Both parents and teachers know that mathematics is a powerful factor intellectual development child, the formation of his cognitive and creative abilities. It is also known that the success of teaching mathematics in primary school depends on the effectiveness of a child’s mathematical development in preschool age.

Why is mathematics so difficult for many children, not only in elementary school, but even now, in preparation for educational activities? Let's try to answer this question and show why generally accepted approaches to the mathematical preparation of a preschool child often do not bring the desired positive results.

In modern primary school educational programs important is given a logical component. The development of a child’s logical thinking implies the formation of logical techniques of mental activity, as well as the ability to understand and trace the cause-and-effect relationships of phenomena and the ability to build simple conclusions based on cause-and-effect relationships. So that the student does not experience difficulties literally from the first lessons and does not have to learn from scratch, already now, in the preschool period, it is necessary to prepare the child accordingly.

Many parents believe that the main thing in preparing for school is to introduce the child to numbers and teach him to write, count, add and subtract (in fact, this usually results in an attempt to memorize the results of addition and subtraction within 10). However, when teaching mathematics using textbooks of modern developmental systems (L. V. Zankov’s system, V. V. Davydov’s system, the “Harmony” system, “School 2100”, etc.), these skills do not help the child in mathematics lessons for very long. The stock of memorized knowledge ends very quickly (in a month or two), and the lack of development of one’s own ability to think productively (that is, to independently perform the above-mentioned mental actions based on mathematical content) very quickly leads to the appearance of “problems with mathematics.”

At the same time, a child with developed logical thinking always has a greater chance of being successful in mathematics, even if he was not previously taught the elements school curriculum(counting, calculations, etc.).

It is no coincidence that last years in many schools working on developmental programs, an interview is conducted with children entering the first grade, the main content of which is questions and tasks of a logical, and not just arithmetic, nature. Is this approach to selecting children for education logical? Yes, it is natural, since the mathematics textbooks of these systems are structured in such a way that already in the first lessons the child must use the ability to compare, classify, analyze and generalize the results of his activities.

However, one should not think that developed logical thinking is a natural gift, the presence or absence of which must be accepted. There is a large number of studies confirming that the development of logical thinking can and should be done (even in cases where the child’s natural abilities in this area are very modest). First of all, let's figure out what logical thinking consists of.

Logical techniques of mental actions - comparison, generalization, analysis, synthesis, classification, seriation, analogy, systematization, abstraction - are also called logical thinking techniques in the literature. When organizing special developmental work on the formation and development of logical thinking techniques, a significant increase in the effectiveness of this process is observed, regardless of the initial level of development of the child.

It is most advisable to develop the logical thinking of a preschooler in line with mathematical development. The process of a child’s assimilation of knowledge in this area is further enhanced by the use of tasks that actively develop fine motor skills, that is
tasks of a logical and constructive nature. In addition, there are various methods of mental action that help enhance the effectiveness of using logical-constructive tasks.

Seriation

Construction of ordered increasing or decreasing series based on a selected characteristic. A classic example of seriation: nesting dolls, pyramids, insert bowls, etc.

Series can be organized by size, by length, by height, by width if the objects are of the same type (dolls, sticks, ribbons, pebbles, etc.), and simply by size (with an indication of what is considered size) if the objects different types (seat toys according to height). Series can be organized by color, for example, by the degree of color intensity (arrange jars of colored water according to the degree of color intensity of the solution).

Analysis

Selecting the properties of an object, or selecting an object from a group, or selecting a group of objects based on a certain characteristic.

For example, the attribute is given: “Find all sour”. First, each object in the set is checked for the presence or absence of this attribute, and then they are isolated and combined into a group based on the “sour” attribute.

Synthesis

Compound various elements(signs, properties) into a single whole. In psychology, analysis and synthesis are considered as mutually complementary processes (analysis is carried out through synthesis, and synthesis is carried out through analysis).

Tasks to develop the ability to identify the elements of a particular object (features), as well as to combine them into a single whole, can be offered from the very first steps of the child’s mathematical development. Let us give, for example, several such tasks for children two to four years old.

1. A task to select an object from a group based on any criterion: “Take the red ball”; “Take the red one, but not the ball”; "Take the ball, but not the red one."

2. A task to select several objects according to the specified criterion: “Choose all the balls”; “Choose round balls, but not balls.”

3. A task to select one or more objects based on several specified characteristics: “Choose a small blue ball”; "Pick a big red ball." The last type of task involves combining two characteristics of an object into a single whole.

Analytical-synthetic mental activity allows the child to consider the same object from different points of view: as big or small, red or yellow, round or square, etc. However, we are not talking about introducing a large number of objects, quite the contrary, in a way organizing a comprehensive review is the technique of setting various tasks for the same mathematical object.
As an example of organizing activities that develop a child’s ability to analyze and synthesize, we will give several exercises for children five to six years old.

Exercise 1
Material: set of figures - five circles (blue: large and two small, green: large and small), small red square.

Assignment: “Determine which of the figures in this set is extra. (Square.) Explain why. (All the rest are circles.).”

Exercise 2
Material: the same as for Exercise 1, but without the square.
Assignment: “Divide the remaining circles into two groups. Explain why you divided them this way. (By color, by size.).”

Exercise 3
Material: the same and cards with numbers 2 and 3.
Assignment: “What does the number 2 mean on the circles? (Two large circles, two green circles.) The number 3? (Three blue circles, three small circles.).”

Exercise 4
Material: the same didactic set (a set of plastic figures: colored squares, circles and triangles).
Assignment: “Remember what color was the square that we removed? (Red.) Open the box, Didactic set.” Find the red square. What other colors are there squares? Take as many squares as there are circles (see exercises 2, 3). How many squares? (Five.) Can you make one big square out of them? (No.) Add as many squares as needed. How many squares did you add? (Four.) How many are there now? (Nine.)".
The traditional form of tasks for the development of visual analysis are tasks for choosing an “extra” figure (object). Here are a few tasks for children five to six years old.

Exercise 5
Material: drawing of figurines-faces.

Assignment: “One of the figures is different from all the others. Which one? (The fourth one.) How is it different?”

Exercise 6
Material: drawing of human figures.

Task: “Among these figures there is an extra one. Find it. (Fifth figure.) Why is it extra?”
More complex shape Such a task is the task of isolating a figure from a composition formed by superimposing some forms on others. Such tasks can be offered to children five to seven years old.

Exercise 7
Material: drawing of two small triangles forming one large one.

Assignment: “There are three triangles hidden in this picture. Find and show them.”
Note. You need to help the child show the triangles correctly (circle with a small pointer or finger).
As preparatory tasks, it is useful to use tasks that require the child to synthesize compositions from geometric shapes at the material level (from material material).

Exercise 8
Material: 4 identical triangles.

Assignment: “Take two triangles and fold them into one. Now take two other triangles and fold them into another triangle, but of a different shape. How are they different? (One is tall, the other is low; one is narrow, the other is wide.) You can Is it possible to make a rectangle out of these two triangles? (Yes.) A square? (No.)."
Psychologically, the ability to synthesize is formed in a child earlier than the ability to analyze. That is, if a child knows how it was assembled (folded, designed), it is easier for him to analyze and identify its component parts. That is why such serious importance is given in preschool age to activities that actively form synthesis - design.
At first, this is a patterned activity, that is, performing tasks of the “do as I do” type. At first, the child learns to reproduce the object, repeating the entire construction process after the adult; then - repeating the process of construction from memory, and finally moves on to the third stage: independently restores the method of constructing a ready-made object (tasks like “make the same one”). The fourth stage of tasks of this kind is creative: “build a tall house”, “build a garage for this car”, “build a rooster”. The tasks are given without a sample, the child works according to the idea, but must adhere to the given parameters: a garage specifically for this car.
For construction, any mosaics, construction sets, cubes, cut-out pictures are used that are suitable for this age and make the child want to tinker with them. An adult plays the role of an unobtrusive assistant; his goal is to help bring the work to completion, that is, until the intended or required whole object is obtained.

Comparison
- a logical method of mental action that requires identifying similarities and differences between the characteristics of an object (object, phenomenon, group of objects).
Performing a comparison requires the ability to identify some features of an object (or group of objects) and abstract from others. To highlight various features of an object, you can use the game “Find it using the specified features”: “Which (of these objects) is big yellow? (Ball and bear.) What is big yellow and round? (Ball),” etc.
The child should use the role of the leader as often as the answerer, this will prepare him for the next stage - the ability to answer the question: “What can you tell about him? (The watermelon is large, round, green. The sun is round, yellow, hot.)” . Or: “Who will tell you more about this? (The ribbon is long, blue, shiny, silk.).” Or: “What is this: white, cold, crumbly?” etc.
It is recommended to first teach the child to compare two objects, then groups of objects. To a small child It is easier to first find signs of differences between objects, then - signs of their similarity.
Types of comparison tasks:
1. Tasks on dividing a group of objects according to some criteria (large and small, red and blue and

etc.).
2. All games of the “Find the same” type. For a child two to four years old, the set of characteristics by which similarities are sought should be clearly defined. For older children, exercises are offered in which the number and nature of similarities can vary widely.
Let us give examples of tasks for children five to six years old, in which the child is required to compare the same objects according to various criteria.

Exercise 9
Material: images of two apples, a small yellow one and a large red one. The child has a set of shapes: a blue triangle, a red square, a small green circle, a large yellow circle, a red triangle, a yellow square.

Assignment: “Find one that looks like an apple among your figures.” An adult offers to look at each image of an apple in turn. The child selects a similar figure, choosing a basis for comparison: color, shape. “Which figure can be called similar to both apples? (Circles. They are similar in shape to apples.).”

Exercise 10
Material: the same set of cards with numbers from 1 to 9.
Assignment: “Put all the yellow figures to the right. What number fits this group? Why 2? (Two figures.) What other group can be matched to this number? (A blue and red triangle - there are two of them; two red figures, two circles; two square - all options are analyzed.)". The child makes groups, uses a stencil frame to sketch and paint them, then signs the number 2 under each group. “Take all the blue figures. How many are there? (One.) How many colors are there in total? (Four.) Figures? (Six.) ".
The ability to identify the characteristics of an object and, focusing on them, to compare objects is universal, applicable to any class of objects. Once formed and well developed, this skill will then be transferred by the child to any situations requiring its use.
An indicator of the maturity of the comparison technique will be the child’s ability to independently apply it in activities without special instructions from an adult on the signs by which objects need to be compared.
Classification
- division of a set into groups according to some criterion, which is called the basis of classification. Classification can be carried out either according to a given basis, or with the task of searching for the basis itself (this option is more often used with children six to seven years old, as it requires a certain level of formation of the operations of analysis, comparison and generalization).
It should be taken into account that when classifying a set, the resulting subsets should not intersect in pairs and the union of all subsets should form this set. In other words, each object must be included in only one set, and with a correctly defined basis for classification, not a single object will remain outside the groups defined by this basis.
Classification with children preschool age can be carried out:
- by name (cups and plates, shells and pebbles, skittles and balls, etc.);
- by size (large balls in one group, small ones in another, long pencils in one box, short pencils in another, etc.);
- by color (this box has red buttons, this one has green buttons);
- in shape (this box contains squares, and this box contains circles; this box contains cubes, this box contains bricks, etc.);
- based on other non-mathematical characteristics: what can and cannot be eaten; who flies, who runs, who swims; who lives in the house and who in the forest; what happens in summer and what happens in winter; what grows in the garden and what in the forest, etc.
All of the examples listed above are classifications based on a given basis: the adult communicates it to the child, and the child carries out the division. In another case, classification is performed on a basis determined by the child independently. Here, the adult sets the number of groups into which many objects (objects) should be divided, and the child independently looks for the appropriate basis. Moreover, such a basis can be determined in more than one way.
For example, tasks for children five to seven years old.

Exercise 11
Material: several circles of the same size, but different color(two colors).
Assignment: “Divide the circles into two groups. By what criteria can this be done? (By color.).”

Exercise 12
Material: several squares of the same colors are added to the previous set (two colors). The figures are mixed.
Assignment: “Try to divide the figures into two groups again.” There are two options for separation: by shape and by color. An adult helps the child clarify the wording. The child usually says: “These are circles, these are squares.” The adult generalizes: “So, they divided it according to shape.”
In exercise 11, the classification was unambiguously specified by the corresponding set of figures on only one basis, and in exercise 12, the addition of a set of figures was deliberately made in such a way that classification on two different grounds became possible.
Generalization
- this is the presentation in verbal form of the results of the comparison process.
Generalization is formed in preschool age as the identification and fixation of a common feature of two or more objects. A generalization is well understood by a child if it is the result of an activity carried out by him independently, for example, classification: these are all big, these are all small; these are all red, these are all blue; these all fly, these all run, etc.
All of the above examples of comparisons and classifications ended with generalizations. Possible for preschoolers empirical types generalizations, that is, generalizations of the results of their activities. To lead children to this kind of generalization, the adult organizes work on the task accordingly: selects objects of activity, asks questions in a specially designed sequence to lead the child to the desired generalization. When formulating a generalization, you should help the child construct it correctly, use the necessary terms and verbiage.
Here are examples of generalization tasks for children five to seven years old.

Exercise 13
Material: set of six figures of different shapes.

Assignment: “One of these figures is extra. Find it. (Figure 4.).” Children of this age are unfamiliar with the concept of a bulge, but they usually always point to this shape. They can explain it like this: “Her corner went inward.” This explanation is quite suitable. “How are all the other figures similar? (They have 4 corners, these are quadrilaterals.).”
When selecting material for a task, an adult must ensure that the child does not end up with a set that focuses the child on unimportant features of objects, which will encourage incorrect generalizations. It should be remembered that when making empirical generalizations, the child relies on external visible signs of objects, which does not always help to correctly reveal their essence and define the concept.
For example, in exercise 14, figure 4, in general, is also a quadrilateral, but non-convex. A child will become acquainted with figures of this kind only in the ninth grade of high school, where a definition of the concept “convex” is formulated in a geometry textbook. flat figure". In this case, the first part of the task was focused on the operation of comparing and identifying a figure that differs in external shape from other figures in this group. But the generalization was made based on a group of figures with characteristic features, frequently occurring quadrangles. If the child has an interest in figure 4, an adult may note that this is also a quadrilateral, but unusual shape. Forming in children the ability to independently make generalizations is extremely important from a general developmental point of view.
Next, we give an example of several interrelated exercises (tasks) of a logical and constructive nature on the formation of an idea of ​​a triangle for five-year-old children. For modeling constructive activities, children use counting sticks, a stencil frame with slots in the shape of geometric shapes, paper, and colored pencils. The adult also uses sticks and figures.

Exercise 14
The purpose of the exercise is to prepare the child for subsequent modeling activities through simple constructive actions, to update counting skills, and to organize attention.

Assignment: “Take from the box as many sticks as I have (two). Place them in front of you the same way (vertically side by side). How many sticks? (Two.) What color sticks do you have (the sticks in the box are of two colors: red and green)? Make them different colors. What color are your sticks? (One is red, one is green.) One and one. How many are together? (Two.)."

Exercise 15
The purpose of the exercise is to organize constructive activities according to the model. Counting exercises, development of imagination, speech activity.
Material: counting sticks of two colors.
Assignment: “Take another stick and put it on top. How many sticks are there? Let’s count. (Three.) What does the figure look like? (Like a gate, the letter “P.”) What words start with “P”?”

Exercise 16
The purpose of the exercise is to develop observation, imagination and speech activity. Formation of the ability to evaluate the quantitative characteristics of a changing structure (without changing the number of elements).
Material: counting sticks of two colors.
Note: the first task of the exercise is also preparatory to the correct perception of the meaning of arithmetic operations.
Assignment: “Move the top stick like this (the adult moves the stick down so that it is in the middle of the vertical sticks). Has the number of sticks changed? Why hasn’t it changed? (The stick has been rearranged, but not removed or added.) What does the figure look like now? ( Starting with the letter "N".) Name the words starting with "N".

Exercise 17
The purpose of the exercise is to develop design skills, imagination, memory and attention.
Material: counting sticks of two colors.
Assignment: “What else can be put together from three sticks? (The child puts together figures and letters. Names them, comes up with words.).”

Exercise 18
The purpose of the exercise is to form an image of a triangle, a primary examination of the triangle model.
Material: counting sticks of two colors, a triangle drawn by an adult.

Task: “Make a figure out of sticks.” If the child does not fold the triangle himself, an adult helps him. “How many sticks were needed for this figure? (Three.) What kind of figure is this? (Triangle.) Why is it called that? (Three corners.).” If the child cannot name the figure, the adult suggests its name and asks the child to explain how he understands it. Next, the adult asks to trace the figure with a finger, count the corners (vertices), touching them with a finger.

Exercise 19
The purpose of the exercise is to consolidate the image of the triangle on the kinesthetic (tactile sensations) and visual level. Recognition of triangles among other figures (volume and stability of perception). Outlining and shading triangles (development of small muscles of the hand).
Note: the task is problematic because the frame used has several triangles and figures similar to them with sharp corners (rhombus, trapezoid). Material: stencil frame with figures of different shapes.
Assignment: “Find a triangle on the frame. Circle it. Color in the triangle along the frame.” The shading is done inside the frame, the brush moves freely, the pencil “knocks” on the frame.

Exercise 20
The purpose of the exercise is to consolidate the visual image of a triangle. Recognition of the desired triangles among other triangles (perceptual accuracy). Development of imagination and attention. Development of fine motor skills.
Assignment: “Look at this drawing: here is a mother cat, a father cat and a kitten. What shapes are they made of? (Circles and triangles.) What triangle is needed for a kitten? For a mother cat? For a father cat? Draw your cat ". Then the child completes the drawings of the remaining cats, focusing on the sample, but independently. The adult draws attention to the fact that the father cat is the tallest. “Place the frame correctly so that the daddy cat turns out to be the tallest.”

Note: this exercise not only contributes to the accumulation of a child’s reserves of images of geometric figures, but also develops spatial thinking, since the figures on the stencil 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 rotate the frame to draw it in that position , which the drawing requires.
It is obvious that the child’s constructive activity in the process of performing these exercises develops not only the child’s mathematical abilities and logical thinking, but also his attention, imagination, trains motor skills, eye, spatial concepts, accuracy, etc.
Each of the above exercises is aimed at developing logical thinking techniques. For example, exercise 15 teaches the child to compare; exercise 16 - compare and generalize, as well as analyze; exercise 17 teaches analysis and comparison; exercise 18 - synthesis; exercise 19 - analysis, synthesis and generalization; exercise 20 - actual classification by attribute; exercise 21 teaches comparison, synthesis and elementary seriation.
Logical development Child development also involves developing the ability to understand and trace the cause-and-effect relationships of phenomena and the ability to build simple conclusions based on cause-and-effect relationships. It is easy to see that when completing all the above examples of tasks and task systems, the child practices these skills, since they are also based on mental actions: analysis, synthesis, generalization, etc.
Thus, two years before school it is possible to have a significant impact on the development of a preschooler’s mathematical abilities. Even if your child does not become an indispensable winner of mathematical Olympiads, he will not have problems with mathematics in elementary school, and if he does not have them in elementary school, then there is every reason to expect that he will not have them in the future.

The development of mathematical abilities in preschool children begins... Conduct a diagnosis of a preschooler in order to select an individual...

Mathematical ability is the ability to think logically. Is it possible to develop mathematical abilities in preschool children? Yes, it's possible. A person is born with an underdeveloped left hemisphere of the brain. It is responsible for logic and is activated gradually, along with the acquisition of new skills. The success of this process largely depends on the baby’s environment. With the right approach, you can achieve good results in the development of his intellect, and therefore his mathematical abilities.

Modern theories and technologies for the mathematical development of preschool children suggest:

1. formation of elementary mathematical representations;
2. development of their logical thinking;
3. use of modern teaching tools and methods.

It is advisable to first diagnose the development of each preschooler in order to select an individual educational program for him.

Mathematical representations

The development of mathematical abilities in preschool children begins with their immersion in a mathematical environment. In order to later feel comfortable among mathematical formulas and problems, they must in preschool age;

• find out what a figure and a number are;
• learn ordinal and quantitative calculations;
• learn to add and subtract within tens;
• find out what the shape of an object and volume are;
• learn to measure the width, height and length of objects;
• distinguish between temporal concepts “earlier”, “later”, “today”, “tomorrow”, etc.;
• navigate in space, understanding the concepts of “further”, “closer”, “ahead”, “behind”, etc.;
• be able to compare: “narrower - wider”, “lower - higher”, “less - more”.

Don't be scared! Mathematical concepts can be mastered at home, casually, in a playful way. How to do it?

Count objects out loud whenever possible or involve your child in doing so. (How many flowers do we have in the vase?, How many plates do we need to put?) Ask your child to follow your instructions: “Please bring me two pencils.”

Thematic material:

Are you walking down the street together? Count to ten and back: in a duet, alternately, then let him count alone.

Teach your child to find the next and previous numbers. (Do you know which number is greater than 3 and less than 5?)

Help him understand addition and subtraction operations. In elementary school, there are children who find it difficult to solve problems because they do not understand the meaning of these mathematical operations. If in one problem the boxes were folded, then in all other problems about boxes these students try to fold them, regardless of the conditions of the problem. Prepare your child before school. Take candy, apples, cups and use a clear example to explain to him what addition means and what subtraction means.

Teach him to compare objects. (Look, a magpie! Is it bigger than a sparrow or smaller?) Draw his attention to the fact that there can be different numbers of objects. (There are a lot of apples and few pears in the vase. What can you do to make the fruits equal?)

Introduce your child to scales. It's great if you have a mechanical kitchen scale with weights. Let the child weigh the apple, an empty mug, or a mug of water.

Explain how to tell the time using a clock with hands.

Place toys on the table. Teach your child to distinguish which toy is closer to him, which is further away, which is in between.

Draw a quadrilateral, triangle, circle, oval. Let him try to explain how the first two figures differ from the second two. Show him where the angle is in the triangle. Count the angles, and the child himself will guess why the triangle has such a name.

Teach your preschooler easily, unobtrusively, and he will become friends with mathematics.

Formation of logical thinking

To successfully master mathematical science, you must be able to perform operations on given objects: find similarities or differences, regroup them according to a given criterion. Start mastering these wisdom before your child enters school. This will help him both in solving mathematical problems and in everyday life.

Techniques for developing mathematical abilities in preschool children:

• The ability to identify an object or group of objects based on a given characteristic (analysis).
• Bringing together some elements, properties or characteristics into a single whole (synthesis).
• Arranging any objects in ascending or descending order according to a given criterion.
• Comparison with the aim of finding similarities or differences between objects (comparison).
• Distribution of objects into groups by name, color, size, shape, etc. (classification).
• Conclusion, comparison result (generalization). This technique is given special significance.

Analysis tasks for children 5-7 years old

Mathematical development of preschool children using simple exercises.

Exercise 1

In Figure 1, find the extra figure. (This is a red square)

Picture 1

Task 2

In Figure 1, distribute the circles into two groups. Explain your decision. (You can distribute by color, or by size).

Task 3

In Figure 2, show three triangles. (Two small and one along the outer contour)

Synthesis problems

Combining elements and aspects of an object into a single system.

Exercise 1

Do what I do. In this task, an adult and a child construct identical objects. The child repeats the actions of the adult.

Task 2

Repeat the same from memory.

Task 3

Build a tower, design a scooter, etc. This is a creative activity. It is done without a sample.

Figure 2

Organizing tasks

Collecting and sorting items from smallest to largest or vice versa.

Exercise 1

Build the nesting dolls according to height, starting with the smallest one.

Task 2

Put on the pyramid rings, starting from the largest to the smallest.

Analysis tasks for children 2-4 years old

Performed with toys or pictures.

Exercise 1

Choose a blue car. Choose a car, but not a blue one.

Task 2

Select all the small cars. Select all the cars, but not the small ones.

Task 3

Choose the little blue car.

Comparison tasks for children 2-4 years old

The difference and similarity of elements according to some characteristic.

Exercise 1

What's round like a ball? (Apple, orange)

Task 2

Play with your child: first you describe the characteristics of the object, and the child guesses, then vice versa.

Example: Small, gray, can fly. Who is this? (Sparrow)

Comparison problems for older children

Same as the previous task, only for older children.

Exercise 1

In Figure 3, find a figure similar to the sun. (Circle)

Task 2

In Figure 3, show all the red shapes. What number corresponds to them? (Number 2)

Figure 3

Task 3

What else corresponds to the number 2 in Figure 3? (Number of yellow pieces)

A task on the ability to classify objects for children 2-4 years old

The adult names the animals, and the child says which of them can swim and which cannot. Then the child chooses what to ask about (about fruits, cars, etc.), and the adult answers.

Task for a child 5-7 years old

In Figure 3, select the polygons into a separate group and divide them by color. (All shapes except the circle. The square and triangle will be in one group, and the rectangle in the other)

Generalization task

Figure 4 shows geometric shapes. What do they have in common? (These are quadrilaterals)

Figure 4

Entertaining games and tasks

Modern construction sets - puzzles - have been invented for preschoolers to play independently. These are flat construction sets “Pythagoras”, “Magic Circle” and others, as well as volumetric construction sets “Snake”, “ Magic balls", "Pyramid". All of them teach the child to think geometrically.

Fun tasks like:

• There were 3 pears on the table. One was cut in half. How many pears are left on the table? (3)
• A team of dogs ran 4 km. How far did each dog run? (4)

By offering your child such tasks, you will teach him to listen carefully to the condition and find the catch. The child will understand that mathematics can be very interesting.

Read and tell your child something from the history of mathematics: how ancient people believed, who invented the numbers we use, where geometric figures came from...

Don't neglect simple riddles. They also teach you to think.

Tools to help parents of young mathematicians

First of all, this is visual didactic material:

• images of objects drawn on cards;
• household items, toys, etc.;
• cards with numbers and arithmetic signs, geometric figures;
• magnetic board;
• regular and hourglass;
• scales;
• counting sticks.

Buy educational games, construction sets, puzzles, counting materials, checkers and chess.

Everybody knows Board games with dice, chips and playing field. This is useful and interesting game. She teaches the child to count and perform tasks carefully. In addition, the whole family can take part in it.

Buy children's educational books with good illustrations.

1. Encourage your child's curiosity.
2. Look for answers to his questions together. Reason with him.
3. Don't complain about lack of time. Talk and play while walking together, before bed.
4. Great importance have a trusting relationship between an adult and a preschooler. Never laugh at your child's mistakes.
5. Do not overload your baby with activities. This will harm his health and discourage him from learning.
6. Pay attention not only to the development of mathematical abilities in preschool children, but also to their spiritual and physical development. Only then will your child become a harmonious personality.

Introduction

The concept of “development of mathematical abilities” is quite complex, comprehensive and multifaceted. It consists of interrelated and interdependent ideas about space, form, size, time, quantity, their properties and relationships, which are necessary for the formation of “everyday” and “scientific” concepts in a child.

The mathematical development of preschoolers is understood as qualitative changes in cognitive activity child, which occur as a result of the formation of elementary mathematical concepts and related logical operations. Mathematical development is a significant component in the formation of a child’s “picture of the world.”

The development of mathematical concepts in a child is facilitated by the use of a variety of didactic games. In the game, the child acquires new knowledge, skills and abilities. Games that promote the development of perception, attention, memory, thinking, and the development of creative abilities are aimed at mental development preschooler as a whole.

In elementary school, the mathematics course is not at all easy. Children often experience various kinds of difficulties when mastering the school mathematics curriculum. Perhaps one of the main reasons for such difficulties is the loss of interest in mathematics as a subject.

Therefore, one of the most important tasks educator and parents - to develop a child’s interest in mathematics in preschool age. Introducing this subject in a playful and entertaining way will help the child in the future to master the school curriculum faster and easier.

1 DEVELOPMENT OF MATHEMATICAL ABILITIES IN PRESCHOOL CHILDREN

1.1 Specifics of the development of mathematical abilities

In connection with the problem of the formation and development of abilities, it should be noted that a number of studies by psychologists are aimed at identifying the structure of schoolchildren’s abilities to various types activities. In this case, abilities are understood as a complex individually - psychological characteristics person who meet the requirements of this activity and are a condition for successful implementation. Thus, abilities are a complex, integral, mental formation, a kind of synthesis of properties, or, as they are called, components.

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

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

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

First, many people believe that mathematical ability lies primarily in the ability to perform quick and accurate calculations (particularly in the mind). In fact, computational abilities are not always associated with the formation of truly mathematical (creative) abilities. Secondly, many people think that schoolchildren who are capable of mathematics have a good memory for formulas, figures, and numbers. However, as academician A. N. Kolmogorov points out, success in mathematics is least of all based on the ability to quickly and firmly memorize a large number of facts, figures, formulas. Finally, it is believed that one of the indicators of mathematical ability is the speed of thought processes. A particularly fast pace of work in itself has nothing to do with mathematical ability. A child can work slowly and deliberately, but at the same time thoughtfully, creatively, and successfully progress in mastering mathematics.

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

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

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

3) Ability to operate with numerical and symbolic symbols;

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

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

6) Reversibility thought process(to the transition from direct to reverse train of thought);

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

8) Mathematical memory. It can be assumed that she characteristics It also follows from the peculiarities of mathematical science that it is memory for generalizations, formalized structures, logical schemes;

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

1.2 Formation of children’s mathematical abilities

preschool age. Logical thinking

Many parents believe that the main thing in preparing for school is to introduce the child to numbers and teach him to write, count, add and subtract (in fact, this usually results in an attempt to memorize the results of addition and subtraction within 10). However, when teaching mathematics using textbooks of modern developmental systems (L.V. Zankov’s system, V.V. Davydov’s system, the “Harmony” system, “School 2100”, etc.), these skills do not help the child in mathematics lessons for very long. The stock of memorized knowledge ends very quickly (in a month or two), and the lack of development of one’s own ability to think productively (that is, to independently perform the above-mentioned mental actions on mathematical content) very quickly leads to the appearance of “problems with mathematics.”

At the same time, a child with developed logical thinking always has a greater chance of being successful in mathematics, even if he was not previously taught the elements of the school curriculum (counting, calculations and

etc.). It is no coincidence that in recent years, many schools working on developmental programs have conducted interviews with children entering first grade, the main content of which is questions and tasks of a logical, and not just arithmetic, nature. Is this approach to selecting children for education logical? Yes, it is natural, since the mathematics textbooks of these systems are structured in such a way that already in the first lessons the child must use the ability to compare, classify, analyze and generalize the results of his activities.

However, one should not think that developed logical thinking is a natural gift, the presence or absence of which should be accepted. There is a large number of studies confirming that the development of logical thinking can and should be done (even in cases where the child’s natural abilities in this area are very modest). First of all, let's figure out what logical thinking consists of.

Logical techniques of mental actions - comparison, generalization, analysis, synthesis, classification, seriation, analogy, systematization, abstraction - are also called logical thinking techniques in the literature. When organizing special developmental work on the formation and development of logical thinking techniques, a significant increase in the effectiveness of this process is observed, regardless of the initial level of development of the child.

To develop certain mathematical skills and abilities, it is necessary to develop the logical thinking of preschoolers. At school they will need the skills to compare, analyze, specify, and generalize. Therefore, it is necessary to teach the child to solve problem situations, draw certain conclusions, and come to a logical conclusion. Solving logical problems develops the ability to highlight the essential and independently approach generalizations (see Appendix).

Entertaining tasks contribute to the development of the child’s ability to quickly perceive cognitive tasks and find the right solutions for them. Children begin to understand that the right decision a logical problem needs to be concentrated, they begin to realize that such an entertaining problem contains some kind of “trick” and to solve it it is necessary to understand what the trick is.

Logic puzzles can be as follows:

Two sisters have one brother each. How many children are in the family? (Answer: 3)

It is obvious that the child’s constructive activity in the process of performing these exercises develops not only the child’s mathematical abilities and logical thinking, but also his attention, imagination, trains motor skills, eye, spatial concepts, accuracy, etc.

Each of the exercises given in the Appendix is ​​aimed at developing logical thinking techniques. For example, exercise 4 teaches the child to compare; exercise 5 - compare and generalize, as well as analyze; Exercise 1 teaches analysis and comparison; exercise 2 - synthesis; exercise 6 - actual classification by attribute.

The logical development of a child also presupposes the formation of the ability to understand and trace the cause-and-effect relationships of phenomena and the ability to build simple conclusions based on cause-and-effect relationships.

Thus, two years before school it is possible to have a significant impact on the development of a preschooler’s mathematical abilities. Even if a child does not become an indispensable winner of mathematical Olympiads, he will not have problems with mathematics in elementary school, and if they do not exist in elementary school, then there is every reason to expect that they will not exist in the future.

2 DIDACTIC GAMES IN THE PROCESS OF MATHEMATICAL DEVELOPMENT OF PRESCHOOL CHILDREN

2.1 The role of educational games

The didactic game as an independent gaming activity is based on the awareness of this process. Independent play activity is carried out only if children show interest in the game, its rules and actions, if these rules have been learned by them. How long can a child be interested in a game if its rules and content are well known to him? This is a problem that needs to be solved almost directly in the process of work. Children love games that are familiar to them and enjoy playing them.

What is the significance of the game? In the process of playing, children develop the habit of concentrating, thinking independently, developing attention, and the desire for knowledge. Being carried away, children do not notice that they are learning: they learn, remember new things, navigate unusual situations, replenish their stock of ideas and concepts, and develop their imagination. Even the most passive of children join the game with great desire and make every effort not to let their playmates down.

In the game, the child acquires new knowledge, skills and abilities. Games that promote the development of perception, attention, memory, thinking, and the development of creative abilities are aimed at the mental development of the preschooler as a whole.

Unlike other activities, play contains a goal in itself; The child does not set or solve extraneous and separate tasks in the game. A game is often defined as an activity that is performed for its own sake and does not pursue extraneous goals or objectives.

For preschool children, 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. The game will be a means of education if it is included in the holistic pedagogical process. By directing the game, organizing the life of children in the game, the teacher influences all aspects of the development of the child’s personality: feelings, consciousness, will and behavior in general.

However, if for the student the goal is the game itself, then for the adult organizing the game there is another goal - the development of children, their acquisition of certain knowledge, the formation of skills, the development of certain personality qualities. This, by the way, is one of the main contradictions of the game as a means of education: on the one hand, there is no goal in the game, and on the other, the game is a means of purposeful personality formation.

This is most evident in the so-called didactic games. The nature of the resolution of this contradiction determines the educational value of the game: if the achievement of a didactic goal is achieved in the game as an activity that contains the goal in itself, then its educational value will be the most significant. If the didactic task is solved in game actions, the purpose of which for their participants is this didactic task, then the educational value of the game will be minimal.

A 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, since in the process of these games the relationships between children, child and parent, child and teacher begin to be more relaxed and emotional.

Free and voluntary inclusion of children in the game: not imposing the game, but involving children in it. Children must understand well the meaning and content of the game, its rules, and the idea of ​​each game role. The meaning of game actions must coincide with the meaning and content of behavior in real situations so that the main meaning of game actions is transferred to real life activities. The game should be guided by socially accepted moral standards based on humanism and universal human values. The game should not humiliate the dignity of its participants, including the losers.

Thus, a didactic game is a purposeful creative activity, during which students comprehend the phenomena of the surrounding reality more deeply and clearly and learn about the world.

2.2 Methods of teaching counting and basic mathematics to preschool children through play activity

In modern schools, the programs are quite rich, and there are experimental classes. In addition, new technologies are entering our homes more and more rapidly: many families are purchasing computers to educate and entertain their children. Life itself demands knowledge of the basics of computer science. All this makes it necessary for a child to become acquainted with the basics of computer science already in the preschool period.

When teaching children the basics of mathematics and computer science, it is important that when they start school they have the following knowledge:

Counting to ten in ascending and descending order, the ability to recognize numbers in a row and separately, quantitative (one, two, three...) and ordinal (first, second, third...) numbers from one to ten;

Previous and subsequent numbers within one ten, the ability to compose numbers of the first ten;

Recognize and depict basic geometric shapes (triangle, quadrangle, circle);

Shares, the ability to divide an object into 2-4 equal parts;

Basics of measurement: a child must be able to measure length, width, height using a string or sticks;

Comparing objects: more - less, wider - narrower, higher - lower;

Fundamentals of computer science, which are still optional and include an understanding of the following concepts: algorithms, information coding, a computer, a program that controls a computer, the formation of basic logical operations - “not”, “and”, “or”, etc.

The basis of the fundamentals of mathematics is the concept of number. However, number, like almost any mathematical concept, is an abstract category. Therefore, difficulties often arise in explaining to a child what a number is.

The development of mathematical concepts in a child is facilitated by the use of a variety of didactic games. Such games teach the child to understand some complex mathematical concepts, form an understanding of the relationship between numbers and numbers, quantities and numbers, develop the ability to navigate in the directions of space, and draw conclusions.

When using didactic games, they are widely used various items and visuals that help keep classes fun, entertaining, and accessible.

If your child has difficulty counting, show him, counting out loud, two blue circles, four red, three green. Ask him to count the objects out loud himself. Constantly count different objects (books, balls, toys, etc.), from time to time ask the child: “How many cups are there on the table?”, “How many magazines are there?”, “How many children are walking on the playground?” and so on.

The acquisition of mental counting skills is facilitated by teaching children to understand the purpose of certain household items on which numbers are written. Such items are a watch and a thermometer.

Such visual material opens up scope for imagination when carrying out various games. After teaching your baby how to measure temperature, ask him to measure the temperature on an outdoor thermometer every day. You can keep a record of the air temperature in a special “magazine”, noting daily temperature fluctuations in it. Analyze the changes, ask your child to determine the decrease and increase in temperature outside the window, ask how many degrees the temperature has changed. Together with your child, draw up a chart of air temperature changes over a week or month.

When reading a book to a child or telling fairy tales, when numerals are encountered, ask him to put down as many counting sticks as, for example, there were animals in the story. After you have counted how many animals there were in the fairy tale, ask who there were more, who were fewer, and who were the same number. Compare toys by size: who is bigger - a bunny or a bear, who is smaller, who is the same height.

Let the preschooler come up with fairy tales with numerals himself. Let him say how many heroes there are, what kind of characters they are (who is bigger - smaller, taller - shorter), ask him to put down the counting sticks during the story. And then he can draw the heroes of his story and talk about them, make their verbal portraits and compare them.

It is very useful to compare pictures that have both similarities and differences. It’s especially good if the pictures have a different number of objects. Ask your child how the pictures differ. Ask him to draw a different number of objects, things, animals, etc.

The preparatory work for teaching children the basic mathematical operations of addition and subtraction includes the development of skills such as parsing a number into its component parts and identifying the previous and subsequent numbers within the first ten.

In a playful way, children have fun guessing the previous and next numbers. Ask, for example, what number is greater than five, but less than seven, less than three, but greater than one, etc. Children love to guess numbers and guess what they have in mind. Think of, for example, a number within ten and ask your child to name different numbers. You say whether the named number is greater than or less than what you had in mind. Then switch roles with your child.

To parse numbers, you can use counting sticks. Ask your child to place two chopsticks on the table. Ask how many chopsticks are on the table. Then spread the sticks on both sides. Ask how many sticks are on the left and how many are on the right. Then take three sticks and also lay them out on two sides. Take four sticks and have your child separate them. Ask him how else you can arrange the four sticks. Let him change the arrangement of the counting sticks so that there is one stick on one side and three on the other. In the same way, sequentially sort out all the numbers within ten. The larger the number, the correspondingly more parsing options.

It is necessary to introduce the baby to basic geometric shapes. Show him a rectangle, a circle, a triangle. Explain what a rectangle (square, rhombus) can be. Explain what a side is and what an angle is. Why is a triangle called a triangle (three angles). Explain that there are other geometric shapes that differ in the number of angles.

Let the child make geometric shapes from sticks. You can give it the required dimensions based on the number of sticks. Invite him, for example, to fold a rectangle with sides of three sticks and four sticks; triangle with sides two and three sticks.

Also make shapes of different sizes and shapes with different quantities chopsticks Ask your child to compare the shapes. Another option would be combined figures, in which some sides will be common.

For example, from five sticks you need to simultaneously make a square and two identical triangles; or make two squares from ten sticks: large and small ( small square made up of two sticks inside a large one). Using chopsticks is also useful to form letters and numbers. In this case, a comparison of concept and symbol occurs. Let the child match the number made up of sticks with the number of sticks that makes up this number.

It is very important to instill in your child the skills necessary to write numbers. To do this, it is recommended to spend a lot of time with him preparatory work aimed at understanding the notebook layout. Take a squared notebook. Show the cell, its sides and corners. Ask your child to place a dot, for example, in the lower left corner of the cage, in the upper right corner, etc. Show the middle of the cage and the midpoints of the sides of the cage.

Show your child how to draw simple patterns using cells. To do this, write individual elements, connecting, for example, the upper right and lower left corners of the cell; upper right and left corners; two dots located in the middle of adjacent cells. Draw simple “borders” in a checkered notebook.

It is important here that the child himself wants to study. Therefore, you cannot force him, let him draw no more than two patterns in one lesson. Such exercises not only introduce the child to the basics of writing numbers, but also instill fine motor skills, which will greatly help the child in learning to write letters in the future.

Logic games Mathematical content instills in children cognitive interest, the ability to creatively search, and the desire and ability to learn. An unusual game situation with problematic elements characteristic of each entertaining task always arouses interest in children.

Entertaining tasks help develop a child’s ability to quickly perceive cognitive problems and find the right solutions for them. Children begin to understand that in order to correctly solve a logical problem it is necessary to concentrate; they begin to realize that such an entertaining problem contains a certain “catch” and in order to solve it it is necessary to understand what the trick is.

If the child cannot cope with the task, then perhaps he has not yet learned to concentrate and remember the condition. It is likely that while reading or listening to the second condition, he forgets the previous one. In this case, you can help him draw certain conclusions from the conditions of the problem. After reading the first sentence, ask your child what he learned and understood from it. Then read the second sentence and ask the same question. And so on. It is quite possible that by the end of the condition the child will already guess what the answer should be.

Solve a problem out loud yourself. Draw specific conclusions after each sentence. Let your baby follow your thoughts. Let him understand how problems of this type are solved. Having understood the principle of solving logical problems, the child will be convinced that solving such problems is simple and even interesting.

Regular riddles created folk wisdom, also contribute to the development of the child’s logical thinking:

Two ends, two rings, and in the middle there are nails (scissors).

The pear is hanging, you can’t eat it (light bulb).

In winter and summer, one color (Christmas tree).

The grandfather is sitting, dressed in a hundred fur coats; whoever undresses him sheds tears (bow).

Knowledge of the basics of computer science is currently not mandatory for studying in primary school, compared, for example, with the skills of counting, reading or even writing. However, teaching preschoolers the basics of computer science will certainly bring some benefits.

First, the practical benefits of learning the basics of computer science will include the development of abstract thinking skills. Secondly, in order to master the basics of actions performed with a computer, a child will need to use the ability to classify, highlight the main thing, rank, compare facts with actions, etc. Therefore, by teaching your child the basics of computer science, you not only give him new knowledge that will be useful to him when mastering a computer, but you also strengthen some skills along the way general.

There are also games that are not only sold in stores, but also published in various children's magazines. These are board games with a playing field, colored chips and cubes or a top. The playing field usually shows various pictures or even whole story and there are turn-by-turn directions. According to the rules of the game, participants are invited to throw a dice or a top and, depending on the result, perform certain actions on the playing field. For example, when a number is rolled, the participant can begin his journey in the game space. And having made the number of steps that appeared on the dice, and getting into a certain area of ​​the game, he is asked to perform some specific actions, for example, jump three steps forward or return to the beginning of the game, etc.

Thus, in a playful way, the child is instilled with knowledge from the field of mathematics, computer science, and the Russian language, he learns to perform various actions, develop memory, thinking, Creative skills. During the game, children acquire complex mathematical concepts, learn to count, read and write. The most important thing is to instill in the child an interest in learning. To do this, classes should be held in a fun way.

CONCLUSION

In preschool age, the foundations of the knowledge a child needs in school are laid. Mathematics is a complex science that can cause some difficulties during schooling. In addition, not all children are inclined and have a mathematical mind, so when preparing for school it is important to introduce the child to the basics of counting.

Both parents and teachers know that mathematics is a powerful factor in the intellectual development of a child, the formation of his cognitive and creative abilities. The most important thing is to instill in the child an interest in learning. To do this, classes should be held in a fun way.

Thanks to games, it is possible to concentrate the attention and attract the interest of even the most disorganized preschool children. At the beginning, they are captivated only by game actions, and then by what this or that game teaches. Gradually, children awaken interest in the subject of study itself.

Thus, in a playful way, instilling in a child knowledge in the field of mathematics, teach him to perform various actions, develop memory, thinking, and creative abilities. In the process of playing, children learn complex mathematical concepts, learn to count, read and write, and in the development of these skills the child is helped by close people - his parents and teacher.

Bibliography

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Application

Exercises to develop mathematical abilities for children five to seven years old

Exercise 1

Material: set of figures - five circles (blue: large and two small, green: large and small), small red square).

Assignment: “Determine which of the figures in this set is extra. (Square) Explain why. (All the rest are circles).”

Exercise 2

Material: the same as for Exercise 1, but without the square.

Assignment: “The remaining circles were divided into two groups. Explain why you divided it this way. (By color, by size).”

Exercise 3

Material: the same and cards with numbers 2 and 3.

Assignment: “What does the number 2 mean on circles? (Two big circles, two green circles.) Number 3? (Three blue circles, three small circles)."

Exercise 4

Material: the same didactic set (a set of plastic figures: colored squares, circles and triangles).

Assignment: “Remember what color was the square that we removed? (Red.) Open the “Didactic Set” box. Find the red square. What other colors are there squares? Take as many squares as there are circles (see exercises 2, 3). How many squares? (Five.) Can you make one big square out of them? (No.) Add as many squares as needed. How many squares did you add? (Four.) How many are there now? (Nine.)".

Exercise 5

Material: images of two apples, a small yellow one and a large red one. The child has a set of shapes: a blue triangle, a red square, a small green circle, a large yellow circle, a red triangle, a yellow square.

Assignment: “Find one that looks like an apple among your figures.” An adult offers to look at each image of an apple in turn. The child selects a similar figure, choosing a basis for comparison: color, shape. “Which figurine can be called similar to both apples? (Circles. They are shaped like apples.).”

Exercise 6

Material: the same set of cards with numbers from 1 to 9.

Assignment: “Put all the yellow pieces to the right. Which number fits this group? Why 2? (Two figures.) What other group can be matched to this number? (A blue and a red triangle - there are two of them; two red figures, two circles; two squares - all options are analyzed.).” The child makes groups, uses a stencil frame to sketch and paint them, then signs the number 2 under each group. “Take all the blue figures. How many are there? (One.) How many colors are there in total? (Four.) Figures? (Six.)".

Mathematics is not an easy science, but it is needed always and everywhere; it is not without reason that they say that mathematics is the queen of sciences! What to do if children have difficulty mastering this subject? What does this mean and how can I help my child?

We should not think that mathematical ability is an innate gift, the presence or absence of which we will have to come to terms with. Mathematical abilities, just like others, can and should be developed. Therefore, we can not only teach a preschooler the basics of reading, writing and counting, but also work on developing the so-called mathematical mindset.

What it is? Let's say, if a child counts, adds and subtracts well, can we conclude that we have a future mathematician? In fact, computational ability is just one facet of the world of mathematical science.

In the generally accepted sense, a mathematical mindset is a predisposition to study the exact sciences, a special view of the world in which there is always a place for formulas, diagrams and tables. In addition, a mathematical mindset implies well-developed spatial, abstract and logical thinking. This is what you and I can work on. With the help of various didactic games, we can develop important components of logical thinking in a preschooler.

How to teach a child to compare. Comparison is expressed in the ability to see the same in the different and the different in the same. You can compare using different parameters and criteria. For example:

• What is the difference between a round table and a square one? (form)
• What is the difference between a wooden door and an iron one? (material)

You can compare objects by color, shape, size, quantity, accessory, function, etc.

Ability to generalize very useful in math lessons at school. Many problems are based on generalization. A preschool child already uses the concepts “square”, “circle”, “triangle” and even “trapezoid” in his speech, but few children are able to name all these concepts in one word. We teach the child to generalize concepts:

• Beets, cabbage, carrots are vegetables.
• Jacket, sweater, trousers - clothes.
• Doctor, teacher, builder - professions.
• Cup, plate, pan - utensils.

You can also play the game in reverse (“limit” the concept, select examples):

• Trees: .... (birch, poplar...)
• Seasons: ....
• Cutlery: ....

Analysis and synthesis. These basic mental operations are present in all areas of human activity. When analyzing, the child mentally divides an object or object into its components: a plant - into roots, stems, leaves and fruits; rainbow - 7 colors; fairy tale - into individual plot twists. Synthesis is an operation, inverse of analysis. Preschoolers can guess a hidden object based on its signs, form words from letters, and sentences from words. All kinds of puzzles, including homemade ones (when we cut a picture or a geometric figure and then assemble or glue it), also help to train these skills.

More high level generalization allows the child to master the classification of objects, objects and their properties. Classification- this is the assignment of an object to a group based on species-generic characteristics. To train this mental operation, you can do the following exercises:

• We divide all animals into wild and domestic; figures - “with and without corners”.
• We remove the unnecessary things in the row: apple, pear, ball (the child must explain what is unnecessary and summarize the remaining group of objects).
• We complicate the task: apple, pear, tomato.

There are often cases when in such tasks children give incorrect answers at first glance, but if the child can justify his choice (say, he highlighted the odd one by color), then his option is worth counting.

Using the above methods, we also develop the preschooler’s speech, gradually helping him master verbal and logical thinking. For a young mathematician, the ability to correlate, reason and draw conclusions is a very useful thing.

All kinds logic puzzles, riddles, puzzles and puzzles- all this is very interesting for preschool children and trains logical thinking well. IN logical problem There is always some “catch”, and the child, knowing this, concentrates his attention and is motivated to make a decision, to find the final result. Here are some examples of such problems:

• Masha and Tanya were drawing. One girl drew a house, another a tree. What did Masha draw if Tanya didn’t draw the house?
• Two boys were planting trees, and one was planting a bush. What did Anton plant if Leonid and Anton and Maxim and Anton planted different plants?
• Ira is 5 cm shorter than Katya. Katya is 8 cm taller than Lisa. Who is tallest?

Of course, this kind of developmental activities should not be one-time, but regular. You can entrust the development of mathematical abilities to a specialist by choosing a proven educational center, or you can work with your child yourself. Thus, by training logical thinking, we can prepare a good foundation for the child’s successful mastery of the school curriculum and understanding of mathematics.

Elena Razukhina educational psychologist at the Aristotle educational center

Discussion

Nowadays there are a lot of all kinds of manuals that help teachers and parents arouse a child’s interest in logical thinking, systematization, analysis and mathematics. I started working with both children at about 4 years old. I found appropriate notebooks and activities according to age. The most beloved Peterson, Sycheva, notebooks ed. Dragonfly and the Sunny steps series. Of course, classes are a goal system; the more understandable you make the classes for your child, the greater results you will achieve. For example, we sculpted them with hardening mass for modeling numbers and signs with the children, decorated them, and then “played” with them. They made their “money” and then played balls for completed tasks and good deeds. We started a “shop” with sweets and toys. With this “money” the children then went to this store and bought all sorts of things for themselves. The effect was with different sides: children learned to achieve something systematically, they learned to count, they learned to make choices, etc. Visualization and playful presentation are very important for children, but the latter should not be overdone, as it seems to me. Because no one will play with them at school much, and if your child is accustomed to the fact that an activity is only a game, then later this may disappoint the child when there is no game, but he will have to study and work. Therefore, everything is needed in moderation. Give examples in a language that the child can understand, for example, if a child is interested in Bakugan, then count the Bakugan, if these are Mostrey High dolls, then come up with problems from the series: there were 8 dolls at the party, then 3 girlfriends left, how many are left, etc.
Both of my children, in addition to the fact that they now know and adore mathematics, do many Olympiads with ease, are now also included in the rating system of the best students in Russia. I hope everything works out for you too! :-)

useful article. I regularly study at home with my kids. When children become interested, you won’t be able to tear them away from their studies. The most important thing is not to force it, otherwise it won’t do any good.

Thank you, interesting article, I’ll try to use the tips.

On the contrary, it always seemed to me that exactly what is inherent and can be developed

Comment on the article "Development of mathematical abilities in a preschooler: 5 ways"

At this age, the child’s interest and general abilities are important. The level of tasks is such that a capable child can solve them without preparation. Plus music, sports and dancing. This is very important and also develops mathematical abilities.

Discussion

We cook at home, ourselves)) starting at the yard school

I’m surprised by the desire to get a child involved in mathematics as early as possible... and in general the idea that “serious mathematics” is possible from the age of 6-7... Free will, of course, but, in my opinion, this is some kind of global delusion, before all because the child is simply not able to perceive and operate with abstractions...
Specifically, my child became interested in mathematics in the 7th grade, in the 8th grade she went to a club at MCSME, in the 9th grade she entered 179, and then to the Faculty of Mechanics and Mathematics at Moscow State University. Back in the fifth or sixth grade, nothing predicted that she would become a mathematician; I remember very well how annoyed I was that she was confused in simple fractions... The school teacher has not changed since the 5th grade, so this is not her merit, it’s just that the child’s brain has matured to a different level of understanding, and it became interesting.

Developing mathematical abilities in a preschooler: 5 ways. The other day I was sorting out another stack of books to prepare for school, and made a list of textbooks that I recommend buying to prepare your child for school. How to develop a child before school.

Developing mathematical abilities in a preschooler: 5 ways. The other day I was sorting out another stack of books to prepare for school, and made a list of textbooks on How to develop a child before school. And you could write a treatise on preparing for school, there’s so much there.

Discussion

1. See how he solves routine problems: does he see beautiful solutions right away or do them head-on, is there any desire to look for good solutions or solutions at all.
2. See how the “olympiad” problem is solved: what is the percentage solved, the solution path, is there a desire (not in the sense of solving olympiad problems for hours - this rarely happens, probably, but in the sense of finishing what you started, finding a solution).
3. If he participates in olympiads, see what the result is, if at the next one school stage can show something without preparation, there is a reason to talk about abilities.
4. Well, see how things are going abstract thinking, analysis and synthesis, this is also visible in high school.
Guided by my own criteria, I have come to the conclusion that my youngest child I don’t have any decent mathematical abilities, but my education allows me to really appreciate it.

Ehh.. with the ability to do mathematics everything is not easy, we got a little burned out on this.. (a month or so ago there was my heartbreaking post about school 57).

What I would do:
1. You can count on anything, but life makes adjustments.
2. Mathematics is a useful thing in any way, even if it does not become a specialty. It puts your brain in order, yes.
3. Interest is more important than ability. Because they give motivation to study at a difficult age. But I didn’t rely only on mathematics, this is not a specialty.

From my point of view, “learning strategy” can be of 2 types.
A. The child passionately wants to learn something specific (mathematics, physics, biology, even classical philology). Perhaps it makes sense to get a fundamental education (Moscow State University is close to that). But. But. Then you will have to complete your studies - either a second education (at whose expense?) or go to work in fact not in your specialty. We don't take geniuses into account.
B. There is a readiness and even a certain interest in some kind of specialty - just so that there is a piece of bread, not sitting on the parents’ necks, and in the future feeding the family. Then education is based on this specialty - well, so that it is not completely disgusting to study this (but this is about studying at a university). Well, it was possible to get minimal training for the Unified State Exam (and sometimes this is nonsense - why does a doctor or psychologist need mathematics??? - only a few people study medical statistics, and even there there is not much to learn).

It seems to me that option “B” is more reasonable, especially taking into account your large number of children. True, I followed option “A” - but then everything changed so quickly that “B” was difficult to implement.

If “B”, then it is NOT SO IMPORTANT whether you have an aptitude for mathematics or not. One thing is important - to understand certain mathematical methods in order to use them meaningfully. They are their own for an engineer, their own for an economist, and third for someone else.
This is the most important thing - DOES the child UNDERSTAND the basic methods he uses?

For example, can one derive the formula for the same roots quadratic equation yourself, without looking at the book? Or prove the Pythagorean theorem? Print the sum of an arithmetic and geometric progression? I deliberately take something relatively simple, maybe a little more complicated. But it is obligatory that he taught a year ago or earlier, so he no longer remembers the evidence.

If not, then it’s worth considering how practical mathematics is used in what your son will do. Less important, but also something to consider, is how much there is in the university curriculum.

Well, about choosing a school. It’s good when mathematics is higher than the school curriculum, but the super-duper physics lyceum is not very good IMHO a good option. But this is ours personal experience, everyone has their own, there are good options.

Mathematical abilities are also abilities; you either have them or you don’t. They usually appear very early or just early, as if the pregnancy was normal and childbirth is also there, if the child is healthy, then it can be developed. A normal teacher is needed.

Discussion

I read an interview with Sergei Rukshin, the head of the St. Petersburg math circle from which the notorious Perelman and Stanislav Smirnov, a Fields Medal winner, came out. He writes that absolutely anyone can be taught, regardless of gender or ability. But he emphasizes that mathematics is a way of life, it requires full dedication.

Are there math genes? Education, development. Child from 7 to 10. Are there math genes? Yesterday I talked to my dad. In my opinion, the child is still too young for anything to be said about his abilities.

Discussion

I doubt something about genes :) we have at least two generations of “mathematicians”, i.e. those who love and understand and she has never caused problems, but our son knows who he is: (somehow it seems to me that at his age mathematics was much easier, maybe, of course, the program was simpler..

I suspect that the atmosphere in the family has a much greater influence. And parents who love mathematics have been throwing out problems wherever they can since childhood. And those who are gifted in literature learn to speak beautifully. Exactly the same thing in between. And the musicians sing.

It seems to me that 90% of a child’s abilities are determined by genes, but such qualities as perseverance, character and perseverance are determined only by upbringing. Dear parents and psychologists, please express your opinions on how to develop these qualities in children?

Discussion

Real, meaningful things for the child. Yesterday my daughter spent two hours drawing an illustration for a book. She loves to draw, hence the “meaningfulness” - but what is needed for the job is “perseverance” and the list goes on :-)

My opinion is exactly the opposite of yours, but I won’t give the exact percentages. Abilities depend much more on how the child spent his early (very early) childhood, i.e. from environment. And perseverance, perseverance and character are more genes. This is more determined by the functioning of the nervous system.

At the Olympiads they are looking for children with developed abilities - children with whom they were involved in development, this was not necessarily true, well, I don’t agree at all about “fading”, mathematical abilities do not disappear anywhere... maybe they don’t become mathematicians (mathematics...

Discussion

I would like to apologize to Sephia for the fact that with my message I diverted the discussion on the proposed topic a little.
It’s simple, everything is so interconnected (primary school -> specific program -> level of teaching -> teacher’s obsession ->
student interest - > result (grade, desire to learn beyond the program).
Mathematics is difficult and very interesting science, and therefore there is something to talk about. Topics cling one after another :-))
“I can’t understand – is this a problem with the school (they don’t teach you to think?), the program (weak?), the child (not capable?), or mine (am I doing it wrong?) Or do I want too much?”
Sephia did not write what program her daughter is studying in, but this program may at the same time be sufficient for other “weaker” classmates, and be a definite inhibitor for her “advanced” girl. And the fact that some teachers replace the ability to think with templates and memorization - this, unfortunately, is the case:-(
This conf is read (some write) very much interesting people. If they do this, then EVERYONE is definitely puzzled by the good
raising their children and the desire to provide a quality education. Otherwise they wouldn't come here.
So let's try to help our children and ourselves. Whoever can do what.
Who will bring interesting problems, who will share a non-standard solution to the problem. Whoever can. Perhaps we will cope with the problems of our education.

I also wanted to write about a “mathematical” topic, but I still don’t have enough time. My daughter is in 2nd grade. In mathematics a solid A,
There are simply no other assessments. They study according to Morro and Uzorova (30,000 tasks for oral calculation). But it seems to me that this is not enough.
Out of 28 people, only three are excellent students. In 1st grade, at the beginning of the year, the teacher suggested that parents take a course on Heidman in addition to the main course. There were immediately mothers who were categorically against it, citing their heavy workload.
children in English language (special school). That's where we stopped. Me and two other mothers bought a textbook on our own and studied on our own.
At the beginning of the 3rd quarter, my daughter was told that on the weekend she and her classmate would go to the district Olympiad in mathematics.
She comes home on Friday (the eve of the Olympiad) and says that in class they did work, based on the results of which they will select children for the next Olympiad. He says that no one in the class solved one problem. Here is her condition:
There were 15 birds sitting on two bushes. When 2 birds flew from the 1st to the second, and 3 birds flew away from the second, the second bush became 4
There are more birds than in the first one.
How many birds were there on each bush at the beginning?
Let me make a reservation right away that they have not yet gone through multiplication and division. On summer holidays after 1st grade they were asked to start
learn the multiplication table.
I was surprised by this task, because... in my opinion, it did not correspond to the program they were studying.
But my daughter was interested in how this problem was solved. I told her how to solve it first in one way (15-3=12, 12:2=6, 12 -4= 8,
8:2=4, 4+2=6, 15-6=9), and then she told me how to designate the unknown through X. We solved this problem, and then came up with
a couple more like this. We studied for an hour. My daughter understood everything and liked it.
The next day, after the Olympics, she comes out happy and says that one problem was similar, and she immediately beat it
decided.
So I had a question: is it possible to identify gifted children at the Olympiad in this way?
IMHO, no. This example suggests that certain programs are simply lagging behind. I didn’t tell my daughter the day before about the solution -
and she couldn't. By the way, she then took 3rd place.
It’s a pity that I still can’t get the conditions for all the problems from the Olympiad. I'm very interested in seeing the rest.

Child from 3 to 7. Education, nutrition, daily routine, visits kindergarten and relationships with teachers, illnesses and I would like not to miss out, if anything... And please share who has any successes (in general, not just mathematical ones) at 3 years old...

Discussion

Girls Olya, Irina, Murzya, Gazelle, sorry, but you are not entirely right when you say, “counts to 10, 20,” etc. The child does not count, but names numbers from 1 to 10, 20, etc. Irina correctly said that such “counting” is mechanical and not meaningful.
There is a certain number - 5 fingers, there are the numerals "one", "two".. And there are also symbols - the numbers 1 2 3 4 5... When the child masters all three concepts and combines them into something whole, for example, name "three", show 3 objects or imagine 3 objects in your mind, and then also math. performs the action, then, in my opinion, we can talk about what the child believes.
Olya Your son is a great guy, because... really counts (“you have an apple, they gave you another”), and besides, he moved from the concrete - counting objects, to the abstract - imagining a certain number and adding it up in his mind.

P.S. My son is exactly 4. He started talking early and at the age of 2 he “counted” to 15. For his birthday (2 years old) he was given a toy - a house, the roof is divided into 6 sectors with a hole in the shape of some animal, there are 6 in the walls of the house doors of different colors with holes in the form of geometric contours. items + animal inserts, geom inserts. bodies. Sasha immediately remembered the new colors - pink, orange.
After I called each one a geom a couple of times. body and hole, two-year-old Sasha remembered a square, cube, circle, ball, prism, triangle, oval. I realized that a child absorbs like a sponge everything he sees and touches. This knowledge just needs to be systematized in your head. It's the same with the score.

Nastya is 2 and 9. She counts up to 20, but can’t go further (she asks what 30, 40, etc. is called, i.e. she asks what 30 is called, and then counts 31, 32...). In the mind he adds and subtracts only up to 5, if more, then on the fingers (if it’s a plus, then count all the fingers, apples, etc. together, and if it’s a minus, then the part needs to be closed :-))). She really likes arithmetic, but it seems to me that this is more training than a manifestation of mathematical abilities...
He has known geometric figures (both flat and three-dimensional) for a very long time, but again more due to the fact that they played a lot with Montessori frames and Nikitin Kradrats, building from various three-dimensional figures.