Methods of teaching mathematics in preschool educational institutions. | Educational and methodological material in mathematics on the topic:

Methods of teaching children elements of mathematics

Anna Fadyunina

Methods of teaching children elements of mathematics

Methods of teaching children elements of mathematics

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.

In the theory and methodology of children's mathematical development, the term method is used in a broad and narrow sense. The method can denote a historically established approach to the mathematical preparation of children in kindergarten (monographic, computational and the method of mutually inverse actions).

When choosing methods, the following are taken into account : goals, learning ; 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 towards certain methods ; specific conditions in which the learning , etc.

I. G. Pestalozzi,

F. Froebel,

M. Montessori I. is considered the founder of the theory of primary education . G. Pestalozzi.

He proposed teaching children to count based on understanding operations with numbers, and not on simply memorizing the results of calculations, and sharply criticized the dogmatic teaching methods . the methodology developed by I. G. Pestalozzi was the transition from simple elements to more complex ones. Particular importance was attached to visual methods that facilitate the assimilation of numbers.

F. Frebel and M. Montessori paid great attention to visual and practical methods . Developed special manuals ( “Gifts”

F. Froebel and M. Montessori's didactic sets) ensured the acquisition of sufficiently conscious knowledge in
children . In the method of F. used a game as his main , in which the child received sufficient freedom.
According to F. Frebel and M. Montessori, the child’s freedom should be active and based on independence. The role of the teacher in this case comes down to creating favorable conditions. Ya. A. Komensky Currently, there are several different classifications of didactic methods .

One of the first was classification, which was dominated by verbal methods .

Y. A. Komensky, along with verbal ones, began to use another method based on acquiring information not from words, but “from the ground, from oaks and beeches”

, that is, through knowledge of
the objects . The main thing in this technique was the reliance on the practical activities of children . At the beginning of the 20th century, the classification of methods was mainly carried out according to the source of knowledge: verbal, visual, practical.
E. I. Tikheyeva The theory and practice of teaching have accumulated some experience in using different methods in working with preschool children. During the period of the formation of public preschool education, the development of methods for the formation of elementary mathematical concepts was influenced by methods of teaching mathematics in elementary school . Working with preschoolers. E.I. Tikheyeva contributed a lot of new things to the development of methods for teaching children ; the games she compiled and the games she created combined words, actions and visuals. In her opinion, children under seven years old should learn to count through play and everyday life. Game as a teaching method E. I. Tikheyeva proposed introducing as one or another numerical representation has already been “extracted by children from life itself”

F. N. Blecher. Proposed the idea of using games in teaching preschoolers (30s-40s)

A. M. Leushina She considered practical methods in the system of verbal and visual methods . It is with practical actions with objective sets that children begin to become acquainted with elementary mathematics . (from the 50s)

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 consisting of a number of operations. For example, counting objects : name 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.
However, excessive use of practical methods and delays at the level of practical actions can negatively affect the development of the child.

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 at all detract from their importance in the mathematical development of children .

Visual teaching methods include : demonstration of objects and illustrations, observation, display, examination of tables and models. Verbal methods include storytelling, conversation, explanation, explanations, and verbal didactic games. Often in one lesson different methods in different combinations.

The components of the method are called methodological techniques . The main ones used in mathematics 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?” ?

,
“Get things in order”
, etc.).

widely used methodological technique is demonstration . This technique is a demonstration; it can be characterized as visually practical and effective. Certain requirements are imposed on the display: clarity and dissection; consistency of action and word; accuracy, brevity, expressiveness of speech.

One of the essential verbal techniques in teaching children mathematics is 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. In this case, the questions must be accurate, specific, and concise. They are characterized by logical consistency and variety of formulations. In the learning there should be an optimal combination of reproductive and productive issues depending on the age of the children the material being studied . Questions are valuable because they enable the development of thinking. Prompt and alternative questions should be avoided.

children's questions and answers is called a conversation. During the conversation, the teacher monitors the children’s correct use of mathematical terminology and the literacy of their speech, accompanying it with various 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, they are the same. A square has corners. Show me the corners." Or another example. The teacher teaches children to measure , showing practical actions with explanations of how to apply a measure, mark its end, remove it, and apply it again. Then he shows and tells how measures are calculated.

The older the children, the more important problematic issues and problematic situations are learning Problem situations arise when:

— the connection between fact and result is not revealed immediately, but gradually. This raises the question, “Why does this happen?”
(we lower different objects into the water: some drown, others don’t)
;

- after presenting some part of the material, the child needs to make an assumption (experiment with warm water, melting ice, problem solving)

;

- use of words and phrases “sometimes”

,
“some”
,
“only in certain cases”
serves as a kind of identifying signs or signals of facts or results
(games with hoops)
;

- for the concept of a fact, it is necessary to compare it with other facts, create a system of reasoning, i.e., perform some mental operations (measurement with different measures, counting in groups, etc.)

Numerous experimental studies have proven that when choosing a method, it is important to take into account the content of the knowledge being generated. Thus, in the formation of spatial and temporal concepts, the leading methods are didactic games and exercises (T. D. Richterman, O. A. Funtikova, etc.)

.
When introducing children to shape and size, along with various play methods and techniques, visual and practical ones are used.
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 and mathematical representations (properties, operations with sets)

based on usage

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)
.

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. children's interest in play to interest in learning is completely natural.

Principles of mathematical learning and development of preschoolers

The method of mathematical development of a child is based on the following principles of mathematical teaching and development of preschool children:

The principle of visualization of learning . Training will be effective when using visual teaching aids that meet the age and individual characteristics of children’s cognitive development and perception of information.
The principle of clarity in organizing classes . Mathematics classes should have a clear structure. The plot of the game and the sequence of actions must have a clear structure in accordance with which the development of the preschooler will take place.
The principle of relying on developmental psychology . Mathematical learning tasks should be developed in accordance with the age-related characteristics of the child’s development, his needs and capabilities of mathematical perception.
The principle of learning variability . It is necessary to use different methods and means of forming the child’s mathematical concepts and ideas. This can be gaming activities, logical tasks, exercises of a creative nature, but with a logical focus, etc.
The principle of multitasking learning. In the course of studying mathematics, one should focus not only on the formation of elementary mathematical concepts in the child, but also on the development of spatial perception,
The principle of game learning . It is important to implement the mathematical development of preschoolers in a playful form, since play is the leading activity of preschoolers. The game motivates to learn. It contains an element of surprise, captivates and develops interest in mathematics.
The principle of orientation towards the development of cognitive activity . The child must develop not just mathematical knowledge, but also a desire to independently study mathematical science and form logical judgments and conclusions.
The principle of creating a developing space . In preschool educational institutions, a subject-development environment is created in which fundamental cognitive processes are formed.
The principle of development of perception of quantitative and qualitative characteristics of objects . If a child masters the differences between objects based on quantitative and qualitative characteristics, this will lay the foundation for the formation of mathematical concepts.

Methods of teaching mathematics in kindergarten, Shcherbakova E.I., 1998

Methods of teaching mathematics in kindergarten, Shcherbakova E.I., 1998. The author, using progressive ideas of classical and modern pedagogy and psychology, proposes a method of teaching mathematics to preschoolers. At the same time, the purpose of the classes is not only to familiarize children with elementary mathematical concepts, but also to develop their mathematical abilities. The meaning and tasks of mathematical development of preschool children. The problem of teaching mathematics in modern life is becoming increasingly important. This is explained primarily by the rapid development of mathematical science and its penetration into various fields of knowledge. Increasing the level of creative activity, problems of production automation, modeling on electronic computers and much more presupposes that specialists in most modern professions have a sufficiently developed ability to clearly and consistently analyze the processes being studied. Therefore, education in kindergarten is aimed primarily at instilling in children the habit of full-fledged logical argumentation of the environment. Learning experience shows that the development of logical thinking of preschoolers is most facilitated by the study of elementary mathematics. The mathematical style of thinking is characterized by clarity, brevity, dissection, accuracy and logic of thought, and the ability to use symbolism. In this regard, the content of mathematics teaching in school and kindergarten is being systematically restructured. CONTENT. From the author. THEORETICAL FOUNDATIONS OF THE METHODS OF MATHEMATICAL DEVELOPMENT OF PRESCHOOL CHILDREN. ORGANIZATION OF TRAINING AND MATHEMATICAL DEVELOPMENT OF PRESCHOOL CHILDREN. MATHEMATICAL DEVELOPMENT OF EARLY CHILDREN. MATHEMATICAL DEVELOPMENT OF CHILDREN IN THE FOURTH YEAR OF LIFE. MATHEMATICAL DEVELOPMENT OF CHILDREN IN THE FIFTH YEAR OF LIFE. MATHEMATICAL DEVELOPMENT OF CHILDREN IN THE SIXTH YEAR OF LIFE. FEATURES OF MATHEMATICAL DEVELOPMENT OF CHILDREN IN THE SEVENTH YEAR OF LIFE. CONTINUITY IN THE MATHEMATICAL DEVELOPMENT OF KINDERGARTEN AND SCHOOL CHILDREN. MATHEMATICAL DEVELOPMENT OF CHILDREN IN THE FAMILY. APPLICATIONS.

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Published date: 10/25/2019 13:31 UTC

Shcherbakova :: books on pedagogy :: pedagogy :: manual :: kindergarten

Methods of mathematical development as a science

Definition 1
Methodology of mathematical development is a branch of scientific knowledge that studies the processes of development of the cognitive sphere of children and the formation in them of the foundations of logical thinking and skills in performing elementary mathematical operations.

The methodology of mathematical development is focused on the formation of elementary mathematical concepts in preschoolers. She develops a methodology for their formation and determines the patterns of functioning of different areas of thinking and logic, which affect the overall development of the individual and the mastery of mathematical science.

Mathematical development is important for a child's overall development. Therefore, teaching mathematics occupies the core of the preschool educational program. Mathematical concepts activate the cognitive activity of a preschooler and develop his thinking abilities.

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The methodology of mathematical development, as a science, is aimed at developing elementary mathematical concepts in children. This determines the following tasks of the methodology of mathematical development:

Scientific confirmation of the level of mathematical development of preschool children at each stage of their development and the requirements for children to master the educational program.
Development of the content of a preschool educational program in the area of mathematical education and development.
Determination of optimal means and methods, technologies and forms of teaching preschoolers the basics of mathematics.
Creating conditions for continuity in mathematical education of preschoolers and primary schoolchildren.
Preparing teachers for professional activities in the field of mathematical education and development of preschool children.
Development of recommendations for the mathematical development of a child by parents.
Development of the main directions of cognitive activity, focused on the child’s mathematical development when engaged in different types of activities (work, sports, etc.).

Finished works on a similar topic

Course work Methodology of mathematical development 440 ₽ Abstract Methodology of mathematical development 220 ₽ Examination Methodology of mathematical development 190 ₽

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Since the methodology of mathematical development is a scientific branch, it has connections with other sciences. It is closely related to developmental psychology, which determines the functioning of a child’s mental processes, sensitive periods of development of specific areas, and helps in developing optimal methods for the formation of elementary mathematical concepts in preschoolers of different age groups. In addition, the methodology of mathematical development is closely related to pedagogy. This connection can be traced in the reliance of this science on didactic methods and principles of teaching children mathematics.

In addition, there is a connection between this scientific field and sociology, anthropology, mathematics, special pedagogy and cultural studies.

The subject of the methodology of mathematical development is teaching mathematics, implemented in certain forms and focused on achieving specific goals and objectives.

The object of research into the methodology of mathematical development is the methods and means of mathematical teaching used in the preschool education system.

Methods and techniques for forming mathematical concepts in preschoolers.

Principles of teaching mathematics

The principle of science.

Its essence lies in the fact that real knowledge that correctly reflects reality should penetrate into the child’s consciousness. In the course of cognitive and research activities, the teacher definitely forms in children specific ideas and knowledge about the world around them, which do not conflict with what the school will teach. The scientific principle ensures the formation in preschool children of elements of a dialectical-materialistic understanding of the world around them.

The principle of visibility.

The importance of this principle is determined by the specific thinking of a child in kindergarten. In preschool educational institutions, the following types of visualization are used in the process of educational activities: substantive and pictorial. Using object visualization, the teacher shows children natural objects of the outside world, three-dimensional images (models of vegetables, fruits). When using visual aids, the teacher shows pictures, diagrams and other illustrative material. In the course of direct educational activities, visualization is used in obtaining new knowledge, as well as in consolidating it, and in organizing children’s independent activities.

The principle of accessibility.

What the teacher says to the children should be understandable to him, and also definitely correspond to the child’s development.

An essential feature of the principle of accessibility is the connection of the acquired knowledge with that which has already been formed in the child’s mind. If such a connection cannot be established, then knowledge will be inaccessible to children.

The principle of activity and consciousness.

The meaning of this principle is that the more a child solves practical and cognitive problems on his own, the more effective his development is. The most important indicator of effectiveness is the children’s manifestation of cognitive activity and independence.

Principles of systematicity and consistency

and gradualism.

Didactic rules: go from easy to more difficult, from what children already know to something new, unknown, from simple to complex, from close to distant.

Consistency involves studying the material in such a way that the assimilation of new things is based on the children’s existing knowledge and prepares a further stage in the children’s cognitive activity.

The principle of developmental education.

In order for learning to be an exciting, inspired work for children, it is necessary to awaken in children and constantly support the desire to learn new things. The secret of developing interest in cognitive activity lies in the child’s personal successes, in his sense of growth in his capabilities.

The principle of taking into account age characteristics and individual approach to children

The principle of individualization means the implementation of educational activities taking into account the individual characteristics of children (temperament, character, abilities, inclinations, motives, interests, etc.). The teacher must know what each child is capable of. Some of the 25-30 children quickly grasp cognitive material, and some - slowly. You cannot demand the impossible from a preschooler. The main goal of individualization of education is to build educational activities based on the individual characteristics of each child, in which the child himself becomes active in choosing the content of his education and becomes a subject of education.

Assistance and cooperation of children and adults, recognition of the child as a full participant (subject) of educational relations;

Supporting children's initiative in various activities.

Formation of cognitive interests and cognitive actions of the child in various types of activities.

Age adequacy of mathematical education (compliance of conditions, requirements, methods with age and developmental characteristics).

Methods and techniques for forming mathematical concepts in preschoolers.

“The method is the core of educational activity, the link between the designed goal and the final result. Its role in the system “goals – content – methods – forms – means of teaching” is decisive.”

Method - a way of action, activity; a set of relatively homogeneous techniques, operations of practical or theoretical mastery of reality, subordinated to solving a specific problem.

Teaching methods (didactic methods) are a set of ways, methods of achieving goals, solving educational problems. The concept of “teaching methods” in didactics is usually referred to as the joint activity of the teacher and the child.

Teaching methods can be classified according to different indicators. Today there are more than a hundred classifications. The traditional classification is based on the source of knowledge.

In the process of forming elementary mathematical concepts in preschoolers, the teacher uses a variety of teaching methods: practical, visual, verbal, and playful.

in the formation of elementary mathematical concepts is the practical method . Its essence lies in organizing the practical activities of children, aimed at mastering certain methods of acting with objects or their substitutes (images, graphic drawings, models, etc.). Practical methods are associated with the development and application of knowledge, skills and abilities in practical activities through exercises, in various games, dramatizations, projects, assignments, trainings, etc.

Characteristic features of the practical method in the formation of elementary mathematical concepts:

— performing various practical actions;

- widespread use of didactic material;

- the emergence of ideas as a result of practical actions with didactic material:

- development of counting skills, measurement and calculations in the most elementary form;

- widespread use of formed ideas and mastered actions in everyday life, play, work, i.e. in various types of activities.

When forming elementary mathematical concepts, the game acts as an independent teaching method. Game elements are included in exercises in all age groups: younger ones - in the form of a surprise moment, imitation movements, a fairy-tale character, etc.; in older children they take on the character of search and competition.

The most widely used are educational games . In a didactic game, thanks to a learning task presented in a game form, the child unintentionally learns new mathematical knowledge, applies and consolidates it. All types of didactic games (subject, board-printed, verbal) are an effective means and method of forming elementary mathematical concepts. Subject and verbal games are carried out in the course of direct educational activities and educational activities in special moments. Desktop - printed, as a rule - in special moments. Didactic games perform the main functions of education: educational, educational and developmental.

All didactic games for the formation of elementary mathematical concepts can be divided into several groups:

1. Games with numbers and numbers.

This group of games includes teaching children to count forward and backward. Using a fairy tale plot, I introduce children to the formation of all numbers within 10 (20) by comparing equal and unequal groups of objects. Two groups of objects are compared, located either on the lower or on the upper strip of the counting ruler. This is done so that children do not have the misconception that the larger number is always on the top band and the smaller number is always on the bottom. By playing such educational games as “Which number is missing?”, “How much?”, “Confusion?”, “Correct the mistake”, “Remove the numbers”, “Name the neighbors”, these games teach children to freely operate with numbers within 10 (20) and accompany your actions with words. Didactic games such as “Think of a number”, “Number what’s your name?”, “Make a sign”, “Make a number”, “Who will be the first to name which toy is missing?” and many others are used in free time, with the aim of developing children's attention, memory, and thinking. The game “Count without making a mistake!” helps to master the order of numbers in the natural series, exercises in forward and backward counting.

2. Time travel games.

This group of math games is used to introduce children to the days of the week. Having introduced the children to the days of the week through the game “Fairy Dwarfs”, she explained that each day of the week has its own name. In order for children to better remember the names of the days of the week, you can name each gnome the corresponding day of the week.

She told the children that the names of the days of the week indicate which day of the week it is: Monday is the first day after the end of the week, Tuesday is the second day, Wednesday is the middle of the week, Thursday is the fourth day, Friday is the fifth. the game “Live Week”, “Wrong Week” In the future, you can use the following games “Name it quickly”, “Days of the week”, “Name the missing word”, “All year round”, “Twelve months”, which help children quickly remember the names of the days weeks and names of months, their sequence.

3. Games for spatial orientation.

Children's spatial representations are constantly expanding and strengthened in the process of all types of activities. Children master spatial concepts: left, right, above, below, in front, behind, far, close. With the help of didactic games “Puss in Boots”, “Imagine a Landscape”, “Architects’ Intentions” and exercises, children master the ability to use words to determine the position of one or another object in relation to another: to the right of the birch tree is a house, to the left of the house is a doll, etc.

4. Games with geometric shapes.

To consolidate knowledge about the shape of geometric shapes, children can be asked to recognize the shape of a circle, triangle, or square in surrounding objects. For example, I ask: “What geometric figure does the bottom of the plate resemble?” (table top surface, sheet of paper, etc.). Knowledge of geometric shapes (oval, circle) can be consolidated in the didactic game “Pick by Shape” (like lotto). The presenter puts a card with a picture of a circle on the table and says: “Who has round objects?” Each child looks for a round object in his cards - a ball, a button, a watch, a ball, a watermelon, etc. In this game you need to carefully monitor the correct selection of geometric shapes, their names and find such shapes in the surrounding reality. Then, invite the children to name and tell what they found. The didactic game “Geometric Mosaic” can also be used in your free time, in order to consolidate knowledge about geometric shapes, in order to develop attention and imagination in children.

5.Logical thinking games.

Any mathematical task involving ingenuity, no matter what age it is intended for, carries a certain mental load. In the course of solving each new problem, the child engages in active mental activity, striving to achieve the final goal, thereby developing logical thinking.

In order to develop children's thinking, you can use various games “Subject Pairs”, “Associations”, “Sudoku” and exercises.

Visual methods include organizing observations, displaying objects, paintings, illustrations, teaching aids, etc. Visual methods can be direct (observation, excursion, inspection, viewing, etc.) and indirect. The latter are based on the use of visual clarity (examining paintings, toys, photographs, illustrations, watching cartoons, television programs, etc.). Indirect methods are recommended to be used when it is impossible to get acquainted with objects and objects directly.

Verbal methods are associated with the use of words as a means of communication and information transfer. With the development of visual-figurative thinking in children of senior preschool age, showing is replaced by explanation; story, conversation, reading without relying on visualization, verbal didactic games, etc. are more often used.

In the practice of a teacher’s work, methods do not exist in their pure form: visual methods are accompanied by words, verbal methods use visual aids, and practical methods are associated with both methods.

AND I. Lerner and N.M. Skatkin proposed a classification of teaching methods according to the type (nature) of cognitive activity of students: explanatory-illustrative ( informational-receptive

), reproductive, problematic presentation, partially search (
heuristic
), research.

The problem presentation method allows the teacher to develop in children the ability to analyze problems, educational tasks, and show examples of cognitive and research activities. When using this method, all cognitive processes are developed: perception, memory, thinking, imagination, speech.

Partially, the search (heuristic) method is characterized by the fact that the teacher organizes not a message, but the acquisition of knowledge. The most important result of its use is children’s mastery of ways of knowing. This method is partly called a search method due to the fact that it involves the help of a teacher in situations where students cannot solve a problem or solve a problem on their own.

The research method is associated with children’s independent acquisition of knowledge, methods of acquiring it, and the choice of methods of cognition. The use of this method determines the high cognitive activity of children, interest in activities, consistency and awareness of the knowledge gained.

Experimentation is a method of mental education that allows the child to discover independently through trial and error. For example, experimentation in measurement (size, measurement, volume).

In the work of preschool educational organizations, verbal and visual, explanatory and illustrative methods traditionally prevail, often to the detriment of practical, problem-based and search methods. This prevents the preschooler from taking an active position in understanding the surrounding reality, applying the acquired knowledge, skills, and experience in various types of activities.

Solving modern problems of mathematics education requires the use of active methods of organizing children's activities - the method of problem presentation, partly search and research methods. The choice of active methods for organizing children's activities makes it possible to ensure the child's subjective position in educational activities, to support the natural course of development of mental processes, communication abilities, and personal development.

The teacher needs to be able not only to choose the right teaching methods, but also to ensure that the level of complexity of tasks and situations in which children are immersed is appropriate to the child’s zone of proximal development.

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

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