Beloshistaya, A. V. Formation and development of mathematical abilities. White-haired formation and development of mathematical abilities of preschoolers Catalog of information resources with a brief annotation

Beloshistaya, A. V. Formation and development of mathematical abilities of preschoolers: questions of theory and practice: a course of lectures for students. doshk. faculties of higher textbook establishments. - M.: Humanit. ed. center VLADOS, 2003. - 400 s: ill. The publication is a course of lectures, which deal with the formation and development of mathematical abilities of preschoolers. The manual reflects the modern understanding of the continuity of mathematical education of preschoolers and primary schoolchildren, the possibility of forming the components of educational activities and the development of cognitive processes of preschoolers. It highlights the principles of selecting 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.

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"Mathematical game" - Question for decision. 21. Under the ashes of Pompeii, archaeologists have discovered many objects made of bronze. Do you hear how quickly the speech fell silent? Game progress: Mathematics, you give us hardening to overcome difficulties. Fan competition. Station work. Question: What is in the black box? (Compass.). Station number 2.

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

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

"Human abilities" - Abilities? Field feeling. Forecast (30s of the 20th century): -100 m-10.0 sec, -height-2.25 m Barbell-200kg, What's in the way? Social science. Outstanding Human Achievement. Human abilities. Remains of knowledge of ancient civilizations? Eastern medicine. Telepathy. Unexplained possibilities. World records (2000): -100 m-9.81 sec, height-2.45 m Barbell-280kg,

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

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

The publication is a course of lectures that deal with the formation and development of mathematical abilities of preschoolers. The manual reflects the modern understanding of the continuity of mathematical education of preschoolers and primary schoolchildren, the possibility of forming the components of educational activities and the development of cognitive processes of preschoolers. It highlights the principles of selecting 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.

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

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

Put the figurines in the right place.
In the tasks on p. 4-19 the child lays out figures of three main shapes in the drawings:
It is convenient to cut out these figures in 20 pieces of each in different colors and keep a supply of them in an envelope. When unfolding the figures, they can be counted, compared by number (more-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 each page every other day or two until the child can easily cope with the choice without your prompting.
After that, you can glue the figures into place with a glue stick and move on to the next tasks. Do not forget to renew the supply of figurines 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, Guidelines for organizing classes with children 4-5 years old, Beloshistaya A.V., 2007
Mathematics simulator 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 proposed to organize a discussion on this topic for the educator1 and methodologists of preschool educational institutions working with children of all ages: from early age to the preparatory group. In all cases: the educators usually confidently answered the question whether they could name and single out children capable of mathematics in their group.

This question was answered in a similar way by teachers of both primary level and subject teachers. At the same time, the main criterion for such a choice among teachers is the success of the child 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 was to justify their choice of a child capable of mathematics for a preschool teacher. And this is natural, since the younger the child, the less opportunity the teacher has to replace the cause with 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 not only mathematicians, but also preschool teachers should study this issue.

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

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

Work experience of Sibogatova N.A. - educator of GBOU School No. 2083

Kindergarten "Semitsvetik"

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

in one way or another, a huge number of

people of various professions.

It is known that the special role of mathematics is in mental education and in the development of intellect. This is explained by the fact that the results of learning are not only knowledge, but also a certain style of thinking. Mathematics contains enormous opportunities for the development of children's thinking in the process of their learning from a very early age, and the omissions here are difficult to make up.

Psychology has established that the basic 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 difficulty and often remains incomplete.

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

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

We recognize that one of the main tasks of preschool education is the mathematical development of the child. The purpose of the work: to promote a better understanding of the mathematical essence of the issue, to clarify and form mathematical knowledge among preschoolers.

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

1. To develop children's interest in mathematics.

2. To 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. The study and generalization of pedagogical experience in the development of children's mathematical abilities.

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 “design” objects, signs and words in the world around them.

In embodying L. S. 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 effort to master the material. It is known that intellectual work is very difficult and, given 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.

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

Didactic games provide an opportunity to solve various pedagogical tasks 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 of directly educational activities.

In our work, we use a complex-game technique. It is based on developing entertaining games, selected according to the topic of the lesson. This makes it possible to purposefully develop the child's mental abilities, the logic of thought, reasoning and action, the flexibility of the thought process, ingenuity and ingenuity. Introducing children to numbers, I use didactic games aimed at getting to know numbers:

"Lay out the number from the sticks";

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Development of 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 object, graphic and mental models.

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

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

A careful analysis of the development of flexagons 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, the formation of ideas in all sections of mathematics for preschoolers is activated.

The use of flexagons in the development of elementary mathematical concepts of children is a deeply creative process that dialectically combines the unity of creation and negation. Therefore, when designing the author's local method of using flexagons, I, first of all, deeply studied the available theoretical and practical developments on the issues of interest to me, took into account the specifics of the children of my group, and only on this basis created 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 a number from units; relations “more”, “less”, etc.; numbers; taught to compose and solve simple and indirect arithmetic problems. To do this, I used a variety of coloring of the sides of the flexagon, taking into account the interests of the children of a particular group.

Secondly, in the section on geometric shapes - to introduce children to the triangle, circle, ellipse, square, rectangle, quadrilaterals as a class of shapes, etc. Flexagons will help to find similarities and differences between figures, to classify them.

Thirdly, flexagons are good for children to master 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 development of sensory, intellectual culture and creative activity was accompanied by a phased introduction of flexagons into classes.

1) When getting acquainted 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) offered the children to tell what they can play with the flexagon. It is specified to which class this figure can be attributed.

3) I “accidentally” folded the flexagon so that it opened up. Give the children 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, vertices, angles?

2) She suggested folding 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) She offered to fold the rhombus on her own, count the angles; open the flexagon and tell about it.

1) I remembered with the children what the axis of symmetry is. She suggested showing and counting the number of symmetry axes of the flexagon. Show them.

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

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

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

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

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

The conducted experimental work, 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 the flexagon, I advise you to simultaneously consolidate the distinction between colors and their shades, since multi-colored flexagons are introduced into the kindergarten group.
Older preschoolers can be offered to collect flexagons by color. For example: each side of a hexahexaflexagon can consist of six triangles of additional colors that differ 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 a child's mathematical development has shown their effectiveness in solving the problem of harmonizing affect and intellect, which, in turn, allows solving a wide range of tasks that require a high level of generalization without classical formalization. At the same time, the process of development of sensory, intellectual culture and creative activity is accompanied by positive emotions of children due to the variants of “cognitive” coloring of flexagons.

Conclusion. The work done by me gave the following results: by the end of the year, the children learned to correlate the shape of objects with geometric shapes, highlight the elements of geometric shapes (angle, vertex, sides), They have formed knowledge of the basic concepts of flexagons, internal motivation and a steady interest in this type of activity .

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

LITERATURE

Afonkin S. Games and tricks with paper / S. Afonkin, E. Afonkina .- M .: Rolf, AKIM, 1999. - P. 12–67.
BeloshistayaA. B. Formation and development of mathematical abilities of preschoolers: Questions of theory and practice: A course of lectures. - M.: VLADOS, 2003. - S.11–77.
Games and entertainment: Book. 3 / Comp. L. M. Firsova. - M.: Mol. Guard, 1991.
MikhailovaZ. A. Game entertaining tasks for preschoolers. - M.: Enlightenment, 1990.
NikitinB. P. Steps of creativity or educational games. - M.: Enlightenment, 1991.
Origami and Pedagogy: Proceedings of the First All-Russian Conference of Origami Teachers. - St. Petersburg, 1996.
RepinaG. A. Technologies of mathematical modeling with preschoolers. - Smolensk, 1999.
RepinaG. A. Perspective approaches to the mathematical development of the child. - Smolensk, 2000.
365 educational games / Comp. E. A. Belyakov. - M.: Rolf, Iris-press, 1998.

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Beloshistaya AV 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 selecting 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 by:

The relationship between the development of cognitive processes and the 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 arrangement and quantitative characteristics of objects. Obviously, of these characteristics, the fastest and easiest to perceive sensory shape, size and spatial arrangement.

As noted earlier, for an adequate identification and perception of quantitative characteristics by a child, special training is required. For the formation and development of perception, it is necessary to provide the child with the opportunity to examine the perceived object, ways and means of creating its adequate model (its likeness), first in a material form in external activity, in order to then ensure its interiorization 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 must 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 being studied is easy to ensure when working primarily with geometric material, since for any geometric figure or geometric body it is easy to construct a wide variety of models from a wide variety of materials, 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, blackboard, etc. will be a model of the same concept, reflecting its main properties: the presence of four equal straight sides and four right angles. The child can perform all of the above models on his own, 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 the angles, and also establish many other of its properties by simple manipulation of the model.

The way to organize such a child's cognitive activity is an appropriately designed task (exercise), performing which, the child carries out a 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, update counting skills, and organize attention.

Materials. Counting sticks of two colors, a flannelograph with cardboard models of sticks from the teacher.

Exercise.

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

Exercise 2

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

Exercise.

Take another stick and place it on top (II) . How many sticks were there? Let's count. (Three.)
What does the figure look like? (On the gate, on the letter P). Who knows words that start with P?

Children say words.

Exercise 3

Target. Develop observation, imagination and speech activity; to form the ability to evaluate the quantitative characteristics of a changing 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? (Starting with the letter N.) List words that start with N.

Exercise 4

Target. To form design skills, imagination, memory and attention.

Exercise.

- Fold these three sticks into different figures.

Children put together figures and letters. Name them, make up words. One of the children will definitely fold the triangle.

Exercise 5

Target. To form the image of a triangle, the primary examination of the triangle model.

Materials. Counting sticks, flannelgraph.

Execution method. The teacher invites everyone to lay down such a figure:

How many sticks did you need for this figure? (Three.) Who knows what it 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 to circle the figure with a finger, count the corners (vertices), touching them with a 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 stability of perception). Outline and hatch triangles (develop small muscles of the hand).

Materials. Frame-stencil with slots in the form of geometric shapes, paper, pencils.

Note. The task is problematic, because the frame used has several triangles and shapes similar to them with sharp corners (rhombus, trapezium).

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. Fix the visual image of the triangle. Recognize the right triangles among other triangles (perception accuracy). Develop imagination and attention, fine motor skills.

Materials. Stencil, paper, pencils.

Look at this picture: Mother cat, father cat and kitten, what figures are they made up of? (Circles and triangles.)

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

Draw your cat.

Children draw using the triangle that they have, i.e. each gets their own cat. Then they draw 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.

Set the frame correctly so that 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 right one, you need to recognize it in a different position, and then rotate the frame to draw it in such the position required by the drawing.

The given fragments of the lessons show a way to build an interconnected system of tasks for the formation and development of sensory cognitive abilities on the basis of mathematical material. Obviously, the activity of the child in this fragment is also organizing his attention and stimulating his imagination.

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

The process of development of thinking methodically consists in the formation and development generalized methods of mental actions(comparison, generalization, analysis, synthesis, seriation, 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 no coincidence 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 Number in a Child”1, in which the author quite 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 seriations. Classification and seriation 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 techniques. For example, exercise 1 teaches the child to compare; exercise 2 - compare and generalize, as well as 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 seriation.

Thus, the mathematical content is optimal for the development of all cognitive abilities (both sensory and intellectual), leading 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 issue of organizing external conditions for the development of the child's mathematical abilities brings us back to the problem of selecting adequate mathematical content for classes with preschool children. The younger the child, the greater the need for him to be able to receive information about the studied objects and their relationships directly through sensory channels, with the hands and eyes being most important before the age of 6-7 years.

It is no coincidence that everything that the teacher brings to class, the child seeks to at least touch, or better, 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 what this characteristic is and that, as a rule, it does not depend on other properties and qualities of an object (a fly has more legs than an elephant; and in Parrots, the Boa constrictor is no longer than in Monkeys, although Popugaev - 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 have already dwelled on the specifics of the mathematical characteristics of objects and phenomena, on the specifics of mathematical symbolism. The complexity of these concepts is often not realized even by educators-practitioners.

For example, when asked whether it is possible to give a child in hand number or show children 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 dice", etc. These answers show that even an adult does not always differentiate such elementary mathematical concepts as number, number and set.

The 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 engage in the mathematical development of the baby. Geometric material is a full-fledged mathematical material, it is just less familiar to the traditional perception of an adult in the content of preschool education than arithmetic.

From a psychological and methodological point of view, geometric material is much more convenient for teaching a preschooler, since it is perceived by sensors and easily lends itself to visual (real and graphic) modeling. At the same time, any geometric object has quantitative characteristics, both perceived with a child’s minimal preparation (number of sides, angles), and allowing you to repeatedly return to the analysis of these objects in order to identify new numerical characteristics (later at school, the child will get acquainted with methods for measuring the lengths of sides and degree measure of angles, methods for calculating perimeters and areas, etc.). For example, in the fragment of the lesson considered above, 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 holding 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 rejection of work with the quantitative characteristics of objects and 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 children learning mathematical concepts), as well as in accordance with the didactic principles of the organization of 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 relationships between them requires a certain shift in emphasis in the selection and building the content basis of this process.

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Catalog of information resources with a brief annotation

Beloshistaya, A.V. Formation and development of mathematical abilities. Questions of theory and practice. - M. - Vlados, 2004. The manual reflects the modern understanding of the continuity of mathematical education of preschoolers and primary schoolchildren, the possibility of forming the components of educational activities and the development of cognitive processes of preschoolers. It highlights the principles of selecting 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.

Bartkovsky A., Lykova I. Color geometry.

Genis A.L., Zimnukhova I.A., Shitov A.M. Counting.

Kolesnikova E.V. Geometric figures.

Sharygin I., Sharygina T. "First steps in geometry"

The presented workbooks contain tasks for preschoolers to consolidate the skills to highlight the elements and properties of geometric shapes, compare objects by spatial features, highlight the relative position of objects and geometric shapes.

Morgacheva, I.N. Child in space. - St. Petersburg. – 2009.

In this manual, the issue of mastering spatial terminology by preschoolers is widely disclosed, game tasks are presented, exercises for strengthening the ability of children to use spatial characteristics in speech.

Cribs for every day. Methods of mathematical development of preschool children. Authors-compilers: Rocheva O.I., Kravtsova N.V. - Syktyvkar, 2006. The methodological manual presents methods for consolidating the ability of children to compare objects by signs, the ability to highlight the properties and elements of geometric shapes. In addition, the manual contains a list of the main properties of geometric shapes available to preschool children. 8. Formation of elementary mathematical representations in preschoolers / Ed. A.A. Stolyar. M., "Enlightenment", 1988. The manual reveals the forms and methods of teaching children mathematics in all age groups of the kindergarten, substantiates the need for systematic preparation of children in preschool institutions for mastering the school curriculum. 9. M. Fidler. Mathematics is already in kindergarten. M., "Enlightenment", 1981. The book reveals the experience of working on the formation of mathematical representations in preschoolers. A large methodological and illustrative material is offered. The use of Gyenesh logical blocks in games with preschoolers is described, which allow modeling important concepts not only of mathematics, but also of computer science. The main purpose of using didactic material (named after the author called "Gyenes blocks"): to teach preschoolers to solve logical problems for partitioning by properties.10. "Logic and mathematics for preschoolers" Methodical edition of E.A. Nosov; R.L. Nepomnyaschaya. (Library of the program "Childhood") "St. Petersburg". "Accident," 2000. The book tells about the possibilities of using Gyenesh blocks and Kuizener's sticks for children 3(2)-6 years old. A variety of games are described, most at three difficulty levels. The whole complex of tasks is a long intellectual ladder, and the games and exercises themselves are its steps. On each of these steps, the child must climb. If he misses one of them, then it will be much more difficult for him to reach the next one. If he runs very quickly along the ladder, it means that he has already “outgrown” these steps - and let him run. But there will definitely be one in front of which he will stop. And it is possible that here he will need help.

Books is the best source of information ever. For centuries, people have drawn their knowledge directly from the books obtained in the library. But in the 21st century, simple paper books have been replaced by electronic books. Along with them appeared digital libraries where you can download books for free and upload them to your e-reader. It's really convenient to use electronic versions of books in fb2, pdf, lit, epub format to download them to your favorite reader. One of the main criteria of any electronic library is the freedom and accessibility of information. It is very important that books can be free download, without registration, without SMS and the like.

Book search, download books for free

We believe that it is books for free save this world from copying and other wickedness. But the availability of books in the electronic library is not the only criterion. It is also important to have a comfortable book search in the library to be able to quickly find the right book. Our library has over 1,500,000 books and magazines absolutely free. On Z-Library, you can also find, in addition to books and magazines, various comics, non-fiction, children's books, novels, detective stories, and much more. by category will help you sort through the abundance of literature on our free website even faster. Remember that by downloading books for free, you maintain common sense, and do not overpay for electronic copies. E-library B-OK.org is the best source to find and download the right books and magazines. In our library, you can also convert the book into a format convenient for you or read it online. To replenish the library, we use open sources of information and the help of readers. You yourself can add a book to replenish the library. Together we will build the largest digital library on the web.

Z-Library is one of the largest online libraries in the world that contains over 4,960,000 books and 77,100,000 articles. We aim to make literature accessible to everyone.

You may remember that during the last time, we experienced some technical difficulties. But we held out, and continue to move forward. And now we really need your help. Today (March 15, 2020) we"ve started additional fundraising to project maintenance and development. Please read more or make a donation . ( 27.1% raised)

Also UNLIMITED downloads (for 31 days after the day of making donation) are available for ALL contributors who will donate during the fundraising period.