Logical and mathematical development of preschool children. Logical and mathematical activity of preschool children Logical and mathematical development and logical and mathematical representations

Under logico-mathematical development children's activity is understood, saturated with problem situations, creative tasks, games and game exercises, search situations with elements of experimentation and practical research, schematization of mathematical content.

Theoretical basis.

According to researchers (J. Piaget, G. Donaldson and others), logical and mathematical knowledge of the world around is represented by the child's mastery of spatial features (location of objects), classification and seriation, quantity.An active search for approaches to the content of the mathematical development of preschoolers, as well as means, forms and methods for its implementation began in the 60-70s of the XX century. At this time, developing games by B. Nikitin appeared, teaching logical and mathematical games by A.A. joiner. Particularly significant for this period was the recognition abroad of developing and educational games using Z. Gyenes blocks and H. Kuizener's colored sticks.In the 80s, the domestic techniquedevelopment of mathematical concepts in children up to school age enriched with the ideaprelogical preparationproposed by A.A. joiner. The main content of prelogical training was the development of statements by children, including the operation of negation, the use of logical connectives “and”, “or, “if .., then”; development of skills to analyze, compare, generalize, classify. At the same time, initially educational games were focused on 6-year-old children.

In the 90s, a student of A.A. Stolyara E.A. Nosov, began research aimed at studying the manifestations of children in games with Gyenesh blocks and practical experience in implementing the ideas of logical and mathematical training in a kindergarten. It became possible to develop a system of games and techniques for children more early age(3-5 years). The main lines of movement in the pedagogical development of children were identified preschool age(in games with Gyenesh blocks):

• From simple objective actions to mental actions (comparison, generalization, classification);
• From actions with one property to actions with two, with three properties (shape and size)

Further, a system and technology for implementing the ideas of the logical and mathematical development of preschool children was developed. It was proposed to use as teaching aids: Gyenesh blocks, a set of geometric figures (flat Gyenesh blocks) and Kuizener colored sticks. New approaches to the logical and mathematical development of children of middle and senior preschool age were partially already presented in 1981 in educational and methodical publications by Z.A. Mikhailova "Game entertaining tasks for preschoolers" and in the manual Nosova E.A. "Logic and Mathematics for Preschoolers". Then Nosovy E.A. a set of games and exercises with Gyenes blocks was developed, the development process of which is represented by three stages:

1. games and exercises to identify properties: color, shape, size, thickness.
2. games and exercises for children to master comparison, classification and generalization (“Paths”, “Settled houses”).
3. games and exercises for mastering logical actions and mental operations (“Where did Jerry hide”, “Riddles without words”).

Today, logic-mathematical games are designed taking into account modern look development of mathematical abilities in children 4-7 years old. Modern logical and mathematical games stimulate the child's persistent desire to get a result (collect, connect, measure), while demonstrating cognitive initiative and creativity. They help develop attention, memory, speech, imagination and thinking, create a positive atmosphere. Many modern games contribute to the development in children of the ability to act consistently, use symbols (geocontact, a transparent square, cubes for everyone, a logical mosaic, etc.). However, in the practice of preschool educational institutions, logical and mathematical games in all their diversity have not found proper application. Most often they are used haphazardly, spontaneously, singly. The most important didactic aids for the logical and mathematical development of preschoolers, which represent a single, consistent system of implementation in the pedagogical process, are:

• Gyenes logic blocks and their flat version.
• Cuisener colored sticks and their planar variant.
• Visual and didactic aids for games with blocks and sticks.

As you know, game methods are the most popular in preschool education. The advantage of such methods has been proven. In addition, they can be used in combination with other methods: problematic, research, situational.

The logical and mathematical development of children cannot be carried out without including them in problematic, research activities, experimentation, modeling, therefore preschool teachers are offered problem-game methods . The purpose of using problem-game methods is the development of cognitive activity in children, intellectual and creativity.

When using problem-playing methods, a demonstration and a detailed explanation by an adult, overprotection of a child are usually excluded. The child is forced to independently find ways to achieve the goal and, in the absence of the necessary skill, to master it here, within the framework of the current situation. At the same time, the child naturally accepts help from an adult (partial hint, dialogue about the development of the situation, assessment of the stage passed, etc.) Problem-playing methods provide an active, conscious search for a way to achieve a result. An indispensable condition for such a search is the child's acceptance of the purpose of the activity and independent reflection on the actions leading to the result.

The activity of the child in the activity is achieved through:

• Motivation (accessible, really vital, bright)
• Participation of the child in the performance of interesting, moderately complex actions.
• Expression of the essence of these actions in speech.
• The manifestation of appropriate emotions, especially cognitive ones.
• Using experimentation, solving creative problems and applying them in different activities.

Problem-playing methods of logical and mathematical development of preschool children are implemented using a variety of means:

1. Problem situations, tasks, questions

Let us consider in more detail the means of implementing problem-game methods:

1) Logic and math games are currently widely used. Aimed at planar and volumetric modeling, combination (color, shape, size); making a whole out of parts. In each of the games, the child is faced with the need to realize the goal; implementation of practical action; getting a result.

The result of the child’s mastery of games is the development of his interest in knowledge (“I want to know everything!”), in participation in games, the child’s statements “I want to play”, “Let's play again”, “it's a pity that so little”, etc. All this indicates that the child has a sustainable interest. This means that the child develops the ability to think, he becomes more persistent, concentrated in activities, capable of taking initiative.

2) Problem situations- in the conditions of application of the problem-game method, it is considered not only as a means of activating thinking, but also as a means of mastering research actions, the ability to formulate one's own thoughts (assumptions) about the search methods and the result. One of the main purposes of the problem situation is to promote the development of the child's creative abilities.

The structure of the problem situation includes problematic issues(for example, the teacher asks "How to distribute all the blocks in three hoops?").

Problem situations include entertaining questions, tasks, joke tasks(for example, there are two red sticks on the table, a black stick between them. What needs to be done to make the black stick last without touching it?).

3) Creative situations, tasks, questions- contribute to the clarification and deepening of the child's ideas about various properties, connections, relationships and dependencies, the development of creative initiative. For example, the creative task “How to draw a sun if you only have sticks” (take more small sticks). Or children are invited to build paths according to certain rules; draw a picture "Winter forest".

4) Logic-mathematical story games- built on the basis of a modern view on the development of the mathematical development of the child. These games are characterized by:

• the presence of a plot plot, characters and following the storyline
• the presence of schematization, transformation, cognitive tasks
• mastering the actions of correlating, comparing, recreating, grouping, classifying

A mandatory requirement for these games is their developmental impact (ensuring the development of mental processes in unity with personal development). For example, during the construction of a “house” (the game “Logic house”), the child, making the next move, focuses on the connections between objects drawn on the “bricks” (the main building material). Compliance with the number of storeys of construction and the requirements for the size of the house provides for the establishment of quantitative relationships.

5) Experimentation and research activities- a special type of intellectual and creative activity, which includes search activity, analysis of the results obtained, their evaluation. Children's experimentation is characterized by extreme flexibility. It manifests itself when a child in the process of activity receives an unexpected result and, as a result, changes the direction of activity. As new information about the object is obtained, the child may set new and complex goals and try to achieve them.

The main ways of knowing colors, shapes, sizes, lengths, heights, quantities and other features that a child learns in preschool age are comparison, classification and seriation.

1) Comparison. As a result of the comparison, children discover that among the objects that surround them there are different, dissimilar, and there are the same. The success of children's knowledge of the relations of groups of objects depends on the mastery methods of comparison.

• Objects can be compared by eye
• The most effective techniques: overlay, application and connection of points)

In situations where the compared objects cannot be spatially brought closer to each other, intermediary objects are used. (for example, using Kuizener's sticks, you can find out why there are more trees or bushes in the area, the children put a red stick near the tree, and a yellow one near the bush. Then they collect all the sticks, count and compare).

2) Seriation- is carried out on the basis of identifying and ordering objects according to a certain attribute (for example, by length or height). The sticks, laid out from the shortest to the longest, or vice versa, represent a serial row. For the first time, children meet with seriation at 2-3 years old (matryoshka dolls), at this age children can arrange 3 sticks; at 4 years old, children arrange 4-5 sticks (strips). Children 6-7 years old arrange up to 10 or more items.

3) Classification- a complex mental action, is the distribution of elements of the set by class. The classification is based on splitting (separation) according to such features as shape, color, thickness, size. First, the partition goes on one property, then on two or more. For example, give the bear only yellow blocks; Give the bear yellow round blocks; Give the bear yellow round thick blocks. You can use buckets, houses, hoops, etc. for classification.

The competence of the teacher in the logical and mathematical development of children

Mathematics is a complex science. In order to develop a preschool child in the logical and mathematical direction, it is also necessary for the teacher to be ready to implement the tasks of the logical and mathematical development of preschool children.

1) the teacher must know the goal, tasks, content of the logical and mathematical development of the child at each age level.

2) know the ways of pedagogical support of the child in logical and mathematical activities.

3) be able to create conditions for productive advancement in logical and mathematical activities

4) understand the essence and features of the development of logical methods of cognition by children: comparison, seriation, classification.

(All this is described in detail in the manual by Mikhailova Z.A., Nosova E.A. "Logical and mathematical development of preschoolers" pp. 55-70)

Monitoring of personal manifestations of a child in logical and mathematical activities .

As the most important indicator of a child's development in cognitive, research and productive activities, modern researchers N.A. Korotkova and P.G. Nezhnov is singled out cognitive initiative as one of the most significant personality manifestations. Convenient and effective method Evaluation of a child's progress in development is observation.

The teacher can judge the cognitive initiative (curiosity) by the degree of the child's involvement in logical and mathematical activities.

The cognitive initiative of the child manifests itself at different levels:

The first level is characterized by the manifestation of interest in new objects. Child:

• Actively examines objects, highlights properties, but does not always name them
• Practically detects ways to use objects (manipulates them, collects them in a group, lays them out in a chain, disassembles and assembles without trying to get an exact result)
• Repeats actions many times, absorbed in the process.

On the second level:

• Anticipates or accompanies with questions the practical study of new objects (“What is it?”, “What for?”)
• Detects an intent to learn something new about a specific use of game materials and aids (“How does it work?”, “Why is it like this?”, “How to do it?”)
• Makes simple assumptions about the relationship between action and possible outcome, seeks to achieve certain results (If you do so ... ")
• Begins to use learned methods of action in other situations: story game, drawing, constructing (arranges objects in order, combines by color, shape)

On the third level:

• Detects a desire to explain the relationship of objects, uses simple causal reasoning (“Because ...”)
• Strives to streamline, systematize specific materials (in the form of a collection)
• Shows interest in cognitive literature, in symbolic languages
• Independently undertakes to do something according to graphic schemes (for example, sculpt, design), draws up maps, diagrams, pictograms “records” stories, observations.

cognitive initiative - curiosity(observation of cognitive research and productive activities)
list of group children	shows interest in new objects, manipulates them, practically discovering their possibilities; replay actions over and over	asks questions about specific things and phenomena (What? How? Why?); makes simple assumptions; performs variable actions in relation to the object, achieving the desired result	asks questions about abstract things; reveals a desire to streamline facts and ideas; capable of simple reasoning; shows interest in symbolic languages
Anya M., 3 years 2 months	No	usually	occasionally
Andrey S., 3 years 5 months	usually	occasionally	No
	usually	No	No

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 the relationship 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, goals and objectives for 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 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 search technologies. research activities 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 on the table different lengths. 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 different size). 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, develops fine motor skills child.

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. Better time from time to time to replace one material with another. 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, you need to include in the environment plastic containers with lids of different shapes and sizes, boxes, other household items that are out of use. 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 game library can be placed various options books, workbooks for reviewing and completing assignments. 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.

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 succession and alternation, 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 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.

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 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.

From the experience of a preschool teacher

Mathematical development of preschool children, the development of logic. (from work experience)

“Scientific concepts are not assimilated and
are not memorized by a child, are not taken
memory, but arise and add up
through the tension of all the activity of his own thought"
A.S. Vygodsky.
A necessary condition for the qualitative renewal of society is the multiplication of its intellectual potential. The solution to this problem largely depends on the construction of the educational process. Most of the existing educational programs are focused on transferring the socially necessary amount of knowledge to students, on their quantitative growth, on practicing what the child already knows how to do. However, the ability to use information is determined by the development of logical methods of thinking. The need for purposeful formation of logical methods of thinking in the process of studying specific educational disciplines is already recognized by psychologists and teachers.
Work on the development of the child's logical thinking goes without awareness of the significance psychological tricks and funds in this process. This leads to the fact that most students do not master the techniques of systematizing knowledge based on logical thinking even in high school, and these techniques are already necessary. junior schoolchildren: without them, there is no full assimilation of the material. The main intellectual skills include logical skills that are formed when teaching mathematics. Math is a powerful factor intellectual development child, the formation of his cognitive and creative abilities. It is also known that the success of teaching mathematics in preschool depends on the effectiveness of the mathematical development of a child in preschool age. primary school.
Why is mathematics so difficult for many children, not only in elementary school, but even now, in the period of preparation for educational activities? Let's try to answer the question why generally accepted approaches to the mathematical preparation of a preschool child often do not bring the desired positive results.
The development of a child's logical thinking implies the formation of logical methods of mental activity, as well as the ability to understand and trace the cause-and-effect relationships of phenomena and the ability to build simple conclusions based on a cause-and-effect relationship. So that the student does not experience difficulties literally from the first lessons and does not have to learn from scratch, now, in the preschool period, it is necessary to prepare the child accordingly.
Working with preschoolers for more than a year, especially with older ones, we found it possible to start the process of forming logical methods of thinking from an earlier age - from 4 to 5 years.

They based their choice on several reasons:
1. Exists a large number of studies confirming that the development of logical thinking can and should be dealt with (even in cases where the natural inclinations of the child in this area are very modest) and that it is most expedient to develop the logical thinking of a preschooler in line with mathematical development.
2. The group of children with whom we work has shown its contrast in terms of overall development. Some children are significantly ahead of their peers. They are curious, inquisitive, show great interest in the new, unknown, while having a good stock of knowledge. These are children who receive a lot of attention from adults at home.
Such children, having come to the mini-center or to the pre-school class, should rise to a higher level, training their intellect.
To do this, the teacher needs to create a good developing environment that best meets the needs of the child, to diversify tasks.
3. Questions of the development of logic have always occupied a central place among the problems not only of preschool pedagogy and psychology. Regularly attending lessons in the first grade and having little experience in elementary school, I came to the conclusion that children experience difficulties in solving problems, in the ability to reason, which prompted them to work on this topic.
The purpose of the work is to create conditions and promote the mathematical development of children, the development of logical thinking.
The main objectives of my work are:
1. Formation of methods of logical operations of preschoolers (analysis, synthesis, comparison, generalization, classification, analogy), the ability to think and plan their actions.
2. Development in children of variable thinking, imagination, creative abilities, the ability to argue their statements, build the simplest conclusions.
These tasks are solved in the process of familiarizing children with different areas of mathematical reality: with quantity and counting, measuring and comparing quantities, spatial and temporal orientations.
The essence of the work lies in the selection and systematization, as well as testing of material on the mathematical development of preschoolers, the selection of developmental tasks and entertaining material for the formation of the foundations of logic. Expected results: Since logical thinking in preschool age is mainly manifested through separate structural components, their holistic development is possible by solving a system of logical problems on mathematical material. When organizing special developmental work on the formation and development of logical methods of thinking on mathematical material, the effectiveness of this process will increase, regardless of the initial level of development of the child.
We must not forget that the work on the development of logic in terms of content is built on the basis of arithmetic and geometric material. The work on mathematical development consists of several sections: arithmetic, geometric, and a section of content-logical problems and assignments.
The first two sections - arithmetic and geometric are the main carriers of mathematical content, because. they determine the nomenclature and volume of the studied issues and topics. Therefore, at the first stage, special attention should be paid to the formation of basic knowledge in mathematics. First of all, it is necessary to think over and arrange a place for conducting mathematical classes, as well as prepare and use a variety of didactic material Organization of work in the classroom.
All work is based on a development environment, which is built as follows:
1. Math fun(games for plane modeling Tangram, etc., joke tasks, entertaining puzzles)
2. Didactic games.
3. Educational games are games that contribute to the solution of mental abilities and the development of intellect (games are based on the process of finding solutions (According to TRIZ), on the development of logical thinking)
Here are general methodological approaches to organizing work: a typical structure for working with each number:
1. The educator tells a fairy tale with a continuation about the numerical kingdom and its new representative, the formation of a number.
2. Revealing where the number occurs in the objective world, in nature.
3. Drawing on the theme of a number, laying out a number series with the addition of a new number, populating a new number, i.e. his figures are in the teremok.
4. Modeling the corresponding number, games like “What does it look like?”, working with stencils, laying out counting sticks, coloring, shading.
5. Acquaintance with the corresponding class of geometric figures, drawing, cutting out flat figures, modeling and constructing three-dimensional bodies, identifying in which objects of the surrounding world they “live”.
6. Rhythmic movement exercises, finger games.
7. Educational games.
The leading activity of preschoolers is play activity. Therefore, classes, in fact, are a system of games during which children explore problem situations, identify essential features and relationships, compete, and make “discoveries”. During these games, the personality-oriented interaction of an adult with a child and children among themselves, their communication in pairs, in groups, is carried out. Therefore, we try to conduct all classes in mathematics, combining all parts of the lesson with one game goal, the plot. For example, “Shop”, “Sea Voyage”, etc. Classes are held with the whole group or in subgroups, but at the same time, when children receive different tasks, or the lesson is conducted in a playful way. In the classroom for mathematical development, it is advisable to use Kuizener's sticks (but in their absence, you can use multi-colored stripes), tangrams, counting sticks. From the experimental corner, material can be borrowed for research activities. For example, to get acquainted with the unit of measurement in the mathematical development of children, they are led to the conclusion that it is possible to measure both water and sand and a ribbon, but only with the help of a suitable measure - a glass, sticks, etc.
During the course, the following game techniques are used:
1. Game motivation, motivation for action (including mental activity);
2. Finger gymnastics (stimulating brain activity, in addition - which is an excellent speech material). Every week we try to learn a new game.
3. Elements of dramatization - to increase the interest of children in the material supplied by the teacher, the creation emotional background classes. When settling in the next figure in the tower, the children take on a role and a fairy tale is played out. Children are happy to pronounce words in verses about numbers. You can also dramatize fairy tales that are suitable for studying the ordinal and quantitative account such as "Gingerbread Man", "Turnip", etc. (see more details below)

It is very important that the children themselves want to do it. Let the lesson be a game for them, like an exciting task, an interesting thing. The arrival of fairy-tale heroes, the use of toys, game situations, problematic situations will make the lesson interesting.

1. Work with arithmetic material.
Familiarization with the formation of a new number, its correlation with a figure, with a quantitative and ordinal account, are carried out, respectively, by the methods. In addition to the work carried out in the classroom, we pay great attention to the mathematical development of children in other classes and outside. Here are some features of the work from the experience to consolidate numeracy skills. If a child has difficulty counting, count aloud. We ask him to count the objects aloud. We constantly count different objects (books, balls, toys, etc.), from time to time we ask the child: “How many cups are on the table?”, “How many books, pencils are there?”, “How many children play cubes?” "How many boys are there today? “etc., but we do it unobtrusively, using a game motive. For example: “I don’t know how many pencils to prepare, Milena, please count how many kids we have today in the mini-centre.” The acquisition of oral counting skills is facilitated by teaching children to understand the purpose of some household items on which numbers are written. These items are watches and a thermometer. Different types hours are available in our classroom. Children are often interested in what time it is, they enjoy playing with mock-up clock faces and alarm clocks. Thus, there is an improvement in counting skills.
Orientation in space.
It is very important to teach children to distinguish between the location of objects in space (in front, behind, between, in the middle, right, left, bottom, top). For this we can use different toys. We arrange them in a different order and ask what is in front, behind, near, far, etc. We play games like “Find your place”, “Put down the toy”, etc. Mastering such concepts as many, few, one, several, more, less, equally (with pupils of the mini-center). During a walk or in class, we ask the child to name objects that are many, few, one object. For example, there are many chairs, one table; many books, few notebooks. When reading a book to a child or telling fairy tales, when numerals are encountered, we ask him to put aside as many counting sticks as, for example, there were animals in history. After we counted how many animals there were in the fairy tale, we ask who was more, who was less, who was the same number. We compare toys in size: who is larger - a bunny or a bear, who is smaller, who is the same height.
We invite children to come up with fairy tales with numerals. . And then they can draw the heroes of their story and talk about them, make their verbal portraits and compare them. Preparatory work for teaching children elementary mathematical operations of addition and subtraction includes the development of such skills as parsing a number into its component parts and determining the previous and subsequent numbers within the first ten (older group)
In a playful way, children are happy to guess the previous and next numbers. Let's ask, for example, what number is more than five, but less than seven, less than three, but more than one, etc. Children are very fond of guessing numbers and guessing what they have planned. Think, for example, of a number within ten and ask the child to name different numbers. You say whether the named number is greater than what you intended or less. Then we switch roles.
For parsing, we use counting sticks or, with older children, matches cleaned of sulfur. Have the children place two chopsticks on the table. How many sticks are on the table? Then lay out the sticks on both sides. We ask how many sticks are on the left, how many are on the right. Then we take three sticks and also lay them out on two sides. We offer to take four sticks and the children share them. Ask him how else to arrange the four sticks. Have them change the arrangement of the counting sticks so that one stick is on one side and three are on the other. In the same way, we sequentially parse all numbers within ten. The higher the number, the more parsing options, respectively.
Learning numbers is easy and fun.

Numbers are harder. There are children who like abstract icons, and they are happy to learn letters and numbers. But others have to be motivated additionally. How to do it:
- play the phone game. At the same time, it will be very effective if the children play in pairs.
Plot- role-playing game"Shop" also contributes to the development of not only counting skills, but also to fixing the numbers, if you use checks or with a certain number of circles and, accordingly, "money", in the game the children will learn to correlate the number with the number and remember the number.
In the game "Buses" prepare numbers for buses or numbers for cars.
It will also be very effective to use numbered colorings, for example, all yellow fragments are numbered “1”, red ones are numbered “2”, etc. Give instructions on which color corresponds to each number verbally (as many times as the child asks). Children like such tasks, they are happy to do them, especially older children.
Using counting sticks is also useful to make up letters and numbers - children like these tasks. In this case, a comparison of the concept and the symbol takes place. Let the children pick up the number of sticks or counting material, toys that this number indicates to the number made up of sticks.

Development of quantitative and ordinal counting skills with the help of fairy tales, poems and counting rhymes.
Mathematical tales
Folk and author's tales, which the pupils of the mini-center already know by heart from repeated readings, are our invaluable helpers. In any of them, a whole lot of all kinds of mathematical situations. And they are assimilated as if by themselves. "Teremok" will help to remember not only the quantitative and ordinal count (the first came to the teremok the mouse, the second - the frog, etc.), but also the basics of arithmetic. The kid will easily learn how the amount increases if you add one at a time each time. A hare jumped up - and there were three of them. A fox came running - there were four. It's good if the book has visual illustrations, according to which the baby will be able to count the inhabitants of the tower. And you can play a fairy tale with the help of toys. "Kolobok" and "Turnip" are especially good for mastering ordinal counting. Who pulled the turnip first? Who met Kolobok third? And in the "Turnip" you can talk about the size. Who is the biggest? Grandfather. Who is the smallest? Mouse. It makes sense to remember the order. Who is in front of the cat? And who is behind the grandmother? "Three Bears" is generally a mathematical super fairy tale. And you can count the bears and talk about the size (large, small, medium, who is larger, who is smaller, who is the largest, who is the smallest), and correlate the bears with the corresponding plate chairs. Reading "Little Red Riding Hood" will provide an opportunity to talk about the concepts of "long" and "short". Especially if you draw long and short paths on a piece of paper or lay them out of cubes on the floor and see which of them will run faster for little fingers or a toy car.
Another very useful tale for mastering the account - "About a kid who could count to ten." It seems that it was created for this very purpose. Count the heroes of the fairy tale together with the goat and the children will easily remember the quantitative count up to 10.
Almost all children's poets can find verses with a score. For example, "Kittens" by S. Mikhalkov or "Merry Account" by S. Marshak. A. Usachev has many counting verses. Here is one of them, "Counting for Crows":

I decided to count the crows:
One two three four five.
Six crows - on a pole,
Seven crows - on the pipe,
Eight - sat on the poster,
Nine - feeds crows ...
Well, ten is a jackdaw.
This is where the countdown ends.

2. Working with geometric material.
In parallel with the work on the number, we introduce children to the basic geometric shapes, flat figures are little people who are interested in everything, they are very curious, and they also differ in color. (See photo 3)
Let the children make geometric shapes from sticks, cut, sculpt, draw. You can set them the required size, based on the number of sticks. For example, fold a rectangle with sides into three sticks and four sticks; triangle with sides two and three sticks. We also make figures of different sizes and figures with a different number of sticks. Please compare figures. Another option would be combined figures, in which some sides will be common.
For example, from five sticks you need to simultaneously make a square and two identical triangles; or make two squares out of ten sticks: large and small (a small square is made up of two sticks inside a large one). Combining counting sticks, children begin to better understand mathematical concepts ("number", "greater", "less", "same" , "figure", "triangle", etc.).
Children really like the transformation game, when the figures proposed to them turn into objects. The same type of exercise, “In what objects does the figure live ...?”
Of the variety of entertaining mathematical material in preschool age, didactic games are most widely used. Their main purpose is to ensure the exercise of children in distinguishing, highlighting, naming sets of objects, numbers, geometric shapes, directions, etc. In didactic games, it is possible to form new knowledge, introduce children to methods of action. Each of the games solves a specific problem of improving the mathematical (quantitative, spatial, temporal) representations of children. In the process of teaching preschoolers mathematics, the game is directly included in the lesson, being a means of forming new knowledge, expanding, clarifying, consolidating educational material. We use didactic games in solving problems of individual work with children, and also conduct them with all children or with a subgroup in their free time. There is a wide variety of didactic games that we use in the classroom and outside.

2. Development of logic.
In the formation of mathematical representations in children, various didactic game exercises that are entertaining in form and content are widely used. They differ from typical educational tasks and exercises in the unusual setting of the problem (find, guess), unexpected presentation) We offer tasks for the development of logic on behalf of Aldar Kose. and fix the error. Children are invited to consider how geometric shapes are located, in which groups and on what basis they are combined, to notice an error, correct and explain. The answer is addressed to Aldar Kose.
To develop certain mathematical skills and abilities, it is necessary to develop the logical thinking of preschoolers. At school, they will need the ability to compare, analyze, specify, generalize. Therefore, it is necessary to teach the child to solve problem situations, draw certain conclusions, and come to a logical conclusion. Solving logical problems develops the ability to highlight the essential, to independently approach generalizations. Logic games of mathematical content educate children in cognitive interest, the ability for creative search, the desire and ability to learn. An unusual game situation with problematic elements characteristic of each entertaining task always arouses interest in children. Game exercises should be distinguished from didactic games in terms of structure, purpose, level of children's independence, and the role of the teacher. They, as a rule, do not include all the structural elements of a didactic game (didactic task, rules, game actions). Content-logical tasks and tasks based on the mathematical content of the first two sections (arithmetic and geometric) are a means of achieving the goal and objectives, so we chose games and exercises for the development of logical thinking, creative and spatial imagination, brought them into the system. The logical development of the child also involves the formation of the ability to understand and trace the cause-and-effect relationships of phenomena and the ability to build the simplest conclusions on the basis of a cause-and-effect relationship. It is easy to make sure that when performing tasks and task systems, the child exercises these skills, since they are also based on mental actions: serialization, analysis, synthesis, generalization, comparison, classification, generalization, abstraction.
Seriation - construction of ordered ascending or descending series according to the selected attribute. Seriations can be organized by size, length, height, width, size, shape, or color. These are exercises for comparing objects on different grounds.
Analysis - the selection of the properties of an object, or the selection of an object from a group, or the selection of a group of objects according to a certain attribute.
Synthesis is the combination of various elements (features, properties) into a single whole.
Comparison is a logical method of mental actions that requires identifying similarities and differences between the features of an object (object, phenomenon, group of objects).
Classification is the division of a set into groups according to some attribute, which is called the basis of the classification.
Generalization is the formalization in verbal (verbal) form of the results of the comparison process.
These mental operations underlie the proposed exercises. We offer the following types of exercises and tasks for the development of logic.

1. Tasks of a logical and constructive nature (geometric material, numbers).
The use of tasks of a logical-constructive nature further enhances the process of assimilation of knowledge in the field of mathematics by a child. It is based on various methods of mental actions that help to enhance the effectiveness of the development of logical operations. At the first stage, we propose to use tasks with geometric material and numbers, then move on to using cards aimed at developing mathematical abilities, logical operations, which also actively develop fine motor skills, orientation on the sheet. These exercises can be done anywhere in the class. These tasks were selected and compiled by age groups. (See Appendix)

2. Games for the development of spatial imagination: construction material; counting sticks, constructors.
Games with building materials develop spatial imagination, teach children to analyze a model of a building, and a little later - to act according to the simplest scheme (drawing). The creative process also includes logical operations - comparison, synthesis (recreation of the object).
Games with counting sticks develop not only subtle hand movements and spatial representations, but also creative imagination. During these games, you can develop the child's ideas about the form, quantity, color. Of all the variety of puzzles, puzzles with sticks are most acceptable at senior preschool age (5-7 years old) (matches without sulfur can be used). They are called problems of ingenuity of a geometric nature, since in the course of solving, as a rule, there is a transfiguration, the transformation of one figure into another, and not just a change in their number. At preschool age, the simplest puzzles are used. To organize work with children, it is necessary to have sets of ordinary counting sticks for compiling visually presented puzzle tasks from them. In addition, you will need tables with figures graphically depicted on them, which are subject to conversion. On the reverse side of the tables it is indicated what transformation needs to be done and what figure should be the result. Tasks for ingenuity vary in the degree of complexity, the nature of the transformation (transfiguration). They cannot be solved in any previously learned way. In the course of solving each new problem, the child is included in an active search for a solution, while striving for the final goal, the required modification or construction of a spatial figure. At first, the children were reluctant to accept such tasks, they said that they did not know how, they were bored, then they beat these tasks: either we saved the princess - we opened heavy doors, then we picked up the key to the lock, destroyed the witch's spell, the children perked up, began to play. Also, children are just happy to lay out figures, numbers, objects. Games with sticks can be accompanied by reading riddles, poems, nursery rhymes, counting rhymes, suitable for the topic.
3. Educational(i.e. having several levels of complexity, diverse in application): GYENESH blocks, Kuizer sticks, etc. Kuizener sticks are a universal didactic material. Its main features are abstractness and high efficiency. Their role is great in the implementation of the principle of visibility, the presentation of complex abstract mathematical concepts in a form accessible to children. Working with sticks allows you to translate practical, external actions into an internal plane. Children can work with them individually or in subgroups. Games can be competitive. The use of sticks in individually - corrective work with children who are lagging behind in development is quite effective. The sticks can be used to perform diagnostic tasks. Operations: comparison, analysis, synthesis, generalization, classification and seriation act not only as cognitive processes, operations, mental actions, but also as methodological techniques that determine the path along which the child’s thought moves when performing exercises Note: Unfortunately, we do not have a real benefit of Kuizener's sticks, but we successfully replace it with multi-colored stripes.

4. Riddles, games for the development of imagination(including - according to TRIZ - technology for the development of systems thinking, see the appendix), logical tasks in verse, tasks-jokes (see the appendix), which are presented in verbal form.
You can start working with this type of tasks with riddles. Children of the fifth year of life are offered a wide range of topics of riddles: about domestic and wild animals, household items, clothing, food, natural phenomena, and vehicles. The characteristic of the subject of the riddle can be given in full, in detail, the riddle can act as a story about the subject. Teaching children the ability to guess riddles does not begin with their guessing, but with educating the ability to observe life, to perceive objects and phenomena from different angles, to see the world in diverse connections and dependencies. The development of a general sensory culture, the development of attention, memory, observation of the child is the basis for the mental work that he does when guessing riddles. Thematic selection of riddles makes it possible to form initial logical concepts in children. To do this, after guessing the riddles, it is advisable to offer children tasks for generalization, for example: “But how to name the forest inhabitants in one word: a hare, a hedgehog, a fox? (animals), etc. And we pay special attention to riddles with numerals.

Logic tasks, tasks - jokes.

Children are very active in the perception of tasks-jokes, puzzles, logical tasks. They are persistently looking for a course of action that leads to a result. In the case when an entertaining task is available to a child, he develops a positive emotional attitude towards it, which stimulates mental activity. The child is interested in the ultimate goal: to reach the right solution. Children actively participate in the discussion of problems, sometimes thoughtlessly put forward an erroneous assumption, then gradually begin to control themselves, reason. Children are also very active in solving problems in verse, especially if they are accompanied by illustrations. (See Appendix)
5. Finger games, counting rhymes, physical minutes on mathematical material.
These games activate the activity of the brain, develop fine motor skills of the hands, contribute to the development of speech and creative activity. "Finger games" is a staging of any rhyming stories, fairy tales with the help of fingers. Many games require the participation of both hands, which allows children to navigate in terms of "right", "up", "down", etc. If a child learns any one finger game”, he will definitely try to come up with a new staging for other poems and songs.
Example: "Boy - finger"
- Boy - finger, where have you been?
- I went to the forest with this brother,
I cooked cabbage soup with this brother,
I ate porridge with this brother,
I sang songs with this brother.
For the successful assimilation of logical operations by children, it is necessary to work in the system, both in the classroom and outside them. The use of such entertaining material is based on material containing numerals. (See Appendix)
6. Games for modeling on a plane.
These types of games include the most famous Tangram, Leaf and others. Tangram is one of the most interesting puzzle games. Tangram is a geometric puzzle invented in China over 4000 years ago. When organizing work on the game "Tangram", it is necessary to follow the principles of consistency and consistency. At the first stage, it is advisable to offer students simple tasks that will allow the children to get used to the puzzle and its parts, learn to recognize the various geometric shapes included in the Tangram. The peculiarity of the work was that the work goes through the stages:
1. Children make the manual themselves (under the guidance they cut it into pieces), get acquainted with the parts-figures of the "magic square", recognize them, learn to make a square.
2.Offer free modeling at will.
3. Modeling by model, copying.
4. The children were offered an image where the figures were drawn.
5. The most difficult tasks were tasks where the task was given - a silhouette, where the children themselves must, by trial and error, make it up from the figures. Such a task is given only after the children have firmly mastered the methods of composing figures.
In order to interest children in working with the “magic square”, various game situations were played out: for example, to disenchant the little animals, unfreeze, save, etc. Another effective method is the competitive one, preschoolers participate in the game with pleasure.
Efficiency.
Perhaps it is still difficult to judge the change in the level of mental development of children in the process of systematic pedagogical activity. The time interval is quite small.
However, observing the growth of mental and speech activity, which is obvious with the reusable use of logical operations, we can safely say that:
a) All children are familiar with the method of comparison, analysis, synthesis, classification.
b) several pupils of the pre-school class of children have a steady interest in educational games. The degree of their activity in independent activity has increased.
c) Children take the first steps in expressing judgments, proofs. This is a rather complicated speech activity, but it is very necessary. (The child should be able to explain his position, express his opinion and not be shy about it).
d) Work on the development of logic, thinking based on game exercises gives its results.
Conclusion: Task preschool education does not consist in maximizing the development of the child, not in speeding up the timing and pace of transferring him to the "rails" of school age, but, above all, in creating conditions for each preschooler for the most complete disclosure of his age-related capabilities and abilities. Mathematics has a unique developmental effect. “She puts the mind in order”, i.e. the best way forms the methods of mental activity and the qualities of the mind, but not only. Its study contributes to the development of memory, speech, imagination, emotions; forms perseverance, patience, creative potential of the individual. A mathematician plans his activities better, predicts the situation, expresses his thoughts more consistently and more accurately, and is better able to justify his position. It is this humanitarian component that is certainly important for the personal development of each person. Mathematical knowledge in it is not an end in itself, but a means of forming a self-developing personality. Thus, two years before school, one can have a significant impact on the development of the mathematical abilities of a preschooler. The development of logical thinking in preschoolers. Abstract of an individual lesson

A child is born without thinking. In order to think, it is necessary to master sensory and practical experience fixed by memory.

Memory- this is the consolidation, preservation and reflection in the mind of everything that happened in the past experience of a person.

Thinking- this is the process of human cognition of objects and phenomena of objective reality in their essential properties, connections and relationships.

Logical thinking is formed on the basis of visual-figurative thinking and is the highest stage of thinking in general. Psychological research confirms that only by the age of fourteen does a child reach the stage of formal-logical operations, after which his thinking becomes more and more like the thinking of an adult.

However, the foundation for the development of logical thinking is laid as early as preschool age.

Let us consider the possibilities of active inclusion in the process of the mathematical development of the child of various methods of mental action on mathematical material.

Seriation- 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” (indicating what is considered “size”) - if the objects are of different types (seat the toys according to their height).

Seriations can be organized by color: according to the degree of color intensity.

Colored water (per series according to color saturation).
Purpose: to consolidate children's ideas about shades of color, to teach children to find three shades of any color and call them: “dark”, “light”, “darkest”, “lightest”.

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

For example, the sign is given: sour. First, each object of the set is checked for the presence or absence of this attribute, and then they are selected and combined into a group according to the “sour” attribute.

Synthesis- connection 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).

N.B. Istomina notes that “the ability for analytical and synthetic activity is expressed not only in the ability to single out the elements of an object, its various features or combine elements into a single whole, but also in the ability to include them in new connections, to see their new functions” .

Tasks for the formation of the ability to single out the elements of an object (features), as well as to combine them into a single whole, can be offered from the very first steps of the child's mathematical development.

A. Assignment to choose a subject from a group on any basis (2-4 years):

• Take the red ball.
• Take the red one, but not the ball.
• Take the ball, but not the red one.

B. Task for the choice of several subjects on the indicated basis (2-4 years):

• Select all balls.
• Choose round, but not balls.

B. The task of choosing one or more subjects according to
several indicated signs (2-4 years):

• Choose a small blue ball.
• Choose a big red ball.

The assignment of the latter type involves the combination of two features of the object into a single whole.

Above, there were many tasks of a synthetic nature for connecting various elements of an object into a single whole at a material-constructive level.

For the development of productive analytical-synthetic mental activity in a child, the methodology recommends tasks in which the child needs to consider the same object from different points of view. The way to organize such a comprehensive (or at least multi-aspect) consideration is the method of setting different tasks for the same mathematical object.

The traditional form for the development of visual analysis is the task of finding an "extra" figure. A more complex form of such a task is the selection of a figure from a composition formed by the imposition of some forms on others. Such tasks can be offered to children of the senior and preparatory groups.

Psychologically, the ability to synthesize is formed in a child earlier than the ability to analyze. On this basis, it is possible to build the formation of an analytical-synthetic process: if a child knows how it was assembled (folded, constructed), it is easier for him to analyze and isolate its constituent parts.

The activity that actively forms the synthesis in preschool age is construction. At first, this activity is purely synthetic, with a pattern of a “do as I do” type of execution process. At first, the child learns to reproduce the object, repeating the entire design process after the teacher, then repeating the process of building from memory, and, finally, proceeds to the third stage: self-restoration of the method of constructing an already finished object. (Assignments of the type "Make the same"). The fourth stage of tasks of this kind is already creative task: build a tall house, build a garage for this car, lay down a rooster (tasks are given without a sample, the child works according to the idea, but must adhere to the specified parameters - the garage is for this car).

For construction, any mosaics, constructors, cubes, split pictures that are suitable for this age and make the child want to mess with them are used. An adult in these games plays the role of an unobtrusive assistant, his goal is to help bring the work to the end, that is, to obtain the intended or required whole object.

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

Comparison requires the ability to single out some features of an object and abstract from others. To highlight various features of an object, you can use the Find It game:

• Which of these items are big yellow? (Ball and honey after all.)
• What's the big yellow round? (Ball.), etc.

The child should use the role of leader as often as the responder, this will prepare him for the next stage - the ability to answer the question: What can you tell about this subject? (The watermelon is large, round, green. The sun is round, yellow, hot.)

Option. Who will tell more about it? (The ribbon is long, blue, shiny, silk.)
Option. “What is it: white, cold, crumbly?” etc.

Tasks for dividing objects into groups according to some attribute (large and small, red and blue, etc.) require comparison.

All games of the "Find the same" type are aimed at developing the ability to compare. For a child of 2-4 years old, the signs by which similarity is sought should be well identifiable. For older children, the number and nature of similarities can vary widely.

Let us give an example of a task in which the child is required to compare the same objects according to various criteria.

Materials. On the flannelgraph there are images of two apples: a small yellow one and a large red one. Children have a set of figures - two triangles: blue and red, two squares: red and yellow, two circles: small green and large yellow.

The ability to identify the features of an object and, focusing on them, to compare objects is universal, applicable to any class of objects.

Classification- division of a set into groups according to some feature, which is called the basis of classification.

The basis for the 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 with preschool children can be carried out ... ..

• by the name of the items (cups and plates, shells and pebbles, skittles and balls, etc.);
• by size (large balls in one group, small balls in another; long pencils in one box, short ones in another, etc.);
• by color (red buttons in this box, green in this one);
• in shape (squares in this box, and circles in this box; in this
  box - cubes, this one - bricks, etc.);
• on other grounds (edible and inedible, floating and flying animals, forest and garden plants, wild and domestic animals, etc.).

All of the above examples are classification according to a given basis: the teacher himself informs his children. In another case, children determine the basis on their own. The teacher sets only the number of groups into which the set of objects (objects) should be divided. In this case, the basis can not be defined in a unique way.

Execution method. There are two options: classification by shape and by color. The teacher helps the children clarify the wording - if the children divide the figures into circles and squares, then the teacher generalizes: “So they divided them according to shape.”

Generalization- this is the formulation in verbal (verbal) form of the results of the comparison process.

Generalization is formed at preschool age as the selection and fixation of a common feature of two or more objects. Generalization is well understood by a child if it is the result of an activity carried out by him independently, for example, classification: all these objects are large, and all these are small; these are all red, these are all blue; these all fly, these all run, etc. All the above examples of comparisons and classifications ended with generalizations.

The formation in children of the ability to independently make generalizations is extremely important from a general developmental point of view. In connection with changes in the content and methodology of teaching mathematics in elementary school, which aim to develop students' ability to empirical, and in the future, theoretical generalization, it is important to teach children in kindergarten various methods of modeling activity using real, schematic and symbolic visibility (V.V. Davydov), to teach the child to compare, classify, analyze and summarize the results of their activities.

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State autonomous educational institution

higher professional education

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

Boksitogorsk Institute (branch), SPO

Graduate work

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 director

teacher PM.03 E.N. Nesterov

Boksitogorsk 2017

INTRODUCTION

Nowadays, there is an ever-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 concise dictionary systems 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. In them, logical and mathematical constructions are modeled and in the course of the game such tasks are solved that help to 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 problems 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 teenagers, but modern research it has been 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. Rubenstein prove that neither logical thinking, nor creative imagination and meaningful memory can develop in a child regardless of education, 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 child development, 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 sound 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, they use different kinds simple tasks and exercises. 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;

Ability to simulate in games available to the child 4-6 years of logical and mathematical relations (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, search collectively, 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.)

BEHIND. 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", "Cross" (with colored counting sticks), “Unicube”, “Color panel”, “Little designer”, “Kaye honeycombs”, “Logoforms”, “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 intensified the activities 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 Gyeneš, 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 volumetric figures, differing in shape (circles, squares, rectangles, triangles), in color (yellow, blue, red), in 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 next to each other (operating with one property), the other - so that there are no identical blocks next to them in shape and color (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 related to perception thinking person surrounding reality cannot be accomplished 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.

Development of visual-effective and visual-figurative thinking is carried out 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 such as a geographic map to select right way in an extensive system of paths, on a chessboard, they look for the “address of a figure”.

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 use ready schemes Don't impose your own ideas. At this age, the development of fantasy and the ability to generate one's own, new images are the key to the development of intellectual abilities - after all, thinking is figurative, than better baby invents 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: length, height, width - if the objects are of the same type (dolls, sticks, ribbons, pebbles, etc.) and simply "in size" (with an indication of what is considered "size") - if the items different type(seat the toys according to their height). Seriations can be organized by color: according to the degree of color intensity.

Most Suitable didactic manual for the formation of this logical operation - colored Kuizener sticks. Sticks of the same length are painted in the same color. Each wand displays certain number in cm, the sticks united by a common shade 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 gaming activity based on the development of the imagination and creativity of the child.

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. fulfill 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 the 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 preschoolers;

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 teaching 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 based on MBDOU " Kindergarten No. 7 KV "Pikalevo with children 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		State of the art
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		State of the art
2. Vasilisa
10. Timothy

From the data obtained, we can conclude that Kirill, Sasha, Varya, 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 activities corresponded thematic planning according to the program, as well as the speech and age characteristics of 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		State of the art
			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 result with low level development of logical thinking to average performance. 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		State of the art
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.

...

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