4. Ways of knowing properties and relationships in preschool age

The main ways of learning such properties as shape, size and quantity, which a child masters already in preschool age, are comparison, seriation and classification. The knowledge of properties and relationships includes the knowledge of shape, size, quantity in the process of comparison.

Comparison is the first way of learning properties and relationships, which preschool children master and one of the main logical methods of learning about the outside world.

Knowledge of any object begins with the fact that we distinguish it from all others and at the same time find its similarity with other objects. By establishing differences, the properties of objects are revealed. Each subject is associated with specific cognitive actions. Thus, the establishment of similarities and differences in color, shape, size, quantity occurs on the basis of visual, tactile - motor, tactile examination of objects.

As a result of comparison, children discover that among the objects that surround them, some are different, not similar to each other, and some are the same. Children highlight differences that make objects look different from each other. This dissimilarity may be due to color, shape, size, spatial arrangement of parts, taste, temperature, tactile and other properties. The more differences a child finds between objects, the more properties he discovers and the more differentiated his perception becomes.

The success of learning the quantity and quantitative relationships of groups of objects depends on mastering the techniques of comparison. You can compare objects by eye. More effective are the methods of direct comparison (overlay, application, connection by lines) and indirect comparison using an intermediary object. These techniques are based on establishing a one-to-one correspondence between the elements of two sets. As a result, children form pairs of objects different groups. More complex and accurate indirect methods of comparison by quantity and size include counting and measurement with a conventional measure.

The overlay technique allows you to detect similarities and differences in quantity, size, shape, color and other characteristics. To compare two groups of objects by quantity, children place each object of one group element by element on objects of another group, to find out whether the objects are equal or whether the stripes are the same in width and length.

Application is a complex method of comparison. The essence lies in the spatial approximation of the compared objects to each other. In this case, it is more difficult for the child to detect similarities or differences between groups of objects.

In situations where the objects being compared cannot be spatially brought closer to each other, methods of connecting them with lines or intermediary objects are used.

Comparison using intermediary objects takes place in cases where the above methods cannot be applied. In order to find out whether an object has the same lengths, use a third object - an intermediary (rope, stick, tape). The intermediary must be longer than both objects being compared or equal in length to the larger object. The child alternately applies the intermediary object to the compared lengths and records the length of each object on it with a pencil or felt-tip pen.

The most complex methods of comparison that preschool children master are counting and measurement. They refer to indirect methods of comparison. When using them, conclusions about the relationships between the objects being compared are made based on a comparison of numbers expressing the size or number of objects.

Seriation as a way of knowing size, quantity, numbers

Seriation (ordering of a set) is carried out on the basis of identifying a certain characteristic of objects and their distribution in accordance with this characteristic. Serial series are constructed in accordance with the rules. The rule determines which element of two (arbitrarily taken) precedes the other element. The main characteristics of an ordered series are the immutability and uniformity of the direction of increase (or decrease in value) of the attribute on the basis of which the series is constructed.

For example, if the smaller of two objects must always precede the larger, then the set is ordered in the direction from the smallest to the largest element. So, the ribbons are laid out from shortest to longest.

Seriation as a way of cognition of properties and relationships allows:

identify order relationships;

establish sequential relationships: each next object is greater than the previous one, each previous one is less than the next one (or vice versa: each next object is less than the previous one, each previous one is greater than the next one);

establish mutually inverse relationships: any object in an ordered series is greater than the previous one and less than the next one (any object in an ordered series is less than the previous one and greater than the next one);

discover patterns of sequence and order.

Preschool children master seriation in the process of arranging specific objects in order. The initial condition for mastering seriation is the mastery of comparison.

In practice, various serialized didactic materials are used: frames-inlays, toys-inserts (matryoshka dolls, cubes, barrels, etc.), serialized sets by M. Montessori for ordering objects according to different characteristics (color, smell, size, different lengths, etc.) .

Cuisenaire rods (colored numbers) and colored stripes, which differ not only in length, but also in color. Moreover, all sticks of the same length have the same color. The number of sticks in the set is such that it allows you to build two rows in different directions.

Children master seriation through the following game exercises:

· construction of a serial series based on a model;

· continuation of the started row;

· construction of serial series according to the rule with given extreme elements;

· construction of rows according to the rule from the starting point;

construction according to the rule with self-determination starting point of the row;

· construction of a series from any element;

· search for missing elements of a series.

With the help of analysis, children identify mistakes they made while completing the task. Thus, confirmation of the effectiveness of logical operations in children is the ability to identify and name the general property of educated classes.

5. Concept and content mathematical representations in preschoolers

The development of elementary mathematical concepts in preschool children is of great value for the intensive mental development of the child, his cognitive interests and curiosity, logical operations: comparison, generalization, classification.

The formation of elementary mathematical concepts is a purposeful and organized process transfer and assimilation of knowledge, techniques and methods of mental activity provided for by program requirements. Its main goal is the successful mastery of mathematics at school, in kindergarten and the comprehensive development of the child’s personality. .

According to E. I. Shcherbakova, the mathematical development of preschool children should be understood as shifts and changes in cognitive activity that occur as a result of the formation of elementary mathematical concepts and related logical operations. .

It has been proven that introducing children to different types of mathematical activities in the process of targeted learning orients them towards understanding connections and relationships. The formation of initial mathematical knowledge and skills in preschool children should be carried out in such a way that training gives not only immediate practical results (counting skills, performing basic mathematical operations), but also a broad developmental effect. The mathematical development of preschoolers is usually understood as qualitative changes in the forms of cognitive activity of the child that occur as a result of the formation of elementary mathematical concepts and related logical operations. Analysis scientific research teaching experience such as: A.M. Leushina, N.I. Nepomnyashchaya, A.A. Stolyar and many others, convinces that rationally organized teaching of preschoolers mathematics provides general mental development children. Rationally organized learning is timely, appropriate for the age and interests of children, and pedagogical guidance from an adult (teacher or parents) is important. Children acquire basic knowledge about the set, number, size and shape of objects, learn to navigate in time and space. They master counting and measuring linear and volumetric objects using conventional and generally accepted measures, and establish quantitative relationships between quantities, wholes and parts.

In the program "Education and training in kindergarten" edited by Vasilyeva M.A. and others with general tasks for the development of elementary mathematical concepts formed; by the end of preschool age, it is important to teach the child to understand, distinguish and perform various operations with numbers, improve counting skills, introduce the numbers of the second heel of units, find the previous and subsequent numbers; measure, compare, length, width, height of objects; One of the many important tasks is the child’s ability to navigate on a sheet of paper in a square. The methodology for forming elementary mathematical concepts in children is constantly developing, improving and enriching with the results of scientific research and advanced pedagogical experience. Currently, thanks to the efforts of scientists and practitioners, a scientifically based methodological system for the development of mathematical concepts in children has been created, is successfully functioning and is being improved. Its main elements - purpose, content, methods, means and forms of organizing work - are closely interconnected and mutually condition each other.

The mathematics program is aimed at developing and shaping mathematical concepts and abilities, logical thinking, mental activity, ingenuity, i.e. the ability to make simple generalizations, comparisons, conclusions, prove the correctness of certain judgments, and use grammatically correct figures of speech.

Among the tasks for the formation of elementary mathematical knowledge and the subsequent mathematical development of children, the main ones should be highlighted, namely:

· Acquiring knowledge about set, number, size, shape, space and time as the basis for mathematical development;

· Formation of a broad initial orientation in quantitative, spatial and temporal relations of the surrounding reality;

· Formation of skills and abilities in counting, calculations, measurement, modeling, general educational skills;

· Mastery of mathematical terminology;

Development of cognitive interests and logical thinking abilities, general intellectual development child.

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The cognitive development of preschool children is a continuous and very interesting process. The baby begins to get acquainted with the world from the first moments after birth.
The human brain is designed in such a way that it must constantly receive and process this or that information, ignoring some of it, leaving some, and completely getting rid of some. This sorting of information is most clearly expressed in preschoolers. A child under the age of 7 learns to form his own attitude towards people and objects. Parents must guide this process in the right direction.
Cognition can certainly be considered an active activity, clearly aimed at acquiring and applying knowledge. Here the child’s cognitive activity and his active position as a direct subject of such activity are manifested.

Age from one to three years

The youngest children are tireless researchers, since all areas of their activity are permeated with the desire for knowledge. It is also important here that the baby not only wants to look at objects, but also to manipulate them: connect, separate, experiment and design.
Thanks to activities with objects, the baby develops:

• perception;
• memory;
• thinking
• other cognitive processes.

At the same time, perception develops most intensively, constituting the center of the child’s consciousness. Perception is a fundamental mental function that allows a child to navigate his environment. In preschoolers, perception is most active during the process of action - the child, through trial and error, finally assembles a pyramid or puts a part into a hole of a suitable size and shape.
By repeatedly comparing color, shape and size, selecting matching or identical elements or parts of objects, the baby finally gets a practical result.
At first, the comparison is quite rough and approximate. The kid tries it on, makes mistakes, corrects mistakes until he achieves the result. But after one and a half years, the number of preliminary fittings quickly decreases, since the baby is already moving on to visual perception, having learned to evaluate the relationship between static and dynamic objects. This transition occurs at 21-22 months and is quite noticeable. Practical activity trains the child, in addition to perception, also thinking, which at this age is characterized by a visual and effective character. By experimenting in practice, the child discovers new ways to achieve the goal.
So, he learns to use one object to reach another: he uses a stick to get a rolled ball, climbs onto a chair to get to the object of interest. When new means are invented, new properties of objects are also revealed to the child. For example, when trying to scoop up water with a sieve, like sand, the baby discovers that water is pouring out of it.
This surprises him a lot and contributes to further research and new discoveries. The simplest household objects (pillows, armchairs, chairs) allow the baby to discover new ways of movement: rolling, sliding, sliding.

By the end of the third year, the baby gradually abandons external tests, fantasizing and experimenting more in his mind. Communication with surrounding objects is becoming more and more clearly cognitive in nature. Generalization of experience and expansion of cognitive activity are manifested in the child’s numerous questions, with which he literally bombards adults. Thus, based on practical actions with objects and communicating with adults, children gradually build their ideas about the world around them.

Emotional development of preschool children

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Cognitive development in early preschool age continues in three main directions:

• the child’s ways of navigating the environment expand and change qualitatively;
• new ways of orientation appear;
• The child’s knowledge and ideas about the world are enriched in content.

The cognitive activity of preschool children at the age of 3-5 is significantly enriched, and qualitatively new sensory processes of perception and sensation appear. Getting involved in diversity different types activities (play, communication, drawing, design, etc.), the child learns to distinguish individual properties and characteristics of objects more subtly. His color discrimination, phonemic hearing, perception of the shape of objects and visual acuity are improved.
Gradually, perception is separated from objective action, after which it develops as a purposeful independent process with specific methods and tasks. Instead of manipulating an object, children begin to become familiar with it at the level of visual perception. At the same time, the hand “teaches” the eye (the movement of the gaze on the object is accompanied by the movement of the hand).
In preschool age, visual perception turns into one of the leading processes of direct study of phenomena and objects. That is, in early preschool age the ability to examine objects is formed. Looking at new objects (stones, objects, etc.), the baby not only visually gets acquainted with them, but moves on to auditory, tactile and olfactory perception - stretches, bends, scratches, shakes, brings to the ear, smells the object, while often not still being able to define it with a word. The baby’s varied active orientation towards a new object stimulates the appearance of more accurate images in his brain. Mastering the system of sensory standards ( geometric shapes, colors of the spectrum) help develop the child’s actions of perception.
At the same age, children begin to use symbolic representations of events and objects, thanks to which they gain greater freedom from the field of perception, often without direct contact with the objects under study. Small child learns to represent objects with the help of bodily movements (time-delayed imitation), and older children use images stored in memory (when looking for a hidden object, the child clearly knows what he is looking for). An even higher form of representation are symbols, with the help of which you can represent not only concrete, but also abstract objects.
Speech is the clearest example symbolic means. A child is able to think about an object that is not in front of his eyes, he fantasizes with objects that he has not had in his experience of cognition. He develops the ability to virtually reproduce the hidden parts of objects based only on their visible sides and operate with images of such hidden parts.
In the mental development of younger preschoolers, a qualitatively new achievement is the symbolic function, which personifies the formation of an internal plan of thinking, for which at this age external supports (figurative, play and other symbols) are still needed.
The thinking of younger preschoolers is characterized by qualitative originality. Children's spontaneity makes the child a realist, so it is difficult for him to distinguish reality from fantasy or dreams. Children are still self-centered, because they are not able to look at the situation through someone else’s eyes, but start only from their own point of view.
Children are characterized by animistic ideas, that is, all surrounding objects think and feel the same way as the child himself. That is why the baby feeds and puts the doll to sleep. When examining an object, he singles out one, usually its most striking feature, and generally evaluates the object, focusing specifically on this feature. He is more interested in the result of an action, and not in the process of achieving it, which he does not yet know how to trace. The child thinks about what is now or will be in the next moment, but cannot yet understand how what he sees now happened. That is, at this age it is still difficult for them to correlate the goal and the conditions, so the main goal is easily lost by children. The ability to set goals is just beginning to form, so it is still difficult for children to set new goals on their own. So far they have been able to relatively easily predict only the course of events that children have observed many times. Anticipate changes in phenomena
younger preschoolers can only be based on one parameter, so the forecast is rarely accurate.

At this age, children have a very developed curiosity, “why?” and why?" heard from them all the time.

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5-6 years old - senior preschool age

Cognitive development in older preschool age already becomes a complex complex phenomenon, where cognitive processes such as thinking, perception, attention, memory, and imagination continue to develop. These are all different forms of a child’s orientation in himself, in the world around him, which regulate the child’s activities.
Children's perception loses its original universal character. Through design and various options visual arts The baby begins to separate the object itself from its properties. After this, for the child, the signs and properties of the object become objects of separate consideration. After being designated by a word, they become categories of cognitive activity - this is how a preschooler develops categories of shape, size, spatial relationships, and color. As a result, the child already perceives the world in categories, and the process of perception becomes more and more intellectual.
Various types of activities, and play first of all, make children's memory focused and voluntary. The child is already able to set himself the task of remembering something for subsequent, even if not too distant, action.
His imagination is rebuilt, becoming anticipatory from reproducing (reproductive). In the mind or in a drawing, the child can already imagine the intermediate stages, and not just the final result of the efforts. The child begins to regulate and plan his actions through speech. Inner speech is also formed. For older preschoolers, orientation becomes an independent, very intensively developing activity. Special methods of orientation continue their development, for example, modeling or experiments with new materials. Experimentation among preschoolers is closely linked to the practice of transforming phenomena and objects.
When, during experimentation, a child transforms objects, this is now given a step-by-step clear character. This step-by-step nature is manifested in the fact that the transformation occurs piecemeal, in the form of successive acts, and after each such act, an analysis of the changes that have occurred begins. The very sequence of transformations carried out by the child indicates that his thinking has reached a fairly high level.
Children can engage in experimentation and speculation, as a result of which they can unexpectedly gain new knowledge, that is, they have new opportunities for cognitive activity. As a result childish thinking itself pushes its own development. This is inherent in all children and is of great importance for the development of a creative personality. This process is especially pronounced in talented children. To promote experimentation, it is useful to use “open type” problems in which several correct solutions are proposed.
For preschoolers, modeling can be present in a variety of activities: playing, drawing, designing, modeling, etc. Thanks to modeling, a child can solve cognitive problems indirectly.
In preschool children, the range of modeled relationships becomes wider. Using models, the baby can materialize logical, mathematical, and time relationships. To model hidden connections, they resort to conditionally symbolic images in the form of graphic diagrams.
Verbal-logical thinking is added to visual-figurative thinking. But since it is in the embryonic period of development, then in children's logic we can still see gross mistakes. For example, a baby may be happy to count family members, but at the same time he will probably forget to count himself.

Thanks to the development of cognitive activity, meaningful learning and communication, the baby gradually forms an image of the world around him: initially situational ideas are systematized, which gradually turn into knowledge, general categories of thinking gradually emerge (causality, part - whole, object - system of objects, space, chance). Scientists have long been studying how this happens, but this process is still not fully understood. For example, it has been noticed that young children have tremendous intuition: they immediately determine which of the adults truly loves them and is interested in them, and who is pretending. Ask any actor which audience is easier for him to work with – adults or children? Of course, with an adult! And why? Because you can’t fool children, they sense falsehood from afar, so you can’t “cheat”; you have to live on the stage of a children’s theater!

Knowledge of the surrounding world by preschool children

To understand how children interact with the world and learn about it, you can watch the kids. Mostly Scientists have long been studying how this happens begins at two years of age. Everything that surrounds him becomes an object of study: toys, pets, people, furnishings, etc.

His experience cannot be called orderly, because kids do not systematize their knowledge, but only receive impressions, but this is very important for the subsequent perception of the world. Information imprinted in the mind at a tender age becomes the basis, the core on which further knowledge about the environment is “strung”.

It is during this period that it is necessary to broaden the child’s horizons and introduce him to different areas of everyday life. It’s good if parents give explanations, drawing the baby’s attention to the people who live nearby, calling things by their proper names. It is useful to tell your child: “You are Kolya. Where are Kolya’s eyes and hands? etc." This is how the baby self-identifies in the world.

By the age of three, a child’s knowledge of the world leads him to master nature and the environment. In a familiar environment, he already navigates well, but the world of the park, forest, public places becomes a true discovery for him! Adults should draw his attention to various natural phenomena: wind, snow, rain.

It is useful to observe the behavior of animals with your child, for example, in a zoo. Show how animals take care of their babies, how they bathe, eat, etc. This is new and very interesting for kids!

From the age of five to six years, preschool children’s knowledge of the world around them can occur through travel. They are already quite intelligent, curious, impressionable, and are able to retain information about sights in their memory for a long time. Traveling is a wonderful means for developing children’s horizons, memory, and speech, and a source of new knowledge about the traditions and lifestyles of other peoples and countries.

The child’s active knowledge of the world around him

The best thing the world children learn by actively influencing it. It is important that from the very early age They developed a sense of responsibility for their actions. What actions are useful for child's knowledge of the world?

• . By giving children feasible tasks to clear paths of snow, create spring dams for the purpose of snow removal, etc., adults show that through their own labor a person can transform the world around them.

• Caring for living things. Having animals in the house or in the garden is a great way to introduce your child to caring for them and learning their habits. It is necessary to interest the child in observing the “smaller brothers”, to show how responsive they are to kindness and sweet Nothing how selflessly they serve a person

• Work in the garden and vegetable garden, indoor floriculture. If from a young age you introduce your child to working in his own small garden bed, this will have a beneficial effect on his worldview. With what pleasure do children water their carrots and cucumbers, and with what pride do they treat their mothers and fathers to them! And at home, caring for their own, “best” flower will bring them a lot of joy.

Try to do everything to turn it into an exciting process in which he himself can participate!

The most unforgettable and educational time is childhood. Time for searches, research, questions, experiments. Anyone who has encountered small, inquisitive children knows that this is the time of the “whys”: charming children eagerly seeking answers to the questions that torment them. A small child explorer of the natural world around him. He gets to know this world with the help of personal sensations, actions, experiences, through his, albeit small, life experience.

Today, the development of cognitive abilities of preschool children is a pressing problem of the modern world. An important stage is the development of the child’s thinking, attention, speech, awakening interest in the world around him, developing the ability to discover new things and be surprised by them.

Development of a preschooler

If a healthy baby is born, then he has an innate cognitive interest, thanks to which he adapts to new living conditions. Over time, interest turns into cognitive activity, which is responsible for the path of learning the previously unknown. Further growth and development lead to the formation of cognitive activity in the child, which is characteristic of adults.

During childhood Before the onset of the school period, cognitive activity allows you to form the first image of the world around you. The formation of the outlines of the world occurs due to the development of the following components:

• cognitive processes;
• information;
• attitude towards the world.

All components of the field of cognition have a strong relationship. We must not forget that the knowledge of a child and an adult have practically nothing in common. An adult perceives his surroundings with his mind, while a small person perceives his surroundings with his emotions. If adults study information first, then attitude, then children study completely differently: attitude comes first, information comes second. Accordingly, when starting work on developing the cognitive aspect, one should not forget about age characteristics children.

Cognitive development of early preschoolers

The cognitive process begins from birth and can be divided into the following stages:

• First year of life- at this time, the baby, with the support of his mother or someone who replaces her, gets acquainted with the world around him. And her task is to provide both care and positive emotions for the baby. Good music, bright toys, a gentle voice, and a pleasant aroma in the apartment will help you cope with this task.
• One year or two years- at this age, children are able to differentiate between what they like and what they don’t. At this time, it is worth consolidating what you have previously learned and teaching new skills.
• Before three years - at this age, when the baby begins to develop thinking and intellectual abilities, the child will be completely immersed in the cognitive process. Cognitive development of this age category, as a rule, occurs through play.

Cognitive development of preschoolers - second junior group

The perception of the world by a child of three years of age is based on the objective content of reality. The world consists of isolated concrete objects, objects, and phenomena. A child’s cognition works according to the principle: what I see and what I come into contact with, I explore. He examines objects from two angles: he is interested in how they are appearance, and internal parameters. But a three-year-old preschooler is unable to understand on his own the hidden parameters of objects.

Children whose age corresponds to the second youngest group the first connections and dependencies begin to form- relationship between external and internal parameters of the object. They begin to realize the role and significance of various objects in their life.

Children of this age group are given an excursion around the territory of the kindergarten at least once a month, where they get acquainted with the aquarium and its inhabitants, interior items, birds and other things. Since preschoolers love gifts, during this period they are interested in the gifts of nature - beautiful autumn leaves, rowan berries, snowflakes, frosty patterns on glass, the first spring flowers emerging from under the snow, and others.

A “we fix it - we help” scheme is formed: if someone is upset, then they should be consoled, and when something becomes faulty, then it is worth repairing. It is very important to understand that cognitive development lies not only in classes; a significant role in the development of a preschooler’s cognitive activity is played by correctly planned and implemented activities in everyday life: individual conversations and in groups, observations, studying the structure of one’s own body, caring for indoor flowers.

Middle group

When a baby turns four years old, his development undergoes significant changes. This is due to a number of factors: changes in the structure of the brain, improvement of mental processes, a high level of speech acquisition, and the formation of some kind of stock of images about the immediate environment. Accordingly, there is a transition cognitive development to the next and higher level, which is qualitatively different from the previous one.

For a four year old it becomes possible correctly perceive and assimilate the information that he received through words. These kinds of changes in cognitive development enable the child to cross the boundaries of his immediate environment. Ahead of him awaits a lot of knowledge and discoveries, before which he must pass preparatory work to facilitate the perception of information at the verbal level. The process is divided into two stages:

1. The preschooler is provided with information in verbal form about some object or phenomenon;
2. an object or phenomenon is demonstrated to the baby, and the demonstration is accompanied by a repeated story.

This new cognitive technique allows children to both learn and understand a variety of information about the world. Every educator and parent has the right to independently choose the content offered to children for learning. However, a number of conditions regarding the content offered should be taken into account:

• it should be based on experience and those images about the world around us that children already have;
• information should only be presented that arouses interest and positive emotions in the most adult person, and in which he is very well versed;
• priority should be given to objects and phenomena living in close proximity.

Preschool children who are in middle group, introduce and consolidate the concept of “sequence”. Demonstrates how important it is to maintain consistency in life. This period is ideal for getting to know different types of work and meeting interesting people. There is an acquaintance with both the appearance of objects and the quality parameters of man-made materials - paper, fabric, glass and others. For this purpose, work is underway to create collages and layouts, which includes 3 stages:

1. repetition of such general features of a certain place as soil, mountains, water, snow and ice, in combination with some significant dependencies - low temperature, ice;
2. populating a replicated landscape with inhabitants typical of this environment, taking into account significant connections;
3. inclusion of a person in this scheme and determination of his relationship with the outside world.

This age is characterized by the formation of selective interests in children. Therefore, an important point is the child’s participation in the “My Collection” exhibition, where children’s works are presented in accordance with their personal interests - inserts, calendars and others.

Senior group

The world of a preschool child, consisting of his immediate environment, is strong and understandable. Quite a lot has accumulated in his mind a large number of information that requires constant updating. This explains the desire of children of this age group to expand the cognitive horizons of reality, comprehend the connections and relationships that exist in the world, and affirm their own attitude towards the world around them. They are interested in new information sources.

The following means and ways of understanding the world that are inherent in this age should be highlighted:

• through actions and own practical experience;
• through words - stories from adults;
• through books and television programs with educational content.

During this period, parents and teachers should pay attention to one of the main tasks, which is to organize a subject-development environment for cognitive development. Some items are waiting for kids from the beginning of the school year, others appear during the process of getting to know them.

Children at the age of five have a mental and intellectual level that allows them to begin the primary elementary assimilation of concepts such as “sign”, “symbol”, “sign systems”, “time”. Knowledge of such terms begins with familiarizing preschoolers with a map, globe, various symbols and signs. And also further development of already comprehended concepts is carried out: climatic zones, landscape relief and others.

Among the serious topics, it is worth highlighting “time”, which is a complex concept that even now has no definition. Children of this age should be taught to record time using clocks and various calendars, make their own daily routine calendar, and be introduced to the past using the example of dinosaurs.

To deepen and expand children's understanding of living and inanimate nature, the information stock should be classified into blocks. For example, living nature includes the kingdoms of plants and animals, which, in turn, also have their own sections: wild plants and cultivated plants, wild and domestic animals. Information from the field of knowledge about inanimate nature is also presented in a systematic way - atmospheric phenomena, solar system, seasons and others.

Adults, developing the cognition of children of this age, should use the following techniques:

• conversations with kids on educational topics;
• detailed consideration problem situations and riddles;
• demonstration, discussion of paintings, television programs, videos, films;
• detailed, competent answers to children’s questions related to educational topics.

Preparatory group

When children reach the age of six, they have a wealth of knowledge about our world. The task of adults is to direct the cognitive process to establish the order of information according to content, form meaningful cause-and-effect relationships, and develop a positive attitude towards the world. At the same time, it is worth understanding that ordering by content is the division of accumulated and received information about the world into spheres of knowledge focused on a specific block of knowledge - historical, geographical, cultural and other spheres.

So, the cognitive development of preschool children is a process that is not only very exciting, but also continuous. A baby's exploration of the world begins immediately after birth. The very structure of the human brain presupposes the constant acceptance of any information, its processing, as a result of which complex processes of accumulation, ignoring and deletion of information occur. But for correct formation, parents must constantly be nearby to guide in the right direction.

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OGBOU "Tomsk State Pedagogical College" (OGBOU "TGPC")

Home test

in the academic discipline “Theory and Methods of Mathematical Development”

Features of preschool children’s knowledge of the size of objects

Completed:

Bylina Olga Ivanovna

Course attendee

professional retraining

Checked:

Zakharova G.N., teacher

Tomsk - 2014

size general educational eye gauge preschool

Introduction

Conclusion

Bibliography

Application

Introduction

In kindergarten, children develop elementary mathematical concepts, and the children’s future success in mathematics depends on how correctly they are formed.

Ideas about the size of objects are an important component of mathematical concepts in preschool children. The ability to identify a quantity as a property of an object and give it a name is necessary not only for knowing each object separately, but also for understanding the relationships between them. This has a significant impact on the formation in children of more complete knowledge about the surrounding reality.

Awareness of the size of objects has a positive effect on the child’s mental development, as it is associated with the development of the ability to identify, recognize, compare, generalize, leads to an understanding of size as a mathematical concept and prepares for mastering the corresponding section of mathematics at school. Previously, when preschoolers were introduced to elementary mathematical concepts, number was the result of counting; recently, number is also perceived as the result of measurement, and older preschoolers become familiar with the functional dependence of number (counting result) on the size of the measure.

The concept of “quantity” in mathematics is considered as fundamental. Magnitude is length, volume, speed, mass, number, etc. Speaking about the problem of developing ideas about the size of objects in preschoolers, we narrow the concept of “size” and characterize the size of objects with it.

The size of an object, like any other mathematical quantity, can be determined only on the basis of comparison. Using the criteria for comparing objects with each other, relationships of equality or inequality of their values ​​are established.

The size of an object also depends on its location in space. The same object can be characterized either as tall (low) or as long (short). It depends on whether it is in a horizontal or vertical position.

The actual size of an object, independent of the distance at which the object is located from the perceiver.

Comparative size of objects located at different distances from the perceiver.

The comparative size of objects located at the same distance from the perceiver.

When determining the size of an object, its properties should be taken into account. The main property of a quantity is comparability. Only as a result of comparison can a quantitative characteristic of any value be obtained. The quantity is also characterized by variability. Example: changing the length of a table only changes its size, but does not change its content and quality; the table remains a table. The third property of quantity is relativity. The magnitude of any object is relative, it depends on what other magnitude it is considered in relation to. In fact, one and the same object can be defined by us as larger or smaller depending on the size of the object with which it is compared.

The perception of magnitude occurs through the establishment of complex systems of connections, both intra-analyzer (between the muscular and optical components of the eye) and inter-analyzer (between the tactile and motor, motor and visual analyzers). It follows that young children, without sufficient experience, often make false conclusions about the size of an object, since they judge it only by the available images on the retina.

The problem of the perception of magnitude should also be considered as a problem of thinking. There is a complex dialectical relationship between feelings and reason, which finds concrete manifestation, for example, in the fact that the process of perceiving magnitude (as well as other properties) is mediated by thinking through comparison, analysis, the use of relevant concepts, judgments, inferences, etc. An indispensable mental operation that provides an assessment of the size of objects is comparison.

Thus, it should be noted that the concept under consideration is quite complex for preschoolers to perceive and understand.

2. Peculiarities of perception and knowledge of quantity by preschoolers

To form the most basic knowledge about size, it is necessary to form specific ideas about objects and phenomena of the surrounding world.

Awareness of the size of objects has a positive effect on the child’s mental development, as it is associated with the development of the ability to identify, recognize, compare, and generalize; leads to an understanding of quantity as a mathematical concept; prepares for mastering the relevant section of mathematics at school.

Cognition of magnitude is carried out, on the one hand, on a sensory basis, and on the other hand, it is mediated by thinking and speech. The sensory experience of perceiving and assessing size begins to take shape already in early childhood as a result of the establishment of connections between visual, tactile and motor-tactile sensations from those toys and objects of various sizes that the baby operates with. Repeated perception of objects at different distances and in different positions promotes the development of constancy of perception.

Children's orientation in the size of objects is largely determined by the eye - the most important sensory ability. The development of the eye is directly related to the mastery of special methods of comparing objects. Initially, children compare objects by length, width, height by practical application and application, and then based on measurement. The eye seems to generalize practical actions hands. By highlighting one or another specific dimension, the child strives to show it (runs his finger along the length, shows the width with spread arms, etc.). These inspection actions are very important for a more differentiated perception of the size of an object.

Preschoolers firmly attach the sign of size to a specific object that is familiar to them: “The elephant is big, and the mouse is small.” If you put 4-5 toys in front of your child, gradually decreasing in size, for example, matryoshka dolls, and ask him to show the largest one, then he will do it correctly. If you then remove it and again ask to point to a large toy, then children 3-4 years old, as a rule, answer: “Now there is no big one.”

Children three years old perceive the size of objects undifferentiated, i.e. they focus on the total volume of the object, without highlighting its length, width, height.

Four-year-old children already have a differentiated approach to choosing objects based on length or width, but only on condition that the length of the object exceeds the width. For children of senior preschool age, a short period of time is required to master all three dimensions.

Children 5-6 years old know that to determine the length, width, height of an object, it must be measured, and they name what objects this can be used with: a ruler, a meter, a centimeter. Sometimes measuring instruments are not quite accurately designated: “stick”, “pattern”, “an oilcloth with numbers, all sorts of numbers are drawn on it”, etc.

Children describe the process of measuring their height very roughly, since they do not know how it is measured, although growth is measured repeatedly in kindergarten. They talk about the methods that are usually used in families: “you need to stand together, with your backs to each other,” “measure with your heads”; “You can highlight it on the wall,” etc. Preschoolers strive to expand their knowledge about measurements (“Mom will show me how to measure, I’ll see when I go to the store with my mother”).

Thus, in primary and middle preschool age, children determine the sizes of objects by directly comparing them (application or superimposition); in older children, an indirect method of comparison is also used (assessment of the sizes of perceived objects in comparison with well-known ones encountered in the child’s experience earlier, measurement with a conventional yardstick).

Any program includes in mathematical preparation teaching children to count, developing quantitative concepts within the first ten, learning to solve and compose simple arithmetic problems. The program for each age group includes the following sections: “Quantity and counting”, “Size”, “Form”, “Orientation in space”, “Orientation in time”.

The “Childhood” program is aimed at satisfying the individual inclinations and interests of the child, at developing curiosity and cognitive abilities. The tasks are disclosed in the “First steps in mathematics” section for all age groups, starting from the second youngest group.

Program for Education and Training in Kindergarten, edited by M.A. Vasilyeva, V.V. Gerbova, T.S. Komarova carries the task of forming ideas about the size of objects in preschool children, which are very meaningful and voluminous.

4. Identification of the level of ideas of children in the older group about the sizes of objects

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 acquire knowledge about geometric figures, their size, 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 using special didactic material separately for each age group (see appendix).

IN senior group Children are taught to measure and determine, using a conventional measure, the size of objects and the volume of liquid and granular bodies. Children must firmly grasp the rules of measurement, since in subsequent lessons they carry out measurements independently from beginning to end. It is important that children not only remember the sequence, but also perform it correctly.

As a result of this activity, children develop an eye; they can determine the size of objects by eye, then checking the correctness of their measurement using the selected conventional measure. Children learn that different types of quantity are measured by different standards.

Conclusion

The methodology for the formation of elementary mathematical concepts in the system of pedagogical sciences is intended to provide assistance in mathematics, one of the most important subjects in school, and to contribute to the education of a comprehensively developed personality.

In kindergarten, children master several types of conventional measurement. The first type includes linear measurement, when children learn to measure the length, width, height of various objects using strips of paper, sticks, ropes, steps and other conventional measures. The second type of measurement is determining the volume of bulk solids using a conventional measure: children learn to measure the amount of cereal and granulated sugar in a bag with a mug, glass, spoon and other containers. The third type is measuring liquids with a conventional measure to find out how many glasses of water are in the carafe, etc.

Thus, in preschool educational institution measuring activity is of an elementary, propaedeutic nature. The child first learns to measure objects with conventional standards, and only as a result of this are the prerequisites created for mastering the “real” measurement.

Bibliography

Asmolov A.G. “Psychology of Personality” .-M.: Education, 1990.

Makarychev K.L. Preparation for school // Preschool education No. 9 2004

Metlina, L.S. Mathematics in kindergarten [Text] / L.S. Metlina. - M.: Education, 2004. - 246 p.

Mikhailova Z.A. and others. Theories and technologies of mathematical development of preschool children. - St. Petersburg: “Childhood-PRESS”, 2008.

Nosova, E.A. Prepositional training of preschool children. Usage gaming methods in the formation of mathematical concepts in preschoolers [Text] / E.A. Nosova. - L.: Pedagogy, 2000. - 235 p.

Silaeva M.N. Using the process of forming elementary mathematical concepts in kindergarten. - L., 1990.

Freilakh N.I. Methods of mathematical development. - M.: Publishing House "Forum": INFRA-M, 2011.

Application

Getting to know the signs: short - long

Classification game

On the table there are long and short sausages made of plasticine. Both sausages are the same thickness and the same color. The teacher hands out plasticine to the children and asks them to make the same sausages: one long and one short. At the end of the lesson, the children examine their modeling and show it. Which sausage is long and which is short. You can invite the children to connect all the sausages and make a long bunch of sausages.

Naming game

We are walking.

Children walk around the room. When they hear the word “short,” they take short steps, and when they hear the word “long,” they take very long steps. Additions can be made to this game. For example: children take (short) steps on their toes. You can use a dance that alternates long and short steps.

Consolidation of material throughout the day.

During construction, children select long and short bars from the building material and build a bridge, first only from short, and then only from long bars.

When making crafts, children make a star out of straws, having previously sorted the long and short straws.

During the conversation, the teacher talks about the long and short way to kindergarten, about a long and short period of time (for example, while waiting for something), asks children to talk about their impressions.

During physical education exercises, children line up in long and short rows. You can build a long and short train.

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