Development of a child's mathematical abilities. How to develop mathematical abilities in a preschooler

Parents who want to teach their child mathematics are faced with the question of what exactly needs to be taught to the child. What abilities can and should be developed in preschool age to ensure successful completion of the school curriculum.

What abilities are considered mathematical in children under 7 years of age?

You should not think that mathematical abilities only mean the ability to count quickly and accurately. It's a delusion. Mathematical abilities include a whole range of skills aimed at creativity, logic, and counting.

The speed of counting and the ability to memorize a large array of numbers and data are not genuine mathematical abilities, since even a slow and thorough child who studies thoughtfully can successfully comprehend mathematics.

Mathematical abilities include:

Ability to generalize mathematical material.
The ability to see what different objects have in common.
The ability to find the main thing in a large amount of different information and exclude what is not necessary.
Use numbers and signs.
Logical thinking.
The child's ability to think in abstract structures. The ability to distract yourself from the task at hand and see the resulting picture as a whole.
Think both forward and backward.
The ability to think independently without using templates.
Developed mathematical memory. Ability to use acquired knowledge in various situations.
Spatial thinking – confident use of the concepts of “up”, “down”, “right” and “left”.

How are mathematical abilities formed?

All abilities, including mathematical ones, are not a predetermined skill. They are formed and developed through training and reinforced by practice. Therefore, it is important not only to develop this or that ability, but also to improve it through practical exercises, leading to automation.

Any ability goes through several stages in its development:

Cognition. The child gets acquainted with the subject and learns the necessary material;
Application. Applies new knowledge in independent play;
Consolidation. Returns to classes and repeats what was previously learned;
Application. Using fixed material when playing independently;
Extension. There is an expansion of knowledge about the subject or ability;
Application. The child supplements independent play with new knowledge;
Adaptation. Knowledge is transferred from the game situation to life.

Any new knowledge must go through the application stage several times. Give your child the opportunity to use the received data in independent play. Children need some time to comprehend and consolidate every minor change in knowledge.

If a child cannot master the acquired skill or knowledge through independent play, there is a high probability that it will not be consolidated. Therefore, after each lesson, let your baby go out to play or take a break and play with him. During the game, show how to use new knowledge.

How to develop mathematical abilities in a child

You need to start mathematical development in the form of a game and use things that will interest your baby. For example, toys and household items that he encounters every day.

From the moment the child shows interest in a particular object, the parent begins to show the child that the object can not only be examined and touched, but also performed various actions with it. By focusing on some features of an object (color, shape), in an unobtrusive manner, you can show the difference in the number of objects and introduce the first concepts of plurality and spatial position.

After the child learns to separate objects into groups, you can show that they can be counted and sorted. Pay attention to geometric features.

Development mathematical abilities should go along with the basics of number operations.

Any new knowledge must be presented with obvious interest child to learning. If there is no interest in the subject and its study, the child should not be taught. It is important to maintain a balance in your child's learning to develop a love for mathematics. Almost all problems associated with studying the foundations of this discipline have their origin in the initial lack of desire to know.

What to do if your child is not interested

If your child gets bored every time you try to teach him the basics of mathematics, then you need to:

Change the form of presentation of the material. Most likely, your explanations are too complex for a child to understand and do not contain game elements. Children preschool age cannot perceive information in classic look lesson, they need to show and tell new material during a game or entertainment. Dry text is not perceived by a child. Use it in teaching or try to involve the child directly in teaching;
Show interest in the subject without your child's participation. Children younger age are interested in everything that interests their parents. They love to imitate and copy adults. If the child does not show interest in any activity, then try to start playing with the selected objects in front of the child. Talk out loud about what you are doing. Show your own interest in the game process. The child will see your interest and join;
If the child still quickly loses interest in the subject, you need to check whether the knowledge and skills that you want to instill in him are too difficult or easy;
Remember the duration of classes for of different ages. If a child under 4 years old loses interest in a subject after 5 minutes, then this is normal. Since at this age it is difficult for him to concentrate on one subject for a long time.
Try introducing one element at a time into your lesson. For children 5-7 years old, the duration of classes should not exceed 30 minutes.
Don't be upset if your child doesn't want to study on a particular day. You need to try to involve him in training after some time.

The main thing to remember:

The material must be adapted to the age of the child;
The parent must show interest in the child’s material and results;
The child must be ready for class.

How to develop mathematical thinking

The order of teaching a child mathematical thinking consists of interconnected activities that are presented in order of increasing complexity of the material.

1. You need to start learning with concepts about the spatial arrangement of objects

The child must understand where right is left. What is “above”, “below”, “before” and “behind”. Having this skill allows you to perceive all subsequent activities easier. Orientation in space is fundamental knowledge not only for the development of mathematical abilities, but also for teaching a child to read and write.

You can offer your child the following game. Take a few of his favorite toys and place them at different distances in front of him. Ask him to show which toy is closer, which is further, which is to the left, etc. If you have any difficulty choosing, please tell me the correct answer. Use in this game various options words that determine the location of objects relative to the baby.

Use this approach to learning and repetition not only in class, but also in everyday life. For example, ask your child to determine the spatial arrangement of objects on the playground. More often in ordinary life ask to give something, orienting the baby in space.

In parallel with spatial thinking, they teach generalization and classification of objects according to their external signs and functional accessories.

2. Explore the concept of set of objects

The child must distinguish between the concepts many - few, one - many, more - less and equally. Offer different types of toys in different quantities. Offer to count them and say how many or few there are, which toys are fewer and vice versa, also show the equality of toys.

A good game to reinforce the concept of set is “What’s in the Box.” The child is offered two boxes or drawers containing different numbers of items. By moving objects between boxes, the child is asked to make the number of objects more or less, to equalize. Under the age of 3 years, the number of objects should not be large so that the child can clearly assess the difference in objects without counting.

3. It is important to teach a child simple geometric shapes in early childhood.

Teach your child to see them in the world around them. It is good to use applications from mathematical shapes to develop knowledge of geometric shapes. Show your child a drawing of an object with clear contours (house, car). Offer to make an image of an object from prepared triangles, squares and circles.

Show and explain what the angle of the figures is, invite the child to guess why the “triangle” has such a name. Offer your child to familiarize himself with figures with a large number of angles.

Consolidate geometric knowledge through drawing the studied material, folding different figures from other objects (sticks, pebbles, etc.). You can use plasticine and other materials to create different shapes.

Ask them to draw a series of shapes different types, count them with your child. Ask which figures are many and which are few.

When walking with your child, pay attention to the shape of houses, benches, cars, etc. Show how to combine various figures can create new and familiar objects among themselves.

4. The ability to navigate in space and classify objects allows you to teach measuring the size of an object

Early learning to measure length with a ruler and using centimeters is not recommended, as this will be difficult to understand material. Try measuring objects with your child using sticks, ribbons and other materials at hand. This training does not involve the measurement itself, but the principle of its implementation.

Most teachers advise teaching your child to measure using counting sticks. They justify this by convenience for the child and teaching him to use special material. These sticks will come in handy when learning units of counting. They can also be used as visual material when working with books (putting a stick aside according to the number of characters), studying geometric shapes (a child can lay out the desired shape with chopsticks), etc.

5. Quantitative measurements

After learning basic math concepts, you can move on to quantitative measurements and studying numbers. The study of numbers and their written notation occurs with early age according to a certain system.

6. Addition and subtraction

Only after mastering quantitative measurements and numbers should you introduce addition and subtraction. Addition and subtraction are introduced at the age of 5-6 years and are the simplest one-step operations with small numbers.

7. Division

Division in preschool age is introduced only at the level of shares, when the child is asked to divide an object into equal shares. The number of such parts should not exceed four.

Examples of activities with a child to develop mathematical abilities

To solve this problem you do not need any refined ways, you just need to make some additions to your regular life.

When walking outside, invite your child to count any items or objects (tiles, cars, trees). Point to many objects, ask to find a generalizing feature;
Encourage your child to solve problems to find the correct answer by guiding him. For example, Masha has 3 apples, and Katya has 5, Lena has one more apple than Masha and one less than Katya. The problem can be simplified by asking what number is between 1 and 3;
Clearly explain to your child what addition and subtraction are. Do this on apples, toys or any other objects. Let your child touch objects and show these simple operations by adding or subtracting an object;
Ask your child what the differences between objects are;
Show what scales are and how they work. Explain that weight can not only be felt by holding an object in your hands, but can also be measured in numbers;
Teach how to use a clock with hands;
Please pay attention Special attention spatial arrangement of objects;
You can study shapes not only on cards, but also look for them in objects around;
Show your child that mathematics is in everything around him, if you just look closely.

What additional materials will help teach your child mathematics?

Cards and pictures with different numbers of objects, with numbers and mathematical symbols, geometric figures;
Magnetic or chalk board;
Clock with hand and scales;
Counting sticks;
Construction sets and puzzles;
Checkers and chess;
Lotto and dominoes;
Books that contain counting and allow you to carry out mathematical operations;
Methodological aids for the development of logic and other abilities according to the child’s age.

Tips for parents who want to teach their child the basics of mathematics

1. Encourage your child to find answers. Help him find them by reasoning. Don't scold for mistakes or laugh at incorrect answers. Each child’s attempt to draw a conclusion or solve a problem trains his abilities and allows him to consolidate knowledge;

2. Use your time joint games to develop the necessary skills. Focus on what has been studied previously, show how new and already learned material can be used in practice. Create situations in which the child will need to use knowledge to achieve a certain result;

3. Do not overload your child with a large amount of new information. Give him time to comprehend the acquired knowledge through free play;

4. Combine the development of mathematical abilities with spiritual and physical development. Introduce counting into physical education classes and logic into reading, and role-playing games. Diversified development of the child - the path to the full development of the baby. A physically and spiritually developed child comprehends mathematics much easier;

5. When teaching a child, try to use all channels of information absorption. Except oral history, show it on various objects, give the opportunity to touch and evaluate the weight and texture. Use a variety of forms of presenting information. Show how you can use the acquired knowledge in life;

6. Any material should be in the form of a game that will interest the child. Excitement and involvement in the process are good for remembering. If your child is not interested in the material, stop. Think about what was done wrong and correct it. Each child is individual. Find a method that suits your baby and use it;

7. The ability to concentrate on a task and remember the conditions is important for the successful development of mathematical fundamentals. Ask a question about what the child understood from the given task after each condition. Work to improve concentration;

8. Before asking your child to decide on his own, show an example of how to reason and decide. Even if the child has carried out a certain calculation operation more than once, remind him of the procedure. It is better to show the correct course of action than to allow the child to reinforce the wrong approach;

9. Don't force your child to study if he doesn't want to. If the baby wants to play, then give him this opportunity. Offer to study after some time;

10. Try to diversify knowledge in one lesson. The best option it will be if during the day you pay a little attention to a variety of areas of mathematical knowledge than if you memorize the same type of material, bringing it to automatism;

11. The task of a parent in preschool age is not to teach counting and calculations, but to develop abilities. If you don’t teach your child to add and subtract before school, that’s okay. If a child has mathematical thinking and knows how to draw conclusions, then he will be able to comprehend any complex operations quickly and at school.

What books help develop mathematical abilities?

The solution to the issue of teaching mathematics to a child under 7 years old with the help of books begins from an early age. For example, the fairy tale “Teremok”. In it, the appearance of various characters occurs as they increase in size. Using this example, you can teach your child the concepts of big and small. Try playing this fairy tale in a paper theater. Invite your child to arrange the figures of the fairy tale characters in in the right order and tell a story. The fairy tale “Turnip” also teaches the child the concepts of more and less, but its plot develops from the opposite (from large to small).

It will be useful from a mathematical point of view to study the fairy tale “The Three Bears” through the concepts of large, medium and small; the child can easily master counting to three.

When choosing books to read to your child, pay attention to the following:

The presence of an account in the book and the possibility of comparing heroes according to certain criteria;
The images in the book should be large and interesting. Using them you can show your child what geometric figures used to create different objects (a house - a triangle and a square, a hero's head - a circle, etc.);
Any plot should develop linearly and contain certain conclusions at the end. Avoid books with complex plots that do not develop linearly. Teach your child that any action has its consequences and how to draw conclusions. This approach will make it easier to understand the principles logical thinking;
Books should be selected according to age.

Available for sale a large number of various publications that allow you to familiarize yourself with most mathematical operations and terms using the examples of heroes. The main thing is to discuss the material read with your child and ask leading questions that will stimulate the development of mathematical abilities.

Buy methodological books for the development of mathematical abilities in a child according to his age. Now there are a large number of different materials that contain tasks for the development of a child’s mathematical abilities. Bring such publications into the game. Remind your child of the tasks he previously completed using this publication to solve new problems.

Developing a child's mathematical abilities is not a difficult task. A child under 7 years of age seeks new knowledge on his own and is glad when it is presented to him in game form. Find a lesson option that suits your child and have fun learning math basics.

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. At the right approach you can achieve good results in the development of his intellect, and therefore his mathematical abilities.

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

formation of elementary mathematical concepts in preschoolers;
development of their logical thinking;
usage modern means and teaching 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;

learn what a number is;
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 representations 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 primary 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 given characteristic. 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 creative task. 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;
ordinary 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.

Encourage your child's curiosity.
Look for answers to his questions together. Reason with him.
Don't complain about lack of time. Talk and play while walking together, before bedtime.
Great importance have trusting relationship between an adult and a preschooler. Never laugh at your child's mistakes.
Do not overload your baby with activities. This will harm his health and discourage him from learning.
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.

It’s not for nothing that mathematics is called the queen of all sciences; Mikhail Lomonosov said that it puts the mind in order, and this is true. Mathematical thinking must be developed in childhood, paying due attention to this issue. Wherein optimal age To begin exercises to develop mathematical thinking, 1-3 years can be considered. Later, in preschool age, it is convenient to work with an already formed base of mathematical thinking, developing it to the level required at school.

Many adults find mathematics boring. Basically, it is not their fault, but the parents who did not pay the necessary attention when learning, referring to textbooks. Those children whose parents developed their child’s mathematical abilities through interesting puzzles and clear examples generally have positive results.
So, main advice– turn the learning and development of your child’s mathematical thinking into an interesting process. Use not abstract concepts, but what is closer to the child - toys, natural and everyday phenomena, colors. In addition, calculating simple mathematical expressions in your head is a great help in life, demonstrate to your child illustrative examples this. Use money to have your child calculate how much he needs to make a certain purchase (for example, candy).
Training any component of a person’s thinking is a continuous process. The more and more regularly the brain is trained, the more amazing and obvious the result is. It is a misconception that all people are divided into humanists and mathematicians. In fact, successful man can understand these areas of science equally well.
Organize interesting and varied leisure activities. Use visuals educational materials– posters, counting rhymes, puzzles. Solutions to problems can be written not only in a notebook, but also on the board for greater clarity.
To educational process was not tedious, choose modern online simulators that allow you to develop mathematical thinking in a new and interesting form. In our catalog of BrainApp games you will find many interesting mathematical exercises.

Be sure to alternate mental activity with physical activity. The brain needs nourishment, not only intellectually, but also physically. It is very important for children to devote at least a couple of hours a day active games(optimally - in the fresh air). It is important not to overexert the child, but to allow him to develop systematically, in a convenient and individual way.
Latest Research talk about importance proper nutrition for brain function and development of mathematical thinking. It is important for a child to receive daily required amount protein, calcium, vitamins.
So, when developing mathematical thinking, regularity of classes, variety and interesting approaches are very important. You will find all this on our service, where you can develop your mathematical abilities in a convenient form by watching your daily progress.

To explain where the ability for mathematical operations developed in humans, experts suggested two hypotheses. One of them was that aptitude for mathematics is side effect the emergence of language and speech. Another suggested that the reason was the ability to use an intuitive understanding of space and time, which has much more ancient evolutionary origins.

In order to answer the question of which hypothesis is correct, psychologists posed experiment involving 15 professional mathematicians and 15 ordinary people with an equal level of education. Each group was presented with complex mathematical and non-mathematical statements that had to be judged as true, false, or meaningless. During the experiment, the participants' brains were scanned using functional tomography.

The results of the study showed that statements that related to calculus, algebra, geometry and topology activated areas in the parietal, inferotemporal and prefrontal cortices of the brain in mathematicians, but not in the control group. These zones were different from those that were excited in all participants in the experiment during ordinary statements. “Mathematical” areas were activated in ordinary people only if the subjects were asked to perform simple arithmetic operations.

Scientists explain the result by the fact that mathematical thinking high level involves a neural network that is responsible for the perception of numbers, space and time and is different from the network associated with language. According to experts, based on the study, you can predict whether a child will develop math skills if you assess him spatial thinking skills.

Thus, to become a mathematician you need to develop spatial thinking.

What is spatial thinking?

To solve a huge number of problems that our civilization poses to us, we need a special type of mental activity - spatial thinking. The term spatial imagination refers to the human ability to clearly imagine three-dimensional objects in detail and color.

With the help of spatial thinking, you can manipulate spatial structures - real or imaginary, analyze spatial properties and relationships, transform original structures and create new ones. In the psychology of perception, it has long been known that initially only a few percent of the population possesses the rudiments of spatial thinking.

Spatial thinking is a specific type of mental activity that takes place in solving problems that require orientation in practical and theoretical space (both visible and imaginary). In its most developed forms, this is thinking with patterns in which spatial properties and relationships are recorded.

How to develop spatial thinking

Exercises to develop spatial thinking are very useful at any age. At first, many people have difficulty completing them, but over time they gain the ability to solve increasingly complex problems. Such exercises ensure normal functioning of the brain and help avoid many diseases caused by insufficient functioning of neurons in the cerebral cortex.

Children with developed spatial thinking often succeed not only in geometry, drawing, chemistry and physics, but also in literature! Spatial thinking allows you to create entire dynamic pictures in your head, a kind of movie, based on a read passage of text. This ability greatly facilitates the analysis of fiction and makes the reading process much more interesting. And, of course, spatial thinking is indispensable in drawing and labor lessons.

With developed spatial thinking it becomes much more It is easier to read drawings and maps, determine locations and visualize the route to the goal. This is a must-have for orienteering enthusiasts, and will greatly help everyone else in everyday life in the city.

Spatial thinking develops from early childhood, when the child begins to make his first movements. Its formation goes through several stages and ends approximately in adolescence. However, during life, its further development and transformation is possible. You can check the level of development of spatial thinking using a small interactive test.

There are three types of such operations:

Changing the spatial position of the image. A person can mentally move an object without any change in its appearance. For example, moving according to a map, mentally rearranging objects in a room, redrawing, etc.
Changing the image structure. A person can mentally change an object in some way, but at the same time it remains motionless. For example, mentally adding one shape to another and combining them, imagining what an object will look like if you add a detail to it, etc.
Simultaneous change in both the position and structure of the image. A person is able to simultaneously imagine changes in the appearance and spatial position of an object. For example, mental rotation of a three-dimensional figure with different sides, an idea of how such a figure will look from one side or the other, etc.

The third type is the most advanced and provides more opportunities. However, to achieve it, you must first master the first two types of surgery well. The exercises and tips presented below will be aimed at developing spatial thinking in general and all three types of actions.

3D puzzles and origami

Folding three-dimensional puzzles and paper figures allows you to form images of various objects in your head. After all, before starting work, you should present the finished figure in order to determine the quality and order of actions. Folding can take place in several stages:

Repeating actions after someone
Work according to instructions
Folding a figure with partial support according to the instructions
Independent work without relying on the material (can be carried out not immediately, but after several repetitions of the previous stages)

It is important that the student clearly traces each action and remembers it. Instead of puzzles, you can also use a regular construction set.

Divided into two types:

Using visual material. To do this, you need to have several blanks of various volumetric geometric shapes: cone, cylinder, cube, pyramid, etc. Task: study the shapes; find out what they look like from different angles; put shapes on top of each other and see what happens, etc.
Without the use of visual material. If the student is well acquainted with various three-dimensional geometric shapes and has a good idea of what they look like, then the tasks are transferred to the mental plane. Task: describe what this or that figure looks like; name each side of it; imagine what will happen when one figure is superimposed on another; say what action needs to be performed with a figure in order to turn it into another (for example, how to turn a parallelepiped into a cube), etc.

Redrawing (copying)

Tasks of this type proceed in increasing complexity:

Simple re-drawing of a figure. The student has a model/sample of a figure in front of him, which he needs to transfer onto paper without changes (dimensions and appearance must match). Each side of the figure is drawn separately.
Copying with addition. Task: redraw the figure without changes and add to it: 5 cm in length, an additional edge, another figure, etc.
Scalable redrawing. Task: copy a shape changing its size, i.e. draw 2 times larger than the model, 5 times smaller than the sample, decreasing each side by 3 cm, etc.
Copy from view. Task: present three-dimensional figure and draw it from different sides.

Representation

The representation objects will be segments and lines. Tasks can be very diverse, for example:

Imagine three differently directed segments, mentally connect them and draw the resulting figure.
Imagine that a triangle is superimposed on two segments. What happened?
Imagine two lines approaching each other. Where will they intersect?

Drawing up drawings and diagrams

They can be carried out based on visual material or based on represented objects. You can make drawings, diagrams and plans for any subject. For example, a plan of a room showing the location of each thing in it, a schematic image of a flower, a drawing of a building, etc.

Game "Guess by touch"

The child closes his eyes and receives some object that he can touch. The object must be of such dimensions that the student has the opportunity to study it in its entirety. A certain amount of time is allotted for this depending on the age of the student and the volume of the subject (15-90 seconds). After this time, the child must say what exactly it was and why he decided that way.

You can also use it in the game different types fabrics, similar-shaped fruits (apples, nectarines, oranges, peaches), non-standard geometric shapes and more.

Game "Fly in a Cage"

This game requires at least three people. Two directly participate in the game, and the third monitors its progress and checks the final answer.

Rules: two participants present a grid of 9 by 9 squares (graphics cannot be used!). There is a fly in the upper right corner. Taking turns making moves, players move the fly across the squares. You can use movement symbols (right, left, up, down) and the number of cells. For example, a fly moves three squares up. The third participant has graphic diagram hash marks and denotes each move (each movement of the fly). Next he says “Stop” and the other players must say where they think the fly is in this moment. The winner is the one who correctly named the square where the fly stopped (checked according to the diagram drawn up by the third participant).

The game can be made more complex by adding the number of cells in the grid or a parameter such as depth (making the grid three-dimensional).

Graphic exercises

They are performed by eye without the use of any auxiliary objects (ruler, pen, compass, etc.).

1. To what level should a person move so that a falling tree does not hit him?

2. Which of the figures will be able to pass between object A and object B?

Picture from the book by Postalovsky I.Z. “Imaginative thinking training”

3. Imagine that the ovals in the picture are cars. Which one will be at the intersection first if the speed of the cars is equal?

Picture from the book by Postalovsky I.Z. “Imaginative thinking training”

4. Restore the part of the figure that was covered by the ruler.

Picture from the book by Postalovsky I.Z. “Imaginative thinking training”

5. Determine where the ball will fall.

Picture from the book by Postalovsky I.Z. “Imaginative thinking training”

Mathematics is one of those disciplines that begins to be studied in the first grade. However, even before your child becomes a student, you should pay attention to developing his counting skills. In the future, this will allow the child to learn new material faster and better.

From this article you will learn how the development of a child’s mathematical abilities is carried out, and you will also find out what mathematics tasks for preschoolers you can use in practice.

Development of a child's mathematical abilities

Already at the age of 5-6 years, a child is able to absorb a large amount of new information, and you can begin to introduce him to numbers. While walking in the yard, invite your child to count the number of flowers or fallen leaves. Count bushes, trees, cars. Such activities can be combined with studying colors: let the baby find 5 objects of blue color, and you will look for 5 red objects, after which you will share your results with each other.

It is important that before you develop your preschooler's math skills, you are able to explain to him the difference between "one" and "many." This can be done by showing your child one car and several Vehicle. For example, you can use trees, balls, apples, pencils, etc.

Introduce your child to such concepts as “more-less”, “length-width”. For these purposes, you can use any available materials: leaves, cones, etc.

You can hang posters with numbers and multiplication tables around the apartment. By the way, before you start studying the latter, make sure that the baby understands the essence of addition and subtraction operations.

To introduce your child to positive and negative numbers, you can draw a house with 10 above-ground and 10 underground floors. Start counting from floor 0 and explain to your child what the difference is between the tiers that are above and below the ground.

Try to switch roles with your child: let him turn into a teacher, and you into a student. This way you can turn the learning process into a fun game. At the same time, you will find out how well the baby has learned what you told him about. Also, the child’s toys can act as “students”.

At the age of 6, you can teach your child to solve examples in a column - by this time, children are happy to solve such problems and are happy to be the first correct results.

Yes, you can expect your child to master all the necessary sciences at school. However, if it is possible to teach your child mathematics now, then why not do it?

How to develop math skills in a child?

The ability to analyze, synthesize, classify, generalize and evaluate - the development of mathematical abilities. The following exercises can be done with children:

Help your child see how math concepts are applied in practice. For example, ask him to count how many days are left before some interesting and significant event for them, for example, before a trip out of town. You may want to ask if there are enough napkins for everyone at the table. The cooking process also provides the opportunity for the practical application of mathematical knowledge (measuring raw materials using cups, teaspoons, etc.).

In order to develop your child's math skills, organize an impromptu store at home. Let your child decide what to sell, what prices to set, how to record purchases, etc.

Analysis

Offer children several tasks (puzzles) to classify geometric shapes by color and size.

Ask to draw (or indicate) a triangle figure, which should follow the following sequence: triangle - circle - square - triangle - circle - square - triangle - ...

Ask the children to line up the tin cans in order of height. Then fill these jars various materials and ask the children to put them in order of increasing weight.

Synthesis

Invite your child to invent a new geometric figure and give it a name.

Development of mathematical skills in a child. Tell your child that it is as if some robber has stolen all the watches in the city. How can you keep track of the passage of time until a new clock is installed in the city?

Grade

Ask the children which tool (ruler or standard) is better for measuring the following objects: an ant, your height, a log, your finger, a house, a car.

Is it better to measure the ingredients included in a chocolate cake: flour, water, salt, sugar, vanillin, cocoa - using measuring spoons or cups?

How to promote the development of mathematical abilities in a child?

Of all the school disciplines, it is mathematics that most often causes difficulties for children. If your child is not yet going to school, you can now think about how to promote the rapid development of your child’s mathematical abilities, and in this case, he will better perceive new information when he becomes a student.

How difficult is it to develop children's mathematical abilities at home, and what methods can be used for these purposes?

Even if the baby is not yet 1 year old, you can develop his fine motor skills. Many will be surprised and ask what connection is observed between hand motor skills and mathematics. In fact, scientists have found that the development fine motor skills contributes to the formation of logic and abstract thinking, and these qualities are known to be directly related to mathematics. So, let the child more often sort through cereals, toys, or simply hold fabric bags with sand, peas, and balls in his hands.

For those parents who do not know how to promote the development of mathematical abilities in a child, didactic materials are suitable. You can make them yourself or buy them in a store. Essentially, it is a set of various geometric shapes. You can lay out compositions from them, and then ask the child to determine which of the figures is extra.

You can also ask your child to divide the shapes into groups, sort them by color, etc.

Almost every home has a computer, and it can become your faithful assistant in teaching your child mathematical intricacies. For example, the popular game “Hidden Numbers” helps your child learn to recognize numbers and solve problems. There are other games of this type that teach the child to count and perform various operations with numbers. Training takes place in a playful way, which contributes to better memorization of the material.

Draw animals with your child more often, using simple geometric shapes. Such activities develop logic and spatial imagination.

You can even use the time allotted for a walk to study. Ask your child to find objects that resemble a circle, square, triangle, painted in a certain color, etc.

In fact, developing a child's mathematical abilities is not as difficult as it seems. Moreover, a creative approach will allow the child to better assimilate new knowledge and not get tired of the flow of information. Having become a student, your child will not experience difficulties in lessons and will begin to learn with pleasure!

How to stimulate math development in your child?

Mathematical abilities will be useful to a child not only at school, but also in adult life. That is why it is better to start working with your baby as early as possible. In this case, having become a student, he will not experience discomfort and stress when mastering new material, and will become good at counting and solving more complex problems.

Math assignments for preschoolers

How younger child, the easier it absorbs all new information. Interestingly, you don’t need to force your child to study for this - just hang up bright colorful posters in his room with the multiplication table, the rules of addition, subtraction, and division. Throughout the day, periodically draw your child's attention to the posters and ask him to say a number out loud, count how many toys are on the floor, and then use the multiplication table for these purposes. Creativity to compiling assignments will help you work with your baby without special problems.

Children love to play with household items: cups, spoons and even socks. Introduce ordinal numbers and counting to little ones using these toys to build a foundation for successful development math skills later.

How to stimulate your child’s mathematical development when you have absolutely no time for classes? No problem! Bring your child to the kitchen, give him spoons, plates, glasses and ask him to count them. While the baby is busy, you can calmly prepare dinner and at the same time pay attention to the baby.

In the kitchen, you can also introduce your child to measurements of volume and weight. Give your child a glass with the divisions marked and explain what they are for. You can also introduce your child to kitchen scales.

You can strengthen your counting skills by stringing beads or buttons on a thread. The development of fine motor skills directly affects the thinking process, which improves mathematical abilities.

Exercise with your baby even while walking. Ask him to find 5 objects of a certain color, collect 4 green objects, count the number of flowers in the flowerbed, etc. Children love to explore new things, and therefore they happily take part in such games. Try to ask your child about numbers unobtrusively. If you see that the baby just wants to play, do not refuse him this.

Try to study with your child regularly, and in this case he will study with pleasure already at school!