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The theory of L.S. Vygotsky about the leading role of education in the development of the child, as well as the provisions on the leading role of activity in human development and the theory of phased formation mental actions which were developed and studied by such psychologists and educators as P.Ya. Galperin, A.N. Leontiev, N.F. Talyzina.
To modern concepts mathematical development children of early and preschool age include the following: early mathematical development, early introduction of children into the world of the logic of mathematics, mastering the methods of cognition, creating prerequisites for school age to form theoretical thinking in primary school schools that develop the focus of the proposed gaming activities, a combination of practical and gaming activities.

Preschool education is the first and most responsible link in the general education system. At preschool age, the foundation of ideas and concepts is laid, which ensures the successful mental development of the child. In a number psychological research found that the rate of mental development of preschool children is very high compared with later age periods(L.A. Wenger, A.V. Zaporozhets, V.S. Mukhina). Any defects in upbringing made during preschool childhood are in fact difficult to overcome at an older age and have a negative impact on the entire subsequent development of the child.

When developing issues of mental education of preschoolers, Russian scientists proceed from the main provisions domestic psychology which considers the process of human mental development as a result of the appropriation of social experience embodied in the products of physical and spiritual labor. At the same time, the mental development of the child acts as the assimilation of the simplest forms of this experience: the mastery of objective actions, elementary knowledge and skills as the most universal means of consolidating and transmitting general human experience.

Thus, the mental, including the mental development of the child acts as a concrete historical and social process, all the main stages of which are due to the peculiarities of the transfer of social experience. This position of domestic psychology sets the direction for the study of the problem of interaction between biological and social factors during the development of the individual.

As is known from the works of L.S. Vygotsky, in the spontaneous experience of preschoolers, pre-conceptual formations first arise - complexes, pseudo-concepts, and only then full-fledged concepts are formed in the process of schooling. In the works of P.Ya. Galperin, N.F. Talyzina provides data indicating that under the conditions of organized learning, the process of concept formation itself has significantly different patterns than in spontaneous learning. Used in the work of P.Ya. Galperin's method of gradual formation of mental actions allows the formation of full-fledged concepts in the senior preschool age, and their volume is limited only by the presence of the necessary preliminary knowledge and skills.

The most significant changes in mental development child are the result of the assimilation of not any individual knowledge and skills, but, firstly, a certain system of knowledge that reflects the essential connections and dependencies of a particular area of ​​reality, and, secondly, general forms mental activity underlying this system of knowledge. In this regard, there is an acute problem of developing the basic principles for the selection and systematization of preschool knowledge.

The system of preschool knowledge, of course, should be fundamentally different from the system of school knowledge, be more elementary. So, P.G. Samorukova notes that the systematization of knowledge is possible at different degrees of their depth and generalization: and empirical level, when the main content of knowledge is presented in the form of representations (images of previously perceived objects and phenomena), and at a higher theoretical level when knowledge has the form of concepts, and connections are characterized as deep regularities. She further points to great opportunities expansion and deepening of the system in the process of teaching children.

pedagogical sciences: 13.00.02 / Voronina Lyudmila Valentinovna; [Protection Location: Lv. state ped. un-t].- Yekaterinburg, 2011.- 437 p.: ill. RSL OD, 71 12-13/88">

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Voronina, Lyudmila Valentinovna Mathematical education in the period of preschool childhood: design methodology: dissertation... Doctor of Pedagogical Sciences: 13.00.02 / Voronina Lyudmila Valentinovna; [Protection Location: Lv. state ped. un-t].- Yekaterinburg, 2011.- 437 p.: ill. RSL OD, 71 12-13/88

Introduction

Chapter I Theoretical Foundations of Mathematical Education in Preschool Childhood 26

1.1. Genesis of ideas for the formation of mathematical representations in preschool children 26

1.2. Trends in the development of mathematical education in the period of preschool childhood in the context of informatization and technologization of society 57

1.3. Mathematical education in the period of preschool childhood in the aspect of universal culture 103

Conclusions on the first chapter 125

Chapter II. Methodological foundations of pedagogical design 130

2.1. Historical and philosophical aspects design problems... 130

2.2. The concept and essence of pedagogical design 147

2.3. Methodological approaches to the problem of pedagogical design 162

Conclusions on the second chapter 179

Chapter III. Mathematical education during preschool childhood: the concept and methodology of design 181

3.1. The concept of culture-forming mathematical education of preschool children 181

3.2. Methodology for designing culture-forming mathematical education in the period of preschool childhood 203

3.3. The project of mathematical education in the period of preschool childhood.. 224

Conclusions on the third chapter 286

Chapter IV. The system of organizational and methodological support for the implementation of the project of mathematical education in the period of preschool childhood. 290

4.1. Development of organizational and methodological support for the implementation of the project of mathematical education for preschool children 290

4.2. Organization and results of experimental work 319

4.3. Teacher training preschool education ways of designing mathematical education during childhood 345

Conclusions on the fourth chapter 361

Conclusion 364

Bibliographic list 370

Applications 421

Introduction to work

The relevance of research. Modernization Russian system education is one of the main directions and conditions for the development Russian society and formation of the innovative economy of Russia. This process gives modern education systems such innovative features as dynamism, variability, diversity. organizational forms and content. According to the national education initiative "Our New School", main task modern system education is the disclosure of the abilities of each child, the upbringing of a personality ready for life in a high-tech information society, the main features of which are high level rationalization and algorithmization of activities, the ability to use information technology, lifelong learning. Preschool education is the initial link in lifelong education and is aimed at providing conditions for the self-realization of the child and his socialization. Mathematical education in this process is given special role, since mathematics is one of the areas of knowledge that is very significant for modern society, accumulated and widely used by mankind. Mathematical education is a means of intellectual development of the child, expanding the possibilities of its successful adaptation to the processes of informatization of society.

The relevance of research on the socio-pedagogical level caused by the reform of education based on the interaction of the rational-cognitive and culture-forming components of the new educational paradigm, which is characterized by a shift in emphasis from social order and the requirements of science for the self-realization of the individual. The process of human education can now be defined by the formula: from a knowledgeable person to a “man of culture” (V.S. Bibler). In this regard, education from a method of transferring experience to a growing person turns into a mechanism for the development of his internal culture and natural gifts. This determines the need to correlate the results of the learning process with the phenomenon of "culture".

The renewal of education should begin with the system of preschool education, since, according to many psychologists (L.I. Bozhovich, A.L. Venger, L.S. Vygotsky, A.V. Zaporozhets, A.N. Leontiev, D.B. Elkonin and others), preschool age is the age at which the child not only intensively develops all mental functions, but the laying of a common foundation cognitive abilities, intellectual potential personality, its culture.

Through mathematical education, already at preschool age, the prerequisites for successful social adaptation of the individual to the accelerating processes of informatization and technologization of society, the foundations for the necessary modern man mathematical culture: mathematical education contributes to the development of critical thinking, logical rigor and algorithmic thinking, which largely determine the success and effectiveness of a child's activity in understanding the world outside and inside himself.

Relevance of the research on scientific and methodological level due to the vector of development of the methodology of modern pedagogy, aimed at strengthening the cultural conformity of the pedagogical process. This determines the need to develop and test a system of scientifically based principles and methods of pedagogical design of mathematical education in the period of preschool childhood, which would ensure the interaction of culture-forming and rational-cognitive components. modern education. An analysis of well-known dissertations devoted to solving topical problems of teaching mathematics to children aged 3-11 showed that despite the innovative potential of the original approaches and concepts of the formation of elementary mathematical representations in young children (V.A. Kozlova) justified in these works, mathematical development preschooler and primary school student (A.V. Beloshistaya, A.I. Golikov), didactic system continuous general education, focused on the values ​​of personal self-development (L.G. Peterson), they did not reflect the problem of developing a methodology for designing mathematical education in the period of preschool childhood, which would correspond to the above indicated trends.

On the scientific and theoretical level the relevance of the study is as follows. The problem of designing mathematical education in the period of preschool childhood requires substantiation of the essential characteristics and patterns of mathematical education of preschoolers, which should be reflected in the formation of the foundations of the child's mathematical culture. Although at present there are various theoretical models of teaching mathematics during childhood (E.I. Aleksandrova, V.F. Efimov, N.B. Istomina, etc.), these theories have not received a holistic scientific understanding of issues related to the substantiation of the structure and functions of mathematical education in the period of preschool childhood in the paradigm of education as a mechanism for developing the foundations of a child's mathematical culture. Conceptual understanding of these theoretical aspects will increase the adequacy and adaptability of mathematical education in the period of preschool childhood to the processes of informatization and technologization taking place in society.

On the scientific and methodological level the urgency of the problem is connected with the need to develop scientific and methodological support for the process of forming the foundations of mathematical culture in children, including mathematical concepts important for life at a given age and the ability to apply them in solving practical problems that are significant for the child, which involves the development of appropriate methods, forms and teaching aids preschool math.

In this regard, there is a need to design mathematical education in such a way that it allows creating conditions for the formation of the foundations of a mathematical culture in children, taking into account the changes taking place in society for the full implementation by students of their individual inclinations and needs. The success of designing such an education is directly related to the decision Problems search for the specific design principles, rules and regulations necessary for this pedagogical conditions their implementation. The solution of this problem involves understanding the essential characteristics of the mathematical education of preschool children and its patterns.

An analysis of the philosophical and psychological-pedagogical literature made it possible to establish degree of development highlighted problem.

Aspects relationship between culture and education in terms of revealing the essential powers of a person, changing the view of the world, changing the person himself and the world he perceives are reflected in a culturally appropriate approach to education and its design (E.V. Bondarevskaya, E.D. Visangiriyeva, B.S. Gershunsky, M. S. Kagan and others). Essence mathematical culture, its functions, development trends, the conditions for its formation and the role of mathematical education in the process of its individual appropriation are disclosed in the works of G.M. Buldyk, B.V. Gnedenko, D.I. Ikramova, L.D. Kudryavtseva, S.A. Rozanova, A.Ya. Khinchin, V.N. Khudyakova and others.

In general methodological terms, the development of mathematical education was significantly influenced by the results of research into the processes of goal-setting and the development of the content of education, obtained by both foreign (B. Bloom, D. Kratvol, R. Meijer, A. Romishovsky, etc.) and domestic scientists (Yu. K. Babansky, V. P. Bespalko, E. V. Bondarevskaya, B. S. Gershunsky, E. N. Gusinsky, V. V. Davydov, I. I. Ilyasov, M. V. Klarin, V. V. Kraevsky, V.S. Lednev, I.Ya. Lerner, M.N. Skatkin, A.V. Khutorskoy, etc.). Various aspects system development goals and content of mathematics education considered in the works of E.I. Alexandrova, A.V. Beloshistaya, N.Ya. Vilenkina, M.B. Volovich, H.Zh. Ganeeva, A.I. Golikova, V.A. Guseva, V.A. Dalinger, G.V. Dorofeeva, V.F. Efimova, N.B. Istomina, Yu.M. Kalyagin, V.A. Kozlova, G.G. Levitas, I.G. Lipatnikova, A.G. Mordkovich, V.M. Monakhova, L.G. Peterson, L.M. Friedman and others.

Mathematics education for preschoolers cannot be considered in isolation from the study of the main trends in the development of education during childhood. Therefore, the works of Ya.A. Comenius, I.G. Pestalozzi, K.D. Ushinsky, V.I. Vodovozov, F. Frebel, M. Montessori, D.L. Volkovsky and others. An invaluable contribution to the theory and methodology mathematical preparation of preschoolers introduced by E.I. Tiheeva, L.V. Glagoleva, F.N. Bleher, A.M. Leushina, L.S. Metlin, A.A. Stolyar, Z.A. Mikhailova, T.V. Taruntaeva, T.I. Erofeeva, E.I. Shcherbakova, L.G. Peterson, A.V. Beloshistaya and many other teachers.

Theoretical prerequisites for the design of mathematical education in the period of preschool childhood were the results of research in the field of design methodology (M. Azimov, I.V. Bestuzhev-Lada, V. Gasparsky, V.I. Ginetsinsky, P. Hill, etc.) and pedagogical design methodology (N.A. Alekseev, V.S. Bezrukova, B.S. Gershunsky, G.L. Ilyin, V.M. Monakhov, etc.). Design methodological systems considered in the works of O.B. Episheva, V.E. Radionova, T.K. Smykovskaya et al. Design problem pedagogical technologies covered in the works of V.P. Bespalko, Z.F. Mazura, Yu.K. Chernov and others.

However, despite the undoubted theoretical and practical significance of the presented studies, the problem of designing mathematical education in the period of preschool childhood today has not found sufficient scientific justification precisely in the aspect of compliance with modern trends in strengthening the interaction of culture-forming and rational-cognitive components of education. In pedagogical theory, the conceptual understanding of the structure and functions of mathematical education of preschoolers is considered in the context of the development of mathematical abilities of children (A.V. Beloshistaya), however, there are no studies devoted to the conceptual understanding of the structure and functions of mathematical education of preschoolers in the paradigm of education as a mechanism for developing the foundations of a child’s mathematical culture, which does not allow increasing the adequacy and adaptability of mathematical education in the period of preschool childhood to the processes of informatization and technologization taking place in society.

The analysis of the state of the problem of designing mathematical education in the period of preschool childhood made it possible to identify the following contradictions:

– at the socio-pedagogical level: between the need of society to ensure the social adaptation of the younger generation to the processes of informatization and technologization of society through the formation of the necessary mathematical culture of a growing person, the culture of logical, analytical and algorithmic thinking and insufficient realization of the possibilities of forming such a culture in the education system of the period of preschool childhood;

– at the scientific and methodological level: between the need to design education for the period of preschool childhood in accordance with modern paradigm interaction between the culture-forming and rational-cognitive trend of its development and insufficient methodological justification for the process of designing mathematical education in this aspect;

– at the scientific and theoretical level: between the need to modernize mathematical education in the period of preschool childhood in terms of increasing its role in the adaptation of the younger generation to the processes of informatization and technologization of society and the incompleteness of the theoretical understanding of the structure and functions of mathematical education for preschoolers in the paradigm of education as a mechanism for developing the foundations of a child's mathematical culture;

– at the scientific and methodological level: between the need to organize the educational process of forming the foundations of the mathematical culture of preschool children, contributing to their adaptation to life in a modern technologized society, and the lack of development of scientific and methodological support for this process.

These contradictions made it possible to clarify the boundaries research problems, which consists in a conceptual understanding of the structure and functions of mathematical education of preschoolers in the paradigm of education as a mechanism for developing the foundations of a child’s mathematical culture and in the corresponding development of a methodology for designing mathematical education in the period of preschool childhood that meets modern requirement strengthening the interaction of culture-forming and rational-cognitive components of education.

The identified contradictions and the formulated research problem made it possible to determine topic research"Mathematical Education in Preschool Childhood: Design Methodology".

Purpose of the study consists in the scientific substantiation and development of a methodology for designing mathematical education in the period of preschool childhood in the context of the interaction of culture-forming and rational-cognitive trends in the development of education.

An object research- the process of preschool education.

Subject research– methodology for designing culture-forming mathematical education in the period of preschool childhood.

Research hypothesis. The process of modernization of mathematical education in the period of preschool childhood will meet modern trends in increasing the adequacy of mathematical education to the changes taking place in society if:

1. The methodology for designing mathematics education during childhood will be built

– in accordance with the concept of culture-forming mathematical education developed in the course of the study, which meets the modern requirement of strengthening the interaction between the rational-cognitive and culture-forming components of education;

- in accordance with system of design principles: harmonization of the components of mathematical education in the period of preschool childhood, taking into account the stages of development of children's thinking, the relationship between play and cognitive activity, taking into account the adequacy and adaptability of mathematical education to changes taking place in society, the correspondence of the design algorithm to the algorithms for functioning and managing the process of teaching and educating preschool children that meet specific patterns: dependence of design on the harmony of reflection of all components of mathematical education, determination of the quality of design by the accuracy of taking into account certain factors, dependence of design on taking into account the adaptive function of mathematical education, on the level of algorithmization of the design process itself.

2. The leading ideas of the concept of culture-forming mathematical education in the period of preschool childhood will be the following:

mathematical education has an undisclosed potential for the implementation of its adaptive function to the processes of informatization and technologization developing in society and therefore is a necessary component of the process of forming a culture of a growing person;

the core of the concept consists of a system sense-forming categories and concepts, such as "mathematical education in the period of preschool childhood", "mathematical culture of a child of preschool age", "formation of mathematical culture in the period of preschool childhood", "design of mathematical education in the period of preschool childhood";

it is advisable to organize the mathematical education of children as a system that ensures the integration of the mathematical activity of the child into his independent activity based on the inclusion in the goals, content and forms of mathematical education of an adaptive component related to the need for social adaptation of the child to the processes of technologization and informatization of society;

the development of mathematical education in the period of preschool childhood is determined by the following patterns: the dependence of the quality of mathematical education on the degree of practical significance of the knowledge acquired by the child; the dependence of the effectiveness of mathematical education on the structuring of content, the selection of methods, forms and means of education and training in accordance with the age capabilities of children; the dependence of the quality of mathematical education on the provision of subjective cognitive activity of all participants in the educational process (teachers, children, parents); the dependence of the success of the formation of the foundations of mathematical culture on the completeness of the representation of the necessary structural components of mathematical culture in the content of the cognitive-playing activity of a preschool child and the corresponding methods of its organization;

a necessary condition for the functioning of the mathematical education system is a systematic increase in the professional competence of preschool teachers through the organization of their special theoretical and methodological training in order to create conditions for the implementation of mathematical education, corresponding to modern trends in strengthening the interaction of culture-forming and rational-cognitive components of education.

The problem, goal, object and subject of research determined the solution of a number of research objectives:

1. Analyze historical aspects theories and methods of teaching mathematics during childhood in the context of universal culture in order to determine the main characteristics state of the art mathematical education during childhood and clarification of the structural components of the mathematical culture of a preschool child.

2. Determine methodological foundations pedagogical design: to conduct a historical and philosophical analysis of the problem of design, to clarify the essence, structure, content and methodological approaches to pedagogical design.

3. Develop the concept of culture-forming mathematical education in the period of preschool childhood, substantiate the methodology for designing mathematical education in the period of preschool childhood and design mathematical education in the period of preschool childhood, aimed at adapting children to the processes of informatization and technologization taking place in society.

4. Develop organizational and methodological support for the implementation of the project of mathematical education in the period of preschool childhood and conduct its approbation.

Methodological basis of the study. General methodology research is based on the fundamental ideas of philosophical anthropology about a person and his upbringing, about the nature and essence of human activity, its expedient and creative character; on the basic principles of dialectics - objectivity, development and interaction; on the main positions of systemology (P.K. Anokhin, V.G. Afanasiev, L. Von Bertalanffy, I.V. Blauberg, A.A. Bogdanov, V.P. Kuzmin, V.G. Sadovsky, A.I. Subetto, W.R. Ashby, E.G. Yudin) and their development in relation to pedagogical systems (Yu.K. Babansky, V.P. Bespalko, Yu.A. Konarzhevsky, V.S. Lednev, V.M. Monakhov , G. N. Serikov, E. G. Yudin and others); on the basics of structural modeling (M. Vartofsky, J. Van Gig, A.I. Uemov, V.A. Shtof, G.P. Shchedrovitsky, W.R. Ashby, etc.).

The methodological guidelines of the study were: systemic an approach(A.N. Averyanov, V.G. Afanasiev, I.V. Blauberg, A.I. Uemov, E.G. Yudin and others), according to which mathematical education in the period of preschool childhood is considered as a pedagogical system; synergistic an approach(A.I. Bochkarev, Yu.S. Brodsky, V.G. Vinenko, Yu.S. Manuilov, N.M. Talanchuk and others), which focuses on intersystem interaction, which ensures the construction of the pedagogical process, taking into account patterns of development of complex self-organizing systems and allows us to consider each subject of the pedagogical process as self-developing subsystems that make the transition from development to self-development; cultural approach(E.V. Bondarevskaya, E.N. Ilyin, E.N. Shiyanov, etc.), which implies reliance on the principle of cultural conformity of education, which contributes to the preservation and development of a common basic culture as a whole, creates favorable opportunities in the process of education and teaching mathematics to form the foundations of mathematical culture in children; axiological approach(B.S. Bratuev, D.A. Leontiev, R.Kh. Shakurov, etc.), which allows you to choose from the sphere of humanitarian culture the content with which the child will form a system of mathematical knowledge, skills, as well as a set of values, common ground which are the globally recognized values ​​of mathematics education; person-centered approach(E.V. Bondarevskaya, O.S. Gazman, V.V. Serikov, D.I. Feldshtein, I.S. Yakimanskaya and others), which reflects the main landmark of the humanistic paradigm: a central place in the mathematical educational process belongs to the child activity approach(I.A. Zimnyaya, A.V. Petrovsky, S.L. Rubinshtein, V.I. Slobodchikov and others), which transforms the understanding of the quality of education, which should not be determined by the measure of the child’s mastering the mathematical knowledge, skills and skills, but by the extent to which the results of his personal development correspond to the development opportunities contained in the culture, to what extent the child has formed the appropriate types of activities.

Theoretical basis of the study is determined by a set of historically entrenched ideas in the field of mathematical education and pedagogical design. These include: concepts of philosophy and methodology of education(K.A. Abulkhanova-Slavskaya, V.V. Kraevsky, A.M. Novikov, V.N. Sagatovsky, M.N. Skatkin, P.G. Shchedrovitsky and others), axiology theory, suggesting the need to search for value orientations in pedagogical process(S.F. Anisimov, O.S. Gazman, B.S. Gershunsky, B.T. Likhachev, A.F. Losev, N.D. Nikandrov, D.I. Feldshtein, N.E. Shchurkova, V .A. Yadov and others), the concept of humanization and humanitarization of education(E.D. Dneprov, V.P. Zinchenko, B.M. Nemensky, A.V. Petrovsky, V.V. Serikov, G.I. Sarantsev, etc.), the concept of the leading role of activity in the development and formation of personality (L.S. Vygotsky, V.V. Davydov, A.N. Leontiev, S.L. Rubinshtein, N.F. Talyzina, D.B. Elkonin, etc.), idea continuity of education(Sh.I. Ganelin, B.S. Gershunsky, S.M. Godnik, V.T. Kudryavtsev and others), theory of educational content(B.S. Gershunsky, V.V. Kraevsky, V.S. Lednev, I.Ya. Lerner and others), methodology and methods of teaching mathematics(E.I. Aleksandrova, A.V. Beloshistaya, Kh.Zh. Ganeev, V.A. Gusev, V.A. Dalinger, G.V. Dorofeev, V.F. Efimov, N.B. Istomina, V. A. Kozlova, Y. M. Kolyagin, V. A. Krutetsky, A. M. Leushina, I. G. Lipatnikova, L. G. Peterson, etc.), amplification theory child development and the idea of ​​the special significance of “specifically childish” activities in the development of a preschooler (A.V. Zaporozhets), the idea of ​​self-worth of preschool childhood as a period of formation of the foundations for the further development of the child (L.S. Vygotsky, A.V. Zaporozhets, L.V. Kolomiychenko, V.T. Kudryavtsev, G.P. Novikova, L.V. Trubaychuk, D.I. Feldshtein and etc.), ideas of integration in preschool education(L.M. Dolgopolova, T.S. Komarova, G.P. Novikova, T.F. Sergeeva, etc.), formation of a holistic picture of the world in preschoolers (I.E. Kulikovskaya, R.M. Chumicheva, etc.), pedagogical design theory(V.S. Bezrukova, V.P. Bespalko, B.S. Gershunsky, M.P. Gorchakova-Sibirskaya, E.S. Zair-Bek, I.A. Kolesnikova, V.V. Kraevsky, V.E. (Radionov, V.M. Rozin, I.M. Slobodchikov, N.O. Yakovleva, etc.).

Conceptually, it is important methodology of pedagogy and methods of psychological and pedagogical research(E.V. Berezhnova, B.S. Gershunsky, V.V. Davydov, V.I. Zagvyazinsky, M.S. Kagan, V.V. Kraevsky, N.D. Nikandrov, A.M. Novikov, M .N. Skatkin and others).

Research methods determined by its purpose, the need to resolve methodological, theoretical and practical problems. This led to the choice of a set of theoretical and empirical methods. Theoretical Methods: logical-historical analysis was used to identify progressive trends in the history of Russian mathematical education; theoretical and methodological analysis made it possible to formulate the main positions of the study; conceptual and terminological analysis was used to characterize and streamline conceptual apparatus research; modeling and design were used to build the design process and present its results; forecasting was used to substantiate the prospects for the development of mathematical education during preschool childhood; analysis, synthesis and generalization were used in the process of substantiating and presenting the results of the study. empirical methods: study of normative documents in the field of education, research and generalization of effective experience and mass practice mathematical training of preschoolers, observation (external, included, standardized and other types), questioning and testing - were used at the search-orientation stage of experimental work in order to identify the problem and research topic; at the theoretical-technological and experimental-search stages, questioning, testing and method expert assessments allowed to confirm the results of the study; at the final and generalizing stage, qualitative diagnostic methods with elements of qualimetric analysis and a statistical method for processing the results were used.

Research base. The study was conducted on the basis of the Institute of Pedagogy and Childhood Psychology of the Ural State Pedagogical University and 18 preschool educational institutions Yekaterinburg and Sverdlovsk region.

The study consisted of several interrelated stages.

On the first stage(1995-1999) - search and orientation - the study and analysis of the current state of the research problem was carried out; the study and systematization of literature on research methodology, pedagogy, psychology, pedagogical design was carried out; the key positions of the study, its conceptual and categorical apparatus were determined.

Second phase(2000-2003) - theoretical and technological - was devoted to the theoretical and methodological development of the concept of mathematical education for preschoolers based on systemic, synergistic, axiological, cultural, personality-oriented and activity approaches.

On the third stage(2004-2007) - experimental and exploratory - work was carried out with the aim of practical test the provisions of the research hypothesis, the main ideas of the methodology for designing mathematical education in the period of preschool childhood were clarified, monographs were written and teaching aids to prepare students and specialists for the implementation of the main ideas of the developed concept of mathematical education in the period of preschool childhood.

Fourth stage(2008-2010) - final and generalizing - included the final processing of the results obtained, the introduction of the developed project of mathematical education of preschool children into practice work of preschool educational institution completed the dissertation research.

Scientific novelty research is as follows:

1. A set of methodological approaches is substantiated, on the basis of which the methodology for designing mathematical education in the period of preschool childhood is built: the systemic and synergetic approaches are the general scientific basis; theoretical and methodological strategy is determined by cultural and axiological approaches; practice-oriented tactics are personality-oriented and activity approaches.

2. Specific patterns identified

design process mathematical education of the period of preschool childhood: the dependence of design on the harmony of the reflection of all components of mathematical education, the conditionality of the quality of design by the accuracy of taking into account certain factors, the dependence of design on taking into account the adaptive function of mathematical education, the dependence of the design result on the algorithmization of the design process itself;

mathematics education the period of preschool childhood: the dependence of the quality of mathematical education on the degree of practical significance of the knowledge acquired by the child; the dependence of the effectiveness of mathematical education on the structuring of content, the selection of methods, forms and means in accordance with the age capabilities of children; the dependence of the quality of mathematical education on the provision of subjective cognitive activity of all participants in the educational process (teachers, children, parents); the dependence of the success of the formation of the foundations of mathematical culture on the completeness of the representation of the necessary structural components of mathematical culture in the content of the cognitive-playing activity of a preschool child and the corresponding methods of its organization.

3. The principles on the basis of which the mathematical education of the period of preschool childhood is designed are formulated: harmonization of the components of mathematical education of the period of preschool childhood, taking into account the stages of development of children's thinking, the relationship between play and cognitive activity, taking into account the adequacy and adaptability of mathematical education to changes taking place in society, the conformity of the algorithm designing mathematical education for preschoolers algorithms of the educational process.

4. The concept of culture-forming mathematical education of the period of preschool childhood has been created, which is based on the idea of ​​interaction between the culture-forming and rational-cognitive components of the new educational paradigm, includes the patterns of mathematical education that correspond to the structural components of the formed mathematical culture of the child, the core of this concept is sense-forming categories and concepts.

5. The structure of mathematical education of preschool children has been developed, which ensures the integration of the mathematical activity of the child into his independent activity on the basis of the inclusion in the goals, content and forms of mathematical education of the adaptive component associated with the need for social adaptation of the child to the processes of technologization and informatization of society.

6. A theoretical model of the content of mathematical education in the period of preschool childhood has been developed. The model includes: sources of mathematical education, principles of content selection (general: scientific, systematic, continuity, visibility, accessibility - and specific: integrity of the picture of the world, integrativity, activity orientation), general didactic and particular methodological criteria for selecting content, stages (conceptual, design and analytical -diagnostic) formation of the content of mathematical education.

Theoretical significance of the study is that his findings:

deepen the understanding of mathematical education in the period of preschool childhood, reveal its functions (adaptive, cultural, developmental, prognostic), structure (teachers and children, patterns and principles, goals and content, upbringing and learning processes with appropriate methods, means and organizational forms), goals (formation of the foundations of mathematical culture among preschoolers), content (arithmetic, algebraic, algorithmic, geometric concepts, the concept of quantities), the adaptive component (in the content structure it is expressed through the selection of an algorithmic line, and within the framework of organizational forms - through different kinds games, regime moments connecting algorithmic and practical activities) in the paradigm of education as a mechanism for developing the foundations of a child's mathematical culture;

enrich the pedagogical theory in terms of the conceptual and terminological apparatus by clarifying the basic concepts for research "methodology for designing mathematical education in the period of preschool childhood", "mathematical education in the period of preschool childhood", "designing mathematical education in the period of preschool childhood", "mathematical culture of a child of preschool age";

the identified patterns and principles of designing mathematical education expand the range of didactic and methodological principles and contribute to the terminological ordering of the theoretical and methodological space of the problem under study;

clarify the structure of the mathematical culture of a preschool child, which includes the following components: value-evaluative, cognitive-informational, reflective-evaluative and effective-practical.

Practical significance research.

2. The organizational and methodological support of the project developed in the course of the dissertation work (monographs, educational, methodological manuals, etc.) is used to increase the scientific and methodological level of organization of the work of methodological associations of preschool educational institutions, all-Russian and city scientific and practical conferences and seminars .

3. The programs and technologies for improving the professional qualifications of educators developed by the author ensure the effective implementation of the idea of ​​forming the foundations of mathematical culture in preschool children. On the topic of the study, author's advanced training courses for preschool education workers have been developed.

4. Scientific and methodological materials developed and implemented by the author on the problem of preschool mathematical education (lecture plans, guidelines, programs and content of special courses) are used in the process of course preparation of teachers.

5. On the basis of the dissertation materials, innovative educational activities were organized in preschool educational institutions of the Sverdlovsk region. The innovative results that have been tested can be broadcast to preschool, secondary and higher institutions. teacher education Russia.

Reliability and validity of the conclusions obtained in the dissertation are supported by the methodology of the theory universal values in determining the initial provisions, the synthesis of philosophical and psychological-pedagogical approaches in substantiating the leading ideas; implementation of systemic, axiological, cultural, personality-oriented and activity approaches; rational application of a set of methods of theoretical and experimental research, adequate to the tasks and logic of the study; a combination of objective qualitative and quantitative indicators for evaluating the results of the process in the education system; completeness of implementation theoretical research into practical activities; applicability of ideas, concepts and models in preschool institutions; reproducibility of the obtained results in mass practice.

Results and conclusions of the study have applied value for the activities of state and socio-political organizations involved in solving the problems of mathematical education of preschool children; can be used in the formation of regional policy in the field of preschool education, in the planning and implementation of federal and regional educational projects.

Approbation of the study. The results of the study were tested 1) through publications in the press, in particular in the leading pedagogical journals "Education and Science", "Preschool Education", "Primary School", etc.; 2) during international, all-Russian and regional conferences: Yekaterinburg (1996, 1997, 1999, 2000, 2001, 2004-2010), Samara (1998), Irkutsk (2000), St. Petersburg (2000, 2003, 2010), Penza (2004, 2008), Chelyabinsk (2004), Surgut (2005), Petrozavodsk (2005), Kolomna (2007), Sterlitamak (2007), Magnitogorsk (2009), Shadrinsk (2009), Novosibirsk (2010), Cheboksary (2010) , Moscow (2011); 3) in the course of the dissertation's pedagogical activity as an assistant professor of the Department of Mathematics and Methods of Teaching it in the Primary Schools of the USPU through the introduction of the developed lecture courses "Theory and Methods of Mathematical Development of Preschool Children", "Methods of Teaching Mathematics in Primary Schools", "Theoretical Foundations of Mathematical Education during childhood”, special courses “Logic training in preschool educational institutions”, “Continuity and prospects in teaching mathematics”, “Designing mathematical education during childhood”.

Implementation of research results. The results obtained in the course of the study are being introduced into the practice of preschool educational institutions in Yekaterinburg (No. 5, 9, 10, 68, 129, 135, 165, 368, 422, 516, 534, 563, etc.) and the Sverdlovsk region (No. Berezovsky, Kamensk-Uralsky, Sysert, Rezh, etc.). The implementation of the results was also carried out during teaching activities the author at the Ural State Pedagogical University at lectures, seminars, practical classes, in the process of teaching practice, reading special courses; in the process of cooperation with the faculty of advanced training of educators of USPU; in the process of cooperation with the Development Institute regional education Sverdlovsk region; in the process of cooperation with the State Educational Institution of Higher Professional Education "Shadrinsk State Pedagogical Institute"; while working with coordinating council on preschool and primary education at the Institute of Pedagogy and Childhood Psychology, USPU, Yekaterinburg; within the framework of the complex research program of the Ural Branch of the Russian Academy of Education "Education in the Ural region: scientific foundations development and innovation” project 1.1.14 “Designing an innovative model of mathematical education in childhood”, the territory of which is the Greater Urals.

The following are defended:

1. The development of mathematical education in the period of preschool childhood is determined by the design methodology based on the following patterns:

- the effectiveness of the design of a system of mathematical education in the period of preschool childhood depends on the harmony in the reflection of all components of mathematical education in the project and the objectivity of the relationships between them, on the degree to which the accessibility and practical significance for children of the designed content elements are taken into account;

- the quality of the design of mathematical education in the period of preschool childhood is determined by the accuracy of taking into account the following factors: the stages of development of the child's thinking - from visual-active through visual-figurative to verbal-logical, the specifics of the relationship between the game and cognitive activities of a preschooler, the dynamics of the transition from the child's sign-symbolic activity to modeling ;

– the effectiveness of designing mathematical education in the period of preschool childhood is due to the degree of consideration of the adequacy and adaptability of mathematical education to the processes of informatization and technologization taking place in modern society;

- the effectiveness of the design of mathematical education in the period of preschool childhood depends on the level of algorithmization of the design process itself and its compliance with the algorithms for functioning and managing the process of teaching and educating children of preschool age.

2. The design of mathematical education in the period of preschool childhood is carried out taking into account a set of principles:

– harmonization of the components of mathematical education in the period of preschool childhood;

- taking into account the stages of development of children's thinking;

- the relationship of gaming and cognitive activities;

- taking into account the adequacy and adaptability of mathematical education to the changes taking place in society;

– compliance of the algorithm for designing mathematical education with the algorithms for functioning and managing the process of teaching and educating preschool children.

3. The leading ideas of the concept of culture-forming mathematical education in the period of preschool childhood are the following:

mathematical education of the period of preschool childhood has the potential of an adaptive function to the processes of informatization and technologization taking place in society and therefore is a necessary component of the process of forming the culture of a growing person;

in line with the interaction of the rational-cognitive and culture-forming components of education, the core of the concept is the system of fundamental categories and concepts of mathematical education in the period of preschool childhood: “mathematical education in the period of preschool childhood”, “mathematical culture of a preschool child”, “formation of a mathematical culture of a child of preschool age”, “ designing mathematical education in the period of preschool childhood”;

based on the inclusion of an adaptive component in the goals, content and forms of mathematical education, mathematical education in the period of preschool childhood is organized as a system that ensures the integration of the child's mathematical activity into his independent activity;

Mathematical education of the period of preschool childhood is built taking into account the following patterns:

The effectiveness of mathematical education depends on the degree of compliance of the structure and content of education with the main trends in the development of society in the current period, primarily the processes of informatization and technologization, and the learning outcomes depend on the degree of inclusion of mathematical knowledge and skills in the process of adapting the child to modern conditions associated with technologization and informatization;

the quality of mathematical education is determined by the structuring of the content, the selection of methods, forms and means of education and training in accordance with the age capabilities of children, and educational outcomes do not depend on the amount of information received by the child in the process of studying mathematics, but on the degree of its accessibility and practical significance;

the effectiveness of mathematical education during preschool childhood depends on its implementation on the basis of the subjective cognitive activity of all participants in the educational process (teachers, children, parents);

the success of the formation of the foundations of mathematical culture in children depends on how much the applied methods of organizing cognitive-playing activity ensure the development of the structural components of the mathematical culture of a preschool child (value-evaluative, cognitive-informational, effective-practical and reflective-evaluative), which contribute to the integrity of the mathematical education of the child and the implementation of the adaptive function of mathematical education in the period of preschool childhood to the processes of informatization and technologization of society.

The implementation of a systematic increase in the professional competence of preschool teachers through the organization of their special theoretical and methodological training in order to create conditions for the implementation of mathematical education, corresponding to modern trends in strengthening the interaction of culture-forming and rational-cognitive components of education, is a necessary condition for the functioning of the system of mathematical education.

Work structure. The work consists of an introduction, four chapters, a conclusion, a list of references, including 591 titles, 3 appendices. The volume of the dissertation is 420 pages of text (without appendices), illustrated with 15 tables, 6 figures.

Trends in the development of mathematical education in the period of preschool childhood in the context of informatization and technologization of society

Currently, various terms are used to refer to the process of teaching preschoolers mathematics: “formation of elementary mathematical representations”, “mathematical development”, “mathematical preparation”. The first two concepts in the pedagogical and methodological literature are defined as follows: - the formation of elementary mathematical representations is a purposeful and organized process transfer and assimilation of knowledge, techniques and methods mental activity, stipulated by program requirements ; - the mathematical development of preschoolers is a qualitative change in the cognitive activity of the individual, occurring as a result of mastering, mathematical representations and related logical operations.

special definitions - concepts we did not find mathematical preparation, therefore we deduced it ourselves, using the definitions of the concepts "preparation" and "prepare", given in " explanatory dictionary Russian language”: “Preparation - 1) prepare; 2) a stock of knowledge acquired by someone (from a student good preparation)"; “Prepare - 1) do something in advance for the device; organizing something (preparing material for work); 2) to teach, to give the necessary knowledge for something (to prepare a student for exams). From these definitions, we get that the mathematical training of preschool children can be understood as the stock of necessary mathematical knowledge acquired by a child of preschool age for further education at school.

However, in modern conditions neither the formation of elementary mathematical concepts, nor mathematical development, nor mathematical training are able to realize main goal education, noted in the federal state requirements for the structure of the main general education program preschool education, namely the focus on the formation common culture providing social success and success in schooling, since the general culture of a person in the conditions of informatization and technologization of society cannot be formed without the formation of a mathematical culture within the framework of mathematical education.

According to Doctor of Physical and Mathematical Sciences, Professor V.M. Tikhomirov, mathematics has always been an integral and essential integral part human culture, it is the key to understanding the world, the basis of scientific and technological progress and an important component of personality development. Mathematical education is a blessing to which any person has the right and the obligation of society (the state and world organizational structures) to provide each individual with the opportunity to exercise this right.

Mathematical education is given a special role, since mathematics forms a culture of thinking and is an indispensable tool that contributes to the development of such personality traits as the ability to critical thinking, logical rigor and algorithmic thinking; the ability to abstract, which largely determine the success and effectiveness of the child's activity in understanding the world outside and inside himself.

From the point of view of A.V. Lokhanko, the main features of the modern information society are its “informatization, the creation of new intellectual technologies, the acceleration of the pace of technological development, the transformation of information into the most important global resource of mankind. These factors lead to a deep, multi-level change social system, changing the environment, under the influence of which the personality changes ", and, consequently, to a change in the functions, goals and content of education. According to F.M. Makhnina, “the defining criteria of informatization are in the field of sociocultural. Without changing the people themselves, their views, habits, guidelines, it is impossible to talk about fundamental changes in society. The formation of developed needs for information and its use, as well as the consolidation of information as one of the main values ​​of the individual - these two aspects of the entire socio-cultural complex can determine the success of the informatization process. And for these changes to occur (of the people themselves, their views, habits), it is necessary to make changes in the education system. And as rightly noted by I.G. Ovchinnikov "one of priority areas process of informatization of modern society is the informatization of education. ... The informatization of education requires the improvement of the methodology and strategy for selecting the content, methods and organizational forms of training, education, corresponding to the tasks of developing the personality of the student in modern conditions of informatization of society. Informatization is the construction of an information society, strengthening the role of reliable, comprehensive and advanced knowledge in all areas of human activity. Simultaneously with the processes of informatization, the technologization of society takes place, which also has big influence to reforms in the field of education. These transformations are reflected in federal law"On Education", "Concepts for the modernization of domestic education for the period up to 2010" and, as noted by many researchers (V.I. Baidenko, G.B. Kornetov, A.N. Novikov, L.G. Semushina, Yu.G. . Tatur and others), mean the process of changing the educational paradigm.

The structure and content of education today do not correspond to the structures of modern culture and human activity and are unable to ensure its main purpose - an adequate reflection and effective appropriation of human experience (culture). According to H.G. Tkha-gapsoeva of the three forms of "spiritual objectivity" - knowledge, value and project (M.S. Kagan) in the space of education, only one is properly reflected - knowledge.

Methodological approaches to the problem of pedagogical design

To identify the features of the design of mathematical education in the period of preschool childhood, it is necessary to reveal the historical prerequisites for the formation of pedagogical design, as well as philosophical approaches having methodological significance, and analyze them in order to identify the theoretical foundations of the study.

AT scientific literature the history of design development is considered in two directions: the development of design as a special type of activity and as an industry scientific knowledge.

J.K. Jones reveals four stages in the development of design as a special activity.

The first stage begins during the formation of handicraft production and crafts, when necessary changes made on the product itself by trial and error.

The second stage in the development of design includes the emergence of a drawing method for designing handicraft products, when changes were already made on the drawing, and the trial and error method was eliminated. As a result, in the manufacture of products, there was a division of labor into design and practical activities.

The third stage includes the division of design activities into engineering and artistic design, architectural design, scientific modeling, economic forecasting and social planning and design.

At the fourth stage of development, design is defined as a tool for controlling evolution built environment. On the this stage there was a need for the training of professional designers and the need for new design methods. BUT. Yakovleva identifies three periods in the development of design as a branch of scientific knowledge. In the first period (from antiquity to the 20s of the XX century), design becomes independent view activities, its ideology is formed, and methods are developed. The second period (20-50s of the XX century) is characterized by the fact that design has become the subject of special scientific research. In the third period (from the 50s of the 20th century to the present, time), designing extends from the technical field to the social sciences, including pedagogy. Let's explore these periods in more detail.

The longest period is the first one: To characterize it, we will use the stages of the genesis of technical design identified in the philosophical literature as the basis of social design.

Man almost from the very beginning of his conscious activity one way or another, he was engaged in design in the sense that he imagined in advance the image of the future product, the principles of its manufacture and tried to improve the technological process.

In the Middle Ages, the design of structures and the organization of work on the implementation of the project were not separated from each other, they were perceived as a single process. The lack of interaction between craft and science, the rejection of the new led to the long-term preservation of the old forms, the rules of design activity. Only towards the end of the Middle Ages began to develop economic design, characterized by the dismemberment of the system economic enterprise on business operations, based on the functioning of capital. Subsequently, economic design turns into an organizational one, which is mainly associated with the growing activity of connecting various production organizations.

Note that these design modifications were the result of a long development practical activities human and the improvement of social relations, but were almost not associated with scientific research. It was not until the Renaissance that science began to penetrate the craft.

This, in turn, influenced the formation of technical design as an independent field of activity. The designer ceased to be a manufacturer: when designing a product, he practically did not refer to the object, but used mock-ups, diagrams, engineering knowledge, etc. as means.

Methods scientific solution technical problems as a whole were formed by the 18th century, the first technical educational institutions arose, special literature. V.F. Sidorenko notes that design has become "the main way of human existence new era”, and the design was recognized as an intellectual activity to create a future object.

The technological revolution contributed to the spread of technological design, the task of which was to break down the process of mass production into its component parts, in order to exclude the manual labor of the worker as much as possible. These processes were accompanied by the formation of science as an institution of public life. By the end of the XIX century. in design arose new form- morphological design, where the understanding of the project as a certain sample, the carrier of a particular function, for which the material and appearance is not preserved, becomes the main one. His logical development became functional design. This type of design was reoriented to modeling the processes of human life, working conditions, modes of movement, etc.

Ideas for planning long-term changes and processes for their implementation were reflected in a number of projects created in the 17th-18th centuries, such as: “Project for the education of Monsieur de Sainte-Marie”, created by J.-J. Rousseau; "Project on the organization of schools" V.F. Odoevsky, the draft Regulations of Moscow gymnasiums M.V. Lomonosov and others. These projects were designed to form impeccably educated people (J.-J. Rousseau), to lead the student on the road along which he can gradually reach from unconscious concepts to conscious ones (V.F. Odoevsky), etc.

At the end of the XIX century. The Russian Technical Society prepared a "Draft General Normal Plan for Industrial Education in Russia", in which the main place was given to the improvement of higher technical education.

E.V. Kupinskaya, characterizing the projects of the late XIX - early XX centuries, highlights them common features, such as: 1) awareness of the need to reform the secondary school in order to best adapt it to the needs of society; 2) appeal to various social strata, scientists, teachers, teachers of higher and secondary schools in the development of projects; 3) studying the world experience in setting up secondary education; 4) desire to create single school while maintaining a classical education; 5) search optimal ratio humanitarian and natural science subjects in the content of secondary education.

Methodology for designing culture-forming mathematical education in the period of preschool childhood

At present, a synergistic approach is being intensively developed (V.I. Arshinov, E.N. Knyazeva, S. P. Kurdyumov, N.M. Talanchuk, etc.), the subject of which is the processes of self-organization in open systems Oh different nature. Since the pedagogical system is a complex system of an open type, therefore, the laws of synergetics can be applied to it.

N.M. Talanchuk identifies as the starting points of the synergetic approach: 1) systemic synergy is determined by the essence of all pedagogical phenomena and processes; 2) synergetic integrity is understood as any pedagogical system; 3) systemic synergy is the source and driving force development of all pedagogical systems, not contradictions, struggles and not denial of denial; 4) pedagogy is the science of systematic human studies; 5) objective and scientific knowledge of all pedagogical phenomena and processes can only be systemic-synergetic, that is, adequate to their essence; 6) specific synergetic patterns of pedagogical phenomena and processes are studied and explained by pedagogy; 7) the development of pedagogy and pedagogical practice becomes directly dependent on the development by society of a new systemic-synergetic philosophy of life.

From the point of view of synergetics, the future determines the present. Therefore, the main task of modeling and prediction is to determine possible ways development of complex systems. The control force should not be energetic, but correctly topologically organized. Weak, but properly organized, the so-called resonant effects on a complex system, are extremely effective. Within the framework of the synergetic approach, development factors are not generally objective patterns, but real situation, random changes that constitute a constructive beginning, the basis for the development process. Random changes (fluctuations) take over the system, forcing it to evolve to a new regime. When the system reaches its threshold of stability, there comes a turning point in the development of the system - a bifurcation point - two or more development paths appear, and the system finds itself in a state of choice. The process of transition from equilibrium conditions to highly non-equilibrium ones is the transition "from repetitive and general to unique and specific".

IN AND; Arshinov notes that “in synergetics as a new interdisciplinary direction, the main, key features of the paradigm of post-non-classical science are focused, primarily due to its inherent nonlinear style of thinking, pluralism, ambiguity of theoretical concepts and formulations, and finally, a new understanding of the role of chaos in the universe as its necessary start. In this capacity, chaos in the paradigm of post-non-classical science is comprehended as a necessary creative moment of the overall picture of the emerging, self-organizing reality.

The use of a synergetic approach in the pedagogical design of education causes a shift in emphasis from the rooted linear, deterministic approach, from the study of system invariants to the study of special states of especially complex open systems in the area of ​​unstable equilibrium, more precisely, the dynamics of their self-organization near bifurcation points, when even a small impact can lead to unpredictable rapid development process.

The synergetic approach leads to a new understanding of the essence of the problem of pedagogical design. Based on these positions, the process of designing and implementing education is presented as a complex-organized, self-organizing system. It is necessary to study the processes of interaction between the subjects of the educational process, to identify trends, mechanisms and internal reserves for the development of the system, to outline ways and means of improving and updating both the system as a whole and its individual subsystems in order to improve the process of interest to us. At the same time, we consider it very important that the future state of the system coincides with the trajectory of its exit to the optimal level of its evolution.

One of the promising areas for improving the content of education is problematic, and in recent times problem-modular approach (M.A. Choshanov, P.A. Yutsyavichene, N.B. Lavrentieva, etc.), which is focused on the development of completed learning modules.

In the problem-modular design of the content of education, M.A. Choshanov distinguishes the following stages: the layout of the course around the fundamental methods of cognitive activity, such as the method of mathematical modeling, the axiomatic method, the method of coordinates, the vector method, etc.; determination of the content of the basic problematic modules, while it is necessary to take into account the criteria of the basic content” (fundamentality, generalization, continuity, continuity and humanitarization of education); allocation of professionally applied enlarged problems, taking into account the specifics various groups professions; selection of content and determination of the volume of variable modules aimed at ensuring profile and level differentiation, as well as creating conditions for the individual pace of students' progress through various options for a problem-module program.

Modular programs and modules are built in accordance with the following general principles(according to I.A. Yutsyavichen): 1) intended purpose of information material; 2) combinations of complex, integrating and particular didactic goals; 3) completeness of the educational material in the module; 4) relative independence of module elements; 5) implementation of feedback; 6) optimal transmission of information and methodological material.

The principle of intended purpose of information material indicates that the content of the information bank is built on the basis of didactic goals. If it is required to achieve cognitive goals, an information bank is built on an epistemological basis, and an operational approach to building an information bank is applied to achieve activity goals.

The principle of combining complex, integrating and particular didactic goals is realized in determining the structure of modular programs and individual modules. A complex didactic goal is the top of the pyramid of goals and is implemented by the entire modular program. This goal combines integrating didactic goals that are implemented by the corresponding modules. Each integrating didactic goal consists of particular didactic goals. Private goals can be completely autonomous or interconnected.

The principle of the completeness of the educational material in the module specifies the principle of modularity and reveals the following rules: 1) the main points of the educational material, its essence are stated; 2) explanations are given (possibly at several levels) to this material; 3) the possibilities of additional deepening into the material or its extended study through the use of TCO and teaching methods are indicated; 4) appear practical tasks and explanations for their decision; 5) theoretical and practical tasks are set and answers to them are given.

Teaching preschool teachers how to design mathematical education in childhood

The organization of mathematical education for preschoolers by trained teachers is built in two directions: the first is the systematization of mathematical knowledge obtained from various sources, the second is the construction of proper systemic mathematical knowledge. The organization of systemic mathematical knowledge is carried out by integrating the child's mathematical activity into his independent activity, as well as by directing the content of education to the personal meaning of learning, to the development of reflective consciousness.

Various sources were analyzed to compile the program. In mathematical education, we have identified 5 meaningful lines: arithmetic, algebraic, geometric, magnitude and algorithmic. These lines are considered not only in the process of forming elementary mathematical representations, but also in the depths of the activity that best contributes to this, that is, the integration of the child's mathematical activity into his independent activity is carried out. Thus, mathematical education is built on the basis of the "serial-parallel" use of the child's cognitive, play, subject-practical and speech activities, as well as the use of interdisciplinary connections in the learning process: mathematical material is revealed in the following interrelated areas: mathematics in the life of the child himself, mathematics in other people's lives and mathematics and the natural environment.

Let us reveal the approximate content of the mathematical education of preschool children, the main purpose of which is to form the foundations of mathematical culture in children.

Within the framework of arithmetic and algebraic content lines, the concepts of "set", "number", "count", comparison of numbers, equalities, inequalities, arithmetic operations (addition and subtraction), solving arithmetic problems are considered.

Lots of. The implementation of the classification of objects around the child, according to two or more features (color, shape, size); union of subsets into a single set, addition, removal of part (s) from the set; formation of ideas that a set consists of subsets (family - dad, mom, child, grandfather, grandmother, etc.); comparing the number of sets by establishing a one-to-one correspondence between their elements; the formation of ways of ordering (ascending, descending, location in space) a variety of objects and the formation of awareness of the importance of order, harmony of objects surrounding the child; establishing links between single and multiple parts of the body and their significance for the life of the child; the formation of ideas that a holistic natural object is represented by a multitude of its components, which are interconnected and interdependent, which ensures the vital activity of the object; the formation of the idea that the life forms of plants (grass, shrub, tree) differ from each other in quantity (many and one).

Number and count. Formation of ideas about the number and figure as a sign for writing a number; learning to count, the formation of ideas about different ways of counting, depending on the subject and socio-cultural certainty; formation of the basic properties of the natural series of numbers; familiarization with the universal culture through familiarization: with various ways of writing numbers in antiquity and at the present time, using them in games, cognitive activities and in everyday life, with the history of the origin of money and their name, with the device of some counting instruments; the formation of the ability to count objects surrounding the child or used by him in the game, sounds, movements; the ability to compare (equal in age, unequal in height, hair color, etc.), comparing the part and the whole and determining the significance of both for oneself; familiarization with the signs, =, -, + and their role in the communication and activities of the child and the people around him, the formation of skills to write down the relationship between the objects under consideration using the signs, =; the formation of ideas about equality and inequality; the formation of ideas about the actions of addition and subtraction.

Tasks. Formation of the translation experience of the system real relationship people on mathematical language, familiarization with the structural parts of the problem, the formation of the ability to solve problems for addition and subtraction.

The main areas of work within the framework of the geometric content line are: familiarization with the types of lines, types of geometric shapes and bodies, as well as the development of children's spatial orientation in space and on the plane.

Geometric figures. Formation of ideas about a point, a straight line, a segment, a ray, an angle, a circle, an oval, a triangle, a square, a rectangle, a quadrilateral, a polygon, a cube, a cone, a pyramid, a ball and the ability to find these figures in toys and objects surrounding the child, the ability to establish correspondence between figures and parts of one's own body; familiarization with the elements of figures; formation of the ability to model figures from sticks, wire, rope, etc.; familiarization with the tools and the formation of ideas about their purpose and value in educational, construction and engineering, sewing and other activities; learning how to construct a segment, rectangle, square, circle, etc. on a plane; comparison and modification of figures; the formation of skills to distinguish geometric shapes in complex natural objects, to see and find symmetry in natural objects; formation of methods for isolating figures from natural diversity and establishing a correspondence between a figure and an integral natural object; the formation of ideas about the immutability and constancy of geometric shapes used by artists, architects, scientists to reflect the objects of the surrounding reality.

Orientation in space. Formation of ideas about one's location in space relative to various points reference and methods of location recognition (visual, tactile, auditory); formation of ideas about the presence of socio-cultural standards that determine a single order; the formation of the ability to navigate on a small area (a sheet of paper, the surface of the table), as well as indoors, on the street, in the city and to be aware of one’s location and significance in a particular space, the formation of the ability to establish a connection between one’s location in space and the emotional state, desires and needs ( sociocultural and physical), conditions of activity; the formation of ideas about the constant change of space by people, that relations in space are regulated by rules (traffic, etiquette, etc.), signs (allowing, warning, prohibiting, etc.); formation of ideas about the vertical and horizontal construction of buildings, experience in creating a culturally appropriate space vertically and horizontally; the formation of skills to model spatial relationships using a scheme and plan; formation-understanding of space as a container of objects and objects (one or many), the relationship of various spaces and objects; nature; give an idea of ​​two-dimensional and three-dimensional, real and virtual space, the use of various means for orientation in space.

Modern approaches to the formation of the foundations of the mathematical culture of preschoolers.

The entry of children into the world of mathematics begins already in preschool childhood. Mathematics is a universal method of cognition of the surrounding and objective world, and its role in modern science is constantly growing. Changing conceptual approaches to determining the content and choosing methods for teaching mathematics at school, the widespread use of modern educational technologies determined the requirements for the mathematical preparation of preschool children.

Today "mathematics is more than a science, it is a language". The study of mathematics improves the culture of thinking, teaches children to reason logically, educates them in the accuracy of their statements.

Mathematical knowledge and skills are necessary for the successful adaptation of the child to the processes of social communication, informatization and technologization of society. They broaden the horizons of the child. Mathematical culture - component the general culture of the individual, and in the period of preschool childhood has its own characteristics associated with the age and individual capabilities of children.

Traditionally, four lines are distinguished in the content of mathematical education of preschool children: arithmetic, algebraic, geometric and magnitude. Today, taking into account the renewal of the content of preschool education, a fifth content line is added - algorithmic (schemes, models, algorithms). The use of information in a symbolized form contributes to the development of the ability to act mentally, develops logical and creative thinking, imagination.

The adoption of the GEF of preschool education will require the need to provide, as a prerequisite, the possibility of self-realization of the child at all stages of work on mathematical development in the preschool education system.

Mathematical material should be revealed during excursions, acquaintance with literary works and small forms of folklore, games with natural material (water, sand, beans, peas, cereals), through game exercises with sensory standards, household items, constructive and didactic games, in problem situations. All these forms vary according to age.

During their stay in kindergarten, our graduate must learn to apply mathematical knowledge and ideas in practical activities that are significant for him: a game, children's experimentation, design, labor activity, artistic and visual.

And as a result of self-realization, the child will develop learning motivation.

Thus, the priority tasks of continuous education of children will be solved.

Games with natural material

Small forms of folklore

Reading fiction

Direct educational activities

constructiveanddidactic games, logic

Mathematically educatedie

Excursions

Creative game exercises and problem situations

Theatricalization with mathematical content

Learning to compare objects by size, measurementconditionalmeasure , division into 2 and 4 equal parts (modeling the relationship "part- whole")

Learning to countand computational activity in solving problems in one action for addition and subtraction (within 10). Counting techniques and countdownone by one

Formation of ideas about the set and natural series of numbers (up to 10). number likeaccount result. quantitative andordinal count of items. Composition of numbers from units. Composition of numbers of two smaller numbers.

Orientation in space ("toward", "from oneself", from the subject, between subjects(plan) and in time (parts of a day, a week , month, year) hour, minutesa(1,3,5 minutes)

Orientation on the plane (notebook sheet)

Introduction to geometryand shapes (circle, square, triangle, oval, rectangle, quadrilateral, polygon, sphere, cube, cylinder, prism, cone and shape definition items) .

Straight, curved, closed line.

The use of information in the symbolized form of schemes, models, algorithms contributes to the stimulation and development of the ability to act mentally, develops logical and creative thinking.

Application of mathematical knowledge and skills in practical activities

Construction

(by design, according to plan, according to plan- mdressed, using templates, stencils)

Children's experimentation

(sand, earth, water, snow, air, magnet, paper, peas, beans)

Labor

(labor in nature, artistic, handle)

The game

(plot - role-playing,theatrical, didactic, educational games , (puzzles, labyrinths, checkers, chess (movable)

artisticabout-pictorial (color, form, composition, application,drawing)

note

teachers' council

Topic:"First Steps in Mathematics"

Conduct form: "round table"

Target. Creation optimal conditions for successful learning preschoolers elementary mathematics.

Show the ways of forming mathematical thinking through the formation and development of cognitive (sensory and intellectual) abilities of preschoolers.

To increase the professional competence of teachers in solving problems of the mathematical development of pupils. Help educators reach a new level of work.

The agenda of the teachers' council.

The significance of the problem. Modern approaches to teaching preschoolers mathematics.

The state of educational work and features of the formation of the foundations of the mathematical culture of preschoolers in a preschool institution. Results of the thematic review.

PerformanceBorovlevaN.P.,

Withsenior educator

"How I use educational games and game exercises with mathematical content aimed at the intellectual development of children."

Communication and presentation of experience

KomarnitskayaT.A,

educator junior group

The role of entertaining forms of presentation of material and promising methods of teaching children mathematics.

Presentation of work experience

SherstobitovaL.V.,

insenior group teacher

Review of methodological literature on the mathematical development of preschoolers, recommendations for its use.

Information Tkach L.N.,

junior group teacher

"Creativity of the educator".

Presentation of didactic aids, educational games with mathematical content.

"Your option" (solving a crossword puzzle, puzzles).

Adoption and approval of the draft decision of the pedagogical council.

Questionnaire

dfor self-assessment of the educator in the section:

"Formation of elementary mathematical representations"

P/P		Answers
	What do you consider the most relevant for children in your age group in the work on FEMP? The assimilation of certain knowledge by children. The development of preschoolers' thinking abilities, the ability to solve various logical problems. Developing in children the ability to apply the acquired knowledge in practice. Teaching children how to act.
	To Do you compose your own abstracts for classes or do you use ready-made ones published in teaching aids?
	What forms of work with children at FEMP do you prefer? individual work; Front work; subgroup;
	What teaching methods and techniques do you use in the classroom and in your free activities? Practical Visual (showing by the educator methods of action, the use of didactic material); Verbal (instructions, explanations, clarifications, questions); Game elements (fairy tale character; surprise moment; game-competition); Didactic games and exercises. Modeling (creation of models and their use); Logical and mathematical games.
	What difficulties did you face in your work?
	Are the parents of your pupils familiar with the problems of the mathematical development of their children? How do you organize interaction with the family in the direction of FEMP?

Individual manifestations of children in development classes

uhelementary mathatic representations

List of children	Individual Pbirths of children	Pedagogical tasks
	Show a special interest in activities; are active; are good at math; like interesting tasks	Maintain and develop their interest; give difficult tasks; make higher demands on their answers
	They do not show their activity outwardly, but are always attentive; questions are answered correctly, but only on call; little initiative	Cultivate self-confidence; encourage initiatives; develop creative initiative; carry out individual work; give instructions in the course of household activities.
	They show external activity in the classroom, they like to prompt, although they do not know the answer, they are waiting for prompts.	Cultivate modesty, in the classroom often call, ask, questions that make you think.
	Show no interest in activities not attentive; not always able to answer the teacher's question	Reveal the reasons for such behavior, conduct individual classes; make extensive use of visibility.
	They listen attentively, but cannot answer the questions posed; prefer to remain silent; shy; have problems in class	Conduct individual work to overcome shyness; Eliminate knowledge problems in separate lessons

OproWith-questionnaire

Dear parents!

We know well how your children are engaged and interested in kindergarten. What are they like at home? Help us to get to know your children better so that we can improve our pedagogical work with them. Share your experience family education. Thank you in advance for your attention.

Please answer the following questions:

P/P		Answers
	Does your child tell you about his/her math achievements or difficulties in kindergarten?
	Do you have the opportunity to play math games with your child at home?
	Do you offer your child to pay in the store for purchases with real money, to receive change? Does he ask to pay for the purchase himself?
	What, in your opinion, the child's mathematical representations need to be improved? (counting, geometric standards, spatial relationships, orientation in time, comparison of objects by size, solving arithmetic problems)
	What is your child experiencing difficulty, what is he best versed in?
	Who in the family has the most opportunity to take care of the child?
	Does the child like to solve problems for intelligence?
	How does the child apply his acquired mathematical knowledge?
	What does the child want to learn?

Having filled in the empty cells horizontally correctly, you will read the name of modern science in a vertical column.

1. A set of objects or phenomena perceived as a whole?

2. Symbol numbers?

3. Structural component of the account activity (account total) ?

4. Type of math classes in kindergarten?

One of the most important tasks raising a child preschool age - this is the development of his mind, the formation of such mental skills and abilities that make it easy to learn new things.

For the modern educational system (and the development of cognitive activity is one of the tasks of mental education) . It is so important to learn to think creatively, outside the box, to find the right solution on your own.

It is mathematics that sharpens the child's mind, develops the flexibility of thinking, teaches logic, forms memory, attention, imagination, and speech.

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Modern approaches to the organization of the formation of mathematical representations of preschoolers in accordance with the requirements of the Federal State Educational Standard

“On how elementary mathematical representations are laid down, to a large extent depends further way mathematical development, the success of the child’s advancement in this field of knowledge” L.A. Wenger

One of the most important tasksraising a preschool child- this is the development of his mind, the formation of such mental skills and abilities that make it easy to learn new things.

For the modern educational systemthe problem of mental education(and the development of cognitive activity is one of the tasks of mental education)extremely important and relevant. It is so important to learn to think creatively, outside the box, to find the right solution on your own.

It is mathematicssharpens the child's mind, develops flexibility of thinking, teaches logic, forms memory, attention, imagination, speech.

GEF DO requires the process of mastering elementary mathematical conceptsattractive, unobtrusive, joyful.

In accordance with the Federal State Educational Standard, the main goals of the mathematical development of preschool children are:

1. The development of logical and mathematical ideas about mathematical properties ah and relations of objects (specific quantities, numbers, geometric shapes, dependencies, regularities);
2. Development of sensory, subject-effective ways of knowing mathematical properties and relationships: examination, comparison, grouping, ordering, splitting);
3. Mastering by children of experimental and research methods of cognition of mathematical content (experimentation, modeling, transformation);
4. Development in children of logical ways of knowing mathematical properties and relationships (analysis, abstraction, negation, comparison, classification);
5. Mastering by children mathematical methods of cognition of reality: counting, measurement, simple calculations;
6. The development of intellectual and creative manifestations of children: resourcefulness, ingenuity, guesswork, ingenuity, the desire to find non-standard solutions;
7. Development of accurate, reasoned and evidence-based speech, enrichment of the child's vocabulary;
8. Development of initiative and activity of children.

Targets for the formation of elementary mathematical representations:

Mathematical development of preschoolers- positive changes in the cognitive sphere of the individual, which occur as a result of the development of mathematical concepts and related logical operations.

Formation of elementary mathematical representations- this is a purposeful process of transferring and assimilating knowledge, techniques and methods of mental activity provided for by program requirements. Its main goal is not only preparation for the successful mastering of mathematics at school, but also the comprehensive development of children.

Mathematics education of a preschooler- this is a purposeful process of teaching elementary mathematical concepts and ways of knowing mathematical reality in preschool institutions and the family, the purpose of which is to foster a culture of thinking and the mathematical development of the child.

How to "wake up" the cognitive interest of the child?

Answers: novelty, unusualness, unexpectedness, inconsistency with previous ideas.

That is, you need to doentertaining learning. Entertaining learning intensifies emotional and thought processes that make you observe, compare,argue, argue, prove the correctness of the actions performed.

The task of an adult is to keep the interest of the child!

Today, the teacher needs to build educational activities in kindergarten in such a way that each child is actively and enthusiastically engaged.When offering children tasks of mathematical content, it must be taken into account that their individual abilities and preferences will be different, and therefore the development of mathematical content by children is purely individual.

Mastering mathematical concepts will be effective and efficient only when children do not see that they are being taught something. They think they are just playing. Not noticeable to yourself in the process game actions with game material they count, add, subtract, solve logical problems.

The possibilities of organizing such activities are expanded if the group creates kindergarten developing object-spatial environment. After alla properly organized object-spatial environment allows each childfind an occupation to your liking, believe in your strengths and abilities, learn to interact with teachers and peers, understand and evaluate feelings and actions, argue your conclusions.

Using an integrated approach in all types of activities helps teachers to have entertaining material in each group of the kindergarten, namely card files with a selection of mathematical riddles, funny poems, mathematical proverbs and sayings, counting rhymes, logical tasks, tasks-jokes, mathematical fairy tales.(a photo) Entertaining in content, aimed at developing attention, memory, imagination, these materials stimulate children's manifestations of cognitive interest. Naturally, success can be ensured under the condition of a child-oriented interaction with an adult and other children.

So, puzzles are useful for fixing ideas about geometric shapes, their transformation. Riddles, tasks - jokes are appropriate in the course of learning to solve arithmetic problems, operations on numbers, in the formation of ideas about time.Children are very active in the perception of tasks - jokes, puzzles, logical exercises. The child is interested final goal: add, find desired shape, transform - which captivates him.

DOE work experience

In the 2015-2016 academic year, our preschool educational institution continues to work on the formation of the cognitive interests of preschoolers through developing math games and the creation of a developing subject-spatial environment for the formation of mathematical representations in accordance with the Federal State Educational Standard.

Particular attention is paid tosaturation of the environment -the educational space should be equipped with the means of training and education (including technical ones). Yes, in kindergartenvariousmodern educational games: designers - designer Polikarpov, plot constructor "Transport", "City", "Castle", designer TIKO "Balls", "Geometry", mathematical tablet, arithmetic account, logical pyramids "Colored columns","Learning to count" with numbers, logical dominoes, mazes,wooden building designers "Tomik",counting material "Geometric shapes",educational games of Voskobovich.

Construction

tool for the development of creative and logical abilities children perform practical exercises with the "TIKO"-designer for planar and volumetric modeling.In our preschool teachers, working enthusiastically with the TIKO constructor, discovered its great opportunities for the mathematical development of children, starting from an early age. In the game with the designer, the child remembers the names and appearance of planar figures (triangles - equilateral, acute-angled, rectangular), squares, rectangles, rhombuses, trapezoids, etc. children learn to model objects of the world around them and gain social experience. Children develop spatial thinking, they can easily change the color, shape, size of the structure, if necessary. Skills acquired inpreschool period, will serve as the foundation for gaining knowledge and developing abilities at school age. And the most important among these skills is the skill logical thinking, the ability to "act in the mind."

Wooden constructors are a convenient didactic material. Multi-colored details help the child not only learn the names of colors and geometric flat and voluminous figures, but also the concepts of “more-less”, “higher-lower”, “wider-narrower”.

For young children, working with a logical pyramid makes it possible to manipulate the components and compare them in size using the comparison method. Folding the pyramid, the child not only sees the details, but also feels them with his hands.

Lego

At the end of 2015, we purchased the LEGO Wedo 9580 protobot to work with older preschool children. It is designed to assemble and program simple LEGO models that connect to a computer. The WeDo constructor is based on a corporate base LegoSystem - bricks with spikes, with which modern children, as a rule, get acquainted very early. Added to these are sensors and a USB switch to connect to a computer and bring the designs to life. Therefore, laptops were purchased for the groups and appropriate programs were installed. From the constructor, you can create different models, both according to Lego instructions, and inventing it yourself. In the form of a game, you can get acquainted with various mechanisms and even learn to design.

We plan to introduce you to this constructor in more detail at a seminar in the fall.

Educational games by Voskobovich

Voskobovich's educational games are of particular interest to teachers and children. The use of Voskobovich's games in the pedagogical process makes it possible to restructure educational activities into cognitive gaming activities.

There are many educational games by Voskobovich. Among the most common in our kindergarten are: "Two-color and four-color squares", Igrovisor, "Transparent square", "Geokont", "Miracle - crosses", "Miracle flower", "Cord-entertainer", "Logo moulds”, “Carpet graph “Larchik”,Ship "Spray - spray" and others. During the game, the child masters the numbers; recognizes and remembers color, shape; trains fine motor skills hands; improves thinking, attention, memory, imagination. Games are based on three main principles - interest, knowledge, creativity. These are not just games - these are fairy tales, intrigues, adventures, funny characters that encourage the baby to think and be creative.

To develop the mathematical concepts of children, teachers use another modern form of work with children - iris folding.

Iris folding develops the ability to compare and find differences between two or more objects, restores previously seen from memory (diagram, drawing, model), and also allows children to create unusual visual images to remember the desired operation.

Iris folding allows children to develop the ability to think logically: find similarities and differences, highlight the essential, establish causal investigative links. All mental activity is activated.

Interaction with parents

An equally important condition for the formation of elementary mathematical concepts in children is Active participation in the educational process of parents.

In kindergarten, we use the following forms of work with the family: consultations, designing folders, conducting mathematical entertainment, fairs, master classes on the topics: “Logic - a mathematical game - as a means of teaching and educating preschool children”; “Fabulous labyrinths of V.V. Voskobovich".

In groups, parents made mini-books with their childrenfairy tales on mathematical plots: "Numbers", "Circle and Square" and others.

The teachers brochures with assignments on the logic blocks of Gyenesh, Kuizener's sticks were developed; booklets "Math games with a child at home", "Mathematics for the development of your child" and others to consolidate mathematical ideas with children at home.

Project activity

Undoubtedly, one of the modern and effective forms of supporting children's initiative is project activity, in which the participation of parents is always relevant. Using project activities for the development of mathematical representations of children, teachers thereby activate the cognitive and creative development of the child, and also pay attention to the formation personal qualities child. The knowledge acquired by children during the implementation of the project becomes the property of their personal experience. Math projects such as "Fun Math" in middle group No. 9, "Entertaining Math" in middle group No. 14, "ABC of Numbers" middle group No. 1 and others made it possible to embody the personality-developing nature of the interaction between adults and children in practice, taking into account their needs, opportunities, desires in the educational process.

Personnel

The quality of pedagogical activity on the use modern means for the formation of mathematical representations mainly depends on qualified teachers. In this regard, 2 teachers of our kindergarten were trained in KOIRO on gaming technology intellectual and creative development of children aged 3-7 years “Fairytale labyrinths of the game V.V. Voskobovich". Education in KOIRO under the advanced training program "Updating the content of educational and upbringing activities in a technical association"; under the program "Development of technical creativity in educational organization in the conditions of the Federal State Educational Standard ", 2 teachers studied, according to the program" Tutoring activities in additional vocational education» - 1 teacher.

Teachers actively participate in seminars, workshops held in the preschool educational institution on the topics: "Organization and conduct of work on the formation of the cognitive interests of preschoolers through developing mathematical games", "Peculiarities of the organization of mathematical games in preschool age"; in municipal seminars on the topics: “Development of technical creativity of students within the framework of networking institutions of general and additional education", "Dissemination of innovative models of development of the technosphere of activities of institutions of additional education in the framework of the development of a network model of interaction with preschool educational institutions»; regional seminars "Game is the most important area of ​​self-expression", international seminars "Preschool education: the experience of Italy", where teachers exchanged experience in TIKO design, as well as in webinars organized by FGAU "FIRO" and the magazine "Obruch", such as "How to prepare a preschooler to the solution of arithmetic problems", "Geometric propaedeutics in modern preschool education" and others.

Note: This article does not provide a summary of the event, but its possible structural components. The duration of the event, the number of classes, the content of tasks are determined on the basis of the identified difficulties of teachers in the field of mathematical education for preschoolers.

Leading: Does modern man need mathematics? What is it for? Give examples. The one who answered “palm on palm” passes the baton to answer any other teacher. We recommend using this technique in working with children in order to activate them. Name professions in which mathematics is not needed. ( There is no such).

Thus, you yourself proved the relevance of our workshop. For a substantive conversation, we need to establish ourselves at what age does a child's mathematical education begin? Why do you think so? Justify your claim. All possible assumptions are heard. ( Summary of facilitator's responses: the prerequisites for mathematical education are observed from the first days of a child’s life, when a mother talks to a child (“you grow up big, big”, “we’ll wash our left hand, then our right hand”, etc.), sing lullabies to the baby, read nursery rhymes, etc.)

Warm up: With the introduction of the Federal State Educational Standard, many are asking the question, in what form should the mathematical education of preschoolers be carried out: in the form of classes or in the form of directly educational activities? What does the Order of the Ministry of Education and Science say about this? Russian Federation dated October 17, 2013 No. 1155?

Exercise: One of the principles of the standard (clause 1.4.3.) - « assistance and cooperation of children and adults, recognition of the child as a full-fledged participant (subject) of educational relations. According to this principle, analyze the tasks of cognitive activity (mathematics) for their compliance with the Federal State Educational Standard. Use arrows to indicate in the table the correspondence (←) or non-correspondence (→) of the listed tasks of forming elementary mathematical representations to the federal state educational standard preschool education. Justify your choice.

Corresponds to GEF	Tasks ← or →	Does not comply with GEF
	To consolidate the ability to name parts of the day (day - night, morning - evening), the sequence of days in a week
	Clarify children's ideas about the parts of the day, improve the ability to establish their sequence
	Improve the skills of establishing the identity and difference of objects according to their properties: size, shape, color
	Contribute to the development of search activities when comparing the size of the subject
	Encourage to establish relationships between the whole set and each of its parts, to understand that the set is greater than the part, and the part is less than the whole set
	Learn to determine the location of objects in relation to the child (far, close, high)
	Engage in joint research activities with peers when comparing values
	Learn to distinguish objects by shape and name them (cube, brick, ball, etc.).
	To form the experience of comparing adjacent numbers within 8, based on clarity
	Learn to use planar and volumetric forms as standards
	Introduce spatial relationships: far - close

Leading: At an early age, children need repeated examination of different objects on the same basis, repeated pronunciation of speech combinations with the naming of this sign. Consequently, the educator must show the same sign every day on new objects of the world around him, in new situations. Let's agree that there are thirty-six 5-day working weeks in the academic year. This means that the educator should have in his arsenal an average of 210 examples for the feature (quality) of the subject being mastered by the children.

Exercise: at an early age, children comprehend such signs of objects of the world as "big - small". Give examples of familiarizing young children with the value from the immediate subject environment of babies. ( Mom has big gloves, and children have small ones; dad has big shoes, and the children have small ones; the teacher has a large chair, and the children have small chairs; children have large plates, and the doll has small plates; the matryoshka is big, and in it the nesting doll is small, etc.). Participants can be activated using a relay baton.

Task (similar to the previous one): Give examples of the formation of the concepts of "One - many" in young children from the immediate subject environment of babies

Exercise: Give examples of the integration of cognitive and productive activities on the example of mathematics ("one - many") and drawing. ( Stars in the sky (Fig. 1), fireworks, rain, snowing, lights on the Christmas tree, leaf fall, dandelions in the grass, grains for birds, etc.). The teacher prepares the main image in advance. Children with a poke or finger complete the drawing, saying together with an adult: "One star, one more star, ... many stars."

Exercise: Give examples of comparing groups of objects from the everyday environment of the 2nd junior group using the overlay technique. ( To find out what is more - bears or cars, you need to put one bear in each car; put one spoon on each plate (put one cup); put one scoop in each bucket, one child sit on each chair, etc.).

Exercise: Give examples of comparing groups of objects from the household environment of the 2nd junior group by using the application. ( To find out what is more - dolls or plates, you need to put one plate in front of each doll; we will give each child an apple, etc.). Reception of activation of participants: the one who last gave an example will win.

Leading: Exist didactic principles selection of demonstration and handout based on physiological and psychological characteristics every age.

Exercise: On what form (Fig. 2) will we begin to form the ability to lay out objects in the 2nd junior group? Why?

(On the strip, because this form helps children lay out objects strictly in one line, does not distract children from the important rules for laying out objects from left to right, leaving “windows” between them)

Exercise: With what forms of handouts (Fig. 3) will we begin to form the ability to lay out objects on the strip in the 2nd junior group? Why?

(From the image of objects that have a rounded silhouette, for example, balls, and then from circles, because no matter how you put a round shape, it will lie correctly)

Leading: In accordance with paragraph 2 of part 3 of article 28 of the Law "On Education in the Russian Federation", the competence of the educational organization includes the material and technical support of educational activities, equipment of premises.

Exercise: Name the games, materials and equipment that contribute to the mathematical education of younger preschoolers.

(Seals, stencils, templates; natural and waste material; board and printed games; sets of split pictures, puzzles; various plastic constructors; mosaics; insert games; polyfunctional panels on themes; games for familiarization with color, shape, size, etc.). P.)

Leading: The work on the mathematical education of preschoolers contains a huge potential for the development of speech. It is important to take children away from monotonous speech stereotypes, to give them many samples competent speech, show a variety of speech constructions "question - answer". First, these are short two-word questions. Accordingly, the answers will be from two words. Gradually, the construction of questions increases, respectively, the speech construction of answers also increases.

Exercise: Formulate on the cards (Fig. 4, 5) questions to the children of the 2nd junior group and answers to them in different ways. In order to activate teachers, they can be divided into two teams. Each team asks questions on a card, and the opponents answer. The team with the most questions and answers wins.

Question Options	Answer options
What more?	More squirrels
What is less?	less mushrooms
What can be said about whites?	There are more squirrels than mushrooms
How to say differently?	More squirrels, less mushrooms
What can be said about mushrooms?	There are fewer mushrooms than squirrels Less mushrooms, more squirrels
What can be said about squirrels and mushrooms?	They are not equal
How many more squirrels than mushrooms?	Squirrels have more mushrooms by one
How many fewer mushrooms than squirrels?	Mushrooms less squirrels by one
Why are there more squirrels than mushrooms?	One squirrel is missing one mushroom

Leading: The development of speech is closely related to cognitive development. Activation of children's speech is facilitated by the technique "Say it differently"

Exercise: Where is the circle? (Fig. 6). Say it differently.

(The circle is (located, lies) in the center of the sheet; in the middle of the sheet; under the red triangle; above the yellow triangle; to the right of the blue triangle; to the left of the green triangle; between the red and yellow triangles; between the blue and green triangles)

Exercise: Read the examples: 5+1=6; 6-1=5. Read these examples differently.

(Five plus one equals six. Five plus one equals six. Five plus one equals six. Six minus one equals five. Subtract one from six equals five. Six minus one equals five.)

Leading: In mathematics, every action has an inverse - checking - action. This principle is taken into account when dividing the whole into parts.

Exercise: From which figure (Fig. 7) do we begin to divide the whole into two equal parts? Why?

(We start with a circle, because the circle is divided into two equal parts in one single way, with the reverse (test) action - to assemble the whole from the parts - only the circle gives one single initial version).

Leading: In working with children of older preschool age, mathematical warm-ups are relevant.

Exercise: What are the tasks for clarifying ideas about adjacent numbers

(Name the missing number; Name the number between the numbers; Name the neighbors of the number; Name the previous number; Name the next number; Name the number 1 more; Name the number 1 less, etc.)

Leading: At the end of any lesson, entertaining logical tasks are appropriate.

Exercise: Guess the fairy tale (Fig. 8). Prove it.

(Fairy tale "Three little pigs") Make your schemes according to the famous fairy tales "Three Bears", "Turnip", "Teremok", "The Wolf and the Seven Kids", etc.