Theory and methodology of mathematical development of preschool children

Preschool age is a time when the cognitive, moral, and physical development of a child occurs especially intensively. In particular, it is before the age of 5-6 that a child acquires more than half of the total thinking skills that will be useful to him in the future. That is why it needs to be given special attention. In particular, it is at this age that the child should develop his first mathematical skills. Let's consider the theoretical foundations of the mathematical development of children of junior and senior preschool age.

Math lesson in kindergarten, senior group

Why is this so important?

Mathematics is one of the most significant subjects. However, it is precisely this that often causes considerable difficulties for students.
Studying this subject has a beneficial effect on the child’s cognitive abilities (thinking, memory, speech)
Mathematical skills improve the emotional-volitional sphere, form perseverance and determination
Improves the basics of a child's imagination

The role of mathematics in life

What skills should a child develop by the end of the preschool period?

By the end of the preschool period, the child should have the following mathematical skills:

Ability to compare values based on basic characteristics; the formation of ideas about the concepts of “more-less”, “higher-lower”, etc.
The ability to group objects according to their basic properties (basics - size, color, purpose, material, shape)
Ability to compare parts and wholes; ability to assemble a picture from at least 12-24 fragments
Developed counting skills and the ability to perform mathematical operations with numbers within ten
Children’s development of quantitative and qualitative representations of the subject

The essence of mathematical development

Necessary conditions for conducting math classes with a child

What is the theory and methodology of mathematical development for preschoolers based on? In order for the lessons to be truly interesting for the child, and for him to assimilate information faster and easier, they must be built taking into account the following recommendations:

The use of visual didactic material selected taking into account the age and other individual characteristics of the child
The presence of a clear plot for the lesson according to which its development will take place
Selection of tasks in strict accordance with the age characteristics of the child and the level of his intellectual development
Using a variety of methods and forms to create the basis of work (these include solving logical problems, didactic games, working with handouts, etc.)
Multitasking (focus on the development of spatial, temporal, quantitative concepts)
Using a game form of conducting classes
Emphasis on the formation of gaming motivation; elements of surprise and surprise
Helping the child not only master a certain system of knowledge and skills, but also develop his skills of independent cognitive activity, independence of judgment, etc.
Formation of an optimal developmental environment for the development of basic cognitive processes in a child
Teaching children to perceive the quantitative and qualitative features of objects, forming appropriate ideas

Objectives for the development of mathematical abilities

Methods and techniques for teaching preschoolers elements of mathematics

Methods and techniques for teaching preschoolers elements of mathematics

The concept of "Method"

In the theory and methodology of children's mathematical development, the term “method” is used in two senses: broad and narrow.

The method is a historically established approach to the mathematical preparation of children in kindergarten (monographic, computational and the method of reciprocal actions).

When choosing methods, the following are taken into account:

goals, objectives of training;
the content of the knowledge being formed at this stage;
age and individual characteristics of children;
availability of necessary teaching aids;
the teacher’s personal attitude to certain methods;
specific conditions in which the learning process takes place, etc.

At the beginning of the 20th century. classification of methods was mainly carried out according to the source of knowledge - these were verbal, visual, practical

methods.

Practical methods

(exercises, experiments, productive activities) are most consistent with the age characteristics and level of development of thinking of preschoolers. The essence of these methods is that children perform actions that consist of a number of operations.
Practical methods are characterized primarily by independent performance of actions and the use of didactic material. On the basis of practical actions, the child develops the first ideas about the knowledge being formed. Practical methods ensure the development of skills and abilities and allow the widespread use of acquired skills in other types of activities.

Visual and verbal

methods in teaching mathematics are not independent. They accompany practical and playful methods. But this does not detract from their importance in the mathematical development of children.

Visual and verbal methods

Towards visual methods

training includes: demonstration of objects and illustrations, observation, display, examination of tables, models.

Towards verbal methods

include: storytelling, conversation, explanation, explanations, verbal didactic games. Often in one lesson different methods are used in different combinations.

Techniques

Components of the method

are called methodological
techniques.
The main ones used in mathematics classes are: overlay, application, didactic games, comparison, instructions, questions for children, examination

etc.

Reception "Show"

A widely used method is: show
.
This technique is a demonstration; it can be characterized as visually practical and effective.
There are certain requirements for the display: clarity and dissection; consistency of action and word; accuracy, brevity, expressiveness of speech.

Reception "Instructions"

One of the essential verbal techniques in teaching children mathematics is instruction.

, reflecting the essence of the activity that children have to perform.

Reception “Questions for Children”

Questions for children occupy a special place in the methodology of teaching mathematics.

. They can be reproductive-mnemonic, reproductive-cognitive, productive-cognitive. In this case, the questions must be accurate, specific, and concise. They are characterized by logical consistency and variety of formulations.

Features of the formation of mathematical concepts depending on age

Considering that preschool age is conventionally divided into three main periods, goals, objectives, as well as methods and forms of mathematical education of children will also differ.

Junior preschool period. At this time, the necessary mathematical skills and concepts are just beginning to develop. Therefore, the child needs to be given an idea of basic operations. The best games for developing thinking skills are children's mosaics (from 5 fragments), addition of geometric shapes (from 4 parts). The method of developing quantitative and qualitative concepts in preschoolers requires special attention.

Middle preschool period. There is an active development of the sign-symbolic function of consciousness. The child can already be taught to count and the simplest mathematical operations. The foundations of logical thinking are laid. The most preferred games include: “Nonsense”, “Count the objects”, “Find a pair”, “Mathematical lotto”, “Domino figures”. To develop a child’s analytical and synthetic abilities, you can offer him games like tangram, where he will need to make a geometric figure, a silhouette of an animal, etc. from individual parts.

Individual lesson to determine the level of mathematical development

In older preschool age, the child’s independence and his ability to self-organize begin to play an increasingly noticeable and significant role. Logical thinking is becoming increasingly important.

The child begins to try to compose stories from pictures, compose logical series, observing the correct sequence of elements.

Math tests for kids 3-4 years old

Features of the theory and methodology of mathematical development of children depending on the age group

The content of the theory and methodology of mathematical development of preschool children depends on the age group. However, the basis for all age groups is developmental teaching methods.

Definition 2

Developmental teaching methods are methods aimed at systematizing acquired knowledge through the use of various techniques for their assimilation.

Second junior group of preschool educational institution. Program material for mathematical development is limited to the “pre-numerical” period of training. Children of this age group learn to group objects, identify one object from a group based on distinctive features, and learn the concept of “one” and “many.” Children are taught to compare objects using the techniques of application and superposition.

Middle group of preschool educational institutions. The program for this age group provides for the further development of elementary mathematical concepts in children. Children are taught to count within five and compare two groups of sets. It is important to learn the ability to establish equality and inequality between groups of objects.

Senior group and preschool group of preschool educational institutions. The mathematical development program is aimed at deepening, expanding and generalizing previously acquired elementary mathematical knowledge and concepts. Children are taught to count within ten, introduced to numbers, their order and writing rules. In addition, children learn to compare 3-4 groups of objects based on characteristic features and quantity. The ability to identify an object from a group, group objects according to similar characteristics, etc. continues to be developed.

It is important to develop children’s motivation for subsequent learning and obtaining mathematical knowledge, the desire to obtain it not only as part of a lesson, but also independently.

What methods are best used to develop a preschooler's mathematical understanding?

The visual method plays the most important role in teaching children mathematics, especially when it comes to the early preschool period.

Methods for developing mathematical knowledge

There are the following types of visual teaching methods:

Working with handouts or demonstration materials. Using a plotless or plot method (you can take as a basis the plot of any fairy tale familiar to a child, where counting or numbers would appear)
Volumetric or planar. Classes using special counting materials (for example, children's abacus, sticks, cubes, etc.)
Homemade or factory made.

Handouts for mathematical classes
In order to use visual material more effectively, it is necessary to build developmental classes taking into account the following patterns:

The study of each new topic should begin with more voluminous visual material. This will make it easier for the child to understand
As the child grows up, it is necessary to ensure that the proportion of volumetric and plot-based visual material decreases, and the proportion of flat and plotless material increases
It is advisable to use several types of visual material to solve one software problem
It is very advisable to familiarize the child with new material in advance.

Separately, it is worth considering the requirements for visual aids.

Didactic material for classes
As we have already indicated above, it can be either ready-made at the factory or made by parents. However, it is important that it matches the following:

Hygiene. Toys must be made from environmentally friendly, safe materials and have all the necessary certificates
Aesthetics. Attractive material is more likely to attract the child's attention
A reality that allows a child to perceive the material being studied without distortion
Durability and reliability
Variety and sufficient quantity to allow the use of variable techniques
The principle of logical construction that combines the basics of the material
Uniformity

Play corner with didactic materials
A significant advantage of the practical teaching method is that it most fully explains to the child why he is studying this or that material. And how exactly will the knowledge gained be useful to him in the future?

Active application in practice of a variety of didactic material
Performing a variety of both mental and practical activities
Development of the skill of predicting the outcome of actions with various types of didactic material
Not only instilling mathematical skills in the child, but also a detailed explanation of their role in the child’s life (in play activities, in everyday life, etc.)

The verbal method of teaching is based on direct interaction between the child and the parent or teacher.

That is why the main requirements for this method will be aimed at the speech of the participants in the process

The speech of the parent or teacher should be:

Literate
Rosary
Emotional and alive
Available
Friendly
Moderately loud

Speech development in mathematics classes
The pace of speech, its intonation and other features must be adjusted depending on the individual age characteristics of the child. For example, a child of primary preschool age perceives rather slow speech much better; unformed memory processes require repeated repetitions.

Development of logic and spatial thinking in a playful way

When talking with an older child, you can somewhat speed up the pace of speech and also make more active use of problem situations.

Certain requirements are also imposed on children’s speech. She must be:

Competent
Contain the necessary mathematical terminology and basic mathematics by age
Legible and understandable
The child must speak in complete common sentences with correct grammatical structure
Have sufficient volume

3.4. Forms of work on pre-mathematical development of children

3..4. Forms of work on pre-mathematical development of preschool children.

Forms of work on pre-mathematical development of preschool children.
Types and types of occupations, their features, structure
Forms of work outside of class

Forms of work on pre-mathematical development of preschool children.

In didactics, “form” (device, structure, system of organization, internal structure) is considered as a way of constructing educational activities. Organizational forms of education must reliably ensure the implementation of the objectives of the educational process, the ultimate goal of which is to promote the comprehensive and, first of all, intellectual development of children.

Variety of training forms

is determined by the number of students, the place and time of classes, the methods of children’s activities, as well as the methods of managing this activity by the teacher.

Based on the characteristics of the organization of training, determined by the number of students, there are individual, collective and group (differentiated) forms of training.

Individual training

– lies in the fact that the child receives new ideas, performs different tasks, and has the opportunity to receive direct help from an adult.

Collective learning

– involves the work of a teacher with a group of children. There is mutual assistance and mutual learning. The disadvantage is that individual differences are not sufficiently taken into account.

Differentiated learning

in pedagogical practice it is called “group”, “individual-group”, or “collective-group” learning.
Differentiated training is carried out according to the following criteria:

by ability or inability to learn;
by interest;
by volume of material and degree of complexity;
by the degree of independence and pace of progress in learning.

In the 40s of the 20th century, Leushina A.M. first proposed classes as a form of teaching mathematics in kindergarten

. Metlina L.S. in the 80s she developed notes for mathematics lessons for all age groups of preschool children. Until the 90s, it was believed that the main form of teaching mathematics to preschoolers was the classroom. To teach children mathematics, classes were held once a week.

However, it must be taken into account that those mathematical concepts that are formed in preschool age are of an applied nature for children. Children need mathematical concepts for daily orientation in the world around them. Therefore, they should be formed in a variety of activities (communication, play, cognitive-practical, artistic, labor).

Types and types of occupations, their features, structure.

At the present stage of development of the preschool education system, state documents (Code on Education of the Republic of Belarus, Standards of Preschool Education, Model Curriculum for Preschool Education) determine the status of the game, classes

as
the main form
of a specially organized educational process.

The number of classes in
the educational field
“
Elementary mathematical concepts
” and the time allotted for their implementation are regulated by the Standard Preschool Education Curriculum.

first junior group – once every 2 weeks (10 min.)
second junior group – 1 time per week (15 min.)
middle group – 1 time per week (20 min.)
senior group 5-6 years old – once a week (25 min.)
senior group 6-7 years old – once a week (30 min.)

Classes in the educational area “Elementary Mathematical Concepts” are held mid-week in the morning in combination with classes that do not require a high mental load (physical education, music classes or visual arts classes).

During the holidays, these classes are not conducted; the concepts and skills acquired by children are consolidated in everyday life: in games, play exercises, on walks, etc.

In all age groups, classes are conducted frontally, i.e. simultaneously with all children. Only in the first junior group is it recommended to conduct classes in subgroups (6-8 people), including all children, in order to gradually teach them to study together.

Requirements for conducting classes
in the educational field “Elementary mathematical concepts”

are built taking into account general didactic principles: scientific character, systematicity and consistency, accessibility, clarity, connection with life, individual approach to children, etc.;
implement all the contents of the educational field “Elementary mathematical concepts”;
the implementation of educational, educational and developmental tasks in the classroom occurs in a comprehensive manner;

the content of each specific lesson, the formulation of its tasks, is carried out on the basis of the content of the educational field “Elementary mathematical concepts”, taking into account the characteristics of children and their level of development;

each lesson occupies its own, strictly defined place in the system of lessons for the study of a specific program task in the educational field “Elementary mathematical concepts”;
The program objectives of the lesson determine its structure. In the structure of the lesson, separate parts are distinguished: from one to four or five, depending on the number, volume, nature of the tasks and the age of the children. All parts of the lesson are independent, varied and related to one another;
in one lesson one new problem is solved, the rest are for repetition and consolidation;
new material is given in the first part of the lesson, as it is mastered, it moves to other parts; subsequent parts of the lesson are usually conducted in the form of a didactic game, in which children’s ideas and skills are consolidated and applied in new conditions;
widespread use of didactic games and exercises with handouts;
organization of physical education (after the first or second part).

Since the leading activity in preschool age is play, play methods and techniques of interaction between teacher and student are predominant in the lesson, i.e. classes can be of a playful nature or presented as play-based didactic complexes.

In accordance with the didactic objectives, the type of lesson is determined:

Training type
(learning new ideas).
Goal:
setting cognitive tasks for children, presenting, expanding and clarifying children’s ideas about quantity, size, geometric figures and the shape of objects, space and time;

Fastening type
(consolidation and systematization of children’s accumulated experience).
Goal:
understanding the perceived ideas and forming primary generalizations.

Combined (mixed) type
classes.
Goal:
learning new content and repetition, consolidation and systematization

Types of activities

in the educational field "Elementary mathematical concepts"

Combined lesson

can be integrated - by selecting objects of knowledge from different educational fields or components of one educational field; can be playful or non-playful - according to the predominance of methods of educational interaction, according to the nature of the interaction between students and the teacher, and between students.

Its structure:

Organizing time.
Implementation of the learning task. Mastering new material.
Consolidating newly acquired ideas in children’s independent activities.
Movable pause.
Implementation of educational content from other components of the educational field.
Bottom line.

Complex lesson

involves a combination of classes in the educational area “Elementary mathematical concepts” with classes in other educational areas. In this case, in the lesson on the formation of elementary mathematical concepts (it is the first part of a complex lesson), learning tasks are implemented, children master new educational content, and in classes in other educational areas - the use, consolidation, expansion, clarification, deepening of the newly mastered educational content takes place. content. The structure of a complex lesson is flexible and variable. It should be remembered that the greatest pedagogical effect can be achieved by combining classes in the educational area “Elementary mathematical concepts” with classes in the educational area “Art”, “Child and Society”, “Child and Nature”.

Game complexes with mathematical content

(as a game version of a combined lesson):

didactic in nature.
A didactic game is selected to solve each program problem, and children play it either in a sequence determined by the plot of the lesson, or in a random sequence determined by the “magic arrow”, spinning top, child’s choice, etc.;

2) educational and developmental in nature.

Complex diagram:

a game or gaming exercise to develop attention, perception, sensation, and activate memory;
a game or game task for the development of reproductive thinking, the formation of certain mathematical concepts (training);
a game or play exercise that helps develop independent reproductive thinking and consolidate acquired ideas in independent practical activities;
an outdoor game or exercise aimed at increasing motor activity, consolidating mathematical concepts, and developing cognitive processes;
a game or play exercise for the development of divergent thinking (creative, productive), imagination, logical thinking, the formation in children of the ability to use their ideas in new conditions, the development of elements of logical thinking;
a game or play exercise for relaxation and imagination development.

Lesson using educational visual aids
(
with individual notebooks).

Structure:

Didactic game or game exercise.
Work with educational visual aids (formation of new ideas, expansion and deepening of the mastered material).
An outdoor game, or a relay game, or a physical education break.
Working with educational visual aids (completing graphic tasks, actions with cut material).
Didactic game or game exercise.

Classes using computers.

In some preschool institutions there are computer and gaming complexes (one room is a computer class, the second is a room for mental and physical relaxation).

Advantage

this form: the possibility of an individual approach to learning, the computer is an interesting toy for the child - children develop attention and interest in learning, etc.

If you violate the rules for using a computer, your work can have a negative effect.

A child 4-6 years old can be at the computer for no more than 10 minutes, 1-2 times a week (otherwise the child’s posture, vision, and psyche will be impaired). Therefore, with the help of a computer it is necessary to solve only those software problems that are solved less effectively in other forms.

Forms of work outside of class

(unregulated activity)

Individual work

with the child allows for pedagogical correction. The forms of this work are exercises, work with individual material (notebooks, didactic material), etc.

Game with mathematical content.

It is planned at least 2-3 times a week individually, in a group (or part of it).
All types of games can be planned. Didactic games.
There are many collections with d/i on mathematics by such authors as Sai, Udaltsova, Mironova, Starzhinskaya, Novikova.

Plot-didactic games

(this term was proposed by A. Smolentsova, “Plot-didactic games with mathematical content,” 1985)

Educational games

. Proposed by Z.A. Mikhailova, B.P. Nikitin (“Steps of creativity or educational games”).

On the day of the lesson in the educational area “Elementary mathematical concepts”, a game with mathematical content is not planned.

Examination.

It is planned at least 2 times a week individually, in a group (or part of it) when developing the ability to group objects; establishing a one-to-one correspondence in a practical way; bills by touch; dividing a whole into parts; comparing quantities and ordering; examination of geometric figures and determination of the shape of an object; orientation from oneself, in the surrounding environment.

Experiences, experiments.

Planned as needed, but no more than once a week individually, in a group (or part of it) while developing an understanding of the independence of number from qualitative and spatial characteristics; understanding the dependence of the result of ordinal counting on the direction of counting and the independence of the result of quantitative counting on the direction of counting; skills of transfiguration and transformation.

Observations.

Planned daily individually, in a group while forming ideas about the parts of the day and their sequence; ideas about the seasons and their sequence.

Story, conversation.

Planned as necessary individually, in a group when forming temporary ideas; ideas about geometric figures and the shape of objects; ideas about size, about ordering by size.

Entertainment with mathematical content.

It is planned no more than 1 time per quarter by group. It can be planned as a competition, theatrical or circus performance, folklore festival, travel, etc. It can replace a complex lesson or game complex. On this day, a lesson in the educational area “Elementary Mathematical Concepts” is not planned.

Viewing works of fine art.

It is planned as needed, but at least once a month by the group (or part of it) when forming quantitative, spatial and temporal ideas; ideas about size and space. Artistic illustrations, photographs, reproductions of paintings, paintings (still lifes, everyday life, animalistic, mythological genres) are used.

Reading literary works with mathematical content.

It is planned as needed, but at least once a month by the group (or part of it). When reading, mathematical characteristics, mathematical actions (their necessity, sequence, correctness, adequacy of the situation, etc.) that are performed by the heroes of the works are highlighted.

Independent cognitive activity

games with didactic material,
role-playing games,
situations of work and everyday activities.
working with a book (coloring, cutting out, comparing by size): books like coloring books, books like math notebooks - “Geometry for Kids”, etc.,
performing entertaining exercises (puzzles, games with sticks)

Signs of independent cognitive activity are:

children's interest in it; manifestation of creative initiative; independence in choosing a game and how to implement the plan.

In independent cognitive activity, children’s ideas about numbers, sizes, geometric shapes, time, and space are clarified, deepened and expanded.

Each of the listed forms is planned in different types of activities with a certain frequency and has specifics in the way children are organized, depending on the age group and the content of the problem being solved.

LITERATURE

Zhitko, I.V. Formation of elementary mathematical concepts in children from 4 to 5 years old: educational method. A manual for preschool teachers. education. Minsk: Ecoperspective, 2016. – 200 p.
Formation of elementary mathematical concepts in preschoolers / ed. A.A.Stolyar. – M., Education 1988
Shcherbakova, E.I. Methods of teaching mathematics in kindergarten: a textbook for preschool students. department and faculty avg. ped. textbook establishments. M., Ed. , 1998 – 272s

Structure of a math lesson for a preschooler

The correct structure of the lesson is another important condition on which the methodology for the mathematical development of preschool children is based.

Games used in mathematics classes

Introductory part. Logical warm-up. Includes the simplest tasks for children, which should “warm up” the child’s mind, interest him and prepare him for the lesson.
The main part of the lesson, during which new material is studied to form mathematical concepts, or reinforcement of what has already been learned. Exercises can be selected using special methodological literature (a good example is the book compiled by E.I. Shcherbakova “Theory and Methods of Mathematical Development for Preschool Children”).
3Finger gymnastics. Redirects the child's attention and serves as a warning against fatigue. For the same purposes, you can use physical exercise (if the lesson was associated primarily with intellectual activity), articulatory gymnastics or eye exercises (if the child had an active lesson using outdoor games).
Repetition of covered material.
Drawing, lacing, or games aimed at developing fine motor skills.

Studying shape and size in physical education classes
Developed mathematical skills in preschool children will allow him not only to successfully start school, but also to develop such qualities as perseverance, attention, and determination.
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Mathematical development of preschool children in the context of the Federal State Educational Standard (FSES) Consultation on mathematics on the topic

Mathematical development of preschool children in the context of Federal State Educational Standards for Preschool Education

“The further path of mathematical development and the success of a child’s advancement in this area of knowledge largely depend on how elementary mathematical concepts are laid down.”

L.A. Wenger

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

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

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

The Federal State Educational Standard for Education requires making the process of mastering elementary mathematical concepts attractive, unobtrusive, and joyful.

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

Development of logical and mathematical ideas about the mathematical properties and relationships of objects (specific quantities, numbers, geometric figures, dependencies, patterns);
Development of sensory, subject-effective ways of knowing mathematical properties and relationships: examination, comparison, grouping, ordering, partitioning);
Children's mastery of experimental and research methods of learning mathematical content (experimentation, modeling, transformation);
Development in children of logical ways of knowing mathematical properties and relationships (analysis, abstraction, negation, comparison, classification);
Children's mastery of mathematical ways of understanding reality: counting, measurement, simple calculations;
Development of intellectual and creative manifestations of children: resourcefulness, ingenuity, guesswork, ingenuity, desire to find non-standard solutions;
Development of accurate, reasoned and demonstrative speech, enrichment of the child’s vocabulary;
Development of children's initiative and activity.

Target guidelines for the formation of elementary mathematical concepts:

Oriented in quantitative, spatial and temporal relationships of the surrounding reality

Counts, calculates, measures, models

Knows mathematical terminology

Developed cognitive interests and abilities, logical thinking

Possesses basic graphic skills and abilities

Knows general techniques of mental activity (classification, comparison, generalization, etc.)

How to “awaken” a child’s cognitive interest?

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

That is, it is necessary to make learning entertaining. With entertaining learning, emotional and mental processes are intensified, forcing you to observe, compare, reason, argue, and prove the correctness of the actions performed.

The adult’s task is to maintain the child’s interest!

Today, the teacher needs to structure educational activities in kindergarten in such a way that every child is actively and enthusiastically engaged. When offering children tasks with mathematical content, it is necessary to take into account that their individual abilities and preferences will be different and therefore children’s mastery of mathematical content is of a purely individual nature.

Mastering mathematical concepts will only be effective and efficient when children do not see that they are being taught something. They think they are just playing. Unbeknownst to oneself, during game actions with game material, one counts, adds, subtracts, and solves logical problems.

The possibilities for organizing such activities are expanded provided that a developing subject-spatial environment is created in the kindergarten group. After all, a properly organized subject-spatial environment allows every child to find something to their liking, believe in their strengths and abilities, learn to interact with teachers and peers, understand and evaluate feelings and actions, and give reasons for their conclusions.

Each group should be provided with entertaining material, namely card files with a selection of mathematical riddles, funny poems, mathematical proverbs and sayings, counting rhymes, logical problems, joke problems, and mathematical fairy tales. Entertaining in content, aimed at developing attention, memory, and imagination, these materials stimulate children's display of cognitive interest. Naturally, success can be ensured under the condition of personality-oriented interaction between the child and adults and other children.

Particular attention is paid to the richness of the environment - the educational space must be equipped with teaching and educational means (including technical ones).

For 1st junior group

It is recommended that the sensory development center have a variety of didactic and visual materials:

Didactic games on color, shape, size, development of tactile sensations;

Educational games - Dienesh blocks, Cuisenaire sticks, Montessori frames, etc., with teaching aids for them (albums, instructions, etc.);

Attributes and materials for playing with sand and water;

Visual material on sensory education;

Board and printed games;

"Wonderful bag";

A card index of artistic words for introducing children to sensory standards.

Helper devices: magnifying glass, hourglass, magnets, measuring spoons, rubber bulbs of different sizes

For children 3-4 years old

The center of entertaining mathematics can include didactic toys and board games that develop children’s skills:

compare objects according to various criteria - size, shape, color, purpose, etc.;

group objects based on common characteristics (this is dishes, these are shoes; ribbons are the same length and the same color); compose a whole image from 6-8 parts (“Toys”, “Animals”, “Flowers”): lotto (dishes, clothes, furniture, animals, plants);

make rows of identical objects in descending or ascending order of one or another characteristic: volume, height, color intensity, etc.;

real objects: games “Freeze”, “Magic Pictures”, “Invent It Yourself”, etc.;

Didactic games: “Loto”, paired pictures, large and medium plastic mosaics, for example: “Geometric Shapes”, puzzles from 6 to 18 parts, sets of cut pictures on cubes, pictures - stencils: “Fold the flower”, “Fold the Christmas tree”, “Build a house with a window (for a cockerel)”, “Wonderful bag”, etc.

Educational games: “Fold the pattern”, “Dots”, “Corners”, “Unicube”, “Dyenesh Blocks”, “Cuisenaire Sticks”, Montessori frames, etc. in accordance with age goals.

For children 4-5 years old

An entertaining mathematics center for the middle group may contain:

Didactic toys and board games that develop children's skills:

- compare objects according to various criteria - size, shape, color, purpose, etc.;

- group objects based on common characteristics (this is dishes, this is shoes, this is furniture; ribbons are the same length and the same color); compose a whole image from 6-8 parts (“Toys”, “Animals”, “Flowers”, etc.): lotto (dishes, clothes, furniture, animals, plants); geometric mosaic;

- make rows of identical objects in descending or ascending order of one or another characteristic: volume, height, color intensity, etc.;

- draw up a simple plan diagram using various substitutions of real objects: games “Freeze”, “Magic Pictures”, “Invent It Yourself”, “Where is Mom?” and etc.;

Didactic games:

-games for understanding symbolism, schematics and conventions (“What does it look like?”, “Complete”);

-models: numerical ladder, a series of quantities, spiral models for the knowledge of time relations;

-games for mastering magnitude, numerical, space-time relationships (“Make the same pattern”);

-games with algorithms, including 3-5 elements (“Growing a Tree”), etc.

Educational games: “Fold the pattern”, “Dots”, “Corners”, “Unicube”, “Dyenesh Blocks”, “Cuisenaire Sticks”, Montessori frames, etc. in accordance with age goals

For children 5-7 years old

In senior preschool age groups, an entertaining mathematics center may contain:

Stencils, rulers and other measuring standards

Didactic games:

- games for dividing a whole object into parts and composing a whole from parts (“Fractions”, “Make a circle”);

- games with numbers, coins;

— games for the development of numerical concepts and the ability to quantify different quantities. (“Compare and match”);

- Games with algorithms).

— Models of numerical and temporal relations (“Number ladder”, “Days of the week”).

— Calendar, calendar model.

Educational games

- games that develop mental processes: chess, checkers, backgammon, lotto-barrels, etc.

— game-aid “Hundred Counting” by N.A. Zaitseva, designer watch, scales;

- Nikitin’s games, Dienesh’s blocks, Cuisenaire’s sticks, Voskobovich’s games, etc. in accordance with age-related tasks, natural and “waste” material.