"The importance of mathematical development of preschool children." We form elementary mathematical concepts in preschoolers of different ages Mathematical exercises in kindergarten

Forms of control

Interim certification - test

Compiled by

Guzhenkova Natalya Valerievna, senior lecturer at the Department of Technologies of Psychological, Pedagogical and Special Education at OSU.

Accepted abbreviations

Preschool educational institution - preschool educational institution

ZUN - knowledge, skills, abilities

MMR - method of mathematical development

REMP - development of elementary mathematical concepts

TiMMR - theory and methodology of mathematical development

FEMP - formation of elementary mathematical concepts.

Topic No. 1 (4 hours of lecture, 2 hours of practical work, 2 hours of laboratory, 4 hours of practical work)

General issues in teaching mathematics to children with developmental disabilities.

Plan

1. Goals and objectives of mathematical development of preschoolers.

in preschool age.

4. Principles of teaching mathematics.

5. FEMP methods.

6. FEMP techniques.

7. FEMP means.

8. Forms of work on the mathematical development of preschoolers.

Goals and objectives of mathematical development of preschool children.

The mathematical development of preschoolers should be understood as shifts and changes in the cognitive activity of the individual that occur as a result of the formation of elementary mathematical concepts and related logical operations.

The formation of elementary mathematical concepts is a purposeful and organized process of transferring and assimilating knowledge, techniques and methods of mental activity (in the field of mathematics).

Objectives of the methodology of mathematical development as a scientific field

1. Scientific justification of program requirements for the level
formation of mathematical concepts in preschoolers in
every age group.

2. Determination of the content of mathematical material for
teaching children in preschool educational institutions.

3. Development and implementation of effective didactic tools, methods and various forms of organizing work on the mathematical development of children.

4. Implementation of continuity in the formation of mathematical concepts in preschool educational institutions and at school.

5. Development of content for the training of highly specialized personnel capable of carrying out work on the mathematical development of preschool children.

The goal of mathematical development of preschoolers

1. Comprehensive development of the child’s personality.

2. Preparing for success in school.

3. Correctional and educational work.

Tasks of mathematical development of preschool children

1. Formation of a system of elementary mathematical representations.

2. Formation of prerequisites for mathematical thinking.

3. Formation of sensory processes and abilities.

4. Expansion and enrichment of the dictionary and improvement
connected speech.

5. Formation of initial forms of educational activity.

Brief summary of the sections of the program on FEMP in preschool educational institutions

1. “Quantity and counting”: ideas about set, number, counting, arithmetic operations, word problems.

2. “Value”: ideas about various quantities, their comparisons and measurements (length, width, height, thickness, area, volume, mass, time).

3. “Form”: ideas about the shape of objects, geometric figures (flat and three-dimensional), their properties and relationships.

4. “Orientation in space”: orientation on one’s body, relative to oneself, relative to objects, relative to another person, orientation on a plane and in space, on a sheet of paper (blank and checkered), orientation in motion.

5. “Time orientation”: an idea of ​​the parts of the day, days of the week, months and seasons; development of a “sense of time”.

3. The importance and possibilities of children’s mathematical development
in preschool age.

The Importance of Teaching Children Math

Education leads development and is a source of development.

Education must come before development. It is necessary to focus not on what the child himself is already capable of doing, but on what he can do with the help and guidance of an adult. L. S. Vygodsky emphasized that we must focus on the “zone of proximal development.”

Orderly ideas, correctly formed first concepts, well-developed thinking abilities are the key to children’s further successful education at school.

Psychological research convinces us that during the learning process, qualitative changes occur in the mental development of the child.

From an early age, it is important not only to provide children with ready-made knowledge, but also to develop children’s mental abilities, teach them independently, consciously obtain knowledge and use it in life.

Learning in everyday life is episodic. For mathematical development, it is important that all knowledge is given systematically and consistently. Knowledge in the field of mathematics should become more complex gradually, taking into account the age and level of development of children.

It is important to organize the accumulation of a child’s experience, teach him to use standards (shapes, sizes, etc.), rational methods of action (counting, measuring, calculations, etc.).

Given the insignificant experience of children, learning proceeds primarily inductively: first, specific knowledge is accumulated with the help of an adult, then it is generalized into rules and patterns. It is also necessary to use the deductive method: first assimilation of the rule, then its application, specification and analysis.

To carry out competent training of preschoolers, their mathematical development, the teacher himself must know the subject of the science of mathematics, the psychological features of the development of children’s mathematical concepts and the methodology of work.

Opportunities for the comprehensive development of a child in the process of FEMP

I. Sensory development (sensation and perception)

The source of elementary mathematical concepts is the surrounding reality, which the child learns in the process of various activities, in communication with adults and under their teaching guidance.

The basis for young children’s cognition of qualitative and quantitative characteristics of objects and phenomena are sensory processes (eye movements tracing the shape and size of an object, feeling with hands, etc.). In the process of various perceptual and productive activities, children begin to form ideas about the world around them: about the various characteristics and properties of objects - color, shape, size, their spatial arrangement, quantity. Gradually, sensory experience accumulates, which is the sensory basis for mathematical development. When forming elementary mathematical concepts in a preschooler, we rely on various analyzers (tactile, visual, auditory, kinesthetic) and simultaneously develop them. The development of perception occurs through the improvement of perceptual actions (looking, feeling, listening, etc.) and the assimilation of systems of sensory standards developed by humanity (geometric figures, measures of quantities, etc.).

II. Development of thinking

Discussion

Name the types of thinking.

How does the work of a teacher on FEMP take into account the level
development of a child's thinking?

What logical operations do you know?

Give examples of mathematical tasks for each
logical operation.

Thinking is the process of consciously reflecting reality in ideas and judgments.

In the process of forming elementary mathematical concepts, children develop all types of thinking:

visually effective;

visual-figurative;

verbal-logical.

III. Development of memory, attention, imagination

Discussion

What does the concept of “memory” include?

Offer children a math task to develop memory.

How to activate children's attention when forming elementary mathematical concepts?

Formulate a task for children to develop their imagination using mathematical concepts.

Memory includes memorization (“Remember - this is a square”), recollection (“What is the name of this figure?”), reproduction (“Draw a circle!”), recognition (“Find and name familiar figures!”).

Attention does not act as an independent process. Its result is the improvement of all activities. To activate attention, the ability to set a task and motivate it is crucial. (“Katya has one apple. Masha came to her, she needs to divide the apple equally between the two girls. Watch carefully how I will do this!”).

Imaginative images are formed as a result of the mental construction of objects (“Imagine a figure with five corners”).

IV. Speech development
Discussion

How does a child’s speech develop in the process of forming elementary mathematical concepts?

What does mathematical development provide for the development of a child’s speech?

Mathematical classes have a huge positive impact on the development of a child’s speech:

vocabulary enrichment (numerals, spatial
prepositions and adverbs, mathematical terms characterizing shape, size, etc.);

agreement of words in the singular and plural (“one bunny, two bunnies, five bunnies”);

formulating answers in full sentences;

logical reasoning.

Formulating a thought in words leads to better understanding: by formulating a thought, a thought is formed.

V. Development of special skills and abilities

Discussion

- What special skills and abilities are formed in preschoolers in the process of forming mathematical concepts?

In mathematics classes, children develop special skills and abilities that they need in life and study: counting, calculation, measurement, etc.

VI. Development of cognitive interests

Discussion

What is the significance of a child’s cognitive interest in mathematics for his mathematical development?

What are the ways to stimulate cognitive interest in mathematics in preschool children?

How can you arouse cognitive interest in FEMP classes at a preschool educational institution?

The meaning of cognitive interest:

Activates perception and mental activity;

Broadens the mind;

Promotes mental development;

Increases the quality and depth of knowledge;

Promotes the successful application of knowledge in practice;

Encourages independent acquisition of new knowledge;

Changes the nature of the activity and the experiences associated with it (the activity becomes active, independent, versatile, creative, joyful, productive);

Has a positive impact on the formation of personality;

Has a positive effect on the child’s health (stimulates energy, increases vitality, makes life happier);

Ways to stimulate interest in mathematics:

· connection of new knowledge with childhood experience;

· discovery of new aspects in children’s previous experiences;

· gaming activity;

· verbal stimulation;

· stimulation.

Psychological prerequisites for interest in mathematics:

Creating a positive emotional attitude towards the teacher;

Creating a positive attitude towards classes.

Ways to stimulate cognitive interest in FEMP classes:

§ explanation of the meaning of the work being performed (“The doll has nowhere to sleep. Let’s build a bed for her! What size should it be? Let’s measure it!”);

§ working with your favorite attractive objects (toys, fairy tales, pictures, etc.);

§ connection with a situation close to the children (“Misha’s birthday. When is your birthday, who comes to you?
Guests also came to Misha. How many cups should be put on the table for the holiday?");

§ activities that are interesting for children (games, drawing, design, appliqué, etc.);

§ feasible tasks and help in overcoming difficulties (the child should experience satisfaction from overcoming difficulties at the end of each lesson), a positive attitude towards children’s activities (interest, attention to each child’s answer, goodwill); encouraging initiative, etc.

FEMP methods.

Methods of organizing and implementing educational and cognitive activities

1. Perceptual aspect (methods that ensure the transmission of educational information by the teacher and the perception of it by children through listening, observation, and practical actions):

a) verbal (explanation, conversation, instructions, questions, etc.);

b) visual (demonstration, illustration, examination, etc.);

c) practical (subject-related practical and mental activities, didactic games and exercises, etc.).

2. Gnostic aspect (methods characterizing the assimilation of new material by children - through active memorization, through independent reflection or a problem situation):

a) illustrative and explanatory;

b) problematic;

c) heuristic;

d) research, etc.

3. Logical aspect (methods characterizing mental operations when presenting and mastering educational material):

a) inductive (from particular to general);

b) deductive (from general to specific).

4. Managerial aspect (methods characterizing the degree of independence of children’s educational and cognitive activity):

a) work under the guidance of a teacher,

b) independent work of children.

Features of the practical method:

ü performing a variety of subject-specific, practical and mental actions;

ü wide use of didactic material;

ü the emergence of mathematical concepts as a result of action with didactic material;

ü development of special mathematical skills (counting, measurement, calculations, etc.);

ü use of mathematical concepts in everyday life, play, work, etc.

Types of visual material:

Demonstration and distribution;

Plot and non-plot;

Volumetric and planar;

Special counting (counting sticks, abacus, abacus, etc.);

Factory and homemade.

Methodological requirements for the use of visual material:

· it is better to start a new program task with voluminous plot material;

· as you master the educational material, move on to plot-flat and plotless visualization;

· one program task is explained using a wide variety of visual material;

It is better to show new visual material to children in advance...

Requirements for homemade visual material:

Hygienic (paints are covered with varnish or film, velvet paper is used only for demonstration material);

Aesthetics;

Reality;

Diversity;

Uniformity;

Strength;

Logical connection (hare - carrot, squirrel - pine cone, etc.);

Sufficient quantity...

Features of the verbal method

All work is based on the dialogue between teacher and child.

Requirements for the teacher's speech:

Emotional;

Competent;

Available;

Quite loud;

Friendly;

In younger groups, the tone is mysterious, fabulous, mysterious, the pace is slow, multiple repetitions;

In older groups, the tone is interesting, with the use of problem situations, the pace is quite fast, approaching the teaching of a lesson at school...

Requirements for children's speech:

Competent;

Understandable (if the child has poor pronunciation, the teacher pronounces the answer and asks to repeat it); full sentences;

With the necessary mathematical terms;

Quite loud...

FEMP techniques

1. Demonstration (usually used when communicating new knowledge).

2. Instructions (used in preparation for independent work).

3. Explanation, indication, clarification (used to prevent, identify and eliminate errors).

4. Questions for children.

5. Verbal reports of children.

6. Subject-based practical and mental actions.

7. Control and evaluation.

Requirements for teacher questions:

accuracy, specificity, laconicism;

logical sequence;

variety of wording;

small but sufficient amount;

avoid prompting questions;

skillfully use additional questions;

Give children time to think...

Requirements for children's answers:

short or complete depending on the nature of the question;

to the question posed;

independent and conscious;

precise, clear;

quite loud;

grammatically correct...

What to do if your child answers incorrectly?

(In younger groups, you need to correct, ask to repeat the correct answer and praise. In older groups, you can make a remark, call another and praise the one who answered correctly.)

FEMP means

Equipment for games and activities (typesetting cloth, counting ladder, flannelgraph, magnetic board, writing board, TCO, etc.).

Sets of didactic visual material (toys, construction sets, building materials, demonstration and handout materials, “Learn to count” sets, etc.).

Literature (methodological manuals for educators, collections of games and exercises, books for children, workbooks, etc.)...

8. Forms of work on the mathematical development of preschool children

Assignment for independent work of students

Laboratory work No. 1: “Analysis of the “Program of education and training in kindergarten” of the section “Formation of elementary mathematical concepts.”

Topic No. 2 (2 hours of lecture, 2 hours of practical work, 2 hours of laboratory, 2 hours of practical work)

PLAN

1. Organization of mathematics classes in a preschool institution.

2. Approximate structure of mathematics classes.

3. Methodological requirements for a lesson in mathematics.

4. Ways to maintain good performance of children in the classroom.

5. Formation of skills in working with handouts.

6. Formation of skills in educational activities.

7. The meaning and place of didactic games in the mathematical development of preschool children.

1. Organizing a math lesson in a preschool institution

Classes are the main form of organizing children's mathematics education in kindergarten.

The lesson begins not at their desks, but with the gathering of children around the teacher, who checks their appearance, attracts attention, and seats them taking into account individual characteristics, taking into account developmental problems (vision, hearing, etc.).

In younger groups: a subgroup of children can, for example, sit on chairs in a semicircle in front of the teacher.

In older groups: a group of children usually sits at desks in twos, facing the teacher, as they work with handouts and develop learning skills.

The organization depends on the content of the work, the age and individual characteristics of the children. The lesson can begin and be carried out in a playroom, in a sports or music hall, on the street, etc., standing, sitting and even lying on the carpet.

The beginning of the lesson should be emotional, interesting, and joyful.

In younger groups: surprise moments and fairy-tale plots are used.

In older groups: it is advisable to use problem situations.

In preparatory groups, the work of those on duty is organized, and what they did in the last lesson (in order to prepare for school) is discussed.

Approximate structure of mathematics lessons.

Organization of the lesson.

Progress of the lesson.

Summary of the lesson.

2. Progress of the lesson

Sample parts of a math lesson

Mathematical warm-up (usually from the older group).

Working with demo material.

Working with handouts.

Physical education lesson (usually from the middle group).

Didactic game.

The number of parts and their order depend on the age of the children and the tasks assigned.

In the younger group: at the beginning of the year there can be only one part - a didactic game; in the second half of the year - up to three hours (usually working with demonstration material, working with handouts, outdoor didactic games).

In the middle group: usually four parts (regular work with handouts begins, after which physical education is required).

In the senior group: up to five parts.

In the preparatory group: up to seven parts.

Children's attention is maintained: 3-4 minutes for younger preschoolers, 5-7 minutes for older preschoolers - this is the approximate duration of one part.

Types of physical education minutes:

1. Poetic form (it is better for children not to pronounce, but to breathe correctly) - usually carried out in the 2nd junior and middle groups.

2. A set of physical exercises for the muscles of the arms, legs, back, etc. (best performed with music) - it is advisable to carry out in the older group.

3. With mathematical content (used if the lesson does not carry a large mental load) - more often used in the preparatory group.

4. Special gymnastics (finger, articulation, for the eyes, etc.) - regularly performed with children with developmental problems.

Comment:

if the activity is active, physical education may not be carried out;

Instead of physical education, you can do relaxation.

3. Summary of the lesson

Any lesson must be completed.

In the younger group: the teacher summarizes after each part of the lesson. (“We played so well. Let’s collect our toys and get dressed for a walk.”)

In the middle and senior groups: at the end of the lesson, the teacher himself sums up the lesson, introducing the children. (“What did we learn new today? What did we talk about? What did we play?”). In the preparatory group: children draw their own conclusions. (“What did we do today?”) The work of the duty officers is organized.

It is necessary to evaluate the children's work (including individual praise or reprimand).

3. Methodological requirements for a mathematics lesson(depending on the principles of training)

2. Educational tasks are taken from different sections of the program for the formation of elementary mathematical concepts and combined in interconnection.

3. New tasks are presented in small portions and are specified for a given lesson.

4. In one lesson, it is advisable to solve no more than one new problem, the rest for repetition and consolidation.

5. Knowledge is given systematically and consistently in an accessible form.

6. A variety of visual material is used.

7. The connection between the acquired knowledge and life is demonstrated.

8. Individual work is carried out with children, a differentiated approach to the selection of tasks is carried out.

9. The level of learning by children is regularly monitored, gaps in their knowledge are identified and they are eliminated.

10. All work has a developmental, correctional and educational orientation.

11. Mathematics classes are held in the first half of the day in the middle of the week.

12. It is better to combine mathematics classes with classes that do not require much mental stress (physical education, music, drawing).

13. Combined and integrated classes can be conducted using different methods if the tasks are combined.

14. Each child must actively participate in every lesson, perform mental and practical actions, and reflect their knowledge in speech.

PLAN

1. Stages of formation and content of quantitative ideas.

2. The importance of the development of quantitative concepts in preschoolers.

3. Physiological and psychological mechanisms of quantity perception.

4. Features of the development of quantitative concepts in children and methodological recommendations for their formation in preschool educational institutions.

1. Stages of formation and content of quantitative ideas.

Stages formation of quantitative ideas

(“Stages of counting activity” according to A.M. Leushina)

1. Pre-number activities.

2. Counting activities.

3. Computing activities.

1. Pre-numerical activity

For correct perception of numbers, for the successful formation of counting activities, it is necessary, first of all, to teach children to work with sets:

See and name the essential features of objects;

See the multitude as a whole;

Select elements of a set;

Name a set (“generalizing word”) and list its elements (define a set in two ways: indicating a characteristic property of the set and listing
all elements of the set);

Compose a set from individual elements and from subsets;

Divide a set into classes;

Arrange the elements of a set;

Compare sets by quantity through one-to-one correlation (establishing one-to-one correspondences);

Create equal sets;

Unite and separate sets (the concept of “whole and part”).

2. Accounting activities

Account ownership includes:

Knowledge of numeral words and naming them in order;

The ability to relate numerals to the elements of a set “one to one” (to establish a one-to-one correspondence between the elements of the set and a segment of the natural series);

Highlighting the total number.

Mastery of the concept of number includes:

Understanding the independence of the result of a quantitative count from its direction, the location of the elements of the set and their qualitative characteristics (size, shape, color, etc.);

Understanding the quantitative and ordinal meaning of a number;

The idea of ​​the natural number series and its properties includes:

Knowledge of the sequence of numbers (counting forward and backward, naming the previous and subsequent numbers);

Knowledge of the formation of adjacent numbers from each other (by adding and subtracting one);

Knowledge of connections between neighboring numbers (more, less).

3. Computing activities

Computing activities include:

· knowledge of connections between neighboring numbers (“more (less) by 1”);

· knowledge of the formation of neighboring numbers (n ± 1);

· knowledge of the composition of numbers from units;

· knowledge of the composition of numbers from two smaller numbers (addition table and corresponding cases of subtraction);

knowledge of numbers and signs +, -, =,<, >;

· Ability to compose and solve arithmetic problems.

To prepare for mastering the decimal number system you need to:

o mastery of oral and written numbering (naming and recording);

o mastery of arithmetic operations of addition and subtraction (naming, calculation and recording);

o mastery of counting in groups (pairs, triplets, heels, tens, etc.).

Comment. A preschooler needs to master this knowledge and skills qualitatively within the first ten. Only after fully mastering this material can you begin to work with the second ten (it is better to do this at school).

ABOUT VALUES AND THEIR MEASUREMENT

PLAN

2. The importance of developing ideas about quantities in preschoolers.

3. Physiological and psychological mechanisms of perception of the size of objects.

4. Features of the development of ideas about quantities in children and methodological recommendations for their formation in preschool educational institutions.

Preschoolers become familiar with various quantities: length, width, height, thickness, depth, area, volume, mass, time, temperature.

The initial idea of ​​size is associated with the creation of a sensory basis, the formation of ideas about the size of objects: show and name length, width, height.

BASIC properties of the quantity:

Comparability

Relativity

Measurability

Variability

Determining a value is possible only on the basis of comparison (directly or by comparing it with a certain image). The characteristic of the quantity is relative and depends on the objects chosen for comparison (A< В, но А >WITH).

Measurement makes it possible to characterize a quantity with a number and move from directly comparing quantities to comparing numbers, which is more convenient because it is done in the mind. Measurement is a comparison of a quantity with a quantity of the same kind taken as a unit. The purpose of measurement is to give a numerical characteristic of a quantity. The variability of quantities is characterized by the fact that they can be added, subtracted, and multiplied by a number.

All these properties can be comprehended by preschoolers in the process of their actions with objects, the selection and comparison of quantities, and measuring activities.

The concept of number arises in the process of counting and measuring. Measuring activities expand and deepen children's ideas about number, already developed in the process of counting activities.

In the 60-70s of the XX century. (P. Ya. Galperin, V. V. Davydov) the idea arose about measuring practice as the basis for the formation of the concept of number in a child. There are currently two concepts:

Formation of measuring activities based on knowledge of numbers and counting;

Formation of the concept of number on the basis of measuring activities.

Counting and measurement should not be opposed to each other, they complement each other in the process of mastering number as an abstract mathematical concept.

In kindergarten, we first teach children to identify and name different size parameters (length, width, height) based on eye comparison of sharply contrasting objects in size. Then we develop the ability to compare, using the method of application and superposition, objects that are slightly different and equal in size with a clearly expressed one value, then according to several parameters simultaneously. Work on laying out serial rows and special exercises for developing the eye strengthen ideas about quantities. Familiarity with a conventional measure, equal in size to one of the objects being compared, prepares children for measuring activities.

The measurement activity is quite complex. It requires certain knowledge, specific skills, knowledge of the generally accepted system of measures, and the use of measuring instruments. Measuring activities can be developed in preschoolers under the condition of targeted guidance from adults and a lot of practical work.

Measuring circuit

Before introducing generally accepted standards (centimeter, meter, liter, kilogram, etc.), it is advisable to first teach children to use conventional standards when measuring:

Length (length, width, height) using strips, sticks, ropes, steps;

Volume of liquid and bulk substances (amount of cereals, sand, water, etc.) using glasses, spoons, cans;

Squares (figures, sheets of paper, etc.) in cells or squares;

Masses of objects (for example: apple - acorns).

The use of conventional measures makes measurement accessible to preschoolers, simplifies the activity, but does not change its essence. The essence of measurement is the same in all cases (although the objects and means are different). Usually, training begins with measuring length, which is more familiar to children and will be useful in school first of all.

After this work, you can introduce preschoolers to standards and some measuring instruments (ruler, scales).

In the process of developing measurement activities, preschoolers are able to understand that:

o measurement gives an accurate quantitative description of the quantity;

o for measurement it is necessary to choose an adequate measure;

o the number of measurements depends on the quantity being measured (the more
quantity, the greater its numerical value and vice versa);

o the measurement result depends on the selected measure (the larger the measure, the smaller the numerical value and vice versa);

o to compare quantities it is necessary to measure them with the same standards.

Measurement makes it possible to compare quantities not only on a sensory basis, but also on the basis of mental activity, and forms the idea of ​​a quantity as a mathematical

Tasks and content of logical and mathematical development of preschool children. Tools for the logical and mathematical development of preschool children (educational 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 developmental 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 preschool children.”

Logical and mathematical development of preschool children - these are shifts and changes in the child’s cognitive activity that occur as a result of the formation of elementary mathematical concepts and related logical operations.

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 preschool children:

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

* observation, cognitive interests;

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

* ability to compare, classify, generalize;

* forecasting changes in activities and results;

* clear and precise expression of thoughts;

* carrying out an 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), play and others.

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

* inclusion of the child in active process to identify the properties of objects through examination, comparison, and effective practical action;

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

* use of simulation.

The ability to visually model is 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 identifying common features in objects - mass, length, width, height ( Galperin, Leushina, Davydov, etc.). This activity ensures the development of relations of equality and inequality through comparison. Children master practical ways of identifying relationships in magnitude, for which numbers are not required. Numbers are mastered following exercises when comparing quantities by measurement.

IV position– is based on the idea of ​​the formation and development of a certain style of thinking in the process of children mastering properties and relationships (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 process of working 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 for logical and mathematical development of children.

Variable technologies for logical and mathematical development of preschool children

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

Orientation in modern programs for the development and education of children in kindergarten, studying them provides the basis for choosing a methodology. Modern programs (“Development”, “Rainbow”, “Childhood”, “Origins”, etc.), as a rule, include 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, personality-oriented developmental technologies and exclude “discrete” learning, i.e., separate formation of knowledge and skills with subsequent consolidation (V. Okon).

The following is characteristic of modern programs for the mathematical development of children.

■ The focus of the mathematical content mastered by children on their development cognitive and creative abilities and in the aspect of familiarization with human culture. Children master a variety of geometric shapes, quantitative, spatio-temporal relationships of objects in the world around them in interconnection. They master the methods of independent cognition: comparison, measurement, transformation, counting, etc. This creates the conditions for their socialization and 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 developmental and play situations), and in independent and joint activities with adults (in games, experimentation, game training, exercises in workbooks, educational -game books, etc.).

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

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

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

■ Design and construction of the process of development of mathematical concepts is carried out on a diagnostic basis.

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

The property of the child’s subjective experience becomes orientation in the properties and relationships of objects, dependencies; the ability to perceive the same phenomenon or action from different positions. The child's cognitive development becomes more advanced.

Tasks and content of logical and mathematical development of preschool children

Tasks:

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

2. Children’s mastery of mathematical ways of understanding reality: counting, measurement, simple calculations.

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

4. An idea of ​​the mathematical properties and relationships of objects, specific quantities, numbers, geometric figures, dependencies and patterns.

5. Children's mastery of experimental and research methods of learning mathematical content (recreation, experimentation, modeling, transformation).

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

7. Development of intellectual and creative manifestations of children: resourcefulness, ingenuity, guesswork, ingenuity, etc.

The first and most important component content of 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, and 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 by the number of angles, sides and vertices. Children develop constructive abilities and spatial thinking. They master the ability to mentally rotate an object, look at it from different sides, dismember, assemble, modify it.

3) In knowledge quantities children move from direct methods (overlay, application) to indirect methods of comparing them (using measurement with a conventional yardstick). This makes it possible to organize objects according to their properties (size, height, length, thickness, weight)

4) Spatiotemporal representations – the most difficult thing for a preschool child, they are mastered through realistically presented relationships (far and near, today and tomorrow).

5) Cognition of numbers and mastering operations with numbers – the most important component of the content of mathematical development. Quantities and magnitudes are expressed through numbers. By counting objects of different sizes and spatial locations, children come to understand the independence of numbers from other properties of objects and become familiar with numbers and signs.

Tools for the logical and mathematical development of preschool children (educational and didactic games, universal aids, problem situations, experimentation, logical tasks).

Logical and mathematical games.

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

desktop-printed:“Color and shape”, “Count”, “Game square”, “Transparent square”, “Logic train”, etc.

volumetric 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”, “Colored panel”, “Multi-colored squares”, “Triangular domino”, “So that the color does not repeat”, etc.

games for composing a whole from parts:“Fractions”, “Fold the square”, “Greek cross”, “Fold the ring”, “Chessboard”, etc.

fun games: labyrinths, permutations (“Tower of Hanoi”, “Tea Set”, “Goats and Rams”, “Stubborn Donkey”);

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

Problem situations.

This is a means of mastering search actions, the ability to formulate one’s own thoughts about search methods and the expected result, and 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 sawed off? How many months of the year contain 30 days?),

entertaining problems (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 football teams “Spartak” and “Dynamo” before the start of the match, and won the bet. What was the score?),

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

First, the adult poses a problem to the children, seeks to understand it, and directs the children’s attention to the need to solve it. Then comes the formulation of hypotheses and their practical testing, collective discussion of the situation and ways to solve it. For example: “There are three pencils of different lengths on the table. How to remove the longest pencil from the middle without touching it?”, “How to use one stick to lay out a triangle on the table?”

Logical and mathematical story games (activities).

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, and schematization. This set of games was proposed by E.A. Nosova based on Dienesh blocks: Mice are noobs. Winter supplies. Highway. Growing a tree. Where is whose garage? Teach Dunno. Riddles without words. Translators. Build a chain. Two tracks. Who's guest is Winnie the Pooh and Piglet? Factory. Architects. Help the figures get out of the forest. Let's set up a window display. Build a house. Separate the blocks - 1. blocks - 2. Help the toy. Divide the blocks - 3. Gifts for the three little pigs. And etc.

Experimentation and research activities.

This activity is aimed at searching and acquiring new information. It is not set by adults, but is built by the preschooler himself as he receives new information about the object. It is characterized by emotional richness and 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, combining and rearranging them.

In the course of experimentation and research, children master the actions of measuring, transforming materials and substances, become familiar with instruments, and learn to use educational books as a source of information.

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

Technologies for logical and mathematical development of preschool children.

The essence of the technology is the creation by adults of situations in which the child strives for active activity and gets a positive creative result.

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

Third year of life

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

The didactic games used are built primarily on the principle of inserts. The materials must be large enough and durable; “vividly” imagine differences in size, size, shape. Elements of games must be durable, 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 learning properties, mastering certain standards, and operating with objects. This period refers to the stage of “sensorimotor” standards. Children identify certain properties of objects (shape, size, color) and designate them by the name of objects they know well (a square is “like a window”, a triangle is “like a carrot”). Children are just learning to distinguish the properties of objects and to designate them with words. At this age, the practical tactile-motor method of cognition of objects predominates: preschoolers need to feel the object, touch it; they often carry out actions of a manipulative nature. This way of understanding an object forms the establishment of an eye-hand relationship. To develop ideas about properties, it is necessary to include in the toy library the set “Dyenesh’s Logic Blocks” and teaching aids for it.

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

To develop the perception of sets, children 2-3 years old use toys, objects, “life” and abstract materials. To facilitate the identification of elements of the set, these materials are located in the children’s “field of perception” (on a tray, box lid). At this age, the “Colored Stripes” set is used - an analogue of the “Cuisenaire Colored Sticks”. Games such as paired pictures and lotto (botanical, zoological, lotto transport, furniture, dishes) are recommended. These game materials generate interest in recounting.

You also need cut-out pictures of 4-8 parts, large puzzles of 4-9 parts. Folding cubes (when parts can be used to assemble an object picture) are of great interest in independent games for children. It is advisable to include in the toy library the games “Fold a pattern” of 9 cubes, “Fold a square”, various insert games, pyramids of 6-8 rings (children 2.5-3 years old - of 8-10 (12) rings ) and figured pyramids. Insert games, games “Rainbow Basket”, “Miracle Crosses”, “Miracle Honeycombs”, “Insert Cups”, “Multi-Colored Columns”, etc., and boxes with figured slots for sorting are actively used.

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

5-, 7-seater toys.

The kids are excited to play with geometric mosaics. You can use tabletop, floor, large magnetic mosaics, and a variety of soft construction sets.

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

Teachers should remember that children’s interest in the same material quickly decreases. Therefore, it is not advisable to keep all available games and gaming materials in the group room. It is better to replace some materials with others from time to time. It is advisable to use industrially manufactured games, manuals and materials.

Fourth year of life

It is necessary to take into account that children come to modern kindergarten with different experiences in mastering mathematical concepts. The process of children's mathematical development should not be intensified. However, when selecting material, it is important to take into account the different levels of development of preschoolers.

Objects in the immediate environment are a source of curiosity for a small child and the first stage of knowledge of 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 a group reflect the richness and diversity of properties and stimulate interest and activity. It is important to remember that the child sees a lot for the first time and perceives what he observes as a model, a kind of standard with which he will compare everything he sees later.

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

In groups of children of primary preschool age, the main attention is paid to mastering the technique of direct comparison of quantities, objects by quantity, properties. Among didactic games, games like lotto and paired pictures are preferred. There should also be a mosaic (plastic, magnetic and large nail), a puzzle of 5-15 pieces, sets of cubes of 4-12 pieces, educational games (for example, “Fold a pattern”, “Fold a square”, “Corners”), and also games with elements of modeling and substitution. A variety of “soft construction sets” on a carpet base allow you to play the game in different ways: sitting at a table, standing against a wall, lying on the floor.

Children of this age are actively mastering standards of shape and color, which is why this period is called the stage of “subject standards.” As a rule, children identify 3-4 shapes, but find it difficult to abstract shape and 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 and elements; they do not see the difference in size if the stripes (objects) differ slightly; undifferentiatedly perceive a large number of elements of sets (“many”).

To successfully distinguish properties, children need practical examination, “manipulation” with an object (holding a figure in their hands, clapping, feeling, pressing, etc.). The accuracy of distinguishing properties depends directly on the degree of examination of the object. Preschoolers can successfully carry out simple actions: grouping abstract shapes, sorting according to a given characteristic, arranging 3-4 elements according to the most clearly represented property. It is recommended to use abstract materials that facilitate the process of comparison with the standard and abstraction of properties. Children are especially interested in the so-called “universal” sets - Dienesh's logical blocks and Cuisenaire's colored counting sticks. The manuals are interesting because they present several properties at the same time (color, shape, size, thickness in blocks; color, length in sticks); The set contains many elements, which encourages manipulation and play with them. 1-2 sets are enough for a group.

To develop fine motor skills, you need to include plastic containers with lids of different shapes and sizes, boxes, and other household items that have gone out of use. By trying on lids to 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 assigned to the child by an adult in advance in the form of one scheme or another, but is built by the preschooler himself as he receives more and more 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 (shape, color, dimensional manifestations) by 4-5 year old children. Children successfully abstract meaningful properties of objects.

The child's developing thinking, the ability to establish simple connections and relationships between objects awaken interest in the world around him. The child already has some experience of knowing the environment and requires generalization, systematization, deepening, and clarification. For this purpose, the group organizes a “sensory center” - a place where objects and materials are selected that can be perceived using various senses. For example, musical instruments and noisy objects can be heard; books, pictures, kaleidoscopes can be seen; jars with scented substances, perfume bottles can be identified by their smell.

Materials and aids are used that make it possible to organize a variety of practical activities for children: count, correlate, group, organize. For this purpose, various sets of objects are widely used (abstract: geometric shapes; “life”: cones, shells, toys, etc.). The main requirement for such sets will be their sufficiency and variability in the 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 should be quite diverse and constantly change (about once every 2 months). About 15% of games should be intended for children in the older age group to enable children who are ahead of their peers in development to not stop, but to move forward.

In middle preschool age, children actively master the means and methods of cognition. In the process of comparing objects, preschoolers more differentiated the manifestations of properties, not only established their “polarity,” but also compared them according to the degree of manifestation.

Games are needed to compare objects based on various properties (color, shape, size, material, function); grouping by properties; recreating a whole from parts (such as “Tangram”, a puzzle of 12-24 parts); seriation according to different properties; games for mastering counting. 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 to highlight properties (“Treasures”, “Dominoes”), grouping according to given properties (games with one and two hoops). When using colored Cuisenaire counting sticks, attention is paid to distinguishing by color and size and to establishing the relationship color - length - number. To stimulate 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 story-based didactic games and practical situations with scales, balances, and a stadiometer.

The mathematical toy library can contain various versions of books and workbooks for reviewing and completing assignments. To enhance children's activity with such materials, you can use sheets with tasks (pictures for completing drawings, labyrinths), which are also placed in the mathematics corner.

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 group environment, iconic symbolism and models are actively used to designate objects, actions, and sequences. It is better to come up with such signs and models together with children, leading them to understand that they can be denoted not only with words, but also graphically. For example, work with your children to determine the sequence of activities throughout the day in kindergarten and figure out how to label each activity. In order for the child to better remember his address, street, city, place a diagram in the group on which you indicate the kindergarten, streets and houses in which the children of the group live. Draw the routes that children take to kindergarten, write the names of the streets, place other buildings that are in the area, designate a children's clinic, a stationery store, "Children's World". Refer to this diagram more often, find out for which of the children the path to kindergarten is longer or 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 of the doll's room space. The main requirement is the subject-schematic form of these models.

Sixth year of life

In older preschool age, it is important to develop any manifestations of independence, self-organization, self-esteem, self-control, self-knowledge, and 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 group environment, into which content is introduced that expands the child’s personal experience.

In the group, a special place and equipment is allocated for the toy library. It contains gaming materials that promote the speech, cognitive and mathematical development of children. These are didactic, educational 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 a diagram, model; to carry out control and verification actions (“Does this happen?”, “Find the artist’s mistakes”); for following and alternating, etc.

For example, for the development of logic, games with logical blocks of Dienesh, other games: “Logic Train”, “Logic House”, “Odd Four”, “Search for the Ninth”, “Find the Differences” are suitable. Printed notebooks and educational books for preschoolers are required. Games for the development of counting and computational skills, also aimed at developing mental processes, especially attention, memory, and thinking, are useful.

To organize children's activities, a variety of educational games, didactic aids, and materials are used to “train” children in establishing relationships and dependencies. The relationship between play and cognitive motives at a given age determines that the process of cognition will be most successful in situations that require intelligence, cognitive activity, and independence of children. The materials and manuals used must contain an element of “surprise”, “problematic”. When creating them, the existing experience of children should be taken into account; they should allow organizing various options for activities and games.

Manual "Columbus Egg"

Traditionally, a variety of educational games are used (for planar and three-dimensional modeling), in which children not only lay out pictures and designs based on samples, but also independently invent and create silhouettes. The older group presents different versions of recreation 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 forming and the composition of numbers, comparing numbers, laying out Cuisenaire sticks, and drawing a “House of Numbers” model.

To gain experience in operating with sets, logical blocks and Cuisenaire rods are used. As a rule, several sets of data aids are sufficient for a group. It is possible to use special visual aids that allow one to master the ability to identify significant properties (“Search for a reserved treasure”, “On the golden porch”, “Let’s play together”, etc.).

The variability of measuring instruments (different types of watches, calendars, rulers, etc.) activates the search for what is common and different, which contributes to the generalization of ideas about measures and methods of measurement. These benefits are used in children’s independent and joint activities with adults. Materials and substances must be present in sufficient quantities; be aesthetically presented (stored, if possible, in identical transparent boxes or containers in a permanent place); allow you to experiment with them (measure, weigh, pour, 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).

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

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

For individual work with children, clarifying and expanding their mathematical concepts, didactic aids and games are used: “Airplanes”, “Dancing Men”, “City Building”, “Little Designer”, “Domino Number”, “Transparent Number”, etc. These games should be presented in sufficient quantities and, as children’s interest in them declines, 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 them understand the world, for example 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 in kindergarten for older preschoolers for experiments using technical means.

In older preschool age, children show interest in crossword puzzles and cognitive tasks. For this purpose, you can lay out grids of crossword puzzles on the carpet using thin long tapes and attach sheets of paper with pictures or texts of tasks.

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

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

The development of arbitrariness and planning makes it possible to more widely use games with rules - checkers, chess, backgammon, etc.

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

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

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

The basis for the interpretation of the concept of “mathematical development” of preschool children was also laid in the works of L.A. Wenger. and today it is the most common in the theory and practice of teaching mathematics to preschoolers. “The purpose of teaching in kindergarten classes is for the child to master a certain range of knowledge and skills specified by the program. The development of mental abilities is achieved indirectly: in the process of acquiring knowledge. This is precisely the meaning of the widespread concept of “developmental education”. The developmental effect of training depends on what knowledge is imparted to children and what teaching methods are used.”

From the research of E.I. Shcherbakova, the mathematical development of preschool children should be understood as shifts and changes in the cognitive activity of the individual that occur as a result of the formation of elementary mathematical concepts and related logical operations. In other words, the mathematical development of preschool children is qualitative changes in the forms of their cognitive activity that occur as a result of children mastering elementary mathematical concepts and related logical operations.

Having separated from preschool pedagogy, the method of forming elementary mathematical concepts has become an independent scientific and educational field. The subject of her research is the study of the basic patterns of the process of formation of elementary mathematical concepts in preschool children in the conditions of public education. The range of problems of mathematical development solved by the methodology is quite extensive:

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

Determining the content of the material to prepare a child in kindergarten for mastering mathematics at school;

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

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

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

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

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

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

Elena Chupina
Features of mathematical development of children in preschool education

Mathematical development of children preschool age still remains one of the pressing problems of preschool education. In accordance with the Federal State Educational Standard for preschool education, this area of ​​work is carried out within the framework of solving problems in the educational field "cognitive development» . The formation of preschool age should be carried out in different types of children's activities and is associated with knowledge of surrounding objects. The learning process itself should contribute not only acquisition and consolidation mathematical representations, but also development mental operations (analysis, synthesis, generalization, grouping, seriation, etc., fine motor skills.

In accordance with the Federal State Educational Standard within the educational field Cognitive development involves developing children's interests, curiosity and cognitive motivation; formation of cognitive actions, formation of consciousness; development imagination and creativity; the formation of primary ideas about oneself, other people, objects in the surrounding world, about the properties and relationships of objects in the surrounding world (shape, color, size, material, sound, rhythm, tempo, quantity, number, part and whole, space and time, movement and rest, causes and effects, etc., about the small homeland and the Fatherland, ideas about the socio-cultural values ​​of our people, about domestic traditions and holidays, about planet Earth as the common home of people, about features of its nature, the diversity of countries and peoples of the world.

In the process of forming elementary mathematical ideas in preschoolers, the teacher uses a variety of teaching and mental methods education: practical, visual, verbal, game.

Tab. 2 FEMP methods.

Types of methods Description

Visual methods: demonstration, illustration, examination, etc.

Practical methods: objective-practical and mental activities, didactic games and exercises, etc.

Verbal methods: explanation, conversation, instructions, questions, etc.

Game methods Didactic games, word games, games with objects and board-printed games.

Tab. 3 Methods of organizing and implementing educational and cognitive activities

Peculiarities practical method

Performing a variety of subject-specific, practical and mental actions;

widespread use of didactic material;

emergence mathematical ideas as a result of action with didactic material;

development of special math skills(accounts, measurements, calculations, etc.);

usage mathematical representations in everyday life, play, work, etc.

Features of the visual method

Types of visual material:

demonstration and distribution;

plot and plotless;

volumetric and planar;

special-counting (counting sticks, abacus, abacus, etc.); factory and homemade.

Methodological requirements for the use of visual aids material:

It is better to start a new software task with a plot-oriented material;

as you master the educational material move to plot-flat and plotless visualization;

one software task is explained in a wide variety of visual terms material;

new visual material It is better to show the children in advance.

Features of the verbal method

All work is based on the dialogue between teacher and child.

Requirements for teacher speech:

emotional; literate; accessible; clear;

quite loud; friendly;

in younger groups the tone is mysterious, fabulous, mysterious, the pace is slow, multiple repetitions;

in older groups the tone is interesting, with the use of problem situations, the pace is quite fast, approaching the teaching of a lesson at school...

Peculiarities game method Games use specific didactic material, selected according to certain characteristics. Modeling mathematical concepts, it allows you to perform logical operations.

Classes on mathematics are carried out in a playful way that is understandable and interesting for children. With each lesson, children become more and more involved in the learning process, but at the same time the lessons remain a game, maintaining their attractiveness. In addition to training and development, mathematics for preschoolers allows the child to more easily adapt to classes at school, and parents will not have to worry when he goes to first grade. Mathematics for preschoolers will allow you to fully reveal the child’s potential and develop mathematical abilities. The presence of game characters in class encourages children to mathematical activities, overcoming intellectual difficulties.

Tab. 4 Types of children's activities in accordance with the Federal State Educational Standard for preschool education formation mathematical concepts in children preschool age.

Activities Types of activities

Play activity is a form of child activity aimed not at the result, but at the process of action and ways implementation and characterized by the child’s acceptance of conditional (unlike his real life) positions - games with construction material(with specially created material: floor and tabletop construction material, construction kits, constructors, etc.; with natural material; with junk material)

Games with rules:

- didactic in content: mathematical, according to didactic material: games with objects, board-printed.

-developing;

Computer (based on the plots of works of fiction; strategies; educational)

Cognitive and research activity is a form of child activity aimed at learning the properties and connections of objects and phenomena, mastering ways of knowing, promoting formation of a holistic picture of the world Experimentation, research; modeling:

Substitution;

Drawing up models;

Activities using models; -by the nature of the models (objective, symbolic, mental)

Productive activity

Construction from various materials- a form of child activity that develops he has spatial thinking, forms ability foresee the future result, makes it possible to creativity development, enriches speech Construction:

From construction materials;

From boxes, reels and other junk material;

From natural material.

Artistic work:

Application;

Paper construction

Rice. 1 Forms of training FEMP.

No. Form of training Organization of training

1. Custom shape. The organization of training allows you to individualize training (content, methods, means, but it requires a lot of nervous effort from the child;

creates emotional discomfort; uneconomical training;

limiting cooperation with other children.

2. Group form. (Individual-collective).

The group is divided into subgroups. Reasons for configuration: personal sympathy, common interests, but not by level development. At the same time, it is first of all important for the teacher to ensure interaction children in the learning process.

3. Frontal shape. Work with the whole group, clear schedule, uniform content. At the same time, the content of training in frontal classes can be activities of an artistic nature. The advantages of the form are a clear organizational structure, simple management, and the ability to interact children, cost-effectiveness of training; The disadvantage is the difficulty in individualizing training.

Tab. 5 Forms and organization of training mathematical development of children preschool age.

Tab. 6 Forms of work mathematical development of preschoolers

Form Objectives Time Coverage children Leading role

Lesson Give, repeat, consolidate and systematize knowledge, skills and abilities Planned, regularly, systematically (duration and regularity in accordance with the program) Group or subgroup (depending on age and problems in development) Educator

Didactic game Consolidate, apply, expand ZUN In class or outside of class Group, subgroup, one child Teacher and children

Individual work Clarify the knowledge of learning and fill gaps In class and outside of class One child Teacher

Leisure (math matinee, holiday, quiz, etc.) Captivate mathematics, summarize 1-2 times a year Group or several groups Teacher and other specialists

Independent activity Repeat, apply, practice learning skills During routine processes, everyday situations, everyday activities Group, subgroup, one child Children and teacher

FEMP means.

Equipment for games and activities (typesetting cloth, counting ladder, flannelgraph, magnetic board, writing board, TCO, etc.).

Didactic visual kits material(toys, construction kits, construction material, demonstration and distribution material, sets "Learn to count" and etc.).

Literature (methodological manuals for educators, collections of games and exercises, books for children, workbooks, etc.).

One of the main forms in the process of education and upbringing children in kindergarten is an independent activity children. Independent activity children– free activity of pupils in the conditions of the subject-spatial space created by teachers developing an educational environment that ensures that each child chooses activities based on his interests and allows him to interact with peers or act individually. Promotes the development of independence children’s mastery of the skills to set a goal, think about the path to achieving it, implement their plan, and evaluate the result from the position of the goal.

FEMP at children preschool age is carried out in different types of children's activities. One of these activities is design. It is known that construction occupies a significant place in preschool education and is a complex cognitive process, as a result of which intellectual child development: the child acquires practical knowledge, learns to identify essential features, establish relationships and connections between details and objects. Children's construction refers to an activity in which children create from various materials(paper, cardboard, wood, special construction kits and construction sets) various play crafts (toys, buildings, in other words, construction is a productive activity for a preschooler, which involves the creation of structures according to a model, according to conditions and according to one’s own plan.

During design classes children generalized ideas about the objects that surround them are formed. They learn to generalize groups of homogeneous objects based on their characteristics and at the same time find differences in them depending on practical use. Each house, for example, has walls, windows, doors, but houses differ in their purpose, and therefore in their architectural design. Thus, along with common features, children will also see differences in them, that is, they acquire knowledge that reflects significant connections and dependencies between individual objects and phenomena.

Wednesday develops child only if it is of interest to him and moves him to action and research. The environment is organized in such a way that every child has the opportunity to do what they love.

Subject-spatial developing the environment must meet individual and age characteristics of children, their leading activity is play. A game promotes the development of creative abilities, awakens imagination, activity, teaches communication, vivid expression of one’s feelings. In my group, I highlight two options for organizing independent cognitive activities: independent didactic games and construction.

Educational games developed by the authors: L. L. Wenger, games by V. V. Voskobovich, B. N. Nikitin and others or created independently, taking into account the level of cognitive child development and requirements for independent didactic games:

The rules of the game should provide children with the opportunity to choose the knowledge and skills needed for a given situation that they have already mastered during the learning process;

Variability of each game is necessary, complicating the gaming situation, which allows children to apply a variety of actions and newly acquired knowledge, maintaining long-term interest children to complete tasks;

Most games should involve mutual control and assessment of actions and decisions by children, which leads them to cooperation, joint actions, discussion, exchange of experience, and also activates their existing knowledge and ways their application to each specific situation.

Also in the lesson on mathematics It is good to use games and exercises with Dienes blocks. Logic blocks were invented by the Hungarian mathematician and psychologist Zoltan Dienes. Games with blocks are accessible and visually introduce children with uniform, color, size and thickness of objects, with mathematical ideas and basic knowledge of computer science. Developed in children mental operations (analysis, comparison, classification, generalization, logical thinking, creative capabilities and cognitive processes (perception, memory, attention and imagination). While playing with Dienesh blocks, the child performs a variety of object actions (splitting, laying out according to certain rules, rebuilding, etc.). Dienesha blocks are designed for children from three years old.

Preschoolers play independent didactic games more actively and creatively when, through joint activities, they have previously acquired the knowledge necessary to complete game tasks and have also learned the basic rules of the game. In the group there are such games V.V. Voskobovich: "Geocont", "Transparent square", "Voskobovich Square", "Lanterns", "Eight", "Miracle Designers"; games B.N. Nikitina: "Fold the pattern", "Fold a square", "Unicube", "Cuisenaire's Sticks". Such games develop design abilities, spatial thinking, attention, memory, creative imagination, fine motor skills, ability to compare, analyze and contrast. In the zone mathematical development games presented"Magnetic mosaic" with diagrams, "Parts and Wholes", "Studying time", “Counting to...”, "Addition and subtraction with Carlson", "Colorful figures", "It's All About Time", "Dominoes with numbers", "Little Designer". Where children can consolidate their knowledge of geometric shapes, spatial and temporal concepts, learn numbers and master operations with numbers. Designers.

Creating conditions for organizing joint activities in accordance with the requirements of the Federal State Educational Standard based on work experience.

To organize joint independent activities children appropriate conditions must be created in the group.

Firstly, at children a certain level of skills and abilities must be formed. The child begins a new activity, first under the guidance of a teacher, following the demonstration and explanation of an adult, and only after having gained some experience in performing this activity together can he perform it independently.

Creating developing environment in the group we use a large number of operational cards, they remind children of the sequence of actions during visual activities, in experimental, play, and work activities. Methodological basis for organizing classes on FEMP in the process design:

Construction of lessons according to mathematics is based on basic modern approaches to the process education:

Activity;

- developing;

Personality-oriented.

The most effective way to conduct classes promotes mathematics compliance with the following conditions:

1. taking into account individual, age-related psychological characteristics of children;

2. creating a favorable psychological atmosphere and emotional mood (a friendly, calm tone of speech of the teacher, creating situations of success for each student);

3. widespread use of gaming motivation;

4. integration mathematical activities in other kinds: gaming, musical, motor, visual;

5. change and alternation of activities due to fatigue and distractibility children;

6. developmental nature of tasks.

You can use it in class: game methods, problem-search methods, partial search methods, problem-practical game situations, practical methods.

Maksimova Marina Viktorovna Educator MBDOU DS No. 72 "Watercolor"

“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) 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, the main goals of the mathematical development of preschool children are:

1. Development of logical-mathematical ideas about mathematical properties and relationships of objects (specific quantities, numbers, geometric figures, dependencies, patterns);
2. Development of sensory, subject-effective ways of knowing mathematical properties and relationships: examination, comparison, grouping, ordering, partitioning);
3. Children's mastery of experimental and research methods of learning mathematical content (experimentation, modeling, transformation);
4. Development in children of logical ways of knowing mathematical properties and relationships (analysis, abstraction, negation, comparison, classification);
5. Children's mastery of mathematical ways of understanding reality: counting, measurement, simple calculations;
6. Development of intellectual and creative manifestations of children: resourcefulness, ingenuity, guesswork, ingenuity, desire to find non-standard solutions;
7. Development of accurate, reasoned and demonstrative speech, enrichment of the child’s vocabulary;
8. 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.)

Basic concepts, cognitive and speech skills that are mastered by children 4-5 years old in the process of mastering mathematical concepts:

PROPERTIES.

Items size: by length (long short); in height (high Low); in width (wide narrow); by thickness (thick, thin); by weight (heavy, light); in depth (deep, shallow); by volume (big small).

Geometric shapes and bodies: circle, square, triangle, oval, rectangle, ball, cube, cylinder.

Structural elements of geometric shapes: side, angle, their number.

Shape of objects: round, triangular, square. Logical connections between groups of quantities, shapes: low, but thick; find common and different in groups of figures of round, square, triangular shapes.

Links between changes (shift) basis for classification (groups) and the number of received groups and objects in them.

Cognitive and verbal skills. Purposefully visually and tactilely examine geometric shapes and objects in a motor way in order to determine the shape. Compare geometric shapes in pairs in order to identify structural elements: angles, sides, their number. Independently find and apply a way to determine the shape, size of objects, geometric figures. Independently name the properties of objects and geometric figures; express in speech a way of determining such properties as shape, size; group them by characteristics.

RELATIONSHIP.

Relationships between groups of objects: by quantity, by size, etc. Sequential increase (decrease) 3-5 items.

Spatial relations in paired directions from oneself, from other objects, in movement in the indicated direction; temporal - in the sequence of parts of the day, present, past and future tense: today, yesterday and tomorrow.

Generalization of 3-5 objects, sounds, movement according to properties - size, quantity, shape, etc.

Cognitive and verbal skills. Compare objects by eye, by superimposition, application. Express in speech quantitative, spatial, temporal relationships between objects, explain their sequential increase and decrease in quantity and size.

NUMBERS AND FIGURES.

Designation of quantity by number and figure within the range of 5-10. Quantitative and ordinal assignment of numbers. Generalization of groups of objects, sounds and movements by number. Connections between number, number and quantity: the more objects, the larger the number they are designated; counting both homogeneous and dissimilar objects, in different locations, etc.

Cognitive and verbal skills.

Count, compare by characteristics, quantity and number; reproduce quantity according to pattern and number; count down.

Name numbers, coordinate numeral words with nouns in gender, number, case.

Reflect in speech a method of practical action. Answer the questions: “How did you find out how much there is?”; “What will you find out if you count?”

PRESERVATION (UNCHANGEABLE) QUANTITIES AND VALUES.

Independence of the number of objects from their location in space, grouping.

Consistency of size, volume of liquid and granular bodies, absence or presence of dependence on the shape and size of the vessel.

Generalization by size, number, level of filling of vessels of the same shape, etc.

Cognitive and verbal skills to visually perceive sizes, quantities, properties of objects, count, compare in order to prove equality or inequality.

Express in speech the location of objects in space. Use prepositions and adverbs: to the right, from above, from..., next to..., about, in, on, for, etc.; Explain the method of comparison and detection of correspondence.

ALGORITHMS.

Designation of the sequence and stages of educational game action, dependence of the order of objects by symbol (arrow). Using the simplest algorithms of different types (linear and branched).

Cognitive and verbal skills. Visually perceive and understand the sequence of development and execution of an action, focusing on the direction indicated by the arrow.

Reflect in speech the order of actions: first; Then; earlier; Later; if... then.

I. Methods for studying quantitative concepts

Count yourself in.

1. Name the parts of your body, one at a time (head, nose, mouth, tongue, chest, stomach, back).

1. Name the paired organs of the body (2 ears, 2 temples, 2 eyebrows, 2 eyes, 2 cheeks, 2 lips: upper and lower, 2 arms, 2 legs). 3.
2. Show those body organs that can be counted to five (fingers and toes).

Light up the stars.

Game material: a sheet of dark blue paper - a model of the night sky; brush, yellow paint, number cards (up to five).

1. "Light up" (end of brush) there are as many “stars in the sky” as there are figures on the number card.
2. The same. Perform based on hearing the number of hits on the tambourine or under the table cover made by an adult.

Help Pinocchio.

Game material: Pinocchio toy, coins (within 7-10 pieces). Task: help Pinocchio take away the number of coins that Karabas Barabas gave him.

II. Magnitude

Ribbons.

Game material: strips of paper of different lengths - tape models. Set of pencils.

1. Color over the longest “ribbon” with a blue pencil, color over the shorter “ribbon” with a red pencil, etc.
2. Align all the “ribbons” in length.

Lay out your pencils.

By touch, arrange pencils of different lengths in ascending or descending order.

Lay out the rugs.

Arrange the “rugs” in ascending and descending order by width.

III. Methods for studying ideas about geometric figures.

What shape?

Game material: a set of cards depicting geometric shapes.

1. The adult names an object in the environment, and the child names a card with a geometric shape corresponding to the shape of the named object.
2. The adult names the object, and the child verbally determines its shape. For example, a triangle scarf, an oval egg, etc.

Game material: a set of geometric shapes. Using geometric shapes to lay out complex pictures.

Fix the rug.

Game material: illustration with a geometric image of torn rugs.

Find the right one (by shape and color) patch and "fix" (overlay) her on the hole.

IV. Methods for studying spatial representations.

Correct mistakes.

Game material: 4 large squares of white, yellow, gray and black colors - models of parts of the day. Scene pictures depicting children's activities throughout the day. They are placed on top of the squares without taking into account the correspondence of the plot to the model. Correct the mistakes made by Dunno, explain your actions.

Determine the direction of movement away from you (right, left, forward, backward, up, down).

Game material: card with a pattern made up of geometric shapes.

Describe the pattern yourself.

Find the differences.

Game material: a set of illustrations with opposite images of objects.

Find differences.

Stages of the formative experiment

Stage 1 - the following games were proposed to develop mathematical concepts:

"Trouble" the goal is to develop the ability to distinguish between contrasting and adjacent parts of the day.

"What changed?"

"Doll's Birthday" the goal is the ability to distinguish colors and shapes.

"Remember the pictures" the goal is to develop attention and memory, distinguish geometric shapes by characteristic features.

"Repeat after each other" the goal is to develop an understanding of the schematic representation of human posture.

"How are they similar and how are they different" , "We assume"

“Find an equal number of toys” , "Pick a Pair" The goal is to teach the child quantitative and ordinal counting.

"Animals on the tracks" the goal is the ability to identify two properties of a figure (shape and size; size and color).

"Workshop of Forms" the goal is to develop ideas about geometric figures, identifying them according to their characteristic features.

“Draw a picture with chopsticks” The goal is the development of thinking, ordinal and quantitative calculation.

"Learning to compare" The goal is the ability to compare objects by length and width.

“Color objects of different geometric shapes” the goal is to develop ideas about geometric shapes.

"What's next?" the goal is the development of quantitative and ordinal counting. "Games with Dienesh blocks" the goal is the development of quantitative and ordinal counting, size, length, width, height, color. The ability to compare two properties at the same time: shape - size, size - color, shape - color.

“When does this happen?” the goal is to develop ideas about time and parts of the day.

"Colored Houses" the goal is to simultaneously highlight two properties of figures: shape and color.

"Color Lotto" The goal is to highlight size and color.

Stage 2 - the following games:

"What changed?" , "Who's hiding here?" the goal is orientation in the group room, the ability to move in a given direction.

“What did you get?” the purpose is the manipulation of liquids and bulk materials.

"Attention - guess what" the goal is to manipulate liquids.

“Identify the differences by eye” the goal is the development of memory, the ability to generalize all geometric shapes.

“Learning to find visible differences” the goal is orientation on the plan in the group and on the site according to the plan.

“What does it look like?” the goal is to develop attention, generalize geometric shapes by size.

"Half to Half" , "Dots"

"Magic Mosaic" the goal is to generalize geometric shapes by color.

Games with Dienesh blocks - with complication.

"Gnomes with bags" goal is to develop the ability to identify spatial relationships (up-down, right-left, side-top, back-front).

"Learning to compare" the goal is the ability to compare objects by length, width, height.

“Who left and where did he hide?” the goal is the ability to move in a given direction following a verbal command.

"Pass the package" The goal is quantitative and ordinal counting.

“Where did the bee fly?” the goal is the ability to compare (same, more, one more, one less).

Lotto "Color and Shape" the goal is to develop ideas about color and shape, enrich thinking.

"Logical Lotto" The goal is counting and geometric shapes.

Stage 3 - the following games:

"Attention" the goal is the ability to navigate according to the kindergarten plan.

"What changed?" the goal is orientation with complication.

“How are they similar and how are they different?” the goal is the ability to simultaneously identify two properties of a figure (shape-color, size-color, shape-size). “Continue the row. Dots" The goal is quantitative and ordinal counting. "Correct the mistake" the goal is the ability to compare objects by thickness, height and mass.

Lotto "Count" , "Name the neighbors" The goal is to develop ordinal counting. “Who knows, let him keep counting!” The goal is to count backwards. "Wonderful bag" the goal is the development of sensation and perception.

"Cut pictures" , "Fold the pattern" the goal is geometric shapes and the development of thinking.

“Copying and sketching geometric shapes” The goal is geometric shapes and counting.

"When it was?" the goal is to develop the ability to distinguish contrasting parts of the day, determine their sequence yesterday-today-tomorrow).

"Fast slow" goal - geometric shapes, counting, color, shape, size.

"Cubes for everyone" goal - orientation on a sheet of paper, the ability to perform a certain pattern according to a pattern (scheme).

Mathematics education of a preschooler is a purposeful process of teaching elementary mathematical concepts and ways of understanding mathematical reality in preschool institutions and the family, the purpose of which is to cultivate a culture of thinking and the mathematical development of the child.

How "to wake" cognitive interest of the child?

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

Those. learning needs to be made fun. 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, educators need to structure educational activities 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.

Teaching mathematics to preschool children is unthinkable without the use of entertaining games, tasks, and entertainment.

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.

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.

Teachers are helped to use an integrated approach in all types of activities by the presence of entertaining material in each kindergarten group, namely card files with a selection of mathematical riddles, funny poems, mathematical proverbs and sayings, counting rhymes, logical problems, joke problems, 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.

Thus, puzzles are useful for consolidating ideas about geometric shapes and their transformation. Riddles, tasks - jokes are appropriate during learning to solve arithmetic problems, operations with numbers, and when forming ideas about time. Children are very active in the perception of tasks - jokes, puzzles, logical exercises. The child is interested in the final goal: adding, finding the right shape, transforming - which captivates him.

The group continues to work on the formation of cognitive interests of preschoolers through educational mathematical games and the creation of a developing subject-spatial environment for the formation of mathematical concepts in accordance with the Federal State Educational Standard for Education.

Having analyzed the sets of games existing in the group, I came to the conclusion that educational games are not enough. Therefore, I prepared manuals, didactic games with mathematical content, included games and exercises to develop the child’s attention, fantasy, imagination and speech; games for classifying objects by purpose. To develop attention and the ability to make logical conclusions, I use logical tables when working with children.

I also offer children independent play and practical exercises outside of class, based on self-control and self-esteem. For example games: "Geometric Lotto" , "The Fourth Wheel" . "Magic bag" . “Which number is missing?” , "How many?" , "Confusion?" , "Correct the mistake" , "Removing the numbers" , "Name the neighbors" , "Think of a number" , “Number, what’s your name?” , "Make up a number" , “Who will be the first to name which toy is gone?” develop children's attention, memory, and thinking.

A series of games were included in the work with children: "Fold a square" , "Fold a circle" . They develop the ability to compose a whole from parts, contribute to the development of imagination, constructive thinking, willpower, and the ability to finish a job.

Children examine and analyze rows of figures, and then choose the missing figure from the proposed samples.

To navigate in space, I use a plan chart in my work, on which children consolidate their knowledge: right, left, up, down, forward, back. Working with a plan chart teaches children to consistently build their story, for example, “How to get to house A” .

Develop children's memory, attention, logical thinking, sensory and creative abilities; learn to count, count out the required quantity, become familiar with spatial relationships and magnitude; Voskobovich’s games help to correlate the whole and the parts.

A tool for developing children’s creative and logical abilities are practical exercises with a constructor for planar and three-dimensional modeling. When playing with a construction set, a child remembers the names and appearance of plane figures. (triangles – equilateral, acute, rectangular), squares, rectangles, rhombuses, trapezoids, etc. children learn to model objects in the surrounding world and gain social experience. Children develop spatial thinking; they can easily change the color, shape, size of the structure if necessary. The skills and abilities acquired in the preschool period will serve as the foundation for acquiring knowledge and developing abilities at school age. And the most important among these skills is the skill of logical thinking, the ability "act in the mind" .

Wooden construction sets are a convenient teaching material. Multi-colored details help the child not only learn the names of colors and geometric flat and three-dimensional figures, but also concepts "more less" , "higher lower" , "wider-narrower" .

For children, working with a logic pyramid gives them the opportunity to manipulate the components and compare them by size using the comparison method. When folding a pyramid, the child not only sees the details, but also feels them with his hands.

In conclusion, we can draw the following conclusion: the development of cognitive abilities and cognitive interest of preschool children is one of the most important issues in the upbringing and development of a preschool child.

A child who is interested in learning something new, and who succeeds in doing so, will always strive to learn even more - which, of course, will have the most positive impact on his mental development.

Literature:

1. Tikhomorova L.F. Development of logical thinking in children. - SP., 2004.
2. Formation of elementary mathematical concepts in preschoolers. Ed. A.A. Joiner. M., Education, 1988. -303 p.