We develop spatial thinking. How to develop spatial thinking. Construction as a means of developing spatial thinking

Everyday life is filled with spatial designations and directions, symbols and signs, in which the child must navigate almost on a par with adults. Timely development of spatial thinking in preschoolers will help them become aware of themselves when surrounded by objects and develop the skills to correctly estimate distances, correlate sizes, and find landmarks.

What is meant by spatial thinking in preschool children?

Spatial thinking is the process of assimilation of the relationships of the surrounding reality, the use of visual models to reflect connections between objects and orientation in the surrounding space.

Spatial thinking develops most intensively in older adults preschool age, as a component.

The child masters not only thought processes, but also learns to be aware of himself and the place of objects in space.

The main ones in preschool children are the ability to:

Use coordination skills in space: determine your location relative to people or objects;
Assess the size and shape of an object;
Visually break the object into geometric figures(for example, a bear consists of balls and elongated sausages);
Draw a picture, taking into account the relative position of objects to each other;
Make or construct a three-dimensional model of a house or animal.

Using visual models, a preschooler masters symbolic and schematic systems, which significantly speed up subsequent learning in mathematics.

Stages of formation of spatial thinking

Like any function, spatial thinking is formed in stages. The first stage is the presence of communication between the analyzers: the baby in the crib sees the toy and realizes that he needs to raise his hand and touch it to receive sounds.

At 3 years old, a child’s space consists of awareness of himself among objects. He understands what part of the room he is in, where to move to approach his mother or take a toy.

In the period from 3 to 7 years, the understanding of space improves significantly, and by the beginning of educational activities, the child is already able to internally operate with the size of objects, the understanding of “far-close,” left-right” and similar relationships.

Mastering space in early preschool age

At 2-3 years of age, the desire to “do it yourself” prevails. Sometimes parents think that their son or daughter is being naughty, although in fact, they are learning to feel space in ways available to them:

Climb into the closet to realize how little space there may be around.
Build a pyramid, observing changes in shape and size.
Walk around the room in different directions to find the shortest path.

Many independent games are aimed at unconsciously modeling spatial situations. Hiding candy “behind” your back, building barricades “BETWEEN” yourself and possible enemies, placing toys “IN FRONT” of yourself, because it’s more convenient to play.

The baby models driving situations, imagining himself either as a pilot or as a driver, and with interest directs a toy locomotive along a children's railway, and all this helps him develop visual-spatial coordination.

According to experts, at the age of 3-5, a child can already navigate the shapes of geometric shapes without any problems and knows that it is possible to hit a corner. And the rapid dash from the entrance door to the slide on the playground indicates that the shortest route is already known for sure.

If you have LEGO bricks or construction sets, you can see amazing structures suggested by your child’s imagination.

Understanding of space by a senior preschooler

In older preschool age, the development of space in more complex activities comes to the fore. First of all, this is drawing. If a kid can draw a mom and dad the size of a house, and behind them the same tree, then an older preschooler, observing living nature and objects around, is able to correlate the sizes by size.

In the process of depicting a picture or object, the child learns to see the central parts of his canvas and the secondary ones. The first attempts will most likely be unsuccessful - there will not be enough space for some parts, and other objects will have to be reduced.

Regular practice allows an older preschooler to accurately select the center of the sheet for the main part of the image, correlate the sizes of near and distant objects, and fit everything planned within one landscape page.

Story games are the second way to develop orientation in space. Such entertainment involves not just one toy, but a whole set, which must first be placed in accordance with the idea, and then the gameplay itself can begin.

For example, arrange a name day for one of the dolls. The child places food on the table and seats the guests. Dolls can sit on the left and stuffed animals on the right.

Doctor games are one of the favorites, especially among girls. The process also actively involves all elements of spatial thinking. The patient should be put to bed suitable size, place the thermometer exactly under left hand or paw.

IN story games children create a visual spatial model - a kitchen, a doctor's office - always using the most noticeable features and arranging objects so that they are convenient to use.

Construction as a means of developing spatial thinking

One of the best ways Psychologists believe that the formation of such features of thinking is the construction of three-dimensional models. If at 2 years old the child puts together parts at random, then by the age of 5 the preschooler clearly understands what the result should be.

Modeling from plasticine gives more space for creativity, because you can imagine any house or train, and then begin to create three-dimensional figures, fasten them, and use other materials to add completeness.

Construction kits with ready-made circuits are also a great way to develop. Learning to read a schematic image helps to imagine the final craft; a description of the actions teaches you to follow the sequence of necessary operations.

A separate point is the need to select, find and attach a part of the right size in the right way. Just one mistake can ruin all your hard work.

In the process, the preschooler applies the principle of examining objects. He perceives the object as a whole, determines its three-dimensional shape and its constituent details. The following mental operations are used:

Comparison – necessary when choosing the required part or shape;
Classification – the parts used are divided according to the selected criterion;
Synthesis – from the presented details the child forms an image of the finished result;
Analysis - a visual model is decomposed into parts, which allows you to create a sequence of actions for construction.

Tasks for the development of spatial thinking

The child’s desire to get comfortable in space must be supported by adults. There is an opinion that 5-15 minutes of exercise a day is enough to intensify the process and speed up the formation of spatial orientation.

Stimulating games for younger preschoolers

Activities with kids include outdoor games and others in the form of exercises with objects:

Any child will understand such a pointer.

Doing the simplest gymnastic exercises to children's songs. Commands must contain the concepts “right”, “left”, “up”, “down”. Movements of arms, legs and combinations with jumps are used;
A game with a ball that must be pushed or thrown with a specific hand or foot;
Help toys and objects during walks. Moving objects or picking up a ball or scoop in a certain hand reinforces the concept of “right-left.”

Exercises to develop the thinking of older children

In older preschool age, tasks become much more varied. To increase the level of orientation in space, it is recommended:

Connecting dots by numbers or to depict a figure;
Completing half of the picture;
Copying patterns and ornaments;
Reproduction of a figure by changing dimensions or adding details;
Passage of labyrinths drawn on paper;
Creating an appliqué of familiar objects using only geometric shapes;
Description of the location of the characters in the pictures using appropriate prepositions;
Creation of three-dimensional crafts from various materials;
Place an imaginary animal in a container of suitable size;
Memorizing the position of objects and subsequent description of their arrangement;
Hiding “treasures” for searching using diagrams and hints.

Parents can play most games with their children, stimulating the spatial thinking of preschoolers and preparing them for successful learning mathematics and geometry.

Spatial thinking is one of the important components of intelligence. With its help, we can navigate in space, solve geometric problems, and imagine objects in three dimensions. And not everyone has it to the same extent. Today we’ll talk in detail about spatial thinking and figure out how you can train it.

Spatial thinking is one of the types of intellectual activity with which it is possible to create three-dimensional images and act with them in the process of solving various problems. In other words, this is a person’s ability to imagine an object in all its details and manifestations and in some way transform this object.

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 analysis 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 easier to read drawings and maps, determine locations and imagine a route to a 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.

Types of operating with spatial images

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 what such a figure will look like 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 for instructions (in case the child has forgotten some action)
Independent work without relying on the material (can be carried out not immediately, but after several repetitions of the previous steps)

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

Actions with geometric shapes

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: imagine a 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 represent 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 a graphical grid diagram and represents each move (each movement of the fly). Next he says “Stop” and the other players must say where they think the fly is at the 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”

Spatial thinking is a type of mental activity during which spatial images are created and operated on to solve problems. The development of this begins at 3-4 years of age. Even after 30 years, a person can significantly improve his ability to represent images in space.

Orientation in space is not just the ability to find a way in an unfamiliar area, and not only an unmistakable determination of where is “right” and where is “left”.

Well-developed spatial thinking is necessary for mastering such professions as architect, designer, pilot, sailor, and fashion designer. Wherever you need the ability to imagine images, change spatial objects in your imagination, this type of thinking will be required.

In order to develop this ability, there are simple exercises. Let's take a closer look at ways to work with spatial objects.

Think about what shapes are obtained when two segments intersect? Under what condition does the intersection of two segments produce one?

You can try to solve this problem mentally, or start by drawing these segments on paper. But try to avoid drawing as it makes things easier.

What shapes can be obtained if a triangle and a segment are superimposed on each other?
What shapes are obtained when two triangles are superimposed on each other?

These are fairly simple tasks. They can be used not only for adults, but also when teaching children in order to develop such qualities as spatial thinking.

More complex tasks are related to the representation of a plane in You yourself can come up with tasks for yourself and your child, using more or less complex conditions.

In addition to the exercises described, the development of spatial thinking in children includes playing with construction sets, making three-dimensional puzzles and much more.

The development of this characteristic must necessarily include the formation correct concepts about the location of the item. The child must learn to name in words the place of a thing in relation to others. For example, when asked where the toy is, a 4-year-old child should be able to answer that it is, say, under the bed or on a chair. Thus, the combination of sensory experience with the development of a conceptual apparatus is very important.

In adult life, when concepts have already been formed, an important factor will be the ability to mentally reproduce various objects in space relative to each other. For example, upon entering an unfamiliar room, carefully examine the situation, and upon leaving it, try to sketch the location of objects in it as accurately as possible.

Spatial thinking helps us solve complex problems in our minds. For example, if you need to determine how a new closet will look in a room, you will have to mentally “fit” it into the interior, taking into account not only its size and shape, but also the color and placement of other items.

Spatial thinking is closely related to memory. For example, the ability to remember and then mentally reproduce the location of guests for festive table characterizes not only the ability to navigate in space, but also the skill of remembering details.

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.

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Hi all! Yuri Okunev is with you.

Can you draw? Can you imagine the object with your eyes closed in all its details? The ability to “see three-dimensionally” is one of the key positions of highly developed intelligence. It is this quality that allows you to count well in your head and be an expert in literature. Today we will analyze exercises to develop spatial thinking.

If you always have a GPS navigator at hand, this does not mean that you do not need to develop the ability to think spatially. Why?

Let's look in the dictionary:

Speaking in simple language, spatial thinking is what allows us to create a three-dimensional picture in our heads, change and transform it at our discretion.

What does it mean?

The artist paints a picture. For his drawing to be convincing, he must correlate the real dimensions of objects with the drawn dimensions, that is, create the illusion of SPACE on paper. The same principle applies to drawing.
A writer writes a novel. He creates images of heroes, places them in an imaginary SPACE. Thinks through the plot line, fills the space with events.
The chef, before preparing the next work of culinary art, must mentally imagine it in all details: what it will look like, what the dish will taste like, in what ratio it is better to take the ingredients - to create an IMAGE of the future creation.
Mathematical calculations are also associated for us with the concepts of SPACE and images. This applies not only to geometry. A student who can imagine a “cartoon” with the conditions of a task will cope with it much easier and faster.
The process of memorizing any information consists of creating a clear IMAGE and placing it in the internal SPACE of thoughts. If an image is not created, the information will quickly be forgotten.

As you can see, the scope of application of spatial thinking is quite extensive. Any type of human activity is connected with it to a greater or lesser extent.

Types of operations on images

Spatial thinking is a rather complex process that includes both the ability to think logically and the ability to translate a real image into a graphic diagram and vice versa, as well as the ability to imagine an object in the imagination in all details. There are three types of operations on images in space:

Changing location (mentally moving an object without changing its appearance)
Metaphorses of an object (mental change in the appearance of an object without moving)
Combined change (both view and location change)

A person’s ability to perform these actions determines his degree of success in life, how quickly he can navigate new conditions, and whether he can realize his goals.

A simple pattern

A study was conducted at the University of Michigan in the USA. Children aged 6 to 8 years were taught to assemble three-dimensional figures from cubes. It turned out that as soon as a child begins to understand the principles of constructing figures, his ability to perform arithmetic operations improves dramatically.

The correlation can be traced not only in mathematics. When reading fiction, a whole movie is created in the imagination, reviving the events of the book. This allows for a deep analysis of the work, and, of course, the reading process becomes more interesting.

Without this type of thinking, the process of memorization becomes impossible, since we remember nothing more than images.

IN Everyday life Before starting any activity, we clearly imagine the result, laying out all the details. Otherwise, the end result may not be what was intended.

Exercises for kids

Spatial thinking actively develops in babies from the age of 2 months. The child first looks for his mother, focuses his gaze on the toy, then, crawling, explores the world with all possible ways– in color and volume.

A 2-3 year old child should not be prohibited from crawling under the table or into a closet, building a pyramid from his father’s books and painting himself as an Indian. Your child is unconsciously trying to develop the makings of a mathematical genius and logical abilities.

Take part in these games with him - climb under the table with him, be in the role of a guest. The child will be delighted. Buy special paints and paint together with your baby with your fingers or palm.

Children 5-6 years old have access to more complex elements of training. At this age, you need to learn to distinguish between “right”, “left” and “up” - “down”.

Place several palm prints on a piece of paper and let the child guess where the right hand is and where the left hand is;
Place items of clothing in front of him, turning both the front and back sides, and ask him to identify the right and left sleeve (trouser leg);
When reading a fairy tale, focus the preschooler’s attention on the prepositions “in”, “on”, “before”. Pick up a toy and show your child how it will be: “the bunny sat on a stump”, “hid behind a bush”;
Play confusing phrases. For example: “There is a feather bed on the wall, and a picture on the bed.”
Develop fine motor skills: modeling, origami, finger games, braiding

Exercises for schoolchildren

According to the findings of scientists, the peak development of spatial thinking occurs at the age of 9-11 years. In general, the active development of this type of thinking lasts until the age of 15 years.

In our schools, the subject “Geometry” is usually taught from the 7th grade when children reach the age of 12-13 years, when the development of this type of thinking begins to slow down. This is probably why for most children geometry is such an unloved subject, and teachers are sounding the alarm about the low level of spatial knowledge of students.

If you want your child not to have problems with geometry and spatial skills, start studying with him from the first grades of school. Here are a few tasks, placing them in order of increasing difficulty:

Folding origami figures from paper;
Working with 3D puzzles, constructing with Legos;
Drawing up a plan of an area or premises, fluency in the concept of scale;
Obtaining a stereometric figure by rotating a flat figure;
Working with a Rubik's cube;
Determine a stereo figure by its projection, compiling a scanned image;
Obtain a new complex figure by combining 2-3 simple stereometric figures. Find what happens if you subtract another from one figure.

It will also be very useful to teach your child to compose a story from a picture, while clearly identifying the emotions of each character and building a line of cause and effect; solve logic problems, anagrams, as well as various planimetric and volumetric puzzles.

By the way, such puzzles can be found in large quantities on the website Brainapps. Don't forget to also spend enough time developing your child's memory. Exercises . And encourage him to paint and sculpt.

Methods for adults

Spatial thinking constantly develops and improves throughout life, so adults can also achieve success in mastering these skills.

While reading a book, stop and put it aside. Close your eyes and imagine the characters of the plot in volume: who is located where, if they are going, then in which direction, imagine a picture of the area;
Having arrived from among the guests, remember in detail the route you took, the decor of the house where you were, the faces of the guests and the places where they sat at the table;
When placing things in the trunk of a car, pack them as compactly as possible;
Solve word puzzles, develop memory;
Start creating a handmade model - a model of a sailboat, for example, on a scale of 1:20, or a model of a tram depot.
When heading to an unfamiliar address, use a paper map instead of the usual GPS navigator, or even take up orienteering.

With this, I think I’ll finish my story about space. As you can see, this skill is quite useful. Spatial thinking is the basis on which the understanding of any objects and phenomena is built, from “how much is 2+2” to the definition.

That's all. I wish you success and look forward to your feedback in the comments. Subscribe to news, invite friends.
Goodbye! Yours, Yuri Okunev.

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 results by saying 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, it is necessary special kind 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

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 what such a figure will look like from one side or the other, etc.

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 faces a mock-up/sample of a figure, which he needs to transfer onto paper without changes (the 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: imagine a 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.

Also in the game you can use different types of fabric, 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 a graphical grid diagram and represents each move (each movement of the fly). Next he says “Stop” and the other players must say where they think the fly is at the 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).