Methods and techniques for teaching preschoolers elements of mathematics

Methods and techniques for teaching preschoolers elements of mathematics

Methods and techniques for teaching preschoolers elements of mathematics

The concept of "Method"

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

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

When choosing methods, the following are taken into account:

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

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

methods.

Practical methods

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

Visual and verbal

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

Visual and verbal methods

Towards visual methods

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

Towards verbal methods

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

Techniques

Components of the method

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

etc.

Reception "Show"

• A widely used method is: show

  .

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

Reception "Instructions"

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

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

Reception “Questions for Children”

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

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

MAGAZINE Preschooler.RF

Different sciences use the concept of method due to their specificity. Thus, philosophical science interprets method (Greek metodos - literally “path to something” ) in the most general sense as a way of achieving a goal, a certain way of ordering activity.

A method is a method of reproduction, a means of cognition of the subject being studied. The methods are based on objective laws of reality. The method is inextricably linked with theory.

In pedagogy, the method is characterized as a purposeful system of actions of the teacher and children that correspond to the goals of learning, the content of educational material, the very essence of the subject, and the level of mental development of the child.

The most rational, as experience shows, is a combination of various methods.

When choosing methods, the following are taken into account:

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

The theory and practice of teaching has accumulated some experience in using different teaching methods in working with preschool children. In this case, the classification of methods is used based on teaching aids.

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

Practical methods (exercises, experiments, productive activities) are most consistent with the age characteristics and level of development of thinking of preschoolers. The essence of these methods is that children perform actions that consist of a number of operations. For example, counting objects: name the numerals in order, correlate each numeral with a separate object, pointing at it with a finger or fixing your gaze on it, correlate the last numeral with the entire quantity, remember the total number.

Practical methods are characterized primarily by independent performance of actions and the use of didactic material. On the basis of practical actions, the child develops the first ideas about the knowledge being formed.

Visual and verbal methods in the formation of elementary mathematical concepts are not independent. They accompany practical and playful methods.

Visual teaching methods include: demonstration of objects and illustrations, observation, demonstration, examination of tables and models.

Verbal methods include: storytelling, conversation, explanation, explanations, verbal didactic games.

The components of the method are called methodological techniques.

The main ones used in classes on the formation of elementary mathematical concepts are: overlay, application, didactic games, comparison, instructions, questions for children, examination, etc.

As is known, mutual transitions are possible between methods and methodological techniques. Thus, a didactic game can be used as a method, especially in working with younger children, if the teacher develops knowledge and skills through the game, but it can also be used as a didactic technique when the game is used, for example, to increase the activity of children ( “Who is faster?” ? " , "Clean up the order" ).

A widely used methodological technique is demonstration. This technique is a demonstration; it can be characterized as visually practical and effective.

One of the essential verbal techniques in teaching children mathematics is the instruction, which reflects the essence of the activity that the children have to perform. In the senior group, the instructions are holistic in nature and are given before completing the task. In the younger group, the instructions should be short, often given as the actions are performed.

Questions for children occupy a special place in the methodology of teaching mathematics. They can be reproductive-mnemonic, reproductive-cognitive, productive-cognitive. Prompt and alternative questions should be avoided.

In pedagogy, the system of children's questions and answers is called a conversation. During the conversation, the teacher monitors the children’s correct use of mathematical terminology and speech literacy. This is accompanied by various explanations. Thanks to explanations, children’s immediate perceptions are clarified. For example, a teacher teaches children to examine a geometric figure and explains: “Take the figure in your left hand - like this, trace it with the index finger of your right hand, show the sides of the square (rectangle, triangle), they are the same. A square has corners. . "

The place of the game method in the learning process is assessed differently. In recent years, the idea of ​​the simplest logical training of preschoolers has been developed, introducing them to the field of logical-mathematical concepts (properties, operations with sets) based on the use of a special series of “educational” games (A. A. Stolyar). These games are valuable because they actualize the hidden intellectual capabilities of children and develop them (B. P. Nikitin).

It is still possible to ensure comprehensive mathematical training for children with a skillful combination of game methods and direct teaching methods. Although it is clear that the game captivates children, it does not overload them mentally and physically. The gradual transition from children's interest in play to interest in learning is completely natural.

Doman method

2.1. The secret of the method

The secret of the method is to introduce the child to numbers and their true essence by showing him images with a certain number of red dots. For adults, the image of the number "three" as "3" or the image of three red dots are the same thing. The goal of the method is to teach the child to distinguish between them.

Adults can recognize up to twenty dots in a picture with more or less confidence. Any number greater than 20 can only be guessed at. Children can easily cope with this task if they are first taught the essence of numbers rather than their symbols .

If you name an adult a number, for example “six,” then he will rather imagine the number six, but not see six objects at all.

It's not that he won't "see" it. He will not understand that this is exactly the number of points in the picture. An adult needs to count all the points manually. The child sees the correct answer just by looking at the picture.

The ability to distinguish between “three” as “3” and “three” as three red dots will be an advantage for children over adults. You can teach your child mathematics, even if you yourself are not a master of this matter. It's even easier than teaching him to read. Moreover, the whole process will take no more than half an hour a day. Within just a few weeks you will notice progress.

It is important to remember the following points:

1. Until the age of five, a child easily absorbs a colossal amount of information.

2. Until the age of five, the child accepts all information.

3. The more information a child receives before the age of five, the more information remains.

4. Children under five years old have an enormous amount of energy.

5. Children under five years old have a great desire to learn.

6. Children under five years old can and want to learn to read.

7. All young children are brilliant linguists.

8. Before the age of five, they can learn an entire language or even several languages ​​if you help them with it.

Math is also a language that your child can easily learn.

2.2. Basics of training

As a parent and teacher, you must learn that learning is the biggest adventure in a child's life . This is the most interesting game of all. You must keep this in mind throughout the entire process. Some people believe that we should not take away a child’s childhood by forcing him to study. This indicates a certain attitude towards learning. This is not work or punishment. If you or your child are not enjoying the process, then you are doing something wrong.

The game should be enjoyable, and if the child or parent is tired or in a bad mood, you need to postpone the process for a while.

It is also important to remember that the time for providing information should be as short as possible. For example, you can conduct such sessions two or three times a day, but the duration of each should be no more than a few seconds. You must stop until your child wants it.

Adults expect children to look at learning material, concentrate on it, and try to remember it. Children don't need this; they pick up information on the fly. Speed, new material and a good mood from parents is all that is needed.

You will be surprised how hungry your child will be for new information when you start teaching. Let him guide you. Don't let him get bored. There is nothing more boring than learning the same examples by heart.

Be consistent - prepare all the training material in advance, and if you had to postpone the session, then when the time comes to continue, do not return to what has already been completed. Continue where you left off. And never try to check the mastery of the material, do not test your baby. All tests are perceived as something unpleasant.

The training material is very simple:

1. White cards of 30 x 30 cm format. For the first time, you will need at least 100 pieces, so it will be more convenient to buy ready-made ones and not waste precious time on cutting.

2. Red dots on adhesive paper with a diameter of approximately 2 cm. The red color attracts babies.

3. Thick red marker , the thicker the better.

It will take time to prepare the material, but overall it is not at all difficult. There is a ready-made set of cards with dots from one to one hundred, developed by the publisher. But if you couldn’t find it, here are some tips to simplify the task:

1. Start with the “hundred” card and continue in descending order. The greater the number of points, the more difficult it is. We tend to be more focused and attentive in the beginning.

2. Count the red dots before placing them on the card.

3. On the back of the card, write a value in each corner before gluing the dots onto the card.

4. Make sure that the pasted dots do not resemble any shape (for example, a square or triangle).

5. Glue the dots onto the card so that they do not overlap each other.

6. Leave margins so your fingers don't cover the dots when you hold the card.

2.3. Step 1: Quantity Recognition

The first thing you need to start learning mathematics is to learn the denomination or the essence of numbers . For the first lessons, cards with values ​​from one to ten will be enough. For one session you need only five cards. Wait until the child is in a good mood and nothing bothers him. Choose a place where the child will not be distracted. TV, radio - everything needs to be turned off.

Take a card with one dot. Show it to your child and say loud and clear, “This is one.” Don't linger. Say the phrase just long enough to say it. Then remove the card with one dot, take out the card with two and say: “That’s two,” and so on until five. Watch your child carefully. Don't ask your child to repeat numbers. Hug and kiss him. Let him understand that you really enjoy this joint process. This is one session. Repeat it three times during the day.

The next day, show your child cards six to ten. Also give praise at the end of each session. Don't bribe him with sweets. Once you have shown the cards in ascending order, mix them up and show the cards in random order during subsequent sessions. It is extremely important not to hesitate. Children remember information with lightning speed.

Show your child cards from one to ten for five days, shuffling them, then add a couple of new cards (next in order) and remove the same number of old ones (one, two, three, etc.). It is important to remember the basic rule - the child should not be bored! If he gets bored, you slowly show the cards.

It is enough to learn cards from one to one hundred so that the child can immediately understand how many dots are in the picture - twenty-eight or twenty-nine. It's so simple. Now he won’t need to remember the ill-fated phrase “we write two, one in our mind.” He will understand what we are talking about. He will “see” the real quantity hidden behind the number. You will be tempted to test what you have already learned. Do not do that. You may scare your child and he will lose interest in learning.

2.4. Step 2: Arithmetic operations

Perhaps even before your child masters 100, he or she will be ready for the next step— simple arithmetic . For the study material, take ready-made cards and write on the back a series of examples of addition, subtraction, multiplication and division.

Start with addition. This is the simplest example because the child is already familiar with it. When you showed him the cards in ascending order, you were essentially adding one to each card.

Take three cards and place them face down on your lap. Then, while saying the equation, start showing the cards. For example, “one” (show the “one” card) “plus two” (show the “two” card) “equals three” (show the “three” card). Say the entire phrase loudly and clearly. At this stage, there is no need to explain to your child the meaning of the words “plus” and “equals”. He himself will understand them along the way. It is important to use the same terminology all the time.

Show three equations per session, for a total of nine examples per day. Don't repeat examples. Learn addition for two weeks.

The same principle applies to other arithmetic operations.

2.5. Step 3. Solving examples

As has been said many times, don't try to test your child. Children love to learn, but hate tests. The learning process can either drag on or stop completely. The child will suspect that you do not believe that he can solve this or that example until he proves it to you. Essentially, this is an attempt to find out what the child does not know, but you, in turn, know.

Instead, you need to give your child a chance to prove himself. Offer him to solve the problem. For example, take two cards “thirty-eight” and “twelve”, show them to the child and ask: “Where is thirty-eight?” Have your child look at or touch the correct card. If the child does not answer immediately, present the correct card and ask again: “That’s thirty-eight, right?”

Add one example of this to each training session. This way you will alternate numbers, arithmetic operations and solving examples.

To keep your child engaged, add variety to your equations. For example, you can create a number of examples with a similar component.

• 4 x 3 x 5 = 60
• 3 x 5 x 4 = 60
• 5 x 3 x 4 = 60

At this stage, it is important not to mix addition and subtraction with multiplication and division, in order to avoid mistakes. Add up to four components per example, and you will be surprised how quickly your baby will learn to cope with them.

More advanced parents can continue to teach their child other arithmetic functions—arithmetic and geometric progressions, greater than and less than, inequalities, and basic algebra.

2.6. Step 4. Digit recognition

Once a child has learned to understand the quantitative essence, you can teach him to recognize the numbers themselves, namely the graphic display of numbers, as we adults are used to seeing them. To do this, you need to take the blank cards we already know and write the numbers from one to one hundred with a black marker. Be consistent and attentive. The numbers should be visually the same size, approximately 15 cm in height and 8 cm in width. The learning principle is similar to the first step. You will need no more than fifty days to study numerals. You can add examples of numerals greater than a hundred - 200, 300, 400, etc., as well as non-round numerals - 258, 369, 1256, etc.

Once your child has mastered the numbers, mix up the dot and number cards and create their own equations. Show him a card with a familiar number, say, “twelve,” and say it out loud. Then say “equals” and show a card with twelve red dots, say “twelve”.

This step is usually the easiest for the child.

2.7. Step 5. Equations with numerals

This step repeats all the previous ones with only one difference. Now the equations involve the numbers we are used to. For equations with numerals you will need new rectangular cards, 45cm long and 10cm wide, with a smaller font. Something like this:

25 + 5 = 30

Always have the correct answer handy. The child should not see your doubts in finding the right answer.

When you go through all the steps with your child, you can consider that you have opened the doors to the magical world of mathematics, where he will feel like a fish in water.

The use of visual material in teaching children elementary mathematical concepts

CONTENT

1. The importance of visualization in teaching children the elements of mathematics. 3

2. Types of visual material used in the development of elementary mathematical concepts in preschoolers. 5

3. Pedagogical requirements for visual material and its use at different stages of teaching preschoolers elementary mathematical concepts 7

4. Selection of visual aids for work on the development of elementary mathematical concepts in children of a particular age group.. 9

References.. 11

1. The importance of visualization in teaching children the elements of mathematics

In the theory of learning, a special place is given to learning tools and their influence on the result of this process.

The means of teaching are understood as: sets of objects, phenomena (V.E. Gmurman, F.F. Korolev), signs (models), actions (P.R. Atutov, I.S. Yakimanskaya), as well as the word (G.S. Kasyuk, A.R. Luria, M.N. Skatkin, etc.), participating directly in the educational process and ensuring the assimilation of new knowledge and the development of mental abilities.

We can say that teaching aids are sources of obtaining information; as a rule, they are a set of models of a very different nature.

There are material-object (illustrative) models and ideal (mental) models.

In turn, material-subject models are divided into physical, subject-mathematical (direct and indirect analogies) and spatio-temporal.

Among the ideal ones, a distinction is made between figurative and logical-mathematical models (descriptions, interpretations, analogies).

Scientists M.A. Danilov, I.Ya. Lerner, M.N. Skatkin understands “means” as “with the help of which the transmission of information is ensured - the word, visualization, practical action.”

Teaching mathematics in kindergarten is based on specific images and ideas.

These specific ideas prepare the foundation for the formation of mathematical concepts on their basis. Without enriching sensory cognitive experience, it is impossible to fully acquire mathematical knowledge and skills.

Making learning visual means not only creating visual images, but also involving the child directly in practical activities. In mathematics classes and in kindergarten, the teacher, depending on the didactic tasks, uses a variety of visual aids. For example, to teach counting, you can offer children real (balls, dolls, chestnuts) or fictitious (sticks, circles, cubes) objects. Moreover, objects can be different in color, shape, size.

Based on a comparison of different specific sets, the child draws a conclusion about their number, in this case the visual analyzer plays the main role.

Another time, these same counting operations can be performed by activating the auditory analyzer: offering to count the number of claps, hits on a tambourine, etc. You can count based on tactile and motor sensations.

The principle of visual teaching is based on the real ideas of students.

This is one of the most well-known and intuitive principles of learning, used since ancient times. A logical justification for this principle was obtained relatively recently: human sensory organs have different sensitivity to external stimuli; in the vast majority of people, the organs of vision have the greatest sensitivity.

Thus, having examined the historical development of the principle of visibility, we can come to the conclusion that such teachers as Komensky Ya.A., Ushinsky K.D., Pestalozzi I.G. made a great contribution to the theoretical development and application of the principle of visibility. and etc.

Comenius believed that the principle of visual teaching presupposes, first of all, that students acquire knowledge through direct observations of objects and phenomena, through their sensory perception. Comenius considers visibility to be the golden rule of learning.

Ushinsky contributed a lot of valuable things to the theoretical development and application of the principle of visibility: he gave a materialist justification for the principle of visibility.

He gave visibility its place in the learning process; he saw in it one of the conditions that ensures that students receive complete knowledge and develop their logical thinking.

Pestalozzi reveals the essence of the principle of visibility more widely than his predecessors. He fills it with new content, considering visibility as the foundation for the comprehensive development of the child. It should be noted that modern principles of didactics determine the requirements for all components of the educational process - the logic of learning, goals and objectives, the formation of content, the choice of forms and methods, stimulation and analysis of achieved results. Having studied the material, we can conclude that visibility in didactics is one of the most well-known and intuitively understood teaching principles, used since ancient times. A logical justification for this principle was obtained relatively recently: human sensory organs have different sensitivity to external stimuli; in the vast majority of people, the organs of vision have the greatest sensitivity.

2. Types of visual material used in work on the development of elementary mathematical concepts in preschoolers

Visual aids can be real objects and phenomena of the surrounding reality, toys, geometric shapes, cards depicting mathematical symbols - numbers, signs, actions.

When working with children, various geometric shapes are used, as well as cards with numbers and signs.

Verbal clarity is widely used - a figurative description of an object, a phenomenon of the surrounding world, works of art, oral folk art, etc.

The nature of visualization, its quantity and place in the educational process depend on the purpose and objectives of learning, on the level of children’s acquisition of knowledge and skills, on the place and ratio of the concrete and abstract at different stages of knowledge acquisition. Thus, when forming children’s initial ideas about counting, a variety of concrete sets are widely used as visual material, and their diversity is very significant (a variety of objects, their images, sounds, movements). The teacher draws the children's attention to the fact that a set consists of individual elements; it can be divided into parts (under a set). Children practically work with sets and gradually learn the main property of sets through visual comparison—quantity.

Visual material helps children understand that any set consists of separate groups and objects. Which can be in the same and not the same quantitative ratio, and this prepares them for mastering counting with the help of words - numerals. At the same time, children learn to arrange objects with their right hand from left to right.

Gradually, mastering the counting of sets consisting of different objects, children begin to understand that the number does not depend either on the size of the objects or on the nature of their placement. By practicing visual quantitative comparison of sets, children in practice become aware of the relationship between adjacent numbers (4<5, and 5>4), and learn to establish equality.

At the next stage of training, concrete sets are replaced by “Number figures”, “Number ladder”, etc.

Pictures and drawings are used as visual material.

Thus, examining artistic paintings makes it possible to realize, highlight, and clarify temporal and spatial relationships, characteristic features of the size and shape of surrounding objects.

At the end of the third - beginning of the fourth life, the child is able to perceive sets represented with the help of symbols, signs (squares, circles, etc.).

The use of signs (symbolic clarity) makes it possible to highlight essential features, connections and relationships in a certain sensory-visual form.

The aids used are applications (a table with replaceable parts that are fixed on a vertical or inclined plane, for example using magnets).

This form of visibility allows children to take an active part in making applications and makes learning activities more interesting and productive.

Benefits - applications are dynamic, they provide the opportunity to vary and diversify models.

Visual aids also include technical teaching aids. The use of technical means makes it possible to more fully realize the teacher’s capabilities and use ready-made graphic or printed materials.

Teachers can make visual material themselves, and also involve children in this (especially when making visual handouts).

Natural materials (chestnuts, acorns, pebbles) are often used as counting material.

3. Pedagogical requirements for visual material and its use at different stages of teaching preschoolers elementary mathematical concepts

Visual material must meet certain requirements:

- objects for counting and their images should be known to children; they are taken from the surrounding life;

- in order to teach children to compare quantities in different aggregates, it is necessary to diversify didactic material that could be perceived by different senses (hearing, visual, touch);

— visual material must be dynamic and in sufficient quantity; meet hygienic, pedagogical and aesthetic requirements.

Special requirements are imposed on the method of using visual material.

When preparing for a lesson, the teacher carefully considers when (in what part of the lesson), in what activity and how this visual material will be used.

It is necessary to dose visual material correctly. Both insufficient use and excess use of it have a negative impact on learning outcomes.

Visualization should not be used only to stimulate attention.

This is too narrow a goal. It is necessary to analyze didactic tasks more deeply and select visual material in accordance with them. So, if children receive initial ideas about certain properties, signs of an object, we can limit ourselves to a small amount of means.

In the younger group, children are introduced to the fact that a set consists of individual elements; the teacher demonstrates many rings on a tray.

When introducing children, for example, to a new geometric figure - a triangle - the teacher demonstrates triangles of different colors, sizes and shapes (equilateral, scalene, isosceles, rectangular). Without such diversity, it is impossible to identify the essential features of a figure - the number of sides and angles; it is impossible to generalize and abstract. In order to show children various connections and relationships, it is necessary to combine several types and forms of visualization. For example, when studying the quantitative composition of a number from units, various toys, geometric figures, tables and other types of visual aids are used in one lesson.

There are different ways to use visuals in the educational process - demonstration, illustrative and effective. The demonstration method (use of clarity) is characterized by the fact that first the teacher shows, for example, a geometric figure, and then examines it together with the children. The illustrative method involves the use of visual material to illustrate and concretize information by the teacher. For example, when introducing the division of a whole into parts, the teacher leads children to the need for this process, and then practically performs the division. An effective way to use visual material is characterized by a connection between the teacher’s words and action. Examples of this could be teaching children to directly compare sets by superimposing and applying, or teaching children to measure, when the teacher tells and shows how to measure. It is very important to think about the place and order of placement of the material used. Demonstrative material is placed in a place convenient for use, in a certain sequence. After using visual material, it must be removed so that children’s attention is not distracted.

4. Selection of visual aids for work on the development of elementary mathematical concepts in children of a specific age group

The senior preschool group, compared to the middle preschool age, is distinguished by an expansion of the types of visual aids and some changes in their nature.

Toys and things continue to be used as illustrative material. But now a big place is occupied by working with pictures, color and silhouette images of objects, and the drawings of objects can be schematic.

From the middle of the school year, the simplest schemes are introduced, for example, “numeric figures”, “number ladder”, “path diagram” (pictures on which images of objects are placed in a certain sequence).

“Substitutes” of real objects begin to serve as visual support. The teacher represents objects that are currently missing with models of geometric shapes.

For example, children guess who was more on the tram: boys or girls, if boys are indicated by large triangles and girls by small ones. Experience shows that children easily accept such abstract clarity. Visualization activates children and serves as a support for voluntary memory, therefore, in some cases, phenomena that do not have a visual form are modeled.

For example, the days of the week are conventionally indicated by multi-colored chips. This helps children establish ordinal relationships between the days of the week and remember their sequence.

1. Beloshistaya A.V. Formation and development of mathematical abilities of preschool children. - M.: VLADOS, 2003. - 400 p.

2. Erofeeva T.I., Novikova L.N. Mathematics for preschoolers: Book. for a kindergarten teacher. - M.: Education, 1992 - 191 p.

3. Petrova I.A. Training, education and development of preschool children: A manual for teachers. M.: Education, 1990. – 280 p.

4. Pyshkalo A.M. Methods of teaching mathematics. M.: Education, 1995. – 250 p.

5. Taruntaeva T.V. Development of elementary mathematical concepts in preschool children. - M.: Education, 1998. - 64 p.

6. Shatalova E.V. Pedagogical practice on the theory and methodology of development of mathematical concepts in preschool children: Educational and methodological manual. Belgorod: IPC “POLITERRA”, 2007 .- 75 p.

7. Shcherbakova E.I. Methods of teaching mathematics in kindergarten - M: Academy, 2000 - 272 p.

Program requirements for methods of teaching mathematics to preschoolers in modern preschool educational institutions

The current state of mathematical concepts in preschool children

1.2 Program requirements for methods of teaching mathematics to preschoolers in modern preschool educational institutions

A modern mathematics program is aimed at the development and formation of mathematical concepts and abilities, logical thinking, mental activity, ingenuity, that is, the ability to make simple judgments and use grammatically correct figures of speech.

In the mathematical training provided for by the program, along with teaching children to count, developing ideas about quantity and numbers within the first ten, dividing objects into equal parts, much attention is paid to operations with visual material, taking measurements using conventional measures, determining the volume of liquid and granular bodies, development of the children's eye, their ideas about geometric figures, time, and the formation of an understanding of spatial relationships. In mathematics classes, the teacher carries out not only educational tasks, but also solves educational ones. The teacher introduces preschoolers to the rules of behavior, instills in them diligence, organization, the habit of precision, restraint, perseverance, determination, and an active attitude towards their own activities.

The teacher organizes work on developing elementary mathematical concepts in children in class and outside of class: in the morning, during the day during walks, in the evening; 2-3 times a week. Teachers of all age groups should use all types of activities to strengthen children's mathematical knowledge. For example, in the process of drawing, sculpting, and designing, children gain knowledge about geometric shapes, the number and size of objects, and their spatial arrangement; spatial concepts, counting skills, ordinal counting - in music and physical education classes, during sports entertainment. In various outdoor games, children’s knowledge of measuring the sizes of objects using conventional standards can be used. To reinforce mathematical concepts, educators widely use didactic games and game exercises separately for each age group. In the summer, program material in mathematics is repeated and reinforced during walks and games. The methodology for teaching mathematical knowledge is based on general didactic principles: systematicity, consistency, gradualism, and individual approach. The tasks offered to children sequentially, from lesson to lesson, become more complex, which ensures accessibility of learning. When moving on to a new topic, you should not forget to repeat what you have covered. Repeating material in the process of learning new things not only allows children to deepen their knowledge, but also makes it easier to focus on new things.

In mathematics classes, teachers use various methods (verbal, visual, game) and techniques (story, conversation, description, instructions and explanations, questions for children, children’s answers, samples, showing real objects, paintings, didactic games and exercises, outdoor games) .

Developmental teaching methods occupy a large place in working with children of all age groups. This includes the systematization of the knowledge he offers, the use of visual aids (reference samples, simple schematic images, substitute objects) to highlight various properties and relationships in real objects and situations, and the use of a general method of action in new conditions.

If teachers themselves select visual material, they should strictly comply with the requirements arising from the learning objectives and the age characteristics of the children. These requirements are as follows:

— a sufficient number of objects used in the lesson;

- variety of objects in size (large and small);

- playing with children all types of visual aids before the lesson at different periods of time, so that during the lesson they are attracted only by the mathematical side, and not by the gaming side (when playing with the gaming material, you need to indicate to the children its purpose);

- dynamism (children act with the object offered to them in accordance with the teacher’s instructions, so the object must be strong, stable, so that it can be rearranged, moved from place to place, or picked up);

- decoration. Visual material should attract children aesthetically. Beautiful manuals make children want to study with them, contribute to the organized conduct of classes and good assimilation of the material. For the mental development of preschoolers, classes on the development of elementary mathematical concepts are of great importance. In classes in this section of the program, children not only learn counting skills, solve and compose simple arithmetic problems, but also become familiar with geometric shapes, the concept of set, and learn to navigate time and space. In these classes, to a much greater extent than in others, intelligence, ingenuity, logical thinking, and the ability to abstract are intensively developed, and laconic and precise speech is developed. The “Program of Education and Training in Kindergarten” provides for a continuous connection with the program in this subject for the 1st grade of the school. If a child has not mastered any rule or concept, this will inevitably lead to his falling behind in mathematics classes at school.

The task of a kindergarten teacher conducting mathematics classes is to include all children in the active and systematic assimilation of program material. To do this, he, first of all, must know well the individual characteristics of children, their attitude towards such activities, the level of their mathematical development and the degree of their understanding of new material. An individual approach to conducting mathematics classes makes it possible not only to help children master the program material, but also to develop their interest in these classes. Ensure the active participation of all children in common work, which leads to the development of their mental abilities, attention, prevents intellectual passivity in individual children, fosters perseverance, determination and other volitional qualities. The teacher must take care of the development of children's abilities to carry out counting operations, teach them to apply previously acquired knowledge, and take a creative approach to solving the proposed tasks. He must solve all these questions, taking into account the individual characteristics of children that manifest themselves in mathematics classes.

Teaching and raising a child is one of the possible means of managing him. Educational programs for preschool institutions guide teachers to persistently and consistently teach children to notice time, to correlate it with the time of play, activities, and everyday life, to teach children to give an account of what has been done and could have been done at one time or another. This does not mean that you need to constantly talk about time and control children. It is necessary to organize life in such a way that it is meaningful, interesting and useful for developing a sense of time in children. The sense of time in its general definition represents the ability to navigate when performing actions at a certain time without the indication of special instruments and auxiliary means. Nurturing a sense of time is carried out throughout the entire process of forming ideas about time and is inseparable from it.

Developed by A.M. Leushina’s concept was implemented in the Standard “Program of Education and Training in Kindergarten”; new approaches to the content and methods of forming temporary representations were determined on the basis of a number of studies of the 60-70-80s (E.D. Richterman, E. Shcherbakova, N. Funtikova and others).

In the second younger group, work with three-year-old children on the development of elementary mathematical concepts is mainly aimed at developing ideas about set. Children are taught to compare two sets, compare elements of one set with elements of another, distinguish between equality and inequality of groups of objects that make up the set.

The program material of the second junior group is limited to the pre-numerical period of study. Children of this age learn to form groups of individual objects and select objects one at a time: to distinguish between the concepts of “many” and “one”. When comparing two quantitative groups, using the techniques of superposition and application, determine their equality and non-equality by the number of elements included in them.

Children learn to form a group of homogeneous objects and select one object from it, and correctly answer the question “how many?” This problem is solved mainly through play and practical activities. There are many games in which children learn to identify one object, form a group of objects, and master the terms “one” and “many.” For example: “Bear and the Bees”, “Lanterns”, “Train”, “Cat and Mice”, etc.

The “Size” section of the program is associated with the development of preschoolers’ initial ideas about the size of objects of contrasting and identical sizes in length, width, height, thickness, volume (larger, smaller, equal in size). Children learn to use words to determine the size of objects: long - short, wide - narrow, tall - short, thick - thin, larger - smaller.

At each lesson, be sure to give children geometric shapes in pairs: for example, a circle and a square or a square and a triangle, a triangle and a circle.

Children receive their first information about geometric shapes during play. Based on the experience accumulated through classes, children are introduced to the names of plane geometric shapes (square, circle, triangle). They are taught to identify, distinguish and name these figures. It is important that the children examine these figures with visual and motor-tactile analyzers. Preschoolers trace the outline, run their hands along the surfaces of the models - thus, a general perception of the form occurs. Application and superposition techniques should be used to compare figures.

It is advisable to develop spatial concepts in a group of children of the fourth year of life using everyday life, routine moments, didactic, outdoor games, morning exercises, music and physical education classes. By the end of the school year, children should learn to clearly distinguish spatial directions from themselves: forward, backward (behind), right, right, left, left, down, below, as well as parts of their body and their names. Of particular importance is the distinction between the right and left hands, the right and left parts of your body.

The “Time Orientation” section mainly involves teaching children the ability to distinguish between parts of the day and name them: morning, evening, day and night. Children master these concepts in everyday life, during routine moments.

In the second junior group, they begin to carry out special work on the formation of elementary mathematical concepts. The further mathematical development of children depends on how successfully the first perception of quantitative relationships and spatial forms of real objects is organized.

Modern mathematics, when justifying such important concepts as “number”, “geometric figure”, etc., is based on set theory, and therefore the formation of concepts in the school mathematics course occurs on a set-theoretic basis.

Performing various operations with object sets by preschool children allows children to further develop their understanding of quantitative relationships and form the concept of natural numbers. The ability to identify qualitative characteristics of objects and combine objects into a group based on one characteristic common to all of them is an important condition for the transition from qualitative to quantitative observations.

Work with children begins with tasks for selecting and combining objects into groups based on a common characteristic. Using the techniques of superposition or application, children establish the presence or absence of a one-to-one correspondence between the elements of groups of objects (sets).

In modern mathematics teaching, the formation of the concept of natural number is based on the establishment of a one-to-one correspondence between the elements of the compared groups of objects.

Children are not taught to count, but by organizing various actions with objects, they lead to the mastery of counting and create opportunities for the formation of the concept of natural number.

The middle group program is aimed at further developing mathematical concepts in children. It involves learning to count to 5 by comparing two sets expressed by adjacent numbers. An important task in this section remains the ability to establish the equality and inequality of groups of objects, when the objects are at different distances from each other, when they are different in size, etc. Solving this problem leads children to understand an abstract number.

Grouping objects according to characteristics develops in children the ability to compare and carry out logical classification operations. In the process of various practical actions with aggregates, children learn and use in speech simple words and expressions that indicate the level of quantitative ideas: many, one, one at a time, none, not at all, few, the same, the same, the same, equally; as much as; more than; less than; each of..., all, all.

Children in the middle group must learn to name numerals in order and relate each numeral to only one object.

At the end of the count, sum it up in a circular motion and call it by the name of the items counted (for example, “one, two, three. Three dolls in total”). When summing up the count, always pay attention to the fact that children always name the number first, and then the object. Children are taught to distinguish the counting process from the counting result, count with their right hand from left to right, name only numerals while counting, correctly coordinate numerals with nouns in gender, number, case, and give a detailed answer.

Simultaneously with learning to count, the concept of each new number is formed by adding a unit. Throughout the entire academic year, quantitative counting up to 5 is repeated. When teaching counting, in each lesson, special attention should be paid to such techniques as comparing two numbers, matching, establishing their equality and inequality, overlapping techniques and applications.

The program for the senior group is aimed at expanding, deepening and generalizing elementary mathematical concepts in children, and further developing counting activities. Children are taught to count within 10 and continue to be introduced to the numbers of the first ten. Based on actions with sets and measurement using a conditional measure, the formation of ideas about numbers up to ten continues. The formation of each of the new numbers from 5 to 10 is given according to the method used in the middle group, based on a comparison of two groups of objects by pairwise correlating the elements of one group with the elements of another, children are shown the principle of number formation.

They continue to introduce the numbers. Correlating a certain number with a number formed by a particular number of objects, the teacher examines the depicted numbers, analyzing it, compares it with already familiar numbers, the children make figurative comparisons (one is like a soldier, eight is like a snowman, etc.).

The number 10 deserves special attention, since it is written with two digits: 0 and 1. Therefore, it is first necessary to introduce children to zero.

Throughout the school year, children practice counting within ten. They count objects, toys, count out smaller ones from a larger number of objects, count objects according to a given number, according to a number, according to a pattern. The sample can be given in the form of a number card with a certain number of toys, objects, geometric shapes, in the form of sounds, movements. When performing these exercises, it is important to teach children to listen carefully to the teacher’s tasks, remember them, and then complete them.

Children must be taught to count, starting from any specified object in any direction, without skipping objects or counting them twice. For the development of counting activities, exercises with the active participation of various analyzers are essential: counting sounds, moving by touch within ten. In the older group, work continues on mastering ordinal numbers within ten. Children are taught to distinguish between ordinal and quantitative counting. When counting objects in order, you need to agree on which side to count from. Since the result of the calculation depends on this. In the older group, children develop the concept that some objects can be divided into several parts: two, four. For example, an apple. Here it is imperative to draw the children’s attention to the fact that the parts are smaller than the whole, and show this with a clear example.

In the preparatory group for school, special attention is paid to the development in children of the ability to navigate in some hidden essential mathematical connections, relationships, dependencies: “equal”, “more”, “less”, “whole and part”, dependencies between quantities, dependence of the measurement result on magnitudes of measures, etc. Children master ways of establishing various kinds of mathematical connections and relationships, for example, the method of establishing correspondence between elements of sets (practical comparison of elements of sets one to one, using superposition techniques, applications for clarifying relationships of quantities). They begin to understand that the most accurate ways to establish quantitative relationships are by counting objects and measuring quantities. Their counting and measurement skills become quite strong and conscious.

The ability to navigate essential mathematical connections and dependencies and mastery of the corresponding actions make it possible to raise the visual-figurative thinking of preschoolers to a new level and create the prerequisites for the development of their mental activity in general. Children learn to count with their eyes alone, silently, they develop an eye and a quick reaction to form.

No less important at this age is the development of mental abilities, independence of thinking, mental operations of analysis, synthesis, comparison, the ability to abstract and generalize, and spatial imagination. Children should develop a strong interest in mathematical knowledge, the ability to use it, and the desire to acquire it independently. The program for the development of elementary mathematical concepts of the preparatory group for school provides for the generalization, systematization, expansion and deepening of the knowledge acquired by children in previous groups.

In the middle group, counting skills are carefully practiced. The teacher repeatedly shows and explains counting techniques, teaches children to count objects with their right hand from left to right; during the counting process, point to objects in order, touching them with your hand; Having named the last numeral, make a generalizing gesture, circle a group of objects with your hand.

Children usually find it difficult to coordinate numerals with nouns (the numeral one is replaced with the word once). The teacher selects masculine, feminine and neuter objects for counting (for example, colored images of apples, plums, pears) and shows how, depending on which objects are counted, the words one, two change.

A large number of exercises are used to strengthen counting skills. To create the prerequisites for independent counting, they change the counting material, the classroom environment, alternate group work with independent work of children with aids, and diversify the techniques. A variety of game exercises are used, including those that allow not only to consolidate the ability to count objects, but also to form ideas about shape, size, and contribute to the development of orientation in space. Counting is associated with comparing the sizes of objects, distinguishing geometric shapes and highlighting their features; with determination of spatial directions (left, right, ahead, behind).

Children are asked to find a certain number of objects in the environment. First, the child is given a sample (card). He is looking for which toys or things are as many as there are circles on the card. Later, children learn to act only on words. When working with handouts, it is necessary to take into account that children do not yet know how to count objects. The tasks are first given those that require them to be able to count, but not count. Learning how to count objects. After children learn to count objects, they are taught to count objects and independently create groups containing a certain number of objects. This work is given 6-7 lessons. During these classes, work is carried out in parallel on other sections of the program.

Learning to count objects begins with showing its techniques. Usually a new method of action absorbs the child's attention, and he forgets how many objects need to be counted. Many children, when counting, correlate numerals not with objects, but with their movements, for example, they take an object in their hand and say one, put it down and say two. Explaining the method of action, the teacher emphasizes the need to remember the number, shows and explains that the object must be taken silently and only when it is placed, the number must be called. When conducting the first exercises, children are given a sample (a card with circles or drawings of objects). The child counts out as many toys (or things) as there are circles on the card. The card serves as a means of monitoring the results of the action. Children count the circles first out loud, and then silently. The circles on the sample card can be arranged in different ways. First, the child receives the sample in his hands, and later the teacher only shows it. Exercises in equalizing sets of objects such as “Count out and bring so many coats so that there is enough for all the dolls” are especially useful. The child counts the toys and brings what is required. These exercises allow you to emphasize the importance of counting.

In the third lesson, children learn to count objects according to the named number. The teacher constantly warns them about the need to memorize numbers. From the exercise of reproducing one group, children move on to composing two groups at once, to memorizing two numbers. When giving such tasks, they name adjacent numbers in the natural series. This allows children to practice comparing numbers at the same time. Children are asked not only to count a certain number of objects, but also to place them in a certain place, for example, put them on the top or bottom shelf, put them on the table on the left or right, etc. The teacher changes the quantitative relationships between the same objects, as well as the place their locations. Connections are established between number, qualitative characteristics and spatial arrangement of objects. Children increasingly independently, without expecting additional questions, talk about how many, what objects and where they are located. They check the counting results by counting the objects. In the next 2-3 lessons, children are asked to make sure that there is an equal number of different objects. (3 circles, 3 squares, 3 rectangles - 3 of all shapes.)

A common feature for all groups of objects in this case is their equal number. After such exercises, children begin to understand the general meaning of the final number. Showing the independence of the number of objects from their spatial characteristics. Children learn (in a total of 8-10 lessons) to count and count objects. However, this does not mean that they have an idea of ​​the number. Educators are often faced with the fact that a child, having counted objects, evaluates as a large group the one in which there are fewer objects, but they are larger in size. Children also evaluate a group of objects that occupies a large area as large, despite the fact that it may contain fewer objects than another group that occupies a smaller area. It is difficult for a child to distract himself from the diverse properties and characteristics of objects that make up sets. Having counted objects, he can immediately forget the counting result and estimates the quantity, focusing on spatial features that are more clearly expressed. Children's attention is drawn to the fact that the number of objects does not depend on spatial characteristics: the size of objects, the shape of their arrangement, the area they occupy. 2-3 special lessons are devoted to this, and then until the end of the school year they are periodically returned to at least 3-4 times. At the same time, children are trained to compare objects of different sizes (length, width, height, etc.), clarify some spatial concepts, learn to understand and use words left and right, top and bottom, top and bottom, close and far; arrange objects in one row on the left and right, in a circle, in pairs, etc.

The independence of the number of objects from their spatial characteristics is determined by comparing sets of objects that differ either in size, or in the shape of their location, or in the distances between objects (the area they occupy). Constantly change quantitative relationships between populations. Quantitative differences between populations are acceptable within ± 1 item.

Children have already become familiar with the formation of all numbers within 5, so they can immediately compare groups containing 3 and 4 or 4 and 5 objects in the very first lesson. This serves to more quickly generalize knowledge and develop the ability to abstract quantity from spatial characteristics of sets of objects. Work should be organized in such a way as to emphasize the importance of counting and set comparison techniques to identify “greater than,” “less than,” and “equal to” relationships.

Children are taught to use various techniques for practical comparison of sets: superimposition, application, pairing, and the use of equivalents (substitutes for objects). Equivalents are used when it is impossible to apply objects of one set to objects of another. For example, to convince children that one of the cards has the same number of objects drawn as the other, circles are taken and superimposed on the drawings of one card, and then on the drawings of the other. Depending on whether there is an extra circle left, or not enough, or whether there are as many circles as there are pictures on the second card, a conclusion is made about which card has more (less) objects or whether there are equal numbers on both cards. The use of counting in different types of children's activities. Strengthening counting skills requires a lot of exercises. Counting exercises should be included in almost every lesson until the end of the school year. However, teaching numeracy should not be limited to formal exercises in the classroom. The teacher constantly uses and creates various life and play situations that require children to use counting skills. In games with dolls, for example, children find out whether there are enough dishes to receive guests, clothes to collect dolls for a walk, etc. In the “shop” game, they use check cards on which a certain number of objects or circles are drawn. The teacher promptly introduces the appropriate attributes and prompts game actions, including counting and counting objects.

In everyday life, situations often arise that require counting: on the instructions of the teacher, children find out whether certain aids or things are enough for children sitting at the same table (boxes with pencils, coasters, plates, etc.). Children count the toys they took for a walk. When getting ready to go home, they check if all the toys are collected. The guys also love to simply count the objects they encounter along the way. In an effort to deepen children's understanding of the meaning of counting, the teacher explains to them why people think and what they want to learn when they count objects. He repeatedly counts different things in front of the children, figuring out whether there is enough for everyone. Advises children to see what their mothers, fathers, and grandmothers think.

Counting groups of objects (sets) perceived by different analyzers (auditory, tactile-motor). Along with relying on visual perception (visually presented sets), it is important to train children in counting sets perceived by ear and touch, and teach them to count movements. Exercises in counting by touch, as well as in counting sounds, are carried out without asking children to close their eyes. This distracts the guys from counting. The teacher makes sounds behind a screen so that the children only hear them, but do not see the hand movements. They count objects placed in bags by touch. Various aids are used for this purpose. For example, you can count buttons on cards, holes in a board, toys in a bag or under a napkin, etc. Accordingly, sounds are produced on various musical instruments: a drum, a metallophone, sticks.

When training children in counting movements, they are asked to reproduce the specified number of movements either according to the model or according to the named number. The teacher gradually complicates the nature of the movements, asking the children to stamp their right (left) foot, raise their left (right) hand, lean forward, etc. However, four-year-old children should not be offered too complex movements, this distracts their attention from counting.

The sets perceived by different analyzers are compared, which contributes to the formation of inter-analyzer connections and ensures the generalization of knowledge about the number. Children are asked, for example, to raise their hand as many times as they heard sounds, or how many buttons were on the card, or how many toys there are. This work is carried out in parallel with exercises in counting objects and is largely linked to them.

Conclusion

The modern education system widely uses art as a pedagogically valuable means of developing a child’s personality. It is art that reflects the artistic image of time and space of people’s life that allows a child to discover new cultural and philosophical facets of these concepts. Knowledge of space and time in the cultural and historical concept makes it possible to intensify the process of child development and lay the foundations of philosophical and logical thinking, starting from preschool childhood.

In preschool age, the foundations of the knowledge a child needs in school are laid. Mathematics is a complex subject that can present some challenges during schooling. In addition, not all children are inclined and have a mathematical mind, so when preparing for school it is important to introduce the child to the basics of counting.

List of used literature

1. Bantikova S. Geometric games // Preschool education – 2006 – No. 1 – p.60-66.

2. Beloshistaya A.V. Why does a child have difficulty with mathematics already in elementary school? Primary school – 2004 – No. 4 – pp. 49-58.

3. Let's play: Mathematical games for children 5-6 years old: A book for kindergarten teachers and parents / N.I. Kasabutsky, G.N. Skobelev, A.A. Stolyar, T.M. Chebotarevskaya; Edited by A.A. Stolyar - M: Education, 1991 -80 p.

4. Didactic games and activities with young children/E.V. Zvorygina, N.S. Karpinskaya, I.M. Konyukhova and others / Edited by S.L. Novoselova - M.: Education, 1985 - 144 p.

5. Kononova N.G. Musical and didactic games for preschoolers - M.: Education, 1982

6. Mikhailova Z.A. Entertaining game tasks for preschoolers - M.: Education, 1987

7. Smolentseva A.A. Plot-didactic games with mathematical content - M.: Education, 1987 - 97 p.

8. Sorokina A.I. Didactic games in kindergarten - M.: Education, 1982 - 96 p.

9. Taruntaeva T.V. Development of elementary mathematical concepts in preschoolers - M.: Education, 1973 -88 p.

10. Training in psychotherapy / Edited by T.D. Zinkevich-Evstigneeva - St. Petersburg: Rech, 2006 - 176 p.

11. Usova A.P. Education in kindergarten - M.: AProsveshchenie, 2003-98 p.

12. Shcherbakova E.I. Methods of teaching mathematics in kindergarten - M: Academy, 200 - 272 p.

1. Ed. Godina G.N., Pilyugina E.G. Education and training of children of primary preschool age. – M., 1987

2. Metlina L.S. Mathematics in kindergarten. – M., Education, 1984

3. Fiedler M. Mathematics already in kindergarten. M., Education, 1981

Rubinshtein S.L. Problems of general psychology. - M.: Pedagogy, 1973. - 423 p.

The current state of mathematical concepts in preschool children

Information about the work “Current state of mathematical concepts in preschool children”

Section: Pedagogy Number of characters with spaces: 49838 Number of tables: 0 Number of images: 0

Similar works

The use of gaming techniques in the formation of elementary mathematical concepts in preschoolers

94102

2

4

... ideas of preschool children, and this confirms our hypothesis. CONCLUSION The purpose of the study was to study the problem of using game techniques in the formation of elementary mathematical concepts in preschoolers. To achieve it, we analyzed the psychological and pedagogical literature on the research problem, reviewed and analyzed the game method in ...

Pedagogical conditions for the intellectual development of older preschoolers in the process of forming mathematical concepts

131247

4

8

... views. It is high-class teachers who are able to bring into play the reserves of the main educational age - preschool. 1.4. Pedagogical conditions for the intellectual development of a senior preschooler in the process of forming primary mathematical concepts Academician A.V. Zaporozhets wrote that the optimal pedagogical conditions for realizing the potential capabilities of a small child are ...

Development of elementary mathematical concepts in children 4-5 years old in the light of modern requirements

75096

5

3

... and a qualitative improvement in the system of mathematical development of preschoolers allows teachers to look for the most interesting forms of work, which contributes to the development of elementary mathematical concepts. 3. Didactic games give a great charge of positive emotions and help children consolidate and expand their knowledge in mathematics. PRACTICAL RECOMMENDATIONS 1. Knowledge of properties by children 4-5 years old ...

Application of general didactic principles in organizing classes on the development of mathematical concepts in children in preschool educational institutions

45655

0

1

... application in the organization of classes on the development of mathematical concepts of general didactic principles. [13] II. Experimental work on the application of general didactic principles in the organization of classes on the development of mathematical concepts in preschool educational institutions 2.1 Ascertaining stage of the experiment To conduct experimental work, I selected the middle group No. 4 of the MDOU “Bendery Kindergarten ...