The mathematical development of preschool children is carried out both as a result of the child’s acquisition of knowledge in everyday life (primarily as a result of communication with an adult), and through targeted training in classes to develop basic mathematical knowledge. It is the elementary mathematical knowledge and skills of children that should be considered as the main means of mathematical development.
G.S. Kostyuk proved that in the process of learning, children develop the ability to more accurately and completely perceive the world around them, identify the signs of objects and phenomena, reveal their connections, notice properties, interpret what is observed; mental actions, methods of mental activity are formed, internal conditions for transition are created to new forms of memory, thinking and imagination.
Psychological experimental research and pedagogical experience indicate that thanks to the systematic teaching of mathematics to preschoolers, they develop sensory, perceptual, mental, verbal, mnemonic and other components of general and special abilities. In the studies of V.V. Davydov, L.V. Zankov and others It has been proven that the inclinations of an individual are transformed into specific abilities through learning. The difference in the levels of development of children, as experience shows, is expressed mainly in the pace and success of their acquisition of knowledge.
However, despite the importance of learning in the mental development of the individual, the latter cannot be reduced to teaching. Development is not limited to those personality changes that are a direct consequence of learning (G.S. Kostyuk). It is characterized by those “mental turns” that occur in a child’s head when he learns the art of speaking, reading, counting, and assimilates the social experience transmitted to him by adults ( I.I.Sechenov).
As studies show (A.V. Zaporozhets, D.B. El-konin, V.V. Davydov, etc.), development goes beyond what is learned at one time or another during training. During the learning process and under the influence of learning, a holistic, progressive change in personality, its views, feelings, abilities. Thanks to training, opportunities expand
Further learning of new, more complex material creates new learning reserves.
There is a reciprocal relationship between learning and development. Learning actively contributes to the development of the child, but it also depends significantly on his level of development. In this process, much depends on how much the training is aimed at development.
Learning can develop a child in different ways depending on its content and methods. It is the content and its structure that guarantee mathematical development child.
In methodology, the question “what to teach?” has always been and remains one of the main questions. Whether to give children the basics of scientific knowledge, whether to equip them only with a set of specific skills with which they would have some practical orientation, is an important problem in kindergarten didactics.
Selecting educational material for study, taking into account its significance and in accordance with the capabilities of children, is a very difficult matter. The content of training, i.e., the program for the formation of elements of mathematics, has been worked out over many years. In the last 50 years, this process has been carried out on the basis of experimental research ( A. M. Leushina, V. V. Danshgova, T. V. Taruntaeva, R. L. Berezina, G. A. Korneeva, N. I. Nepomnyashchaya, etc.).
An analysis of various (variable) mathematics programs in kindergarten allows us to conclude that the main content of their content is a fairly diverse range of ideas and concepts: quantity, number, set, subset, magnitude, measure, shape of an object and geometric figures; ideas and concepts about space (direction, distance, relative position of objects in space) and time (units of measurement of time, some of its features).
At the same time, it is important to emphasize that each mathematical concept is formed gradually, step by step, linearly.
but to the concentric principle. Different mathematical concepts are closely related to each other. Thus, when working with children of the fourth year of life, the main attention is paid to the formation of knowledge about sets. Children learn to compare “contrasting” and “adjacent” sets (many And one; more (less) for one). Later, in groups of the fifth, sixth, seventh years of life, knowledge about the set deepens: children compare the set of elements by the number of components, divide the set into subsets, establishing dependencies between the whole and its parts, etc.
Based on ideas about set, children form ideas and concepts about numbers and quantities, etc. By mastering the concepts of numbers, the child learns to abstract quantitative relationships from all other features of the elements of the set (size, color, shape). This requires the child to be able to identify individual properties of objects, compare, generalize, and draw conclusions.
The formation of concepts about size is closely related to the development of numerical concepts in children. The formation of estimates of size and knowledge about number has a positive effect on the formation of knowledge about the shape of objects (a square has 4 sides, all sides are equal, and a rectangle has only opposite sides, etc.).
In to school age basic mathematical concepts are introduced descriptively. Thus, when becoming familiar with numbers, children practice counting specific objects, real and drawn (counting girls and boys, bunnies and foxes, circles and squares), and at the same time become familiar with the simplest geometric figures, without any definitions or even descriptions these concepts. In the same way, children learn the concepts: more, less; one two Three; first, second, last etc.
Each concept is introduced visually, through contemplation of specific objects or practical operation of them.
During the period of preschool childhood, as noted by N.N. Poddyakov, A.A. Stolyar and others, there is a fairly extensive area of “pre-conceptual”, “everyday” concepts. The content of “everyday” concepts is very vague, diffuse, it covers a variety of forms that precede real concepts. Nevertheless, “everyday concepts” are important for the child’s mathematical development.
The specific feature of “everyday concepts” is that they are built on the basis of a generalization of the characteristics of objects that are significant from the point of view of any human needs.
catcher, performing various types of practical activities.
Interesting data in this regard were obtained by Z.M. Boguslavskaya (1955), who studied the peculiarities of the formation of generalizations in children of various preschool ages in the process of didactic play. In younger preschoolers, cognitive activity was subordinated to the solution of one or another specific game task and served it. Children learned only the information given to them that was necessary to achieve a certain practical effect in the game. The assimilation of knowledge was of a utilitarian nature. The acquired knowledge was immediately used to complete a given grouping of pictures.
In older preschoolers, cognitive activity in the process of didactic games went beyond the scope of just the direct service of practical tasks, losing its purely empirical character, and appeared in the form of extensive meaningful activity with characteristic specific methods of implementation. As a result, the ideas and concepts formed in children quite fully and adequately reflected a certain circle of phenomena.
Another direction in teaching preschoolers mathematics is to familiarize them with a number of mathematical dependencies and relationships. For example, children understand some relationships between objective sets (equal numbers - unequal numbers), the order relation in the natural series, time relations; dependencies between the properties of geometric figures, between magnitude ,measure and measurement result, etc.
Particular attention should be paid to the requirements for the formation of certain mathematical actions in children: applying, applying, recalculating, counting, measuring, etc. It is the mastery of actions that has the greatest impact on development.
The methodology distinguishes two groups of mathematical actions:
basic: counting, measurement, calculations;
additional: propaedeutic, designed for didactic purposes; practical comparison, imposition, application (A.M. Leushina); equalization and acquisition; comparison (V.V. Davydov, N.I. Nepomnyashchaya).
As we see, the content of “pre-mathematics” preparation in kindergarten has its own characteristics. They are explained by: the specifics of mathematical concepts;
traditions in teaching preschoolers; the requirements of a modern school for the mathematical development of children (A.A. Stolyar).
The educational material is programmed so that, based on what has already been learned, more simple knowledge and new methods of activity were formed in children, which in turn will act as a prerequisite for the development of complex knowledge and skills, etc.
In the process of learning, along with the formation of practical actions in children, cognitive (mental) actions are also formed, which the child cannot master without the help of adults. It is mental actions that play the leading role, since the object of knowledge in mathematics is hidden quantitative relationships, algorithms, and relationships.
The entire process of forming the elements of mathematics is directly related to the assimilation of special terminology. The word makes the concept meaningful, leads to generalizations, to abstraction.
A special place in the implementation of educational content (program objectives) is occupied by the planning of educational work in the classroom and outside of it in the form of a long-term and calendar plan. Significant assistance in the work of the teacher can be provided by indicative long-term plans; plans-notes of lessons in mathematics. The teacher should use these plans and notes as indicative ones, and their content should be constantly compared with the level of mathematical development of children of this group.
The lesson plan for mathematics includes the following structural components: topic of the lesson; program objectives (goals); activation of children's vocabulary; didactic material; course of the lesson (methodological techniques, their use in different parts of the lesson), summary.
The teacher conducts classes in accordance with the plan. Each lesson, regardless of its duration and form, is an organizationally, logically and psychologically complete whole. The organizational integrity and completeness of the lesson lies in the fact that it begins and ends at a clearly designated time.
Logical integrity lies in the content of the lesson, in logical transitions from one part of the lesson to another.
Psychological integrity is characterized by achieving a goal, a feeling of satisfaction, and the desire to continue working further.
Self-test exercises
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In the process of teaching children... their..., in particular mathematical, development takes place.
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In the preschool period, children master a fairly large volume of... concepts, acquire practical and... skills.
The content of education is considered in the methodology... of children's development primarily as... leading to the accumulation of knowledge, skills and to those internal changes that constitute... the basis of development. In choosing the specific content of education... the teacher should focus on A program... and education of children, reflecting... the standard of knowledge of preschoolers and their actual level in this group.
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Voronina, Lyudmila Valentinovna. Mathematical education during preschool childhood: design methodology: dissertation... Doctor of Pedagogical Sciences: 13.00.02 / Voronina Lyudmila Valentinovna; [Protection location: Lv. state ped. University].- Ekaterinburg, 2011.- 437 p.: ill. RSL OD, 71 12-13/88
Introduction
Chapter I. Theoretical foundations of mathematical education during preschool childhood 26
1.1. Genesis of ideas formation mathematical representations in preschool children 26
1.2. Trends in the development of mathematical education during preschool childhood in the context of informatization and technologization of society 57
1.3. Mathematics education during preschool childhood in the aspect of universal human culture 103
Conclusions on the first chapter 125
Chapter II. Methodological basis 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. Mathematics education during preschool childhood: concept and design methodology 181
3.1. The concept of culture-forming mathematical education for preschool children 181
3.2. Methodology for designing culture-forming mathematical education during preschool childhood 203
3.3. Project of mathematical education for the period of preschool childhood.. 224
Conclusions on the third chapter 286
Chapter IV. A system of organizational and methodological support for the implementation of a mathematics education project during preschool childhood. 290
4.1. Development of organizational and methodological support for the implementation of a project on mathematics education for preschool children 290
4.2. Organization and results experimental work 319
4.3. Training preschool teachers in ways to design mathematical education during childhood 345
Conclusions on the fourth chapter 361
Conclusion 364
Bibliography 370
Applications 421
Introduction to the work
Relevance of the study. Modernization of the Russian education system is one of the main directions and conditions for the development of Russian society and the formation of an innovative economy in Russia. This process gives modern education systems such innovative features as dynamism, variability, diversity organizational forms and content. According to the national educational initiative “Our New School”, the main task modern system education is to reveal the abilities of each child, to educate an individual ready for life in a high-tech information society, the main features of which are high level rationalization and algorithmization of activities, ability to use information technology, lifelong learning. Preschool education is the initial link of lifelong education and is aimed at providing conditions for the child’s self-realization and his socialization. Mathematics education in this process is given special role, since mathematics is one of the most significant areas of knowledge for modern society, accumulated and widely used by humanity. Mathematical education is a means of intellectual development of a child, expanding his capabilities. successful adaptation to the processes of informatization of society.
Relevance of the study on socio-pedagogical level caused by the reform of education based on the interaction of 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 to individual self-realization. The process of human education at present can be defined by the formula: from a knowledgeable person to a “man of culture” (V.S. Bibler). In this regard, education from a way of transferring experience to a growing person turns into a mechanism for his development. 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 preschool education system, since, according to many psychologists (L.I. Bozhovich, A.L. Wenger, L.S. Vygotsky, A.V. Zaporozhets, A.N. Leontiev, D.B. Elkonin, etc.), preschool age is the age at which a child not only develops everything intensively. mental functions, but a common foundation is also being laid cognitive abilities, intellectual potential personality, its culture.
Through mathematical education, already in preschool age, the prerequisites for the successful social adaptation of an individual to the accelerating processes of informatization and technologization of society can be laid, the foundations for the necessary to modern man mathematical culture: mathematical education contributes to the development critical thinking, logical rigor and algorithmic thinking, which largely determine the success and effectiveness of a child’s activities in understanding the world outside and inside himself.
Relevance of the study on scientific and methodological level due to the vector of development of the methodology 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 during preschool childhood, which would ensure the interaction of the culture-forming and rational-cognitive components of modern education. An analysis of well-known dissertation works devoted to solving current problems of teaching mathematics to children aged 3-11 years showed that despite the innovative potential of the original approaches and concepts substantiated in these works for the formation of elementary mathematical concepts in young children (V.A. Kozlova), mathematical development preschooler and junior schoolchildren (A.V. Beloshistaya, A.I. Golikov), didactic system of 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 during preschool childhood, which would correspond to the above-mentioned trends.
On scientific and theoretical level The relevance of the study is as follows. The problem of designing mathematical education during 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.), in these theories the issues related to the justification of the structure have not received a holistic scientific understanding and the functions of mathematical education during preschool childhood in the paradigm of education as a mechanism for developing the foundations of a child’s mathematical culture. A conceptual understanding of these theoretical aspects will make it possible to increase the adequacy and adaptability of mathematical education during preschool childhood to the processes of informatization and technologization occurring in society.
On scientific and methodological level the relevance of the problem is related to the need to develop scientific and methodological support for the process of forming the foundations of mathematical culture in children, including those important for life at this age mathematical concepts 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 means of teaching preschoolers mathematics.
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 occurring in society for the full realization by students of their individual inclinations and needs. The success of designing such education is directly related to the solution problems searching for the specific design principles, rules and pedagogical conditions for their implementation necessary for this. The solution to this problem involves understanding the essential characteristics of the mathematical education of preschool children and its patterns.
Analysis of 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 consistent approach to education and its design (E.V. Bondarevskaya, E.D. Visangirieva, B.S. Gershunsky, M. S. Kagan and others). Essence mathematical culture, its functions, development trends, conditions for its formation and the role of mathematical education in the process of its individual appropriation are revealed in the works of G.M. Buldyk, B.V. Gnedenko, D.I. Ikramova, L.D. Kudryavtseva, S.A. Rozanova, A.Ya. Khinchina, V.N. Khudyakova and others.
In general methodological terms, the results of studies of the processes of goal setting and development of educational content, obtained both by foreign (B. Bloom, D. Krathwohl, R. Meijer, A. Romiszowski, etc.) and domestic scientists (Yu. K. Babansky, V.P. Bondarevskaya, E.N. Gusinsky, I.I. Kraevsky, V.S. Lednev, I.Ya. Lerner, M.N. Skatkin, A.V. Various aspects system development goals and content of mathematics education discussed in the works of E.I. Alexandrova, A.V. Beloshistaya, N.Ya. Vilenkina, M.B. Volovich, Kh.Zh. Ganeeva, A.I. Golikova, V.A. Guseva, V.A. Dalinger, G.V. Dorofeeva, V.F. Efimova, N.B. Istomina, Yu.M. Kalyagina, V.A. Kozlova, G.G. Levitas, I.G. Lipatnikova, A.G. Mordkovich, V.M. Monakhova, L.G. Peterson, L.M. Friedman et al.
Mathematics education for preschoolers cannot be considered in isolation from the study of the main trends in the development of education during childhood. Therefore, important guidelines in solving current problems of mathematics education are the works of Ya.A. Komensky, I.G. Pestalozzi, K.D. Ushinsky, V.I. Vodovozov, F. Frebel, M. Montessori, D.L. Volkovsky and others. Invaluable contribution to theory and methodology mathematical training for preschoolers contributed by E.I. Tikheyeva, L.V. Glagoleva, F.N. Bleher, A.M. Leushina, L.S. Metlina, 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.
The 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 discussed in the works of O.B. Episheva, V.E. Radionova, T.K. Smykovskaya et al. Design problem educational technologies covered in the works of V.P. Bespalko, Z.F. Mazura, Yu.K. Chernova and others.
However, despite the undoubted theoretical and practical significance of the presented research, the problem of designing mathematical education for the period of preschool childhood today has not found sufficient scientific justification precisely in the aspect of compliance with modern trends in enhancing the interaction between the culture-forming and rational-cognitive components of education. In pedagogical theory, the conceptual understanding of the structure and functions of preschoolers’ mathematical education is considered in the context of the development of children’s mathematical abilities (A.V. Beloshistaya), but there are no studies devoted to the conceptual understanding of the structure and functions of preschoolers’ mathematical education 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 during preschool childhood to the processes of informatization and technologization occurring in society.
The analysis of the state of the problem of designing mathematical education during preschool childhood allowed us 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, a culture of logical, analytical and algorithmic thinking and the insufficient implementation of the opportunities for the formation of such a culture in the education system of preschool childhood;
– at the scientific and methodological level: between the need to design education during preschool childhood in accordance with modern paradigm interaction between the culture-forming and rational-cognitive tendency of its development and the 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 during 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 theoretical understanding of the structure and functions of mathematical education of preschool children 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 for organization educational process the formation of the foundations of the mathematical culture of preschool children, facilitating their adaptation to life in a modern technologized society, and the lack of development of scientific and methodological support for this process.
The listed contradictions made it possible to clarify the boundaries research problems, which consists in a conceptual understanding of the structure and functions of mathematical education for preschool children 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 requirements strengthening the interaction between the culture-forming and rational-cognitive components of education.
The identified contradictions and the formulated research problem made it possible to determine topic research“Mathematics education during preschool childhood: design methodology.”
Purpose of the study consists of scientific substantiation and development of a methodology for designing mathematical education during preschool childhood in the conditions of interaction between culture-forming and rational-cognitive trends in the development of education.
Object research– the process of preschool education.
Item research– methodology for designing culture-forming mathematical education during preschool childhood.
Research hypothesis. The process of modernizing mathematics education during preschool childhood will meet modern trends in increasing the adequacy of mathematics education to changes occurring in society if:
1. A methodology for designing mathematical education during childhood will be built
– in accordance with the concept of culture-forming mathematical education developed during 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 during preschool childhood, taking into account the stages of development children's thinking, the relationship between gaming and cognitive activity, taking into account the adequacy and adaptability of mathematical education to changes occurring in society, the correspondence of the design algorithm to the algorithms for the functioning and management of the process of teaching and upbringing of preschool children who meet specific patterns: dependence of design on the harmonious 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 during preschool childhood will be the following:
mathematical education has an untapped potential for realizing its adaptive function to the processes of informatization and technologization developing in society and therefore is a necessary component of the process of forming the culture of a growing person;
the core of the concept consists of a system meaning-forming categories and concepts, such as “mathematical education in the period of preschool childhood”, “mathematical culture of a preschool child”, “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 child’s mathematical activity into his independent activity based on the inclusion in the goals, content and forms of mathematical education of an adaptation component associated with the need for the child’s social adaptation 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 mathematics education on the structuring of content, selection of methods, forms and means of education and training in accordance with the age capabilities of children; dependence of the quality of mathematical education on the provision of subject cognitive activity 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 and play activity of a preschool child and the appropriate methods of its organization;
a necessary condition for the functioning of the mathematics education system is the 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 mathematics education that corresponds to modern trends in strengthening the interaction between the culture-forming and rational-cognitive components of education.
The problem, goal, object and subject of the study determined the solution to a number of research objectives:
1. Analyze historical aspects theories and methods of teaching mathematics during childhood in the context of universal human culture in order to determine the main characteristics of the current state of mathematical education during childhood and clarify the structural components of the mathematical culture of a preschool child.
2. Determine the methodological foundations of pedagogical design: conduct a historical and philosophical analysis of the design problem, clarify the essence, structure, content and methodological approaches to pedagogical design.
3. To develop the concept of culture-forming mathematical education during preschool childhood, to substantiate the methodology for designing mathematical education during preschool childhood, and to design mathematical education during preschool childhood, aimed at adapting children to the processes of informatization and technologization occurring in society.
4. Develop organizational and methodological support for the implementation of a project for mathematics education during preschool childhood and conduct its testing.
Methodological basis of the study. The general research methodology is based on the fundamental ideas of philosophical anthropology about man and his upbringing, about nature and essence human activity, its expediency and creative nature; on the basic principles of dialectics - objectivity, development and interaction; on the main positions of systemology (P.K. Anokhin, V.G. Afanasyev, L. Von Bertalanffy, I.V. Blauberg, A.A. Bogdanov, V.P. Kuzmin, V.G. Sadovsky, A.I. Subetto, U.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, etc.); on the basis of structural modeling (M. Wartofsky, J. Van Gigh, A.I. Uemov, V.A. Shtof, G.P. Shchedrovitsky, W.R. Ashby, etc.).
The methodological guidelines for the study were: systemic approach(A.N. Averyanov, V.G. Afanasyev, I.V. Blauberg, A.I. Uemov, E.G. Yudin, etc.), according to which mathematical education during preschool childhood is considered as a pedagogical system; synergistic approach(A.I. Bochkarev, Y.S. Brodsky, V.G. Vinenko, Y.S. Manuilov, N.M. Talanchuk, etc.), which places emphasis 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 involves relying 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. Leontyev, R.Kh. Shakurov, etc.), which allows you to select from the sphere of humanitarian culture the content with the help of which the child’s system will be formed mathematical knowledge, skills, as well as a set of values, the common basis of which is the internationally recognized values of mathematical education; person-centered approach(E.V. Bondarevskaya, O.S. Gazman, V.V. Serikov, D.I. Feldshtein, I.S. Yakimanskaya, etc.), which reflects the main guideline of the humanistic paradigm: the 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, etc.), transforming the understanding of the quality of education, which should not be determined by the measure of the child’s mastery of the things offered to him training programs mathematical knowledge, abilities 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 mathematics 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, etc.), axiology theory, suggesting the need to search value orientations in the 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, etc.), concept of humanization and humanization of education(E.D. Dneprov, V.P. Zinchenko, B.M. Nemensky, A.V. Petrovsky, V.V. Serikov, G.I. Sarantsev, etc.), 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, etc.), theory of educational content(B.S. Gershunsky, V.V. Kraevsky, V.S. Lednev, I.Ya. Lerner, etc.), 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, A.M. Leushina, L.G. amplification theory child development and the idea of the special importance of “specifically children’s” types of activities in the development of a preschooler (A.V. Zaporozhets), the idea of self-worth of preschool childhood as the period of formation of the foundations of the child’s further development (L.S. Vygotsky, A.V. Zaporozhets, L.V. Kolomiychenko, V.T. Kudryavtsev, G.P. Novikova, L.V. Trubaychuk, D.I. Feldshtein and etc.), ideas for integration into 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 essential 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 complex of theoretical and empirical methods. Theoretical methods : logical-historical analysis was used to identify progressive trends in the history of domestic 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 organize the conceptual apparatus of the study; modeling and design were used to structure the design process and present its results; forecasting was used to substantiate the prospects for the development of mathematics education during preschool childhood; analysis, synthesis and synthesis were used in the process of justifying and presenting the research results. Empirical methods : study of regulatory documents in the field of education, research and synthesis effective experience and mass practice of mathematical training of preschoolers, observation (external, included, standardized and other types), questioning and testing - were used at the search and orientation stage of the experimental work in order to identify the problem and research topic; at the theoretical-technological and experimental-search stages, questionnaires, testing and the method of expert assessments made it possible to confirm the results of the study; at the final generalizing stage we used qualitative methods diagnostics with elements of qualimetric analysis and statistical method processing the results.
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 in Yekaterinburg and Sverdlovsk region.
The study consisted of several interrelated stages.
On first stage(1995-1999) – search and orientation – study and analysis of the current state of the research problem was carried out; the literature on research methodology, pedagogy, psychology, and pedagogical design was studied and systematized; the key positions of the study and its conceptual and categorical apparatus were determined.
Second stage(2000-2003) – theoretical and technological – was devoted to the theoretical and methodological development of the concept of mathematical education for preschool children based on systemic, synergetic, axiological, cultural, personality-oriented and activity-based approaches.
On third stage(2004-2007) – experimental research – work was carried out to practically test the provisions of the research hypothesis, the main ideas of the methodology for designing mathematical education in the preschool period were clarified, monographs and textbooks were written to prepare students and specialists for the implementation of the main ideas of the developed concept mathematical education during preschool childhood.
Fourth stage(2008-2010) – final and generalizing – included final processing of the results obtained, implementation of the developed project for mathematical education of preschool children into practice preschool work, the dissertation research was completed.
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 preschool childhood is built: the general scientific basis is the systemic and synergetic approaches; the theoretical and methodological strategy is determined by cultural and axiological approaches; Practice-oriented tactics are person-oriented and activity-based approaches.
2. Specific patterns have been identified
design process mathematical education of the preschool childhood period: the dependence of design on the harmonious 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 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 mathematics education on the structuring of content, selection of methods, forms and means in accordance with the age capabilities of children; the dependence of the quality of mathematical education on ensuring the 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 and play activity of a preschool child and the appropriate methods of its organization.
3. The principles on the basis of which mathematical education is designed during preschool childhood are formulated: harmonization of the components of mathematical education during 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 occurring in society, the correspondence of the algorithm designing mathematical education for preschoolers and algorithms of the educational process.
4. A concept of culture-forming mathematical education during 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 laws of mathematics education corresponding to the structural components of the child’s mathematical culture being formed, the core of this concept is meaning-forming categories and concepts.
5. The structure of mathematical education for preschool children has been developed, ensuring the integration of the child’s mathematical activity into his independent activity based on the inclusion in the goals, content and forms of mathematical education of an adaptation component associated with the need for the child’s social adaptation to the processes of technologization and informatization of society.
6. A theoretical model of the content of mathematics education during preschool childhood has been developed. The model includes: sources of mathematical education, principles for selecting content (general: scientific, systematic, continuity, visibility, accessibility - and specific: integrity of the picture of the world, integrativeness, activity orientation), general didactic and specific 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 its conclusions:
deepen the understanding of mathematical education in the period of preschool childhood, reveal its functions (adaptation, cultural, developmental, prognostic), structure (teachers and children, patterns and principles, goals and content, processes of education and training with appropriate methods, means and organizational forms), goals (formation of the foundations of mathematical culture in preschoolers), content (arithmetic, algebraic, algorithmic, geometric concepts, the concept of quantities), adaptation component (in the structure of the content it is expressed through the allocation of an algorithmic line, and within the framework of organizational forms - through various types of games, regime points connecting algorithmic and practical activities) in the educational paradigm as a mechanism for developing the foundations of a child’s mathematical culture;
enrich pedagogical theory in terms of the conceptual and terminological apparatus by clarifying the basic concepts for research: “methodology for designing mathematical education during preschool childhood,” “mathematical education during preschool childhood,” “designing mathematical education during preschool childhood,” “mathematical culture of a preschool child”;
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. Developed in process dissertation work organizational and methodological support for the project (monographs, educational, methodological manuals, etc.) is used to increase the scientific and methodological level of work organization methodological associations 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 research, proprietary 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 mathematics education (lecture plans, methodological instructions, programs and content of special courses) are used in the course training of teachers.
5. Based on the dissertation materials, innovative educational activities were organized in preschool educational institutions of the Sverdlovsk region. Innovative results that have been tested can be transmitted to institutions of preschool, secondary and higher pedagogical education in Russia.
Reliability and validity of the conclusions obtained in the dissertation are provided by relying on the methodology of the theory universal human values in determining the starting points, by synthesizing philosophical and psychological-pedagogical approaches in substantiating leading ideas; implementation of systemic, axiological, cultural, personality-oriented and activity-based 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 assessing the results of the process in the education system; complete implementation of theoretical research into practical activities; the applicability of ideas, concepts and models in preschool institutions; reproducibility of the results obtained in mass practice.
Results and conclusions of the study have applied significance for the activities of state and socio-political organizations involved in solving 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) during the pedagogical activity of the dissertation candidate as an associate professor of the department of mathematics and methods of teaching it in the primary grades of the USPU through the implementation of developed lecture courses “Theory and methodology of mathematical development of preschool children”, “Methodology of teaching mathematics in primary school”, “Theoretical foundations of mathematical education” during childhood”, special courses “Logical training in preschool educational institutions”, “Continuity and prospects in teaching mathematics”, “Designing mathematical education during childhood”.
Implementation of research results. The results obtained during 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 (Sverdlovsk region). Berezovsky, Kamensk-Uralsky, Sysert, Rezh, etc.). The implementation of the results was also carried out during the author’s teaching activities at the State Educational Institution of Higher Professional Education “Ural State Pedagogical University” at lectures, seminars, practical classes, in the process teaching practice, reading special courses; in the process of cooperation with the Faculty of Advanced Training of Education Workers of the USPU; in the process of cooperation with the Institute for the Development of Regional Education of the Sverdlovsk Region; in the process of cooperation with the State Educational Institution of Higher Professional Education "Shadrinsk State pedagogical institute"; while working as part of the coordinating council on the problems of preschool and primary education at the Institute of Pedagogy and Psychology of Childhood, Ural State Pedagogical University, Yekaterinburg; within the framework of the comprehensive research program of the Ural Branch of RAO “Education in the Ural region: scientific foundations of development and innovation”, project 1.1.14 “Designing an innovative model of mathematical education during childhood”, the implementation area of which is the Greater Urals.
The following provisions are submitted for defense:
1. The development of mathematical education in the preschool period is determined by the design methodology based on the following patterns:
– the effectiveness of designing a mathematical education system during preschool childhood depends on the harmonious reflection in the project of all components of mathematical education 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 designing mathematical education during preschool childhood is determined by the accuracy of taking into account the following factors: the stages of development of a child’s thinking - from visual-actional through visual-figurative to verbal-logical, the specifics of the relationship between the play 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 during preschool childhood is determined by the degree to which the adequacy and adaptability of mathematical education to the processes of informatization and technologization taking place in modern society is taken into account;
– the effectiveness of designing mathematical education during 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 raising preschool children.
2. The design of mathematical education during preschool childhood is carried out taking into account a set of principles:
– harmonization of the components of mathematical education during preschool childhood;
– taking into account the stages of development of children's thinking;
– relationships between gaming and cognitive activities;
– taking into account the adequacy and adaptability of mathematical education to changes occurring in society;
– correspondence of the algorithm for designing mathematical education to the algorithms for functioning and managing the process of teaching and raising preschool children.
3. The leading ideas of the concept of culture-forming mathematical education during preschool childhood are the following:
mathematical education in the period of preschool childhood has the potential of an adaptive function to the processes of informatization and technologization occurring 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 of the period of preschool childhood: “mathematical education of the period of preschool childhood”, “mathematical culture of a preschool child”, “formation of the mathematical culture of a preschool child”, “ designing mathematical education during preschool childhood”;
based on the inclusion of an adaptation component in the goals, content and forms of mathematical education, mathematical education during 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 preschool period is built taking into account the following patterns:
the effectiveness of mathematics education depends on the degree of compliance of the structure and content of training with the main trends in the development of society in the current period, primarily the processes of informatization and technologization, and the learning results depend on the degree of inclusion of mathematical knowledge and skills in the process of adaptation of 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 results depend not 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 mathematics 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 forming the foundations of mathematical culture in children depends on the extent to which the methods used for organizing cognitive and play activities 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 a child and the implementation of the adaptive function of mathematical education during 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 mathematics education, corresponding to modern trends in strengthening the interaction of the culture-forming and rational-cognitive components of education, is a necessary condition for the functioning of the mathematics education system.
Work structure. The work consists of an introduction, four chapters, a conclusion, a list of references, including 591 titles, and 3 appendices. The volume of the dissertation is 420 pages of text (without appendices), illustrated with 15 tables, 6 drawings.
Trends in the development of mathematical education during preschool childhood in the context of informatization and technologization of society
Currently, various terms are used to denote the process of teaching preschoolers mathematics: “formation of elementary mathematical concepts”, “mathematical development”, “mathematical preparation”. The first two concepts in pedagogical and methodological literature are defined as follows: - the formation of elementary mathematical concepts is a purposeful and organized process transfer and assimilation of knowledge, techniques and methods of mental activity provided for by program requirements; - mathematical development of preschoolers is qualitative changes in the cognitive activity of the individual, occurring as a result of mastering mathematical concepts and related logical operations.
Special definitions - concepts We didn’t find mathematical preparation, so we derived it ourselves, using the definitions of the concepts “preparation” and “prepare” given in the “Explanatory Dictionary of the Russian Language”: “Preparation - 1) prepare; 2) a stock of knowledge acquired by someone (the student has good preparation)”; “Prepare - 1) do something in advance for the device; organizing something (preparing material for work); 2) teach, give necessary knowledge for something (to prepare a student for exams)." From these definitions we obtain that the mathematical preparation of preschoolers can be understood as the stock of necessary mathematical knowledge acquired by a preschool child for further education at school.
However, in modern conditions, neither the formation of elementary mathematical concepts, nor mathematical development, nor mathematical training are capable of realizing the main goal of education, noted in the federal state requirements to the structure of the basic general education program of preschool education, namely the focus on the formation general culture, ensuring social success and success in school education, 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 integral and essential integral part human culture, it is the key to understanding the world around us, the basis of scientific and technological progress and an important component personality development. Mathematical education is a benefit to which every person has the right and the responsibility of society (the state and the world) organizational structures) provide every individual with the opportunity to exercise this right.
Mathematics education has a special role, since mathematics forms a culture of thinking and is an indispensable tool that promotes the development of such personality traits as the ability for critical thinking, logical rigor and algorithmic thinking; the ability to abstract, which largely determine the success and effectiveness of a child’s activities in understanding the world outside and within 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 technology development, the transformation of information into the most important global resource humanity. These factors lead to deep, multi-level changes social system, changing the environment under the influence of which the personality changes”, and, consequently, changing 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, and 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 from the entire sociocultural 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 to the education system. And as rightly noted by I.G. Ovchinnikov, “one of the priority directions in the process of informatization of modern society is the informatization of education. ... Informatization of education requires improving the methodology and strategy for selecting the content, methods and organizational forms of training and education that correspond to the tasks of developing the student’s personality 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 also occurs, which also has an impact great influence for transformations in the field of education. These transformations are reflected in the Federal Law “On Education”, “Concept of Modernization national education for the period until 2010" and, as noted by many researchers (V.I. Bidenko, G.B. Kornetov, A.N. Novikov, L.G. Semushina, Yu.G. Tatur, etc.), mean the process of change educational paradigm.
The structure and content of education today do not correspond to the structures modern culture and human activity and is unable to ensure its main purpose - an adequate reflection and effective appropriation of human experience (culture). According to H.G. Tha-Gapsoev, of the three forms of “spiritual objectivity” - knowledge, value and project (M.S. Kagan), only one is properly reflected in the educational space - knowledge.
Methodological approaches to the problem of pedagogical design
To identify the features of designing mathematical education during preschool childhood, it is necessary to reveal historical background the formation of pedagogical design, as well as philosophical approaches that have methodological significance, and analyze them in order to identify the theoretical foundations of the study.
In the scientific literature, the history of the development of design is considered in two directions: the development of design as a special type of activity and as a branch of scientific knowledge.
J. K. Jones reveals four stages in the development of design as a special type of activity.
The first stage begins during the formation of craft production and crafts, when the necessary changes were made on the product itself by trial and error.
The second stage in the development of design includes the emergence of the drawing method of designing craft products, when changes were made already in 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 the evolution of the built environment. At this stage, there was a need for the training of professional designers and the need for new design methods. BUT. Yakovleva identifies three periods of development of design as a branch of scientific knowledge. In the first period (from antiquity to the 20s of the XX century), design becomes an independent species activity, its ideology is formed, and methods are developed. The second period (20-50s of the XX century) is characterized by the fact that design became the subject of special scientific research. In the third period (from the 50s of the 20th century to the present time), design spreads from the technical field to the social sciences, including pedagogy. Let's look at these periods in more detail.
The longest period is the first: 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.
Almost from the very beginning of his conscious activity, man was in one way or another 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 to implement the project were not separated from each other, but 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 old forms and rules of design activity. Only towards the end of the Middle Ages did economic design begin to develop, characterized by the division of the economic enterprise system into business operations, based on the functioning of capital. Subsequently, economic design turns into organizational design, which is mainly associated with the growing activity of connecting various production organizations.
Note that these design modifications were the result long-term development practical human activity and improving social relations, but were almost not associated with scientific research. It was only during the Renaissance that science began to penetrate the craft.
This, in turn, influenced the development of technical design as an independent field of activity. The designer ceased to be a manufacturer: when designing a product, he practically did not turn to the object, but used layouts, diagrams, engineering knowledge, etc. as tools.
Methods for scientific solution of technical problems were generally formed by the 18th century, the first technical educational institutions, appeared specialized literature. V.F. Sidorenko notes that design has become “the main way of existence of a person of the new era,” and 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 mass production process into its component parts, to eliminate as much as possible manual labor worker. These processes were accompanied by the emergence of science as an institution of public life. By the end of the 19th century. in design, a new form has emerged - morphological design, where the basic understanding of the project as a certain sample, a bearer of one or another function, for which the material and appearance. Its logical development was functional design. This type of design has been reoriented towards modeling human life processes, working conditions, methods of movement, etc.
The ideas of planning long-term changes and the processes of 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” by V.F. Odoevsky, draft Regulations for Moscow gymnasiums M.V. Lomonosov and others. These projects were designed to form flawlessly educated people(J.-J. Rousseau), lead the student onto the road along which he can gradually reach conscious concepts from unconscious ones (V.F. Odoevsky), etc.
At the end of the 19th century. The Russian Technical Society prepared the “Draft of a 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 projects late XIX- the beginning of the 20th century, distinguishes them common features, such as: 1) awareness of the need for reform high 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 when developing projects; 3) study of world experience in setting up secondary education; 4) the desire to create a unified school while maintaining classical education; 5) search for the optimal balance of humanities and natural sciences in the content of secondary education.
Methodology for designing culture-forming mathematical education during preschool childhood
Currently, a synergetic 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 of various natures. Since the pedagogical system is a complex open system, the laws of synergetics can be applied to it.
N.M. Talanchuk identifies the following 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 for the development of all pedagogical systems, and not contradictions, struggle and not the negation of negation; 4) pedagogy is the science of systemic 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-synergistic philosophy of life.
From a synergetic point of view, the future determines the present. Consequently, the main task of modeling and prediction is to determine possible development paths for complex systems. The control force should not be energetic, but correctly topologically organized. Weak, but properly organized, so-called resonant influences 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 the 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, a turning point in the development of the system occurs - a bifurcation point - two or more development paths arise, and the system finds itself in a state of choice. The process of transition from equilibrium conditions to highly nonequilibrium conditions is a transition “from the repetitive and general to the unique and specific.”
V.I; Arshinov notes that “synergetics as a new interdisciplinary direction focuses on the main, key features of the paradigm post-non-classical science, conditioned, first of all, by 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 beginning. In this capacity, chaos in the paradigm of post-non-classical science is conceptualized as a necessary creative moment of the overall picture of an emerging, self-organizing reality."
The use of a synergetic approach in pedagogical design of education causes a shift in emphasis from the entrenched linear, deterministic approach, from the study of system invariants to research special conditions especially complex open systems in the region of unstable equilibrium, or more precisely, the dynamics of their self-organization near bifurcation points, when even a small impact can lead to unpredictable, rapid development of the process.
The synergetic approach provides 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, self-organizing system. It is necessary to study the processes of interaction between subjects of the educational process, identify trends, mechanisms and internal reserves for the development of the system, outline ways and means of improving and updating both the system as a whole and its individual subsystems in the interests of improving the process that interests us. At the same time, we consider it very important that the future state of the system coincides with the trajectory of its reaching the optimal level of its evolution.
One of the promising areas for improving the content of education is problematic, and in lately problem-modular approach (M.A. Choshanov, P.A. Jutsevichene, N.B. Lavrentieva, etc.), which is focused on the development of completed training modules.
In problem-modular design of educational content M.A. Choshanov identifies the following stages: layout of the course around fundamental methods of cognitive activity, such as the method of mathematical modeling, the axiomatic method, the coordinate method, the vector method, etc.; determining the content of basic problem modules, while it is necessary to take into account the criteria for basic content” (fundamentality, generalization, continuity, continuity and humanitarization of education); highlighting professional and applied integrated 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 of the problem-modular program.
Modular programs and modules are built in accordance with the following general principles(according to I.A. Yutsyevichene): 1) the intended purpose of the information material; 2) combinations of complex, integrating and private didactic goals; 3) completeness of the educational material in the module; 4) relative independence of module elements; 5) implementation of feedback; 6) optimal transfer of information and methodological material.
The principle of the intended purpose of information material indicates that the content of the information bank is based on didactic purposes. If it is necessary to achieve cognitive goals, the information bank is built on an epistemological basis, and to achieve activity goals, an operational approach to building an information bank is used.
The principle of combining complex, integrating and private didactic goals is implemented in determining the structure of modular programs and individual modules. The complex didactic goal represents 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 private didactic goals. Particular goals can be completely autonomous or interconnected.
The principle of completeness of educational material in a module specifies the principle of modularity and reveals the following rules: 1) outlines the main points of the educational material, its essence; 2) explanations are given (possibly at several levels) to this material; 3) opportunities for additional depth in the material or its extended study through the use of TSO and teaching methods are indicated; 4) practical problems and explanations for their solution are presented; 5) theoretical and practical tasks are given and answers to them are given.
Training preschool teachers in ways to design mathematical education during childhood
The organization of mathematical education of preschool children 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 systemic mathematical knowledge itself. The organization of systematic mathematical knowledge is carried out by integrating the child’s mathematical activity into his independent activity, as well as by focusing the content of education on the personal meaning of learning, on the development of reflexive consciousness.
Various sources were analyzed to compile the program. In mathematical education, we have identified 5 content lines: arithmetic, algebraic, geometric, magnitude and algorithmic. These lines are considered not only in the process of forming elementary mathematical concepts, but also in the depths of the activity that best contributes to this, that is, the child’s mathematical activity is integrated into his independent activity. Thus, mathematical education is built on the basis of the “series-parallel” use of cognitive, gaming, subject-practical and speech activity child, 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 the lives of other people, and mathematics and the natural environment.
Let us reveal the approximate content of mathematical education for preschool children, the main goal of which is to form the foundations of a mathematical culture in children.
Within the framework of arithmetic and algebraic content lines, the concepts of “set”, “number”, “counting”, comparison of numbers, equalities, inequalities, arithmetic operations(addition and subtraction), solution arithmetic problems.
Plenty. Classifying objects around the child according to two or more characteristics (color, shape, size); combining subsets into a single set, adding, removing part(s) from the set; the formation of ideas that a set consists of subsets (family - dad, mom, child, grandfather, grandmother, etc.); comparison of the number of sets by establishing a one-to-one correspondence between their elements; the formation of methods of ordering (ascending, descending, location in space) of many objects and the formation of awareness of the importance of order, harmony of objects surrounding the child; establishing connections between single and multiple parts of the body and their significance for the child’s life; the formation of ideas that an integral natural object is represented by many 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, shrubs, trees) differ from each other in quantity (many and one).
Number and counting. Formation of ideas about number and figure as a sign for writing a number; teaching counting, forming ideas about different methods of counting depending on subject and sociocultural certainty; formation of the basic properties of the natural series of numbers; familiarization with universal human culture through familiarization with: in various ways records of numbers in ancient times and at the present time, their use in games, cognitive activities and in everyday life, with the history of the origin of money and its name, with the design of some calculating devices; developing the ability to count objects surrounding the child or used by him in play, sounds, movements; ability to compare (equal in age, unequal in height, hair color, etc.), comparing parts and wholes 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 the ability to write down the relationships between the objects in question using the signs, =; formation of ideas about equality and inequality; formation of ideas about the operations of addition and subtraction.
Tasks. Formation of experience in translating the system of real relationships between people into mathematical language, familiarization with the structural parts of the problem, developing the ability to solve addition and subtraction problems.
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 spatial orientation in space and on the plane.
Geometric shapes. Formation of ideas about a point, straight line, segment, ray, angle, circle, oval, triangle, square, rectangle, quadrangle, polygon, cube, cone, pyramid, ball and the ability to find these figures in toys and objects surrounding the child, the ability to establish correspondences between figures and parts own body; familiarization with the elements of figures; developing the ability to model figures from sticks, wire, rope, etc.; familiarization with tools and the formation of ideas about their purpose and value in educational, construction and engineering, sewing and other types of activities; learning how to construct a segment, rectangle, square, circle, etc. on a plane; comparison and modification of figures; developing the ability to identify geometric shapes in complex natural objects, to see and find symmetry in natural objects; the formation of methods for isolating figures from natural diversity and establishing correspondence between a figure and an integral natural object; the formation of ideas about the immutability and constancy of geometric figures used by artists, architects, scientists to reflect objects of the surrounding reality.
Orientation in space. Formation of ideas about one’s location in space relative to various reference points and methods of location recognition (visual, tactile, auditory); the formation of ideas about the presence of socio-cultural standards that determine a unified order; formation of the ability to navigate a small area (sheet of paper, table surface), as well as indoors, on the street, in the city and to be aware of one’s location and significance in a specific space, formation of the ability to establish a connection between one’s location in space and emotional state, desires and needs ( sociocultural and physical), operating conditions; the formation of ideas about the constant change of space by people, that relationships in space are regulated by rules ( traffic, etiquette, etc.), signs (permitting, warning, prohibiting, etc.); the formation of ideas about the vertical and horizontal construction of buildings, experience in creating culturally compatible space vertically and horizontally; developing the ability to model spatial relationships using diagrams and plans; formation of an 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, and the use of various means for orientation in space.
One of the most important tasks raising a child preschool age - this is the development of his mind, the formation of such thinking skills and abilities that make it easy to learn new things.
For a 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, and to independently find the right solution.
It is mathematics that sharpens a child’s mind, develops flexibility of thinking, teaches logic, forms memory, attention, imagination, and speech.
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Modern approaches to organizing the formation of mathematical concepts of preschoolers in accordance with the requirements of the Federal State Educational Standard for Education.
“The further path of mathematical development and the success of a child’s advancement in this area of knowledge largely depend on how elementary mathematical concepts are laid down” L.A. Wenger
One of the most important tasksraising a preschool child- this is the development of his mind, the formation of such thinking skills and abilities that make it easy to learn new things.
For a modern educational systemproblem 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, and to independently find the right solution.
It's mathematicssharpens the child’s mind, develops flexibility of thinking, teaches logic, forms memory, attention, imagination, speech.
The Federal State Educational Standard for Education requires the process of mastering elementary mathematical concepts to be completedattractive, unobtrusive, joyful.
In accordance with the Federal State Educational Standard for Preschool Education, the main goals of the mathematical development of preschool children are:
- Development of logical and mathematical ideas about the mathematical properties and relationships of objects (specific quantities, numbers, geometric figures, dependencies, patterns);
- Development of sensory, subject-effective ways of knowing mathematical properties and relationships: examination, comparison, grouping, ordering, partitioning);
- Children's mastery of experimental and research methods of learning mathematical content (experimentation, modeling, transformation);
- Development in children of logical ways of knowing mathematical properties and relationships (analysis, abstraction, negation, comparison, classification);
- Children's mastery of mathematical ways of understanding reality: counting, measurement, simple calculations;
- Development of intellectual and creative manifestations of children: resourcefulness, ingenuity, guesswork, ingenuity, desire to find non-standard solutions;
- Development of accurate, reasoned and demonstrative speech, enrichment of the child’s vocabulary;
- Development of children's initiative and activity.
Target guidelines for the formation of elementary mathematical concepts:
Mathematical development of preschoolers– positive changes in the cognitive sphere of the individual that occur as a result of mastering mathematical concepts and related logical operations.
Formation of elementary mathematical conceptsis 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 successful mastery of mathematics at school, but also comprehensive development children.
Mathematics education for preschoolersis a purposeful process of teaching elementary mathematical concepts and ways of understanding mathematical reality in preschool institutions and the family, the purpose of which is to cultivate a culture of thinking and the mathematical development of the child.
How to “awaken” a child’s cognitive interest?
Answers: novelty, unusualness, surprise, inconsistency with previous ideas.
That is, it needs to be donelearning in an entertaining way. With entertaining learning, emotional and mental processes are intensified, forcing you to observe, compare,reason, argue, prove the correctness of the actions performed.
The adult's task is to maintain the child's interest!
Today, the teacher needs to structure educational activities in kindergarten in such a way that every child is actively and enthusiastically engaged.When offering children tasks with mathematical content, it is necessary to take into account that their individual abilities and preferences will be different and therefore children’s mastery of mathematical content is of a purely individual nature.
Mastering mathematical concepts will only be effective and efficient when children do not see that they are being taught something. They think they are just playing. Unbeknownst to oneself, during game actions with game material, one counts, adds, subtracts, and solves logical problems.
The possibilities for organizing such activities are expanded provided that a developing subject-spatial environment is created in the kindergarten group. After alla properly organized subject-spatial environment allows every childfind something you like, believe in your strengths and abilities, learn to interact with teachers and peers, understand and evaluate feelings and actions, and justify your conclusions.
Teachers are helped to use an integrated approach in all types of activities by the presence of entertaining material in each kindergarten group, namely card files with a selection of mathematical riddles, funny poems, mathematical proverbs and sayings, counting rhymes, logical problems, joke problems, mathematical fairy tales.(photo) Entertaining in content, aimed at developing attention, memory, and imagination, these materials stimulate children's display of cognitive interest. Naturally, success can be ensured provided personality-oriented interaction of the child with adults and other children.
Thus, puzzles are useful for consolidating ideas about geometric shapes and their transformation. Riddles, tasks - jokes are appropriate during learning to solve arithmetic problems, operations with numbers, and when forming ideas about time.Children are very active in the perception of tasks - jokes, puzzles, logical exercises. The child is interested in the final goal: adding, finding the right shape, transforming - which captivates him.
Experience of preschool education
In 2015-2016 academic year In our preschool educational institution, work continues on the formation of the cognitive interests of preschoolers through educational mathematical games and the creation of a developing subject-spatial environment for the formation of mathematical concepts in accordance with the Federal State Educational Standard for Preschool Education.
Particular attention is paidmedium saturation –The educational space must be equipped with teaching and educational means (including technical ones). So, in kindergarten we werevariousmodern educational games: constructors – Polikarpov constructor, plot constructor “Transport”, “City”, “Castle”, TIKO constructor “Balls”, “Geometry”, mathematical tablet, arithmetic counting, logical pyramids “Colored Columns”,"Learning to count" with numbers, logical dominoes, labyrinths,wooden building sets "Tomik",counting material “Geometric figures”,educational games by Voskobovich.
Construction
A tool for developing children’s creative and logical abilities is practical exercises with “TIKO”-constructor for planar and volumetric modeling.In our preschool institution, teachers, enthusiastically working with the TIKO construction set, opened it great opportunities for the mathematical development of children, starting from a young age. When playing with a construction set, a child remembers the names and appearance of planar figures (triangles - equilateral, acute-angled, rectangular), squares, rectangles, rhombuses, trapezoids, etc. Children learn to model objects in the surrounding world and gain social experience. Children develop spatial thinking, they can easily change the color, shape, size of the structure if necessary. Skills and abilities acquired inpreschool period will serve as the foundation for acquiring knowledge and developing abilities at school age. And the most important among these skills is the skill of logical thinking, the ability to “act in the mind.”
Wooden construction sets are convenient didactic material. Multi-colored details help the child not only learn the names of colors and geometric flat and volumetric figures, but also the concepts of “more-less”, “higher-lower”, “wider-narrower”.
For young children, working with a logic pyramid gives them the opportunity to manipulate components and compare them by size using the comparison method. When folding a pyramid, the child not only sees the details, but also feels them with his hands.
Lego
At the end of 2015, we purchased a LEGO Wedo 9580 first robot construction set to work with children of senior preschool age. It is designed for assembling and programming simple LEGO models that connect to a computer. The WeDo designer is based on a proprietary base LegoSystem - bricks with spikes, which modern children, as a rule, become familiar with very early. Sensors and a USB switch have been added to them for connecting to a computer and bringing the created structures to life. Therefore, laptops were purchased for the groups and the appropriate programs were installed. From the constructor you can create different models, both according to Lego’s instructions and by inventing it yourself. In the form of a game, you can get acquainted with various mechanisms and even learn how to design.
We plan to introduce you to this designer 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 allows us to rebuild educational activities into cognitive gaming activities.
There are many educational games by Voskobovich. Among the most common ones in our kindergarten are: “Two-color and four-color squares”, Igrovisor, “Transparent square”, “Geocont”, “Miracle - crosses”, “Miracle flower”, “Cord-entertainer”, “Logo molds", "Carpet "Larchik",Ship "Splash - splash" and others. During the game, the child masters numbers; recognizes and remembers color, shape; trains fine motor skills of the hands; improves thinking, attention, memory, imagination. Games are based on three basic principles - interest, knowledge, creativity. These are not just games - these are fairy tales, intrigues, adventures, funny characters that encourage the child to think and be creative.
To develop children’s mathematical understanding, teachers use another modern form of working with children - iris folding.
Iris folding develops the ability to compare and find differences between two or more objects, restores from memory what was previously seen (diagram, drawing, model), and also allows children to create unusual visual images to remember the required operation.
Iris folding allows children to develop the ability to think logically: find similarities and differences, highlight the essential, establish causality. investigative connections. All mental activity is activated.
Interaction with parents
An equally important condition for the formation of elementary mathematical concepts in children is the active participation of parents in the educational process.
In kindergarten we use the following forms of work with families: consultations, design of moving folders, holding mathematical entertainment, fairs, master classes on the topics: “Logical - mathematical game - as a means of teaching and educating preschool children”; “Fairy-tale labyrinths of games by V.V. Voskobovich."
In groups, parents made mini-books together with their children.fairy tales on mathematical subjects: "Numbers", "Circle and Square" and others.
Teachers Brochures with tasks on Dienesh logic blocks and Cuisenaire rods have been developed; booklets “Mathematical games with a child at home”, “Mathematics for the development of your child” and others for reinforcing mathematical concepts with children at home.
Project activities
Certainly one of the modern and effective forms support of children's initiative is project activity, in which the participation of parents is always relevant. Using project activities to develop children’s mathematical understanding, teachers thereby activate cognitive and creative development child, and also pay attention to the formation of the child’s personal qualities. The knowledge acquired by children during the implementation of the project becomes the property of their personal experience. Mathematics projects such as “Fun Mathematics” in middle group No. 9, “ Entertaining mathematics“in middle group No. 14, “ABC of Numbers”, middle group No. 1 and others made it possible to put the personal developmental nature of interaction between adults and children into practice, taking into account their needs, capabilities, desires in the educational process.
Personnel
The quality of teaching activities using modern means to form mathematical concepts mainly depends on qualified teachers. In this regard, 2 teachers of our kindergarten were trained at KOIRO in gaming technology intellectual and creative development of children 3-7 years old “Fairytale labyrinths of the game V.V. Voskobovich." Training at KOIRO under the advanced training program “Updating the content of educational and educational activities in the unification of technical areas”; under the program “Development of technical creativity in educational organization in the conditions of the Federal State Educational Standard" 2 teachers were trained, according to the program "Tutor activity in additional vocational education» - 1 teacher.
Teachers actively participate in seminars and workshops held in preschool educational institutions on the topics: “Organization and implementation of work on the formation of cognitive interests of preschool children through educational mathematical games”, “Features of organizing mathematical games in preschool age”; in municipal seminars on the topics: “Development of technical creativity of students within the framework of network interaction between institutions of general and additional education", "Dissemination of innovative models for the development of the technosphere of activities of institutions of additional education within the framework of the development of a network model of interaction with preschool educational institutions"; regional seminars “Game is the most important sphere of self-expression”, international seminars “Preschool education: the experience of Italy”, where teachers exchanged experience on TIKO design, as well as in webinars organized by the Federal State Autonomous Institution “FIRO” and the magazine “Obruch”, such as “How to prepare a preschooler to solving arithmetic problems", "Geometric propaedeutics in modern preschool educational institution"and others.
Modern approaches to the formation of the foundations of mathematical culture of preschool children.
Children's entry into the world of mathematics begins already in preschool childhood. Mathematics is a universal method of understanding the surrounding and objective world and its role in modern science is constantly increasing. Changes in conceptual approaches to determining the content and selection of methods for teaching mathematics at school, and the widespread use of modern educational technologies have also determined the requirements for the mathematical training of preschool children.
Today “mathematics is more than a science, it is a language.” Studying mathematics improves the culture of thinking, teaches children to reason logically, and develops accuracy in their statements.
Mathematical knowledge and skills are necessary for the child’s successful adaptation to the processes social communication, informatization and technologization of society. They broaden the child's horizons. Mathematical culture is an integral part of the general culture of the individual, and during preschool childhood it has its own characteristics associated with the age and individual capabilities of children.
Traditionally, the content of mathematical education for preschoolers is divided into four lines: arithmetic, algebraic, geometric and magnitude. Today, taking into account the updating of the content of preschool education, a fifth content line is being 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, and imagination.
The adoption of the Federal State Educational Standard for preschool education will require the need to provide, as a prerequisite, the possibility of self-realization of a child at all stages of work on mathematical development in the education system of a preschooler.
Mathematical material should be revealed during excursions, familiarization with literary works and small forms of folklore, games with natural materials (water, sand, beans, peas, cereals), through game exercises with sensory standards, household objects, constructive and didactic games, in problematic situations. All these forms vary according to age.
During his stay in kindergarten, our graduate must learn to apply mathematical knowledge and concepts in practical activities that are significant to him: play, children's experimentation, design, work, artistic and visual arts.
And as a result of self-realization, the child will develop educational motivation.
Thus, the priority tasks of lifelong education of children will be solved.
Games with natural materials
Small forms of folklore
Reading fiction
Direct educational activities
ConstructiveAnddidactic games, logic
Mathematical educatedno
Excursions
Creative game exercises and problem situations
Theatrical performance with mathematical content
Learning to compare objects by size, measurementconditionalyardstick , division into 2 and 4 equal parts (modeling the “part” relationship- whole")
Learning to countAnd computational activity when solving problems in one action involving addition and subtraction (within 10). Counting techniques and countingone at a time
Formation of ideas about the set and natural series of numbers (up to 10). Number ascounting result. Quantitative andordinal counting of objects. Composition of numbers from units. Composition of numbers of two smaller numbers.
Orientation in space (“towards oneself”, “away from oneself”, from the subject, between objects(plan) and in time (parts of the day, week , month, year) hour, minutesA(1,3,5 minutes)
Orientation on a plane (notebook sheet)
Introduction to geometricAnd 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 diagrams, models, algorithms helps stimulate and develop the ability to act mentally, develops logical and creative thinking.
Application of mathematical knowledge and skills in practical activities
Construction
(according to plan, according to plan, according to model- mdressed, use of templates, stencils)
Children's experimentation
(sand, earth, water, snow, air, magnet, paper, peas, beans)
Labor
(labor in nature, art, pen)
Game
(plot - role-playing,theatrical, didactic, educational games , (puzzles, labyrinths, checkers, movable chess)
ArtisticO-fine (color, form, composition, applique,drawing)
note
Teachers' Council
Subject:"First steps into mathematics"
Form of conduct: "round table"
Target. Creating optimal conditions for the successful teaching of elementary mathematics to preschoolers.
Show formation paths mathematical thinking through the formation and development of cognitive (sensory and intellectual) abilities of preschool children.
Promote professional competence teachers in addressing issues of mathematical development of students. Help teachers reach out new level work.
Agenda of the teachers' council.
The significance of the problem posed. Modern approaches to teaching mathematics to preschoolers.
The state of educational work and features of the formation of the foundations of mathematical culture of preschoolers in a preschool institution. Results of the thematic audit.
PerformanceBorovlevaN.P.,
Withsenior teacher
“How I use educational games and gaming exercises with mathematical content aimed at the intellectual development of children.”
Communication and presentation of experience
KomarnitskayaT.A,
kindergarten teacher
The role of entertaining forms of presenting material and promising methods of teaching children mathematics.
Presentation of work experience
SherstobitovaL.V.,
Vsenior group teacher
Review of methodological literature on the mathematical development of preschool children, recommendations for its use.
Information Tkach L.N.,
kindergarten teacher
"Creativity of the teacher."
Performance teaching aids, educational games with mathematical content.
“Your option” (solving crossword puzzles).
Adoption and approval of the draft decision of the pedagogical council.
Questionnaire
dFor self-assessment of the teacher according to the section:
“Formation of elementary mathematical concepts”
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n/p | Answers |
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What do you consider most relevant in the work on FEMP for children in your age group? Children's acquisition of certain knowledge. Development in preschoolers thinking abilities, ability to solve various logical problems. Developing in children the ability to apply acquired knowledge in practice. Children's mastery of methods of action. | ||
TO Do you prepare notes for classes yourself or use ready-made ones published in teaching aids? | ||
What forms of work with children at FEMP do you prefer? Individual work; Frontal work; Subgroup; | ||
What teaching methods and techniques do you use in classes and in free activities? Practical Visual (teacher showing methods of action, using didactic material); Verbal (instructions, explanations, clarifications, questions); Game elements ( fairy tale character; surprise moment; game-competition); Didactic games and exercises. Modeling (creating models and their use); Logical and mathematical games. | ||
What difficulties have you encountered in your work? | ||
Are the parents of your students familiar with the problems of their children’s mathematical development? How do you organize interaction with your family in the direction of FEMP? |
Individual manifestations of children in development classes
uhelementary mathematicsatic ideas
List of children | Individual nbirths of children | Pedagogical tasks |
Show special interest in activities; are active; cope well with mathematical operations; love interesting tasks | Maintain and develop their interest; give complex tasks; place higher demands on their responses |
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They do not show their activity outwardly, but are always attentive; questions are answered correctly, but only when called; have little initiative | Develop self-confidence; encourage initiatives; develop creative initiative; carry out individual work; give instructions in the course of everyday activities. |
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They show external activity in class, like to give hints, although they don’t know the answer, they wait for hints | Cultivate modesty and often challenge and ask thought-provoking questions in class. |
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Do not show interest in classes; not attentive; cannot always answer the teacher’s question | Reveal the reasons for such behavior, conduct individual lessons; make extensive use of visualization. |
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They listen attentively, but cannot answer the questions asked; prefer to remain silent; shy; have problems in classes | Conduct individual work to overcome shyness; eliminate knowledge problems in separate lessons |
OproWith-questionnaire
Dear parents!
We know well how your children are doing and what they are interested in in kindergarten. What are they like at home? Help us get to know your children better so we can improve pedagogical work with them. Share your experience of family education. Thank you in advance for your attention.
We ask you to answer the following questions:
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n/p | Answers |
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Does your child tell you about his 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 for a purchase in a store with real money and receive change? Does he ask to pay for the purchase himself? | ||
From your point of view, what mathematical concepts of a child need to be improved? (counting, geometric standards, spatial relationships, time orientation, comparison of objects by size, solving arithmetic problems) | ||
What is your child struggling with and what is he/she best at? | ||
Who in the family has the opportunity to spend the most time with the child? | ||
Does your child like to solve mental problems? | ||
How does the child apply his acquired mathematical knowledge? | ||
What does the child dream of learning? |
Having filled in the empty cells horizontally correctly, you will read the name of modern science in a vertical column. |
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1. A set of objects or phenomena perceived as a single whole? | |||||||||||||
2. Conventional sign of the number? | |||||||||||||
3. Structural component account activity (account total) ? | |||||||||||||
4. Type of math classes in kindergarten? | |||||||||||||
Olga Stulnikova
Concept of mathematical development in preschool education
Concept of mathematical development in preschool education
Stulnikova Olga Gennadievna, senior teacher,
SP GBOU Secondary School No. 10 "OTs LIK" kindergarten No. 16,
Samara region, Otradny
Mathematical development of children in preschool educational the institution is designed based on preschool concept education and training, institution programs, goals and objectives child development, diagnostic data, predicted results. concept the ratio is determined pre-mathematics and prelogical components in the content education. The predicted results: development intellectual abilities children, their logical, creative or critical thinking; formation of ideas about numbers, computational or combinatorial skills, methods object transformations, etc.. d.
The acquisition of knowledge and skills is influenced by developing
training and thanks to the special organization educational process are developing all cognitive mental processes associated with sensation, perception, memory, attention, speech, thinking, as well as volitional and emotional processes in general. Developmental the learning effect should be focused on "the zone of the closest development» . Children are offered, along with tasks that they can now complete independently, and tasks that require their guesswork, ingenuity, and observation. Purchased this way way of knowledge, and most importantly - systematic improvement of their quality, plus development of thinking, provide general child development.
PROCESS MATHEMATICAL DEVELOPMENT
Process child's mathematical development is related, first of all, with development
his cognitive sphere (diverse ways of knowing, educational
activities, etc., as well as with development of mathematical thinking style.
Thanks to mathematical development in preschoolers develop personal qualities: activity, curiosity, perseverance in overcoming difficulties, independence and responsibility. In progress mathematical development there is general intellectual and speech child development(evidential and reasoned speech, vocabulary enrichment).
Purpose mathematical development of a preschooler is an introduction to the basics
mathematical culture and instilling interest in further knowledge
the surrounding world using elements of this culture (Order of the Government of the Russian Federation “On approval Concepts for the development of mathematics education in the Russian Federation", December 2013).
MAIN TASKS MATHEMATICAL DEVELOPMENT:
Formation of skills and abilities in counting, calculations, measurement,
modeling.
Development of logical-mathematical ideas and ideas about
mathematical properties and relationships of objects, specific quantities, numbers, geometric figures, dependencies and patterns.
Development of sensory(subject-effective) ways of knowing
mathematical properties and relationships, namely surveys, comparisons,
grouping, ordering.
Development children have logical ways of knowing mathematical properties and
relations, namely analysis, comparison, generalization, classification, seriation.
GENERAL DIDACTIC PRINCIPLES OF TEACHING PRESCHOOL CHILDREN ELEMENTS OF MATHEMATICS
The principle of educational training.
Education and training - educational training characterized by
concrete mental and practical work of children, which develops in them
organization, discipline, accuracy, responsibility.
Level preschooler development depends on specially organized
"mental education", which represents pedagogical process, aimed at forming preschoolers elementary knowledge and skills, methods of mental activity, as well as development children's abilities and their needs for mental activity. The main component of mental education preschooler are ways of mental action. Every mental action is a corresponding mental operation. These operations are different, interconnected aspects of thinking that transform into each other.
Basic thinking operations: analysis, synthesis, comparison, classification, generalization, abstraction. All of these operations cannot manifest themselves in isolation without connection with each other, that is, it is impossible to form any mental operation separately without connection and reliance on other operations. “An indicator of mastering a technique is its conscious transfer to solving new problems.” U preschooler methods of mental action must be laid down precisely at this age; moreover, without the formation of mental operations, the mental education of a child is impossible.
The principle of humanization of the pedagogical process.
This is the principle of personal oriented model education and training.
The main thing in training should be development opportunities to acquire knowledge and
skills and use them in life, individualization of learning, creating conditions for the development of the child as an individual.
The principle of an individual approach.
The principle of an individual approach provides for the organization of training based on deep knowledge individual abilities child, creating conditions for active cognitive activity of all children in the group and each child individually.
The principle of scientific teaching and its accessibility.
This principle means the formation in children preschool age
elementary, but essentially scientific, reliable mathematical knowledge.
Ideas about quantity, size and shape, space and time are given to children in such a volume and at such a level of specificity and generality that it is accessible to them, and that this knowledge does not distort the content, taking into account the age of the children, the characteristics of their perception, memory, attention, thinking.
The implementation of the principle of accessibility is also facilitated by the fact that material, which
studied, presented in accordance with rules: from simple to complex; from the known to the unknown; from general to specific.
So way, children's knowledge gradually expands, deepens, better
they are absorbed, but new knowledge should be offered to children in small doses, ensuring repetition and consolidation of it through various exercises using their application in different types activities.
The principle of accessibility also provides for the selection not too much material
difficult, but not too easy either. When organizing children's education, the teacher must
based on the accessible level of difficulty for children of a certain age.
The principle of awareness and activity.
Conscious assimilation of educational material provides for the activation
mental (cognitive) processes in a child.
Cognitive activity is independence, awareness,
meaningfulness, initiative, creativity in the process of mental activity, the child’s ability to see and independently set cognitive tasks, draw up a plan and choose ways to solve the problem using the most reliable and effective techniques, achieve results.
The principle of systematicity and consistency.
Logical order of study material, in which knowledge is based on
previously received. This principle is especially important when studying mathematicians, where each new knowledge seems to follow from the old, known. The teacher distributes the program material this way, to ensure its consistent complication, the connection of subsequent material with previous. It is this kind of study that provides lasting and deep knowledge.
The principle of visibility.
This principle has important in teaching children preschool age, since the child’s thinking is predominantly visual figurative character. In the methodology of teaching children mathematics the principle of clarity is closely connected with the child’s activity. Conscious mastery of elements mathematical knowledge is possible only if children have some sensory cognitive experience, through direct perception surrounding reality or knowledge of this reality through fine art and technical means.
SUBJECT-SPATIAL ENVIRONMENT
For successful work, a specially organized subject-matter is required.
spatial development environment: a room with both space for children to work at tables and enough space for games, including outdoor games. Availability of a game library, materials for making games and material. Availability of balls, cubes and other physical education equipment.
PRINCIPLES OF ORGANIZATION EDUCATIONAL PROCESS
For organization educational a three-block model was selected for the process,
which collects all the known basic models on which they work
preschool institutions: educational, complex-thematic, subject-specific
spatial - environmental. This takes advantage of the strengths of each separate model, and, if possible, their shortcomings are eliminated.
I block. Specially organized training in the form of classes - content
organized by "subjects".
II block. Joint adults and children (affiliate) activity - content
is organized comprehensively – thematically.
III Block. Free independent activity children - in accordance with
traditional types of children's activities.
Within the first block, training is organized in the form of special
classes based on the program. Learning process preschoolers is built taking into account the age characteristics of children preschool age. Mainly used gaming techniques and means of activities that are attractive to children (the principle is implemented "learning with passion", a combination of voluntary and involuntary, static and dynamic forms in the classroom is ensured that is comfortable for the child’s psychophysiological state.
Within the framework of the second block, educational and research work is organized
children's activities based on standards. The goal is to help students learn to independently acquire knowledge, develop research skills, to form a holistic picture of the world and an understanding of one’s place in it. During research pupils: conduct experiments and practical work; collect information and process data; make projects and give presentations;
Within the third block, children’s independent activities are carried out in classes at activity centers and in free play activities.
Activities are aimed at development cognitive abilities and
children's search actions. In activity centers the room is divided into
several zones, each of which contains materials for classes, games,
conducting experiments and research.
The role is undeniable preschool preparation for school is not only in the formation, development and replenishment of mathematical knowledge, skills and abilities preschooler, but also in the intellectual development of the child as a whole. Mathematics education in the early stages of development - powerful tool the formation of a personality with developed logical thinking, skills of analysis and synthesis, classification and systematization. These skills will be the key to success not only in school mathematics, but also in other subjects of the school cycle, and in the further professional activity of the growing citizen. Preparing the base mathematical knowledge should take important place in programs preschool education and training.
LITERATURE.
1. N. N. Poddyakov. Contents and methods of mental education preschoolers.
2. N. Yu. Boryakova, A. V. Soboleva, V. V. Tkacheva. Workshop on development mental activity at preschoolers.
3. E. A. Yuzbekova. Steps of creativity.
4. A. V. Beloshistaya. Education mathematics at preschool educational institution.
5. Z. A. Mikhailova. Mathematics from three to seven.
6. T. I. Erofeeva. Preschooler studying mathematics.
7. A. A. Smolentseva. Plot-didactic games with mathematical content.
8. Dagmar Alythauz, Erna Doom. Color, shape, quantity.
9. A. I. Ivanova. Naturally - scientific observations and experiments in kindergarten.
10. A. I. Savenkov. Methodology for conducting educational research in kindergarten.
