Digital library. The development of mathematical abilities in preschool children through play activities in the context of the implementation of FGOS to Beloshistaya formation of elementary mathematical concepts

Classes on the development of the mathematical abilities of children 3-4 years old, Book 2, Beloshistaya A.V.

The publication is a course of lectures in which questions of the formation and development of mathematical abilities of preschoolers are considered. The manual reflects the modern understanding of the continuity of mathematical education of preschoolers and younger students, the possibility of forming components learning activities and development cognitive processes preschoolers. It highlights the principles of selection of the content of the course of preschool mathematical training, issues of methodological analysis of classes and programs in mathematics, the organization of an individual approach to the child in teaching mathematics. The manual includes questions of a private methodology for the formation of elementary mathematical representations of preschoolers from the standpoint of developmental education, as well as the experience of organizing relevant classes.

Examples.
Fold with sticks.
In tasks, the child uses ordinary counting sticks for folding.

Fold from triangles.
In these tasks, the child uses triangles of the basic shape (isosceles rectangular) to fold.
It is convenient to use ready-made "Didactic sets" containing figures of this shape. You can cut triangles from thick cardboard.

Put the figures in the right place.
In the tasks on p. 4-19 the child lays out figures of three basic forms in the drawings:
It is convenient to cut these figurines in 20 pieces of each in different colors and store them in an envelope. When laying out the figures, they can be counted, compared by quantity (more or less, one-many, how many ...) and by color. You can color the drawings with colored pencils, then it is advisable to ask the child to choose the figures of the desired shape and color.
Repeat work on each page after a day or two, until the child begins to easily cope with the choice without your prompting.
After that, you can glue the figures in place with a glue pencil and move on to the next tasks. Do not forget to renew the stock of figures and introduce more colors.

Free download e-book in a convenient format, watch and read:
Download the book Classes for the development of mathematical abilities of children 3-4 years old, Book 2, Beloshistaya A.V. - fileskachat.com, fast and free download.

Mathematics around you, Methodological recommendations for organizing classes with children 4-5 years old, Beloshistaya A.V., 2007
Simulator in mathematics for grade 1, Learning to solve problems, Beloshistaya A.V., 2007
Methods of teaching mathematics in elementary school, Beloshistaya A.V., 2007

The following tutorials and books.

Studying the problem of the formation and development of the mathematical abilities of preschoolers, for several years we suggested organizing a discussion on this topic for the teacher1 and the methodologists of preschool educational institutions working with children of all ages: from early age to the preparatory group. In all cases: educators, as a rule, confidently answered the question, can they name and identify children capable of mathematics in their group.

Both the primary-level teachers and the subject students answered this question in a similar way. At the same time, the main criterion for such a choice among teachers is the child's success in the subject itself (although it is quite obvious that this success is only a consequence of the presence of abilities).

A much more difficult task turned out to be the justification of their choice of a child capable of mathematics for preschool educator... And this is natural, because what younger child, the less the teacher has the opportunity to substitute the cause for the effect, referring to the child's success in the subject, when identifying capable children.

Mathematical abilities belong to the group of early abilities, which is an indisputable historical fact and confirmation that the study of this issue should be dealt with not only by mathematicians, but also by preschool educators.

Further analysis of the concept of "capable child" most often leads to the isolation of the characteristic "curiosity".

Material from the site www.i-gnom.ru

"Development of mathematical abilities in older children preschool age through play activities "

Work experience Sibogatova N. A. - teacher GBOU School No. 2083

Kindergarten "Seven-flower"

In our time, in the age of "computers", mathematics

in one way or another is needed by a huge number

people of various professions.

It is known that the special role of mathematics is in mental education and in the development of intelligence. This is because the learning outcomes are not only knowledge, but also a certain style of thinking. In mathematics, there are tremendous opportunities for the development of the thinking of children in the process of their learning from a very early age, and the omissions here are difficult to compensate.

Psychology has established that the main logical structures of thinking are formed approximately at the age of 5 to 11 years. The belated formation of the logical structures of thinking of these structures proceeds with great difficulties and often remains incomplete.

Therefore, mathematics rightfully occupies a very large place in the system of preschool education. It hones the child's mind, develops the flexibility of thinking, teaches logic. All these qualities are useful for children, and not only in teaching mathematics.

It is known that play is the main institution for the upbringing and development of a preschooler's culture, a kind of academy for his life. In play, the child is the creator and the subject. In the game, the child embodies, creative transformations and, generalizing everything that he has learned from adults, from books, TV shows, films, his own experience, and provides a connection between generations and the conditions of the culture of society.

We recognize that one of the main tasks preschool education is the mathematical development of the child. Purpose of the work: promoting a better understanding of the mathematical essence of the issue, clarification and formation of mathematical knowledge in preschoolers.

Working on this topic, we have identified the following tasks for ourselves,

1. To develop children's interest in mathematics.

2. Introduce them to this subject in a playful and entertaining way.

The following methods contributed to the solution of these problems:

1. Study, analysis and generalization of literary sources on the topic.

2. Study and generalization of pedagogical experience in the development of mathematical abilities of children.

We do not strive to teach a preschooler to count, measure and solve arithmetic problems, but develop their ability to see, discover properties, relationships, dependencies, the ability to "construct" objects, signs and words in the world around them.

Embodying LS Vygotsky's idea of advanced development, we strive to focus not on the level reached by children, but on the zone of proximal development, so that children can make some efforts to master the material. It is known that intellectual work is very difficult and, taking into account the age characteristics of children, we understand and remember that the main method of development is problem-search, the main form of organizing children's activities is play.

Teaching mathematics to preschool children is unthinkable without the use of entertaining games, tasks, and entertainment. You need to "play" math with children.

Didactic games make it possible to solve various pedagogical problems in a playful way, the most accessible and attractive for children. Their main purpose is to provide children with exercise in distinguishing, highlighting, naming sets of objects, numbers, geometric shapes, directions. We include such didactic games in the content directly educational activities.

In our work, we use a complex game methodology. It is based on educational entertaining games, selected according to the topic of the lesson. This makes it possible to purposefully develop the mental abilities of the child, the logic of thought, reasoning and actions, the flexibility of the thought process, ingenuity and ingenuity. Introducing children to numbers, I use didactic games aimed at acquaintance with numbers:

"Lay out the number from the sticks";

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Development of the mathematical abilities of older preschoolers with the help of flexagons.

Statement of the problem At present, one of the promising approaches to the mathematical development of a child is an orientation towards mathematical modeling, with the help of which children actively master the construction and use of various kinds of subject, graphic and mental models.

While searching for effective means of mathematical modeling with preschoolers, I came to the conclusion that the technology of mathematical modeling based on flexagons is most effective for the mathematical development of older preschoolers, since the peculiarity of play materials for this technology consists in unlimited combinatorial possibilities hidden in an ordinary sheet of paper. If we consider that an ideal intelligent constructor should consist of one part, with the help of which an infinite variety of forms is created, then Flexagon is just such a constructor.

Flexagon - "flexible polygon" - one of the simplest mathematical abstractions. It is based on sensory standards of the form, when correctly assembled, the flexagon contains “hidden” surfaces.

A careful analysis of flexagon sweeps allowed me to identify their developing mathematical potential for preschoolers. Flexagons contribute to the development of fine motor skills, spatial imagination, memory, attention, patience. With a specially thought out coloring, they activate the formation of representations in all sections of mathematics for preschoolers.

The use of flexagons in the development of elementary mathematical representations of children is a deeply creative process, dialectically combining the unity of creation and negation. Therefore, designing the author's local methodology for using flexagons, I, first of all, deeply studied the available theoretical and practical developments on the problems of interest to me, took into account the specifics of the children of my group, and only on this basis did I create innovations.

For the first time in my practice, I used flexagons in the mathematical development of children, firstly, as a means of ordinal and quantitative counting. With the help of flexagons, she introduced children to the composition of the number of units; relationships "more", "less", etc .; numbers; taught to compose and solve simple and indirect arithmetic problems. To do this, I used a variety of colors on the sides of the flexagon, taking into account the interests of the children of a particular group.

Secondly, in the section geometric shapes - to acquaint children with a triangle, circle, ellipse, square, rectangle, quadrangles as a class of shapes, etc. Flexagons will help you find similarities and differences between figures, and make their classification.

Thirdly, flexagons are good for children mastering the concept of “time”. You can use them to show the clock face, it is convenient to show seasonal phenomena, days of the week, months.

The process of developing sensing, intellectual culture and creative activity was accompanied by a phased introduction of flexagons into classes.

1) When familiarizing myself with the flexagon, I used the technique of a problem situation: the character received a magical gift, what to do with it is unknown; help the character.

2) invited the children to tell what they can play with the flexagon. Clarifies what class this figure can be attributed to.

3) I “accidentally” folded the flexagon so that it opened. Gave the kids time to experiment with the flexagon.

1) I offered the children a few minutes to remember the properties of the flexagon. What is the name of this figure? How many sides, peaks, corners does it have?

2) I offered to fold the flexagon in half. Name the resulting figure, count the angles, name the figures that make up the trapezoid (triangle, rhombus). The children were offered to lay out a trapezoid from real geometric shapes, or just name them.

3) I offered to fold the rhombus on my own, count the angles; reveal flexagon and tell about it.

1) I remembered with the children what the axis of symmetry is. She offered to show and count the number of axes of symmetry in a flexagon. Show them.

2) Research problem: if the flexagon is turned out, will the number of symmetry axes change? Why?

3) Task. Fold the flexagon in half. How many identical shapes did you get? What are these figures? How many corners does each shape have?

How many angles will the 2 trapezoids that make up the flexagon plane have? How many corners does a flexagon have?

Analyzing the conducted lessons, it should be noted that the effect of "focus" when introducing flexagon aroused the persistent interest of children, created motivation for several lessons ahead. The children's search activity was motivated by the parents' interest in mathematical puzzles modeled and shown by the children, and by the variety of options for the “mathematical filling” of flexagons.

Thus, technological process classes include a number of interdependent and interrelated components that ensure effective assimilation of educational material and its inclusion in activities.

The experimental work carried out, theoretical modeling and analysis of the mathematical essence of flexagons made it possible to formulate the following guidelines for preschool teachers:

Starting a lesson on introducing children to flexagon, I advise you to simultaneously consolidate the differentiation of colors, their shades, since the group kindergarten multi-colored flexagons are introduced.
Older preschoolers can be encouraged to collect flexagons by color. For example: each side of a hexahexaflexagon can consist of six triangles of complementary colors, differing by 1-3 tones from the main color. We recommend using this exercise to develop fine motor skills and stimulate the intellectual activity of children.

The use of flexagons as a means of mathematical development of a child has shown their effectiveness in solving the problem of harmonization of affect and intellect, which, in turn, allows solving a wide range of problems requiring a high level of generalization without classical formalization. At the same time, the process of development of sensing, intellectual culture and creative activity is accompanied by positive emotions of children due to the variants of “cognitive” coloring of flexagons.

Conclusion: The work I have done gave the following results: by the end of the year, the children learned to correlate the shape of objects with geometric shapes, to highlight the elements of geometric shapes (angle, vertex, sides), They have formed knowledge of the basic concepts of flexagons, intrinsic motivation and sustained interest in this kind activities.

The feeling that all my efforts were not in vain gave me strength in my work. After all, the delight, joy, surprise of children in achieving the final result is the greatest reward in my work and, naturally, an incentive to move on in my profession.

LITERATURE

Afonkin S. Games and tricks with paper / S. Afonkin, E. Afonkina.- M .: Rolf, AKIM, 1999. - pp. 12–67.
Beloshistaya A. V. Formation and development of mathematical abilities of preschoolers: Questions of theory and practice: A course of lectures. - M .: VLADOS, 2003. - P.11–77.
Games and entertainment: Book. 3 / Comp. L. M. Firsova. - M .: Mol. Guard, 1991.
Mikhailova Z. A. Game entertaining tasks for preschoolers. - M.: Education, 1990.
Nikitin B. P. Steps of creativity or educational games. - M .: Education, 1991.
Origami and Pedagogy: Materials of the First All-Russian Conference of Origami Teachers. - SPb., 1996.
Repin G. A. Technologies of mathematical modeling with preschoolers. - Smolensk, 1999.
Repin G. A. Promising approaches to the mathematical development of the child. - Smolensk, 2000.
365 educational games / Comp. E. A. Belyakov. - M .: Rolf, Iris-press, 1998.

On this topic:

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Beloshistaya A. V. Formation and development of mathematical abilities of preschoolers. Questions of theory and practice Free download

A course of lectures for students of preschool faculties of higher educational institutions... - M .: Humanit. ed. center VLADOS, 2003 .-- 400 p .: ill. ISBN 5-691-01229-0. Agency CIP RSL.

It highlights the principles of selection of the content of the course of preschool mathematical training, the issues of methodological analysis of classes and programs in mathematics, the organization of an individual approach to the child in teaching mathematics. The manual includes questions of a private methodology for the formation of elementary mathematical representations of preschoolers from the standpoint of developmental education, as well as the experience of organizing relevant classes. Posted:

The relationship between the development of cognitive processes and mathematical abilities of the child

For the development of mathematical abilities, it is important to selectively perceive the specific characteristics of the external world: shape, size, spatial location and quantitative characteristics of objects. Obviously, of these characteristics, the fastest and easiest are perceived by sensory shape, size and spatial arrangement.

As noted earlier, special training is required for the child to adequately isolate and perceive quantitative characteristics. For the formation and development of perception, it is necessary to provide the child with the possibility of examining the perceived object, methods and means of creating its adequate model (its similarity), first in material form in external activities, in order to ensure then its internalization into an internal form - representation. Thus, there will be an accumulation of stock images of the imagination. In the productive perception of an object, the most important thing for a child is the action that he uses: the activity of tactile examination should precede the activity of visual observation and analysis of the observed object, phenomenon, etc.

Such a sequence of actions of a child with the material under study is easy to ensure with predominant work with geometric material, since for any geometric figure or geometric body it is easy to construct a wide variety of models from the very different material, and all of them will adequately reflect its main characteristics. For example, a square made of paper, sticks, plasticine, constructor, fabric, thread, as well as its drawing on sand, clay, wax tablet, chalkboard, etc. will be a model of the same concept, reflecting its basic properties: the presence of four equal straight sides and four right angles. Everything listed models the child can perform independently, with his own hands, and then conduct a whole series of observations (expressing them verbally) when examining any of them - compare the lengths of the sides, count them, compare the shape and equality of angles, and also establish many of its other properties by simple manipulations with model.

The way of organizing such cognitive activity of a child is an appropriately developed task (exercise), performing which, the child realizes productive perception of the object (examination, modeling) and comprehension of the perceived sensory information (accompanies sensory perception with a word).

Exercise 1

Target. Prepare children for subsequent modeling activities through simple constructive actions, actualize counting skills, and organize attention.

Materials. Counting sticks in two colors, flannelegraph with cardboard models of sticks from the teacher.

Exercise.

Take from the box as many sticks as I have. Place in front of you in the same way (II). How many sticks? (Two.)
Who has the sticks of the same color? Who has a different color? What color are your sticks? (One is red, one is green.)
One and one. How much together? (Two.)

Exercise 2

Target. Organize constructive activities according to the model, exercise in counting, the development of imagination, speech activity. Materials.

Exercise.

Take another stick and place it on top (II). How many sticks have become? Let's count. (Three.)
What does the figure look like? (At the gate, with the letter P). Who knows the words starting with P?

Children speak words.

Exercise # 3

Target. Develop observation, imagination and speech activity; to form the ability to evaluate the quantitative characteristics of the modifying structure (without changing the number of elements); preparation for the correct perception of the meaning of arithmetic operations.

Materials. Counting sticks, flannelgraph.

Exercise.

Move the top stick like this: "H \ Has the number of sticks changed? Why hasn't it changed? (The wand was rearranged, but not removed or added.)
What does the figure look like now? (Letter N.) What are the words starting with N.

Exercise 4

Target. Build design skills, imagination, memory and attention.

Exercise.

- Put together different figures from these three sticks.

Children put together figures and letters. They call them, come up with words. One of the children will definitely fold a triangle.

Exercise 5

Target. Form a triangle image, initial examination of the triangle model.

Materials. Counting sticks, flannelgraph.

Method of execution. The teacher invites everyone to fold this figure:

How many sticks did you need for this figure? (Three.) Who knows what this is? (Triangle.) Who knows why it's called that? (Three corners.)

If the children cannot name the figure, the teacher suggests its name and asks the children to explain how they understand it.

The teacher asks you to circle the figure with your finger, count the corners (vertices), touching them with your finger.

Exercise 6

Target. To fix the image of the triangle on the kinesthetic and visual level. Recognize a triangle among other shapes (volume and perceptual stability). Outline and hatch triangles (develop small arm muscles).

Materials. Stencil frame with cuts in the form of geometric shapes, paper, pencils.

Note. The task is problematic, since on the frame used there are several triangles and shapes, similar to them with sharp corners (rhombus, trapezoid).

Exercise.

- Find a triangle on the frame. Circle it. Shade the triangle around the frame. (Hatching is done inside the frame, the brush moves freely, the pencil "knocks" on the frame.)

Exercise 7

Target. Anchor the visual appearance of the triangle. Recognize the desired triangles among other triangles (perceptual accuracy). Develop imagination and attention, fine motor skills.

Materials. Stencil, paper, pencils.

Look at this picture: Cat-mom, cat-dad and kitten, what figures are they drawn? (Circles and triangles.)

- Who drew such a triangle, what is needed for a kitten? For a mother cat? For papa?

Draw your cat.

Children finish drawing using the triangle that they have, that is, everyone gets their own cat. Then they finish drawing the rest of the cats, focusing on the sample, but on their own.

The teacher draws attention to the fact that the cat-dad is the tallest.

Place the frame correctly so that the cat-dad is the tallest.

This exercise not only contributes to the accumulation of stocks of images of geometric shapes in the child, but also develops his spatial thinking, since the figures on the frame are located in different positions and, in order to find the one you need, you need to recognize it in a different position, and then turn the frame to draw it in this the position that the drawing requires.

The given excerpts from the lessons show a way to build an interconnected system of tasks for the formation and development of sensory cognitive abilities based on mathematical material. It is obvious that the child's activity in this fragment is also organizing his attention and stimulating his imagination.

Let's move on to another group of cognitive abilities - intellectual abilities. As already mentioned, they are based on the developed thinking.

The process of developing thinking methodically consists in the formation and development generalized mental actions(comparison, generalization, analysis, synthesis, serialization, classification, abstraction, analogy, etc.), which is a general condition for the functioning of thinking itself as a process in any field of knowledge, including mathematics. It is unconditional that the formation of mental actions is an absolute necessity for the development of mathematical thinking, it is not by chance that these mental actions are also called methods of logical mental actions.

Their formation stimulates the development of the child's mathematical abilities. One of the most significant studies in this area was the work of the Swiss psychologist J. Piaget "The genesis of a number in a child" 1, in which the author convincingly proves that the formation of the concept of number (as well as arithmetic operations) in a child is correlative to the development of logic itself: the formation of logical structures, in particular, the formation of a hierarchy of logical classes, i.e., classification, and the formation of asymmetric relations, i.e., qualitative serializations. Classification and serialization are methods of mental actions, the formation of which is impossible without the preliminary development of operations in the child. comparison, generalization, analysis and synthesis, abstraction, analogy and systematization.

It is easy to show in the above fragment of the lesson that each of the above exercises simultaneously "works" also for the formation of all these mental devices. For example, exercise 1 teaches a child to compare; exercise 2 - compare and summarize and analyze; Exercise 3 teaches analysis and comparison; exercise 4 - synthesis; Exercise 5 - Analysis, Synthesis and Generalization; Exercise b - actual classification by attribute; Exercise 7 teaches comparison, synthesis and elementary serialization.

Thus, the mathematical content is optimal for the development of all cognitive abilities (both sensory and intellectual), leads to the active development of the child's mathematical abilities.

So, the relationship between mathematical and cognitive abilities is as follows (Scheme 2).

So, the essence of the question of organizing the external conditions for the development of the child's mathematical abilities brings us back to the problem of selecting adequate mathematical content for lessons with preschool children. The younger the child, the greater the need for him to be able to receive information about the objects under study and their relationships directly through the sensory channels, with the hands and eyes being the most important at the age of 6-7 years.

It is no coincidence that everything that the teacher brings to the lesson, the child seeks at least to touch, and better - to get into his own hands for manipulation. Optimal for such manipulation is geometric material.

A quantitative characteristic is indirect, for its perception one must be prepared to understand that this characteristic exists and that it, as a rule, does not depend on other properties and qualities of the object (a fly has more legs than an elephant; and in Parrots the Boa constrictor is no longer than in Monkeys, although Parrots - 38, and Monkeys - 3). In other words, the quantitative characteristics of objects and phenomena (and even more so the relationship between them) are not directly perceived by the child, but require special preliminary training for adequate perception and comprehension.

In the previous lecture, we already dwelt on the specificity of the mathematical characteristics of objects and phenomena, on the specificity of mathematical symbolism. The complexity of these concepts is often not realized even by practicing educators.

For example, when asked whether it is possible to give a child in hand number or show children the number in class, you can often hear: "Yes, you can." To the question: “What exactly will you show by introducing the child to the number two? "- educators often answer:" Number 2 "or" Two cubes ", etc. These answers show that even an adult does not always differentiate such elementary mathematical concepts as number, number and set.

Correct perception and adequate understanding of these concepts requires preliminary special education of the child, but this does not mean that it is impossible to deal with the mathematical development of the baby. Geometric material is a full-fledged mathematical material, it is simply less familiar to the traditional perception of an adult in the content of a preschooler's education than arithmetic material.

From a psychological and methodological point of view, geometric material is much more convenient when teaching a preschooler, since we perceive it by sensing and easily lends itself to visual (material and graphic) modeling. At the same time, any geometric object has quantitative characteristics, both perceived with minimal preparation of the child (the number of sides, angles), and allowing you to repeatedly return to the analysis of these objects in order to identify new numerical characteristics (later in school, the child will get acquainted with the methods of measuring the lengths of the sides and degree measure of angles, methods of calculating perimeters and areas, etc.). For example, in the above fragment of the lesson, any construction (constructive situation) had a quantitative characteristic, but did not require symbolization (digital designation), although it could be accompanied by it. The same fragment of the lesson with symbolic accompaniment could be offered for conducting in the senior and even preparatory group (naturally, with some modernization and complication of the content of the exercises). As you can see, we are not talking about a complete refusal to work with the quantitative characteristics of objects and the relations between them, we are talking about changing the hierarchy of this work in accordance with the principle of conformity to nature (i.e., in accordance with the psychological characteristics of the assimilation of mathematical concepts by children), as well as in accordance with the didactic principles of organizing developmental education.

Thus, the restructuring of the methodological base of the mathematical development of preschoolers based on the use of modeling as the leading method and means of studying mathematical concepts and relations between them requires a certain shift in emphasis in the selection and building of the content basis of this process.

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Municipal Autonomous Preschool Educational institution"Kindergarten No. 8", Kungur

Development of children's mathematical abilities in the game.

Padukova Nadezhda Vladimirovna

2017

One of the most important tasks of raising a small child is the development of his mind, the formation of such thinking skills and abilities that allow him to master something new. Every preschooler is a little explorer discovering the world with joy and surprise. Mathematics rightfully occupies a large place in the preschool education system. Any mathematical task for ingenuity carries a certain mental load. The mental task of finding a solution is realized by means of the game and in game actions. It is important to teach children not only to count, measure and solve arithmetic problems, but also to develop their ability to see, discover properties, relationships and dependencies in the world around them, the ability to “construct”, operate with objects, signs and symbols. The question arises as to how it is possible to activate the thought processes of preschool children without harming their health.

Meanwhile, many scientists emphasize the importance of preschool age for the intellectual development of a person, since about 60% of the ability to process information is formed in children by the age of 5-6 years. The solution to this problem largely depends on the construction of the educational process. The need for the purposeful formation of such qualities in children as the ability to apply the acquired knowledge, skills, and skills in life situations is already realized by psychologists and teachers.

Mathematical ability belongs to a group of special abilities (like musical, visual, etc.). For their manifestation and further development, the assimilation of a certain stock of knowledge and the presence of certain skills, including the ability to apply existing knowledge in mental activity, are required.

Many researchers (both domestic and foreign), the formation and development of mathematical abilities associate it not with the content side of the subject (subject knowledge and skills), but with the process of mental activity, i.e. with the development of children's mathematical thinking.

The basis for the development of mathematical abilities is "mathematical thinking", which is largely due to the special specifics of the so-called cognitive and intellectual abilities.

In modern psychology, there are different directions research of thought processes. They all agree on the recognition that the foundations of these processes are laid in preschool age. However, supporters of one of the directions believe that this happens naturally, without "external stimulation", while others assert the possibility of purposeful pedagogical influence, which ultimately contributes to the development of thinking. In the works of J. Piaget, A. Vallon, B. Inelder, V.V. Rubtsova, E.G. Yudin determined the boundaries within which the process proceeds, based on the spontaneous mechanisms of the development of children's intelligence, which are the main factor determining the success of the formation of mathematical abilities. J. Piaget considers the intellectual development of the individual as a process relatively independent of learning, subject mainly to biological law. According to these views, preschool education is not the main source and driving force development.

In the works of L.S. Vygotsky, L.V. Zankov, N.A. Mechinskaya, S.L. Rubinshtein, A.N. Leontiev, M. Montessori substantiates the leading role of learning as the main stimulus for development, points out the illegality of opposing the development of psychological structures and learning.

For all the heterogeneity of opinions about the essence and content of the concept of "mathematical abilities", researchers note such specific features of the mental process of a mathematically capable child; as flexibility of thinking, i.e. not stereotyped, originality, the ability to vary the ways of solving a cognitive problem, the ease of transition from one solution path to another, the ability to go beyond the usual way of activity and the ability to find new ways to solve a problem under changed conditions.

The concept for preschool education, guidelines and requirements for updating the content of preschool education outline a number of fairly serious requirements for the cognitive development of preschool children, part of which is the development of mathematical abilities. How to ensure the mathematical development of children that is responsive modern requirements... The leading activity of a preschooler is play . Therefore, the system of work on the development of logical and mathematical ideas and skills in older preschoolers is based on the use of non-standard games, exercises and entertaining materials - logical blocks of Dienesh, Kuizener's sticks, "Tangram", "Vietnamese game", "Columbus egg", "Magic circle", "Insert the missing figure", as well as - puzzles, labyrinths, puzzles. Children enjoy playing them both in joint and independent activities. Logic games of mathematical content bring up in children a cognitive interest, the ability to creative search, the desire and ability to learn.

The constructive activity of the child during the performance of such exercises develops not only mathematical abilities and logical thinking, but also his interest, imagination, trains motor skills, the eye, spatial representations, accuracy, etc.

Also, in order to develop logical thinking in the process of working with children, you can use simple logical tasks and exercises, the solution of which develops the ability to highlight the important, to approach generalizations on your own.

Any unusual game situation in which there is an element of problematicity always arouses great interest in children. Such tasks as the search for a sign of the difference between one group of objects from another, the search for missing figures in a row, tasks for the continuation of a logical series contribute to the development of ingenuity, logical thinking and ingenuity, the development of skills with high speed perceive cognitive tasks and find the right solutions for them. Children begin to realize that the correct solution to a logical problem requires concentration, they begin to understand that such an entertaining task contains some kind of "catch" and to solve it, you need to understand what is the trick.

Let the children think they are only playing. But unbeknownst to themselves in the process of playing, preschoolers calculate, compare objects, engage in construction, solve logical problems, etc. They are interested in it because they love to play. Our role in this process is to support the interests of children. By teaching children in play, we strive to ensure that the joy of play gradually passed into the joy of learning. The teaching should be joyful!

It is in these types of activities that the intellectual, emotional - personal development... Children gain self-confidence, learn to express their thoughts and feelings.

Modern requirements for developing learning during preschool childhood make it necessary to create new forms of play activity, in which the elements of cognitive, educational and play communication would be preserved. The key to the development of mathematical abilities is the organization of purposeful intellectual and cognitive activity, it is intellectual games that rely on the child's search activity and ingenuity, and not mastering any specific knowledge and skills. Regular thinking development classes with preschoolers significantly increase interest in intellectual tasks, give pleasure from their implementation, give the child self-confidence.

In conclusion, I would like to say that the development of logical thinking in a child really plays a big role in his further teaching at school. This work is very painstaking and difficult, but also very interesting work. After all, the smallest results bring immeasurable joy and desire to work, light children's eyes and choose various effective means for the all-round development of each child.

Literature:

Kolyagin Yu.M. "Learn to Solve Problems" M., 1979

E.A. Nosova, R.L. Nepomnyashchaya: Logic and mathematics for preschoolers. Publishing house "Aksident" S.P., 1997

Konstantin Shevelev: Preschool mathematics in games. - "Mosaic - Synthesis", M. - 2004.

Beloshistaya A. How to teach preschoolers to solve problems // Preschool education-2008-№8

Kalinchenko A. Methodical approaches to the organization and conduct of classes in mathematics // Child in kindergarten-2006-№4

"Development of mathematical abilities

in preschool children

through play activities

in the context of the implementation of FSES DO "

Educator

MBDOU "Kindergarten with. Kupino "

Ishkova Tatiana Ivanovna

1. Introductory part

2. Main part

2.1. Practical section

2.2. Methods and techniques

3. Conclusion

4. Literature

“The game is the most serious thing. The game reveals to the children the world, the creative abilities of the individual. Without play, there is and cannot be full-fledged mental development. Play is a huge bright window through which the life stream of ideas and concepts about the world around is poured into the child's spiritual world. A game is a game that ignites the spark of inquisitiveness and curiosity. "

V. A. Sukhomlinsky

Introductory part

In our time, in the age of "computers", mathematics is needed to one degree or another by a huge number of people of various professions, not only mathematicians. The special role of mathematics is in mental education, in the development of intelligence. The belated formation of the logical structures of thinking of these structures proceeds with great difficulties and often remains incomplete. Therefore, mathematics rightfully occupies a very large place in the preschool education system. She hones the child's mind, develops the flexibility of thinking, teaches logic. All these qualities are useful for children, and not only in teaching mathematics. Psychology has established that the main logical structures of thinking are formed approximately at the age of 5 to 11 years.

We recognize that one of the main tasks of preschool education is the mathematical development of the child.

Relevance of the topic due to the fact that the Concept for preschool education, guidelines and requirements for updating the content of preschool education outline a number of fairly serious requirements for the cognitive development of preschoolers, part of which is the formation of elementary mathematical concepts. In this regard, I was interested in the problem: how to ensure the mathematical development of children that meets the modern requirements of the Federal State Educational Standard of DO.

Purpose of work:ensuring the integrity of the educational process through the organization of classes in the form of exercises of a game nature; promoting a better understanding of the mathematical essence of the issue, clarification and formation of mathematical knowledge in preschoolers; creating favorable conditions for the development of mathematical abilities; development of a child's interest in mathematics in preschool age.

Working on this topic, we have identified the following tasks for ourselves:

1. Develop a child's interest in mathematics in preschool age.

2. Introduction to the subject in a playful and entertaining way.

The solution to these tasks was facilitated by the following methods:

1. Study, analysis and generalization of literary sources on the topic.

2. Study and generalization of pedagogical experience in the development of mathematical abilities of children.

Embodying the idea of L.S. Vygotsky on advanced development, we strive to focus not on the level reached by children, but on the zone of proximal development, so that children can make some efforts to master the material. It is known that intellectual work is very difficult and, taking into account the age characteristics of children, we understand and remember that the main method of development is problem-search and the main form of organizing children's activities is play.

It is known that play is the main institution for the upbringing and development of a preschooler's culture, a kind of academy for his life. In play, the child is the creator and the subject. In play, the child embodies creative transformations and, generalizing everything that he has learned from adults, from books, TV shows, films, his own experience, and provides a connection between generations and the conditions of the culture of society.

2. Main part

2.1. Practical section

Studying the works of great teachers: Krupskaya N.K., Sukhomlinsky V.A., Makarenko A.S. , as well as modern literature, I set myself the task: to educate a preschooler's interest in the very process of teaching mathematics, to form in children a cognitive interest, a desire and habit to think, a desire to learn new things. To teach a child to study, to study with interest and pleasure, to comprehend mathematics and to believe in oneself is my main goal in teaching children.

I tried to find a form of teaching mathematics that would organically enter the life of a kindergarten, solve the issues of the formation of mental operations (analysis, synthesis, comparison, classification), would have a connection with other types of activity, and most importantly, would be liked by children.

The practice of teaching has shown that success is influenced not only by the content of the proposed material, but also by the form of presentation, which can arouse the interest and cognitive activity of children. Adults should not suppress, but support, not constrain, but direct the manifestations of children's activity, and also specifically create situations in which they would feel the joy of discovery.

For children of preschool age, play is of exceptional importance: play for them is study, play for them is work, play for them is a serious form of education. A game for preschoolers is a way of learning about the world around them. Play will be a means of education if it is included in a holistic pedagogical process. Leading the game, organizing the life of children in the game, the educator affects all aspects of the development of the child's personality: feelings, consciousness, will and behavior in general. However, if for the pupil the goal is in the game itself, then for the adult organizing the game there is another goal - the development of children, their assimilation of certain knowledge, the formation of skills, the development of certain personality qualities.

The game is valuable only if it contributes to a better understanding of the mathematical essence of the issue, clarification and formation of students' mathematical knowledge. Didactic games and play exercises stimulate communication, because in the process of carrying out these games, the relationship between children, child and parent, child and teacher begins to be more relaxed and emotional.

2.2. Methods and techniques.

Children are taught through: 1) organized educational activities; 2) joke tasks; 3) educational games and exercises; 4) puzzle games; 5) riddles; 6) didactic games.

Organized educational activities of children begin with a game minute, a problem situation. This arouses the interest of children and organizes them for cognitive activities. I also use various presentations ("Funny figures", "Hours, minutes, days", "Mathematical train", etc.).

A child, a little explorer of the world, and receiving various information about the world, is in dire need of explanation, confirmation or denial of his thoughts. Often, teachers and parents are faced with the problem of how to teach a child to ask questions in order to obtain comprehensive information from the answers about the subject, understanding what is happening. The question is an indicator of independent thinking. V early age the child acquires vital skills and abilities: use a spoon and fork, wash, dress; skills of obtaining and applying knowledge are no less important. These include the following intellectual skills: 1) observe; 2) see the problem; 3) form questions (filling the lack of information); 4) put forward a hypothesis; 5) give definitions to concepts; 6) compare; 7) structure; 8) classify; 9) observe; 10) draw conclusions; 11) prove and defend ideas. Third on the list is the ability to ask questions - to formulate them correctly. Socrates, as you know, while talking with students, asked them questions, and the students tried to find answers to them, expressing their guesses, putting forward their own hypotheses, and in turn, asking questions to Socrates, the result of the conversations is brilliant education.

In my pedagogical work, I use developing games that allow you to “draw out” knowledge, teach children to ask “strong” questions that help solve a problem. One such game is Magic Belt. This game teaches not only to ask questions, but along the way develops other intellectual skills, systematizes knowledge in the field of mathematics, the ability of children to play by the rules, to get out of conflict situations during the game. After making sure that the children have guessed the intended picture, they feel joy and pride.

In the section "Quantity and Counting", in my opinion, the following didactic games are appropriate: "Even - odd"; “How many of us are without one?”;“What number am I thinking?”; "Tell me the number one more - less"; “Who knows, let him continue to count”; “What numbers are missing?”; "Name your neighbors."

Introducing children to numbers , I use didactic games: "Lay out a number from sticks"; “Collect the number correctly”; "Blind from plasticine"; “What does a number look like?”; "Name the objects that resemble a number." And also we guess riddles with mathematical content, learn poems about numbers, introduce you to fairy tales in which numbers are present, learn proverbs, sayings, catchphrases where there is a number, I use physical education minutes.

I often use the game "Draw a number" in my work. Children show the number with their hands and fingers. In pairs, children like to write on each other's backs or on their palms. Voskobovich's Games are excellent material for intellectual development. Children with great pleasure and interest compose various numbers using colored rubber bands and tablets. This is where the knowledge of color is consolidated.

Introduce children to the world of geometric shapes you can also use educational games, which can be used both in the organized educational activities of children and in their free time. These games include: "Shapes", "Geometric Mosaic". These games are aimed at developing the spatial imagination of children. They develop visual perception, voluntary attention, memory and imaginative thinking, and also consolidate the name of flowers and geometric shapes. Introducing geometric shapes, we use the word game "A couple of words". We say "Circle". Children call an object that looks like a steering wheel or a wheel.

In addition, children really enjoy playingdidactic games : "Name the extra piece";"Pick up a patch"; "Find a lid for each box"; "Geometric Lotto"; "Name the figures."

We often use counting stick games. Children learn to draw patterns according to a model, from memory, then the tasks become more complicated: we suggest that children make 2 equal squares of 7 sticks, a square of two sticks, using the corner of the table.

For the development of spatial orientations I picked up a series of exercises for the children: "Help the bunny get to his house", "Help each ant get into his anthill."

At preschool age, the elements of logical thinking begin to form in children, that is, the ability to reason is formed, to make their own conclusions.

There are many games and exercises that affect development of creativity in children, as they affect the imagination and contribute to the development of lateral thinking in children. These exercises include: “What should be drawn in an empty cell? "," Determine how the last ball should be painted "," Which ball should be drawn in an empty cage? "," Determine what windows should be in the last house? " " etc.

On the development of observation I picked up a series of exercises for children “Find differences in a drawing”, “Find two identical fish”, etc.

To consolidate the concept of "magnitude" I use a series of pictures “Place each animal in a house of the right size”, “Name animals and insects from large to smallest silt from small to large”. I introduce games with folk toys-inserts (nesting dolls, cubes, pyramids), the design of which is based on the principle of taking into account the size.

When forming cyclic representations, we play the following games with children: "Color, continuing the pattern"; “What first, what then?”; "Which figure will be the last?".

To maintain interest, activate, motivate and consolidate what has been learned, we use the following forms of work with children:

· complex of educational games;

· travel;

· experimentation;

· subgroup work;

· travel game;

· mathematical KVN;

· Experiment;

· cognitive games;

· mathematical ring;

· individual work.

In my work, I use a variety of exercises, of varying degrees of difficulty, depending on the individual abilities of the children.

In play complexes, I definitely include music, physical minutes, games for the development of fine motor skills, gymnastics for the eyes and hands. I will not be mistaken if I say that the success of training largely depends on the organization. educational process... At each form of OOD, we necessarily change the types of activities, in order to improve the perception of the educator's information and enhance the activities of the children themselves in a playful way.

3. Conclusion

Teaching mathematics to preschool children is unthinkable without the use of entertaining games, tasks, and entertainment. You need to "play" math with children. Didactic games make it possible to solve various pedagogical problems in a playful way, the most accessible and attractive for children. Their main purpose is to ensure the exercise of children in distinguishing, highlighting, naming sets of objects, numbers, geometric shapes, directions.

It is interesting for children to play mathematical games, they are interesting for them, emotionally captivate children. And the process of solving, looking for an answer, based on interest in the problem, is impossible without active work thoughts. Working with children, every time I find new games that we learn and play. After all, these games will help children in the future to successfully master the basics of mathematics and computer science.

Using various educational games and exercises in working with children, I made sure that while playing, children learn the program material better, and perform complex tasks correctly. Teaching young children in the process of playing, I strove to ensure that the joy of playing turns into the joy of learning. The teaching should be joyful!

Didactic play is one of the main methods of upbringing and educational work, since in didactic games the child observes, compares, juxtaposes, classifies objects according to certain criteria, makes analysis and synthesis available to him, and makes generalizations. At the same time, children develop voluntary memory and attention.

The success of the game depends entirely on the teacher, his ability to play the game vividly, to activate and direct the attention of some, to provide timely help to other children.

My work experience shows that knowledge given in an entertaining form, in the form of a game, is assimilated by children faster, stronger and easier than those that are associated with long "soulless" exercises. "Learning can only be fun ... To digest knowledge, you need to absorb it with appetite.", - these words do not belong to a specialist in the field of preschool didactics, the French writer A. France , but it's hard to disagree with them.

4. Literature

1. Abramov I.A. Peculiarities childhood... - M., 1993.

2. Arginskaya I.I. Mathematics, mathematical games - Samara: Fedorov, 2005 - 32 p.

3. Beloshistaya A.V. Preschool age: the formation of primary ideas about natural numbers // Preschool education. - 2002 - No. 8. - S.30-39

4. Beloshistaya A.V. Formation and development of mathematical abilities of preschoolers. M .: Humanit. Ed. Center VLADOS, 2003

5. Vasina V.V., Day of the Day. M., 1991.

6. Volina V. "Merry Mathematics" - Moscow, 1999.

7. Zhikalkina T.K. "Game and entertaining tasks in mathematics" - Moscow, 1989.

8. Games and exercises for the development of mental abilities in preschool children: Book. for the educator children. garden. - M., 1989.

9. "Playing with numbers" - a series of manuals.

10. Leushina A.M. Formation of mathematical concepts in preschool children: Textbook. - M., 1974.

11. Mikhailova Z.A. Game tasks for preschoolers: Book. for the kindergarten teacher. - SPb: "Childhood-Press", 2010.

12. "Orientation in space" - T. Musseinova - candidate of pedagogical sciences.

13. The program "From birth to school" - Ed. N.E. Veraksa, T.S.Komarova, M.A.Vasilyeva.

14. “We develop perception, imagination” - A. Levin.

15. Uzorova O., Nefedova E. "1000 exercises to prepare for school" - LLC "Astrel Publishing House", 2002.

Beloshistaya, A. V. Formation and development of mathematical abilities of preschoolers: theory and practice: A course of lectures for students. doshk. faculties of higher. study. institutions. - M .: Humanit. ed. center VLADOS, 2003. - 400 s: ill. The publication is a course of lectures in which questions of the formation and development of mathematical abilities of preschoolers are considered. The manual reflects the modern understanding of the continuity of the mathematical education of preschoolers and younger students, the possibility of forming the components of educational activity and the development of cognitive processes in preschoolers. It highlights the principles of selecting the content of the course of preschool mathematics training, issues of methodological analysis of classes and programs in mathematics, the organization of an individual approach to the child in teaching mathematics. The manual includes questions of a private methodology for the formation of elementary mathematical representations of preschoolers from the standpoint of developmental education, as well as the experience of organizing relevant classes.

Picture 9 from the presentation « Cognitive development preschoolers by means of forming mathematical representations "

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"Math game" - Question to be solved. 21. Under the ashes of Pompeii, archaeologists have discovered many items made of bronze. Can you hear how quickly the speech fell silent? The course of the game: You, mathematics, give us hardening for the victory of difficulties. Fan competition. Work by stations. Question: What is in the black box? (Compass.). Station number 2.

"Mathematical sophisms" - However, sophisms alone are not enough to win any dispute. Algebraic sophisms. Sophisms belong to the logical methods of dishonest but successful discussion. Solution. Conclusion. Excursion into History. Those. algebraic sophisms are deliberately hidden errors in equations and numerical expressions.

"Mathematical tournament" - Ray 1. Task 4 ray 1. Didactic game. Game results. Ray 3. Ray 2. Task 4 ray 3. Task 1 ray 1. Task 2 ray 2. Task 1 ray 2. Task 5 ray 2. Task 5 ray 3. Task 3 ray 3. "Mathematical tournament".

"Human Abilities" - Abilities? Sense of the field. Forecast (30s of the 20th century): -100 m-10.0 sec, -height-2.25 m Bar-200kg, What's in the way? Social Studies. Outstanding achievements of people. Human abilities. Remnants of the knowledge of ancient civilizations? Oriental medicine. Telepathy. Unexplained possibilities. World records (2000): -100 m-9.81 sec, -height-2.45 m Bar-280kg,

"Development of creative abilities of students" - The main task of the teacher is to contribute to the development of each personality. We were very happy. Forms of work established in the development of students' creative abilities: Therefore, the formula "human development as an end in itself of creativity" means the following:. Intelligence. Memory, imagination.

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