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The role of preschool educational institutions in the process of forming elementary mathematical representations

Even in early childhood, babies are faced with objects that differ in shape, color and quantity. At this age, the basic elementary ideas and abilities of the child begin to form.

The first toys resemble geometric shapes: cubes, constructors, pyramids. The count begins with mom's questions: "Tell me, how old are you?". Parents of children are taught to name the shapes of toys, their size, quantity.

Through gaming activity the ability to distinguish different properties and features of objects is formed. The baby is forming the first concept of mathematics, although he still does not know and is not aware of this. The consciousness of a child in early childhood is chaotic. Parents teach children to compare, group objects, call them by their proper names.

Through visual-objective actions, they help the child to remember what he heard on the basis of objective images. Before the age of three, the child already knows how to group objects according to their outward signs, color, shape. So, for example, a child can put green toys away from red ones, choose pencils from a pile of other objects and put them together, can add pyramids in size, in order of the pyramid rings.

Being engaged with objects through game activity, the child compares them. This is where the first acquaintance with mathematics begins.

By the age of four, children can easily count up to five, and a little older up to ten, but they can make mistakes in counting.

By the age of six, children are already beginning to understand when the numbers are increasing and when they are decreasing. That is why it is important to start systematic classes from kindergarten in order to increase the mental perception of the child.

In today's modern society, one of the requirements for preschool education is that children receive mathematical knowledge and elementary ideas in kindergarten.

Preschoolers in the course of their development receive the first elementary ideas about mathematics. The available methods and means of forming elementary mathematical representations are developed specifically for age categories, taking into account the gradual development of skills and abilities in preschoolers in this direction.
Mathematics is independent and is designed to develop intellectual abilities depending on the natural potential of preschoolers. Its role in the development of elementary ideas in preschoolers is very great. In the course of such activities, the child develops and develops cognitive and personal abilities.

In the process of learning, through the means of mathematical classes, the child receives the first ideas about mathematical concepts. The task of mathematics is the desire to educate preschoolers, with a perspective on the future, highly qualified personnel.

In order to achieve the goal of education, preschool institutions, while developing targeted programs and methods of education, domestic and foreign best practices should be taken into account, recommendations for parents should be developed. It will be a useful experience for educators if they share information and methods of raising children with other kindergartens and preschool institutions.

Mathematics is one of the few disciplines that covers different aspects of the personality of children. In the process of forming elementary mathematical concepts and learning, preschoolers actively develop all cognitive processes: speech, thinking, memory, perception, and representation. This becomes effective if, when setting up classes, the frequency and sequence of the development of cognitive processes in a child are taken into account, depending on the psychophysical development of each child.

If the child has not reached the age at which he is able to understand mathematical processes, then the lessons will not play any role for his consciousness. The possibilities of the child are determined by his psychology. AT modern world Increasingly, innovative methods and tools are included in the education programs for preschoolers.

Some of the preschool institutions are already using in their educational activities computer science lessons for preschoolers. The whole world is now connected with computer technologies and gradually they penetrate into kindergartens.

Mathematics is not necessarily boring classes, as it may seem at first glance. To teach arithmetic, educators play with children, come up with various counting rhymes, proverbs, sayings, riddles. The child masters the first numerical concepts and forms.

There are also didactic forms and means of education, in which visual aids, illustrations and games are used.
There are many approaches to teaching arithmetic and building elementary knowledge of mathematical concepts in children. Children are taught to count, show the distinctive moments of numbers: more, less, even, odd numbers.

To achieve results, use various materials: counting sticks, natural materials, teach to count and recognize money.

Children are taught to recognize geometric shapes: a circle, a square, a triangle, etc. Children should also master measured values: meter, centimeter, kilogram, gram, etc. During classes, children are taught not only exponential arithmetic, but also to perform arithmetic operations in the mind. They learn to find and compare objects in everyday life, on the street and in nature. For example: three birch trees under the window.

Children on graduation from kindergarten should be ready for the first grade, as well as adapted to external independent life. After all, they will not always and everywhere walk hand in hand with their mother. Children will spend part of the time on their own and rely on their skills - this is the development process. AT last years such a concept as pre-mathematical preparation was introduced into practice.

Preparing the child and his cognitive world for the mathematical way of thinking. Various ways of forming the cognitive sphere allow the child to prepare for the study of the subject - mathematics. When organizing classes, there is an impact on visual and logical thinking, memory, creative imagination, perception, voluntary attention of a preschooler.

The task of such upbringing is to activate the thinking of a preschooler, the desire to overcome difficulties, the needs in solving various kinds of mental problems. Solving such problems of educating preschoolers is a very difficult job for the educator and requires an integrated approach, and only systematic classes will make it possible to carry out the timely mathematical development of preschool children.

The abilities of each child depend on his individual psychological characteristics. Mathematical abilities cannot be innate, since only anatomical and physiological features of a person are innate. Mathematical is a special kind of abilities, they depend on the integral quality of the mind and develop in the process of mathematical activity.

A person's abilities can manifest themselves in various areas, and here, like everyone else, mathematical abilities are revealed in the process of a preschooler's activities. The preschool age is considered the most favorable period for the development of abilities.

Children at preschool age observe and imitate adults, they observe every action and listen carefully to what the teacher says and this is an important property. Children should be taught to act independently, show and tell about their actions. Preschoolers should be encouraged to repeat after the teacher about the properties and qualities of objects. Games with children should contain mathematical actions.

With comparative actions, children themselves must tell the teacher how this or that figure differs from another. If the child finds it difficult to answer, it means that his speech and perception are not sufficiently developed, if the child does not want to answer, then do not put pressure on him and insist too much. Awareness comes to the numbers in children faster if you start using them in everyday life, for example: please give me a second slipper.
Children do not immediately recognize the numerical value - one, because it is not used in everyday speech. For them, the role of mathematical representations in real life is inaccessible. Usually the kids at the same time say "give me the remote, or a spoon or some kind of toy."

Awareness of the number one in children comes later than the rest of the numbers.

At the first stage of learning, children lack attentiveness, and when listing the serial numbers of digits, they often lose sight of the numbers: for example, they call them “1, 2, 4, 7”.

In older groups, it is worth teaching children about the set, breaking the set into groups and explaining to them the difference between a smaller and larger group, as well as the equality of parts. Visually teach preschoolers the sequence of counting up to ten and vice versa. Teach children to count by touch and by ear within ten.

Learn to compare the number of items in different groups, add and remove items up to a given amount.

Preschool children are able to divide objects and name their parts, such as dividing an apple into slices or a pie. Preschoolers need to understand that a whole apple is bigger than a slice or half of an apple. Senior students must learn and understand that the number 7 is greater than six, but less than eight. By the end of the training period, preschoolers should be able to perform simple mathematical operations.

Formation of elementary ideas about time

In kindergarten, you can actively form elementary knowledge of time in children. Children should know all four parts of the day, name what time of day they go to bed, and when it's time to get up and go to kindergarten. In this process, a large role is assigned to the regime of the day in the group.

The teacher calls the time of day and says what the children should do now: whether to have breakfast, whether to go for a walk, or whether they will have an hour.

Conversations should be held regularly with children, in which parts of the day are mentioned, it is explained why this or that action should be carried out at a certain time of the day (sleep - at night, wash and have breakfast - in the morning, walk, dine - in the afternoon, in the evening - play with the family, engage in various activities).

The holistic development of a preschool child is a multifaceted process. Personal, mental, speech, emotional and other aspects of development acquire special significance in it. In mental development, an important role is played by mathematical development, which at the same time cannot be carried out outside the personal, speech and emotional.

The concept of "mathematical development of preschoolers" is quite complex, complex and multifaceted. It consists of interrelated and interdependent ideas about space, shape, size, time, quantity, their properties and relationships, which are necessary for the formation of "everyday" and "scientific" concepts in a child. In the process of assimilation of elementary mathematical concepts, the preschooler enters into specific socio-psychological relations with time and space (both physical and social); he forms ideas about relativity, transitivity, discreteness and continuity of magnitude, etc. These ideas can be considered as a special “key” not only to mastering the types of activities characteristic of age, to penetrating the meaning of the surrounding reality, but also to forming a holistic “ pictures of the world.

The basis for the interpretation of the concept of "mathematical development" of preschoolers was also laid in the works of L.A. Venger. and today is the most common in the theory and practice of teaching mathematics to preschoolers. “The purpose of teaching in the classroom in kindergarten is the assimilation by the child of a certain range of knowledge and skills given by the program. The development of mental abilities in this case is achieved indirectly: in the process of mastering knowledge. This is precisely the meaning of the widespread concept of “developmental education”. The developmental effect of learning depends on what knowledge is communicated to children and what teaching methods are used.

From the study of E.I. Shcherbakova, the mathematical development of preschoolers should be understood as shifts and changes in cognitive activity personalities that occur as a result of the formation of elementary mathematical representations and the logical operations associated with them. In other words, the mathematical development of preschoolers is a qualitative change in the forms of their cognitive activity that occurs as a result of children's mastery of elementary mathematical concepts and related logical operations.

Standing out from preschool pedagogy, the methodology for the formation of elementary mathematical representations has become an independent scientific and educational area. The subject of her research is the study of the main patterns of the process of formation of elementary mathematical representations in preschoolers in the context of public education. The range of problems of mathematical development solved by the method is quite extensive:

Scientific substantiation of program requirements for the level of development of quantitative, spatial, temporal and other mathematical representations of children in each age group;

Determination of the content of the material for preparing a child in kindergarten for learning mathematics at school;

Improving the material on the formation of mathematical representations in the kindergarten program;

Development and implementation in practice of effective didactic tools, methods and various forms and organization of the process of development of elementary mathematical concepts;

Implementation of continuity in the formation of basic mathematical concepts in kindergarten and the corresponding concepts in school;

Development of the content of training highly qualified personnel capable of carrying out pedagogical and methodological work on the formation and development of mathematical concepts in children at all levels of the preschool education system;

Development on a scientific basis of methodological recommendations for parents on the development of mathematical concepts in children in a family setting.

Thus, mathematical development is considered as a consequence of teaching mathematical knowledge. To some extent, this is certainly observed in some cases, but it does not always happen. If this approach to the mathematical development of the child were correct, then it would be enough to select the range of knowledge communicated to the child and select the appropriate teaching method “for them” in order to make this process really productive, i.e. to receive as a result "universal" high mathematical development in all children.

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Introduction

1. The essence of the methodology of mathematical development younger preschoolers

2. The concept of the mathematical development of younger preschoolers

3. Modern requirements for the mathematical development of preschool children

Conclusion

Bibliography

Introduction

The relevance of the topic is due to the fact that preschool children show spontaneous interest in mathematical categories: quantity, shape, time, space, which help them better navigate things and situations, organize and connect them with each other, and contribute to the formation of concepts.

Kindergartens and kindergartens take this interest into account and try to expand children's knowledge in this area (25,26,39). However, acquaintance with the content of these concepts and the formation of elementary mathematical representations is not always systematic, and often, one would like to wish for the best.

Concept for early childhood education, guidelines and requirements for updating the content preschool education outline a number of fairly serious requirements for the cognitive development of younger preschoolers, part of which is mathematical development. In this regard, we were interested in the problem: how to ensure the mathematical development of children 4-5 years old, which meets modern requirements.

The purpose of the work: to identify the features of the mathematical development of children 4-5 years old in the light of modern requirements.

Research objectives: to identify the level of mathematical development of children 4-5 years old; to determine the system of work with children 4-5 years old on mathematical development in the light of modern requirements.

The object is the educational process in the preschool educational institution.

The subject is the formation of elementary mathematical representations of children of primary preschool age.

1. conceptaboutmathematicalohmdevelopmentandjuniorpreschoolers

IG Pestalozzi in the book "How Gertrude teaches her children" (35), says that arithmetic is an art, entirely, arising from the simple connection and separation of several units. Its original form, in essence, is as follows: one and one are two; subtract one from two - one remains. Thus, the original form of any counting is deeply imprinted on the children, and for them, with a full consciousness of their inner truth, the means that serve to preserve the counting, that is, the number, become familiar. In the history of pedagogy, the system of mathematical development of children by M. Montessori has been widely used. Its essence is that when three-year-olds come to school, they already know how to count to two or three. Then they easily learn numbering. One of the ways to teach numbering M. Montessori used coins. "... The exchange of money represents the first form of numbering, quite interesting for exciting the active attention of the child ..." (26). Then she teaches with the help of methodical exercises, applying how didactic material one of the systems already used in the education of the senses, that is, a series of ten bars various lengths. When the children have laid out the bars one by one along their length, they are asked to count the red and blue marks. Now exercises in counting are added to the sense exercises for recognizing longer and shorter bars.

Mathematical preparation of children for school involves not only the assimilation of certain knowledge by children, the formation of their quantitative spatial and temporal representations. The most important is the development of mental abilities in preschoolers, the ability to solve various problems.

The teacher must know not only how to teach preschoolers, but also what he teaches them, that is, the mathematical essence of the ideas that he forms in children must be clear to him. The widespread use of special educational games is also important for awakening preschoolers' interest in mathematical knowledge, improving cognitive activity, and general mental development.

The methodology for the formation of elementary mathematical concepts in the system of pedagogical sciences is designed to assist in mathematics - one of the most important subjects in school, to contribute to the education of a comprehensively developed personality.

Counting is necessary as one of the processes of learning numbers. This is evident from the fact that it is not rejected by the supporters of the direct perception of numbers.

The foregoing gives us reason to believe that both methods should expediently complement each other. Our opinion is also supported by the psychic phenomenon that the direct perception of a number relies primarily on spatial elements, and the calculation - on the temporal elements of the number and actions on numbers.

As for the view of number as a result of measurement, this is also a correct view, but it does not exclude the concept of number as a result of counting, but only expands and deepens the concept of number. But as a more difficult species for children to understand than the previous one, it should not precede it, but follow it.

The question of numerical figures is considered one of the controversial issues in the methodology of arithmetic.

Most of all, this issue, like most methodological issues, was discussed in German literature - the birthplace of numerical figures. In their opinion, numerical figures can have four different purposes. One of them is that numerical figures contribute to the emergence of numerical representations in children. The second most important purpose of numerical figures is to facilitate the production of operations on single-digit numbers. The third purpose of numerical figures is that they can serve as a subject for counting. The fourth purpose - they can facilitate the transition from a number to a digit, because a numerical figure, like a digit, is a sign for a number, clearly showing the number of units in a given number.

Pictures should be one of the visual aids, although important, but not the main one in teaching arithmetic. The main visual aid should be real, material objects, because they, as being subject to touch, and not just as pictures, can really be taken away and added one by one and in groups, which cannot be said about pictures, where such actions can be performed only mentally, in imagination (5).

Why is it important to introduce children to the comparison of the size of objects? There is an opinion that children come to school with ready-made concepts about the size of objects. In practice, a completely different picture emerges. Before teaching children to compare the size of objects, they must be taught to see and consider these objects (10).

F.N. Bleher suggested general ways of working on the formation of mathematical representations (4, 6, 15). She identified two main ways in working with children:

1. The use of all the many occasions that abound everyday life children in the team and various types of children's activities.

2. A path closely related to the first - games and exercises with a special task for the account.

If in the first case the assimilation of the account occurs along the way, then in the second - the work on the account is independent. In working with children, these paths intersect and are applied in each age group of the kindergarten.

Also F.N. Bleher developed the basic didactic material needed in the classes on the formation of elementary mathematical concepts for all age groups.

2 . Essencemethods of mathematical development of younger preschoolers

Having stood out from preschool pedagogy, the methodology for the formation of elementary mathematical representations has become an independent scientific and educational area. The subject of her research is the study of the main patterns of the process of formation of elementary mathematical representations in preschoolers in the context of public education. The range of tasks solved by the technique is quite extensive:

Scientific substantiation of program requirements for the level of development of quantitative, spatial, temporal and other mathematical representations of children in each age group;

Determination of the content of the material for preparing a child in kindergarten for learning mathematics at school;

Improving the material on the formation of mathematical representations in the kindergarten program;

Development and implementation in practice of effective didactic tools, methods and various forms and organization of the process of development of elementary mathematical concepts;

Implementation of continuity in the formation of basic mathematical concepts in kindergarten and the corresponding concepts in school;

Development of the content of training highly qualified personnel capable of carrying out pedagogical and methodological work on the formation and development of mathematical concepts in children at all levels of the preschool education system;

Development on a scientific basis of methodological recommendations for parents on the development of mathematical concepts in children in a family setting.

The theoretical basis of the methodology for the formation of elementary mathematical concepts in preschoolers is not only the general, fundamental, initial provisions of philosophy, pedagogy, psychology, mathematics and other sciences. As a system of pedagogical knowledge, it has both its own theory and its sources. The latter include:

Scientific research and publications that reflect the main results of scientific research (articles, monographs, collections of scientific papers, etc.);

Program and instructional documents ("The program of education and training in kindergarten", guidelines etc.);

Methodological literature (articles in specialized journals, for example, in " preschool education", manuals for kindergarten teachers and parents, collections of games and exercises, guidelines, etc.);

Advanced collective and individual pedagogical experience in the formation of elementary mathematical concepts in children in kindergarten and family, experience and ideas of innovative teachers.

The methodology for the formation of elementary mathematical representations in children is constantly developing, improving and enriching with the results of scientific research and advanced pedagogical experience.

At present, thanks to the efforts of scientists and practitioners, a scientifically based methodological system for the development of mathematical concepts in children has been created, successfully operates and is being improved. Its main elements - the purpose, content, methods, means and forms of organization of work - are closely interconnected and mutually condition each other.

The leading and decisive among them is the goal, since it leads to the fulfillment of the social order of society by a kindergarten, preparing children to study the basics of science (including mathematics) at school.

Four-year-old children actively master counting, use numbers, carry out elementary calculations on a visual basis and orally, master the simplest temporal and spatial relationships, transform objects various forms and magnitudes. The child, without realizing it, is practically included in a simple mathematical activity, while mastering the properties, relationships, connections and dependencies on objects and on a numerical level.

The scope of representations should be considered as the basis cognitive development. Cognitive and speech skills constitute, as it were, the technology of the process of cognition, a minimum of skills, without mastering which further knowledge of the world and the development of the child will be difficult.

Emphasis on working with children given age is done on a figurative basis, and a step has been taken in the direction of "rehabilitation" in the eyes of teachers of associative thinking, which, as you know, is one of the mechanisms of the creative process. However, carried away by the ideals of scientificity, rigor, and logic, we often forget that in order to be truly productive, thinking needs such qualities as mobility and flexibility, the ability to establish unexpected connections, find unexpected analogies, and in this way move along the path of knowledge. new.

Speaking about the development of creative thinking, we often forget about such an important factor as the ability to form associations. This ability (within reasonable limits) develops in children of this age in the course of classes under the "Rainbow" program. L.A. Venger, O.M. Dyachenko (7) propose to carry out mathematical development in the classroom and reinforce it in various types of children's activities, including in the game.

In the process of games, quantitative relationships are fixed (many, few, more, the same), the ability to distinguish geometric shapes, navigate in space and time.

Particular attention is paid to the formation of the ability to group objects according to features (properties), first one by one, and then two (shape and size).

Games should be aimed at the development of logical thinking, namely the ability to establish the simplest patterns: the order of alternation of figures in color, shape, size. This is facilitated and game exercises to find the missing figure in the row. Due attention is paid to the development of speech. During the game, the educator not only asks pre-prepared questions, but also talks to the children at ease on the topic and plot of the game, and helps the child enter the game situation. The teacher uses nursery rhymes, riddles, counting rhymes, fragments of fairy tales. Game cognitive tasks are solved with the help of visual aids. A prerequisite for success in work is the creative attitude of the educator to math games: variation of game actions and questions, individualization of requirements for children, repetition of games in the same form or with complication. The need for modern requirements is caused by a high level modern school to the mathematical preparation of children in kindergarten in connection with the transition to school from the age of six.

Mathematical preparation of children for school involves not only the assimilation of certain knowledge by children, the formation of their quantitative spatial and temporal representations. The most important is the development of mental abilities in preschoolers, the ability to solve various problems. The teacher must know not only how to teach preschoolers, but also what he teaches them, that is, the mathematical essence of the ideas that he forms in children must be clear to him. The widespread use of special educational games is also important for awakening preschoolers' interest in mathematical knowledge, improving cognitive activity, and general mental development.

The methodology for the formation of elementary mathematical representations in the system of pedagogical sciences is designed to assist in mathematics, one of the most important subjects in school, to contribute to the education of a comprehensively developed personality.

Learning leads to development. In the conditions of rationally constructed education, taking into account the age capabilities of preschoolers, it is possible to form in them full-fledged ideas about individual mathematical concepts. At the same time, learning is considered as an indispensable condition for development, which, in turn, becomes a controlled process associated with the active formation of mathematical representations and logical operations. With this approach, spontaneous experience and its influence on the development of the child are not ignored, but the leading role is given to purposeful learning.

3. Modern requirements for the mathematical development of preschool children

The current state of the mathematical development of preschoolers is provided for in various programs. One of them - the program "Childhood" is as follows:

1. The goal is development educational and creativity children (personal development).

Comparison - score

Adjustment - measurement

Acquisition - calculation plus elements of logic and mathematics.

3. Methods and techniques:

Practical (game);

Experimentation;

Modeling;

Recreation;

conversion;

Design.

4. Didactic means:

Visual material (books, computer):

Gyenes blocks,

Kuizener sticks,

5. Form of organization of children's activities:

Individual creative activity,

Creative activity in a small subgroup (3-6 children),

Educational and gaming activities ( educational games, lessons),

Game training.

All this is based on a development environment, which can be built as follows:

1. Math fun:

Plane modeling games (Pythagoras, Tangram, etc.),

puzzle games,

joke tasks,

Crosswords,

2. Didactic games:

touch,

modeling character,

Specially invented by teachers for teaching children.

3. Educational games are games that contribute to the solution of mental abilities. Games are based on simulation, the process of finding solutions. Nikitin, Minskin "From game to knowledge".

Thus, the science of mathematical development in the light of modern requirements has changed, has become more focused on the development of the personality of the child, the development of cognitive knowledge, the protection of his physical and mental health. If, with the educational and disciplinary approach of education, it comes down to correcting behavior or preventing possible deviations from rules through “suggestions”, then the personality-oriented model of interaction between an adult and a child proceeds from a radically different interpretation of the processes of education: to educate means to introduce the child to the world of human values.

Conclusion

The knowledge of the properties of children 4-5 years old is most successful in active actions in comparison, grouping, modifying and recreating geometric shapes, silhouettes, objects different shapes, quantities. Appropriate are games like "Color and Shape", "Shape and Size" and others, which directly include a variety of exploratory activities. The use of Gyenesh logical blocks or a set of logical geometric shapes makes it possible to involve children in performing simple game actions to classify by joint properties, both by the presence and absence of a property. Games and exercises with Kuizener's colored counting sticks most successfully contribute to the knowledge of magnitude and numerical relationships. Practical activities of adults together with children in making cookies, salad, cleaning the premises, planting and caring for plants, caring for animals, accompanied by cognitive conversations, successfully contribute to the development of elementary mathematical relations. Games for mastering the score are very diverse: mobile, constructive, desktop-printed and others. To master comparison, generalization of groups of objects by number, one should specifically, taking into account the level of development of children, select games and vary them.

To consolidate the ideas of children about the preservation of quantity, its independence from the form of location, it is good to use the game "Dots". Children love to communicate, they are pleased with the approval of their elders, this encourages them to learn new activities. To effectively increase the level of mathematical knowledge, a technique is proposed for using various kinds children's activities are predominantly playful.

The purposeful development of elementary mathematical concepts should be carried out throughout the entire preschool period.

Bibliography

1. Asmolov A.G. "Psychology of personality". - M.: Enlightenment 1990.

2. Althaus D., Dum E. "Color, shape, quantity". - M.: Enlightenment

3. 1984, pp. 11-16, 40.

4. Volkovsky D L. "Guide to" Children's world"in numbers". -

5. M.: 1916. pp.7-11,13,24.

6. Wenger L.A. , Dyachenko O.M. "Games and exercises for the development of mental abilities in preschool children." - M.: Enlightenment 1989

7. Galperin P.Ya. "On the Method of Forming Mental Actions".

8. Glagoleva L.V. "Comparison of the sizes of subjects in the zero groups of schools" L-M. : Education worker 1930 pp. 4-6, 12-13.

9. Preschool education, 1969 No. 9 pp. 57-65.

10. Erofeeva T.I. and others. "Mathematics of the Day of Preschoolers", - M .: Enlightenment 1992.

11. Zvonkin A. "The Kid and Mathematics Unlike Mathematics". Knowledge and Power, 1985 pp. 41-44.

12. Loginova V.I. "Formation in preschool children (3-6 years) of knowledge about materials and features, properties and qualities." - L .: 1964

13. Loginova V.I. "Formation of the ability to solve logical problems in preschool age. Improving the process of forming elementary mathematical representations in kindergarten." - L .: 1990. pp. 24-37.

14. Leushina A.M. "Teaching Counting in Kindergarten" - M.: Uchpediz. 1961 pp. 17-20.

15. Menchinskaya N.A. "Psychology of teaching arithmetic". APN RSFSR 1955 -M. pp. 164-182.

16. Metlina L.S. "Mathematics in Kindergarten". - M.: Enlightenment 1984. pp. 11-22, 52-57, 97-110, 165-168.

17. The use of gaming methods in the formation of mathematical representations among preschoolers. "- L .: 1990. pp. 47-62.

18. Nosova E.A. "Formation of the ability to solve logical problems in preschool age. Improving the process of forming elementary mathematical representations in kindergarten." - L .: 1990. pp. 24-37.

19. Nepomnyashchaya N.N. "Psychological analysis of teaching children aged 3-7 years (on the basis of mathematics)". - M .: Pedagogy 1983. pp.7-15.

20. Smolentseva A.A. "Story-didactic games with mathematical content" .- M .: Enlightenment 1987. pp. 9-19.

21. Taruntaeva T.V. "Development of elementary mathematical representations of preschoolers", - M.6 Enlightenment 1980. pp. 37-40.

22. Fedler M. "Mathematics is already in kindergarten". - M.: Enlightenment 1981. pp. 28-32,97-99.

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Contemporary Issues the use of didactic games in the cognitive development of preschool children. Development of recommendations on the organization and methods of using didactic games that contribute to the development of the attention of preschool children.

The holistic development of a preschool child is a multifaceted process. Personal, mental, speech, emotional and other aspects of development acquire special significance in it. In mental development, an important role is played by mathematical development, which at the same time cannot be carried out outside the personal, speech and emotional.

The concept of "mathematical development of preschoolers" is quite complex, complex and multifaceted. It consists of interrelated and interdependent ideas about space, shape, size, time, quantity, their properties and relationships, which are necessary for the formation of "everyday" and "scientific" concepts in a child. In the process of assimilation of elementary mathematical concepts, the preschooler enters into specific socio-psychological relations with time and space (both physical and social); he forms ideas about relativity, transitivity, discreteness and continuity of magnitude, etc. These ideas can be considered as a special “key” not only to mastering the types of activities characteristic of age, to penetrating the meaning of the surrounding reality, but also to forming a holistic “ pictures of the world.

The basis for the interpretation of the concept of "mathematical development" of preschoolers was also laid in the works of L.A. Venger. and today is the most common in the theory and practice of teaching mathematics to preschoolers. “The purpose of teaching in the classroom in kindergarten is the assimilation by the child of a certain range of knowledge and skills given by the program. The development of mental abilities in this case is achieved indirectly: in the process of mastering knowledge. This is precisely the meaning of the widespread concept of “developmental education”. The developmental effect of learning depends on what knowledge is communicated to children and what teaching methods are used. it is understood that the teaching method is “selected” depending on the nature of the knowledge communicated to the child (in this case, the use of the word “reported” obviously nullifies the second half of the statement itself, since once “reported”, it means the method is “explanatory and illustrative”, and , finally, it is assumed that mental development is a spontaneous consequence of this learning.

This understanding of mathematical development is consistently preserved in the works of preschool education specialists. In the study by Abashina V.V. the definition of the concept of "mathematical development" is given: "the mathematical development of a preschooler is a process of qualitative change in the intellectual sphere of the personality, which occurs as a result of the formation of mathematical concepts and concepts in the child."

From the study of E.I. Shcherbakova, the mathematical development of preschoolers should be understood as shifts and changes in the cognitive activity of the individual, which occur as a result of the formation of elementary mathematical representations and related logical operations. In other words, the mathematical development of preschoolers is a qualitative change in the forms of their cognitive activity that occurs as a result of children's mastery of elementary mathematical concepts and the logical operations associated with them.

Having stood out from preschool pedagogy, the methodology for the formation of elementary mathematical representations has become an independent scientific and educational area. The subject of her research is the study of the main patterns of the process of formation of elementary mathematical representations in preschoolers in the context of public education. The range of problems of mathematical development solved by the method is quite extensive:

Scientific substantiation of program requirements for the level of development of quantitative, spatial, temporal and other mathematical representations of children in each age group;

Determination of the content of the material for preparing a child in kindergarten for learning mathematics at school;

Improving the material on the formation of mathematical representations in the kindergarten program;

Development and implementation in practice of effective didactic tools, methods and various forms and organization of the process of development of elementary mathematical concepts;

Implementation of continuity in the formation of basic mathematical concepts in kindergarten and the corresponding concepts in school;

Development of the content of training highly qualified personnel capable of carrying out pedagogical and methodological work on the formation and development of mathematical concepts in children at all levels of the preschool education system;

Development on a scientific basis of methodological recommendations for parents on the development of mathematical concepts in children in a family setting.

Shcherbakova E.I. among the tasks for the formation of elementary mathematical knowledge and the subsequent mathematical development of children, he singles out the main ones, namely:

the acquisition of knowledge about the set, number, size, shape, space and time as the foundations of mathematical development;

the formation of a broad initial orientation in the quantitative, spatial and temporal relations of the surrounding reality;

formation of skills and abilities in counting, calculations, measurement, modeling, general educational skills;

mastery of mathematical terminology;

development of cognitive interests and abilities, logical thinking, general intellectual development of the child.

These tasks are most often solved by the teacher at the same time in each lesson in mathematics, as well as in the process of organizing different types independent children's activities. Numerous psychological and pedagogical studies and advanced pedagogical experience in preschool institutions show that only properly organized children's activities and systematic training ensure the timely mathematical development of a preschooler.

The theoretical basis of the methodology for the formation of elementary mathematical concepts in preschoolers is not only the general, fundamental, initial provisions of philosophy, pedagogy, psychology, mathematics and other sciences. As a system of pedagogical knowledge, it has both its own theory and its sources. The latter include:

Scientific research and publications that reflect the main results of scientific research (articles, monographs, collections of scientific papers, etc.);

Program and instructional documents ("The program of education and training in kindergarten", guidelines, etc.);

Methodical literature (articles in specialized magazines, for example, in "Preschool education", manuals for kindergarten teachers and parents, collections of games and exercises, methodological recommendations, etc.);

Advanced collective and individual pedagogical experience in the formation of elementary mathematical concepts in children in kindergarten and family, experience and ideas of innovative teachers.

The methodology for the formation of elementary mathematical representations in children is constantly developing, improving and enriching with the results of scientific research and advanced pedagogical experience.

At present, thanks to the efforts of scientists and practitioners, a scientifically based methodological system for the development of mathematical concepts in children has been created, successfully operates and is being improved. Its main elements - the purpose, content, methods, means and forms of organization of work - are closely interconnected and mutually condition each other.

The leading and decisive among them is the goal, since it leads to the fulfillment of the social order of society by a kindergarten, preparing children to study the basics of science (including mathematics) at school.

Preschoolers actively master counting, use numbers, carry out elementary calculations on a visual basis and orally, master the simplest temporal and spatial relationships, transform objects of various shapes and sizes. The child, without realizing it, is practically included in a simple mathematical activity, while mastering the properties, relationships, connections and dependencies on objects and on a numerical level.

The need for modern requirements is caused by the high level of the modern school for the mathematical preparation of children in kindergarten in connection with the transition to schooling from the age of six.

Mathematical preparation of children for school involves not only the assimilation of certain knowledge by children, the formation of their quantitative spatial and temporal representations. The most important is the development of mental abilities in preschoolers, the ability to solve various problems. The teacher must know not only how to teach preschoolers, but also what he teaches them, that is, the mathematical essence of the ideas that he forms in children must be clear to him. Widespread use of oral folk art it is also important for awakening preschoolers' interest in mathematical knowledge, improving cognitive activity, and general mental development.

Thus, mathematical development is considered as a consequence of teaching mathematical knowledge. To some extent, this is certainly observed in some cases, but it does not always happen. If this approach to the mathematical development of the child were correct, then it would be enough to select the range of knowledge communicated to the child and select the appropriate teaching method “for them” in order to make this process really productive, i.e. to receive as a result "universal" high mathematical development in all children.

"The value of the mathematical development of preschool children"

Introduction

The concept of "development of mathematical abilities" is quite complex, complex and multifaceted. It consists of interrelated and interdependent ideas about space, shape, size, time, quantity, their properties and relationships, which are necessary for the formation of "everyday" and "scientific" concepts in a child.

The mathematical development of preschoolers is understood as qualitative changes in the cognitive activity of the child, which occur as a result of the formation of elementary mathematical representations and the logical operations associated with them. Mathematical development- a significant component in the formation of the "picture of the world" of the child.

The use of a variety of didactic games contributes to the formation of mathematical representations in a child. In the game, the child acquires new knowledge, skills and abilities. Games that contribute to the development of perception, attention, memory, thinking, the development of creative abilities are aimed at the mental development of a preschooler as a whole.

AT primary school Mathematics is not easy at all. Often, children experience various kinds of difficulties in mastering the school curriculum in mathematics. Perhaps one of the main reasons for such difficulties is the loss of interest in mathematics as a subject.

Therefore, one of the most important tasks of the educator and parents is to develop a child's interest in mathematics at preschool age. Introducing this subject in a playful and entertaining way will help the child to learn the school curriculum faster and easier in the future.

1. Psychological and pedagogical foundations for the development of mathematical concepts in children 4-5 years old.

It is a big mistake to think that the child acquires the concept of number and other mathematical concepts directly in learning. On the contrary, to a large extent he develops them on his own, independently and spontaneously. When adults try to impose mathematical concepts on a child prematurely, he learns them only verbally. The child does not yet distinguish between what can be taken for granted and what is not.

Thus, it can be said that the preschool child does not have sufficient abilities to connect temporal, spatial and causal sequences with each other and include them in a wider system of relations. It reflects reality at the level of representations, and these connections are assimilated by it as a result of direct perception of things and activities with them. When classifying objects or phenomena are combined on the basis of common features into a class or group, for example: all people who can drive a car, etc. Classification forces children to think about what underlies the similarities and differences of various things, since he needs to draw a conclusion about them.

The basic concepts of constancy, classification operations form a more general scheme in all children between about 4 and 7 years of age. They create the foundation for developing logical sequential thinking.

2. Modern requirements for the mathematical development of preschool children.

Four-year-old children actively master counting, use numbers, carry out elementary calculations on a visual basis and orally, master the simplest temporal and spatial relationships, transform objects of various shapes and sizes. The child, without realizing it, is practically included in a simple mathematical activity, while mastering the properties, relationships, connections and dependencies on objects and on a numerical level.

The volume of representations should be considered as the basis of cognitive development. Cognitive and speech skills constitute, as it were, the technology of the process of cognition, a minimum of skills, without mastering which further knowledge of the world and the development of the child will be difficult. The activity of the child, aimed at cognition, is realized in meaningful independent gaming and practical activities, in cognitive developmental games organized by the educator.

The adult creates conditions and conditions favorable for involving the child in the activity of comparison, counting, reconstruction, grouping, regrouping, etc. At the same time, the initiative in the development of the game, the actions belong to the child. The educator singles out, analyzes the situation, directs the process of its development, and contributes to obtaining the result.

The child is surrounded by games that develop his thought and introduce him to mental work. For example, games from the series: "Logic cubes", "Corners", "Make a cube" and others; from the series: "Cubes and color", "Fold the pattern", "Cube-chameleon" and others.

You can not do without didactic aids. They help the child to isolate the analyzed object, to see it in all its variety of properties, to establish connections and dependencies, to determine elementary relationships, similarities and differences. To didactic aids, performing similar functions, include Gyenes logical blocks, colored counting sticks (Kuizener sticks), models and others.

Playing and studying with children, the educator contributes to the development of their skills and abilities:

Operate properties, relations of objects, numbers;

Identify the simplest changes and dependencies of objects in shape, size;

Compare, generalize groups of objects, correlate, isolate patterns of alternation and succession, operate in terms of representations, strive for creativity;

Show initiative in activities, independence in clarifying or setting goals, in the course of reasoning, in fulfilling and achieving results;

Talk about the action being performed or performed, talk with adults, peers about the content of the game (practical) action.

3. Formation of mathematical abilities of children

preschool age.

Many parents believe that the main thing when preparing for school is to introduce the child to numbers and teach him to write, count, add and subtract (in fact, this usually results in an attempt to memorize the results of addition and subtraction within 10). However, when teaching mathematics using textbooks of modern developmental systems (L. V. Zankov’s system, V. V. Davydov’s system, etc.), these skills do not help the child for very long at mathematics lessons. The stock of memorized knowledge ends very quickly (in a month or two), and the lack of formation of one's own ability to think productively (that is, to independently perform the above mental actions on mathematical content) very quickly leads to the appearance of "problems with mathematics".

At the same time, a child with developed logical thinking is always more likely to be successful in mathematics, even if he was not taught the elements of the school curriculum (counting, calculations, etc.) in advance. It is no coincidence that in recent years, many schools working on developmental programs have conducted interviews with children entering the first grade, the main content of which are questions and tasks of a logical, and not just arithmetic, nature. Is this approach to the selection of children for education reasonable? Yes, it is natural, since the mathematics textbooks of these systems are constructed in such a way that already at the first lessons the child must use the ability to compare, classify, analyze and generalize the results of his activity.

However, one should not think that developed logical thinking is a natural gift, the presence or absence of which should be reconciled. Exists a large number of studies confirming that the development of logical thinking can and should be dealt with (even in cases where the natural inclinations of the child in this area are very modest). First of all, let's look at what constitutes logical thinking. Logical methods of mental actions - comparison, generalization, analysis, synthesis, classification, seriation, analogy, systematization, abstraction - are also called logical methods of thinking in the literature. When organizing special developmental work on the formation and development of logical methods of thinking, a significant increase in the effectiveness of this process is observed, regardless of the initial level of development of the child.

To develop certain mathematical skills and abilities, it is necessary to develop the logical thinking of preschoolers. At school, they will need the ability to compare, analyze, specify, generalize. Therefore, it is necessary to teach the child to decide problem situations to draw certain conclusions, to come to a logical conclusion. The solution of logical problems develops the ability to highlight the essential, independently approach generalizations.

Logic games of mathematical content educate children in cognitive interest, the ability for creative search, the desire and ability to learn. Unusual game situation with elements of problematic character for each entertaining task is always of interest to children.

Entertaining tasks contribute to the development of the child's ability to quickly perceive cognitive tasks and find the right solutions for them. Children begin to understand that in order to correctly solve a logical problem, it is necessary to concentrate, they begin to realize that such an entertaining problem contains a certain “trick” and in order to solve it, it is necessary to understand what the trick is.

The logical development of the child also involves the formation of the ability to understand and trace the cause-and-effect relationships of phenomena and the ability to build the simplest conclusions on the basis of a cause-and-effect relationship.

Thus, two years before school, one can have a significant impact on the development of the mathematical abilities of a preschooler. Even if the child does not become the indispensable winner of mathematical Olympiads, he will not have problems with mathematics in elementary school, and if they are not in elementary school, then there is every reason to count on their absence in the future.

Conclusion

At preschool age, the foundations of the knowledge necessary for the child in school are laid. Mathematics is a complex science that can cause certain difficulties during schooling. In addition, not all children have inclinations and have a mathematical mindset, so when preparing for school, it is important to introduce the child to the basics of counting.

Both parents and educators know that math is a powerful factor intellectual development child, the formation of his cognitive and creative abilities. The most important thing is to instill in the child an interest in learning. For this, classes should take place in an exciting game form.

Thanks to games, it is possible to concentrate attention and attract the interest of even the most uncollected preschool children. In the beginning, they are fascinated only by game actions, and then by what this or that game teaches. Gradually, children awaken interest in the very subject of education.

Thus, in a playful way, instilling in a child knowledge from the field of mathematics, the development of memory, thinking, and creative abilities contribute to the overall mathematical development of preschool children. During the game, children learn complex mathematical concepts, learn to count, read and write, and close people help the child in developing these skills - his parents and teacher.