Safronova Nadezhda Vasilievna
Job title: teacher
Educational institution: MBDOU kindergarten No. 19
Locality: Novokuznetsk city, Kemerovo region
Name of material: Toolkit
Subject:"Game technologies for the mathematical development of preschool children"
Publication date: 30.10.2017
Chapter: preschool education

MBDOU Danish garden No. 19.

Toolkit.

Topic: Game technologies for the mathematical development of preschool children

age.

Educator: Safronova N.V.

Novokuznetsk, 2017

Introduction…………………………………………………………………………………...3

Game as the main method of teaching…………………………………...4

The process of forming elementary mathematical

performances, gaming technologies…………………………………..5

Conclusion……………………………………………………………11

Used literature……………………………………………...12

INTRODUCTION

Mastering mathematical knowledge at various stages of school

learning causes significant difficulties for many students. One of

reasons that create difficulties and overload for students in the process

acquisition of knowledge consists in insufficient preparation of thinking

preschoolers to master this knowledge.

The problems of developing thinking based on experience are ideas

domestic and foreign teachers - psychologists:

L.S. Vygotsky.P.P. Blonsky, P.P. Golperin, S.L. Rubinshteina, V.V.

Davydova, A.I. Meshcheryakov, I.A. Menchinskaya, D.B. Elkonina, A.V.

Zaporozhets,

M. Montessori.

Thinking- the highest level of human knowledge of reality.

The question of where and how to start preparing preschool children for

studying mathematics (or pre-mathematics preparation) cannot

be decided now in the same way as it was decided 100 or even 50 years ago.

formation of ideas about numbers and simple geometric

figures, learning to count, add and subtract, measure in

the simplest cases. From the point of view of the modern concept of learning

for the youngest children no less important than arithmetic operations

preparing them for mastering mathematical knowledge is the formation

logical thinking. Children need to be taught not only to calculate and

measure, but also reason.

1.Game as the main method of teaching preschool children.

When we talk about teaching preschoolers, then, of course, we do not mean

direct teaching of logical operations and relations, and preparing children for

mastering the exact meaning of words and phrases denoting these

operations and relationships through practical actions leading to

Thus, pre-mathematical preparation of children seems

consisting of two closely intertwined main lines: logical, i.e.

preparing children's thinking for the methods used in mathematics

reasoning, and actually before the mathematical one, which consists in the formation

elementary mathematical concepts. Note that logical

preparation goes beyond preparation for the study of mathematics, developing

children's cognitive abilities, in particular their thinking and speech.

Analysis of the state of education of preschool children leads many

specialists to the conclusion about the need for development in didactic games

(along with the widespread function of securing and

repetition of knowledge) functions of forming new knowledge, ideas and

ways of cognitive activity. In other words, we are talking about

the need to develop the educational functions of the game, which involves

learning through play.

For them, play is work, study, and a serious form of education. Sometimes

they ask when to play with children, before or after class, without knowing

even that you can play with children during the lesson itself and teach them in the process

games by playing with them.

In teaching children 4-6 years old, play is considered not just one of the

teaching methods, but as the main method of teaching children of this age, in

further gradually giving way to other methods

training. For children 4-6 years old, play is the leading activity:

It is where the child’s psyche most clearly and intensively manifests itself, is formed and

develops.

Learning through play is an interesting and exciting activity for the most

small, contributes to the gradual transfer of interest and passion from

game for educational activities. A game that captivates children, they are not

overloads both mentally and physically. It is obvious that children's interest in

the game gradually turns into not only an interest in learning, but also in the fact that

is being studied, that is, with an interest in mathematics.

2. The process of forming elementary mathematical

performances, gaming technologies

The development and selection of technologies depends on what is being developed and

what will the development of the child’s mental activity consist of?

connections and interconnections of objects and phenomena of the surrounding world. This

mastering the properties of objects (shape, color, size, weight, capacity, etc.)

Gaming technologies:

Logical and mathematical games;

Educational situations (developmental, gaming);

Problem situations, questions;

Experimentation, research activities;

Creative tasks, questions and situations.

The process of forming elementary mathematical concepts

carried out under the guidance of a teacher, as a result systematically

the work carried out at the GCD and outside it, aimed at familiarizing children with

quantitative, spatial and temporal relationships with

using a variety of means. unique tools of the teacher’s labor and

tools for children's cognitive activity.

In practice, the following formation tools are used

elementary mathematical concepts:

Sets of visual teaching materials for classes;

Equipment for independent games and activities for children;

Methodological manuals for kindergarten teachers, in which

reveals the essence of the work on the formation of elementary

mathematical concepts in children in each age group and are given

sample lesson notes;

Team didactic games and exercises for the formation

quantitative, spatial and temporal representations in

preschoolers;

Educational and educational books to prepare children to learn

mathematics at school in a family environment.

When forming elementary mathematical concepts

teaching aids perform various functions:

Implement the principle of visibility;

Adapt abstract mathematical concepts into accessible language

kids uniform;

Help children master the methods of action necessary to

the emergence of elementary mathematical concepts;

Helps children gain sensory experience

properties, relationships, connections and dependencies, its constant expansion and

enrichment, help to make a gradual transition from material

to the materialized, from the concrete to the abstract;

Give the teacher the opportunity to organize educational and cognitive

activities of preschoolers and manage this work, develop in them

desire to gain new knowledge, master counting, measurement,

the simplest methods of calculation, etc.;

Increase the volume of independent cognitive activity of children

in and outside of mathematics classes;

Expand the teacher’s capabilities in solving educational,

educational and developmental tasks;

Rationalize and intensify the learning process.

Thus, teaching aids perform important functions:

activities of the teacher and children in the formation of their elementary

mathematical concepts. They are constantly changing, new

are designed in close connection with the improvement of theory and practice

pre-mathematical preparation of children.

The main means of teaching is visual didactic

material for classes. It includes the following: environmental objects

environments taken in their natural form: various household items, toys,

dishes, buttons, cones, acorns, pebbles, shells, etc.;

Images of objects: flat, contour, color, on stands and without

them, drawn on cards;

Graphic and schematic tools: logical blocks, figures,

cards, tables, models.

When forming elementary mathematical concepts in

In my classes I most widely use real objects and their images.

As children age, there are natural changes in use

separate groups of didactic means: along with visual aids

an indirect system of didactic materials is used.

Modern research refutes the claim that it is inaccessible to

children of generalized mathematical concepts. Therefore, when working with

older preschoolers use visual aids that model

mathematical concepts.

Didactic tools should change not only taking into account age

features, but depending on the ratio of concrete and abstract

at different stages of children’s assimilation of program material. For example, on

at a certain stage, real objects can be replaced by numerical ones

figures, and they, in turn, numbers, etc.

Each age group must have its own kit.

visual material. Visual didactic material corresponds to

age characteristics of children, meets various requirements:

scientific, pedagogical, aesthetic, sanitary and hygienic,

economic, etc.

It is used in classes when explaining new things, consolidating them, for

repetition of what has been covered and when testing children’s knowledge, i.e. at all stages

training.

Usually two types of visual material are used: large,

(demonstration) for showing and working with children and small (distribution),

which the child uses while sitting at the table and simultaneously performing

everyone's task is the teacher's.

Demonstration and handout materials differ in purpose:

the former serve to explain and show methods of action by the teacher,

the latter provide the opportunity to organize independent activities

children, during which the necessary skills and abilities are developed.

These functions are basic, but not the only ones and strictly

fixed.

The size of benefits is taken into account: handouts must be

so that children sitting nearby can comfortably place it on the table and not

interfere with each other while working.

Visual didactic material serves to implement the program

development of elementary mathematical concepts

in the process of specially organized exercises during NOD. With this

the purpose is used:

Aids for teaching children to count;

Aids for exercises in recognizing the size of objects;

Aids for children's exercises in recognizing the shape of objects and

geometric shapes;

Aids for exercising children in spatial orientation;

Aids for teaching children time orientation. Data

sets of manuals must correspond to the main sections

programs and include both demonstration and handout material.

The didactic tools necessary for conducting educational activities are being prepared

teacher, involving parents in this, or are taken ready from

environment.

Equipment for independent games and activities can include:

Special didactic tools for individual work with

children, for preliminary acquaintance with new toys and

materials;

A variety of didactic games: board-printed and with objects;

training developed by A. A. Stolyar; developing, developed by B.

P. Nikitin; checkers, chess;

Entertaining mathematical material: puzzles, geometric

mosaics and constructors, labyrinths, joke problems, tasks on

transfiguration, etc. with the application, where necessary, of samples

(for example, the game "Tangram" requires dissected and

undivided, contour), visual instructions, etc.;

Separate didactic tools: blocks 3. Dienesha (logical blocks),

X. Kusener sticks, counting material (different from what is used

in the classroom), cubes with numbers and signs, children's computers

and much more.

Books with educational and cognitive content for reading to children and

looking at illustrations.

All these facilities are located directly in the independent zone

cognitive and gaming activities. These funds are used in

mainly during gaming hours, but can also be used on GCD

Working with a variety of didactic tools outside of class,

the child not only consolidates the knowledge acquired in the classroom, but also in

In some cases, by assimilating additional content, it can outstrip

requirements of the program, gradually prepare to master it.

Independent activity under the guidance of a teacher, taking place

individually, in a group, makes it possible to ensure the optimal pace

development of each child, taking into account his interests, inclinations, abilities,

peculiarities.

One of the means of developing in preschool children

elementary mathematical concepts are entertaining games,

exercises, tasks, questions. This fun math material

extremely diverse in content, form, developmental and

educational influence.

From entertaining mathematical material in working with preschoolers

The simplest types can be used:

Geometric construction sets: “Tangram”, “Pythagoras”, “Columbus Egg”,

“Magic Circle”, etc., in which from a set of flat geometric shapes

you need to create a plot image based on a silhouette, contour

sample or by design;

- “Rubik’s Snake”, “Magic Balls”, “Pyramid”, “Fold the Pattern”,

Unicube and other puzzle toys consisting of

It expands the ability to create and solve problem situations,

opens effective ways to enhance mental activity,

promotes the organization of communication between children and with adults.

Entertaining math material is a means

complex impact on the development of children, with its help it is carried out

mental and volitional development, problems in learning are created, child

takes an active position in the learning process itself. Spatial

imagination, logical thinking, purposefulness and

purposefulness, ability to independently search and find ways

actions to solve practical and cognitive problems - all this,

taken together, is required for successful mastery of mathematics and other

educational subjects at school.

In the "Childhood" program, the main indicators of intellectual

child development are indicators of the development of such mental

processes such as comparison, generalization, grouping, classification. Children,

having difficulty choosing subjects for certain

properties, in their grouping they usually lag behind in sensory development

(especially in younger and middle age). Therefore, games for the touch

development occupy a large place in working with these children and. usually,

give good results.

In addition to traditional games aimed at sensory development, very

Games with Dienesh Blocks are effective. For example, these:

Make a pattern. Goal: develop perception of shape

Balloons. Purpose: to draw children's attention to the color of the object,

learn to select objects of the same color

Remember the pattern. Goal: develop observation, attention, memory

Find your house. Goal: develop the ability to distinguish colors and shapes

geometric shapes, to form an idea of ​​the symbolic

image of objects; teach to systematize and classify

geometric shapes in color and shape.

Complimentary ticket. Goal: to develop children’s ability to distinguish

geometric shapes, abstracting them by color and size.

Ants. Goal: to develop children's ability to distinguish color and size

items; form an idea of ​​a symbolic image

items.

Carousel. Goal: to develop children's imagination and logical thinking;

exercise the ability to distinguish, name, organize blocks by color,

size, shape.

Multi-colored balls. Goal: develop logical thinking; learn

The further order of the games is determined by the complication: the development of skills

compare and summarize, analyze, describe blocks using

characters, classified according to 1-2 criteria. These and further

complications transform the games into the category of games for gifted children. On the same

“lagging” children themselves can move up the ranks. It is important to implement on time

necessary transition of children to the next stage. So as not to overexpose

children at a certain level, the task should be difficult, but

feasible.

Thus, trying to take into account the interests of each child in the group, the teacher

must strive to create a situation of success for everyone, taking into account his

achievements on this moment development. You must have:

Availability of games with a variety of content - to provide children with

rights of choice

The presence of games aimed at advancing development (for gifted

Compliance with the principle of novelty - the environment must be changeable,

updated - children love new things

Compliance with the principle of surprise and unusualness.

Conclusion

Mathematical work organized in line with gaming technologies

development of children meets the interests of the children themselves, promotes the development

their interest in intellectual activity corresponds to current

requirements for organizing the educational process for preschoolers and

stimulates further creativity in joint activities with

BIBLIOGRAPHY.

Wenger L.A., Dyachenko O.M. "Games and exercises to develop

mental abilities in preschool children."

"Enlightenment" 1989

Erofeeva T.I. "Introduction to mathematics: a methodological guide for

teachers." – M.: Education, 2006.

Zaitsev V.V. "Mathematics for preschool children." Humanitarian.

Ed. Vlados Center

Kolesnikova E.V. “Development of mathematical thinking in children 5-7

years" - M: "Gnome-Press", "New School" 1998.

“Formation of elementary mathematical concepts using OTSM - TRIZ technology methods. Many scientists and practitioners believe that modern requirements for preschool education...”

Formation of elementary mathematical concepts

through OTSM - TRIZ technology methods.

Many scientists and practitioners believe that modern requirements for preschool

education can be carried out provided that when working with children there are

TRIZ-OTSM technology methods are actively used. In educational

activities with children of senior preschool age I use the following methods:

morphological analysis, system operator, dichotomy, synectics (direct

analogy), on the contrary.

MORPHOLOGICAL ANALYSIS

Main goal: To develop in children the ability to give a large number of different categories of answers within a given topic.

Method capabilities:

Develops children's attention, imagination, speech, and mathematical thinking.

Forms mobility and systematic thinking.

Forms primary ideas about the basic properties and relationships of objects in the surrounding world: shape, color, size, quantity, number, part and whole, space and time. (Federal State Educational Standards for Preschool Education) Helps the child learn the principle of variability.

Develops children's abilities in the field of perception and cognitive interest.

Technological chain of educational activities (EA) along the morphological path (MD)

1. Presentation of the MD (“Magic Track”) with pre-established horizontal indicators (feature icons), depending on the purpose of the OOD.

2.Introduction of the Hero who will “travel” along the “Magic Path”.

(The role of the Hero will be played by the children themselves.)

3.Information of the task to be completed by the children. (For example, help the subject walk along the “Magic Path” by answering questions about signs).

4. Morphological analysis is carried out in the form of a discussion (it is possible to record the results of the discussion using pictures, diagrams, signs). One of the children asks a question on behalf of the sign. The rest of the children, being in the “helpers” situation, answer the question asked.

A chain of sample questions:

1.Object, who are you?

2.Object, what color are you?

3.Object, what is your main business?

4. Object, what else can you do?

5.Object, what parts do you have?

6.Object, where are you (“hiding”)? Object, what are the names of your “relatives” among whom you can be found?

Denote the shape I am in the natural world (leaf, tree, triangle of objects, vertices

–  –  –

Note. Complications: introducing new indicators or increasing their number.

Technological chain of educational activities (EA) according to the morphological table (MT)

1. Presentation of a morphological table (MT) with pre-established horizontal and vertical indicators, depending on the purpose of the OOD.

2. A message about the task that the children have to complete.

3. Morphological analysis in the form of discussion. (Search for an object by two specified properties).

Note. Horizontal and vertical indicators are indicated by pictures (diagrams, colors, letters, words). The morphological path (table) remains for some time in the group and is used by the teacher in individual work with children and children in independent activities. First, starting from the middle group, work is carried out on MD, and then on MT (in the second half of the academic year).

In the senior and school-preparatory groups of kindergarten, educational activities are carried out in MD and MT.

What could be a morphological table (track) in a group?

In my work I use:

a) a table (track) in the form of a typesetting canvas;

b) a morphological path, which is laid out on the floor with ropes, on which character icons are placed.

SYSTEM OPERATOR

Main goal: To develop in children the ability to think systematically in relation to any object.

Method capabilities:

Develops children's imagination and speech.

Forms the foundations of systematic thinking in children.

Forms elementary mathematical concepts.

Develops in children the ability to identify an object’s main purpose.

Forms the idea that each object consists of parts and has its own location.

Helps the child build a line of development for an object.

The minimum model of a system operator is nine screens. The numbers on the screens show the sequence of work with the system operator.

In my work with children, I play with the system operator and play games based on it (“Sound the Filmstrip,” “Magic TV,” “Casket”).

For example: Working for CO. (The number 5 is considered. Screens 2-3-4-7 open).

Q: Children, I wanted to show our guests information about the number 5. But someone hid it behind the doors of the casket. We need to open the casket.

–  –  –

Algorithm for working with CO:

Q: Why did people come up with the number 5?

D: Indicate the number of items.

Q: What parts does the number 5 consist of? (Which two numbers can be used to make the number 5? How can the number 5 be made from ones?).

D: 1i4, 4 i1, 2iZ, Zi2, 1,1,1,1i1.

Q: Where is the number 5? Where did you see the number 5?, D: On the house, on the elevator, on the clock, on the telephone, on the remote control, on transport, in a book, Q: Name the numbers - relatives, among which the number 5 can be found.

D: Natural numbers that we use when counting.

Q: What was the number 5 until it was joined by 1?

D: Number 4.

Q: What number will the number 5 be if it is joined by 1?

D: Number 6.

Note.

Children should not use terms (system, supersystem, subsystem).

Of course, it is not necessary to look at all screens during an organized educational activity. Only those screens that are necessary to achieve the goal are considered.

In the middle group, it is recommended, deviating from the order of filling, to begin to consider subsystem features, immediately after the name of the system and its main function, and then determine which supersystem it belongs to (1-3What can a system operator in a group be? In my work I I use a system operator in the form of a typesetting canvas: the screens are filled with pictures, drawings, and diagrams.

SYNECTICS

This work is based on four types of operations: empathy, direct analogy, symbolistic analogy, fantastic analogy. In the FEMP process, a direct analogy can be used. Direct analogy is a search for similar objects in other fields of knowledge based on some characteristics.

Main goal: To develop in children the ability to establish correspondence between objects (phenomena) according to given characteristics.

Method capabilities:

Develops children's attention, imagination, speech, associative thinking.

Forms elementary mathematical concepts.

Develops in children the ability to build various associative series.

Forms the child’s cognitive interests and cognitive actions.

A child’s mastery of direct analogy occurs through the games: “City of Circles (Squares, Triangles, Rectangles, etc.)”, “Magic Glasses”, “Find an object of the same shape”, “Bag of Gifts”, “City of Colored Numbers” and etc. During games, children get acquainted with various types of associations, learn to purposefully build various associative series, and acquire the skills of going beyond the usual chains of reasoning. Associative thinking is formed, which is very necessary for the future schoolchild and for an adult. A child’s mastery of direct analogy is closely related to the development of creative imagination.

In this regard, it is also important to teach the child two skills that help create original images:

a) the ability to “include” an object in new connections and relationships (through the game “Complete the Figure”);

b) the ability to choose the most original one from several images (through the game “What does it look like?”).

Game "What does it look like?" (from 3 years old).

Target. Develop associative thinking and imagination. To develop the ability to compare mathematical objects with objects of the natural and man-made world.

Progress of the game: The presenter names a mathematical object (number, figure), and the children name objects similar to it from the natural and man-made world.

For example, Q: What does the number 3 look like?

D: With the letter z, with a snake, with a swallow, ....

Q: What if we turn the number 3 horizontally?

D: On the horns of the ram.

Q: What does a diamond look like? D: For a kite, for cookies.

DICHOTOMY.

Dichotomy is a method of dividing in half, used for the collective performance of creative tasks that require search work, and is represented in pedagogical activities by various types of “Yes - No” games.

A child’s ability to pose strong questions (questions of a search nature) is one of the indicators of the development of his creative abilities. To expand the child’s capabilities and break stereotypes in the formulation of questions, it is necessary to show the child examples of other forms of questions, to demonstrate the differences and research capabilities of these forms. It is also important to help the child learn a certain sequence (algorithm) for asking questions. You can teach your child this skill by using the “Yes-No” game in your work with children.

Main goal: - To develop the ability to narrow the search field

Teaching mental action is a dichotomy.

Method capabilities:

Develops children's attention, thinking, memory, imagination, and speech.

Forms elementary mathematical concepts.

Breaks stereotypes in the formulation of questions.

Helps the child learn a certain sequence of questions (algorithm).

Activates children's vocabulary.

Develops children's ability to pose exploratory questions.

Forms the child's cognitive interests and cognitive actions. The essence of the game is simple - children must unravel the riddle by asking the teacher questions according to the learned algorithm. The teacher can answer them only with the words: “yes,” “no,” or “both yes and no.” The teacher’s answer “both yes and no” shows the presence of contradictory signs of the object. If a child asks a question that cannot be answered, then it is necessary to show with a pre-established sign that the question was asked incorrectly.

Di. "Not really". (Linear, with flat and volumetric figures).

The teacher pre-sets geometric shapes in a row (cube, circle, prism, oval, pyramid, pentagon, cylinder, trapezoid, rhombus, triangle, ball, square, cone, rectangle, hexagon).

The teacher makes a guess, and the children guess by asking questions using a familiar algorithm:

Is this a trapezoid? - No.

Is it to the right of the trapezoid? - No. (Shapes are removed: trapezoid, rhombus, triangle, ball, square, cone, rectangle, hexagon),

Is this an oval? - No.

Is it to the left of the oval? - Yes.

Is this a circle? - No.

Is it to the right of the circle? - Yes.

Is this a prism? - Yes, well done.

The “VERSE VERSE” method.

The essence of the “vice versa” method is to identify a certain function or property of an object and replace it with its opposite. This technique can be used in working with preschoolers starting from the middle group of kindergarten.

Main goal: Development of sensitivity to contradictions.

Method capabilities:

Develops children's attention, imagination, speech, and the basics of dialectical thinking.

Forms elementary mathematical concepts.

Develops in children the ability to select and name antonymic pairs.

Forms the child’s cognitive interests and cognitive actions.

The “vice versa” method is the basis of the “Verse versa” game.

Game options:

1.Goal: To develop children’s ability to find antonym words.

Main action: the presenter calls a word - the players select and name an antonymous pair. These tasks are announced to children as ball games.

2.Goal: To develop the ability to draw objects “in reverse.”

For example, the teacher shows a page from the “Game Mathematics” notebook

and says: “The Cheerful Pencil drew a short arrow, and you draw the other way around.”

Prepared by teacher Zhuravleva V.A.

CITY THEORETICAL AND PRACTICAL SEMINAR

“MODERN TECHNOLOGIES IN THE FORMATION OF ELEMENTARY MATHEMATICAL CONCEPTS IN PRESCHOOL CHILDREN”

SPEECH BY TEACHER ATAVINA N.M.

“The use of Dienesh blocks in the formation of elementary mathematical concepts in preschoolers”

Games with Dienesh blocks as a means of forming universal prerequisites for learning activities in preschool children.

Dear teachers! “The human mind is marked by such an insatiable receptivity to knowledge that it is, as it were, an abyss...”

Ya.A. Comenius.

Any teacher is especially concerned about children who are indifferent to everything. If a child has no interest in what is happening in class, no need to learn something new, this is a disaster for everyone. The problem for a teacher is that it is very difficult to teach someone who does not want to learn. The problem for parents: if there is no interest in knowledge, the void will be filled with other, not always harmless, interests. And most importantly, this is the child’s problem: he is not only bored, but also difficult, and hence difficult relationships with parents, with peers, and with himself. It is impossible to maintain self-confidence and self-respect if everyone around is striving for something, enjoying something, and he alone does not understand the aspirations, achievements of his comrades, or what others expect from him.

For the modern educational system, the problem of cognitive activity is extremely important and relevant. According to scientists' forecasts, the third millennium will be marked by an information revolution. Knowledgeable, active and educated people will become valued as true national wealth, since it is necessary to competently navigate the ever-increasing volume of knowledge. Already now, an indispensable characteristic of readiness to study at school is the presence of interest in knowledge, as well as the ability to perform voluntary actions. These abilities and skills “grow” out of strong cognitive interests, which is why it is so important to shape them, teach them to think creatively, outside the box, and to independently find the right solution.

Interest! The perpetual motion machine of all human quests, the unquenchable fire of an inquisitive soul. One of the most exciting questions of education for teachers remains: How to arouse sustainable cognitive interest, how to arouse a thirst for the difficult process of learning?
Cognitive interest is a means of attracting children to learning, a means of activating children’s thinking, a means of making them worry and work enthusiastically.

How to “awaken” a child’s cognitive interest? You need to make learning fun.

The essence of entertainment is novelty, unusualness, surprise, strangeness, and inconsistency with previous ideas. With entertaining learning, emotional and mental processes intensify, forcing you to look more closely at the subject, observe, guess, remember, compare, and look for explanations.

Thus, the lesson will be educational and entertaining if children during it:

Think (analyze, compare, generalize, prove);

They are surprised (rejoice at successes and achievements, novelty);

They fantasize (anticipate, create independent new images).

Achieve (purposeful, persistent, show the will to achieve results);

All human mental activity consists of logical operations and is carried out in practical activity and is inextricably linked with it. Any type of activity, any work involves solving mental problems. Practice is the source of thinking. Everything that a person cognizes through thinking (objects, phenomena, their properties, natural connections between them) is verified by practice, which gives an answer to the question of whether he correctly cognized this or that phenomenon, this or that pattern or not.

However, practice shows that mastering knowledge at various stages of education causes significant difficulties for many children.

– mental operations

(analysis, synthesis, comparison, systematization, classification)

in analysis - the mental division of an object into parts and their subsequent comparison;

in synthesis - building a whole from parts;

in comparison - identifying common and different features in a number of objects;

in systematization and classification - constructing objects or objects according to any scheme and arranging them according to any criteria;

in generalization - linking an object with a class of objects based on essential features.

Therefore, education in kindergarten should be aimed, first of all, at the development of cognitive abilities, the formation of prerequisites for educational activity, which are closely related to the development of mental operations.

Intellectual work is not very easy, and, taking into account the age capabilities of preschool children, teachers must remember

that the main method of development is problem-based - search, and the main form of organization is play.

Our kindergarten has accumulated positive experience in developing the intellectual and creative abilities of children in the process of forming mathematical concepts

The teachers of our preschool institution successfully use modern pedagogical technologies and methods for organizing the educational process.

One of the universal modern pedagogical technologies is the use of Dienesh blocks.

Dienes blocks were invented by the Hungarian psychologist, professor, creator of the original “New Mathematics” methodology - Zoltan Dienes.

The didactic material is based on the method of replacing the subject with symbols and signs (modeling method).

Zoltan Dienes created a simple, but at the same time unique toy, cubes, which he placed in a small box.

Over the past decade, this material has been gaining increasing recognition among teachers in our country.

So, Dienesh's logic blocks are intended for children from 2 to 8 years old. As you can see, they are the type of toys that you can play with for years by complicating tasks from simple to complex.

Target: the use of Dienesh's logical blocks is the development of logical and mathematical concepts in children

The tasks of using logical blocks in working with children have been identified:

1.Develop logical thinking.

2.To form an idea of ​​mathematical concepts –

algorithm, (sequence of actions)

encoding, (storing information using special characters)

decoding information (decoding symbols and signs)

coding with a negation sign (using the particle “not”).

3. Develop the ability to identify properties in objects, name them, adequately indicate their absence, generalize objects according to their properties (one, two, three characteristics), explain the similarities and differences of objects, justify their reasoning.

4. Introduce the shape, color, size, thickness of objects.

5. Develop spatial concepts (orientation on a sheet of paper).

6. Develop the knowledge, skills and abilities necessary to independently solve educational and practical problems.

7. Foster independence, initiative, perseverance in achieving goals and overcoming difficulties.

8. Develop cognitive processes, mental operations.

9. Develop creativity, imagination, fantasy,

10. Ability to model and design.

From a pedagogical point of view, this game belongs to the group of games with rules, to the group of games that are directed and supported by an adult.

The game has a classic structure:

Task(s).

Didactic material (actually blocks, tables, diagrams).

Rules (signs, diagrams, verbal instructions).

Action (mainly according to a proposed rule, described either by models, or by a table, or by a diagram).

Result (necessarily verified with the task at hand).

So, let's open the box.

The game material is a set of 48 logical blocks that differ in four properties:

1. Shape - round, square, triangular, rectangular;

2. Color - red, yellow, blue;

3. Size - large and small;

4. Thickness - thick and thin.

And what?

We will take a figure out of the box and say: “This is a big red triangle, this is a small blue circle.”

Simple and boring? Yes, I agree. That is why a huge number of games and activities with Dienesh blocks were proposed.

It is no coincidence that many kindergartens in Russia teach children using this method. We want to show how interesting it is.

Our goal is to interest you, and if it is achieved, then we are sure that you will not have a box of blocks collecting dust on your shelves!

Where to start?

Working with Dienesh Blocks, build on the principle - from simple to complex.

As already mentioned, you can start working with blocks with children of primary preschool age. We would like to suggest stages of work. Where did we start?

We would like to warn you that strict adherence to one stage after another is not necessary. Depending on the age at which work with blocks begins, as well as on the level of development of children, the teacher can combine or exclude some stages.

Stages of learning games with Dienesh blocks

Stage 1 “Acquaintance”

Before moving directly to playing with Dienesh blocks, at the first stage we gave the children the opportunity to get acquainted with the blocks: take them out of the box themselves and examine them, play at their own discretion. Educators can observe such acquaintance. And children can build turrets, houses, etc. In the process of manipulating with blocks, children established that they have different shapes, colors, sizes, and thicknesses.

We would like to clarify that at this stage children become familiar with the blocks on their own, i.e. without assignments or teachings from the teacher.

Stage 2 “Investigation”

At this stage, children examined the blocks. With the help of perception, they learned the external properties of objects in their totality (color, shape, size). Children spent a long time, without distraction, practicing transforming figures, rearranging blocks at their own request. For example, red pieces to red ones, squares to squares, etc.

In the process of playing with blocks, children develop visual and tactile analyzers. Children perceive new qualities and properties in an object, trace the outlines of objects with their fingers, group them by color, size, shape, etc. Such methods of examining objects are important for the formation of operations of comparison and generalization.

Stage 3 “Game”

And when the acquaintance and examination took place, they offered the children one of the games. Of course, when choosing games, you should take into account the intellectual capabilities of children. Didactic material is of great importance. Playing and arranging blocks is more interesting for someone or something. For example, treat animals, resettle residents, plant a vegetable garden, etc. Note that the set of games is presented in a small brochure, which is attached to the box with blocks.

(showing the brochure included with the blocks)

4 Stage “Comparison”

Children then begin to identify similarities and differences between the shapes. The child’s perception becomes more focused and organized. It is important that the child understands the meaning of the questions “How are the figures similar?” and “How are the shapes different?”

In a similar way, children established differences in shapes based on thickness. Gradually, children began to use sensory standards and their generalizing concepts, such as shape, color, size, thickness.

Stage 5 “Search”

At the next stage, search elements are included in the game. Children learn to find blocks according to a verbal task using one, two, three or all four available signs. For example, they were asked to find and show any square.

Stage 6 “Acquaintance with symbols”

At the next stage, children were introduced to code cards.

Riddles without words (coding). We explained to the children that cards would help us guess the blocks.

The children were offered games and exercises in which the properties of the blocks were depicted schematically on cards. This allows you to develop the ability to model and replace properties, the ability to encode and decode information.

This interpretation of the coding of block properties was proposed by the author of the didactic material himself.

The teacher, using code cards, guesses a block, the children decipher the information and find the coded block.

Using code cards, the guys called the “name” of each block, i.e. listed its symptoms.

(Showing cards on the ring album)

Stage 7 “Competitive”

Having learned to search for a figure with the help of cards, the children happily asked each other about the figure that needed to be found, came up with and drew their own diagram. Let me remind you that games require the presence of visual didactic material. For example, “Resettlement of tenants”, “Floors”, etc. There was a competitive element to the block game. There are tasks for games where you need to quickly and correctly find a given figure. The winner is the one who never makes a mistake both when encrypting and when searching for the encoded figure.

Stage 8 “Denial”

At the next stage, games with blocks became significantly more complicated due to the introduction of the negation icon “not”, which in the picture code is expressed by crossing out the corresponding coding picture “not square”, “not red”, “not big”, etc.

Display - cards

So, for example, “small” means “small”, “not small” means “big”. You can enter one cutting sign into the diagram - according to one attribute, for example, “not big” means small. Is it possible to enter a negation sign for all characteristics: “not a circle, not a square, not a rectangle”, “not red, not blue”, “not big”, “not thick” - what block? Yellow, small, thin triangle. Such games form in children the concept of negating a certain property using the particle “not”.

If you started introducing children to Dienesh blocks in the older group, then the “Acquaintance” and “Examination” stages can be combined.

The structural features of games and exercises allow us to vary the possibility of their use at different stages of learning. Didactic games are distributed according to the age of the children. But each game can be used in any age group (complicating or simplifying tasks), thereby providing a huge field of activity for the teacher’s creativity.

Children's speech

Since we work with OHP children, we pay great attention to the development of children’s speech. Games with Dienesh blocks contribute to the development of speech: children learn to reason, enter into dialogue with their peers, construct their statements using the conjunctions “and”, “or”, “not”, etc. in sentences, and willingly enter into verbal contact with adults , vocabulary is enriched, and a keen interest in learning is awakened.

Interaction with parents

Having started working with children using this method, we introduced our parents to this entertaining game at practical seminars. Feedback from parents was very positive. They find this logic game useful and exciting, regardless of the age of the children. We suggested that parents use planar logical material. It can be made from colored cardboard. They showed how easy, simple and interesting it is to play with them.

Games with Dienesh blocks are extremely diverse and are not at all limited to the proposed options. There is a wide variety of different options from simple to the most complex, which even adults are interested in “racking their brains over.” The main thing is that the games are played in a specific system, taking into account the principle “from simple to complex.” Understanding by the teacher the importance of including these games in educational activities will help him use their intellectual and developmental resources more rationally and independently create his own original didactic games. And then the game for his pupils will become a “school of thinking” - a school that is natural, joyful and not at all difficult.

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Games with Dienesha blocks as a means of forming universal prerequisites for educational activities in preschool children PREPARED BY TEACHER ATAVINA NATALYA MIKHAILOVNA Pokachi, April 24, 2015

Objectives: Develop logical thinking. To form an understanding of mathematical concepts. To develop the ability to identify properties in objects. To become familiar with the shape, color, size, and thickness of objects. Develop spatial concepts. Develop the knowledge, skills and abilities necessary to independently solve educational and practical problems. Foster independence, initiative, perseverance; develop cognitive processes and mental operations. Develop creativity, imagination, fantasy Develop the ability to model and design.

Stages of learning games with Dienesha blocks Stage 1 “Acquaintance” to give children the opportunity to get acquainted with the blocks

Stage 2 “Investigation”. For example, red pieces to red ones, squares to squares, etc.

Stage 3 “Game”

4 Stage “Comparison”

Stage 5 “Search”

Stage 6 “Acquaintance with symbols”

Stage 7 “Competitive”

State educational institution of the Samara region, secondary school 5 of the city of Syzran, a structural unit implementing preschool education programs “Kindergarten”
Winter methodological week
Topic of the speech: “Modern technologies in the formation of elementary mathematical concepts in middle preschool age”
Compiled by: teacher of GBOU Secondary School No. 5 SP Preschool Educational Institution No. 29 Gorshunova Galina Mikhailovna
Syzran, 2013
The introduction of state standard education opens up the opportunity to competently and creatively use various educational programs. In our kindergarten they use the “Igralochka” program by L.G. Peterson E.E. Kochemasova.
Many years of experience show that for effective education of children it is important to form their cognitive interest, desire and
the habit of thinking, the desire to learn something new. It is important to teach them to communicate with peers and adults, to engage in joint gaming and socially useful activities, etc. Therefore, the main tasks of the mathematical development of preschoolers in the “Igralochka” program are: are:
Tasks:
1) Formation of learning motivation, focused on satisfying cognitive interests, the joy of creativity.
2) Increased attention span and memory.
3) Formation of methods of mental action (analysis, synthesis, comparison, generalization, classification, analogy).
4) Development of variable thinking, imagination, creative abilities.
5) Development of speech, the ability to give reasons for one’s statements, and build simple conclusions.
6) Developing the ability to purposefully master volitional efforts, establish correct relationships with peers and adults, and see oneself through the eyes of others.
7) Formation of general educational skills (the ability to think and plan one’s actions, make decisions in accordance with given rules, check the results of one’s actions, etc.).
I solve these problems in the process of familiarizing children with different areas of mathematical reality: with quantity and counting, measuring and comparing quantities, spatial and temporal orientations. I don’t give a new building to children in a finished form, it is comprehended
them through independent analysis, comparison, and identification of significant features. Thus, mathematics enters children’s lives as a “discovery” of regular connections and relationships in the world around them. I lead children to these “discoveries”, organizing and directing their search activities. So, for example, I suggest that children roll two objects through the gate. As a result of their own objective actions, they establish that the ball rolls because it is “round”, without corners, and the corners prevent the cube from rolling.
The leading activity for preschoolers is play. Therefore, classes are essentially a system of didactic games, during which children explore problem situations, identify significant signs and relationships, compete, and make “discoveries.” During these games, personality-oriented interaction between an adult and a child and between children and their communication in pairs and groups takes place. Children do not notice that learning is going on - they move around the room, work with toys, pictures, balls, LEGO bricks... The entire system of organizing classes should be perceived by the child as a natural continuation of his play activity.
The saturation of the educational material with game tasks determined the name of the manual - “Igralochka”.
In the program I pay great attention to the development of variable thinking and creative abilities of the child. Children not only explore various mathematical objects, but come up with images of numbers, numbers, and geometric shapes. Starting from the very first lessons, they are systematically offered tasks that allow for various solutions. In preschool age
emotions play perhaps the most important role in personality development. Therefore, a necessary condition for organizing an educational field with children is an atmosphere of goodwill, creating a situation of success for each child. This is important not only for the cognitive development of children, but also for preserving and supporting their health.
Since all children have their own unique qualities and level of development, it is necessary for each child to move forward at his own pace. The mechanism for solving the problem of multi-level learning is the approach formed in didactics on the basis of the ideas of L.S. Vygotsky about the “zone of proximal development” of a child.
It is known that at any age, every child has a range of tasks that he can handle on his own. For example, he washes his hands himself and puts away toys. Outside this circle are matters that are accessible to him only with the participation of an adult or are inaccessible at all. L.S. Vygotsky showed that as a child develops, the range of tasks that he begins to perform independently increases due to those tasks that he previously performed together with adults. In other words, tomorrow the baby will do on his own what he did today with the teacher, with his mother, with his grandmother...
Therefore, I work with children in this course at a high level of difficulty (that is, in the zone of their “proximal development”, or “maximum”): I offer them, along with tasks that they can complete independently, and tasks that require them to guesses, ingenuity, observation. Solving them creates in children the desire and ability to overcome difficulties. IN
As a result, all children without overload master the “minimum” necessary for further advancement, but at the same time the development of more capable children is not hampered.
Thus, the basis for organizing work with children in this program is the following system of didactic principles:
- an educational environment is created that ensures the removal of all stress-forming factors of the educational process (the principle of psychological comfort);
- new knowledge is not introduced in a ready-made form, but through the independent “discovery” of it by children (principle of activity);
- it is possible for each child to progress at his own pace (minimax principle);
- with the introduction of new knowledge, its relationship with objects and phenomena of the surrounding world is revealed (the principle of a holistic view of the world);
- children develop the ability to make their own choices and are systematically given the opportunity to choose (the principle of variability);
- the learning process is focused on children acquiring their own experience of creative activity (the principle of creativity);
- continuous connections are ensured between all levels of education (the principle of continuity).
The principles outlined above integrate modern scientific views on the foundations of organization
developmental education and provide solutions to the problems of intellectual and personal development of children.
The “Igralochka” program is methodologically supported by the following benefits:
1) L.G. Peterson, E.E. Kochemasova. "Player". Practical mathematics course for preschoolers 3 - 4 and 4 - 5 years old (methodological recommendations). -M., Yuventa2010.
2) L.G. Peterson, E.E. Kochemasova. Notebooks “Playing Game”, parts 1-2. Additional material for the practical course “Playing Game”. - M. Yuventa 2010.
The practical course “Igralochka” contains methodological recommendations for educators and parents on organizing activities with children. Their volume and content can be adjusted in accordance with specific working conditions, the level of training of children, and the characteristics of their development.
It should be emphasized that the formation of mathematical concepts is not limited to one area of ​​education, but is included in
the context of all other activities: games, drawing, applique, construction, etc.
When getting acquainted with numbers, I use Marshak’s poems “Numbers.” To reinforce forward and backward counting, I use V. Kataev’s fairy tales “The Flower of the Seven Flowers,” “Snow White and the Seven Dwarfs,” and various games, for example: “A Walk in the Forest.” (Children use triangles to depict (green and white, fir tree and birch) count, compare, establish equality. I create difficulties in a game situation: a talkative magpie lived in the forest, she did not believe that there were equal numbers of fir trees and birches. Children lay out the squares (magpies) over fir trees and birches.
When introducing colors and shades, I use the games “Draw a story” (lay out the picture using multi-colored circles), “Dress up a Christmas tree” (correlate Christmas trees and toys), “Compote” (I use two jars, one jar contains light red compote, and the other is dark red). I'm dropping off the kids
To discover it yourself, I suggest you cook the compote yourself.
To reinforce the concept of “long” and “short”, I create a motivational situation, the game “Shop”. The ribbons are mixed up in the store; you need to sort them by length from longest to shortest.
To get acquainted with spatial concepts (on-above-under, above-below, left-right, top-bottom, wider-narrower, wider-narrower, inside-outside)): I play the following games: “Gift for the hare” (take it to the right hand a large carrot, and in the left hand a small one, give it to the bunny), “The Tale “Turnip” (reinforcing the concept of “in front”, “behind”, “Blankets” (pick up a blanket for the bunny and the bear, introduce the concept of wide-narrow), “Squirrel" (children pick mushrooms and berries, and at the signal “night” they stand in the hoop (inside).
To form the concept of rhythm, I use the seasons (sequence), the games “Artists” (lay out squares alternating by color), “In different rhythms” (move to music in a certain rhythm).
To introduce children to the concept of “Couple,” I use the game “Getting ready for the skating rink” (children list what needs to be dressed and taken in pairs), children conclude that there are things that are only used together.
I also introduce children to geometric shapes: square, circle, oval, rectangle, square, triangle;
geometric bodies: cube, cylinder, cone, prism, pyramid.
To do this, I use the game situation “Shop” (they find objects of geometric shapes), “Rectangle and square”, “Unusual kindergarten” (familiarity with the cone), “Find a passport” (they match geometric bodies to the card).
For individual work, it is convenient to use situations of dressing, walking, preparing for dinner. For example, you can ask a child how many buttons are on his shirt, which of two scarves is longer (wider),
what is more on the plate - apples or pears, where is the right mitten and where is the left, etc.
In my work I use physical education lessons: “Relaxing in the forest” (children lie on the carpet looking at various bugs), “Wild and domestic animals” (depict the movements and voices of various animals), “Bicycle” (lying on their back imitate the movements of riding a bicycle), and etc. thematically related to tasks.
This allows you to switch children’s activity (mental, motor, speech) without leaving the learning situation. It is advisable to learn funny poems and rhymes for physical education minutes in advance. They can also be used during walks, during the day in a group to relieve stress and switch to another activity.
“Igralochka” notebooks provide additional material for individual work with children. They are not intended to be used in educational activities - they are intended for joint work between children and parents, or in individual work that is carried out during the week.
The notebooks are bright, with interesting pictures, so once they get into the baby’s hands, they run the risk of being painted over and looked at from start to finish.
Work on the notebook should begin when the baby is not very excited and is not busy with any interesting activity: after all, he is offered to play, and playing is voluntary!
First you need to look at the picture with him, ask him to name objects and phenomena known to him, and talk about unknown ones. In no case should you rush or stop the baby - each child should work at his own pace.
You cannot immediately explain to the baby what and how he should do. He should try it himself! By his non-interference, the adult seems to be telling the child: “You’re all right! You can do it!
You need to be patient and listen to even the most, at first glance, absurd proposals of the baby: he has his own logic, you need to listen to all his thoughts to the end.
You should not insist that the child complete all the tasks on the worksheet at once. If the baby loses interest, you need to stop. But it is better to complete a task that has already begun, motivating it in a way that is meaningful for the child. For example: “The cockerel will be upset if one of his wings is not painted, because they will laugh at him,” etc.
Methodological manual for the development of mathematical concepts
Notebooks "Igralochka", parts 1-2 are an additional aid to the course "Igralochka" for children 3-4 and 4-5 years old.
They present material that allows you to consolidate and expand knowledge of the “Igrachka” program in the individual work of children with parents or educators.
Educational and methodological manuals “Igralochka” for the development of mathematical concepts of children 3-4 and 4-5, respectively, is the initial link of the continuous mathematics course “School 2000...”. They contain a brief description of the concept, program and conduct of classes with children in accordance with the new requirements for the organization of the educational field “Cognition” according to the didactic system of the activity method “School 2000...”.

Thesaurus Mathematical thinking - if a person knows how to build any model of the concept being studied and describe it in mathematical language, then he has what we call mathematical thinking. Intellectual (mathematical) readiness is the achievement of a sufficient level of maturity of cognitive processes (memory, perception, thinking, imagination, speech) to begin systematic learning, and the child’s mastery of a certain amount of knowledge within the scope of the program.

Non-standard means are those means, problems for which the mathematics course does not have general rules and regulations that determine the exact program for their solution. A non-standard means, the task acts as a problematic one. Unconventional means are problems for which the solution algorithm is unknown (Friedman)

Entertaining mathematical material is a means of complex influence on the development of children, with the help of which mental and volitional development is carried out, and problems in learning are created. This is one of the means that promotes the development of MP in children. This is a means of developing mental activity techniques. Entertaining is a synonym for something interesting that can attract attention.

Mathematical games are those that use mathematical methods or similar pre-mathematical ones (B.A. Kordemsky) Mathematical tools are potential models of those mathematical concepts and relationships that a preschooler is introduced to. A mathematical model is a description of a phenomenon or process that takes place in reality using mathematical structures (numbers, equations)

Pedagogical requirements for entertaining mathematical material Diversity Use in a system that involves gradual complication Combination of direct teaching methods with the creation of conditions for independent search for solutions Meet different levels of general and mathematical development of the child Combination with other teaching tools for FEMP

Teaching aids for FEMP in preschool children are a variety of didactic games: board-printed and with objects; training developed by A. A. Stolyar; developmental, developed by B. P. Nikitin; checkers, chess; entertaining mathematical material: puzzles, geometric mosaics and constructors, labyrinths, joke problems, transfiguration problems, etc. with the application of samples where necessary (for example, the game “Tangram” requires samples, dissected and undivided, contour ), visual instructions, etc.; separate didactic tools: 3. Dienesha blocks (logical blocks), X. Kusener sticks, counting material (different from what is used in the classroom), cubes with numbers and signs, children's computers and much more; books with educational and cognitive content for reading to children and looking at illustrations.

Entertaining mathematical material for working with preschoolers: geometric constructors: “Tangram”, “Pythagoras”, “Columbus Egg”, “Magic Circle”, etc., in which from a set of flat geometric figures you need to create a plot image based on a silhouette, contour pattern or design; logical exercises that require inferences based on logical diagrams and rules; tasks to find a sign(s) of difference or similarity between figures (for example, “Find two identical figures”, “How do these objects differ from each other?”, “Which figure is the odd one here?”); tasks to find a missing figure, in which, by analyzing object or geometric images, the child must establish a pattern in the set of features, their alternation and, on this basis, select the necessary figure, completing the row with it or filling in the missing space; labyrinths - exercises performed on a visual basis and requiring a combination of visual and mental analysis, precision of actions in order to find the shortest and correct path from the starting point to the final point (for example, “How can a mouse get out of a hole?”, “Help the fishermen untangle the fishing rods”, "Guess who lost the mitten"); entertaining exercises for recognizing parts as a whole, in which children are required to determine how many and what shapes are contained in the drawing; entertaining exercises to restore a whole from parts (assemble a vase from fragments, a ball from multi-colored parts, etc.); ingenious tasks of a geometric nature with sticks, from the simplest to reproducing a pattern, to drawing up object pictures, to transfiguration (changing a figure by rearranging a specified number of sticks); riddles that contain mathematical elements in the form of a term denoting quantitative, spatial or temporal relationships; poems, counting rhymes, tongue twisters and sayings with mathematical elements; tasks in poetic form; joke tasks, etc.

Non-traditional mathematical tools Mathematical games (“Tic-tac-toe”, “Five in a row”, “Nim”, “Skittles” (Wythoff’s game), “Star Nim”) Mathematical puzzles (Rubik’s cube, “Magic rings”, “Hole games” "(tags), plane figures - silhouettes of geometric shapes, ancient puzzles, arithmetic, etc.) Combinatorial problems ("Game 15", "Rubik's Cube", maneuvering problems, rearranging checkers, "Tower of Hanoi") Arithmetic puzzles , games - puzzles with matches, topological puzzles Origami in FEMP for preschoolers

Combinatorics is a branch of mathematics that studies the question of how many different combinations, subject to certain conditions, can be made from given objects. Modeling is the construction of copies, models, phenomena and processes used to systematize images.

In how many ways can Petya, Vasya, Galya, Sveta and Marina be seated so that Petya is in the middle? (24) In how many ways can Petya, Vasya, Galya, Sveta and Marina be seated so that Petya and Vasya are not next to each other? (72) In how many ways can Petya, Vasya, Galya, Sveta and Marina be seated so that Sveta is not second from the left? (96)

Educational games by B.P. Nikitin Each educational game by Nikitin is a set of problems that the child solves with the help of cubes, bricks, squares made of wood or plastic, parts of a mechanical designer, etc. Tasks are given to the child in various forms: in the form of a model, a flat drawing, an isometric drawing, a drawing, written or oral instructions, etc., and thus introduce him to different ways of transmitting information. The tasks are arranged approximately in order of increasing difficulty, i.e. they use the principle of folk games: from simple to complex.

Logical blocks of Dienesh Logic blocks of Dienesh are a set of 48 geometric shapes: a) four shapes (circles, triangles, squares, rectangles); b) three colors (red, blue and yellow figures); c) two sizes (large and small figures); d) two types of thickness (thick and thin figures).

How can you play with Dienes blocks? Games with Dienesha blocks for the little ones Invite your child to start with the simplest games: 1) Try to find all the shapes like this one by color (by shape, by size, by thickness). 2) Find shapes that are different from this one by shape (size, thickness, color). 3) Treat Bear with red “candies” - large, square, thick, triangular, small, etc. 4) Place three pieces in front of the child. Invite your baby to close his eyes and remove one of them. What kind of “candy” did Mishka eat? 5) As in the previous game, we lay out three blocks. The child closes his eyes, and we swap the parts. What changed? 6) Game - what is superfluous. Lay out three figures - 2 are common according to some principle, one is not. Ask your child what is unnecessary here? 7) We make pairs (mother and baby, for example). The big one is looking for a small part, the red circle is looking for a red part. 8) Place the blocks in an opaque bag and look for the desired figure by touch.

We play with older children Game “Search” To complicate the task, invite the child to find figures that are the same as this one in color, but of a different shape, or the same in shape, but of a different size. Game "Snake" Place any figure. Build a long row from it, like a snake. Options for constructions can be as follows: We build so that neighboring figures are not repeated (in color, size, thickness). Adjacent figures should not be repeated based on two characteristics - color and size, for example. Adjacent blocks must be the same size and color, but different shapes. Game “Floors” We lay out several figures in a row - 4-5 pieces. These are the residents of the first floor. Now we build the second floor of the house so that under each figure of the previous row there is a piece of a different color (or size, shape). Option 2: part of the same shape, but a different size (or color). Option 3: we build a house with other details in color and size. Game "Dominoes" This game can be played by several participants at the same time (but no more than 4). We divide the blocks equally between the players. Everyone makes a move in turn. If there is no piece, you need to skip a move. The winner is the one who lays out all the pieces first. How to walk? Shapes of a different size (color, shape). Shapes of the same color but a different size or the same size but a different shape. Figures of a different size and shape (color and size). The same shapes in color and shape, but of a different size. We walk with figures of a different color, shape, size, thickness.

V. Voskobovich and his “Fairytale Labyrinths” According to the educational tasks they solve, all Voskobovich’s games can be divided into 3 groups: - games aimed at logical and mathematical development. The purpose of these games is to develop mental operations, and game actions are to manipulate numbers, geometric shapes, and properties of objects. - games with letters, sounds, syllables and words. In these games, the child solves logical problems with letters, composes syllables and words, and engages in word creation. - universal game educational tools. They can be material for games and teaching aids. Game-based learning tools create comfortable conditions for the teacher’s work and bring pleasure to children.

“Voskobovich Square 2-color” By folding the “Square” along fold lines in different directions, the child constructs geometric and object figures according to a diagram or his own design. You can check the folding options. Recommended age 2-5 years Composition: Thick cardboard triangles are glued to a square fabric base (140x140 mm) at some distance from each other. One side of the “Square” is red, the other is green. Colored operational diagrams for adding 19 figures. What develops is the ability to navigate the shape and size of geometric figures, spatial relationships; - the ability to construct planar and three-dimensional figures using a step-by-step diagram or your own design; - attention, memory, spatial and logical thinking; - imagination, creativity; - fine motor skills of hands. Description By folding the “Square” along the fold lines in different directions, the child constructs geometric and object figures according to a diagram or his own design. Folding options

Examples of games with Cuisenaire sticks 1. Mix the sticks on the table. Ask to show orange, red, blue, etc. in turn. 2.Name the color of the shortest and longest stick. 3. Show neither blue nor orange. 4. Collect sticks of the same color and build a house out of them. 5. Connect a short and a long stick together, ask which one is long and which is short. 6. Find sticks equal in length. 7. Arrange the sticks in ascending order - from the shortest to the longest and vice versa. 8. Guess what. Place the sticks in a row. The child wishes for one stick. You ask questions: is this stick shorter than the red one? Is it longer than the yellow one? By the method of elimination, you can guess which stick we are talking about. 9.Make one stick from blue and red so that the blue one is on the left (right). 10.Build a tower out of sticks. Which stick is lower than the orange one, higher than the red one? 11. The white stick is a unit. Move another one towards it so that they form one whole. You need to find a stick that would be equal to the length of the two combined ones. 12.You name the number, the child finds the stick. 13. Show how you can add - add one stick to another. Subtract - take one from two. 14. What sticks can be used to make an orange one? 15. What three are needed to make a black one? 16. Will you be able to make orange out of four? 17. What sticks can be used to make the number 10? 18. Lay out two tracks, yellow and red - which track is longer? Briefly speaking? 19.Find everything shorter than purple. 20. Lay out one train from a blue stick, the second from a black one. What two sticks need to be attached to a short train so that it becomes as long as a long train. 21. Orange and yellow - one train, red and purple - another, how to equalize the trains? 22. Make geometric shapes from sticks.