The mathematical development of children of preschool age


Scientific concepts are not assimilated and

not memorized by the child, not taken

memory but arise and are formed

using the voltage of the whole activity of his own thought

A. S. Profitable.

A necessary condition for a qualitative renewal of the society is to multiply his intellectual capabilities. The solution of this problem depends largely on the construction of the educational process. Most existing educational programs focused on the transfer trainees the socially necessary amount of knowledge on their quantitative growth, practicing what the child already knows how to do. However, the ability to use information is determined by the sophistication of the logical techniques of thinking the Need for purposeful formation of the logical methods of thinking in the process of studying specific academic disciplines already recognized by psychologists and pedagogues.

Work on the development of logical thinking of a child going without an awareness of the importance of psychological methods and means in this process. This leads to the fact that most students do not master the techniques of systematization of knowledge on the basis of logical thinking even in high school, and these techniques need to younger students: without them there is a complete absorption of the material. Among the basic intellectual skills include logical skills generated for math. Mathematics is a powerful factor in intellectual development of the child, formation of his cognitive and creative abilities. It is also known that the effectiveness of mathematical development in the preschool years depends on the success of learning mathematics in primary school.

Why are many children so hard with math, not only in elementary school, but now, in preparation for learning activities? Let’s try to answer the question of why conventional approaches to the mathematical training of preschool often do not bring the desired positive results.

The development of logical thinking of the child involves the formation of the logical methods of mental activity, as well as the ability to understand and trace the causal connection of phenomena and the ability to build a simple reasoning based on causal relationships. To the student experienced difficulties from the very first lessons he had to learn from scratch, now, in the preschool period, it is necessary to prepare the child accordingly.

Working with preschoolers is not the first year, especially with the older age , we found it possible to begin the process of the formation of the logical methods of thinking from an earlier age – 4 – 5 years .

Founded your choice for several reasons:

1. There are a large number of studies confirming that the development of logical thinking can and should do (even in those cases when the natural inclinations of the child in this area are quite modest) and what to develop logical thinking of a preschooler, it is best in the mainstream of mathematical development.

2. A group of children with whom I work , has shown the contrast in terms of overall development. Some children are far ahead of their peers. They are curious, inquisitive, have shown great interest in the new, the unknown, while having a good stock knowledge. These children, who at home is paid much attention by adults.

These children , coming in a mini – Mall or a preschool class, must rise to a higher level, training your intellect .

To do this, the teacher must create a good educational environment that best meets the needs of the child, to diversify the job.

3.The issues of development of logic has always occupied a Central place among the problems not only of preschool pedagogy and psychology. Regularly attending lessons in the first grade and having a little experience in elementary school , came to the conclusion that children have difficulties in solving problems, ability to reason, what motivated you to work on this topic.

The purpose of work creation of conditions and promotion of the mathematical development of children, the development of logical thinking.

The main objectives of my work are:

  1. Forming techniques of logical operations of preschoolers (analysis, synthesis, comparison, generalization, classification, analogy), the ability to think and plan their actions.
  2. The development of children’s divergent thinking, imagination, creative abilities, the ability to substantiate their statements, build simple reasoning.

These problems are solved in the course of acquaintance of children with different areas of mathematical reality: the number and counting, measurement and comparison of magnitudes, spatial and temporal orientations.

The essence of the work lies in the selection and systematization, and also testing material on the mathematical development of preschool children, the selection of developmental tasks and entertaining material for forming the foundations of logic. Expected results: since logical thinking in preschool age, primarily appears through separate structural components, their holistic development is possible by solving a system of logical problems in mathematical material. When organizing a special educational work on the formation and development of logical methods of mathematical thinking on the material will increase the performance of the process regardless of the initial level of development of the child.

We must not forget that the work on the development of logic in terms of content is built on the basis of the arithmetic and geometric material. Work on mathematical development consists of several sections: arithmetic, geometric and section content and logic problems and tasks.

The first two sections – arithmetic and geometric are the main carriers of mathematical content , since they determine the range and volume study of issues and topics. Therefore, the first phase, special attention should be paid to developing basic knowledge of mathematics. You first need to think of and arrange a venue for mathematical zanyatiya also prepare and use a variety of didactic material

Organization of work in the classroom.

All work is based on developing an environment that is structured in the following way:

  1. Math fun (games on planar modeling the Tangram and etc ,tasks, jokes, entertaining puzzles)
  2. Didactic games.
  3. Educational games are games that contribute to the solution of mental ability and intelligence development ( the game is based on the process of finding solutions(TRIZ), the development of logical thinking )

Here is a General methodological approaches to the organization of work: typical structure of each number:

  1. Telling tutor tales with further numerical Kingdom and its new representative, education number .
  2. Identification, where the number in the objective world, in nature.
  3. Drawing on the theme of the number, putting some of the numerical range with the addition of new numbers, the colonization of the new numbers , i.e. the numbers in the chamber.
  4. Modeling appropriate figures, games like what’s it like?, working with stencils, the lay out of counting sticks, coloring, shading.
  5. Familiarity with the appropriate class of geometric shapes, drawing, cutting flat shapes , modeling and design of volumetric bodies, identifying, in any items the surrounding world they live in.
  6. Rhythmic motor activities, finger games.
  7. Educational games.

The leading activity in preschool children is play activity. So the classes, in fact, are system games, in which children explore a problem situation, identify essential features and relationships, compete, and make discoveries. During these games and is personal-oriented interaction with an adult child and children among themselves, their conversations in pairs, in groups. Because all the math trying to capture part of the class, one purpose of the game plot. For example, a Store, boat trip and etc. the Classes are conducted with the whole group or by subgroups, but at the same time, when the kids get different jobs, or employment is carried out in the form of a game. In the classroom for mathematical development, it is desirable to use chopsticks Kyuizenera (but in their absence you can use different colored stripes) , Tangram, counting sticks. From the experimental corner may be the material is taken to conduct research activities. For example, to discover the unit of measure in the mathematical development of children led to the conclusion that what can be measured and the water and the sand and the ribbon, but only with a suitable measurements – cups, sticks, etc.

1. Gaming motivation, motivation for action (including mental activity);

2. Finger gymnastics (stimulating brain activity, in addition – is a wonderful speech material). Every week try to learn a new game.

3. The elements of drama to enhance children’s interest submitted by teacher material, creating the emotional background of the lesson. When you check into the chamber of the next figures, children take on the role and played up the tale. The children say the words in verses about the numbers. You can dramatize and tales that are suitable for learning ordinal and quantitative accounts of the Bun, Turnip, etc. (see more below)

It is very important that the children themselves wanted to do .Let them a lesson is to play, how exciting assignments, interesting work. The arrival of fairy-tale characters, the use of toys, play situation, the problematic situation will make the lesson interesting.

Familiarization with the formation of a new number, its correlation with digit , cardinal and ordinal score are respectively methods. In addition to their work in the classroom, greater attention to the mathematical development of children in other classes and outside. Here are some features works from experience to consolidate numeracy skills. If a child has difficulties with the score, think out loud. Ask him to count the objects aloud. Constantly think of different items (books, balls, toys, etc.) from time to time ask the child: How many cups is on the table?, How many lies have books, pencils ?, How many children are playing with blocks? How many today boys? etc., but do it gently , using a gaming motif. For example: I don’t know how to cook pencils, Milena, count me how many we have today in the mini – center children. The acquisition of skills of oral accounts contributes to the education of children to understand the purpose of some objects of everyday use, on which numbers are written. Such items are clock and thermometer. Different kinds of watches available in the class. Children are often interested in how much time, fun playing with the layout of the dial and alarm clocks. Thus, there is the improvement of numeracy skills.

It is very important to teach children to distinguish the location of objects in space (front, behind, between, middle, right, left, bottom, top). For this you can use different toys. We arrange them in a different order and ask , what is ahead, behind, near, far, etc. we Play games like Find your seat,Put the toy down, etc. while Learning concepts such as many, few, one, several, more, less, equally (with the pupils of mini center).While walking or in class, ask the child to name items which is a lot, a little, one thing. For example, many chairs, table one; many books, little notebooks. Reading child a book or telling stories, when there are numbers, ask him to postpone so many counting sticks, how much, for example, were the animals in the story. After, count how many in the story were animals, ask who had more, others less, others the same amount. Compare toys largest: who is a Bunny or a bear less than one who is the same height.

We invite children to invent stories with numerals . . And then they can draw the characters in his stories and tell about them, to make their sketches and compare them. Preparatory work for teaching children the basic mathematical operations of addition and subtraction involves the development of skills, such as parsing the number into its component parts and defining the previous and subsequent numbers within the first ten( senior group)

In the form of a game children love to guess previous and next numbers. Ask for example, what number is more than five but less than seven, less than three but greater than one, etc. Children love to guess the number and guess conceived. Decides , for example, to ten and ask the child to name different numbers. You say, more than the number you planned or less. Then the roles are reversed.

For analysis use counting sticks or with the older children , cleaned from sulphur matches. Ask the children to put on the table two sticks. How many sticks on the table? Then put the sticks on both sides. Ask how many sticks on the left, as on the right. Then take three sticks and also put it on two sides. We offer you to take four sticks and the children share them. Ask him how to put four sticks. Let them change the location of the counting of the sticks so that one side lay one stick, and on the other three. Similarly, sequentially parse all numbers within ten. The higher the number, the more options parsing.

Learning numbers can be easy and fun.

With numbers difficult.

There are children who like abstract icons, and they letters and figures with fun learning. But the rest need to be motivated additionally. How to do it:

– play the game Telephone. It is very effective method is when children play in pairs.

Role – play also contributes to the development of not only skills , but also to consolidate the numbers, if you use checks or a certain number of circles and therefore the money in the game, children will learn to correlate the number with the number and remember the number.

In the game to prepare Bus bus numbers or numbers cars.

Also very effective is the use of coloring numbered , for example, all fragments of the yellow number “1”, red the numeral “2”, etc. the User which color corresponds to each number let us verbally (as many times as the child asks). Kids love these jobs, and they love to play with them, especially the older children.

With the help of counting sticks is also useful to make letters and numbers – kids love this job. Thus there is a mapping of concepts and symbols. Let the children to drawn stick figure will pick up that number of sticks or counting of material, toys that specifies this figure.

Develop skills for quantitative and ordinal account using tales , poems and rhymes.

Mathematical tales

Folk and author of fairy tales, which the pupils of the mini-center from multiple readings already know by heart, our invaluable helpers. In any of them a whole lot of all kinds of mathematical situations. And they are absorbed as if by themselves. The chamber will help to learn cardinal and ordinal account (first came to the house mouse, the second frog, etc.), but also the foundations of arithmetic. The kid easy to learn, it increases the number, if each time to add the unity. Rode rabbit – and became three of them. Ran Fox became four. Well, if the book has illustrations, which the kid can count residents attics. But you can play out a story with toys. Kolobok and Repka is especially good for mastering ordinal account. Who pulled the turnip first? Who met the Gingerbread man the third? But the turnip can and about size to talk. Who is the greatest? Grandfather. Who is the smallest? Mouse. Makes sense and how to remember. Who stands in front of the cat? And who is behind the headstock? The three bears – it’s all mathematical superskate. And bears can count on the size to talk (large, small, medium, who more, who less, who is the biggest, who is smallest), and to correlate bears with matching chairs-plates. Reading little red riding hood will provide an opportunity to talk about the concepts long and short. Especially if you draw the long and short track on a sheet of paper or lay out the blocks on the floor and see which of them will run faster little fingers or drive a toy car.

Another useful tale for the development of account – About a kid who could count to ten. It seems that for this purpose she created. Count along with the kid heroes of the tale and children will easily remember quantitative score to 10.

Almost all children’s poets can find poems. For example, Kittens Mikhalkov or Hilarious account by S. Marshak. A lot of poems, counting have A. Usacheva. Here is one of them rhymes for the Raven:

I decided ass:

One, two, three, four, five.

Six crow on a pole,

Seven crow – on the tube,

Eight sat on the poster

Nine – feeds the ravens…

Well, ten is a jackdaw.

That was the end rhymes.

2. Work with the geometric material.

In parallel with work on a number of acquaint children with basic geometric shapes, flat shapes it’s the little people who is interested in everything, they are very curious , and they differ in color.( see photo 3)

Let the children make geometric shapes made of sticks, carve, sculpt and paint. You can set the necessary dimensions based on the number of sticks. For example, add a rectangle with sides of three sticks and four sticks; triangle with sides two and three sticks. Make shapes of different sizes and shapes with different number of sticks. Please compare the figures. Another option would be a combination of shapes, which some parties will be shared.

For example, five sticks at the same time need to be square and two of the same triangle; or of the ten sticks to make two squares, large and small (the small square is made up of two sticks inside large).Combining counting sticks, children better begins to understand mathematical concepts (number, greater, less, same, shape, triangle, etc.).

Very popular with the children the game– the transformation when a figure turned into objects. The same type of exercise In which the subjects live figure?

From the variety of interesting mathematical material in the preschool years the most widely used are educational games. The main purpose of them is to provide pregnanet children in the discernment, selection, naming sets of objects, numbers, geometric shapes, directions, etc. In the didactic games have the opportunity to generate new knowledge, to acquaint children with ways of action. Each of the games does a particular task of improving the mathematical (quantitative, spatial, temporal) representations of children. In the process teaching preschoolers math game is directly included in the lesson as a means of creating new knowledge, extend, clarify, fixing of educational material. The educational games we use in solving problems individual work with children and conduct with all children or with the sub-group in their spare time. There is a great variety of didactic games, which we use in the classroom and out .

The mathematical development of children of preschool age

2.The development of logic.

In developing children’s mathematical concepts are widely used entertaining in form and content of a variety of didactic exercises. They differ from typical learning tasks and exercises uniqueness formulation of the problem (to find, to guess), a surprise present ) Tasks for the development of logic from a person of aldara.For example, in the preschool class for the purpose of exercise of children in the group of geometric shapes is exercise Help Aldara is to find and fix the problem. The children are encouraged to consider how geometric figures are placed in which group and on what basis the United, spot the error, correct and explain. Response to address the Aldara .

For the development of certain mathematical skills you need to develop logic thinking of the preschoolers. At school they will need the ability to compare, analyze, specify, generalize. It is therefore necessary to teach the child to solve problem situations, to draw conclusions, to come to a logical conclusion. Solving logic problems develops the ability to allocate essential, to make independent conclusions. Logic games math content develop children’s cognitive interest, the ability to generate, the desire and ability to learn. Unusual game situation with the elements of problems that are specific to each engaging activities, always arouses interest in children. Game exercises should be distinguished from the didactic games in the structure, purpose, levels of child autonomy, the role of the teacher. They usually do not include all the structural elements of the teaching games (didactic task, the rules of the game action). Content-logic puzzles and job, based on the mathematical contents of the first two sections (arithmetic and geometric) , is a means of achieving the goals and objectives, so we have selected games and exercises to develop logical thinking, creativity and spatial imagination, has brought them into the system . Logical development child also involves building skills to understand and to trace the causal connection of phenomena and the ability to build a simple reasoning based on causal relationships. It is easy to verify that in the performance of tasks and systems of tasks the child is practicing these skills as their basis are also mental actions:seriation, analysis, synthesis, generalization , comparison, classification, generalization, abstraction.

The seriation of building a ordered increasing or decreasing ranks in the chosen basis. Seriation can be arranged by size, length, height, width, size, shape or color. It is exercises to compare objects according to various criteria.

Analysis – selection properties object, or select an object from the group or select groups of objects by a particular attribute.

Synthesis – a combination of various elements (features, properties) in a single unit .

Comparison logic receiving mental actions, requiring the identification of similarities and differences between characteristics of an object (object, phenomenon, group of objects).

Classification – the separation of the set into groups according to some feature, which is called classification.

Generalization is making in the verbal (verbal) form of the results of the comparison process.

These mental operations are the basis of the suggested exercises. We offer the following types of exercises and tasks for the development of logic.

1. The task of logical-constructive ( geometrical material, figures).

Even more increases the process of assimilation by the child of knowledge in mathematics using tasks of logical-constructive character. It is based on different methods of mental actions that help increase the effectiveness of the development of logical operations. In the first stage, the proposed use of the task with the geometric material and figures , then move on to use of cards aimed at the development of mathematical ability, and logical operations, which are also actively developing fine motor skills, orientation on the sheet. These exercises can be conducted in any part of the lesson. These job picked up and made up by age groups.( see Appendix)

2.Games on the development of spatial perception: building material; counting sticks, designers.

Game with building blocks develop spatial imagination, teaches children to analyze the sample buildings, and later act in the simplest configuration (drawing). In the creative process are also included logical operations – comparison, synthesis (reconstruction of the object).

Games with counting sticks develops thin movements of hands and spatial representation and creative imagination. During these games you can develop the child’s view of the shape, quantity, color. From the variety of puzzles is most appropriate for preschool age(5-7 years) puzzle with sticks (you can use matches without sulfur). They are called problems on the sharpness of geometric nature, as in the course of solving generally, there is a Transfiguration, a transformation of one figures in others, and not just change their number. At preschool age using the most simple puzzles. For organisations working with children need to have regular sets of counting sticks for the compilation of them clearly presents problems-puzzles . In addition, the required table is graphically depicted in them shapes that are to be converted. On reverse the side table indicates how the conversion should be done and what shape should result. Tasks wit different degrees of complexity, the nature of the transformation (the Transfiguration). They cannot be solved in any learned way. In the course of solving each new task, the child is involved in an active search for solutions, while striving to the ultimate goal, the desired modification or the construction of spatial figures. First, children are reluctant to perceive this kind of job, saying that I do not know how, miss, then these jobs beat: then we saved Princess opened the heavy door, then picked up the key to the lock, destroying the spell of a witch, the kids perked up, began to play. Children just love to lay out shapes , figures, objects. Games with chopsticks to accompany the reading of riddles, poetry, nursery rhymes, counting rhymes, matching theme.

3. Educational (i.e. having multiple levels of difficulty, diverse in application): DIENES Blocks, sticks etc. of Kwizera Sticks Kyuizenera is a universal didactic material. Main features – abstraction, high efficiency. Great is their role in the implementation of the principle of clarity, the representation of the complex abstract mathematical concepts in a child form. Working with sticks allows to translate the practical, external activities into internal plan. To deal with them, children may individually or in subgroups. Games can wear competitive nature. Quite effective is the use of chopsticks in individual correctional work with children lagging in development. Sticks can be used to perform diagnostic tasks. Operations: comparison, analysis, synthesis, generalization, classification and seriation are not only as cognitive processes, surgery, a mental action, but also as methods that determine the path followed by the thought of the child when performing exercises note : unfortunately, we do not have this manual Sticks Kyuizenera , but successfully model multi-colored stripes.

4. Puzzles, games on the development of imagination (including – TRIZ technology for the development of systems thinking, see Appendix ), logical problems in the poems, problem – jokes ( see Annex), which are presented in verbal form.

Work with this type of tasks, you can start with mysteries. Children five years of life offers a wide range of topics riddles: animals, household items, clothing, food, natural phenomena, about the vehicles. Description of the subject of the riddle can be given fully, in detail, the puzzle can serve as a story about the subject. Teaching children the skills to solve the puzzles begin not with their making, and parenting skills to observe life, to perceive the objects and phenomena from different sides, to see the world in diverse relationships and dependencies. The development of a common touch of culture, the development of attention, memory, observation of the child is the basis for the thought of the work he does at guessing. Thematic selection of riddles gives you the opportunity to develop children’s elementary logical concepts. For this, after guessing the riddles, it is advisable to offer children jobs compilation, for example: how in a word to call the inhabitants of the forest: the hare, the hedgehog, the Fox? (animals), etc. and pay special attention to puzzles with numerals. Children are very active in perception tasks-jokes, puzzles, logic problems . They are aggressively looking for solution, which leads to the result. In the case when an entertaining task is available to the child, he / she develops a positive emotional attitude to it, and stimulates mental activity. Child interesting the ultimate goal: to reach the right decision. Children are actively involved in the discussion of the tasks, sometimes rashly put forward a false assumption , then gradually begin to monitor themselves, reason . Also very active children solve problems in poetry, especially if they accompanied by illustrations.( see Annex )

5. Finger games, rhymes, physical minutes on mathematical material.

These games stimulate brain activity, and develop fine motor skills, promote language development and creative activities. Finger games is a re-enactment of any of rhymed stories, tales with your fingers. Many games require the participation of both hands that allows children to navigate the concepts right, up, down, etc. If the child learns one finger game, he will certainly try to come up with new staging for other rhymes and songs.

Example: Boy thumb

– Boy thumb, where have you been?

– With this brother in the woods went,

With this brother was cooking soup,

With this brother ate porridge,

With this brother sang the song.

For the successful assimilation of the children of logical operations necessary to work in the system, both in the classroom and outside. The use of such entertaining material is constructed from material containing numerals.( see Annex)

6. Games simulation plane.

To this types of games include the most famous Tangram, a Leaf, etc., “Tangram” is one of the most interesting puzzle games. Tangram is a geometric puzzle invented in China over 4000 years ago. When working on the game “Tangram” it is necessary to respect the principles of consistency. At the first stage it is advisable to offer the pupils a simple task that will allow children to become familiar with the puzzle and its parts, learn to recognize various geometric shapes included in the Tangram. A perk of the job was the fact that the work is performed in stages:

1. The children themselves are made an allowance( under the leadership cut into pieces), get acquainted with parts– shapes magic square , recognize them, learn to make a square.

2.Offer free modeling at will.

3. Simulation on the model , up .

4. The children were offered the picture where you traced the shape.

5.Most difficult tasks were tasks where given the task of silhouette , where will independently through trial , and guesswork to make it from the figures. Such a task is given only after mastering children methods of compiling the figures.

To interest the children work with the magic square, was played different game situations : for example, spell animals, unfreeze, save, etc. Another effective method is competitive, preschoolers enjoy participating in the game.

The efficiency of the work.

Perhaps more difficult to judge about changes in the level of mental development of children in planned educational activities. The time interval is small enough.


  1. Olga, I read Your article the Mathematical development of children of preschool age, the development of logic (from experience). I as a teacher of physics and mathematics, it was very interesting to see what work is being done in this direction in the DOE. Mathematics is an important component of intellectual development. From the formed basic mathematical concepts such as numbers, mathematical operations, geometric concepts at an early age depend on children’s achievements in the further development of the subject. You are on the subject of reality show the use of these concepts than facilitate further transition to the abstract content. Very interesting and thoroughly written article with examples.

    The only thing is, I wish You could have edited the work to the end. You can contact the editors with request to insert the App, which is link in the article, but it itself is missing or not highlighted. The same can be inserted into the work of 2-3 images or photos with drawings of children on a mathematical topic, teaching material, referred to.

    – in the beginning decided to write Author and place of work, and give Description material.

    Thank you for sharing your experience with colleagues. For the creation of conditions and promotion of the mathematical development of children vote +1. Sincerely, S. A.

  2. Dear Svetlana! I am very pleased that You appreciated my work.And due design, as always, not enough time.Math is my strong point, I always preferred the subjects of natural – mathematical direction, and his pupils try to inculcate interest in mathematics. To this work 7 books– application but I did not publish them and photos, as it so happened.Thanks again!

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