of the educational system; 5. innovation; 6. analysis and evaluation of the results of changes; 7. institutionalization of innovations. Educational activities

15 slide

Description of the slide:

Subjects of innovation Manager Teacher-experimenter Problematizer Researcher Methodologist Designer Designer Designer Planner Decorator

16 slide

Description of the slide:

Technology of innovations Implementation - carried out by the developer himself Engineering - from marketing, pre-project survey, business planning, development to complex supply of equipment, personnel support and subsequent service Consulting - technology of innovations, providing the stage of choosing a strategy for planning innovation activities Training - the stage of preparing personnel support for innovation Technology transfer is the implementation of an innovative project through transfer to another subject area or to other territories

17 slide

Methodological foundations of pedagogical innovation

If practitioners are more often concerned with the specific results of updates, then scientists are interested in the knowledge system and the corresponding types of activities that study, explain, justify pedagogical innovation, its own principles, patterns, conceptual apparatus, means, limits of applicability and other scientific attributes characteristic of theoretical teachings. All these are methodological aspects of studying and constructing pedagogical innovations.

In the process of studying innovative processes in education, scientists discovered a number of problems of a theoretical and methodological nature: the relationship between traditions and innovations, the content and stages of the innovation cycle, the attitude to innovations of different subjects of education, innovation management, training, the basis for the criteria for evaluating the new in education... These problems need to be understood at the methodological level. As a result, the substantiation of the methodological foundations of pedagogical innovation is no less relevant than the creation of pedagogical innovation itself.

N.R. Yusufbekova considers pedagogical innovation to be a direction of methodological research, since it is in this science that a system of knowledge about the creation, development and dissemination of pedagogical innovations can be represented. Pedagogical innovation allows you to reflect the necessary connection between the processes of creating pedagogical innovations and their application, incl. implementation in practice; substantiate and develop the principle of the unity of research activity and the activity of transforming pedagogical reality.

The activity essence of innovations in education and the need to display them in the form of teaching put forward the requirement for understanding the methodology of pedagogical innovation as an organic unity of two components: teaching and activity. To fix this unity at the conceptual level, we will use the definition of the methodology of pedagogy, ĸᴏᴛᴏᴩᴏᴇ was given by M.A. Danilov: ʼʼThe methodology of pedagogy is a system of knowledge about the foundations and structure of pedagogical theory, about the principles of approach and methods of obtaining knowledge, reflecting ... pedagogical realityʼʼ - and developed later by V.V. Kraevsky: ʼʼ...as well as a system of activities to obtain such knowledge and substantiate programs, logic and methods, assess the quality of special scientific pedagogical researchʼʼ,

The above constructions allow us to formulate the following definition: the methodology of pedagogical innovation is a system of knowledge and activities related to the foundations and structure of the doctrine of the creation, development and application of pedagogical innovations.

So, we are interested in the system of knowledge and the corresponding types of activities that study, explain, justify pedagogical innovation, its own principles, patterns, conceptual apparatus, means, limits of applicability and other scientific attributes characteristic of theoretical teachings.

What is the task of pedagogical innovation methodology? Obviously, it is extremely important to give a holistic theoretical presentation of pedagogical innovation, its composition, structure, and functions. To do this, it is necessary to identify the main trends, contradictions, principles, laws of development of innovative processes, to substantiate methodological approaches to their study within the framework of pedagogical innovation. Only the first steps are being taken in this direction.

N.R. Yusufbekova in her research reveals the following trends in the field of education and their corresponding contradictions.

1. Tendency towards continuity of education. It calls for structural and substantive renewal.

2. The growing need for new pedagogical knowledge among teachers and other practitioners. The composition and structure of the pedagogical community is being updated.

3.Introduction trend. The use of the new is becoming widespread.

4.Tendence towards the creation of educational school systems.

The development of educational systems of schools involves the passage of three basic interrelated stages:

1) the emergence of a new pedagogical phenomenon - the educational system of the school and its theoretical understanding in the new pedagogical knowledge, ĸᴏᴛᴏᴩᴏᴇ in the form of theories, concepts characterizes this pedagogical innovation in its specificity;

2) development of innovation by the pedagogical community;

3) application, implementation in the practice of schools.

Each of the three stages is distinguished by its specific contradictions and features of their resolution.

For the first stage, the contradiction lies in the fact that the goal of education - the formation of a harmoniously developed personality - cannot be consistently realized in modern society with its education system.

For the second stage, the contradiction between non-systemic scientific and pedagogical thinking and the systemic class of scientific and practical tasks that are posed and solved when developing the problem of the educational system of the school is essential.

For the third stage, the contradiction between the ready-made, existing ʼʼmodelʼʼ, ʼʼmodelʼʼ of the educational system and the extreme importance of its use and development in the working conditions of a particular school is significant.

From a methodological standpoint, it is extremely important to determine the patterns of development of innovative pedagogical systems and processes. Belarusian scientist I.I. Tsyrkun revealed the following patterns of innovation system development.

1. The system develops unevenly. The logic of culture, scholasticism over cumulativeness and rationality dominate in the development of the innovation system.

2. The determining bases for the development of an innovation system are innovations with substantive scientific justification. Οʜᴎ prevailed until the 70s. 20th century

3. There is a certain sequence in development: first, the resources of subject scientific justification are consistently exhausted, and then a transition is made to deeper sources (didactics, psychology, cybernetics, a systematic approach ...).

4. Various didactic innovations have the property of equivalence with respect to the expected effects.

5. The innovation system is dominated by modifying innovations and innovations that are focused on the value of the result.

6. In the process of development of an innovation system, the complexity of scientific justification increases and the frequency of the appearance of modernist innovations increases.

7. Radical innovations, as a rule, are associated with the aspiration of innovators to achieve the goals of development and self-development of the personality of students.

8. The development of an innovation system is carried out with evolutionary cycles. The development maxima correspond to the periods: 1951-1960, 1971-1975, 1981-1985.

9. In the innovation system, there are changes in the positions of the variables and permanent components of education.

Among these regularities, the seventh regularity is significant, which determines the vector of radical innovations, which is associated with the goals of development and self-development of the personality of students. Indeed, this pattern is semantic, ᴛ.ᴇ. , refers to the essence of education as human development. The rest of the identified regularities relate to a greater extent to the characteristics of the innovation process and the conditions for their implementation.

At the root of any scientific theory are revealed regularities and laws. In innovation as an interdisciplinary field, these patterns have been studied and formulated in the works of economists, managers, and production workers. In relation to educational innovations, this issue has not yet been studied enough and needs additional research. As one of the first generalizations, we present the data of N.R. Yusufbekova, who formulated the following laws of pedagogical innovation.

1. The law of irreversible destabilization of the pedagogical innovation environment. Holistic ideas about any pedagogical processes or phenomena begin to collapse, and subsequently it turns out to be impossible to restore these ideas. In this regard, there are costs associated with the personnel and spiritual capabilities of the pedagogical community.

2. The law of the final implementation of the innovation process. Any innovative process must sooner or later, spontaneously or consciously be realized.

3. The law of stereotyping of pedagogical innovations. Any pedagogical innovation implemented in the innovation process tends to turn into a stereotype of thinking and practical action.

4. The law of cyclic repetition, the return of pedagogical innovations.

The listed laws are to a certain extent characteristic of many innovative processes; in pedagogy, such laws, for sure, will still be clarified. The task of pedagogical innovation is to establish exactly those laws and patterns that relate to its subject of study. For this, it is extremely important to build a theoretical and methodological apparatus, one of the main components of which is the conceptual apparatus.

Methodological foundations of pedagogical innovation - concept and types. Classification and features of the category "Methodological foundations of pedagogical innovation" 2017, 2018.

For the most adequate understanding of the problem of pedagogical innovation, let us define the basic concepts with which it operates. This will reveal the essence of the corresponding representations, establish the meaning of the links between them. From this point of view, such concepts as “new”, “innovation”, “innovation”, “innovative process” are the most important. Therefore, the need for a detailed consideration of these and related concepts at the level of framework definitions is obvious. Various authors often equate these concepts, which is quite understandable.

"New" in the generally accepted view is "created or made for the first time, appeared or emerged recently, instead of the former, re-discovered". The term "innovation" in Russian refers to a new socially significant order, custom, method, means, invention, phenomenon. That is, the concept of "innovation" can be defined as the fact of the emergence (discovery, observation) of something that was not previously known or was not considered in this socially significant context. Russian "innovation", in the literal sense "introduction of the new", can be seen as a process or result of the use of innovation. It is generally accepted that etymologically the term "innovation" comes from the literal translation of the English word innovation, which means "introduction of innovations".

In itself, "innovation" (from lat. novatio- renewal, change) in modern managerial vocabulary means “partial renewal, change of something that already exists; innovation associated with the replacement of a component, connection, relationship, etc.” . Therefore, the lexical phrases "introduction of innovations" and "introduction of innovations" are synonymous.

Thus, from the moment it is accepted for use and distribution, an innovation acquires a new quality - it becomes an innovation.

The word "innovation" is characterized by the fact that it is used both in common and in special meanings. In the common sense, it can be synonymous with the word "innovation", but in terminological usage, "innovation" takes on a narrower and at the same time more capacious sound, and has different meanings depending on the specifics of the application. So, in the Big Economic Dictionary two meanings of the word are given: “1. Investing in the economy, ensuring the change of generations of equipment and technology; 2. New equipment, technology, which are the result of the achievements of scientific and technological progress. This semantic content of the word “innovation” is more detailed in paragraph 1.2.

In another source, innovation is defined as: “1) a process of constant renewal in all areas of activity; 2) new phenomena, innovations within any system; 3) the creation, distribution and use of a new means (innovation) that satisfies the needs of a person and society, at the same time causing social and other changes. At the same time, according to the last criterion, some researchers distinguish between innovations of an evolutionary and revolutionary order, radical and partial nature, wide or narrow use.

We emphasize that innovation refers to "activity" as a class of phenomena - activities to find and obtain new results, ways to create them, eliminate routine, inefficient working conditions, management structures, etc.

Translation of innovative solutions is possible only in case of their unconditional success in comparison with previous solutions. Here, success should be understood as "the timely achievement of consciously set goals." Success, on the other hand, should be considered as a property of an individual (or a certain systemic association of individuals - for example, an apparatus for managing a social process) to systematically achieve consciously set goals.

The basis of innovation is always some kind of innovation. The period of time from the birth of an idea, the creation and dissemination of an innovation to its use is commonly called life cycle innovation . N.V. Gorbunova points out that “the life cycle acts as stages of impact on the environment and on the innovation itself” and distinguishes five stages: start, rapid growth, maturity, saturation, finish or crisis. A characteristic of the life cycle is its completeness and efficiency. Taking into account the sequence of work, the life cycle is considered as innovation process.

In general, the innovation process is understood as "a complex activity for the creation (birth, development), development, use and dissemination of innovations" .

The environment in which the innovation process takes place is extremely important. In this regard, for definiteness, “a set of conditions that promote or hinder the flow of innovative processes within a system is often called innovative environment".

In the context of educational activities, innovation involves the introduction of new goals, content, methods and forms of education and upbringing, and the organization of the pedagogical process. The terms "innovation in education" and "pedagogical innovation", used as synonyms, were scientifically substantiated and introduced into the categorical apparatus of pedagogy by I. R. Yusufbekova in the book "General Foundations of Pedagogical Innovation: Experience in the Development of the Theory of Innovative Processes in Education" (1989) .

Pedagogical innovation (the theory of innovation processes), as N. R. Yusufbekova emphasizes, serves the processes of updating education, their theoretical understanding and justification in order to limit the spontaneity of these processes and effectively manage them.

In general, in the works of N. R. Yusufbekova, pedagogical innovation is considered as an independent branch of pedagogical science, which has its own original object, subject and research methods.

The theoretical content of the subject of pedagogical innovation, in the interpretation of this researcher, includes three blocks of concepts and ideas:

• reveals the features of creating pedagogical innovations, their sources, classification, novelty criteria;
• the problems of perception, evaluation and development of emerging innovations by the pedagogical community are studied;
• data on the application of the new in education are summarized.

In accordance with this, pedagogical innovation includes pedagogical neology, axiology and praxeology.

Pedagogical neology is the doctrine of the new in pedagogy, which systematizes scientific and experimental data on the process of scientific and pedagogical creativity, its features and main results.

Comparative pedagogical axiology reveals the specifics of the assessment and development by the pedagogical community of what arises in pedagogical theory and practice.

Innovative praxeology as a doctrine of the activity of implementation involves understanding the practice of applying pedagogical innovations.

A holistic understanding of innovation processes requires the disclosure of leading trends and contradictions in their development. N. R. Yusufbekova identifies four such trends.

The first trend - the expansion of practice and the implementation of innovative processes - is a pattern in the development of modern education, leading to a steady trend of its permanent renewal. This trend causes contradictions:

• a) between the old and the new - is generated by both social and pedagogical needs;
• b) between the increasing mass of knowledge, facts and the boundaries of the educational process;
• c) the development of society requires a creative personality, and this implies the creative development of existing knowledge. This process corresponds to problem-based learning, which requires more time than explanatory and illustrative methods. This contradiction involves the search for new approaches to its resolution.

The second trend is the growing need for new pedagogical knowledge among teachers and other practitioners. The composition and structure of the pedagogical community is being updated, which gives rise to a contradiction between the capabilities of the pedagogical community and the actual state of mastering and evaluating the new in pedagogy.

The third trend is related to the implementation stage. Its essence lies in the fact that the application of the new takes on a mass character.

And, finally, the fourth trend is towards the creation of educational school systems. The development of educational systems of schools involves the passage of three main interrelated stages:

• the emergence of the pedagogical phenomenon of the educational system of the school and its creative understanding in the new pedagogical knowledge;
• development of innovation by the pedagogical community;
• the stage of application, introduction into the practice of schools.

Each of the three stages is distinguished by its specific contradictions and features of their resolution.

The first stage is characterized by the non-integral, predominantly spontaneous nature of the socio-pedagogical impact on the formation of a person who prevails in society. This contradicts the goal of educating a harmoniously developed person: a “truncated” personality, a “partial” person, is reproduced. This contradiction can be resolved only in the system of an educating society, i.e. a society in which the educational system is part of it, along with other different types of educational systems.

For the second stage, the contradiction between non-systemic scientific and pedagogical thinking, which fixes the established practice of the general education school, and the systemic class of scientific and practical tasks that are posed and solved when developing the problem of the educational system of the school, is essential.

For the third stage, the contradiction between the ready-made, existing “model”, “model” of the educational system and the need for its use and development in the conditions of a particular school is significant.

The revealed trends and contradictions make it necessary to raise the question of the laws of innovation processes. N. R. Yusufbekova considers the following laws.

The law of irreversible destabilization of the pedagogical innovation environment. Holistic ideas about any pedagogical processes or phenomena begin to collapse, and subsequently it turns out to be impossible to restore these ideas. In this regard, there are costs associated with the personnel and spiritual capabilities of the pedagogical community.

The law of the final implementation of the innovation process. Any innovative process must sooner or later, spontaneously or consciously, be realized.

The law of stereotyping of pedagogical innovations. Any pedagogical innovation implemented in the innovation process tends to turn into a stereotype of thinking and practical action.

The law of cyclic recurrence, returnable ™ of pedagogical innovations, their repeated revival in new conditions.

The following principles of innovation process management are distinguished:

• the principle of a controlled innovative change in the state of the education system. This principle focuses on the need for conscious activity in the transition from one state of the education system to another;
• the principle of transition from spontaneous mechanisms of the flow of innovative processes to consciously controlled ones;
• the principle of information, material, technical and personnel security for the implementation of the main stages of innovation processes;
• the principle of predicting reversible or irreversible structural changes in the innovative socio-pedagogical environment;
• the principle of strengthening the sustainability of innovative processes in education;
• the principle of accelerating the development of innovation processes in education.

These principles are aimed at creating an integral system for organizing and managing innovation processes. The first attempt to create such a system was the emergence of scientific and practical centers for pedagogical innovations. In the future, such centers should become the leading component of the innovation service in the education system as a whole.

Pedagogical innovation, noted in her other work, as a system of knowledge about the creation, development and dissemination of pedagogical innovations will allow:

• reflect the necessary connection between the processes of creating pedagogical innovations and their application, including implementation in practice;
• substantiate and develop the principle of the unity of research activity and the activity of transforming pedagogical reality.

The development of pedagogical innovation should be carried out on the basis of a specific analysis and generalization of the changes taking place in the theory and practice of perestroika, the real processes of innovation and the possibilities of managing them.

Innovative processes in pedagogy will depend on the implementation of four research and practical projects:

• restructuring of pedagogical science based on the development and implementation of the concept of a new stage in its development;
• transformation of practice based on the creation and implementation of the pedagogical theory of our time up to applied and developmental levels for all parts of the lifelong education system;
• a radical renewal of the logic and methods of pedagogical research with their primary orientation towards exploratory and fundamental research and reliance on a large-scale pedagogical experiment;
• substantiation and development of effective mechanisms for connecting the research process and the process of transforming pedagogical practice (development of such forms of connection between theory and practice, such as scientific and school associations, school laboratories, etc.).

The applied tasks of innovation are the substantiation and systematization of new areas of pedagogical research. Among them:

• pedagogical theory of our time: as a system of ideas and principles of organization in the conditions of the renewal of society, the education system and the formation of a new type of personality; as a strategic direction for the development of pedagogical science;
• pedagogy of creativity, which studies the formation of a creative personality in the educational process and outside it;
• pedagogical therapy in the system of preventive and compensatory pedagogy, pedagogy of borderline states and extreme situations;
• peace pedagogy, which studies the impact of global problems of mankind on education and is aimed at educating thinking, a new morality and a new psychology that correspond to the realities of the nuclear space age;
• the theory of educational systems, which systematizes the integrative processes of education and upbringing, the patterns of combining social and pedagogical factors of upbringing.

Innovation processes are guided by a systemic, holistic, interdisciplinary and integrated study and change of reality. The initiative passes to a new type of researcher - a teacher-experimenter-practitioner (in science) and a teacher-researcher (in practice).

Innovative processes acquire an international character: there is a kind of globalization of pedagogical problems; global problems force us to pose new ones and see old pedagogical problems in a new way.

It should be noted that time has confirmed the predictability of many of the provisions expressed by Yu. R. Yusufbekova, which in the early 1990s. sounded quite hypothetical.

AI Subetto presents pedagogical innovation from somewhat different methodological positions. In his understanding, it is considered as part of the "systemology of education or educational systems", which was actively developed by him in 1992-1994. and in which educational (pedagogical) system genetics was singled out as independent scientific areas, understood as a general theory of continuity in the development of systems (and according to the principle of inversion - as a general theory of renewal and development of systems); educational and pedagogical innovation and the theory of educational (pedagogical) experiment.

Innovation as a science, according to his definition, in turn includes prognostics (the science of forecasting), creatology and intelligence (the science of the laws of the intellect and the objective laws of creativity).

System genetics developed by A. I. Subetto and his students, revealing the laws of progressive evolution, in particular the concept of the law of duality of control and organization of systems, shows the mechanism of the cyclical development of any systems in the world, including pedagogical, educational, according to which everything in the world, any “existent” in progressive evolution is subject to a kind of “wave law” of the change of the dominant of invariance, stereotype, conservatism, memory, structurality (in which inheritance and determination “from the past”, stability are manifested) and the dominant of variability, creativity, innovation, “memory destruction” , “destructive tendencies” (carrying in themselves the meaning of a violation of stability; this dominant manifests the determination “from the future”, a kind of “inheritance of the future” in the present).

From the standpoint of the law of duality of management and organization of systems, in general, system genetics and educational system genetics, educational and pedagogical innovation is a necessary part of the process of progressive development of educational and pedagogical systems. Pedagogical innovations are born in the educational system as a moment of manifestation of the law of its wave pre-adaptation to a changing external environment (to its impulses): social, educational, economic, psychological, demographic, organizational, scientific and pedagogical, etc.

An important source of pedagogical innovation is pedagogical science. It, changing ideas about the pedagogical process, about the school, about quality standards, about the learning personality, serves as a generator of pedagogical innovations. Pedagogy and, as part of it, pedagogical innovation begin with human studies, since any pedagogical system, first of all, has the status of an anthropogenic system such as "man - man" or "man - society", in which knowledge about the laws of human development is manifested.

The extent to which an innovator - a teacher, teacher-scientist, director of an educational institution, any manager in the field of education - is armed with knowledge of human science and education studies, notes A. I. Subetto, depends on: (1) the effectiveness of pedagogical innovation, (2) the risk ( from its implementation) negative consequences for a person and society, pedopathy, (3) progress or regression in the pedagogical evolution of educational systems, (4) the quality of future generations.

In order for a pedagogical or educational innovation to be accepted by the system, to become part of it, it must correspond to it. Such a correspondence is defined by A. I. Subetto through the concept innovative susceptibility, which he introduced into educational systemology.

The educational system has certain types of innovation susceptibility: scientific and technical, economic, social, psychological, organizational and pedagogical innovation susceptibility.

The innovative susceptibility of pedagogical systems (directorate or administration, teacher, person) occurs under innovative pressure, which, in the interpretation of A. I. Subetto, is a function of the areas of possibility and ability of the system.

Innovative pressure "channels" the flow of innovation and the growth of innovative potential in the direction of development, where there is the greatest tension in needs, where there is an expansion of the realm of the possible. The phenomenon of innovative pressure is a form of manifestation of the action of the system genetic law of heterochrony and system time, i.e. the law of uneven development, as well as the system genetic law of development invariance and cyclicity, which includes the law of periodic crisis development. Innovative pressure increases during development crises, and innovations become a form of overcoming systemic crises.

All of the above has a pedagogical interpretation. The contingent of students is changing, the values ​​of students are changing, the picture of the health of the generation is changing, the idea of ​​the laws of human development, the laws of creativity in human ontogenesis, etc. is changing - the system of pedagogical influence is also changing, the pedagogical ideal of human quality is changing.

From the standpoint of pedagogy, which introduces its own specific features into general scientific ideas, innovation is a complex, multidimensional concept. Most researchers-teachers (N. L. Korshunova, V. A. Slastenin, N. R. Yusufbekova, etc.) consider innovation as a unity of two processes: the appearance, creation of a new one as such, i.e. creation of pedagogical innovations, and at the same time its implementation, development by the pedagogical community, use in the practice of training and education.

A. V. Khutorskoy distinguishes three components of innovation: the creation, development and application of innovations. At the same time, he emphasizes that one should distinguish between innovations and innovations. If under pedagogical innovation understand some idea, method, means, technology or system, then innovation in this case, there will be a process of introducing and mastering this innovation. Thus, the concept of "innovation" for this author is synonymous with the concept of "innovation".

Innovations in education are a creative study of new ideas, principles, technologies, in some cases bringing them to standard projects containing the conditions for their adaptation and application. With the help of designing innovations, it is possible to manage the development of educational systems: both at the level of an educational institution, and at the level of a region, a country.

The innovation process consists in the formation and development of the content and organization of the new. It is a set of procedures and means by which a scientific discovery or idea is transformed into a social, including educational, innovation.

Innovative processes in education are considered in three main aspects: socio-economic, psychological-pedagogical and organizational-managerial. The overall climate and conditions in which innovation processes take place depend on these aspects. Existing conditions can promote or hinder the innovation process. The innovation process can be both spontaneous and consciously controlled. The introduction of innovations is, first of all, a function of managing artificial and natural processes of change.

The innovation process, in its most general form, includes three stages: generating an idea (in a certain case, a scientific discovery), developing an idea in an applied aspect, and implementing an innovation in practice. In this regard, the innovation process can be viewed as a process of bringing a scientific idea to the stage of practical use and implementation of the associated changes in the socio-pedagogical environment.

A more detailed description of the stages of development of the innovation process is offered by V. S. Lazarev, highlighting the following actions:

• determining the need for change;
• collection of information and analysis of the situation;
• preliminary selection or independent development of innovation;
• making a decision on implementation (development);
• the implementation itself, including trial use of the innovation;
• institutionalization or long-term use of an innovation, during which it becomes an element of everyday practice.

The totality of all these stages, from the point of view of V. S. Lazarev, forms a single innovation cycle.

An activity that ensures the transformation of ideas into innovation and forms a management system for this process is innovative activity.

Innovation activity is another systemic concept in pedagogical innovation. In the most general sense, innovation activity is an activity for the development and implementation of innovations. A. V. Khutorskoy defines it more specifically as a set of measures taken to ensure the innovation process at a particular level of education, as well as the process itself.

The main functions of innovation activity include changes in the components of the pedagogical process: the meaning, goals, content of education, forms, methods, technologies, teaching aids, management systems, etc.

General and specific features of innovative pedagogical activity are revealed in the works of many domestic researchers, such as A. A. Arlamov, N. F. Vishnyakova, V. I. Zagvyazinsky, M. V. Klarin, N. V. Kuzmina, S. D. Polyakov, M. M. Potashnik, M. M. Fridman, O. G. Khomeriki, N. R. Yusufbekova and others. In foreign pedagogy, the problems of planning innovations and managing innovative processes are studied by R. Adam, E. Rogers, A. King , B. Schneider, L. Anderson, L. Briggs, X. Barnet and others.

One of the urgent tasks of pedagogical innovation as a developing scientific field is the systematization of pedagogical innovations, since it allows studying the specifics and patterns of development of innovations in education, identifying and analyzing factors that promote and hinder innovation. Such systematization can be carried out on various grounds and on various grounds.

So, according to A. I. Subetto, given that pedagogical innovation itself is a complex and multidimensional phenomenon, it would be correct to raise the question of a multidimensional classification of pedagogical innovations. One can speak, this researcher believes, about pioneering pedagogical innovations born by pedagogical science and having a paradigmatic, long-term character: for example, problem-based or developmental education, certain pedagogical systems - V. A. commune” by A. S. Makarenko, “social pedagogy of life” by N. I. Pirogov, etc. There are pedagogical innovations of medium and short-term effects. Part of pedagogical innovations can be considered as elements of the becoming "author's school" of a teacher, teacher, etc.

Pedagogical innovations cover pedagogical technologies or methods, the content of education, educational programs and standards, educational processes, the organization of lessons, the organization of the pedagogical environment of the school, etc. The spectrum of pedagogical innovations is huge.

But in any case, the scientist emphasizes, pedagogical innovation must correspond to the "order", "need" of the evolution of the pedagogical system, by which it was brought to life.

Based on the research, A. V. Khutorskoy suggests systematics of pedagogical innovations, consisting of 10 blocks. Each block is formed on a separate base and differentiated into its own set of subtypes. The list of grounds is compiled taking into account the need to cover the following parameters of pedagogical innovations: attitude to the structure of science, attitude to the subjects of education, attitude to the conditions for implementation and characteristics of innovations.

According to this taxonomy, pedagogical innovations are divided into the following types and subtypes.

• 1. In relation to the structural elements of educational systems: innovations in positioning, in tasks, in the content of education and upbringing, in forms, in methods, in techniques, in teaching technologies, in training and education tools, in the diagnostic system, in control, in evaluating results, etc.
• 2. In relation to the personal formation of subjects of education: in the field of development of certain abilities of students and teachers, in the field of development of their knowledge, skills, methods of activity, competencies, etc.
• 3. By area of ​​pedagogical application: in the educational process, in the curriculum, in the educational field, at the level of the education system, at the level of the education system, in education management.
• 4. By types of interaction between participants in the pedagogical process: in collective learning, in group learning, in tutoring, in tutoring, in family learning, etc.
• 5. By functionality: innovations-conditions (provide the renewal of the educational environment, socio-cultural conditions, etc.), innovations-products (pedagogical tools, projects, technologies, etc.), managerial innovations (new solutions in the structure of educational systems and management procedures that ensure them functioning).
• 6. By way of implementation: planned, systematic, periodic, spontaneous, spontaneous, random.
• 7. Distribution scale: in the activities of one teacher, a methodological association of teachers, at a school, in a group of schools, in a region, at the federal level, at the international level, etc.
• 8. According to the socio-pedagogical significance: in educational institutions of a certain type, for specific professional-typological groups of teachers.
• 9. In terms of innovative activities: local, mass, global, etc.
• 10. According to the degree of proposed transformations: corrective, modifying, modernizing, radical, revolutionary.

In the proposed taxonomy, the same innovation can simultaneously have several characteristics and take its place in different blocks. For example, such an innovation as the educational reflection of students can be an innovation in relation to the system of diagnosing learning, the development of ways of students' activities, in the educational process, in collective learning, an innovation-condition, periodic, in a senior specialized school, a local, radical innovation.

Many researchers share the opinion that innovations, first of all, should be considered from the point of view of their relevance to one or another part of the educational process.

In this case, groups (types) of innovations corresponding to these parts are easily identified:

• in the content of education;
• in methods, technologies, forms, methods, techniques, means of the educational process;
• in the organization of the educational process;
• in the control system.

The listed parts of the educational process and the corresponding groups (types) of innovations are distinguished by specific specifics in the general goal-setting that determines the general direction of the innovation process. In this regard, each group can, in turn, be divided into subgroups and have a certain structure.

Within the framework of the above classification of innovations, the nature and success of their implementation are largely determined by the scale and volume of transformations required by the necessary innovation.

So, among the innovations are distinguished:

• private (local, single) innovations that are not interconnected;
• modular (which is a complex of private, interconnected innovations related, for example, to one group of teaching subjects or to one age group of students);
• systemic (covering the entire educational system, for example, an educational institution) innovations.

Since innovations are always carried out against the background of previous activities in a specific direction of the educational process, it seems appropriate to consider the classification on this basis as well.

From this point of view, innovations can be divided into:

• 1. Substitute: an innovation is introduced instead of some specific obsolete means (for example, theater and art studios, circles, sections and similar forms of extracurricular educational work with children have replaced pioneer and Komsomol work).
• 2. Cancel - the activity of some body, form of work, association is terminated; programs are canceled without replacing them with others if they are unpromising from the point of view of the development of education or hinder this development. The novelty in this case is in the abolition, termination.
• 3. Opening - there is a development of a new program, a new type of educational services, new technology, etc., if they had no previous analogues at all (an example is the computerization of the educational process).
• 4. Retro-introductions - something new is being mastered at the moment, but once already used in educational practice (the forgotten old has become relevant at the present time) -

In this sense, one can name the Waldorf pedagogy, the Montessori school, etc., which began to be transferred from one system to another. If we look at world culture, then Montessori pedagogy is not an innovation today, but for Russia, the introduction of Montessori methods 50 or 60 years later has become an innovation. The same can be said that for pedagogical psychology, developmental education, its foundations were not an innovation already at the end of the 1970s, but for the school of that period they became an innovation.

Analyzing the pedagogical literature, N. Yu. Postalyuk revealed that innovations in education can be innovations specially designed, developed, or “accidentally discovered” as a pedagogical initiative. The content of innovation can be: scientific and theoretical knowledge of a certain novelty (V. M. Polonsky), new effective educational technologies (V. L. Bespalko, V. V. Serikov), a project of effective innovative pedagogical experience made in the form of a technological description, ready for implementation (N. L. Guzik). Innovations are new qualitative states of the educational process, which are formed either when the achievements of pedagogical and psychological sciences are introduced into practice (A. A. Arlamov), or when advanced pedagogical experience is used (Ya. S. Turbovsky).

Summarizing the results of the analysis, N. Yu. Postalyuk proposes the following classification of innovations-innovations:

• 1) Depending on the functionality, all pedagogical innovations can be divided into:
  • innovations-conditions that ensure an effective educational process (new content of education, innovative educational environments, socio-cultural conditions, etc.);
  • product innovations (pedagogical tools, technological educational projects, etc.);
  • organizational and management innovations (qualitatively new solutions in the structure of educational systems and management procedures that ensure their functioning).
• 2) Depending on the area of ​​implementation or implementation, innovations can be:
  • in the content of education;
  • in teaching technologies, in the field of educational functions of the educational system;
  • in the structure of interaction between participants in the pedagogical process, in the system of pedagogical means, etc.
• 3) In terms of scale and socio-pedagogical significance, innovations can be distinguished: federal, regional and sub-regional or local, intended for educational institutions of a certain type and for specific professional-typological groups of teachers.
• 4) On the basis of the intensity of innovative change or the level of innovation. This criterion allows us to distinguish eight ranks or orders of innovation:
  • zero order innovation - it is practically the regeneration of the original properties of the system (reproduction of the traditional educational system or its element);
  • first order innovation characterized by quantitative changes in the system with its quality unchanged;
  • second order innovation represent a regrouping of system elements and organizational changes (for example, a new combination of known pedagogical tools, a change in the sequence, rules for their use, etc.);
  • third order innovation- adaptive changes in the educational system in new conditions without going beyond the old model of education;
  • fourth order innovation contain a new version of the solution (these are most often the simplest qualitative changes in individual components of the educational system, providing some expansion of its functionality);
  • fifth order innovation initiate the creation of educational systems of the "new generation" (change of all or most of the initial properties of the system). As a result of the implementation sixth order innovation educational systems of a “new type” are being created with a qualitative change in the functional properties of the system while maintaining the system-forming functional principle;
  • seventh order innovation represent the highest, fundamental change in educational systems, during which the basic functional principle of the system changes. This is how a “new kind” of educational (pedagogical) systems appears.

It should be noted that the last three ranks of innovations are characterized by truly systemic innovations and can claim the status of innovative educational (pedagogical) systems. They are extremely rare in modern educational practice. Remaining within the framework of the previously declared systemic approach in education, by analogy with the principles of functioning of complex systems (general systems theory), we can formulate the main pattern of innovation design: the higher the rank of innovations, the greater the requirements for scientifically based management of the innovation process.

A number of researchers consider the problem of typology of pedagogical innovations from a cultural point of view. The significance of this approach is determined by the fact that in conditions of political and economic instability, the loss of spirituality, the aggravation of national relations within Russia, it is extremely important to return education and pedagogy to the context of culture. This is emphasized by many researchers of the problems of the development of domestic education at the present stage.

In this aspect, the fact is actualized that, depending on the values ​​that are put forward as leading ones, we can talk about different paradigms of pedagogical thinking or types of pedagogical culture. As numerous studies show, different types of experience become the leading values ​​in different types of pedagogical culture: cognitive, activity, and emotional-value relations.

In accordance with this, depending on the position of what type of pedagogical culture the innovator acts from, preference is given to certain technologies of the process of mastering the material, which in turn determines three main types of innovative programs and projects - information-cognitive, social-role, behavioral.

This also determines the role that the teacher determines for himself in the educational process: focusing on cognitive experience, he sees himself in the role of a lecturer who transfers knowledge; orientation to the formation of activity experience entails an understanding of the role of the teacher rather as a coach or instructor, who is not “above” the student, pointing to him from the top of his knowledge, training, but “nearby”, along with the student, passing the path of knowledge and helping the ward to realize the experience this path; much less common is the understanding of the role of a teacher as a consultant, who allows his ward to independently work not only on solving the problem, but also on finding it, setting priorities. Figuratively speaking, the instructor has a ready-made "route map", and the consultant leaves the right to determine the route to his sponsor.

Based on this approach, N. M. BorytkoiA. N. Kuzibetsky consider innovative projects in terms of their level of novelty, which is assessed by the level of changes introduced into the system. It can be:

• 1) change of individual elements, partial clarifications, improvements, new details, development of new rules for the use of traditional pedagogical means;
• 2) changes at the level of groups of elements, combinations of known pedagogical means, their combinations, clarification of the sequence of their application;
• 3) changes at the level of the entire system of pedagogical tools, the addition of this system with new tools, the development of rules and technologies for their use, the emergence of new functionality of the system;
• 4) a radical transformation of the entire pedagogical system on a new paradigm basis.

Accordingly, according to the levels of novelty of the changes introduced, innovative programs and projects can be divided into rationalization, inventive, heuristic, and innovative ones.

An interesting typology of innovations is offered by V. M. Lizinsky. He believes that innovative activity involves a long "measuring" and serious reflection before introducing any innovations into an established traditional pedagogical process. V. M. Lizinsky distinguishes three types of innovations: random, useful and systemic.

Random- these are innovations contrived and introduced from the outside, not arising from the logic of the development of the educational system. Most often, they are introduced by order of higher management and are doomed to failure.

Useful- innovations that correspond to the mission of the educational institution, but unprepared, with indefinite goals and criteria that do not form a single whole with the school system.

System innovation- these are innovations derived from the problematic field with clearly defined goals and objectives. They are built on the basis of taking into account the interests of students and teachers and are in the nature of continuity with traditions. Such innovations are carefully prepared, expertized and provided with the necessary means (personnel, material, scientific and methodological).

We can also consider other proposed classification approaches: for example, innovations are divided into expected and random, timely and late, relevant and overturned into the future, easily implemented (mastered) and difficult to implement, etc.

In our opinion, all this diversity of approaches to the systematization of pedagogical innovations testifies to the multidimensionality and complexity of this phenomenon, which requires deep and comprehensive research. And, first of all, taking into account the essence of innovation as a social phenomenon generated by the global trend of social development at the stage of transition to a post-industrial society (see paragraph 1.2), the problem of distinction, the essential distinction pedagogical innovations and actually pedagogical innovations.

From this point of view, under pedagogical innovations we understand innovations in educational activities, which are due to the evolutionary change in social needs and, accordingly, educational goals, the continuous development of educational tools and technologies. Such innovations are inevitable in the process of permanent modernization of education, since they express its continuous development.

AT unlike this, pedagogical innovations- these are innovations that express paradigm changes in the development of education, due to significant socio-cultural transformations that change the very social function of education.

The current stage in the development of domestic education is just such a stage, characterized by cardinal paradigm searches, i.e., the search for a new paradigm of education that will replace the traditional “knowledge” paradigm that dominated at the previous stage of its development, in response to the needs of the formation of a new , post-industrial, informational, innovative society.

For practical innovation in education, attention should be paid to the conceptual content of such terms as "use", "adaptation" and "change" of innovation.

The term "use" implies the possibility of implementing an innovation for different purposes, i.e. practically it is about its versatility. An example is the use in the educational process of such an innovation as computer technology. The use of innovation is possible only if certain changes are made to the system. This requires a deep analysis of the situation in which the innovation will be implemented, and its correlation with the goals of the innovation. Thus, the use is called the process of implementing an innovation universal for various purposes, subject to the necessary changes being made to the corresponding system.

The problem of "adapting innovation" has its own specifics. It is related to the fact that, for example, in the activities of a school, it is often a question of adapting an innovation taken from one branch of activity to the conditions of another branch, in our case, educational. The mechanical transfer of innovation from one system to another often leads to the loss of its meaning, due to ignoring the specifics of the education system, its history and traditions. Particular attention should be paid to the possibilities of adapting what already existed in the past to take place in previous practice. The use of such innovations allows not only to qualitatively influence the development of education, but also to conduct a comparative analysis of the effectiveness of the innovation. As a result, the adaptation of an innovation can be defined as the process of transferring an innovation from one field of activity to another, taking into account the specifics of the particular system in which it is supposed to be used.

The problem of “changing innovations” is becoming relevant in modern conditions at a time when it is already clear that innovation is losing its significance for the educational process. Then there is a need to change it at the stage of stabilization (functioning) in order to provide a new stimulus that is fully consistent with the new situation. That is, we are talking about giving the innovation process the character of permanence, continuous reproduction, and renewal of innovations.

However, these problems are only separate aspects of a more general problem, which, as shown in the previous paragraph, is becoming a key one in the practice of educational activities today, namely, the problem management of innovative processes. Only controlled innovation processes will make it possible to avoid the spontaneous development of innovation activity, which is fraught with significant destructive potential, and really change the quality of education, directing its development in the direction of positive socially promising transformations.

Management (modern Russian management) / Ed. F. M. Rusinova, M. M. Razu. M.: BK-Press, 1998. P. 169. Yusufbekova NR Pedagogical innovation as a direction of methodological research // Pedagogical theory: Ideas and problems. M., 1992. S. 20-26. Khomeriki O. G., Potashnik M. M., Lorensov A. V. School development as an innovative process. S. 18.

Zair-Bek E.S. Analysis of approaches to the design of economic education in the schools of St. Petersburg // Economic education in school: materials for the inter-dunar. seminar. St. Petersburg: Education, 1995. S. 31-33.

Bakuradze A. Factors-motivators // Director of the school. 1997. No. 1. S. 8.

PRINCIPLES AND METHODS OF TEACHING MATHEMATICS

... I consider the best way in education to be the one that provides material for thinking and creative repetitions, provides material for creating ideas, and the ideas themselves arise directly in the soul of the child through the natural activity of his mental apparatus.

D.D. Galanin

I would like to emphasize the legitimacy and dignity of the position of a mathematician who understands the place and role of his science in the development ... of all human culture.

A.N. Kolmogorov

THEME PLAN

3. 1. Basic didactic principles in teaching mathematics
3. 2. Laws of pedagogical innovations
3. 3. Methods of teaching mathematics and their classification
3. 4. Problem based learning
3. 5. Programmed learning
3. 6. Mathematical modeling
3. 7. Axiomatic method
3. 8. Modern teaching methods using ICT

BASIC DIDACTIC PRINCIPLES IN TEACHING MATHEMATICS

Didactics(Greek word meaning - teaching) - a branch of pedagogy that develops the theory of education and learning. The subject of didactics are the laws and principles of education, its goals, the scientific foundations of the content of education, methods, forms and means of education.

Tasks of didactics consist in: describing and explaining the learning process and the conditions for its implementation; to develop a more perfect organization of the learning process, new learning systems and technologies. Didactics summarizes those provisions in the teaching of a particular academic discipline that are universal in nature.

Learning principles- these are guiding ideas, regulatory requirements for the organization and conduct of the didactic process. They are in the nature of general instructions, rules, norms governing the learning process. The principles of education are a system of the most important requirements, the observance of which ensures the effective and high-quality development of the educational process.

Didactic principles teaching mathematics is essentially a set of uniform requirements that must be met by teaching mathematics: the principle of scientific character; the principle of education; the principle of visibility; the principle of accessibility; the principle of consciousness and activity; the principle of the strength of the assimilation of knowledge; the principle of systematicity; sequence principle; the principle of taking into account age characteristics; the principle of individualization of education; the principle of nurturing education.

The basis mathematical education concepts Today the following principles are laid down:

Scientific in teaching mathematics;
- Consciousness, activity and independence in teaching mathematics;
- accessibility in teaching mathematics;
- visibility in teaching mathematics;
- universality and continuity of mathematical education at all levels of secondary school;
- continuity and prospects of the content of education, organizational forms and methods
learning;
- systematic and consistent;
- consistency of mathematical knowledge;
- differentiation and individualization of mathematical education, the creation of such conditions under which a free choice of the level of study of mathematics is possible;
- humanization of mathematical education;
- strengthening the educational function of teaching mathematics;
- practical orientation of teaching mathematics;
- application of alternative educational and methodological support;
- computerization of education, etc.

LAWS OF PEDAGOGICAL INNOVATIONS

1. The law of irreversible destabilization of the pedagogical innovation environment. L Any innovative process in the education system inevitably introduces irreversible changes in the innovative socio-pedagogical environment in which it is implemented. As a result of this, holistic ideas about any pedagogical processes or phenomena begin to collapse. Such an intrusion of pedagogical innovation into the socio-pedagogical environment leads to a polarization of opinions about it, about its significance and value. The more significant the pedagogical innovation, the more fundamental the destabilization that concerns the innovative environment of various types: theoretical, experimental, communicative and practical.

2. The law of the final implementation of the innovation process. Any innovative process sooner or later, spontaneously or consciously, is implemented and ends its existence as an innovation. Indicative in this respect in our time is the experience of V.A. Shatalova.

3. The law of stereotyping of pedagogical innovations. Any pedagogical innovation tends to turn into a stereotype of thinking and practical action. In this sense, it is doomed to routinization, it becomes a stereotype, a barrier to the implementation of other innovations.

4. The law of cyclic repetition of pedagogical innovation. A characteristic feature of the education system is the repeated revival of a phenomenon or innovation in new conditions. That is why in pedagogical theory and practice, innovations cause particular opposition, as they are perceived by some teachers as "long forgotten old". As an example, we can cite the notes of V.A. Shatalov, in which many do not see anything new due to the fact that abstracts have long been used in pedagogy, as well as the restoration of the communal methodology in a number of schools in a number of schools (for example, the school of V.A. Karakovsky).

These laws are not limited to general and specific patterns for pedagogical innovation, which have yet to be explored. But these laws are essential for understanding in general the dynamics of development and the contradictions of innovative processes in the education system.

There are two types of innovation in learning:

1. Innovation-modernization that improve the educational process, aimed at achieving guaranteed results within the framework of the traditional reproductive orientation of students (communication of knowledge, formation of methods of action according to the model). Assimilation of the presented samples.

2. Innovation-Transformation, transforming the traditional educational process, aimed at ensuring the research nature of education, at organizing search educational and cognitive activities (forming students' experience of independent search for new knowledge, the formation of experience in creative activity). Creation by students of a new product (intellectual, cognitive).

Innovative approaches to the educational process are divided into two types:

An approach	Essence	defining trait
Technological	It is a “technological”, conveyor process with clearly fixed expected results. Modernization of traditional education based on the prevailing reproductive students' activities. The educational process is focused on the traditional didactic tasks of reproductive education.	Installation on the guaranteed achievement of diagnostically set goals, orientation of training on criterion-fixed learning outcomes.
Search	Transforms traditional learning based on productive students' activities. The pedagogical process is the mastering of new experience initiated by students. The aim is to develop in students the possibility of acquiring new experiences on their own.	Generation of new knowledge, methods of action, personal meanings.

If practitioners are more often concerned with the specific results of updates, then scientists are interested in the knowledge system and the corresponding types of activities that study, explain, justify pedagogical innovation, its own principles, patterns, conceptual apparatus, means, limits of applicability and other scientific attributes characteristic of theoretical teachings. . All these are methodological aspects of studying and constructing pedagogical innovations.

In the process of studying innovative processes in education, scientists have discovered a number of problems of a theoretical and methodological nature: the relationship between traditions and innovations, the content and stages of the innovation cycle, the attitude to innovations of different subjects of education, innovation management, training, the basis for the criteria for evaluating the new in education, etc. These problems need to be understood at the methodological level. As a result, the substantiation of the methodological foundations of pedagogical innovation is no less relevant than the creation of pedagogical innovation itself.

N. R. Yusufbekova considers pedagogical innovation a direction of methodological research, since it is in this science that a system of knowledge about the creation, development and dissemination of pedagogical innovations can be represented. Pedagogical innovation allows you to reflect the necessary connection between the processes of creating pedagogical innovations and their application, including implementation in practice; substantiate and develop the principle of the unity of research activity and the activity of transforming pedagogical reality.

In the upcoming constructions, we will need to rely on the already existing methodological base. For this, it is quite appropriate to use the scientific apparatus related to the methodology of general pedagogy, which, we note, although it is quite formed, is also at the stage of development.

What is the methodology of pedagogy? In the works of philosophers, methodologists, educators, there are various understandings on this subject, including both problems specific to the pedagogical field and questions of the philosophical and general scientific levels (for example, a systematic approach).

The activity essence of innovations in education and the need to display them in the form of teaching put forward the requirement for understanding the methodology of pedagogical innovation as an organic unity of two components: teaching and activity. To fix this unity at the conceptual level, we will use the definition of the methodology of pedagogy, which was given by

M.A. Danilov: “The methodology of pedagogy is a system of knowledge about the foundations and structure of pedagogical theory, about the principles of approach and methods of obtaining knowledge that reflect ... pedagogical reality” 1 - and later developed by V. V. Kraevsky: “...a also a system of activities for obtaining such knowledge and substantiating programs, logic and methods, assessing the quality of special-scientific pedagogical research” 2 .

The above constructions allow us to formulate the following definition: methodology of pedagogical innovation there is a system of knowledge and activities related to the foundations and structure of the doctrine of the creation, development and application of pedagogical innovations.

So, we are interested in the system of knowledge and the corresponding types of activities that study, explain, justify pedagogical innovation, its own principles, patterns, conceptual apparatus, means, limits of applicability and other scientific attributes characteristic of theoretical teachings.

What does it consist of the task of pedagogical innovation methodology? Obviously, it is necessary to give a holistic theoretical presentation of pedagogical innovation, its composition, structure, and functions. To do this, it is necessary to identify the main trends, contradictions, principles, laws of development of innovative processes, to substantiate methodological approaches to their study within the framework of pedagogical innovation. Only the first steps are being taken in this direction.

NR Yusufbekova in her research reveals the following trends in the field of education and their corresponding contradictions 3 .

1. The trend towards continuity of education. It calls for structural and substantive renewal.

2. Increasing need for new pedagogical knowledge among teachers and other practitioners. The composition and structure of the pedagogical community is being updated.

3. Introduction trend. The use of the new is becoming widespread.

4. The trend towards the creation of educational school systems.

1 D Anilov M.A. The relationship between the general methodology of science and the special methodology of pedagogy // Problems of socialist pedagogy. - M., 1973.-S. 73.

2 Kraevsky V.V. Methodology of pedagogy: a guide for teachers - researchers. - Cheboksary, 2001. - S. 16.

3 See: Yusufbekova N.R. Problems and prospects for the development of the theory of innovation processes // Common educational space of the CIS countries and the Near Abroad. - M., 1994. - S. 31-44.

The development of educational systems of schools involves the passage of three main interrelated stages:

1) the emergence of a new pedagogical phenomenon - the educational system of the school and its theoretical understanding in the new pedagogical knowledge, which in the form of theories, concepts characterizes this pedagogical innovation in its specificity;

2) development of innovation by the pedagogical community;

3) application, implementation in the practice of schools. Each of the three stages is distinguished by its specific contradictions and features of their resolution.

For the first stage, the contradiction lies in the fact that the goal of education - the formation of a harmoniously developed personality - cannot be consistently realized in modern society with its system of education.

For the second stage, the contradiction between non-systemic scientific and pedagogical thinking and the systemic class of scientific and practical tasks that are posed and solved when developing the problem of the educational system of the school is essential.

For the third stage, the contradiction between the ready-made, existing “model”, “model” of the educational system and the need for its use and development in the conditions of a particular school is significant.

From the methodological standpoint, it is necessary to determine the patterns of development of innovative pedagogical systems and processes. Belarusian scientist I. Tsyrkun revealed the following regularities in the development of the innovation system 1 .

1. The system develops unevenly. The logic of culture, stochasticity over cumulativeness and rationality dominate in the development of the innovation system.

2. The determining bases for the development of an innovation system are innovations with substantive scientific justification. They dominated until the 1970s. 20th century

3. There is a certain sequence in development: first, the resources of subject scientific justification are consistently scooped out, and then a transition is made to deeper sources (didactics, psychology, cybernetics, a systematic approach, etc.).

4. Various didactic innovations have the property of equivalence with respect to expected effects.

5. The innovation system is dominated by modifying innovations and innovations that are focused on the value of the result.

1 See: Tsyrkun I.I. Innovative models of the development of pedagogical science // University education: experience of the millennium, problems, development prospects: materials of the Intern. congress. May 27 - 29, 2003 - Minsk, 2003. - S. 5-10.

6. In the process of development of the innovation system, the complexity of scientific justification increases and the frequency of the appearance of modernist innovations increases.

7. Radical innovations, as a rule, are associated with the aspiration of innovators to achieve the goals of development and self-development of the personality of students.

8. The development of the innovation system is carried out with evolutionary cycles. The development maxima correspond to the periods: 1951-1960, 1971-1975, 1981-1985.

9. In the innovation system, there are changes in the positions of the variables and permanent components of education.

Among these regularities, in our opinion, the seventh regularity is significant, which determines the vector of radical innovations, which is associated with the goals of development and self-development of the personality of students. Indeed, this pattern is semantic, i.e. refers to the essence of education as human development. The rest of the identified regularities relate to a greater extent to the characteristics of the innovation process and the conditions for their implementation.

The basis of any scientific theory is the revealed regularities and laws. In innovation as an interdisciplinary field, these patterns have been studied and formulated in the works of economists, managers, and production workers. In relation to educational innovations, this issue has not yet been studied enough and needs additional research. As one of the first generalizations, we present the data of N.R. Yusufbekova, who formulated the following laws of pedagogical innovation.

1. The law of irreversible destabilization of the pedagogical innovation environment. Holistic ideas about any pedagogical processes or phenomena begin to collapse, and subsequently it turns out to be impossible to restore these ideas. In this regard, there are costs associated with the personnel and spiritual capabilities of the pedagogical community.

2. The law of the final implementation of the innovation process. Any innovative process must sooner or later, spontaneously or consciously be realized.

3. The law of stereotyping of pedagogical innovations. Any pedagogical innovation implemented in the innovation process tends to turn into a stereotype of thinking and practical action.

4. The law of cyclic repetition, the return of pedagogical innovations.

The listed laws are to a certain extent characteristic of many innovative processes; in pedagogy, such laws will most likely be clarified. The task of pedagogical innovation

vatiki - to establish exactly those laws and patterns that relate to its subject of study. This requires the construction of a theoretical and methodological apparatus, one of the main components of which is the conceptual apparatus. The next paragraph will be devoted to this issue.

Questions for discussion and creative tasks

1. How do you propose to resolve the contradiction between the implementation essence of innovation and the student-centered approach to learning?

2. Formulate the goals of the same innovation from the standpoint of different subjects of education, its design and implementation: student, teacher, scientist, methodologist, school director, minister of education, director of a publishing house. How can pedagogical innovation ensure that all these goals are achieved in a comprehensive and coordinated manner?

3. Give examples of two educational innovations that you have been a part of. Do they have common patterns? If so, which ones? Justify that these are patterns, and not random repetitions.

4. What tasks of pedagogical innovation can you formulate in relation to the educational innovations taking place in your region?

Basic concepts of pedagogical innovation

New, novelty

Dictionary S.I. Ozhegov offers the following definition of the concept of "new": "first created or made, appeared or emerged recently, instead of the former, newly discovered." 1 Note that in this definition new does not mean better. This is important for understanding innovations in education, where not every new thing leads to a progressive improvement of the system. Some innovations can be or become a brake on the development of the educational system. Issues related to the results of introducing something new into education also belong to the field of pedagogical innovation.

Novelty is one of the main criteria for evaluating pedagogical research, the result of innovation. Novelty is always relative both in personal and objective-temporal terms.

1 Ozhegov SI. Dictionary of the Russian language. - M., 1986. - S. 358.

What is new at one time or for one subject may not be new for another time and subject.

Innovation

Innovation, innovation, innovation - the interpretations of these concepts by different authors turn out to be different.

Innovation in education - it can be a pedagogical tool, method, methodology, technology, program, etc. Innovation is often understood as purposeful progressive change, i.e. certain process. In other cases, innovation is the means itself, the introduction of which into the system leads to its change.

N.R. Yusufbekova understands innovation in pedagogy as “such a content of possible changes in pedagogical reality that leads (when the pedagogical community masters innovations and implements them) to a previously unknown, previously unseen state in this form in the history of education, a result that develops the theory and practice of teaching and upbringing" 1 .

M. M. Potashnik and O. G. Khomeriki write that innovation is “precisely a means (a new method, technique, technology, curriculum, etc.), and innovation is a process of mastering this tool” 2 .

V.S. Lazarev believes that in their meaning innovation and innovation are identical concepts. They consider innovation (innovation) as an implemented (mastered) innovation. “If an innovation is a potentially possible change, then an innovation (innovation) is an implemented change that has become real from a possible” 3 .

Distinguish between innovation and innovation. If under pedagogical innovation understand some idea, method, tool, technology or system, then innovation in this case will be the process of introducing and mastering this innovation. Innovation - something new, specially designed, researched, developed or accidentally discovered. It can be new pedagogical knowledge, technology, methodology, technique. Innovation - it is a product of development and implementation of innovation. By constructing

1 Yusufbekova N. R. General foundations of pedagogical innovation: Experience in developing the theory of innovative processes in education. - M., 1991. - S. 31.

2 Management of school development: a manual for heads of educational institutions / ed. M. M. Potashnik and V. S. Lazarev. - M., 1995. - S. 105.

3 Lazarev V.S. Pedagogical innovation: object, subject and basic concepts // Pedagogy. - 2004. - No. 4. - S. 15.

innovations, it is possible to manage the development of educational systems both at the school level and at the level of the region, country.

In relation to innovations, the innovation process is defined as a complex activity for the creation, development, use and dissemination of innovations.

An innovation can quickly become the property of many, the norm, generally accepted mass practice, or, conversely, become obsolete.

Innovation to innovation is different. The level of the new in education is determined depending on the degree of changes introduced into the educational process or the education system. Let us list the levels of innovation in education.

1. improvement- changing one or more elements of the educational process; adaptation of the known methodology to the new conditions of educational activity.

Example: in the current group learning system, the teacher uses new ways to create groups.

2. Rationalization- establishment of a new rule for the use of well-known pedagogical tools for solving traditional problems.

Example: the head teacher draws up a class schedule in the senior classes in such a way that students have the opportunity to more thoroughly immerse themselves in the subjects being studied while unloading homework (for example, in pairs). In this case, schoolchildren prepare more thoroughly every day for 2-3 subjects instead of 5-7.

3. Modernization- change of several elements of the current educational system.

Example: changing the structure of general secondary education - instead of 11 years of schooling, 12 years are proposed.

4. Heuristic solution- finding a way to solve known pedagogical problems; creation and use of previously unknown pedagogical forms, methods, means for solving actual pedagogical problems.

Example: Shatalov's method of supporting notes is a way of studying the same amount of traditional material in a shorter time.

5. Pedagogical invention- a new tool, technology or a new combination of known pedagogical tools for the implementation of education. A pedagogical invention can be a combination of known means or a completely new approach to teaching.

Example: M.P. Shchetinin's "immersion" system.

6. Pedagogical discovery- setting and solving a new pedagogical task, leading to a fundamental renewal of the educational system as a whole or a significant improvement in its constituent element.

Examples: the concept and technology of student-centered education; Waldorf School; TRIZ - pedagogy; didactic heuristics; competence approach; distance learning using network resources and technologies.

innovation, innovation

Historically, innovation has meant introducing elements of one culture into another. Now innovation is often called innovation - a purposeful change that introduces new stable elements into the implementation environment, causing the system to transition from one state to another.

The term "innovation" comes from the Latin innovatis (in- c, n ovus- new) and is treated as an innovation 1 . N.I. Lapin 2 notes that the etymology of the word "innovation" (innovation) indicates that it means "introduction", i.e. creation and use of any innovation. The author draws attention to the fact that innovation and innovation are not identical concepts. Innovation is a broader definition, it means the process of creating and using an innovation.

Innovation is the introduction of something new into an existing process; “innovation” (V. I. Slobodchikov) is the organic implantation of something new into the fabric of an existing process.

A. I. Prigozhyq 3 believes that innovation acts as a form of controlled development and is such a purposeful change that introduces new, relatively stable elements into the implementation environment. The latter may be purely material or social, but each of them in itself represents only an innovation, i.e. subject of innovation. Innovation is the essence of the process, i.e. the transition of a system from one state to another. Accordingly, the subject of innovation is the creation and distribution of various types of innovations.

According to A.A. Meshkov, innovation is “a complex socio-cultural process that develops according to certain objective laws, closely interconnected with the history and traditions of the social systems under consideration, and radically transforms their structure. It is also a socio-psychological phenomenon, characterized

1 Modern dictionary of foreign words. - M., 1993. - S. 238.

2 See: Lapin N.I. Actual problems of innovation research // Social factors of innovation in organizational systems. - M., 1980. - S. 6.

3 See: Prigozhy A.I. Innovations: Incentives and obstacles: (Social problems of innovation). - M., 1989. - S. 28.

characterized by a peculiar life cycle, with special phases, sequences and dependencies of cognitive and emotional processes occurring in individuals” 1 . That is why modern pedagogical innovation has a conceptual apparatus saturated with terms borrowed from different areas of human knowledge: philosophy, cultural studies, sociology, psychology, pedagogy, management theory, economics.

From the standpoint of the methodology of pedagogical innovation, we are interested in the proposal of A.A. Meshkov, in which he talks about two approaches to the study of innovation: organization-oriented and individually oriented. In the organization-oriented approach, the term "innovation" is used as a synonym for the concept of "invention" and refers to a creative process where two or more representations, ideas, objects are combined by the social subject involved in the process in some special way in order to form a previously non-existent configuration. This subject is called the agent of innovation. innovation is a complex of interrelated processes and is the result of the conceptualization of a new idea aimed at solving a problem and further- to the practical application of the new phenomenon. Novelty is measured not in relation to society, but in relation to the organization under study.

The individually-oriented approach describes the process by which a certain socio-cultural object (innovation) becomes part of a set of patterns of behavior of individuals and one of the components of their cognitive sphere. Innovation is considered as an inventive activity, when two previously unrelated systems intersect in a special way - an individual and an innovation.

In the general scientific sense, the concept of "innovation" is defined as a targeted change in the functioning of the system, and in a broad sense, these can be qualitative and (or) quantitative changes in various areas and elements of the system.

The concept of "innovation" applies to all innovations in both production and organizational, financial, research, educational and other areas, to any improvements that provide cost savings or even create conditions for such savings. The innovation process covers the cycle from the emergence of an idea to its practical implementation.

Innovation also has a general philosophical content. The nature of innovations is dialectical: they are born according to the law of negation,

1 See: Meshkov A.A. The main directions of innovation research in American sociology // Sotsis. - 1996. - No. 5. - S. 117.

growing quantitatively and qualitatively on the basis of resolving the objectively existing contradictions between the needs of society and life, society and the individual, society and school 1 . The creation of the new negates the old.

Innovation expresses the philosophical principle of unity and struggle of opposites. The term "innovation" contains a dualistic understanding: on the one hand, the creation of a new one, on the other, its implementation; creation of the new and its subsequent existence in reality.

Innovation

Innovation is usually understood as a science that studies the nature, patterns of emergence and development of innovations, their connection with the traditions of the past and future.

In the interpretation of A. I. Subetto 2, innovation as a science includes prognostics (the science of forecasting), creatology and intelligence (the science of the laws of the intellect and the objective laws of creativity), system genetics as a general theory of continuity in

development of systems (and by the principle of inversion - as a general theory of renewal and development of systems).

We have already noted that the development of innovation was largely due to entrepreneurial activity and the relevant areas of knowledge and activity - economics, management, enterprise management, etc. In entrepreneurship today, innovations are understood as the achievements of science and technology, embodied in new technologies, means of communication, industrial samples of new technology, new methods of technical and organizational management, etc., planned by enterprises and organizations, management bodies to be introduced into production and the social sphere. Innovations don't just break existing traditions, they bring in much more revenue than ordinary risky business ventures. Americans calculated that the rate of return on the 17 most successful innovations made in the 1970s averaged about 56%. At the same time, the average rate of return on investment in American business over the past 30 years is only 16%. Therefore, there is nothing surprising in the fact that, despite all the adventurism of various projects,

1 See: Belyaev V.I. Pedagogy A.S. Makarenko: traditions and innovation. - M.: 2000 - p.27

2 See: Subetto A.I. Ethics of pedagogical innovations // "Academy of Trinitarianism" - M.: El. No. 77 - 6567, publ. 10929., 12.01.2004 [Electronic resource], 2004 – Access mode: http://www.trinitas.ru/rus/000/a0000001.htm

innovators with good ideas and concrete achievements attract the attention of a large number of potential investors.

Innovative processes are actively studied in the field of economics and management. From the point of view of humanitarian innovation and management, A. Tupitsyn offers the following working definition: “Innovation is a new way of thinking and doing. Note that both words are important in this definition - both "think" and "do". The emergence of a new mode of activity presupposes that this action has already been done in human thinking. Every innovation begins with a new look, with the assumption of a new possibility.

Innovations include new products, knowledge-intensive technological processes, product modifications, new services. The practical development of innovations in innovations means the implementation of a commercial (entrepreneurial) idea to meet the demand in the market of goods for the environmental protection of the noosphere, strengthening the country's defense capability.

The demand for innovation testifies to the public recognition of the intellectual and industrial activities of a wide range of scientists, engineers, technicians and workers. The features of innovation are high uncertainty in achieving the desired results and the associated commercial risk in relation to investment in innovation. The novelty of consumer properties of technical processes as goods and services is one of the important features of innovations, which largely ensure the return on investment.

Innovation activity

This is the area of ​​development and practical development of technical, technological, organizational and economic innovations, it includes not only innovative processes, but also marketing research, as well as a new approach to organizing information, social, educational and other types of services. The alternativeness of the directions of innovation activity is manifested in the fact that it can be carried out not only locally at any of the stages of innovation processes, but also outside them.

Separate components of the integral system of any innovation activity are science and education. Without them, neither production technology nor the economy can successfully develop. The absence of these components will lead to a violation of the integral system of innovation. Similar

1 Humanitarian innovation // Message. - 2002. - No. 3.

insufficient attention to the development of one of the components of an integral system will reduce the effectiveness of its functioning. For example, ignoring the development of science will have a negative impact on the competitiveness of products, as its knowledge intensity will decrease. In turn, insufficient attention to the field of education will lead to an aggravation of personnel problems not only in scientific institutions and organizations that create new products, but also in the economy as a whole. Consequently, innovation activity directly or indirectly through technology, economy or everyday life affects human needs. Changing goals, ideals and interests contributes to the development and emergence of new values ​​that are adequate to the dominant way in social production. The values ​​of one stage in the development of human civilization lose their significance at another, more progressive one.

An element of innovation is innovative search- the process of developing, obtaining new knowledge and new practice.

In the modern theory of innovation, there are innovations-products, innovations-processes and product modification. Innovations-products are considered initial. They appear in the bowels of the previous order. The appearance of extraordinary innovations-products means the phase of the birth of a new way of life. Innovation-processes can have independent significance in innovation activity. For example, the processes associated with the use of health and resource-saving pedagogical technologies, computerization and "internetization" of education, improving the quality of education using progressive forms and methods of education, etc. This kind of innovation processes improve the quality of the educational process and the competitiveness of graduates. Therefore, innovative educational activities related to providing leadership in educational preparation is an additional factor in the development of both individual innovative schools and education in general.

Process innovations are much less subject to change than, for example, product innovations are. Modernization or modification prolongs the life cycle of the established type of education as a possible innovation that was in the past. For example, some changes are made to the structure and content of education, standards, control system in order to better meet the requirements of the time.

Thus, an indispensable and indispensable condition in innovative activity is the dissemination and replication (diffusion) of new products and especially advanced technologies.

methods of organizing production, innovative management. And for this it is necessary to create an innovative environment, the main element of which, its personification is a person - be it a school graduate or a highly educated specialist.

innovative idea

In innovation, an innovative idea is an application for an emerging idea of ​​something new that requires attracting the attention of possible participants in the innovation process (researchers, scientists, educators, administrators, investors, developers, manufacturers, merchants, marketers, administrators, consumers) to organize work on all or individual stages and stages of the innovation cycle. In the process of achieving an innovative goal, many different solutions are required, but the fundamental meaningful role is given to the development of scientific and technical or scientific and pedagogical ideas. On their basis, decisions are developed and made that show the plans for the implementation of ideas. This is the result of the pre-project study stage or the so-called "conceptual design". The consumer - the executor of the next stage of the innovation cycle - receives the idea and concept in the form of a report on research work with terms of reference and a proposal for using the results. In the case of commercial implementation, the results in the form of a proposal and a corresponding business plan enter the market for scientific and technical solutions. In education, these processes are not so pronounced because of its fairly massive and long-term "free". At the same time, if we consider education as a service, innovative ideas can be as important in this area as in other areas.

An innovative idea is based, as a rule, on a general theoretical understanding of an object, process, phenomenon, formed on the basis of an intuitive guess and empirical data. A technical solution is a feasible idea for creating a product or an algorithm for implementing a process, based on an idea and expressed by the necessary means. An innovative idea in pedagogy can be implemented through several different solutions with a combination of various technological features.

Innovation program

The combination of several related projects as a control object differs from a single project. In innovation

In this program, projects are interconnected functionally, as well as in terms of time, performers and resources. The subject of management acts as a network of projects. Programs require a unified leadership, centralized for the functions of strategic planning, financing, monitoring, coordination, and legal support.

Examples of an innovative program can be: a technological breakthrough in a given direction, for example, in the computerization of education, increasing the prestige or competitiveness of the national education system, technical re-equipment of schools, improving the environmental situation, etc.

Only a large association of organizations, a region or metropolis, federal agencies, interstate alliances can form and implement an innovative program. The very formation of an innovation program requires the unification of various organizations, financial institutions, the administration of regions and the state, and in many cases interstate agreements. To develop and implement innovative programs in the field of education, it is necessary to involve specialists from various fields - teachers, scientists, economists, investors, managers, politicians, members of the public, etc. The lack of an integrated approach to the development of innovative programs in the field of education is a typical mistake that leads to negative results. their implementation.

Innovation Doctrine

In relation to education, the innovation doctrine is understood as a system of basic provisions developed by the leadership of the state or its region and determining the policy in this direction. The innovation doctrine should define:

the object in which the update takes place (educational areas, subjects; regions in which innovations are planned, etc.); 2) the subject of influence, i.e. what is being updated (goals, standards, structure and content of education, pedagogical technology, diagnostic and control system, educational resources, management system, organizational structure, etc.) and on the basis of what (on the basis of what goals, principles, concepts); 3) the result in the form of a concept of educational policy and a mechanism for its implementation. The procedure for developing an innovation doctrine is subject to the provisions adopted in innovation. For example, at the state level

The gifts are collected proposals from society, specialists, scientists; After analyzing the proposals, a project is developed, which is tested in the community.