Formation of elementary mathematical concepts in preschoolers (Stolyar) 1988

Library of old Soviet mathematics textbooks

The methodology for forming elementary mathematical concepts in preschoolers 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 formation of elementary mathematical concepts in preschoolers has been created, is successfully functioning and is being improved. Its main elements - the goal, content, methods, means and forms of organizing work - are closely interconnected and mutually condition each other. The leading and determining one among them is the goal, since it is socially determined and objective in nature. The kindergarten fulfills the social order of society, preparing children to study the basics of science (including mathematics) at school.

Soviet pedagogy and psychology, based on Marxist-Leninist teaching, considers the development of personality as a process of assimilation of the socio-historical experience of mankind. This experience in its generalized form is passed on to the younger generation by adults in the learning process. F. Engels wrote that the individual experience of a child is replaced by the result of the experience of his ancestors. And the assimilation of mathematical axioms by children is nothing more than the assimilation of the heredity accumulated by people.

Training and development are in a dialectical relationship. Based on the current level of development, training should be somewhat ahead of it. This means that in the learning process it is necessary to focus not only on what the child himself is capable of doing, but also on what he can do with the help of adults, under their guidance, i.e., on the future, on the zone of proximal development, in which usually contains new and more complex actions and operations than those that the child already knows. When mastering them, “not only the development process that has already been completed today, not only its cycles that have already been completed, not only the maturation processes that have already been completed, but also those processes that are now in a state of formation, that are only maturing, are only developing”2. What a child could recently do with the help of an adult, after some time, as a result of training, he can do independently. The “zone of proximal development” becomes the “actual” level of development.

Learning leads to development, being its source and paving the way for it. Each of these interrelated processes has its own patterns. It is unlawful to both identify and oppose them to each other.

However, to this day, both in theory and in practice, the opinion that the younger the child is, the less interference there should be in the process of his development, has not completely outlived its usefulness. It is believed that the acquisition of quantitative, spatial, and temporal concepts occurs naturally, spontaneously in children’s everyday life and various activities. There are attempts to strictly define age-related opportunities for acquiring knowledge and to deny the programmatic nature of teaching young children. Thus, the Swiss psychologist J. Piaget considers it a big mistake to think that a child perceives the concept of number and other mathematical concepts directly in learning. In his opinion, these concepts are formed in the child independently and spontaneously.

According to J. Piaget, his students and followers, mastery of mathematical concepts occurs on the basis of logical operations of classification and seriation, which the child discovers himself and which is almost impossible to learn. They appear quite late, at 11-12 years old, i.e. already at school age. This point of view does not solve the problem of mathematical development and learning of children in preschool age.

A productive approach to solving this problem developed in Soviet pedagogy and psychology based on data from numerous studies. It is as follows: in the conditions of rationally structured training, taking into account the age capabilities of preschoolers, it is possible to form in them a complete understanding of individual mathematical concepts. In this case, learning is considered as an indispensable condition for development, which in turn becomes a controlled process associated with the active formation of elementary mathematical concepts and logical operations. This approach does not ignore spontaneous experience and its impact on the child’s development, but the leading role is given to targeted learning.

The mathematical development of preschoolers should be understood as shifts and changes in the cognitive activity of the individual that occur as a result of the formation of elementary mathematical concepts and related logical operations.

The formation of elementary mathematical concepts is a purposeful and organized process of transferring and assimilating knowledge, techniques and methods of mental activity provided for by program requirements. Its main goal is not only preparation for successful mastery of mathematics at school, but also the comprehensive development of children.

§ 2. Methodology for the formation of elementary mathematical representations and other sciences

The method of forming elementary mathematical concepts in children in kindergarten is associated with many sciences, and above all with science, the subject of study of which is different aspects of the personality and activity of a preschool child, the process of his upbringing and education.

It has the closest connection with preschool pedagogy, the science of communist education of children. Technique? the formation of elementary mathematical concepts is based on the tasks of teaching and mental education of the younger generation developed by preschool pedagogy and didactics: principles, conditions, ways, content, means, methods, forms of organization, etc. This connection is mutual in nature: research and development of problems of formation elementary mathematical concepts in children in its own way” improves pedagogical theory, enriching it with new factual material.

Multilateral contacts exist between private methods that study specific patterns of the process of raising and teaching young children: methods of forming elementary mathematical concepts, speech development, theory and methods of physical education, etc.

Preparing children to master mathematics at school cannot be carried out successfully without connection with the methods of primary teaching of mathematics and those aspects of mathematics itself that are the theoretical basis for teaching preschoolers and primary schoolchildren. Relying on these sciences allows, firstly, to determine the volume and content of knowledge that should be mastered by children in kindergarten and serve as the foundation of mathematical education; secondly, to use teaching methods and means that fully meet the age characteristics of preschoolers and the requirements of the principle of continuity.

The reform of general education and vocational schools has set the task of improving the quality of teaching in all general education subjects, including mathematics. It is well known that when mastering mathematical knowledge, many students experience serious difficulties, the cause of which, as a rule, is insufficient mathematical preparation in preschool age.

Improving the content and methods of teaching mathematics at school requires a new attitude towards preparing children in the period immediately preceding schooling. At present, significant changes have already been made to the program for the development of mathematical concepts in preschoolers (increasing the volume of mental calculation, counting groups of objects, learning to measure individual quantities, expanding geometric knowledge, etc.); More effective methods and means of teaching have been found and tested (modeling, problematic tasks and situations, developmental and educational games, etc.). The connection with the methods of teaching mathematics in primary school allows us to correctly determine the main ways to further improve the methods of forming elementary mathematical concepts in preschoolers.

Education should be structured taking into account the patterns of development of cognitive activity and the child’s personality, which is the subject of study of psychological sciences. Perception, representation, thinking, speech not only function, but also intensively develop during the learning process.

Psychological characteristics and patterns of a child’s perception of many objects, number, space, time serve as the basis for developing methods for the formation of elementary mathematical concepts. Psychology determines the age-related capabilities of children in mastering knowledge and skills that do not appear as something frozen and change depending on the type of training. Modern psychological research shows that the abilities of preschool children in mastering mathematical concepts are great and have not yet been fully revealed or fully studied.

The rational construction of the learning process is associated with the creation of optimal conditions based on the anatomical and physiological characteristics of young children. The patterns of physiological processes in preschoolers serve as the basis for determining the place and duration of classes on the formation of elementary mathematical concepts for each age group of kindergarten, determine their very structure, the combination and alternation of various methods and means of teaching, different types of activities (inclusion of physical education, dosing educational and cognitive tasks, etc.).

The method of forming elementary mathematical concepts is a relatively young scientific pedagogical discipline, but it has ancient origins. A historical excursion shows how the concepts of initial teaching of mathematics gradually changed depending on the demands of life and the level of development of mathematical science itself, makes it possible to critically evaluate the rich heritage, avoid many mistakes, take into account the positive experience of the past, as well as the results of the latest research. In Marxist-Leninist theory, it finds a solid methodological basis, which provides a comprehensive and in-depth examination of the phenomenon in its development, compliance with the principle of objectivity, specificity, unity of theory and practice.

Connection with various sciences creates a theoretical basis for the methods of forming mathematical concepts in children in kindergarten.

§ 3. Study of problems in the formation of elementary mathematical concepts in preschool children

For a long time, the concepts of the initial teaching of number and counting to young children were built either on the basis of speculative theoretical constructions or through empirical experience. Outstanding thinkers of the past (Ya. A. Komenskin, I. G. Pestalozzi, K. D. Ushnsky, L. N. Tolstoy), prominent figures in the field of preschool education abroad (F. Frebel, M. Montessori) and in our country (E.I. Tikheyeva, F.N. Blekher) successfully combined direct work with children with theoretical understanding of its results.

The formation of methods for the formation of mathematical concepts in preschoolers is associated with the use of experimental research methods, which have begun to be introduced recently.

Scientific research in this area is being carried out at the Institute of Preschool Education of the Academy of Sciences of the USSR and in a number of other scientific and educational institutions of the country. Educators, methodologists, and teachers also take part in this work.

In recent years, research into the problems of teaching six-year-olds has been widely developed (APN of the USSR, Research Institute of Pedagogical Sciences of Ukraine, Georgia, the Baltic and other republics, Mogilev Pedagogical Institute, etc.). These studies have a direct impact on the theory and practice of forming elementary mathematical concepts in preschoolers.

In modern conditions, in connection with the transition to schooling for children from the age of six, the development of methods for improving the preparation of preschoolers for mastering school mathematics is of particular importance.

Research in the field of the formation of elementary mathematical concepts in children is directly related to practice and provides scientific ways to solve its most important problems. The developed content and methodological techniques, didactic means and forms of organizing work are used in the practice of forming elementary mathematical concepts in children in kindergarten. The publication of the main results of the study makes them available to a wide circle of preschool workers. The recommendations of scientists are taken into account when revising the program for the development of elementary mathematical concepts in kindergarten. Periodically, changes are made to it, new requirements and tasks are introduced, taking into account the results of scientific research. The conclusions and recommendations of scientists contribute to the improvement of the work of kindergartens and the development of mathematical concepts in children, and serve as the basis for subsequent scientific research.

Student, educational and research work (tests, coursework, graduation, diploma), in which the knowledge, skills and abilities necessary for a future specialist are acquired, must meet the requirements of relevance, novelty, theoretical and practical significance, objectivity and reliability, as well as any other scientific works devoted to the problems of mathematical development of preschool children.

“Formation of mathematical concepts in preschool children”

author: Chumak Anastasia Valerievna

teacher at MBDOU "Russkopolyansky kindergarten No. 5"

“Formation of mathematical concepts in preschool children”

“Formation of mathematical concepts in preschool children”

Relevance of the project.

Adults never cease to be amazed at how much a child can learn and remember in the early years. The period of preschool childhood is short relative to a person’s entire life, but how rich it is in learning! Every day brings the child something new, unknown; something previously inaccessible becomes close and understandable.

The flow of information that the surrounding life brings down on a small person is great. The source of a preschooler’s knowledge is sensory experience. Its range depends on how finely the child masters the sum of special actions (examining, feeling, comparing, juxtaposing, distinguishing between the main and the secondary, etc.) that influence perception and thinking.

Teaching preschoolers the basics of mathematics is currently given an important place. This is caused by a number of reasons: the beginning of schooling at the age of six, the abundance of information received by the child, increased attention to computerization, the desire to make the learning process more intensive, the desire of parents in this regard, to teach the child to recognize numbers, count, and solve problems as early as possible .

The main goal is being pursued: to raise children as people who can think, navigate well in everything that surrounds them, correctly assess the various situations they encounter in life, and make independent decisions. Adults often rush to give the child a set of ready-made knowledge and judgments, which he absorbs like a sponge. However, does this always give the expected result? For example, should a child be forced to do math if he finds it boring?

The practice of preschool education shows that the success of learning is influenced not only by the content of the material offered, but also by the form of its presentation, which can arouse the child’s interest and cognitive activity.

Entertaining can be provided by an unusual form of learning. You just need to find a middle ground: don’t complicate things—children won’t understand, and don’t simplify things by making learning easier—children will constantly look for easy ways to work less. Receiving food for his mind, the child willingly participates in activities, waits for them, and enjoys them.

Entertaining material not only captivates the child, but also helps improve the preschooler’s observation, attention, memory, thinking and speech skills. Poetic material, riddles, counting rhymes are used depending on the goals of cognitive communication. The possibilities for their use are wide: in group classes in kindergarten, during individual work with children in the family, at quizzes, leisure activities, holidays, during educational conversations, in the toy library, when children receive their parents as guests and play mathematical games with them.

Entertaining mathematics puts preschoolers in search conditions, awakens an interest in winning, therefore, children strive to be fast and resourceful.

The problem to be solved during the implementation of the project.

There are 23 pupils in the senior group: 12 boys and 11 girls.

During classes on the formation of elementary mathematical concepts, many children in the senior group lacked interest in mathematics and had difficulties with thinking and attention.

At the beginning of the year, this area was implemented by 1.5 points

, which ultimately amounted to
37.5%
- a low figure for the group.

In order to increase the level of mathematical development, the activity of children, and develop their interest in mathematics, we decided to use entertaining material: riddles, poems, didactic games, entertaining questions, joke problems, mathematical fairy tales, proverbs and sayings, finger gymnastics, labyrinths, logical endings, mathematical KVNs.

Project participants:

senior group students; educator; parents of pupils.

Objective of the project:

Formation of elementary mathematical concepts in children of senior preschool age through entertaining material.

Tasks:

To develop interest in mathematics in children of senior preschool age, emotional responsiveness through games with mathematical content.
Formation of basic mathematical concepts and speech skills.
To promote the development of mental operations (analysis, synthesis, comparison, classification), logical thinking.
Develop independence of cognition, encourage manifestations of creative initiative and resourcefulness.
Increase your attention span and memory.
Develop speech, the ability to express and justify your opinions;
Cultivate interest in the subject and the learning process in general.

Contents of the project.

Stage I –

preparatory.

Involve parents in the implementation of the project.

Message: “Educational and educational tasks for the formation of elementary mathematical concepts in the senior group” at a parent meeting.

Individual conversations about diagnostic results.

Creating conditions for project implementation.

Selection of entertaining material for individual and face-to-face lessons with children, production of gaming mathematical material.

Primary diagnosis.
Studying methodological literature on the topic.

Search for materials on the Internet.

Stage II –

basic.

Implementation of the main activities in the project areas.

Presentation of the project is an open lesson on the formation of elementary mathematical concepts for parents.

Stage III –

final

Carrying out final diagnostics.

Collection and processing of methodological and practical materials.
Correlation of predicted results with obtained ones.

Summarizing project materials.

Expected results.

positive dynamics of monitoring on the formation of elementary mathematical concepts in children of senior preschool age;
formation of logical thinking operations (analysis, synthesis, comparison, classification, generalization);
children’s use of mathematical knowledge and skills in independent activities and manifestations of creative initiative;
parents’ awareness of the importance of forming elementary mathematical concepts in children with the help of entertaining material, expanding parents’ knowledge about entertaining material;
developing in children an interest in mathematics and a desire to overcome difficulties.

Project implementation.

The development of attention and intelligence is facilitated by joke tasks and puzzles that warn the child against hasty and unfounded conclusions. They should not be solved like ordinary problems, using one or another arithmetic operation. These tasks should encourage children to reason, think, and find an answer using existing knowledge.

Using joke problems and intelligence tasks will help diversify and enliven activities with children. In addition, tasks of this kind can be used during mathematical leisure activities, fun meetings of preschool experts, and KVNs.

Entertaining material not only entertains children, gives them the opportunity to relax and switch gears, but also makes them think, develops independence and initiative, directs them to search for unconventional solutions, and stimulates the development of non-standard thinking.

Children are given the opportunity to listen carefully to the riddle, remember its content, and guess it. The riddle is told emotionally, slowly.

Children know a lot of counting rhymes and most often use them to choose the leader in games. The same technique can be used in mathematics classes. To increase the activity of children in the classroom, you do not need to assign children, but do it with the help of a counting rhyme.

For the formation of full-fledged mathematical concepts and for the development of cognitive interest in preschoolers, it is very important, along with other methods, to use entertaining problem situations. The fairy tale genre allows you to combine both. The plot itself and fairy-tale characters attract children. By getting used to the events of the fairy tale, the child seems to become its protagonist. At the same time, cognitive activity increases: he strives to intervene in situations and influence them. The keen interest that arises in a child can be used to increase the effectiveness of learning.

Materials for activities with children.

Did. game "Show as much"
Playing with sticks.
"Assemble a figure from parts"
"The Fourth Wheel"
Game "White Sheet".
Game “Sew up the carpet”
"Find a neighbor"
"Days of the week"
"Count and compare the quantities"
Game "Circle, Triangle, Square"
Joke tasks, puzzles, labyrinths, tasks for intelligence.
Counting books, riddles.
"Logic coloring pages"
"Model of the Year"
. "Forms and Objects"

Mathematical tales.

"Extraordinary adventures in the city of mathematical mysteries."
"Visiting the gnome watchmaker, or a story about how not to be late for school."
"How Top learned mathematics."
"Zhenya's games."
“Help Dunno find the way.”
"Guess yourself!".
“How Nina taught her brother.”

Results.

Positive dynamics of growth in children's mathematical development.

At the beginning of the year, this area was implemented by 1.5 points, which ultimately amounted to 37.5% - a low figure for the group; at the end of the year – 2.3 points (57.4% average).

Children show cognitive activity, creative initiative, and try to overcome difficulties in joint activities with the teacher and independently.
Increasing pedagogical literacy and parents' interest in the formation of elementary mathematical concepts in children.
An entertaining mathematics corner has been created.
The final lesson “Mathematical Kingdom” was held for parents.

Literature.

Erfeeva T.I. and others. Mathematics for preschoolers: Book. For the teacher of children. garden/T.I. Erofeeva, L.N. Pavlova, V.P. Novikova. – M.: Education, 1992. – 191 p.: ill.
Mathematics from three to seven: Educational and methodological manual for kindergarten teachers / Author. – comp. BEHIND. Mikhailova, E.N. Ioffe; Hood. I.N. Rzhevtseva. – St. Petersburg: “Aktsident”, 1997. – 176 p.: Ill.
Nishcheva N.V. GAME. Games and exercises for the formation and development of elementary mathematical concepts and speech in preschool children. - St. Petersburg: “CHILDHOOD-PRESS”, 2003. – 16 p., ill.
Peterson L.G.,. Kochemasova E.E. Playing game. Practical mathematics course for preschoolers. Guidelines. – “Balass”, 1998. – 160 p.
Pomoraeva I.A., Pozina V.A. Formation of elementary mathematical concepts. – Moscow: Mozaika-Sintez Publishing House, 2015. – 60 p.
Tikhomirova L.F. Development of children's cognitive abilities. A popular guide for parents and teachers. – Yaroslavl: Academy of Development, 1996. – 192 p., ill.
nsportal.ru/…/ispolzovanie-zanimatelnoy-matematike-v-individualnoy-ra…
www.maam.ru/…/konspekt-nod-s-detmi-starsh ei
-grupy-po-fyemp-itogov…

“Formation of mathematical concepts in preschool children”

Tasks of mathematical development of preschool children.

The content being mastered must correspond to the age and individual capabilities of preschoolers and be focused on their zone of proximal development.

6. The relationship between the concepts of “development”, “training”, “education”. Mathematical abilities.

The mathematical development of preschool children is carried out both as a result of the child’s of knowledge in everyday life (primarily as a result of communication with an adult), and through targeted training in

It is the elementary mathematical knowledge and skills of children that should be considered as the main means of mathematical development.

In the process of learning, children develop the ability to more accurately and completely perceive the world around them , identify the signs of objects and phenomena, reveal their connections , notice properties , and interpret what is observed; mental actions and methods of mental activity are formed internal conditions are created for the transition to new forms of memory, thinking and imagination.

Psychological experimental research and pedagogical experience indicate that thanks to the systematic teaching of mathematics to preschoolers, they develop sensory, perceptual, mental, verbal, mnemonic and other components of general and special abilities .

The inclinations of an individual are transformed into specific abilities through learning .

The difference in the levels of development of children, as experience shows, is expressed mainly in the pace and success with which they acquire knowledge.

However, despite the importance of learning in the mental development of the individual, the latter cannot be reduced to teaching. Development is not limited to those personality changes that are a direct consequence of learning . It is characterized by those “ mental turns” that occur in a child’s head when he learns to speak, read, count, and assimilates the social experience transmitted to him by adults.

As studies show (A.V. Zaporozhets, D.B. Elkonin, V.V. Davydov, etc.), development goes beyond what is learned at one time or another during training . In the process and under the influence of learning, a holistic, progressive change in the personality, its views, feelings, and abilities occurs. Thanks to training, the possibilities for further assimilation of new, more complex material are expanded, and new learning reserves are created.

There is a reciprocal relationship between learning and development . Education actively contributes to the development of the child, but is itself based on his level of development . In this process, much depends on how much the training is aimed at development.

Learning can develop a child in different ways depending on its content and methods. It is the content and its structure that guarantee the child’s mathematical development.

Abilities are understood a complex of individual psychological characteristics of a person that meet the requirements of a given activity and are a condition for successful implementation. Thus, abilities are a complex, integral, mental formation, a kind of synthesis of properties, or, as they are called, components.

The general law of the formation of abilities is that they are formed in the process of mastering and performing those types of activities for which they are necessary .

Abilities are not something predetermined once and for all, they are formed and developed in the process of learning , in the process of exercise, mastering the corresponding activity , therefore it is necessary to form, develop, educate, improve the abilities of children and it is impossible to predict in advance exactly how far this development can go.

Speaking about mathematical abilities as features of mental activity , we should first of all point out several common misconceptions among teachers.

First, many people believe that mathematical ability lies primarily in the ability to perform quick and accurate calculations (particularly in the mind). In fact, computational abilities are not always associated with the formation of truly mathematical (creative) abilities.

Secondly, many people think that schoolchildren who are capable of mathematics have a good memory for formulas, figures, and numbers. However, as academician A. N. Kolmogorov points out, success in mathematics is least of all based on the ability to quickly and firmly memorize a large number of facts, figures, and formulas.

Finally, it is believed that one of the indicators of mathematical ability is the speed of thought processes. A particularly fast pace of work, in itself, has nothing to do with mathematical abilities. A child can work slowly and deliberately, but at the same time thoughtfully, creatively, and successfully progress in mastering mathematics.

Krutetsky V.A. in the book “Psychology of Mathematical Abilities of Preschool Children,” he distinguishes nine abilities (components of mathematical abilities):

1) The ability to formalize mathematical material, to separate form from content, to abstract from specific quantitative relationships and spatial forms and to operate with formal structures, structures of relationships and connections;

2) The ability to generalize mathematical material, to isolate the main thing, abstracting from the unimportant, to see the general in what is externally different;

3) Ability to operate with numerical and symbolic symbols;

4) The ability for “consistent, correctly dissected logical reasoning” associated with the need for evidence, justification, and conclusions;

5) The ability to shorten the reasoning process, to think in collapsed structures;

6) The ability to reversible the thought process (to switch from a direct to a reverse train of thought);

7) Flexibility of thinking, the ability to switch from one mental operation to another, freedom from the constraining influence of templates and stencils;

Mathematical memory. It can be assumed that its characteristic features also follow from the features of mathematical science, that it is a memory for generalizations, formalized structures, logical schemes;

9) The ability for spatial representations, which is directly related to the presence of such a branch of mathematics as geometry.

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MAGAZINE Preschooler.RF

Article “Methods and techniques for the mathematical development of preschool children.”

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

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

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

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

When choosing methods, the following are taken into account:

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

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

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

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

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

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

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

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

The components of the method are called methodological techniques.

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

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

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

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

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

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

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

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

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