Organization of classes on mathematical development in preschool educational institutions

Developing mathematical knowledge is not just learning to count

We live in an age of technology. Mathematical knowledge and much related to the exact sciences are needed for everyday life. It's not even a matter of:

• be able to count (minimum);
• know complex mathematical formulas by heart (maximum).

The general concept of the development of mathematical abilities in preschool children is presented in the works of researcher A.V. Beloshistaya. The author explains what we should mean in the words “development of mathematical abilities.” These are skills that will invariably come in handy to:

• be able to look for new solutions;
• deeply understand the essence of a phenomenon or fact;
• build logical connections;
• see the problem as a whole.

Agree, a lot! According to Beloshistaya, math classes in kindergarten should develop the child intellectually. And also prepare him to understand mathematical and logical information at school. Preparation – work with both motor skills and the development of logical structures.

Mathematics gives not just knowledge, but develops a special style of thinking. This science provides enormous potential for the formation of intelligence from kindergarten age. There is no time to waste; the most important mental logical structures are organized at the age of 5-11. This means that emphasis should be placed on mathematics from the senior group of kindergarten. But it is possible earlier.

There are games and activities that teach children to direct their thinking in a logical direction from the age of 2-3. A child may still speak poorly, but can already solve intellectual problems (for his age). The book “Formation of elementary mathematical concepts in kindergarten” suggests studying with children 2-7 years old. It offers methods and examples of classes. The book appears and disappears in the “Labyrinth” - you need to have patience to “catch it”.

For the middle group (4-5 years old) there is a publication entitled “Formation of elementary mathematical concepts” . It contains tasks and game exercises, you can directly take them and use them. The main part of the literature devoted to the development of mathematical thinking is designed for 5-6-7 years, we will return to it.

Kindergarten teachers are given an important task - to awaken interest in mathematics. This can be done through entertaining gaming activities. The process will not go far without self-education at home. There is an endless field of activity for parents here.

Theory and methodology of conducting mathematics classes

Toddlers lack abstract thinking, but mathematics is accessible to children using actions and imaginative thinking. How to implement this in practice is described below.

Classes in the senior group of preschool educational institutions on painting jugs

Geometry lesson notes

When teaching mathematics, the teacher needs to introduce children to abstract concepts in a fun way and teach them how to use them. An example of an activity with the help of which this problem can be solved in the middle and senior groups is given below.

The purpose of such a children's mathematics lesson is to give children basic knowledge of geometry. To increase interest in studying mathematics at 3-4 years old or at an older age, the environment for children’s research activities is recreated, parallels are drawn between the sphere of mathematical knowledge and real life.

Girl at the blackboard

When planning how to teach a child mathematics, it is necessary to ensure the solution of the following problems:

• Children are helped to understand that the essential features of figures do not depend on their size or specific spatial location.
• At the age of 4+, they are instilled with the ability to be mathematically vigilant. At the same time, they are taught to compare objects not only by their appearance, but also by their geometric shape. In particular, they learn to find objects in their immediate environment that are similar or different in geometric shape.
• Kids can learn to design a shape based on its description.
• They teach how to create thematic compositions of figures.
• At the age of 4-5, mathematical thinking abilities are taught.
• They instill the skills of competent logical thinking and teach how to correctly build logical reasoning.
• At 6-7 years old, the connection between abstract mathematical knowledge and productive activity is explained. The kids are explained how to use the knowledge gained in the lessons and apply it usefully in practical life.

The type of lesson is educational and research.

Preparation

To complete the tasks you will need the following materials:

• ball;
• phonogram with recorded music for physical education;
• set of geometric shapes;
• cards depicting the planets of the solar system;
• checkered sheets of paper;
• Every child needs a simple pencil.

For the lesson you will need the following: a computer, an interactive whiteboard and a projector.

It is necessary to carry out preliminary preparation for the lesson. For physical education, you will need to study basic movements in advance. Children, under the guidance of a teacher, will have to tactilely explore the prepared geometric shapes. It is recommended to provide viewing of educational films on the topic “Geometry”. It is necessary to read aloud the fairy tale by N.B. Sytova “How geometric figures built a city.” The collective application “City of Geometric Shapes” is being performed.

Note! The stages of the lesson are presented below.

Start

At the first stage, the teacher asks the kids whether they like to travel. They confirm this. Next, we discuss with them the place they would like to see.

The children are asked the riddle “The peas scattered on a thousand roads.” They guess - “stars”.

The teacher invites everyone to fly to the moon and is interested in what its geometric shape is. Invites the children to draw a rocket and asks them to tell what shape it has. Offers to give examples of objects that have a similar shape.

The teacher says that everyone will ride on a lunar rover and chooses a driver using a counting rhyme.

Main content of the lesson

Various celestial bodies and their shapes are discussed next.

Based on the flight material, they explain that the problem has conditions and it is necessary to obtain an answer. Various types of number problems are discussed.

They look at the lunar landscape and see mountains and craters. Compare them with figures. Children are offered geometric shapes and told that these are moon rocks. Everyone must name the form of their find.

Final part

The journey ends, the children fly home. Then there is a physical training session. At the same time, they sing a song on a geometric theme and make movements learned in advance.

What is the artistic and aesthetic development of preschool children

Finally, children are asked to choose a geometric figure. Then the teacher explains the meaning of each of them.

At the end, the teacher talks about what the children learned during this lesson.

Geometric figures

Useful materials for mathematics in kindergarten

The following can be used as handouts:

• Working cards for teaching counting. They are divided into 10 cells. Each of them shows one of the first ten numbers and the corresponding number of toys.
• Cards with lines of 10 cells. There may be 5-7 or more. In each line the same pictures are drawn, in different lines the pictures are different. When working, they are cut into squares and used as material for teaching counting. Such manuals can be printed from a computer.
• Works of children's literature that touch on mathematical topics can be used.
• Three-dimensional geometric shapes will help kids better understand the features of mathematical concepts and prepare for school.

Creating a suitable environment for children for creative activity and a thoughtful approach to classes will develop their abilities and get them interested in mathematics.

You don't have to understand how it works. The main thing is to do

The fact that mathematical and logical knowledge must be taught on time has become clear long ago. That is why preschool educational institutions spend so much time on mathematics. This discipline teaches you to think logically and not be afraid to use flexible thinking. The goal of a math program for preschool children is to teach them to grasp relationships and dependencies. And also create designs from objects, words and signs.

System is very important in learning. It is presented in this manual . If you don’t have time to systematize your knowledge, you can take ready-made workbooks for the appropriate age and start studying from them. You don’t even need to particularly understand the theory – you just have to do it. Parents and teachers will be helped by workbooks for 5-6 years old, compiled by Kondratyeva:

• "Math games in pictures for 5-6 years old" . General exercises are given, as well as tasks for the prevention of dyscalculia (impaired counting skills).
• "Counting and comparing numbers within ten" . The goal is the same, the tasks are different.
• . ” All three books are suitable for parents and educators who want to develop children.

Bortnikova produced a good notebook. The publication for 4-6 years old is called “Getting Ready for School. Development of mathematical abilities" . It introduces preparatory group students to geometric shapes, numbers, simple operations, and teaches comparison. The author has many other good books. For example, “Fun puzzles” for the little ones. She will interest younger children with bright pictures and rhymes.

Books by Yulia Glagoleva aimed at intellectual development are popular. The publications include quite complex tasks. From the book “Development of mathematical abilities. 1-2 grades. Federal State Educational Standard" parents sometimes try to give something to older preschoolers. But often it’s too early for them. And from a similar publication for grades 3-4 - even more so. But remember these manuals, they will be useful to schoolchildren.

Introducing mathematics in a playful way

For a child, everything in the world is a game. And the game is both study and work, and a way of understanding reality. It needs to be included in the educational process. That is, to lead, direct, organize. Thus, it is possible to influence different aspects of the personality: in total, sensations, consciousness, will and behavior.

Children enjoy play activities as a process. Teachers and parents have a different goal. They need to develop a preschooler, put certain knowledge into his head, and develop personal qualities. Didactic games and exercises are especially useful. They provoke relaxed interaction between participants and teach them how to communicate.

Board games are very helpful in forming ideas about forms, sequences, contradictions and other things. They save you right away. You can make cards for such games yourself. But there are ready-made game sets, they are bright and cost a penny. This is for example:

• lotto “Logical tables” for 3-6 years;
• games like “What’s extra?” (there are many options, for example this one from 3 years old and this one for 4-7 years old );
• funny toy “Whose cat is bigger?” to compare numbers;
• "Find a similar figure";
• "Katamino" (mini road version) develops spatial thinking.

Methodological development: “Organization of work on FEMP in preschool age”

Organization of work on FEMP in preschool age

Organization of work on FEMP in preschool age

The most important means of shaping preschoolers

high mathematical culture, intensification of mathematics learning is the effective
organization
and management of educational activities
of preschoolers
in the process of solving various mathematical problems.
Teaching children mathematics in preschool age
contributes to the formation and improvement of intellectual abilities: logic of thought, reasoning and action, flexibility of the thought process, ingenuity and ingenuity, and the development of creative thinking.

What general didactic principles underlie the FEMP

?

Systematicity (knowledge is given to children in a strictly defined system, and at the same time new material must be accessible to children.)

Sequence (each new large software task is divided into smaller ones)

- geometric figures

Graduality (when moving from one program task to another, it is very important to constantly return to the material covered. This ensures correct assimilation of the material.)

Individual approach (it is necessary to take into account the abilities of each child and, based on this, select the necessary tasks)

During GCD according to FEMP

a number of software problems are solved.
Which? (Statements from teachers)
. Let's understand these tasks.

1) educational - what we will teach the child (teach, reinforce, exercise,

2) developing – what to develop, consolidate:

- develop the ability to listen, analyze, the ability to see the most important, essential, development of awareness,

— continue the formation of logical thinking techniques (comparison, analysis, synthesis)

.

3) educational - what to cultivate in children (mathematical ingenuity, intelligence, ability to listen to a friend, accuracy, independence, hard work, a sense of success, the need to achieve the best results,

4) speech - work

over the active and passive vocabulary precisely in mathematical terms.

The main mistakes encountered during educational activities on FEMP

:

Verbosity, inaccuracy in asking questions.

Monotony of visual material and tasks.

Incorrect placement of material.

The use of unaesthetic visual material that does not meet pedagogical requirements.

In order for educational activities to give good results for GCD, it is necessary to carefully prepare:

- think over the program content and correlate it with the level of development of children, with the level of their knowledge,

- choose a VARIETY of materials,

— think over forms of organizing children’s activities

The entire lesson on FEMP

is based on clarity. What does it mean to make learning visual?

The teacher must remember that visibility is not an end in itself, but a means of learning. Poorly selected visual material distracts children’s attention and interferes with the acquisition of knowledge; correctly selected visual material increases the effectiveness of learning.

We use two types of visual material:

- demonstration material that is used on a flannelgraph, on a magnetic board, etc.

- handout, small material that is distributed to each child.

Both demonstration and handout materials must be artistically designed and meet aesthetic requirements: attractiveness is of great importance - it is more interesting for children to play with beautiful aids. And the brighter and deeper children’s emotions are, the more complete the interaction of sensory and logical thinking is, the more intense the OD is, and the more successfully children acquire knowledge.

There should be enough material for each child + spare material. The material should be different for each lesson. The material should be understandable to children (a hare should be a hare, a cone should be a cone, a carrot should be a carrot)

Benefits need to be selected according to each other (squirrels - cones, hares - carrots, flowers - butterflies, etc.)

In order for a child to learn the material well, the teacher himself must have excellent command of his speech (precision of phrases, expressions, formulations)

.

Speech must be literate in both grammar and mathematics.

The speech of both the teacher and the child should be precise, concise, clear, clear (less “water”)

. In this case, the OA is fast and interesting.

Please tell me what teaching methods are used in FEMP

?
(Answers from educators)
That’s right, game, visual, verbal, practical teaching methods...

The verbal method in elementary mathematics does not occupy a very large place and mainly consists of asking questions to children.

The nature of the question depends on age

and on the content of a specific task.

- at a younger age - straight

, specific questions: How much? How?

- in the older years - mainly search engines: How can this be done? Why do you think so? For what?

Practical methods - exercises, game tasks, didactic games, didactic exercises - are given a large place. The child must not only listen and perceive, but must also participate in performing a particular task. And the more he plays didactic games and completes assignments, the better he will learn the material on FEMP

. In accordance with FGT, the main activity in kindergarten is play. GCD, which takes place in an entertaining way, in the form of a game, is absorbed by children faster and easier. Therefore, the gaming method should be predominant.

Didactic games can be classified according to educational content, cognitive activity of children, game actions and rules, organization

and the relationship of children, according to the role of the teacher:

1. Travel games reflect real facts, revealing the ordinary through the unusual, the purpose of which is to enhance the impression through the fabulous unusualness;

2. Sentence games: “What would happen?”

,
"What would I do?"
;

3. Riddle games with intricate descriptions that need to be deciphered;

4. Conversation games (dialogues based on communication between the teacher and the children, the children with him and with each other with the special nature of play-based learning and play activities.

Using games, teachers teach children to transform equality into inequality and vice versa - inequality into equality. Playing educational games such as “Which number is missing?”

,
“Confusion”
,
“Correct the mistake”
,
“Name the neighbors”,
children learn to freely operate with numbers within 10 and accompany their actions with words.
Didactic games such as “Make up the numbers”
,
“Who will be the first to name which toy is missing?”
and many others are used in classes to develop children's attention, memory, and thinking.
In the older group, children are introduced to the days of the week. They explain that each day of the week has its own name. In order for children to better remember the names of the days of the week, they are designated by a circle of different colors. Children are offered games to reinforce the names of the days of the week and their sequence. For example, the game “Live Week”
.
For the game, 7 people are called to the board, the teacher counts them in order, gives them circles of different colors, indicating the days of the week. Children line up in the same order as the days of the week. A variety of didactic games are also used : “Days of the week”
,
“Name the missing word”
,
“All year round”
,
“Twelve months”
, which help children quickly remember the names of the months and their sequence.

Children are taught to navigate in specially created spatial situations and determine their place according to a given condition. Children freely perform tasks like: “Stand so that there is a closet to your right and a chair behind you. Sit so that Tanya sits in front of you, and Dima sits behind you.” With the help of didactic games and exercises, children master the ability to determine in words the position of one or another object in relation to another: “There is a hare to the right of the doll, a pyramid to the left of the doll.”

etc. To consolidate knowledge about the shape of geometric shapes, children are asked to look for the shape of a circle, triangle, square in surrounding objects.
For example, they ask: “What geometric figure does the bottom of the plate resemble?” (surface of table cover, sheet of paper)
.

The use of didactic games increases the effectiveness of the pedagogical process; in addition, they contribute to the development of memory and thinking in children, having a huge impact on the mental development of the child.

In preschool

In institutions, teachers accumulate interesting experience
formation
of elementary mathematical concepts in children using didactic aids that are widely used throughout the world. These are logical blocks and sticks of X. Kusener, 3. Dienesh, which are a set of volumetric or flat geometric bodies. Each block is characterized by four properties: shape, color, size, thickness.

For example, on the card the sequence of block chains is indicated using symbols. In accordance with the indicated pattern, children lay out chains: after the green block comes red, then blue and again green. The winner is the one who makes the longest chain and makes no mistakes in the sequence of colors.

X. Kusener's rods allow you to simulate a number. This didactic material is a set of sticks in the form of rectangular parallelepipeds and cubes. All sticks differ from each other in size and color. This material is sometimes called "color numbers"

. By laying out multi-colored rugs from sticks, building a ladder, the child gets acquainted with the composition of a number from ones, from two smaller numbers, performs arithmetic operations, etc.

Work practice

convinces of the need to use such didactic material, confirms the increase in
work
when using entertaining mathematics.

Conclusion

Maximum effect in realizing the capabilities of a preschool

is achieved only if learning is carried out in the form of didactic games, direct observations and subject lessons, various types of practical activities, but not in the form of a traditional school lesson.
FEMP
GCD entertaining and unusual, to turn it into a realm of ingenuity, imagination, play and creativity.

And now, following the ancient proverb: “I hear and I forget, I see and I remember, I do and I understand”

, I urge all teachers to do this - to introduce into the practice
of working with children the best
that has been created by pedagogical science and practice.

Examples of games for developing mathematical concepts

It is not necessary to buy game and educational sets to train structural thinking. You can use available tools: counting sticks, checkers, felt-tip pens and paper.

1. Counting sticks will help preschoolers become familiar with the concept of shape. Simple and complex figures are built from the set, which are then easily transformed into each other. But to transform, you need to understand how. For example, from 5 sticks you can make two identical triangles. And from one on the table - one triangle (put it on the corner).
2. What if you invite your child to draw a problem? He must come up with a plot, draw it and explain his problem. It just seems simple, but in reality it’s not very simple. This game develops creative thinking, imagination and invention. Kids learn to invent and express their thoughts.
3. A simple and exciting game - checkers, preschoolers play with pleasure. Such activities teach you to plan moves, think abstractly, and develop ingenuity. Children who win at checkers often do better in school (our common humble observation). The game can be turned into a family hobby, and it will only bring benefits.

Mathematical riddles will help you master terminology

Another good thing is math-themed riddles. They teach kids independence and perseverance. After all, you often need to not just say the answer, but prove it. The beauty of riddles is that they teach you to use mental operations (synthesize, analyze, compare, generalize). Here are examples of riddles:

I am a dash in grammar, and who am I in mathematics? (Minus)

I have no corners, And I look like a dish, Like a plate and a lid, Like a ring and a wheel. (Circle)

The cunning brothers live in a difficult book. There are ten of them, but these brothers will count everything in the world. (Numbers)

There are also humorous puzzles that teach you to look for answers outside the box. For example: “You and I, and you and me, how many of us are there in total?” (2). “How many ends does the stick have, two, two and a half?” (in the latter case – 6).

Other games for logic and mathematics

Here are a couple of games that will allow preschool children 5-7 years old to get used to numbers. And also - they will consolidate quantitative ideas. You can make a set for classes yourself; these are cards with numbers and colored circles.

1. What number escaped? We take several sets of cards with numbers from 0 to 10 and divide the guys into pairs. First, the couple puts the cards in order. Then one of the players closes his eyes, and the second rearranges several cards. When the first one opens his eyes, he should find changes. If found correctly, it starts leading. To make it more difficult, you can offer cards from 0 to 20 or from 10 to 20.
2. Find a pair. The game is fun and noisy, so don’t disturb the kids from running around and having fun. We prepare cards with numbers and the corresponding number of circles. We divide the children into 2 teams. We lay out inverted number cards on one table, and with circles on the other. We invite the children to run around and then, at a signal, take cards from the tables. And after that, find a pair: if there is a number on the card, you need to find a child with a card with the same number of circles.

The first game was about seriation - building an ordered series. Rows can be organized according to different criteria: size, length, height, color. You can use pebbles, ribbons, dolls, sticks - literally anything that is at hand at a certain moment.

Synthesis games are very interesting - combining different objects according to a certain characteristic. For example, these are tasks where you need to choose:

• red balls;
• red, but not balls;
• round, but not balls;
• all the balls;
• the largest green ball (two characteristics are combined here - color and size, this is more complicated).

You can play with objects or cards. Another option is to offer to choose a different figure from a range. Or find three triangles in the picture. All these are also synthesis problems.

Another logical technique is comparison. To compare, you need to learn to concentrate on one feature and abstract from others. Let's say these are tasks like “choose the big yellow one”, “choose the big round one”, etc. Moreover, it is easier for kids to first learn the differences and then the similarities.

"Dividing a set into parts and combining the parts into a whole group"

Mathematics PR

Topic: “Dividing a set into parts and combining parts into a whole group”

Purpose: To practice dividing a set into parts and combining parts into a whole group; improve the ability to establish a relationship between a set and its part. Develop skills in counting forward and backward within 5. Strengthen the ability to divide a circle and square into 2 and 4 equal parts, compare and name them. Strengthen the ability to distinguish and name familiar geometric shapes.

Material. Doll, bear, bunny, 3 cubes, 3 pyramids, 3 cars, 5 circles of the same color, 2 baskets, 2 sets of building materials (with flat and three-dimensional geometric shapes - in accordance with the program content).

Handout. An envelope containing ¼ of a circle or square, a box with the remaining parts of the figures, squares of the same color (5 pieces for each child).

Progress of educational activities

1 part. Game exercise “Count the figures.”

There are 5 circles of the same color on the board. Children determine their number. Children, together with the teacher, count the circles in reverse order (from 5 to 1). Then the teacher asks: “What did we do when we counted from 5 to 1?” (Decreased by 1).

Part 2. Working with handouts.

The teacher suggests completing a similar task using squares of the same color. Children count the squares, remove one at a time and determine how many are left. Together with the teacher, they call the numbers in reverse order. (Five, four, three, two, one).

Part 3. Game - relay race “Who will decompose the building material faster?”

Children are divided into two teams by counting first and second. The first team must find all flat figures in the basket and transfer them to another basket, and the second team must find all three-dimensional figures. In the process of checking the task, children show and name the figures.

Part 4 Didactic game “Make a whole from its parts.”

Children have envelopes with parts of geometric shapes. The teacher offers to create a whole geometric figure by selecting the missing parts from the box. After completing the task, the children determine what shapes they got and how many parts they consist of.

Then the teacher asks the children: “What can you call each part of your figure? What is greater: the whole or one second (one fourth) part? What is less: one second (one fourth) part or the whole?”

Part 5 Game exercise “Collecting toys for a doll.”

The teacher tells the children that a doll has come to visit them and invites them to play with it. He puts three groups of toys on the table (three cubes, three pyramids, three cars) and asks: “How many cubes? How many pyramids? How many cars? What can we say about the number of pyramids and cubes and cars?” (There are equal numbers of cubes, pyramids, and cars - three each).

Developing math skills for life

There are many games online and in various educational textbooks for children aged 5-7 years. Often they try to divide them by age - this is justified, but you need to look at the development of a particular child. I would like to recommend a couple more good publications with exciting puzzles:

• A book for gifted children “Developing mathematical abilities” (for 6-7 years). Many interesting tasks from the easiest to the most difficult. Bright pictures and design will interest the child.
• “A complete course of preparation for school. For those who are going to 1st grade . The authors did their best and collected about 600 exercises - on mastering counting, preparing the hand for writing, etc.

For classes to be meaningful, they must be done systematically. Experts advise giving children logic exercises every day, little by little. This will teach the child to reason and draw conclusions, develop quick wits and intelligence. It will also increase self-esteem and arouse interest in studying at school. Basic skills in logic and mathematics will be useful not only in school, but throughout your future life.

It is much easier to interest preschoolers than older children. But by the 3rd-4th grade of school, motivation usually drops. So this favorable time should not be missed!

The role of mathematics in the development of preschool children

Definition 1
Preschool mathematics is one of the most powerful factors in the intellectual development of a preschool child, as well as the formation of his creative and cognitive abilities.

Mathematics is of great importance in the intellectual and mental development of a child during preschool childhood; the success of subsequent education in primary school largely depends on it.

Mathematics in modern conditions is becoming an increasingly popular science, and its knowledge extends to almost all areas of human activity. Mathematical knowledge is especially relevant in the period of continuous computerization.

Preschool mathematics has great potential in the development of children, starting from a very early age.

Note 1

One of the main tasks of a modern preschool educational institution, in accordance with the Federal State Educational Standard, is the development of mathematical abilities in preschool children.

The mathematical development of preschool children is a qualitative change in the intellectual sphere of the personality of a preschool child, which occurs as a result of the formation of mathematical concepts and ideas.

Finished works on a similar topic

• Course work Preschool mathematics 400 rub.
• Abstract Preschool mathematics 280 rub.
• Test paper Preschool mathematics 190 rub.

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The success of subsequent education at school depends on the quality of mathematical development in preschool educational institutions. In this connection, one of the main tasks of the teacher is not only the organization of mathematics classes, but also the formation in children of interest in these classes, the desire to acquire new knowledge and skills. Mathematics classes must be made interesting, exciting, fun, educational and developmental. In mathematics classes, all abilities and areas of activity of the child should be involved.

Modern requirements for the organization of the educational process in preschool educational institutions pose the need to develop new methods and means of organizing mathematics classes. The main forms of mathematical development in preschool educational institutions are classes in the formation of elementary mathematical concepts (FEMP) and organized mathematical activities of children.