Logical and mathematical development of preschool children. How to develop the logic of thinking in a baby? Logical and mathematical development of preschoolers

Tasks and content of the logical and mathematical development of preschool children. Means of logical and mathematical development of preschool children (developing and didactic games, universal aids, problem situations, experimentation, logical tasks). Technologies of logical and mathematical development of preschool children (M. Fidler, Z. A. Mikhailova, A. A. Smolentseva, L. V. Nepomnyashchaya). Organization of a developing space that ensures the logical and mathematical development of preschool children (A.A. Stolyar, E.A. Nosova, Z.A. Mikhailova).

The concept of "logical and mathematical development of preschoolers."

Logical and mathematical development of preschoolers - these are shifts and changes in the cognitive activity of the child that occur as a result of the formation of elementary mathematical representations and the logical operations associated with them.

Approaches and ideas in the field of logical and mathematical development of children.

Approaches and ideas in the field of logical and mathematical development of preschoolers:

I position- the idea of the predominant development of intellectual and creative abilities in preschool children (Piaget, Elkonin, Davydov, Stolyar).

* observation, cognitive interests;

* research approach (to establish connections, identify dependencies, draw conclusions);

* the ability to compare, classify, generalize;

* forecasting changes in activities and results;

* clear and precise expression of thoughts;

* the implementation of the action in the form of a "mental experiment" (V. V. Davydov).

Active methods and techniques for teaching and developing children were assumed, such as modeling, transformation actions (moving, removing and returning, combining), playing, and others.

II position - development of sensory processes and abilities in children (Zaporozhets, Wenger, etc.):

* inclusion of the child in active process to highlight the properties of objects by examination, comparison, effective practical action;

* independent and conscious use of sensory standards and standards of measures in activities;

* use simulation.

The ability for visual modeling acts as one of the general intellectual abilities.

III position - based on the ideas of children's initial mastery of methods of practical comparison of numbers through the selection of common features in objects - mass, length, width, height ( Galperin, Leushina, Davydov and others). This activity ensures the development of relations of equality and inequality through comparison. Children master practical ways to identify relationships in magnitude, for which numbers are not required. Numbers are mastered following the exercises when comparing values by measurement.

IV position- is based on the idea of the formation and development of a certain style of thinking in the process of mastering properties and relationships by children (Stolyar, Nosova, Sobolevsky, etc.).

Mental actions with properties and relationships are considered as an accessible and effective means of developing intellectual and creative abilities. In the course of actions with sets of objects that have various properties (color, shape, size, thickness, etc.), children practice abstracting properties and performing logical operations on the properties of certain subsets.

Variable technologies of logical and mathematical development of children.

Variable technologies of logical and mathematical development of preschoolers

The mathematical development of children in a specific educational institution (kindergarten, development groups, additional education groups, gymnasium, etc.) is designed on the basis of the concept of a preschool institution, the goals and objectives of the development of children, diagnostic data, predicted results. The concept determines the ratio of pre-mathematical and pre-logical components in the content of education. The predicted results depend on this ratio: the development of the intellectual abilities of children, their logical, creative or critical thinking; the formation of ideas about numbers, computational or combinatorial skills, ways to transform objects, etc.

Orientation in modern programs for the development and education of children in kindergarten, their study provides a basis for choosing a methodology. Modern programs (“Development”, “Rainbow”, “Childhood”, “Origins”, etc.), as a rule, include the logical and mathematical content, the development of which contributes to the development of the cognitive, creative and intellectual abilities of children.

These programs are implemented through activity-based, person-oriented developing technologies and exclude “discrete” learning, i.e., the separate formation of knowledge and skills with subsequent consolidation (V. Okon).

The following is typical for modern programs of mathematical development of children.

■ The focus of the mathematical content mastered by children on the development of their cognitive and creative abilities and in the aspect of familiarization with human culture. Children master a variety of geometric shapes, quantitative, spatio-temporal relations of objects of the world around them in interconnection. They master the methods of independent knowledge: comparison, measurement, transformation, counting, etc. This creates conditions for their socialization, entry into the world of human culture.

■ Children's education is based on the inclusion of active forms and methods and is implemented both in specially organized classes (through developing and game situations), and in independent and joint activities with adults (in games, experimentation, game trainings, exercises in workbooks, educational -game books, etc.).

■ Those technologies for the development of mathematical concepts in children are used that implement the educational, developmental orientation of learning and “first of all, the activity of the student” (V. A. Sitarov, 2002). These are technologies of search and research activity and experimentation, knowledge and evaluation by the child of quantities, sets, space and time based on the allocation of relationships, dependencies and patterns. Therefore, modern technologies are defined as problem-game .

■ The development of children depends on the created pedagogical conditions and psychological comfort, under which the unity of the cognitive, creative and personal development of the child is ensured. It is necessary to stimulate manifestations of the child's subjectivity (independence, initiative, creativity, reflection) in games, exercises, game learning situations (V. I. Slobodchikov). The most important condition for development, first of all, is the organization of an enriched subject-game environment (effective educational games, teaching aids and materials) and positive interaction between adults and pupils.

■ The development and upbringing of children, their advancement in the cognition of mathematical content is projected through the development of means and methods of cognition.

■ The design and construction of the development of mathematical representations is carried out on a diagnostic basis.

Stimulation of cognitive, activity-practical and emotional-value development on the basis of mathematical content contributes to the accumulation of logical and mathematical experience by children (L.M. Klarina). This experience is the basis for the free inclusion of the child in subject, play, research activities: self-knowledge, resolution of problem situations; solving creative problems and their reconstruction, etc.

Orientation in the properties and relations of objects, dependencies become the property of the subjective experience of the child; the ability to perceive the same phenomenon, action from different positions. The cognitive development of the child becomes more perfect.

Tasks and content of the logical and mathematical development of preschool children

Tasks:

1. Development of sensory ways of knowing mathematical properties and relationships: examination, comparison, grouping, ordering, splitting.

2. Mastering by children mathematical methods of cognition of reality: counting, measurement, simple calculations.

3. The development in children of logical ways of knowing mathematical properties and relationships (analysis, abstraction, negation, comparison, generalization, classification, seriation).

4. The idea of the mathematical properties and relationships of objects, specific quantities, numbers, geometric shapes, dependencies and patterns.

5. Mastering by children of experimental and research methods of cognition of mathematical content (recreation, experimentation, modeling, transformation).

6. Development of accurate, reasoned and evidence-based speech, enrichment of the child's vocabulary.

7. The development of intellectual and creative manifestations of children: resourcefulness, ingenuity, guesswork, quick wit, etc.

The first and most important component the content of the mathematical development of preschoolers are:

1)properties and relationships . In the process of various actions with objects, children master such properties as shape, size, quantity, spatial arrangement. The most important prerequisite for abstract thinking is formed in children - the ability to abstract.

2) In the process of carrying out practical actions, children learn a variety of geometric figures and gradually move on to grouping them according to the number of corners, sides and vertices. Children develop constructive abilities and spatial thinking. They master the ability to mentally rotate an object, look at it from different angles, dismember, assemble, modify it.

3) In knowledge quantities children move from direct methods (imposition, application) to indirect methods of comparing them (using measurement with a conditional measure). This makes it possible to arrange objects according to their properties (size, height, length, thickness, mass)

4) Spatio-temporal representations - the most difficult thing for a preschooler, they are mastered through real-life relationships (far, close, today or tomorrow).

5) Knowledge of numbers and mastering actions with numbers - the most important component of the content of mathematical development. Numbers express quantity and magnitude. By counting objects of different size and spatial arrangement, children come to understand the independence of the number from other properties of objects, get acquainted with numbers and signs.

Means of logical and mathematical development of preschool children (developing and didactic games, universal aids, problem situations, experimentation, logical tasks).

Logic and mathematical games.

Modern logic and mathematical games are diverse. In them, the child masters standards, models, speech, masters the methods of cognition, and develops thinking.

desktop printed:"Color and shape", "Count", "Game square", "Transparent square", "Logic train", etc.

3D modeling games: "Cubes for everyone", "Tetris", "Ball", "Snake", "Hedgehog", "Geometric constructor", etc.

plane modeling games: "Tangram", "Sphinx", "T-game", etc.

games from the Shape and Color series:“Fold the pattern”, “Unicube”, “Color panel”, “Colorful squares”, “Triangular domino”, “So that the color does not repeat”, etc.

games for making a whole out of parts:"Fractions", "Fold the square", "Greek cross", "Fold the ring", "Chessboard", etc.

fun games: labyrinths, permutations ("Tower of Hanoi", "Tea service", "Goats and rams", "Stubborn donkey");

puzzles(puzzles, mosaics, "Rainbow", "Fairy of Flowers", "Butterflies", "Fish", "Cunning Clown", "Parsley", mathematical puzzles - magic squares; puzzles with sticks), etc.

problematic situations.

This is a means of mastering search actions, the ability to formulate one's own thoughts about the search methods and the expected result, a means of developing creative abilities.

Structural components of a problem situation are:

problematic questions (In how many ways can a square be cut into 4 parts?),

entertaining questions (The table has four corners. How many corners will the table have if one is cut off? How many months in a year contain 30 days?),

entertaining tasks (How many ends do three sticks have? And three and a half? Kolya bet that he would determine what the score would be in the game of the Spartak and Dynamo football teams before the start of the match, and won the argument. What was the score?),

joke problems (What fence can you jump above? The egg flew three meters and did not break. Why?).

First, an adult poses a problem for the children, achieves its comprehension, directs the children's attention to the need to solve it. Then comes the hypotheses and their testing in a practical way, a collective discussion of the situation and ways to solve it. For example: “There are three pencils of different lengths on the table. How to remove the longest pencil from the middle without touching it?”, “How to lay a triangle on the table with one stick?”.

Logical and mathematical plot games (classes).

These are games in which children learn to identify and abstract properties, master the operations of comparison, classification and generalization. They are characterized by the presence of a plot, characters, schematization. Such a complex of games was proposed by E.A. Nosova based on Gyenesh blocks: Mice are burrows. Stocks for the winter. Highway. Growing a tree. Where is whose garage? Teach the Unknown. Riddles without words. translators. Build a chain. Two tracks. Who is Winnie the Pooh and Piglet visiting? Factory. Architects. Help the figures get out of the forest. Let's set up a window. Build a house. Separate the blocks - 1. blocks - 2. Help the toy. Separate the blocks - 3. Gifts for three piglets. And etc.

Experimentation and research activities.

This activity is aimed at finding and acquiring new information. It is not set by an adult, but is built by the preschooler himself as he receives new information about the object. It is characterized by emotional saturation, provides opportunities for communication.

Trial and error is an important component of children's experimentation. The child tries to apply old ways of doing things by combining and rearranging them.

In the course of experimentation and research, children master the actions of measuring, transforming materials and substances, get acquainted with devices, learn to use cognitive books as a source of information.

One of the conditions is the presence of a specially created subject environment where devices and materials are placed in accordance with the problem that children solve together with the teacher. For example, “What floats, what sinks?”, “Which sand is lighter: wet or dry?”.

Technologies of logical and mathematical development of preschool children.

The essence of technology is the creation by adults of situations in which the child strives for vigorous activity and gets positive results.

Organization of a developing space that ensures the logical and mathematical development of preschool children

third year of life

It is advisable to allocate a special place in the group for the game library, marking it with a bright poster of a mathematical orientation (using figures-images, shapes, objects of different sizes). There should be collected games aimed at developing sensory perception, fine motor skills, imagination, and speech. While playing, the child clarifies ideas about the properties of objects - shape, size, material.

The used didactic games are built mainly on the principle of inserts. Materials must be large enough, durable; "brightly" represent differences in size, size, shape. Elements of the games must be strong, imply the possibility of examination; represent the main standards mastered at a given age (shape, color, size).

By the age of 2-3, children accumulate experience in knowing properties, mastering certain standards and actions with objects. This period refers to the stage of "sensory-motor" standards. Children identify some properties of objects (shape, size, color) and designate them by the name of objects well known to them (square - “like a window”, triangle - “like a carrot”). Children only learn to distinguish the properties of objects, to designate them with a word. At this age, the practical tactile-motor way of knowing objects prevails: preschoolers need to feel the object, touch it; they often carry out actions of a manipulative nature. This way of knowing the subject forms the establishment of the eye-hand relationship. For the development of ideas about properties, it is necessary to include in the game library the set "Logical blocks of Gyenesh" and methodological manuals for it.

With the help of the activating and leading role of an adult, children begin to single out one, two, many objects in a group, establish a one-to-one correspondence between the elements of two sets (dolls and sweets, hares and carrots, birds and houses, etc.).

To develop the perception of sets, children of 2-3 years old use toys, objects, "vital" and abstract materials. To facilitate the selection of elements of the set, these materials are located in the "field of perception" of children (on a tray, on the lid of the box). At this age, the Colored Stripes set is used - an analogue of the Kuizener Colored Sticks. Recommended games such as paired pictures and lotto (botanical, zoological, lotto transport, furniture, dishes). These game materials arouse interest in recalculation.

We also need split pictures from 4-8 parts, large puzzles from 4-9 parts. Of great interest in independent games of children are folding cubes (when you can assemble a subject picture from parts). It is advisable to include in the game library the games "Fold the pattern" of 9 cubes, "Fold the square", various insert games, pyramids of 6-8 rings (for children 2.5-3 years old - from 8-10 (12) rings ) and curly pyramids. The games-inserts, the games "Rainbow basket", "Miracle crosses", "Miracle honeycombs", "Glasses-inserts", "Colorful columns", etc., boxes with figured cuts for sorting are actively used.

Babies love to play with dolls. In the first half of the year (from 2_x to 2.5 years) they assemble and disassemble 3-, 5-seater, and in the second

5-, 7-seater toys.

With enthusiasm, kids are engaged in geometric mosaics. You can use desktop, floor, large magnetic mosaics, a variety of soft constructors.

By organizing games with sand and water, the teacher not only introduces children to the properties of various objects and materials, but also contributes to the development of ideas about color, shape, size, and develops the child's fine motor skills.

Teachers should remember that kids quickly lose interest in the same material. Therefore, it is undesirable to keep all available games, game materials in a group room. It is better to replace one material with another from time to time. It is advisable to use industrially manufactured games, manuals and materials.

fourth year of life

It should be borne in mind that children with different experience in mastering mathematical concepts come to a modern kindergarten. The process of mathematical development of children should not be intensified. However, in the selection of material, it is important to take into account the different levels of development of preschoolers.

The objects of the immediate environment are a source of curiosity for a small child and the first step in understanding the world, therefore, it is necessary to create a rich object environment in which the child's sensory experience is actively accumulated. Toys and objects in the group reflect the richness and diversity of properties, stimulate interest and activity. It is important to remember that a child sees a lot for the first time and perceives what is observed as a model, a kind of standard with which he will compare everything he sees later.

The use of suspension mobiles will simplify the task of developing spatial orientations. The teacher draws the children's attention to hanging objects, uses the words high, below, above and others.

In groups of children of younger preschool age, the main attention is paid to mastering the method of direct comparison of quantities, objects in terms of quantity, properties. Of the didactic games, games like loto and paired pictures are preferred. Mosaic (plastic, magnetic and large carnation), a puzzle of 5-15 pieces, sets of cubes of 4-12 pieces, educational games (for example, "Fold the pattern", "Fold the square", "Corners"), and also games with elements of simulation and substitution. A variety of "soft constructors" on a carpet basis allow you to play the game in different ways: sitting at the table, standing against the wall, lying on the floor.

Children of this age are actively mastering the standards of form, color, therefore this period is called the stage of "subject standards". As a rule, children distinguish 3-4 forms, but find it difficult to abstract the form, color in unfamiliar and "unusual" objects. An insufficient level of development of perception affects the accuracy of assessing the properties of objects. Children pay attention to brighter, "catchy" properties, elements; they do not see the difference in size if the strips (objects) differ slightly; undifferentiated perceive a large number of elements of sets ("many").

To successfully distinguish properties, children need a practical examination, "manipulation" with the object (hold the figure in their hands, clap, feel, press, etc.). The accuracy of distinguishing properties depends directly on the degree of examination of the subject. Preschoolers can successfully perform simple actions: grouping abstract shapes, sorting according to a given attribute, ordering 3-4 elements according to the most vividly presented property. It is recommended to use abstract materials that facilitate the process of comparison with the standard, abstraction of properties. Children are especially interested in the so-called "universal" sets - Gyenes logical blocks and Kuizener's colored counting sticks. Benefits are interesting in that they represent several properties at the same time (color, shape, size, thickness in blocks; color, length in sticks); there are many elements in the set, which activates manipulation and play with them. 1-2 sets are enough for a group.

For the development of fine motor skills, it is necessary to include plastic containers with lids of various shapes and sizes, boxes, and other household items that have become obsolete in the environment. Trying on lids for boxes, the child gains experience in comparing sizes, shapes, and colors. Children's experimentation is one of the most important aspects of personality development. This activity is not given to the child by an adult in advance in the form of one or another scheme, but is built by the preschooler himself as he receives more and more new information about the object.

fifth year of life

At this age, some qualitative changes occur in the development of perception, which is facilitated by the development of certain sensory standards (shapes, colors, dimensional manifestations) by children 4-5 years old. Children successfully abstract meaningful properties of objects.

The developing thinking of the child, the ability to establish the simplest connections and relationships between objects arouse interest in the world around him. The child already has some experience of knowing the environment and requires generalization, systematization, deepening, clarification. For this purpose, a “sensory center” is organized in the group - a place where objects and materials are selected, which can be learned using various sense organs. For example, musical instruments and noise objects can be heard; books, pictures, kaleidoscopes can be seen; jars with flavored substances, perfume bottles can be recognized by smell.

Materials and manuals are used that allow organizing a variety of practical activities for children: count, correlate, group, arrange. For this purpose, various sets of objects are widely used (abstract: geometric shapes; "vital": cones, shells, toys, etc.). The main requirement for such sets will be their sufficiency and variability of manifestations of the properties of objects. It is important that the child always has the opportunity to choose a game, and for this the set of games must be quite diverse and constantly change (about 1 time in 2 months). About 15% of the games should be designed for children of the older age group in order to enable children who are ahead of their peers in development not to stop, but to move on.

In middle preschool age, children actively master the means and methods of cognition. In the process of comparing objects, preschoolers more differentiatedly distinguish manifestations of properties, not only establish their "polarity", but also compare them according to the degree of manifestation.

Games are needed to compare objects according to various properties (color, shape, size, material, function); grouping by properties; recreating the whole from parts (such as "Tangram", a puzzle of 12-24 parts); seriation according to different properties; counting games. Signs of various properties (geometric shapes, color spots, numbers, etc.) should be placed on the carpet.

At this age, various games are organized with blocks for highlighting properties (“Treasures”, “Dominoes”), grouping according to specified properties (games with one and two hoops). When using Kuizener's colored counting sticks, attention is drawn to the distinction in color and size and to the establishment of the color-length-number relationship. To enhance children's interest in these materials, you should have a variety of illustrative aids.

Mastering counting and measurement requires the use of various measures: strips of cardboard of different lengths, ribbons, cords, cups, boxes, etc. You can organize plot-didactic games and practical situations with weights, balances, and a height meter.

In the mathematical toy library, various versions of books, workbooks for reviewing and completing assignments can be placed. To enhance children's activities with similar materials, you can use worksheets (pictures for drawing, mazes), which are also placed in the corner of mathematics.

Middle age is the beginning of a sensitive period in the development of the sign-symbolic function of consciousness; this is an important stage for mental development in general and for the formation of readiness for schooling. In the environment of the group, sign symbols, models for designating objects, actions, sequences are actively used. It is better to come up with such signs, models together with children, leading them to an understanding of what can be denoted not only in words, but also graphically. For example, work with the children to determine the sequence of activities during the day in kindergarten and figure out how to label each of them. In order for the child to better remember his address, street, city, place a diagram in the group on which indicate the kindergarten, streets and houses in which the children of the group live. Draw the routes that children go to kindergarten, write the names of the streets, place other buildings that are in the district, designate a children's clinic, stationery store, "Children's World". Refer to this scheme more often, find out for which of the children the path to kindergarten is longer, shorter; who lives above everyone else, who lives in the same house, etc.

Visualization is used in the form of models: parts of the day (at the beginning of the year - linear; in the middle - circular), simple plans for the space of the doll room. The main requirement is the subject-schematic form of these models.

sixth year of life

At senior preschool age, it is important to develop any manifestations of independence, self-organization, self-esteem, self-control, self-knowledge, self-expression. A characteristic feature of older preschoolers is the emergence of interest in problems that go beyond personal experience. This is reflected in the environment of the group, in which content is introduced that expands the child's personal experience.

For example, games with Gyenes logical blocks, other games are suitable for the development of logic: “Logic train”, “Logic house”, “Fourth extra”, “Search for the ninth”, “Find the differences”. Mandatory notebooks on a printed basis, educational books for preschoolers. Useful games for the development of counting and computational skills, also aimed at the development of mental processes, especially attention, memory, thinking.

For the organization of children's activities, a variety of educational games, didactic aids, materials are used to "train" children in establishing relationships, addictions. The ratio of gaming and cognitive motives at a given age determines that the most successful process of cognition will be in situations that require intelligence, cognitive activity, independence of children. The materials and manuals used should contain an element of "surprise", "problem". When creating them, the existing experience of children should be taken into account; they should allow organizing various options for activities and games.

Columbus Egg Handbook

Traditionally, a variety of educational games are used (for planar and volumetric modeling), in which children not only lay out pictures, designs according to samples, but also invent and make up silhouettes on their own. The senior group presents different versions of recreational games (“Tangram”, “Mongolian game”, “Leaf”, “Pentamino”, “Columbus egg” (ill. 68), etc.).

The development of verbal-logical thinking and logical operations (primarily generalizations) allows children 5-6 years old to approach the development of numbers. Preschoolers begin to master the method of formation and composition of numbers, comparing numbers, lay out Kuizener's sticks, draw the "House of Numbers" model.

To accumulate experience in actions with sets, logical blocks, Kuizener's sticks, are used. As a rule, several sets of these benefits are sufficient for a group. It is possible to use special visual aids that allow you to master the ability to highlight significant properties (“Search for a reserved treasure”, “On the golden porch”, “Let's play together”, etc.).

The variability of measuring instruments (clocks of different types, calendars, rulers, etc.) activates the search for common and different, which contributes to the generalization of ideas about measures and methods of measurement. These benefits are used in independent and joint activities of children with an adult. Materials, substances must be present in sufficient quantity; be aesthetically presented (stored, if possible, in the same transparent boxes, containers in a permanent place); allow experimenting with them (measure, weigh, sprinkle, etc.). It is necessary to provide for the presentation of contrasting manifestations of properties (large and small, heavy and light stones; high and low vessels for water).

The increase in children's independence and cognitive interests determines the wider use of cognitive literature (children's encyclopedias), workbooks in this group. Along with fiction, reference, educational literature, general and thematic encyclopedias for preschoolers should be presented in the book corner. It is advisable to arrange the books in alphabetical order, as in a library, or by topic. The teacher shows the children how to get answers to the most difficult and interesting questions from the book. A well-illustrated book becomes a source of new interests for the preschooler.

Children's interest in puzzles can be maintained by placing rope puzzles, movement games, and using puzzle games with sticks (matches) in the toy library.

When organizing children's experimentation, there is a new task: to show children the various possibilities of tools that help to cognize the world, such as a microscope. Quite a lot of materials are required for children's experimentation, therefore, if conditions permit, it is advisable to allocate a separate room for experiments using technical means in a kindergarten for older preschoolers.

At senior preschool age, children show interest in crossword puzzles, cognitive tasks. For this purpose, crossword puzzles can be laid out on the carpet with the help of thin long ribbons and sheets with pictures or task texts can be attached.

By the end of senior preschool age, children already have some experience in mastering mathematical activities (calculations, measurements) and generalized ideas about the shape, size, spatial and temporal characteristics; also, children begin to develop generalized ideas about the number. Older preschoolers show interest in logical and arithmetic tasks, puzzles; successfully solve logical problems on generalization, classification, seriation.

Assimilated ideas begin to be generalized and transformed. Children are already able to understand some of the more abstract terms: number, time; they begin to understand the transitivity of relations, independently identify characteristic properties when grouping sets, etc. The understanding of the invariance of quantity, magnitude (the principle, or rule, of conservation of magnitude) is significantly improved: preschoolers identify and understand contradictions in these situations and try to find explanations for them.

The development of arbitrariness, planning allows you to more widely use games with rules - checkers, chess, backgammon, etc.

It is necessary to organize the experience of describing objects, practicing in performing mathematical operations, reasoning, and experimenting. For this purpose, sets of materials are used for classification, serialization, weighing, and measurement.

"Logic - mathematical game in the development of speech of preschool children"

Each preschooler is a little explorer, discovering the world around him with joy and surprise. The task of educators and parents is to help him maintain and develop the desire for knowledge, satisfy the child's need for active work, and give food for the development of the child's mind.

Pedagogical practice confirms that, under the condition of a properly organized pedagogical process using various methods, as a rule, gaming, taking into account the characteristics of children's perception, children can already at preschool age, without overload and stress, learn much of what they used to learn only at school. And the more prepared the child comes to school - I mean not even the amount of accumulated knowledge, but the readiness for mental activity - the more successful, and therefore, the happier the beginning of this very important period - school childhood will be for him.

Everyone understands that a child from the first days of his life needs exercises for the development of all muscles. The mind also needs constant training. A person who is able to think constructively, quickly solve logical problems, is most adapted to life. He quickly finds a way out of difficult situations, makes rational decisions; mobile, efficient, shows accurate and fast reactions.

So, mathematics rightfully occupies a very large place in the system of preschool education. It sharpens the child's mind, develops flexibility of thinking, teaches logic.

The assimilation of fairly complex mathematical knowledge (relationships of equivalence, order, combinatorics, the formation of interest in them is helped by the game - one of the most attractive activities for children. The game is a natural type of activity for the child. In the game activity, the child masters a variety of ideas, independently "discovers" methods of action , cognizes some dependencies and patterns of the surrounding world, expands his experience of cognition.

Let us especially emphasize the role of the logical-mathematical game as a method of teaching and developing mathematical concepts.

Logical and mathematical games develop in children: independence, the ability to autonomously, independently of adults, solve available problems in various activities, as well as the ability for elementary creative and cognitive activity. Contribute to: the development of means of cognition by children: standards (color, shape, standards of measures (size, mass, models of images, speech representations); accumulation of logical and mathematical experience, mastery of methods of cognition: comparison, examination, equalization, counting.

This type of games is characterized by: a game orientation of activity, saturation with problem situations, creative tasks, the presence of search situations with elements of experimentation, practical research, schematization. A mandatory requirement for these games is their developmental impact.

Logic-mathematical games are designed on the basis of a modern view on the development of a child's mathematical abilities. These include the child's desire to get results: collect, connect, measure, take the initiative, and be creative; anticipate the outcome change the situation; actively without being distracted, act practically and mentally; operate with images; establish connections and dependencies, fix them graphically.

These games contribute to the development of attention, memory, speech, imagination and thinking of the child, create a positive emotional atmosphere, encourage children to learn, collective search, and activity in transforming the game situation.

Thus, the problem of a logical-developing, mathematical game, as a means of a child's cognitive activity, is relevant.

Let's define its goal - to promote the development of cognitive activity, logical thinking, the desire for independent knowledge and reflection, the development of mental abilities through logic and mathematical games.

We single out the following tasks:

1. To develop in children an interest in solving cognitive, creative problems, in a variety of intellectual activities;

2. To promote the development of figurative and logical thinking, the ability to perceive and display, compare, generalize, classify, modify, etc.

3. Develop arbitrary attention, the ability to use the techniques of mnemonics.

4. Increase the ability to establish mathematical relationships, patterns, sequence, the relationship of arithmetic operations, signs and symbols, relationships between parts of a whole, numbers, measurements, etc.

You can do the following work:

Create an appropriate developmental environment / in the group, a "Game Library" was created, where educational, didactic games are located, the center "Mathematics and Design" is decorated ... /;

Develop a model of the pedagogical process;

Develop a long-term plan on this topic for all age groups;

Develop a cycle of developing educational situations and joint activities with children;

Compile a card index of logical and mathematical games;

As an educator, it is necessary to solve such tasks as: to form the child's personal qualities, develop attention, memory, speech, instill cultural communication skills, the ability to conduct a dialogue with an adult, communicate with peers.

Successful problem solving requires an individual approach to the education and upbringing of children. It is this approach that helps to create ideas about each child, together with the educator and parents, to influence his development in time.

This will help, games with Gyenesh logic blocks and Cuisiner colored sticks with their focus on an individual approach, with their versatility in solving a variety of teaching and educational tasks, with their attractiveness from an aesthetic point of view.

Work on the development of logical thinking in preschoolers will be successful if a number of conditions are met:

1. Work with children will be carried out in the system according to a previously developed plan, that is, a model of the pedagogical process.

2. Activities that implement the program for the formation of logical and mathematical thinking are related to work in everyday life.

3. A variety of forms of work were used (developing educational situations, joint and independent activities, a club, leisure activities, holidays, and activities (games, observations, artistic and productive ...

4. Diagnostic methods were used to determine the level of formation of logical and mathematical thinking in children.

To solve the tasks at hand, use the following methods of work at different stages:

Analysis of scientific and methodological literature on the problem of the development of children's logical thinking;

Studying existing knowledge in children;

Development and testing of models of the pedagogical process;

Analysis of the obtained results.

It should be based on the principles of organization of games /S. A. Shmakov/.

No coercion;

Development of game dynamics /from small successes to big ones/;

Support the game atmosphere, children's real feelings;

The relationship of gaming and non-gaming activities;

The transition from the simplest forms and ways of performing game actions to complex ones.

It should be borne in mind that for the logico-mathematical game the characters are:

The presence of a plot plot, the actions of persons and following the storyline throughout the lesson.

The presence of schematization, transformation, cognitive tasks to identify properties and relationships, dependencies and patterns.

Game motivation and direction of actions, their effectiveness.

The presence of situations of discussion, choice of material and actions, collective search for a way to solve a cognitive problem.

Mastering the actions of correlation, comparison, reconstruction, distribution of grouping.

General focus on the development of children's initiative.

Modern logical and mathematical games are diverse: board games / "Color and Shape", "Game Square", "Logo Forms"/, games for three-dimensional modeling / "Cubes for All", "Geometric Constructor", "Ball"/, games for plane modeling /"Tangram", "Cross", "Honeycombs", "Mongolian game"/, games from the series "Cubes and color" / "Fold the pattern", "Unicube"/, games for composing a whole from parts / "Fractions "," Miracle flower "/, fun games / shifters, labyrinths /.

Intended games and game exercises - included in a certain system - are presented in the form of game activities, united by a single fascinating plot, which will arouse children's activity and interest in further similar activities. In the course of logical and mathematical games, the child consciously perceives the game task, purposefully solves it.

Also, in working with children, they use a large number of collective games, both in joint and in independent activities. These are such games as "Domino", "Guess", "Unusual figures", "Settled houses", "Where, whose garage", "Paths" and others. In these games, in addition to learning tasks, set yourself tasks of a personal nature:

Learn to work in a team;

Adhere to certain rules;

Be able to lose, but strive to win in fair ways;

Cultivate a sense of camaraderie, empathy, sympathy for the loser.

All logical and mathematical games teach children to think logically, to keep in mind several properties of an object at once, to be able to encode and decode information.

The use of developing, logical and mathematical games contributes to the emergence of children's interest in cognitive activity, the development of their thinking, speech, imagination, fine motor skills of hands. Each child learned to play at his own pace, since after classes it was possible to complete the task again, to better understand its essence.

An important role is played by the organization of independent activity in a specially organized developmental environment. In the free use of children there are a variety of logic and mathematical games: "Do It Yourself", "Unicube", "Cubes for All", "Fractions", "Kusiner's Sticks", "Gyenesh Blocks", "Game Square", "Tangram", "Fold the pattern", "Ball", "Playing with color" and others.

The development of logical thinking and cognitive activity is impossible without the participation of parents. At all stages, the support of the child at home, in the family is required.

Joint activities of teachers and parents in this field of activity:

1. Inform parents about the tasks and content of logical, mathematical and educational games used in kindergarten.

2. Participation of parents in the development of cognitive activity of logical thinking of preschoolers (math fairs, holidays, competitions).

3. Creating an enriched developmental environment in the home.

Experience shows that an educator who knows how to choose games correctly and stimulate independent cognitive-playing activity of preschoolers is “doomed” to a good result.

Gyenesh block game

"Help Bunny"

Purpose: To continue to acquaint children with geometric shapes. Compiling geometric shapes from data. Fixing an account.

Game material: Gyenes blocks.

Rules of the game: Use the figures to close the white "holes".

Once upon a time there was a Bunny, who had a very beautiful carpet. One day, the Fox came to his house secretly, and while the Bunny was running through the forest, the Fox gnawed holes in the carpet. Count how many holes there are in the carpet. Now take the pieces and help Bunny fix the carpet.

Game with two hoops.

Purpose: Formation of a logical operation, denoted by the union "and", classification by two properties.

Game material: Two hoops, geometric shapes.

Rules of the game: The game has several stages.

1. Before starting the game, you need to find out where the 4 areas are located, defined on the game sheet by two hoops.

2. Then one of the players calls the rules of the game. For example, arrange the figures like this. So that all red figures are inside the red hoop, and all green figures are inside the green hoop.

3. In accordance with the rule, the players perform moves in turn, and with each move they place one of the pieces they have in the appropriate place.

4. After solving a practical problem on the location of the figures, the children answer the questions: which figures lie inside both hoops; inside the green, but outside the red hoop, inside the red, outside the green hoop; outside of both hoops.

Attention: figures must be named using two properties - color and shape.

The game with two hoops can be played many times by varying the rules of the game.

Game options.

inside the red hoop inside the green hoop

all square shapes all green shapes

all yellow shapes all triangular shapes

all rectangular shapes all large shapes

all small pieces all green pieces

all red shapes all round shapes

all round shapes all square shapes

Tatyana Golikova
The development of logical and mathematical representation in children of senior preschool age, taking into account the Federal State Educational Standard

« The development of logical and mathematical representation in children of senior preschool age, taking into account the Federal State Educational Standard»

Mathematics teaching preschool children unthinkable without the use of entertaining games, tasks, entertainment. Of all the variety of mathematical material in preschool age didactic games are most widely used. The main purpose of games is to provide exercise children in discrimination, selection, naming sets items, numbers, geometric shapes, directions, etc. In didactic games, it is possible to form new knowledge, introduce children with ways of doing things. Each of the games solves a specific problem of improving mathematical children's ideas.

Logico-Mathematical games are included directly in the content of classes as one of the means of implementing program tasks. The place of these games in the structure of the FEMP lesson determined by the age of the children, purpose, meaning, content of the lesson aimed at fulfilling a specific task of forming representations.

In formation at kids math concepts various didactic game exercises entertaining in form and content are widely used. They differ from typical tasks and exercises in the unusual setting of the task (to find, guess, by the unexpectedness of presenting it on behalf of some literary fairy-tale hero (Pinocchio, Cheburashki, Dunno). They are of interest to children, emotionally capture them. And the process of solving, searching for an answer, based on interest in the problem, is impossible without the active work of thought. This position explains the importance logic and mathematical games, tasks and exercises in the mental and comprehensive child development. In the course of games and exercises with entertaining mathematical material, children master the ability to search for solutions on their own. The tutor is arming children only a scheme and direction of the analysis of an entertaining problem, leading in the end to a solution.

In my group, in the morning and evening, I spend games of mathematical content (verbal and using manuals, desktop-printed, such as "Domino Shapes", "Make a Picture", "Arithmetic Domino", "Geometric Mosaic", "Find a Pair", "Math Flowers", checkers game. With the right organization and guidance from educators, these games help development in children cognitive abilities, the formation of interest in actions with numbers, and geometric shapes, quantities, problem solving. Thus, mathematical children's ideas are improving.

In kindergarten, it is necessary to create such conditions for the mathematical activity of the child, under which he would show independence in choosing game material, games, based on developing he has needs and interests. Therefore, in each group there should be a corner of entertaining mathematics. This is a specially designated, mathematically equipped with games, manuals and materials and certain an artistically designed place. Here for the children provided the opportunity to choose a game that interests them, a manual of mathematical content and play individually or together with other children, a small subgroup. When organizing a corner of entertaining mathematics, one must proceed from the principle of the availability of games for children at the moment and place in the corner such games and game materials, the development of which by children is possible at different levels.

In your group, for senior preschool age, in the corner of entertaining mathematics, I use puzzles with sticks. They are called problems of ingenuity of a geometric nature, since during the game there is a transformation of some figures into others, and not just a change in their number. In my group, I use the simplest puzzles. I also use sets of ordinary counting sticks to make visual tasks out of them - puzzles. For the game, many tables have been made with figures graphically depicted on them, which are subject to transformation. On the reverse side of the table it is indicated what transformation needs to be done and what figure should be the result.

The group has games for compiling planar images items, animals, birds, houses, ships from special sets of geometric shapes. The sets of figures were not chosen arbitrarily, but present part of the cut figure in a certain way: square, rectangle, circle, oval. This games: "Tangram", "Columbus egg", "Mongolian game". children captivates the result to compose what he saw on the sample. They try Arrange the shapes to create the silhouette of the selected image. Also in my group, children like to play Gyenish blocks and Nikitin cubes. During these games, children develop fine motor skills, imagination, speech, attention, sensory standards of color, size and shape, spatial orientation are formed. Gyenish blocks and Nikitin cubes can turn into a house, a bird, a butterfly, a boat, etc. You can build a tower, a fungus, a car, a rocket from them.

From diversity logical-math games and entertainment the most accessible and interesting preschool age are riddles, tasks are jokes. In riddles of mathematical content, it is analyzed thing from a temporal point of view, from a quantitative or spatial point of view, the simplest mathematical relationship: Four brothers live under one roof (table). Which number does not change when it is flipped (eight). What will happen to the goat after three years (fourth year coming).Which word has as many numbers as letters (one hundred). How to make four out of three sticks without breaking them (add four).

Smart games, puzzles, entertaining games are of great interest to children. During such lessons, children are formed: mathematical representation, logical thinking, independence, observation, ingenuity, perseverance is developed, develop constructive skills.

Related publications:

What I heard, I forgot. What I saw, I remember. What I did, I know! Chinese wisdom Characteristics of the project The project is calculated.

The scenario of the New Year's performance for children of senior preschool age "In search of Santa Claus" Leading. We are starting a children's ball, Cheerful, noisy carnival! We will dance and sing at the Christmas tree We have fun today. Look everyone, and we will start Ours.

Scenario of the theatrical performance "Fairytale and merry holiday" for children of senior preschool age Presenter: Dear viewers, children and parents. See our entertainment, don't you want to? We invite you, old and young, Santa Claus will be glad to everyone. Ouch,.

Modern technologies of logical and mathematical development and education of preschool children Modern technologies of logical and mathematical development and education of preschool children. Development and selection of logical-mathematical technologies.

Creation of a subject-developing environment, taking into account the requirements of the Federal State Educational Standard in the group of preschool (senior preschool) age 1 slide. Creation of a subject - developing environment in the group of preschool (senior preschool) age MOU City basic general education.

Image Library:

Send your good work in the knowledge base is simple. Use the form below

Students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

Posted on http://www.allbest.ru/

State autonomous educational institution

higher professional education

“Leningrad State University named after A.S. Pushkin"

Boksitogorsk Institute (branch), SPO

Thesis

Logical and mathematical games as a means of forming logical thinking in children of senior preschool age

Completed by: Student 4 D group

Specialty 44.02.01

Preschool education

V.S. Morozova

scientific adviser

teacher PM.03 E.N. Nesterov

Boksitogorsk 2017

INTRODUCTION

In our time, there is an increasing expansion of knowledge acquired in childhood. The skills and abilities acquired in the preschool period serve as the foundation for gaining knowledge and developing abilities at school. And the most important among these skills is the skill of logical thinking, the ability to "act in the mind." A child who has not mastered the methods of logical thinking will find it more difficult to study: solving problems, doing exercises will require a lot of time and effort. Having mastered logical operations, the child will become more attentive, learn to think clearly and clearly, and be able to concentrate on the essence of the problem at the right time.

Thinking is a set of mental processes that underlie the knowledge of the world. In scientific language, this is such a mental process that creates judgments and conclusions through the synthesis and analysis of concepts. Thinking is responsible for ensuring that a person understands what surrounds him, and also builds logical connections between objects.

The concept of "thinking" includes the concept of "logical thinking", and they relate to each other as genus to species.

In a brief dictionary of the system of psychological concepts, logical thinking is defined as "a type of thinking, the essence of which lies in operating with concepts, judgments and conclusions using the laws of logic."

Logical thinking includes a number of components:

The ability to determine the composition, structure and organization of elements and parts of the whole and to focus on the essential features of objects and phenomena; - the ability to determine the relationship of an object and objects, to see their change in time;

The ability to obey the laws of logic, to discover patterns and development trends on this basis, to build hypotheses and draw conclusions from these premises;

The ability to perform logical operations, consciously arguing them.

Research results of L.S. Vygotsky, A.N. Leontiev, N.N. Poddiakova found that the basic logical structures of thinking are formed approximately at the age of 5 to 11 years. These data emphasize the importance of the senior preschool age, create a real basis for the development of the logical thinking of children, since the unique conditions created by it will no longer be repeated, and what will be "missing" here will be difficult or even impossible to make up in the future.

Thinking is one of the highest forms of human activity. Some children by the age of 5 are able to logically formulate their thoughts. However, not all children have these abilities. Logical thinking needs to be developed, and it is best to do it in a playful way.

The means of developing thinking are different, but the most effective are logical and mathematical games and exercises. They develop the ability to understand an educational or practical task, choose ways and means of solving, follow the rules exactly, focus on activities, control themselves, and arbitrarily control their behavior.

The study of the problem of studying and creating logico-mathematical games was carried out by such figures as Zoltan Gyenes, George Kuizener, B.P. Nikitin, V.V. Voskobovich, A.A. Stolyar, O.V. Zozulya, M.O. Sidorova, Z.A. Mikhailova, E.A. Nosova and others.

A.A. The carpenter suggested games rich in logical content for children aged 5-6. They model logical and mathematical constructions and during the game solve such problems that help accelerate the formation and development of the simplest logical structures of thinking and mathematical representations in preschoolers. He emphasized that children should not see that they are being taught something, they should "just" play. But imperceptibly during the game, preschoolers count, add, subtract, moreover, they solve various kinds of logical tasks that form certain logical operations.

Children usefully spend time playing with enthusiasm such logical and mathematical games as Tangram, Magic Circle, Columbus Egg, Nikitin's Cubes, Vietnamese Game, H. Kuizener's Colored Sticks, " Logic Blocks of Gyenes. For a long time, these puzzles served to entertain adults and adolescents, but modern research has proven that they are an effective means of mental, in particular logical, development of preschoolers.

The relevance of research in this area has identified the problem: insufficiently systematized use of logical and mathematical games in the process of forming elementary mathematical representations in order to increase the level of development of logical thinking in older preschool children.

The purpose of the work: to explore the possibilities of logical and mathematical games in the development of logical thinking in children of senior preschool age.

The purpose of the study determined the formulation of the following tasks:

1. Analyze the pedagogical possibilities of logic and mathematical games.

2. Consider the classification of logical and mathematical games.

3. To study the role of the logical and mathematical game as a means of activating the mathematical development of preschoolers.

4. To study the features of the development of thinking in children of the sixth year of life.

5. To study the methods of work on the formation of logical thinking through logic and mathematical games.

6. Organize experimental work to study the influence of logic and mathematics on the level of development of logical thinking in older preschoolers.

Object of research: the process of formation of logical thinking in children of the sixth year of life.

Subject of study: logical and mathematical games as a means of forming logical thinking in children of the sixth year of life.

Hypothesis: if the teacher systematically, taking into account the methodological requirements, use logical and mathematical games when working with children of older preschool age, this will help to increase the level of logical thinking.

We used the following methods of scientific and pedagogical research: the study and analysis of psychological and pedagogical literature, observation, experiment, survey.

CHAPTER 1

math game preschool thinking

1.1 The concept and pedagogical possibilities of logic and mathematical games

Theoretical and experimental works of A.S. Vygotsky, F.N. Leontiev, S.L. Rubenshtein prove that neither logical thinking, nor creative imagination and meaningful memory can develop in a child regardless of upbringing, as a result of the spontaneous maturation of innate inclinations. They develop throughout the entire preschool age, in the process of education, which plays, as L.S. wrote. Vygotsky "leading role in the mental development of the child."

It is necessary to promote the development of the child's thinking, teach him to compare, generalize, classify, synthesize and analyze. Mechanical memorization of various information, copying the reasoning of adults does nothing for the development of children's thinking.

V.A. Sukhomlinsky wrote: “... Do not bring down an avalanche of knowledge on a child ... - inquisitiveness and curiosity can be buried under an avalanche of knowledge. Be able to open one thing in front of the child in the surrounding world, but open it in such a way that a piece of life plays in front of the children with all the colors of the rainbow. Always open something unsaid so that the child wants to return again and again to what he has learned.

The education and development of the child should be arbitrary, occur through the types of activities and pedagogical means characteristic of this age. Such a developmental tool for children of senior preschool age is a game.

Ya.A. Comenius considers play as a valuable form of activity for a child.

A.S. Makarenko drew the attention of parents to the fact that "the upbringing of the future figure should not consist in eliminating the game, but in organizing it in such a way that the game remains a game, but the qualities of the future child, citizen are brought up in the game."

The game reflects the opinions of children about the world around them, their understanding of ongoing events and phenomena. In many games with rules, various knowledge, mental operations, and actions that children must master are displayed. Mastering this goes along with the general mental development, at the same time, this development is carried out in the game.

The combination of a learning task with a game form in a didactic game, the availability of ready-made content and rules enables the teacher to use didactic games more systematically for the mental education of children.

It is very important that the game is not only a way and means of learning, it is also joy and pleasure for the child. All children love to play, and it depends on the adult how meaningful and useful these games will be. While playing, the child can not only consolidate previously acquired knowledge, but also acquire new skills, abilities, and develop mental abilities. For these purposes, special games are used, aimed at the mental development of the child, saturated with logical content. A.S. Makarenko was well aware that one game, even the best, cannot ensure success in achieving educational goals. Therefore, he sought to create a complex of games, considering this task to be the most important in the matter of education.

In modern pedagogy, a didactic game is considered as an effective means of developing a child, the development of such intellectual mental processes as attention, memory, thinking, and imagination.

With the help of a didactic game, children are taught to think independently, to use the acquired knowledge in various conditions in accordance with the task. Many games challenge children to rationally use existing knowledge in mental operations:

Find characteristic features in objects and phenomena of the surrounding world;

Compare, group, classify objects according to certain criteria, draw the right conclusions.

The activity of children's thinking is the main prerequisite for a conscious attitude to the acquisition of solid, deep knowledge, the establishment of various relationships in the team.

Didactic games develop children's sensory abilities. The processes of sensation and perception underlie the child's knowledge of the environment. It also develops the speech of children: the dictionary is filled and activated, the correct pronunciation is formed, coherent speech develops, the ability to correctly express one's thoughts.

Some games require children to actively use specific, generic concepts, exercise in finding synonyms, words similar in meaning, etc. During the game, the development of thinking and speech is decided in continuous connection; when children communicate in the game, speech is activated, the ability to argue their statements and arguments develops.

So, we found out that the developing abilities of the game are great. Through the game, you can develop and improve all aspects of the child's personality. We are interested in games that develop the intellectual side, which contribute to the development of thinking of older preschoolers.

Mathematical games are games in which mathematical constructions, relationships, patterns are modeled. To find an answer (solution), as a rule, a preliminary analysis of the conditions, rules, content of the game or task is necessary. In the course of the solution, the use of mathematical methods and inferences is required.

A variety of mathematical games and tasks are logical games, tasks, exercises. They are aimed at training thinking when performing logical operations and actions. In order to develop the thinking of children, various types of simple tasks and exercises are used. These are tasks for finding a missing figure, continuing a number of figures, for finding numbers that are missing in a number of figures (finding the patterns underlying the choice of this figure, etc.)

Consequently, logical-mathematical games are games in which mathematical relationships are modeled, patterns that involve the performance of logical operations and actions.

A.A. The joiner defined the essential characteristics of logical and mathematical games:

The focus of actions performed in games is mainly on the development of the simplest logical methods of cognition: comparison, classification and seriation;

The possibility of modeling in games accessible to a child of 4-6 years old logical and mathematical relationships (similarity, order, part and whole).

While playing, children master the means and methods of cognition, the appropriate terminology, logical connections, dependencies and the ability to express them in the form of simple logical statements.

The main components of logic-mathematical games are:

The presence of schematization, transformation, cognitive tasks to identify properties and relationships, dependencies and patterns;

Abstraction from the non-essential, techniques for highlighting essential features;

Mastering the actions of correlation, comparison, reconstruction, distribution and grouping, operations of classification and seriation;

Game motivation and direction of actions, their effectiveness;

The presence of situations of discussion, choice of material and actions, collective search for a way to solve a cognitive problem;

The possibility of repeating the logical-mathematical game, complicating the content of the intellectual tasks included in the game-occupation;

General focus on the development of children's initiative.

The rules are strictly fixed, they determine the method, order, sequence of actions according to the rule. Game actions allow you to implement the task through game activity. The results of the game are the completion of the game action or a win.

Logic-mathematical games and exercises use a special structured material that allows you to visualize abstract concepts and relationships between them.

Specially structured material:

Geometric shapes (hoops, geometric blocks);

Schemes-rules (chains of figures);

Function schemes (computers);

Schemes of the operation (chessboard).

Modern logical and mathematical games stimulate the child's persistent desire to get a result (collect, connect, measure), while showing cognitive initiative and creativity. They contribute to the development of attention, memory, speech, imagination and thinking, create a positive emotional atmosphere, encourage children to communicate, collective search, and be active in transforming the game situation.

Many modern companies (“Corvette”, “RIV”, “Oksva”, “Smart Games”, etc.) develop and release games that contribute to the development in children of the ability to act consistently in practical and mental terms, to use symbols (“Cubes for All ”, “Logic and Numbers”, “Logo Forms”, “Entertainer Cord”, “Kaleidoscope”, “Transparent Square”, etc.).

Educational logical and mathematical games are specially designed in such a way that they form not only elementary mathematical representations, but also certain, pre-designed logical structures of thinking and mental actions necessary for the further assimilation of mathematical knowledge and their application to solving various kinds of problems.

So, the pedagogical possibilities of the game are very great. We revealed the concept of a logical-mathematical game, got acquainted with the essential characteristics, the main components of this type of game; learned that specially structured material is used in logic-mathematical games.

1.2 Classification of logic and mathematical games

All logical and mathematical games teach children to think logically, to keep in mind several properties of an object at once, to be able to encode and decode information.

The solution of various kinds of non-standard tasks at preschool age contributes to the formation and improvement of general mental abilities: the logic of thought, reasoning and action, the flexibility of the thought process, ingenuity and ingenuity, spatial representations. Of particular importance should be considered the development in children of the ability to guess at a certain stage of the analysis of an entertaining problem, search actions of a practical and mental nature. A guess in this case testifies to the depth of understanding of the problem, the high level of search actions, the mobilization of past experience, the transfer of learned methods of solution to completely new conditions.

Opening the topic, it is necessary to characterize different groups of logic and mathematical games.

E. A. Nosova developed her own classification of logical and mathematical games:

Games to identify properties - colors, shapes, size, thickness ("Find a treasure", "Guess", "Unusual figures", etc.);

On the development of comparison, classification and generalization by children (“Paths”, “Domino”, “Sat houses”, etc.);

To master logical actions and mental operations (“Riddles without words”, “Where did Jerry hide?”, “Help the figures get out of the forest”, etc.)

PER. Mikhailova presented a classification of logical and mathematical games according to the purpose and method of achieving the result:

1) games for planar modeling (puzzles):

Classical: "Tangram", "Columbus egg", "Pentamino", etc.;

Modern: "Miracle Crosses", "Miracle Honeycombs", "Wonderful Circle", "Three Rings", mosaics "Summer", "Lake", "Pilot", "Jungle", etc.;

Games with matches (for transformation, transfiguration);

2) games to recreate and change in shape and color:

Insert frames M. Montessori, "Secrets", a mosaic of sticks, "Rainbow web" (square, star, circle, triangle), "Geometric train", "Fold the pattern", "Chameleon cubes", "Crosses" (with colored counting sticks), “Unicube”, “Color panel”, “Little designer”, “Kaye honeycombs”, “Logo molds”, “Lanterns”, “Tetris” (flat), “Rainbow basket”, “Fold a square”, “ Logic Constructor (ball), Logic Mosaic;

3) games for the selection of cards according to the rule in order to achieve a result (table-printed):

- "Logic chains", "Logic house", "Logic train", "Fold it yourself";

4) games for three-dimensional modeling (logic cubes, "Cubes for everyone"):

- "Corners" (No. 1), "Collect" (No. 2), "Eureka" (No. 3), "Fantasy" (No. 4), "Riddles" (No. 5), "Tetris" (volumetric);

5) games for correlating cards by meaning (puzzles):

- "Associations", "Colors and shapes", "Playing, learn", "Part and whole";

6) transfiguration and transformation games (transformers):

- "Game square", "Snake", "Cut square", "Lotus flower", "Snake" (volumetric), "Tangle", "Cube";

7) games for mastering relationships (whole - part)

- "Transparent Square", "Miracle Flower", "Geocont", "Cord-Entertainer", "House of Fractions".

Guminyuk Svetlana Andreevna conditionally subdivides logical and mathematical games into three groups:

Entertaining games: riddles, jokes, puzzles, crossword puzzles, labyrinths, mathematical squares, mathematical tricks, games with sticks for spatial transformation, smart tasks; "Tangram", "Magic Circle", "Columbus Egg", "Sphinx", "Leaf", "Vietnamese Game", "Pentamino";

Logic games, tasks, exercises: with blocks, inclusion cubes, finding; games for classification by 1-3 features, logical tasks (for increase, decrease, comparison, reverse action); games with colored caps, checkers, chess; verbal; Gyenes blocks, Kuizener sticks;

Educational exercises: with visual material to search for the missing, highlighting a common feature, determining the correct sequence, highlighting the superfluous; games for the development of attention, memory, imagination, games for finding contradictions: “Where is whose house?”, “What is superfluous?”, “Find the same one”, “Incredible intersections”, “Name it in one word”, “What sets are mixed up?” , “What has changed?”, “What numbers ran away?”, “Continue”, “Pathfinder”.

Thus, we can say that logico-mathematical games are diverse and require extensive study. Each individual game solves certain problems. They can be for identifying the properties of an object, for children to master comparison, classification and generalization, for planar modeling (puzzles), for recreating and changing in shape and color, for volumetric modeling and for mastering relationships (whole - part).

1.3 Logical and mathematical games as a means of enhancing the teaching of mathematics to children of senior preschool age

The modernization of preschool education, and pre-mathematical training in particular, has stepped up the activity of firms that produce educational and game aids for preschoolers. Logic-mathematical games began to appear that contribute to cognition:

Properties and relations of both single objects and their groups in terms of shape, size, mass, location in space;

Numbers and figures;

Dependencies of increase and decrease at the subject level;

The order of succession, transformation, conservation of quantity, volume, mass.

At the same time, children master both prelogical actions, connections and dependencies, and pre-mathematical ones. For example, when building a house (the game "Logic House"), the child takes into account logical connections (dependence of objects in color, shape, purpose, meaning, belonging) and mathematical (compliance with the number of storeys and the overall size of the house).

Logical and mathematical games are designed by the authors based on the modern view of propaedeutics in children aged 5-7 years of mathematical abilities. The most important of them include:

Operating with images, establishing links and dependencies, fixing them graphically;

Presentation of possible changes in objects and prediction of the result;

Changing the situation, the implementation of the transformation;

Active effective actions both in practical and ideal terms.

Logical and mathematical games contribute not only to the development of individual mathematical skills, but also to the sharpness and logic of thought. Involving in the game, the child follows certain rules; at the same time, he obeys the rules themselves not under duress, but completely voluntarily, otherwise there will be no game. And the implementation of the rules is associated with overcoming difficulties, with the manifestation of perseverance.

However, despite the importance and significance of the game in the process of learning, it is not an end in itself, but a means for developing interest in mathematics. The mathematical side of the content of the game should always be clearly brought to the fore. Only then will it fulfill its role in the mathematical development of children and instilling their interest in mathematics.

Didactics has a variety of educational materials. As an example, let's look at the logical blocks developed by the Hungarian psychologist and mathematician Gyennes, which are used to develop early logical thinking and to prepare children for learning mathematics. Gyenes blocks are an effective tool for the mathematical development of preschoolers. They are a set of geometric shapes, which consists of 48 three-dimensional figures that differ in shape (circles, squares, rectangles, triangles), color (yellow, blue, red), size (large and small) in thickness (thick and thin) . That is, each figure is characterized by four properties: color, shape, size, thickness. There are not even two figures in the set that are identical in all properties.

In their practice, kindergarten teachers mainly use flat geometric shapes. The whole complex of games and exercises with Gyenes blocks is a long intellectual staircase, and the games and exercises themselves are its steps. On each of these steps, the child must stand. Logical blocks help the child master mental operations and actions, these include: identifying properties, comparing them, classifying, generalizing, encoding and decoding, as well as logical operations.

In addition, the blocks can lay in the minds of children the beginning of an algorithmic culture of thinking, develop in children the ability to act in the mind, master ideas about numbers and geometric shapes, and spatial orientation.

In the process of various actions with blocks, children first master the ability to identify and abstract one property in objects (color, shape, size, thickness), compare, classify and generalize objects according to one of these properties. Then they master the ability to analyze, compare, classify and generalize objects by two properties at once (color and shape, shape and size, size and thickness, etc.), a little later by three (color, shape, size; shape, size, thickness, etc.) and four properties (color, shape, size, thickness), while developing the logical thinking of children.

In the same exercise, you can vary the rules for completing the task, taking into account the capabilities of children. For example, several children are building paths. But one child is invited to build a path so that there are no blocks of the same shape nearby (operating with one property), the other - so that there are no identical ones in shape and color nearby (operating with two properties at once). Depending on the level of development of children, it is possible to use not the entire complex, but some part of it, first the blocks are different in shape and color, but the same in size and thickness, then different in shape, color and size, but the same in thickness and the end of the complete set of figures.

This is very important: the more diverse the material, the more difficult it is to abstract some properties from others, and, therefore, to compare, classify, and generalize.

With logical blocks, the child performs various actions: lays out, swaps, removes, hides, searches, divides, and argues along the way.

Thus, playing with blocks, the child comes closer to understanding the complex logical relationships between sets. From playing with abstract blocks, children easily move on to games with real sets, with concrete material.

In the first chapter, we revealed the essence and significance of logic-mathematical games in the mathematical development of preschoolers. We have identified the pedagogical possibilities of the logical-mathematical game, and concluded that these games stimulate the child's persistent desire to get a result (collect, connect, measure), while showing cognitive initiative and creativity. Logic-mathematical games are games in which mathematical relationships are modeled, patterns that involve the performance of logical operations and actions.

Logical and mathematical games act as a means of activating the teaching of mathematics to children of senior preschool age, they are developed in such a way that they form not only certain, pre-designed logical structures of thinking and mental actions, but also elementary mathematical representations necessary for the further assimilation of mathematical knowledge and their application to solving various problems.

Therefore, we can say that logico-mathematical games are diverse and require extensive study.

CHAPTER 2

2.1 Features of the development of thinking in children of older preschool age

At the senior preschool age there is an intensive development of the intellectual, moral-volitional and emotional spheres of the personality. The development of personality and activity is characterized by the emergence of new qualities and needs: knowledge about objects and phenomena that the child has not directly observed is expanding. Children are interested in the connections that exist between objects and phenomena. The penetration of the child into these connections largely determines his development. The educator maintains in children a sense of "adulthood" and, on its basis, causes them to strive to solve new, more complex tasks of cognition, communication, and activity.

Thinking as the highest mental process is formed in the process of activity.

In psychology, there are three main types of thinking:

Visual and effective (it is formed in 2.5 - 3 years, is leading up to 4 - 5 years);

Visual-figurative (from 3.5 - 4 years, leading up to 6 - 6.5 years);

Verbal-logical (it is formed at 5.5 - 6 years old, becomes the leader from 7-8 years old).

Visual-effective thinking is based on the direct perception of objects, the real transformation of the situation in the process of actions with objects.

A distinctive feature of the next type of thinking - visual-figurative - is that the thought process in it is directly connected with the thinking person's perception of the surrounding reality and cannot be performed without it. This form of thinking is most fully represented in children of preschool and primary school age.

Verbal-logical thinking functions on the basis of linguistic means and represents the latest stage in the development of thinking. Verbal-logical thinking is characterized by the use of concepts, logical structures, which sometimes do not have a direct figurative expression.

The thinking of a young child acts in the form of actions aimed at solving specific problems: get some object that is in sight, put rings on the rod of a toy pyramid, close or open a box, find a hidden thing, etc. While performing these actions, the child thinks. He thinks by acting, his thinking is visual and effective.

The development of visual-effective and visual-figurative thinking is interconnected with the formation of verbal-logical thinking. Already in the process of solving visual-practical problems, children have the makings of understanding the cause-and-effect relationships between an action and a reaction to this action.

The experiments of such scientists as: Zaporozhets A.V., Venger L.A., Galperin P.Ya. which is possible and expedient for the successful formation of initial logical skills in children. Studies have proven that the basic logical skills at the elementary level are formed in children from the age of 5-6 years.

The possibility of systematic assimilation of logical knowledge and techniques by children of senior preschool and primary school age is shown in the psychological studies of H.M. Veklerova, S.A. Ladymir, L.A. Levitova, L.F. Obukhova, N.N. Poddyakova. They proved the possibility of forming separate logical actions (seriation, classification, inference) in older preschoolers. The basis for the development of thinking is the formation and improvement of mental actions. The mastery of mental actions in preschool age occurs according to the general law of the assimilation of external orienting actions. In these works, it was found that a child of 6-7 years old can be taught full-fledged logical actions to determine "belonging to a class" and "correlation of classes and subclasses".

The ability to move on to solving problems in the mind arises due to the fact that the images used by the child acquire a generalized character, do not reflect all the features of the object, situation, but only those that are essential from the point of view of solving a particular problem. Children very easily and quickly understand various kinds of schematic images and successfully use them. So, starting from the age of five, preschoolers, even with a single explanation, can understand what a room plan is, and, using a mark on the plan, they find a hidden object in the room. They recognize schematic representations of objects, use a diagram like a geographical map to choose the right path in an extensive system of paths, look for the “address of a figure” on a chessboard.

An older preschooler can already rely on past experience - the mountains in the distance do not seem flat to him in order to understand that a large stone is heavy, he does not have to pick it up - his brain has accumulated a lot of information from various channels of perception. Children gradually move from actions with the objects themselves to actions with their images. In the game, the child no longer has to use a substitute object, he can imagine "game material" - for example, "drink" from an imaginary cup. Unlike the previous stage, when in order to think, the child needed to pick up an object and interact with it, now it is enough to imagine it.

During this period, the child actively operates with images - not only imaginary in the game, when a machine is presented instead of a cube, and a spoon “turns out” in an empty hand, but also in creativity. It is very important at this age not to accustom the child to the use of ready-made schemes, not to impose their own ideas. At this age, the development of fantasy and the ability to generate their own, new images are the key to the development of intellectual abilities - after all, thinking is figurative, the better the child comes up with his own images, the better the brain develops. Many people think fantasy is a waste of time. However, how fully figurative thinking develops, its work also depends on the next, logical, stage. Therefore, do not worry if a child at the age of 5 cannot count and write. It is much worse if he cannot play without toys (with sand, sticks, pebbles, etc.) and does not like to be creative! In creative activity, the child tries to portray his invented images, looking for associations with known objects. It is very dangerous during this period to “train” the child in given images - for example, drawing according to a model, coloring, etc. This prevents him from creating his own images, that is, from thinking.

From which we can conclude that logical thinking is formed in the process of children's activities. In older preschool age, visual-figurative thinking prevails in children, which is interconnected with the formation of verbal-logical thinking. It is at this age that a child should not be taught to use ready-made schemes, to plant their own ideas.

2.2 Formation and development of the logical sphere of children of senior preschool age by means of logic and mathematical games

The formation of logical operations is an important factor that directly contributes to the development of the thinking process of an older preschooler. Almost all psychological studies devoted to the analysis of the methods and conditions for the development of a child’s thinking are unanimous in the fact that the methodological guidance of this process is not only possible, but also highly effective, i.e., when organizing special work on the formation and development of logical operations of thinking, there is a significant increase the effectiveness of this process, regardless of the initial level of development of the child.

Let us consider the possibilities of active inclusion in the process of development of the logical sphere of a child of senior preschool age of various logical and mathematical games aimed at the formation of logical operations.

Seriation is the construction of ordered ascending or descending series. A classic example of seriation: nesting dolls, pyramids, loose bowls, etc. Seriations can be organized by size: by length, by height, by width - if the objects are of the same type (dolls, sticks, ribbons, pebbles, etc.) and simply “by size” (with an indication of what is considered “size”) - if objects of different types (seat toys according to height). Seriations can be organized by color: according to the degree of color intensity.

The most suitable didactic aid for the formation of this logical operation is Kuizener's colored sticks. Sticks of the same length are painted in the same color. Each stick displays a certain number in cm, united by a common shade of the sticks form "families". Each "family" displays the multiplicity of numbers, for example, the "red family" includes numbers that are divisible by 2, the "green family" includes numbers that are divisible by 3, etc. Kuizener's sticks act as a visual material that makes work with children's logic and develop counting and measurement skills. And having learned to understand all this, the child lays a solid foundation for further mathematical achievements.

Analysis - selection of object properties, selection of an object from a group or selection of a group of objects according to a certain attribute.

Synthesis is the combination of various elements (features, properties) into a single whole. In psychology, analysis and synthesis are considered as mutually complementary processes (analysis is carried out through synthesis, and synthesis through analysis).

To form the operations of analysis and synthesis in a child, one should use such logical and mathematical games as "Tangram", the Pythagorean puzzle, "Magic Circle", "Columbus Egg", "Vietnamese Game", "Pentamino". All games are united by a common goal, methods of action and result. Introduction to games should proceed from the simple to the complex. Having mastered one game, the child receives the key to mastering the next. Each game is a set of geometric shapes. Such a set is obtained by dividing one geometric figure (for example, a circle in the Magic Circle, a square in the Tangram) into several parts. The method of dividing the whole into parts is given in the description of the game and in visual diagrams. On any plane (table, flannelgraph, magnetic board, etc.), various silhouettes or plot pictures are laid out from the geometric shapes included in the set.

Game activity can be organized in two ways:

1) the gradual complication of patterns and schemes used in games: from a dissected sample to an undivided one;

2) organization of play activities based on the development of the child's imagination and creativity.

Also, the logical operations of analysis and synthesis can be formed by using Nikitin’s set of cubes “Fold the Pattern”, which consists of 16 identical cubes, in work with older preschoolers. All 6 sides of each cube are colored differently in 4 colors (4 sides of the same color - yellow, blue, white, red and 2 sides - yellow-blue and red-white). In the game with cubes, children perform 3 types of tasks. First, they learn to fold exactly the same pattern from cubes according to pattern-tasks. Then they set the inverse problem: looking at the cubes, draw the pattern that they form. And the third is to come up with new patterns of 9 or 16 cubes, which are not yet in the manual, i.e. do creative work. Using a different number of cubes and different not only in color, but also in shape (squares and triangles) coloring of the cubes, you can change the complexity of tasks.

Such games help to accelerate the development of the simplest logical structures of thinking and mathematical concepts in preschoolers.

Comparison is a logical technique that requires identifying similarities and differences between the features of an object (object, phenomenon, group of objects).

Tasks for dividing objects into groups according to some attribute (large and small, red and blue, etc.) require comparison. All logical and mathematical games of the "Find the same" type are aimed at developing the ability to compare. For children of older preschool age, the number and nature of signs of similarity can vary widely.

Classification is the division of a set into groups according to some attribute, which is called the basis of the classification. The basis for classification may or may not be specified (this option is more often used with older children, as it requires the ability to analyze, compare and generalize).

Classification and comparison can be formed using Gyenesh logical blocks. One of the modern educational and game aids "Let's play together" presents variants of logical and mathematical games and exercises with a flat set of Gyenesh blocks. They are an effective didactic material that successfully combines elements of a constructor and an educational game. In the process of working with logical blocks, the guys first acquire the skills to highlight and abstract only one property in the figures: color, thickness, size or shape. After a while, children perform tasks with a higher level of complexity. In this case, two or more properties of the object are taken into account. For the convenience of work, tasks with logical blocks are offered in three versions, which differ in different levels of complexity. The effectiveness of games with logical blocks depends on the individual characteristics of the child and on the professionalism of the teacher.

In the practice of preschool organizations, logical and mathematical games in all their diversity have not found proper application, and if they are used, then most often haphazardly. The main reasons for this phenomenon are probably the following:

Kindergarten teachers underestimate the importance of logical and mathematical games in the development of mathematical concepts in children and in the successful transition to logical thinking;

Teachers are not sufficiently proficient in game methods of the logical and mathematical development of preschool children;

In games, game learning situations, often children's independence and activity are replaced by the teacher's own initiative. The child in the game becomes the executor of the instructions, instructions of the adult, and not the subject of learning game activity (he is not an actor, not a creator, not a discoverer, not a thinker).

In the second chapter, we examined the main types of thinking and concluded that the development of visual-effective and visual-figurative thinking is interconnected with the formation of verbal-logical thinking.

We also revealed the possibilities of active inclusion in the process of development of the logical sphere of a child of senior preschool age of various logical and mathematical games aimed at the formation of logical operations. In order to develop logical operations, Kuizener's sticks, Gyenes blocks, the "Wonderful Circle", etc. are used. We confirmed that the purpose of logical and mathematical games is to contribute to the formation of the logical and mathematical experience of the child on the basis of mastering the actions of comparison, comparison, division, construction logical statements, algorithms.

CHAPTER 3

For practical testing of the results of a theoretical study, we organized an experiment on the basis of the MBDOU "Kindergarten No. 7 KV" in Pikalevo with children of the senior group No. 1, in the amount of ten people. The experiment consisted of three stages: ascertaining, forming and control.

3.1 Diagnostics of the level of development of logical thinking in children of the older age group

Purpose: to identify the level of development of logical thinking in older preschoolers.

At the stage of the ascertaining experiment, we used the following methods:

Method "Divide into groups" (A.Ya Ivanova)

We asked the children to divide the figures shown in the picture into as many groups as possible. Each such group should have included figures distinguished by one feature common to them. The child had to name all the figures included in each of the selected groups, and the sign by which they were selected. It took 3 minutes to complete the entire task. (see Appendix 1).

The data were entered in table 1.

Table 1.

	Number of selected groups of figures	Level of evolution

2. Vasilisa







8. Timothy

The table shows that Varya, Eva, Kirill, Sasha, Sonya and Timofey have an average level of development of logical thinking. When completing the task, these children were able to identify from 7 to 9 groups of geometric shapes. Guessed that the same figure in the classification can be included in several different groups. But nevertheless, no one was able to meet in less than 3 minutes.

The level of development of logical thinking in Vasilisa, Egor, Kupava and Katya is at a low level. When performing the task, they made many mistakes, were not interested in work, were distracted.

Methodology Beloshistaya A.V. and Nepomnyashchaya R.N.

Based on this methodology, we have developed a set of diagnostic tasks aimed at identifying the level of development of skills to analyze, compare, classify, generalize (see Appendix 2).

The data are shown in table 2.

Table 2.

Interpretation of the results of the ascertaining stage of the experiment

	Number of completed tasks	Level of evolution

2. Vasilisa







10. Timothy

From the data obtained, we can conclude that Kirill, Sasha, Vari, Eva, Timofey and Sonya have an average level of development of logical thinking, which coincides with the results of the previous diagnostics. These children made inaccuracies and mistakes when performing assignments, continued to perform correctly with the help of the educator, were interested in the work, showed diligence, and were not distracted. We were able to complete 5 to 7 tasks.

Katya, Kupava, Yegor, Vasilisa are at a low level of development. The children coped with only three of the proposed tasks, did not complete them, did not pay attention to the teacher's prompts, and were distracted.

Children with a high level of development were not identified.

In order to increase the level of logical thinking, it is necessary to carry out correctional and developmental work with children. To this end, we decided to systematically, purposefully and consistently use logical and mathematical games in the organization of direct educational activities in the formation of elementary mathematical concepts and in the independent activities of children.

3.2 The system of using logic and mathematics in the organization of direct educational activities

Purpose: to increase the level of development of logical thinking in children of the older group through the use of logic and mathematical games.

To achieve this goal, we organized directly - educational activities using logical and mathematical games, as well as the inclusion of specially designed exercises in the independent activities of children.

Children were offered such games as: "Columbus egg", "Tangram", "Pentamino", "Magic circle", "Fold the pattern". Also didactic material - Kuizener sticks and Gyenes blocks.

Direct educational activity corresponded to the thematic planning according to the program, as well as to the speech and age characteristics of the children of the older age group.

In the process of GCD on the formation of elementary mathematical representations on the topic: "House for piglets", the children showed a steady interest, curiosity and initiative. They were offered tasks for modeling according to the scheme of Gyenes blocks, which contributed to the formation of such logical operations as comparison and classification. Also, the children were carried away by the distribution of "magic" blocks on hoops with a given color, which contributed to the development of grouping and systematization skills.

In working with children, she used conversation, questions to children for quick wits and the development of logical thinking - all this contributed to the effectiveness of the GCD, the improvement of the processes of mental activity.

At the beginning of the GCD on the formation of elementary mathematical ideas on the topic: "Journey with a bun", the children were offered the logical and mathematical game "Magic Circle", during which they had to make an image of a fairy-tale character by combining several parts into one geometric figure. This task was aimed at the formation of logical operations of synthesis and analysis. In the main part, children from Kuizener's sticks made up a train from the shortest trailer to the longest, which contributed to the development of the ability to build ordered increasing rows. In turn, the logico-mathematical games "Fold the pattern" and "Tangram" contributed to the formation of logical thinking, in particular, the operations of analysis and synthesis.

In the course of the GCD on the formation of elementary mathematical representations on the topic: "Tea drinking for a kitten" Woof ", the children were offered various tasks for silhouette design with colored Kuizener sticks (a teapot, a samovar, a cup with a saucer, etc.), which contributed to the formation of such logical operation as seriation.

Abstracts of the GCD, visual material, as well as an analysis by the educator of the GCD carried out are contained in appendices 3 - 11.

3.3 Studying the effectiveness of a proven system for using logic and mathematical games

After the work on the development of logical thinking in children of senior preschool age, a control experiment was conducted.

Purpose: to identify the effectiveness of the developed and implemented system for the use of logic and mathematical games in the organization of GCD in children of the older group.

To achieve the goal of the control experiment, the methods of Beloshistaya A.V., Nepomnyashchaya R.N. were again used. and A.Ya. Ivanova.

The results are shown in tables 3.4.

Table 3. Interpretation of the results of the control stage of the experiment Method "Divide into groups"

	Number of selected groups of figures	Level of evolution
		Very tall
2. Vasilisa







10. Timothy

The table shows that Eva, Sonya and Timothy have a high level of development. When completing the task, these children were able to identify all 9 groups of geometric shapes in three minutes.

Varya showed a very high level of development of logical thinking. She quickly divided geometric figures into a possible number of groups, united by a common feature. Varya spent less than two minutes to complete the task.

Kupava, Katya, Egor, Vasilisa were able to improve their results from a low level of development of logical thinking to an average level. Up to 7 groups of geometric shapes were identified in three minutes.

Sasha and Kirill showed approximately the same results as before the start of the experiment, they remained at the same level. Nevertheless, Sasha was able to indicate 7 groups of figures in the control experiment in less time, although there were only 5 groups of figures in the ascertaining experiment. But unfortunately, this is not enough for high performance by this method.

Low indicators of the level of development of logical thinking at the final stage of the experiment were not revealed.

Table 4. Interpretation of the results of the control stage of the experiment Method Beloshistaya A.V. and Nepomnyashchaya R.N.

	Number of completed tasks	Level of evolution

2. Vasilisa







10. Timothy

The diagnostic results show a high level of development of logical thinking in Varya, Eva, Sonya and Timofey. These children practically did not make mistakes when performing tasks, were interested in work, showed diligence, and were not distracted.

Vasilisa, Yegor, Kupava and Katya are at an average level of development. Minor errors were made in completing assignments.

The indicators of Sasha and Kirill remained at the average level, but the number of tasks completed increased.

...

Download:

Preview:

State budgetary preschool educational institution

kindergarten №10 Primorsky district of St. Petersburg

ARTICLE

"Modern technologies,

forms and means of logical and mathematical development and education of preschool children”

The article was compiled by the teacher: Saykova G.E.

2016

ARTICLE QUESTIONS:

"MODERN TECHNOLOGIES OF LOGICAL AND MATHEMATICAL DEVELOPMENT AND TRAINING OF PRESCHOOL CHILDREN"

Based on the essence and characteristics of problem-play technology, determine what is its significance for the mathematical development of children?
What means does the problem-game technology of teaching mathematics to preschoolers include?
What is the peculiarity of logic-mathematical games? What knowledge and skills do children learn with their help?
What techniques are used to create problem situations in the process of children mastering logical and mathematical content and experience?
What is the algorithm for applying problem situations in teaching mathematics to preschoolers?
What is the essence of logical and mathematical story games and activities?
What is the difference between experimentation and research and problem-based learning?
Open the stages of leadership of independent research activities of preschoolers.
Give examples of games, exercises, tasks of mathematical content for the organization of experimentation in different age groups.
What is the specificity of creative tasks, questions, situations as a method of enriching the logical and mathematical experience of preschoolers?

MODERN TECHNOLOGIES OF LOGICAL AND MATHEMATICAL DEVELOPMENT AND TRAINING OF PRESCHOOL CHILDREN

Used in teaching preschoolers mathproblem-play technologyincluding the following tools:

The essence of technology - the creation by adults of situations in which the child strives for vigorous activity and receives a positive creative result.

Specific traits technologies:

the child is not limited in the search for practical actions, experimentation, communication to resolve errors and contradictions, the manifestation of joy and grief;
showing and detailed explanation are usually excluded;
the child independently finds a way to achieve the goal or masters it;
the child naturally accepts help from an adult: a partial prompt, participation in the performance or clarification of actions, speech methods of evaluation, etc.;
an adult creates motivation and selects games that are interesting for the child, exercises that develop ingenuity and ingenuity.

Logic and mathematical games.

Modern logic and mathematical games are diverse. In them, the child masters standards, models, speech, masters the methods of cognition, and develops thinking.

desktop printed:"Color and shape", "Count", "Game square", "Transparent square", "Logic train", etc.
3D modeling games: "Cubes for everyone", "Tetris", "Ball", "Snake", "Hedgehog", "Geometric constructor", etc.
plane modeling games: "Tangram", "Sphinx", "T-game", etc.
games from the Shape and Color series:“Fold the pattern”, “Unicube”, “Color panel”, “Colorful squares”, “Triangular domino”, “So that the color does not repeat”, etc.

games for making a whole out of parts:"Fractions", "Fold the square", "Greek cross", "Fold the ring", "Chessboard", etc.
fun games: labyrinths, permutations ("Tower of Hanoi", "Tea service", "Goats and rams", "Stubborn donkey");
puzzles (puzzles, mosaics, "Rainbow", "Fairy of Flowers", "Butterflies", "Fish", "Cunning Clown", "Parsley", mathematical puzzles - magic squares; puzzles with sticks), etc.

problematic situations.

This is a means of mastering search actions, the ability to formulate one's own thoughts about the search methods and the expected result, a means of developing creative abilities.

Structural components of a problem situation are:

problematic questions (In how many ways can a square be cut into 4 parts?),
entertaining questions (The table has four corners. How many corners will the table have if one is cut off? How many months in a year contain 30 days?),
entertaining tasks (How many ends do three sticks have? And three and a half? Kolya bet that he would determine what the score would be in the game of the Spartak and Dynamo football teams before the start of the match, and won the argument. What was the score?),
joke problems (What fence can you jump above? The egg flew three meters and did not break. Why?).

Logical and mathematical plot games (classes).

These are games in which children learn to identify and abstract properties, master the operations of comparison, classification and generalization. They are characterized by the presence of a plot, characters, schematization. Such a complex of games was proposed by E.A. Nosova based on Gyenesh blocks:Mice are burrows. Stocks for the winter. Highway. Growing a tree. Where is whose garage? Teach the Unknown. Riddles without words. translators. Build a chain. Two tracks. Who is Winnie the Pooh and Piglet visiting? Factory. Architects. Help the figures get out of the forest. Let's set up a window. Build a house. Separate the blocks - 1. blocks - 2. Help the toy. Separate the blocks - 3. Gifts for three piglets. And etc.

Experimentation and research activities.

Trial and error is an important component of children's experimentation. The child tries to apply old ways of doing things by combining and rearranging them.

Steps of guidance:

I stage.

Joint activities with the teacher: clarifying children's ideas about the properties and qualities of materials, motivation, creating a problem situation, setting goals, determining research stages, making assumptions about the results, justifying them, conducting an experiment, fixing the results, discussing them.

Ready-made schemes and models are used for discussion: what did you do? what did you get? why?

To improve the ability to plan an experiment, it is proposed to encrypt its course with the help of ready-made models for one child, and for others to decipher it.

II stage.

Independent experimentation: conversations, special games and exercises, practical activities in the experimentation corner. The teacher shows the problem with the help of diagrams, the children offer solutions, select the necessary materials, record the results.

The source of experimentation is children's questions: why is it raining? wind blows? what happens if the cube is glued differently? why doesn't a fly fall from the ceiling?

Sources:

http://066.do.am/load/1-1-0-5
Kostyuchenko M. Experimenting! // Preschool education. - No. 8 - 2006.

http://www.ivalex.vistcom.ru/konsultac145.htm

REMINDER

"Planning work with children on experimentation"
Junior preschool age.

Work with children of this age group is aimed at creating the conditions necessary for sensory development in the course of familiarization with the phenomena and objects of the surrounding world. In the process of forming elementary exploratory actions in children, teachers are recommended to solve the following tasks:

1) combine the display of an object with the active action of the child to examine it: feeling, hearing, taste, smell (a didactic game such as "Wonderful bag" can be used);
2) compare objects that are similar in appearance: a fur coat - a coat, tea - coffee, shoes - sandals (didactic game like "Make no mistake");
3) to teach children to compare facts and conclusions from reasoning (Why is the bus standing?)

4) actively use the experience of practical activities, gaming experience (Why does the sand not crumble?)

The main content of the research carried out by children involves the formation of their ideas:

1. About materials (sand, clay, paper, cloth, wood)

2. About natural phenomena (snowfall, wind, sun, water; games with the wind, with snow; snow, as one of the states of aggregation of water; heat, sound, weight, attraction)

3. About the world of plants (methods of growing plants from seeds, leaves, bulbs; sprouting plants - peas, beans, flower seeds)

4. About methods of studying the object (section "Cooking for dolls": how to make tea, how to make a salad, how to cook soup)

5. About the standard "1 minute"

6. About the objective world (clothes, shoes, transport, toys, paints for drawing, etc.)

In the process of experimentation, the children's vocabulary is replenished with words denoting sensory features of a property, phenomenon or object of nature (color, shape, size: wrinkled - broken, high - low - far, soft - hard - warm, etc.)

Middle preschool age.

Work with children of this age group is aimed at expanding children's ideas about the phenomena and objects of the world around them. The main tasks solved by teachers in the process of experimentation are:

1) active use of the experience of playing and practical activities of children (Why do puddles freeze at night, thaw during the day? Why does the ball roll?)

2) grouping objects according to functional characteristics (What are shoes, dishes for? What is the purpose of using them?)

3) classification of objects and objects according to specific characteristics (teaware, tableware)

I. The main content of research conducted by children involves the formation of the following ideas in them:
1. About materials (clay, wood, fabric, paper, metal, glass, rubber, plastic)

2. About natural phenomena (seasons, weather phenomena, inanimate objects - sand, water, snow, ice; games with colored ice floes).
3. About the world of animals (how animals live in winter, summer) and plants (vegetables, fruits), the conditions necessary for their growth and development (light, moisture, heat)

4. About the objective world (toys, dishes, shoes, transport, clothes, etc.)

5. About geometric standards (circle, rectangle, triangle, prism)

6. About a person (my helpers are eyes, nose, ears, mouth, etc.).
In the process of experimentation, the children's vocabulary is replenished with words denoting the properties of objects and phenomena. In addition, children get acquainted with the origin of words (such as: sugar bowl, soap dish, etc.). At this age, building games are actively used to determine the features and properties of objects in comparison with geometric standards (circle, rectangle, triangle, etc.).

Senior preschool age.

Work with children is aimed at clarifying the entire spectrum of properties and features of objects and objects, the relationship and interdependence of objects and phenomena. The main tasks solved by the teacher in the process of experimentation are:

1) active use of the research results in practical (household, play) activities (How to build a solid house for dolls faster?)

2) classification based on comparison: by length (stockings - socks), shape (scarf - scarf - scarf), color / ornament (cups: single and multi-colored), material (silk dress - woolen), density, texture (game " Who can name more qualities and properties?")

The main content of research conducted by children involves the formation of the following ideas in them:

1. About materials (fabric, paper, glass, porcelain, plastic, metal, ceramic, foam rubber)

2. About natural phenomena (weather phenomena, the water cycle in nature, the movement of the sun, snowfall) and time (day, day - night, month, season, year)

3. On the aggregate states of water (water is the basis of life; how hail, snow, ice, hoarfrost, fog, dew, rainbow are formed; looking at snowflakes through a magnifying glass, etc.)

4. About the world of plants (features of the surface of vegetables and fruits, their shape, color, taste, smell; examination and comparison of plant branches - color, shape, location of buds; comparison of flowers and other plants).
5. About the objective world (generic and specific features - freight, passenger, sea, railway, etc.)

6. About geometric standards (oval, rhombus, trapezium, prism, cone, ball)

In the process of experimentation, the vocabulary of children is enriched by words denoting the properties of objects and phenomena. In addition, children get acquainted with the origin of words, with homonyms, with the ambiguity of the word (key), synonyms (beautiful, beautiful, wonderful), antonyms (light - heavy), as well as phraseological units ("horse in apples").

Creative tasks, questions and situations.

Creative tasks have many solutions that will be correct, but do not have a clear algorithm. These funds are aimed at developing ingenuity, ingenuity, imagination, creative (divergent) thinking. They contribute to the transfer of existing ideas to other conditions, which requires awareness, the appropriation of knowledge itself. The child in the process of solving learns to establish various connections, identify the cause by the effect, overcome stereotypes, combine, transform objects, knowledge, substances, properties.

Examples: “draw a cat without drawing it” (whole in part); draw a bear in a square with a side of 2 cells so that it is the largest ”(relativity of size); “How to draw the Sun if a pencil can only draw circles? (the more angles, the more the figure looks like a circle).

http://www.trizland.ru/

Games:

"Logic Train". Children make up a logical chain of words from pictures, explaining how they are connected. Example: book - tree - linden - tea - glass - water - river - stone - tower - princess, etc.

The game "Black and White".The teacher raises a card with the image of a white house, and the children name the positive qualities of the object, then raises a card with the image of a black house and the children list the negative qualities. (Example: "Book". Good - You learn a lot from books. . . Badly - they break quickly. . . etc.)

TASKS FOR THE ARTICLE:

"MODERN FORMS OF LOGICAL AND MATHEMATICAL DEVELOPMENT AND TRAINING OF PRESCHOOL CHILDREN".

To study the requirements for the development and design of abstracts of classes in mathematics at preschool age.
To select an outline of any lesson in mathematics in the methodological literature and arrange it in accordance with the proposed requirements, put it in a portfolio on the methodology of the mathematical development of preschoolers.
Select and draw up a card file of physical minutes of mathematical content (attach to the portfolio).

MODERN FORMS OF LOGICAL AND MATHEMATICAL DEVELOPMENT AND TRAINING OF PRESCHOOL CHILDREN

BASIC APPROACHES TO THE DEVELOPMENT OF LESSON SUMMARY

WITH PRESCHOOL CHILDREN IN MATHEMATICS.

At present, one of the main forms of work with children in mathematics is collective classes in combination with differentiated teaching; methodologically competent preparation for the lesson includes:

drawing up a summary of the lesson
determination of the place and time of the lesson in a single educational space.

Basic principles for creating an outline:

a detailed summary is written in the first person
the activities of the teacher and children are reflected in detail, while the actions and questions of the educator, the intended actions and answers of the children, explanations for the reader of the summary (“What is this?” (I ask the children, demonstrating the model of the circle).)
A well-written and detailed summary allows any teacher to conduct such a lesson without additional instructions from the author.

Abstract work plan:

Clearly formulate the name (topic) of the lesson (the leading task is indicated in the topic): “The secret of the third planet” (development of skills in measuring linear quantities).
List educational, educational, developmental and speech tasks, compile a hierarchy of tasks according to the degree of complexity and determine their place in the structure of the lesson.
Determine the form of organization of the lesson, its structure (number of parts and time) and select educational material.
Clearly think over the beginning of the lesson, the logic of the transition from one structural part of the lesson to another, the end of the lesson.
Choose didactic tools and techniques for the implementation of each task.
Determine the placement and sequence of use of didactic tools.
Consider, if necessary, preliminary work with children in preparation for the lesson (updating existing experience, preparing lagging children, working with children who will demonstrate methods of action, etc.).

C O N S P E C T

math classes in ____________ group

____________________________________________

title, topic

compiled by ___________________

FULL NAME. educator

the date of the _____________

Tasks /educational, developing, educational, speech/.

Didactic tools: demonstration and handout material/names of images, toys, characters, games, poetic texts, stories, riddles, models, notebooks with a printed basis, task samples, filmstrips, drawing and measuring tools, etc./.

Organization of children.

preliminary work* .

Placement of teaching aids* .

Lesson progress: parts, time, content.

Estimated result* .

* - these parts are planned if necessary

Abstract evaluation criteria:

creativity and independence in development
compliance with the general didactic system: pedagogical literacy in the formulation of tasks, designation of didactic means, structure, age appropriateness
accuracy, clarity, conciseness of speech when formulating tasks, questions, explanations, etc.
coverage in the summary of all organizational issues, a logical transition to the next part
sufficiently high efficiency of the lesson, a variety of techniques and means
thoughtfulness of the plot
well presented application
aesthetic design

Abstract analysis:

establish a correspondence between the set educational (educational, developmental, educational) tasks and the age characteristics of children (peculiarities of perception of educational material)
how justified, in your opinion, is the choice of methods, techniques and forms of work?
What is the ratio between reproductive and productive types of children's activities in the classroom? Is it appropriate under the circumstances?
justify the use of these didactic tools for the implementation of the tasks
imagine that you can calculate the efficiency (efficiency) of the lesson; what could it be in this case? What nuances (conditions) can affect its change (increase, decrease)?
offer your own version of conducting any fragment of the lesson; try to motivate your proposed changes.

QUESTIONS TO THE ARTICLE:

"MODERN MEANS OF LOGICAL AND MATHEMATICAL DEVELOPMENT AND TRAINING OF PRESCHOOL CHILDREN"

What is meant by didactic means and visualization? How are these concepts different?
What are the functions of didactic tools?
What groups are teaching aids divided into?
What is the specificity of visual aids in teaching mathematics?
What are the types of visibility?
What are the requirements for the selection, design and use of didactic tools?
What is the importance of cognitive books and workbooks for the mathematical development of preschoolers?
What is the classification of cognitive books of mathematical content and what are the features of each group?
What is the value of workbooks on the mathematical development of preschoolers?
What are the requirements for books and workbooks in mathematics addressed to preschoolers?
What is meant by the subject-developing environment and what significance does it have in the development of the child?
What components does the subject-developing environment include?

MODERN MEANS OF LOGICAL AND MATHEMATICAL DEVELOPMENT AND TRAINING OF PRESCHOOL CHILDREN

In didactics, a special place is given to teaching aids and their influence on learning outcomes. Didactic means are a tool of the teacher's work and a tool for the cognitive activity of children. Learning tools are sources of information. It is necessary to distinguish between the concepts of "visibility" and "didactic means". Didactic means is a broader concept. This includes sets of objects, phenomena, signs, models, actions, words.

Functions of didactic tools:implement the principle of visibility; translate abstract mathematical concepts into a form accessible to children; contribute to the accumulation of sensory, logical and mathematical experience and the mastery of methods of action; increase the amount of independent activity of children; intensify the learning process.

Groups of didactic tools:

sets of visual didactic material
equipment for independent games and activities
manuals for the educator: textbooks, methodological literature, notes, collections of didactic games, etc.)
educational books for children, workbooks

Kit characteristics

visual didactic material.

Teaching children mathematics is based on specific images and ideas due to the visual-figurative and visual-effective nature of thinking. Therefore, visual didactic means play an important role.

Visualization in mathematics is characterized by the following features:

Attention is drawn only to those features of the demonstrated materials that are the object of study in mathematics;

Gradually, a weakening of the concrete is observed: a natural object→ image of an object in the form of a picture→ dash → number; geometric figure→ abstract image→ diagram, graph, drawing.

Types of visibility:

natural visibility
visual clarity (pictures, drawings, tables, on-screen visual aids, models of objects)

mathematical clarity (numerical figures, lines, arrows, drawings, diagrams, diagrams, signs, graphs, numbers, models of geometric shapes, etc.).

Traditionally, a set of visual didactic material is divided into two types: demonstration (intended to be shown to the entire group of children) and handout (intended for the work of one child, individually).

The first includes: large toys, shelves for displaying objects, large planar images, flannelograph, magnetic board, easel, chalk board, paintings, large tables, large models of geometric shapes, large cards with numbers, large signs, measuring instruments (clocks, scales, abacus), calendars, slides, filmstrips, TCO, TV programs, etc.

The second includes: small objects, small planar images, cards, sets of geometric shapes in pencil cases, small numbers, counting sticks, punched cards, worksheets, notebooks, etc.

There are a number of requirements for visual material. It must be appropriate for the age of the children; it should be well expressed features of objects; images should not be full of details; visibility should be attractive to children, safe, sustainable, durable; be varied. It is necessary to store didactic means separately from other objects and toys. When demonstrating, they must be placed at the level of the children's eyes.

Equipment for self

games and activities:

some didactic tools used in the classroom
didactic games (board-printed and with objects)
educational and educational games
checkers, chess
fun math stuff
separate didactic tools: Gyenes blocks, Kuizener sticks, counting material, cubes with numbers and signs, etc.
books with educational and cognitive material for reading and looking at illustrations

These funds are placed in the zone of independent cognitive and play activities, and are periodically updated. Children must be given free access to them.

Entertaining mathematical material.

Of particular importance for the development of interest in mathematics, mathematical abilities is entertaining mathematical material. It allows you to solve serious educational problems in an exciting way, prevent intellectual passivity, form perseverance and purposefulness. It should be varied and used systematically.

Entertaining mathematical material includes:

geometric constructors: Tangram, Magic Circle, Columbus Egg, etc.
puzzles from three-dimensional figures: "Rubik's Snake", "Rubik's Cube", "Magic balls", "Pyramid", "Fold the pattern", "Unicube", "Cubes for everyone", etc.
logical exercises such as "Continue the row", "Missing figure", "Transformation of words", etc.
tasks to find signs of similarities and differences
labyrinths
exercises for recognizing parts as a whole, restoring the whole from parts
stick puzzles
riddles, poems and other literary material with mathematical content and much more.

Educational books for children, workbooks.

An educational book is a kind of teacher, acts as a "visual support" of activity and ensures the activation of children's interest in the information presented in it. Often such books are addressed to parents and are used in the family in the process and joint activities of the educator and children.

In an educational book, it is possible to present mathematical content in a visual form:

In a literary plot, through vivid images - characters, through the creation of problem situations, to the solution of which children can be involved;

Visual means (illustrations), which causes emotionality, dominance of visual-figurative thinking, preference for gaming activities.

It is conditionally possible to single out: 1) books aimed at enriching the mathematical concepts of preschoolers; 2) books that provide the development of skills, logical operations.

To the first group books include various albums (for example, "Forms", "Opposites"), educational encyclopedias. For them, the leading function is the presentation of new information.

Albums for children of early and younger age are aimed at enriching sensory impressions and visual representation of mastered standards (shapes, colors). The main task of children is to consider images, correlate, for example, the shape of an object and a geometric figure, remember words(top - bottom, large - small).

For older children (5-7 years old), various educational books of an encyclopedic nature are used (for example, “How did you measure time before?”), Which allow you to expand and deepen the ideas of preschoolers about the means and methods of measurement, numbering, etc. As a rule , in these encyclopedias information is presented in an entertaining way; the books contain illustrations and figurative examples, designed for the "zone of proximal development", arouse the cognitive interest of preschoolers. The presentation of information by chapter ensures the limitation of the time and content of classes with children.

In a number of books, new information is presented in an entertaining form - the plot of a fairy tale, history (V. Volina "The Holiday of the Number. Entertaining Mathematics for Children" (M., 1993); L. A. Levinova, K. A. Sapgar "The Adventure of Kubarik and Tomatic , or Merry Mathematics" (M., 1977); Zh. Zhitomirsky, L. Shevrin "Mathematical ABC" (M., 1980)). As a rule, in these books there are "cross-cutting" characters who participate in all episodes and are close to the experience of children; plots and episodes are often similar to children's life or repeat the storylines of works known to children. Identification of children with characters causes emotional experiences and a desire to help the character (suggest, solve a problem, learn something new with him, etc.). The content, as a rule, is structured by chapters, which model the sequence of activities with children.

To the second groupcan be conditionally attributed to a variety of book-albums for preschoolers, providing for the implementation of a sequence of tasks by children (3. A. Serova “I get acquainted with mathematics. A manual for preparing children for school”). Such manuals and books can also be thematic or present tasks in the form of a story (travels of characters; fairy tales and stories, during which children have to complete a series of tasks). Characters are used to create motivation and enhance children's interest in completing tasks. As a rule, tasks in such books are presented in order of complication. Also, the books of the second group take into account the need for a tactile-motor examination and the importance of practical actions in cognition; provides for drawing elements, connecting along lines, laying out images from geometric shapes that are attached to the book; some games are given (games like crosses; games with hoops, etc.).

Often in these books they use various symbols - prompts for actions (draw, color, cut, solve, etc.), which allows children who cannot read, focusing on symbols, to understand the content of the task.

Generalized data analysis allows us to identify a number of requirements to the book of mathematical content:

it must be accessible in terms of content, presentation and form;
comply with sanitary and hygienic requirements (size, materials and paints used, quality and size of drawings, etc.);
have pedagogical value and allow solving educational, upbringing and developmental tasks in unity;
contain increasingly complex and consistently presented mathematical content; provide a "zone of proximal development";
contribute to the formation of realistic ideas about the objects of the world;

be colorful; contain an interesting plot or tasks focused on the existing experience of children;
present the content in sections (chapters, pages) for the effective organization of children's activities;
provide for tasks that are different in content (finish, invent on your own, analyze a sample, etc.) and variable tasks (complicating analogues).

main functionworkbooksconsists in activating the independent fulfillment of tasks of mathematical content; exercise in skills; development of logical operations. For example, workbooks for different age groups have been developed for the educational program "Childhood" ("Mathematics is interesting", compiled by: 3. A. Mikhailova, I. N. Cheplakshina, N. N. Krutova, L. Yu. Zueva) ; for the programs “Player”, “One step, two steps”, colored workbooks with a large number of various tasks are presented; Notebooks for other programs are widely used (Erofeeva T. I., Pavlova L. N., Novikova V. P. “Mathematical Notebook for Preschoolers”; Solovieva E. V. “My Mathematics: A Developing Book for Children of Senior Preschool Age”).

The value of workbooks lies in the fact that the child will be able to perform actions in his "own field of activity." The child performs every task in your own notebook.This increases the activity of children in mastering skills and ideas and makes this process more efficient (rational use of class time, which does not create situations of “waiting” for an answer and observing the actions of another child with the material).

Workbooks contain tasks, the implementation of which is based on practical actions (connect with lines, circle, complete, etc.), which corresponds to age capabilities.

The notebooks present the "successes and failures" of children, which ensures the development of their self-esteem and volitional manifestations.

The use of workbooks should not be regarded as an end in itself and classes should not be built solely on the basis of their use. Notebooks can be one of the means, used in some classes, form the basis for organizing some tasks, or used in joint and independent activities.

When choosing a notebook, you should consider:goals and objectives of the educational program, according to which the development and education of preschool children is carried out; compliance with the age of children; the possibility of combining work with the use of other aids (developing and didactic games, modern multifunctional aids, etc.).

In the younger grouptoy books are used (“baby books”, “folding books”, surprise books), the main function of which is to accumulate experience in examining and recognizing objects, highlighting properties (primarily color, shape, size). In such books, as a rule, standards of color, shape, size are presented; their manifestations are also demonstrated through images and words. In the kindergarten group, a joint examination of books is organized (a lesson that is not limited by time). The teacher pays attention to significant properties (shape, size), calls them a word, activates the naming of manifestations of properties by children. As a rule, these books provide for questions to children, the possibility of practical actions (touch, swipe, etc.) or use a "synthesis of arts" (a colorful image is complemented by a poem, an image game).

Children are especially interested in the so-called "universal" sets - Gyenesch logical blocks and Kuizener sticks. At this age, it is possible to use special albums, which provide for the imposition of blocks (sticks) on a color image (album-game "Gyenes blocks for the smallest (2-3 years)", compiled by B. B. Finkelstein; album-game "House with a bell, Kuizener's sticks, compiled by B. B. Finkelstein and others). Working with albums activates the game with the corresponding materials. Albums can be placed in a subject-developing environment and used for review in individual and subgroup work several times.

The use of workbooks in the younger group of kindergarten is usually limited. The notebook is recommended to be disassembled into worksheets, which are issued to children as they master the material. This is due to the fact that the value of practical actions with objects, the experience of examining objects, organizing the activities of children with subject sets is more important than working with notebooks.

In the middle groupthe tendency to use albums and books for viewing continues. Such books should be bright, present various options for the manifestation of properties, relationships, and activate the process of their comparison by children. It is desirable that books and albums make it possible to organize various practical activities for children (lay them out in a certain order, insert them into slots, overlay them on a picture, etc.).

To enhance children's interest in these books, methodological moments should be used (surprise introduction; preliminary examination; involving children in the design of the "corner" and determining the location of books; exhibition of favorite books; use of books in joint and individual activities).

For the middle group, it is also recommended to embroider workbooks on sheets. Their storage can be played - the sheets are stored in signed (marked with a picture) files in a specially designated place; preschoolers are told that they have to play and work with worksheets, the rules are told (handle carefully, etc.).

At senior preschool agethe expansion of children's independence, their cognitive interests, as well as their mastery of the means and methods of cognition determines the possibility of a wider use of cognitive literature (children's encyclopedias) and workbooks.

It is possible to organize a joint weekly reading of books with a discussion of their content (for example, on Thursday afternoon, an “evening of Kubarik and Tomatic” is held (the next chapter is read and a discussion is held)).

Some chapters and sections of educational children's encyclopedias may precede the development of certain topics in the classroom.

Books with tasks aimed at developing skills and actions should be located in the "corner of the book" (or "corner of cognitive development"). Children should be able to use them at any time.

To stimulate children's interest in books, you can use the following methods and techniques.

Collecting interesting educational books. The teacher draws the attention of children to the idea of collecting interesting books from which they can learn a lot of new and unusual things; informs about the beginning of collecting, the rules for the design and organization of the "corner". Each new book brought in is considered together with the children and included in the collection. From time to time, classes, leisure activities, exhibitions are held in the "corner" using the replenished collection. This collecting is effective if books are used in the activities of children, if during the lesson or joint activities situations are created that require activation of the information presented in the books (for example, you need to find out what an oblique sazhen (pood, mile, span) is); what units measured time before, etc.).

Organization of classes and joint activities according to the method of the project, built on the basis of this cognitive encyclopedia, book.

Coming up with the continuation of the plots of books, new episodes, sketching interesting moments in the albums.

Using these books in a family setting (by creating a library that parents can use on weekends).

Organization of excursions to children's libraries, accompanied by viewing catalogs and exhibitions of books, conversations with librarians and readers; this will enrich the experience of preschoolers, arouse their interest in a cognitive book, and develop a value attitude towards the book as a means of cognition and “preservation of cultural values”.

Use of children's magazines and newspapers with educational information and tasks.

For the development of a “reader culture”, it is necessary to remind older preschoolers the rules for using a book, to note the value of the information presented in it. It is useful to discuss the attitude of people to the book in general and to the book of an educational nature in particular.

Since workbooks involve completing assignments (painting, drawing), children should not be offered to complete assignments in a notebook already colored by someone. Materials that aroused interest among most of the children in the group should be reproduced in the form of worksheets, blanks. "Filled" sheets and notebooks can act as a kind of hint for other children.

Developing environment as a means of developing mathematical concepts of preschoolers.

A modern kindergarten is a place where a child gains experience of wide emotional and practical interaction with adults and peers in the most significant areas of life for his development. The possibilities of organizing and enriching such an experience are expanding provided that an object-spatial developing environment is created in the kindergarten group. Each of its components contributes to the formation in the child of the experience of mastering the means and methods of cognition and interaction with the outside world, the experience of the emergence of motives for new activities, the experience of communicating with adults and peers.

Under the developing object-spatial environmentshould be understood as a natural comfortable environment, rationally organized in space and time, saturated with a variety of objects and play materials. In such an environment, it is possible to simultaneously include all children in the group in active cognitive and creative activity. The activity of the child in an enriched developing environment is stimulated by the freedom to choose activities based on their interests and capabilities, the desire for self-affirmation; he does it of his own free will, under the influence of game materials that have attracted his attention. Such an environment helps to establish a sense of self-confidence.

The conceptual model of the subject-spatial developmental environment includes three components:subject content, its spatial organization and their changes over time.The subject content includes games, objects and game materials with which the child acts mainly independently or in joint activities with adults and peers (for example, a geometric constructor, puzzles); teaching aids, models used by adults in the process of teaching children (for example, a numerical ladder, educational books); equipment for children to carry out various activities (for example, materials for experimentation, measurements).

An indispensable condition for building a developing environment in preschool institutions of any type is the implementation of the ideas of developmental education aimed at developing the personality of the child and carried out through solving problems for the transformation of information, which allows the child to show independence and activity; assumes the prospect of self-development of the child on the basis of cognitive and creative activity.

Features of the organization of the environment for the development of logical and mathematical concepts in children of different ages.

Fourth year of life (2nd junior group).

The use of suspension mobiles will simplify the task of developing spatial orientations. The teacher draws the attention of children to hanging objects, uses wordshigh, below, aboveother. In groups of children of younger preschool age, the main attention is paid to mastering the method of direct comparison of quantities, objects in terms of quantity, properties. Of the didactic games, games like loto and paired pictures are preferred. Mosaic (plastic, magnetic and large carnation), a puzzle of 5-15 pieces, sets of cubes of 4-12 pieces, educational games (for example, "Fold the pattern", "Fold the square", "Corners"), and also games with elements of simulation and substitution. A variety of "soft constructors" on a carpet basis allow you to play the game in different ways: sitting at the table, standing against the wall, lying on the floor.

It is recommended to use abstract materials that facilitate the process of comparison with the standard, abstraction of properties. Children are especially interested in the so-called "universal" sets - Gyenes logical blocks and Kuizener's colored counting sticks. Benefits are interesting in that they represent several properties at the same time (color, shape, size, thickness in blocks; color, length in sticks); there are many elements in the set, which activates manipulation and play with them. 1-2 sets are enough for a group.

Fifth year of life (middle group).

The main requirement for such sets will be their sufficiency and variability of manifestations of the properties of objects. It is important that the child always has the opportunity to choose a game, and for this the set of games must be quite diverse and constantly change (about 1 time in 2 months). About 15% of the games should be designed for children of the older age group in order to enable children who are ahead of their peers in development not to stop, but to move on.

At this age, various games are organized with blocks for highlighting properties (“Treasures”, “Dominoes”), grouping according to specified properties (games with one and two hoops). When using Kuizener's colored counting sticks, attention is drawn to the distinction in color and size and to the establishment of the dependencecolor - length - number.To enhance children's interest in these materials, you should have a variety of illustrative aids.

Middle age is the beginning of a sensitive period of development of the sign-symbolic function of consciousness; this is an important stage for mental development in general and for the formation of readiness for schooling. In the environment of the group, sign symbols, models for designating objects, actions, sequences are actively used. It is better to come up with such signs, models together with children, leading them to an understanding of what can be denoted not only in words, but also graphically. For example, work with the children to determine the sequence of activities during the day in kindergarten and figure out how to label each of them. In order for the child to better remember his address, street, city, place a diagram in the group on which indicate the kindergarten, streets and houses in which the children of the group live.

Sixth year of life (senior group).

At senior preschool age, it is important to develop any manifestations of independence, self-organization, self-esteem, self-control, self-knowledge, self-expression.

In the group, a special place and equipment is allocated for the game library. It contains game materials that contribute to the speech, cognitive and mathematical development of children. These are didactic, developing and logical-mathematical games aimed at developing the logical action of comparison, logical operations of classification, seriation, recognition by description, reconstruction, transformation, orientation according to the scheme, model; for the implementation of control and verification actions (“Does it happen?”, “Find the artist’s mistakes”); for following and alternating, etc. For example, games with Gyenes logical blocks, other games are suitable for the development of logic: “Logic train”, “Logic house”, “Fourth extra”, “Search for the ninth”, “Find differences”. Mandatory notebooks on a printed basis, educational books for preschoolers. Useful games for the development of counting and computational skills, also aimed at the development of mental processes, especially attention, memory, thinking.

For the organization of children's activities, a variety of educational games, didactic aids, materials are used to "train" children in establishing relationships, addictions. Traditionally, a variety of educational games are used (for planar and volumetric modeling), in which children not only lay out pictures, designs according to samples, but also invent and make up silhouettes on their own. In the older group, different versions of recreational games are presented (“Tangram”, “Mongolian game”, “Leaf”, “Pentamino”, “Columbus egg”, etc.).

To accumulate experience in actions with sets, logical blocks, Kuizener's sticks, are used. As a rule, several sets of these benefits are sufficient for a group. It is possible to use special visual aids that allow you to master the ability to isolate significant properties (“Search for a reserved treasure”, “On the golden porch”, “Let's play together”, etc.).

Children's interest in puzzles can be maintained by placing rope puzzles, movement games, and also through the use of puzzle games with sticks (matches) in the toy library.

For individual work with children, clarifying and expanding their mathematical concepts, didactic aids and games are used: "Airplanes", "Dancing Men", "Building a City", "Little Designer", "Domino Number", "Transparent Number", etc. These games should be presented in sufficient quantity and, as children's interest in them decreases, they should be replaced with similar ones. When organizing children's experimentation, there is a new task: to show children the various possibilities of tools that help to cognize the world, such as a microscope. Quite a lot of materials are required for children's experimentation, therefore, if conditions permit, it is advisable to allocate a separate room for experiments using technical means in a kindergarten for older preschoolers.

At senior preschool age, children show interest in crossword puzzles, cognitive tasks. For this purpose, crossword puzzle grids can be laid out on the carpet using thin long Velcro tapes and sheets with pictures or task texts can be attached.

The development of arbitrariness, planning allows you to more widely use games with rules - checkers, chess, backgammon, etc.

Literature:

Formation of elementary mathematical representations in preschoolers. // Ed. A. Stolyar. - M, "Enlightenment", 1988, pp. 124 - 134
Shcherbakova E.I., Methods of teaching mathematics in kindergarten. - M., 1998, pp. 41 - 54
T.I.Erofeeva, L.N.Pavlova, V.P.Novikova. Mathematics for preschoolers. - M., 1992, pp. 8 - 20
Mikhailova Z.A. et al. Theories and technologies of mathematical development of children of preschool age. - St. Petersburg: "CHILDHOOD-PRESS". 2008.-384 p.