A good imagination is one of the best tools in the world for success! The most successful people tend to be creative and imaginative plays an important role in their lives. By imagining something, a person learns to do it faster. Do you also want to develop your imagination? Then just go to the first step!

Steps

Part 1

We develop our imagination

Dream. Dreaming is a process that helps to build different logical connections and remember information without taking much time. Dreaming is far from a meaningless activity. In fact, it contributes to the formation of a state of high concentration and engagement. While you are daydreaming, an absolutely brilliant idea may suddenly come to your mind!

• Try not to be distracted by the computer/video games/Internet/movies, etc. If you are constantly distracted by various little things, the brain will not be able to focus and perceive information.
• The best time to daydream is in the morning (right before you get out of bed) and at night (before you fall asleep). An ordinary walk without headphones with music and other distractions is also suitable for daydreaming.

1. Look for new experiences. Be open, don't be afraid to try new things. A new experience can bring a lot of emotions and become food for thought and fantasy. For example, when you take a cooking class, you already begin to dream about how you will spend your vacation visiting different cafes and eating different delicacies. New experiences always open up new possibilities and develop the imagination.

   • Of course, you should not go to the other side of the world to do something and gain experience. Just the opposite! Take a closer look at your surroundings. You can always go to different lectures and circles. Try to find a new hobby, take up gardening, or just go to places in your city that you haven't been to before.

2. Watch people. In a cafe, on the subway, or on a park bench, watch people pass by. Make up stories and stories about these people, think about what could happen to them in life, use your imagination, feel sympathy for them or sincerely rejoice. Perhaps, by observing people, you will suddenly find the answer to a question that has long been of interest to you.

3. Make art. It doesn't matter what kind of art you decide to do. The main thing is that you should try to express yourself in it. Do not follow patterns and stereotypes, do what you like best. For example, if you are drawing, then draw the sun not yellow, as we are used to seeing it in pictures, but green. Use your imagination to get your drawings out of the box.

   • You can try to do any other kind of art, for example, writing poetry, sculpting from clay. Remember that you don't have to be a master at this. The point is to develop your imagination, not to become a world-class artist or sculptor.

4. Spend as little time as possible on the media. Movies, TV shows, the Internet, computer games are all very fun and interesting, but do not get carried away, otherwise your creativity will begin to noticeably decrease.

   • In our time, people, especially children, are turning into consumers, not creators. They do not create anything, but only follow the patterns already invented.
   • You should control yourself. For example, when you are bored, try not to turn on your computer or TV. Use this free time to sit in silence and calmly think about something and dream.

Part 2

Use your imagination

1. Look for creative solutions! Once you get into the habit of using your imagination, it's easy to come up with creative ways to get out of any situation. This means that a good imagination will help you go beyond and come up with new ways to solve any problems.

   • One of the problems that most people often face is limitation. In the sense that a person who has a less developed imagination will be able to come up with fewer solutions to this issue, focusing only on the proposed subject (situation) and not going beyond. In one experiment, people were given the following task: they had to touch two opposite walls with a rope hanging from the ceiling. The only extra item in the room is the pliers. Most of the subjects could not find a solution, which was to tie the pliers to the rope (i.e. use the pliers as a weight) and why swing it by touching opposite walls.
   • Practice coming up with unusual solutions by walking around your house. Having stumbled upon any obstacles, think about how you can get around them, come up with something non-standard. Take a closer look at different objects and try to dream up what you can do with them and where they can be applied. Every thing has a set of functions that it performs, but that doesn't mean it can't be used for anything else!

2. Don't be afraid of failure and failure. Sometimes your imagination cannot help you, sometimes you simply cannot use it because of fatigue or inability. But there are a couple of tricks to get your imagination going so you can use it whenever you want.

   • Ask yourself how you would solve this problem if there were no wrong solutions. Think about what you could do if you knew there would be no consequences.
   • Think about what your first step would be if you could use any resources, sources and objects to solve the problem.
   • What would you do if you could ask anyone in the world for advice?
   • By answering these questions, you free your mind from any possibility of failure, which, in turn, opens up a perspective for you on any ways to solve the problem. Of course, everything will not turn out right away, finding a creative approach will not work for every situation, but following these tips will greatly improve your imagination.

3. Visualize! Use your imagination to imagine different situations that could happen in your life. For example, you can imagine winning a competition and earning an award while you're just training to compete in those competitions.

   • The more accurately and in detail you imagine this or that situation, the more likely it is that the circumstances will turn out so that this situation really happens to you.

Irina Dzagoeva
How to develop spatial thinking in preschool children?

Formation thinking of man and his main species occurs in preschool and primary school age. This is due to the phase of active intellectual development and in this period of time, learning is much easier and more efficient.

Great importance in age 3-8 years old acquires spatial thinking. This is especially true in modern times, when increased role of schematic, graphic images, symbols.

Spatial thinking is the base, on which most of the educational and subsequently labor activity of a person is built, therefore development and the formation of this type of mental activity is very important for the professional success of the individual. In the structure of the human psyche, it is responsible for orientation in space, creating images in the human mind space and use them in the process of solving various problems.

Distinctive feature spatial thinking is the fact that its unit of measurement is an image that contains specific characteristics space: size, shape, relationship between its parts, location in space, etc.. P.

As soon as the child begins to understand the principles of building figures, his ability to perform arithmetic operations improves dramatically. Without this kind thinking the process of memorization becomes impossible, since we remember nothing but images.

One of the main directions of the organization of mathematical preschool child development is purposeful development of constructive thinking.

The concept of "constructive thinking"consists of the concept thinking and its definitions are constructive. In everyday life, before embarking on any activity, we clearly imagine the result, sorting out all the details. Otherwise, the output may turn out not at all what was intended.

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.

A 2-3-year-old kid should not be forbidden to climb under a table or in a closet, build a pyramid from his father's books and paint himself, depicting an Indian. Your child is unconsciously trying develop in itself the makings of a genius-mathematician, the ability to logic. Age from 2 to 3 years is a period of active acquaintance with the outside world, mastery of speech, objective actions, productive activity and creativity. Construction from building material allows you to create simple buildings: paths, houses, turrets, etc., developing coordination of movements, enriching vocabulary.

AT at the age of 3-4 years, the child increases cognitive activity, forcing him to ask numerous questions to get new information; there is a conscious control of their behavior; all mental processes are improved. Peers for a child are already partners in practical activities. Developing the main function of speech is the function of communication and social connection. When constructing, the baby likes to comment on his actions. He enters into business and verbal communication with peers and adults; tries to plan his activities, influence the partner's actions, distribute roles in the game.

Construction already appears as an activity, but it is still closely connected with the game. For this age characteristically active development practical experimentation. Children love to compare construction details and geometric shapes, sort them, combine them, select them, while discovering their physical and structural properties, inventing their own design techniques. Actively develop children's fantasy and imagination.

AT 4-5 year old preschoolers they have an idea about the basics of design in classes with cubes, a plastic designer, they folded houses from plasticine logs and attached a roof of sticks to them - there it is, constructive activity. Construction from building material and constructors is fully in line with the interests children, their abilities and opportunities, since it is exclusively a children's activity.

Thanks to this activity, skills and abilities, mental and aesthetic child development. At children with well developed design skills faster speech develops, since the fine motor skills of the hands are associated with the centers of speech. Dexterous, precise hand movements give the child the opportunity to quickly and better master the technique of writing.

The child is a born constructor, inventor and explorer. These inclinations laid down by nature are especially quickly realized and improved in design, because the child has an unlimited opportunity to invent and create his own buildings, structures, showing curiosity, ingenuity, ingenuity and creativity.

At children 5-6 years of interest in design, building games increases. Children willingly build a group, make toys. They can already do a lot on their own. Games children the older group become more interesting, more diverse. They reflect a wider range of knowledge that they acquire from direct observations of the world around them, from extensive information on radio, television, from books and adult stories. Reality in games children reflected much better. In defining the intent and development the plot becomes more independent. Children like that the teacher demands much more from them in work than from kids. They have elements self-control: they notice their mistakes, inaccuracies in the image and try to correct them, understand what they have not yet learned, what they have not mastered. They design with great interest when they are given a specific task that requires mental effort. They are particularly satisfied and happy when they complete a task successfully. Success in activities is also achieved by the fact that children can remember and tell how they are going to act, although they still do not succeed so easily. Development speech leads to the fact that communication children becomes more free. They willingly share their experience with their comrades, they are able to answer correctly and explain what they are doing, they are able to agree on what they will design together.

Cognitive processes at the age of 6-7 undergo qualitative changes; develops arbitrariness of actions. Along with visual thinking elements of the verbal-logical thinking. Continue develop generalization and reasoning skills, but they are still largely limited to visual signs of the situation. Continues develop imagination, but it is often necessary to state a decrease development of the imagination at this age compared to the older group. This can be explained by various influences, including the media, leading to the stereotype of children's images. Attention becomes arbitrary, in some activities, the time of arbitrary concentration reaches 30 minutes. At children there is a special interest in the printed word, mathematical relations. They recognize letters, master the sound analysis of a word, count and recount individual objects. By the age of 7, children have largely mastered the construction of building materials. They are fluent in generalized ways of analyzing both images and buildings. Free buildings become symmetrical and proportional. Children accurately imagine the sequence in which the construction will be carried out. In that age children can already master complex forms of addition from a sheet of paper and come up with their own.

Games on development of spatial thinking

A game "Place the cat"

Invite the child to imagine an animal (cat, elephant, cockroach)- let him answer in which object this animal will fit. In a glass? What about a TV box? Maybe a passing truck?

A game "Put it right!"

Give the child various objects and offer to place-arrange them, following your instructions: closer (closer than, farther than, slightly forward, backward, left of, etc.

A game "Metamorphoses"

Ask child draw a circle behind a square, a triangle in front of a rectangle. Can be complicated task: draw a cylinder in front of the cube or draw a house on the other side, from above, "cut" toy dumbbells in half, etc.

A game "Special agent on a mission"

Invite the child to carefully examine the room where he is, and remember the surrounding objects. Then ask questions using pointer words locations: What color is the table on your left? what object is directly under the chandelier? This game is even more interesting on the street - there you can already use moving objects.

A game "Drawing on the back"

Draw various figures on the child's back, then objects - let him try to guess what you are depicting.

A game "Fly"

It is played by two people plus one "observer". The players represent - and the observer draws - the game field: a grid of 9 squares long and 9 squares wide. In the upper left corner you need to mentally place a fly. Players take turns making moves, moving the fly to different squares, and the observer marks these moves on the playing field. When the observer stops the game, each player names the square in which, in his opinion, there is a fly. The one who calls correctly wins.

A game "traffic route"

Draw a complex map of the streets of the city (or just take a card) . Explain to the child that he is a policeman who left point A (show it on the diagram) to point B (also show). The child must drive along the route, naming each turn. In this version of the game, active words will be "right" and "left". Then "change role": now the child is a dispatcher who tracks the trajectory on the map. The route description should include the words "up" and "down".

A game "Magic bag"

Put various figures in a small bag - stereometric ones are better (a cube, a ball, etc., but you can also play (pyramids, nesting dolls, etc.). Invite the child to guess by touch what is in the bag.

Fold origami figures with your child, collect puzzles (including three-dimensional ones, sculpt from plasticine, cut out symmetrical objects or snowflakes from paper, play board games (tangram, checkers, chess, backgammon, "walkers", strategies, Jenga). Draw plans with your child - areas, premises.

hide for him "hoard"- looking for a path on maps, diagrams. Decide riddles: they teach the child to mentally reproduce an object according to its characteristics, thereby building an image.

Description of tasks in section 7 and sample solutions In each task, you are offered one figure, divided into several parts. These parts are given in random order. Mentally connect the parts, and find the figure that you get in this case in a series of figures a), 6), c), d), e). Sample. By connecting the parts of the figures 01, we get the figure “a”, therefore, in your answer sheets in section 7, in line 01, “a” is crossed out, that is, 1.a. When parts 02 are connected, the figure "d" appears. Accordingly, from 03 we get "b", from 04 - "g". stimulus material. Section 7. Tasks 117-136.

Key to subtest 7:

117b, 118d, 119c, 120c, 121d, 122d, 123d, 124a, 125a, 126B, 127d, 128c, 129d, 130d, 131c, 132a, 133d, 134d, 135b, 136c.

Key match - 1 point.

Mismatch with the key - 0 points.

Interpretation of performance for subtest 7

• Subtest 7:"PV" (spatial imagination):

This subtest includes tasks in which the subject needs to determine which of the five figures located in the sample can be added from the following separate parts of the cut figures. The material of the task is planar drawings - parts of individual figures. The task provides for the combination, rotation, convergence of these parts in the same plane, as well as comparison with patterns of figures.

The search for a solution in problems of this type is strictly dictated by its conditions and does not provide for going beyond its boundaries. The subject's activity is subject to a strict decision logic. It is, however, not so much about verbal logic, which is based on the presence of a good conceptual apparatus, a detailed system of reasoning is required. The solution of figurative tasks requires a special kind of logic, in which the “grasping” of a visual situation is carried out simultaneously, its awareness is not accompanied by detailed verbal reasoning.

Tasks in which the purpose and conditions of activity strictly determine the solution process are widely represented in engineering and technical activities, where the transformation of technical objects is subject to special production requirements. Thus, on the basis of a high score on this subtest, success in the field of technical activity can be predicted to a certain extent. At the same time, high performance in the subtest cannot serve as a basis for the conclusion about the high development of abilities for artistic, graphic, visual activity, since the operation of images in these types of activity is carried out in freer conditions. The assessment of conditions in the tasks of the SP subtest is carried out on the basis of an analysis of the shape and size of the parts of the figures. In addition to analytical and synthetic abilities, the implementation of this action involves the development of the ability to accurately perceive the shape and size of planar figures (linear eye).

Having familiarized himself with the conditions of the tasks, the subject proceeds to active mental operation with images. In this case, the original image is transformed according to its structure. This is achieved through the mental regrouping of its constituent elements with the help of movement, as well as various methods of combining parts of the figures. In addition, the transformation of the spatial image also affects the spatial position of the figures. So, in this case, there is a mental rotation of images within the same plane.

Operating images includes their conscious retention in memory, planning them on the basis of upcoming activities, anticipating its results, generalizing in a figurative form.

Based on the analysis carried out, it can be concluded that the GS subtest diagnoses only individual sub-abilities in the structure of spatial thinking. When performing this subtest, there is mainly a manifestation of the ability to operate with two-dimensional images, while the ability to form a new image is practically not manifested here.

is the left hemisphere.

A person has two. For successful learning, they must work in tandem. In mental activity, the right hemisphere represents spatial thinking.

It is useful to develop ideas about space and imagination in a preschooler for school. For example, without a developed imagination, it is generally impossible to be successful in any activity.

Spatial thinking of the child

There is a lot of good advice on the Internet. We offer material that we use in practice and have shown satisfactory results in the development of the necessary qualities. It should be noted that the best way to develop a preschooler is a game.

What is available to all parents:

1. Productive children's activities: modeling, drawing, designing. It is better to start with modeling, as we get three-dimensional figures (three-dimensional space). Blinded and trying to draw (transition from volume to plane). Or vice versa, there is a picture, try to mold the drawn object. Construction is similar.
2. Paper crafts: three-dimensional (design)
3. Games: chess (especially) checkers, Chinese game "tangram", "Columbus egg", etc.
4. Drawing plans for a room, apartment (or house), the surrounding area with the baby. Or draw the plans yourself, and let him correlate the plan and reality. It is useful to arrange games like quests: children like to look for treasures, guided by the schemes.
5. Solving riddles. Describe the object, and the baby will find it by signs. Developing moment: the preschooler will have to build an image in his mind.
6. Going somewhere, ask your child how best to get there.

Tasks and exercises for spatial thinking

What tasks can be found on our website as well? Such classes, in principle, can be started from the age of 4.5, but all children are different. If it doesn't work, simplify. And the simplified version did not work - give up for a while. Then you can offer again.

1. Copying ornaments. The patterns we recommend are suitable for 6-7 year olds.
2. Mirror drawing of the object (draw the second half in the same way).
3. Cutting out symmetrical figures (possibly already from the middle group).
4. Cell dictations. They can be performed in different ways: graphic dictations (simple and complex), drawing by cells.
5. Verbal dictations.
6. Connecting the dots in a sequence of numbers, get a picture of the object.
7. Mirror redraw any drawn things, letters.
8. Draw on the instructions of an adult: draw a house in the upper left corner of the leaf, a sun in the upper right, a flag in the lower left, a boat in the lower right. We start with this task.
9. Everyone knows labyrinths. For kids, it's easy to find the way for the bear to the barrel of honey. Children older than 6-7 years old can go through the mazes with the condition. For example, when going through a maze, do not take your pencil off the paper from beginning to end.
10. Insert frames (also different).
11. Describe the position of an object using prepositions (the cat is sitting on the roof, jumping off the roof, hiding under the porch, etc.)

Games for 5-7 years old

For children older than 5-7 years, tasks can be complicated.

Dots in cells

Psychologists have a simple test to identify the motor pace of six-seven-year-olds. On a sheet in a cell, it is performed line by line. It is necessary to put down dots in each cell of the line at the highest possible pace. This test easily turns into a developmental task. Let us supplement the simple marking of points with the conditions:

1. In the first line, dots are drawn from left to right, in the second line vice versa, in the third line again from left to right, etc.
2. Points can be put down alternating from top to bottom and bottom to top.
3. And you can somehow obliquely or how you come up with.

After such an exercise, children perfectly remember the arrangement in a line and in a column even before school, simplifying their school life.

Arrange the toys

Offer the children a set of small toys. Put a toy on the table. You talk, and they arrange other toys relative to her: an elephant further, a cat on the left, a pig closer, and so on.

Expand the figures

Prepare several geometric shapes (complication: different in color and size). Let the baby arrange them according to your instructions. Similar to the previous task. Only there are voluminous figures, but here they are flat.

Scout

This exercise also trains memory.

Instruction. Look closely at the whole room. Remember. Look away. Answer the questions: what is to the right of the sofa, what color is the table under the TV, what is to the right (left) of the chair, how many cushions are on the sofa, how many are on the chair, what color is the sofa, etc.

Drawing on the back

Draw simple geometric shapes, letters, numbers on the baby's back with your finger. His task is to understand what is drawn.

magic pouch

We play with the nursery group. Put small figures of animals and other toys in a fabric bag. The task of the preschooler is to recognize the object by touch.

Fly

Also a well-known exercise. There are various options on the internet. There is a field of 9*9 cells (for preschoolers 7*7 or 5*5). Game in two stages.

Stage 1. A fly (a toy or a button) sits in the upper left corner and moves through the cells. Adult dictates: two cells down, one to the right. The player moves the fly according to the instructions. Etc.

Stage 2. The preschooler makes the movements of the fly in his mind and immediately moves it to the desired cell. complication: all actions, both the fly itself and the field, the player keeps in mind. He tells the position of the fly to an adult, and then he marks it on the playing field, and in the end it is compared with the workpiece. Once the game is mastered, it can be played by 2-3 players with a leader.

Spatial thinking and grade 1

How can spatial thinking help a student in school?

1. He will quickly navigate indoors and on the ground, which will give him self-confidence.
2. It will be easy to remember the location of your belongings. Will not lose them.
3. Able to quickly concentrate and easily remember information.

This is the minimum that ensures the success of training at its very first stage.

Modern elementary mathematical education is part of the system of secondary education and at the same time a kind of independent stage of education. In recent years, primary mathematical education has undergone a number of changes, which are primarily associated with a change in the goals of primary education, the introduction of the Federal State Educational Standard, and a change in the requirements for the results of mastering the main educational program of primary general education.

A significant place in the mathematics curriculum for elementary school is occupied by geometric material, which is explained by the fact that working with geometric objects, behind which are real objects of nature and made by man, allows, relying on visual-effective and visual-figurative levels of cognitive activity that are relevant for the younger student. activities, to rise to an abstract verbal-logical level; secondly, it contributes to more effective preparation of students for the study of a systematic course in geometry.

The study of geometric figures begins with an acquaintance with a point and a line and a consideration of their relative position. Comparison of different types of lines leads to the appearance of various polygons, and then to acquaintance with spatial figures. Geometric quantities (length, area, volume) are studied on the basis of a single algorithm based on the comparison of objects and the use of various measures. The ability to build various geometric shapes and sweeps of spatial figures, to find the areas and volumes of these figures is necessary when performing various crafts in technology lessons, as well as in life.

The development of spatial imagination in elementary school is relevant, because. spatial representations and spatial imagination of a child are prerequisites for the formation of his spatial thinking and are provided by various mental processes, such as perception (which is based on sensations), attention, memory, imagination with the mandatory participation of speech. The leading role is played by logical methods of thinking: comparison, analysis, synthesis, classification, generalization, abstraction.

In numerous methodological studies devoted to the problem of the formation of spatial representations and imagination in younger students, both the content and procedural aspects of their teaching the elements of geometry are considered.

However, the studies carried out are mainly aimed at the formation of two-dimensional spatial representations. The main attention from the structure of spatial representations is given to the formation of ideas about form and size. Not enough attention is paid to other important areas related to the development of spatial imagination based on the spatial placement of objects, the assimilation of certain relationships and orienting actions in the real surrounding space.

Main part

1. Theoretical aspects of the development of spatial imagination

The need for the development of spatial imagination drew the attention of domestic teachers-geometers. Scientists emphasize the importance of developing spatial imagination for successful work in many areas of human practice: in the work of a scientist, in the classroom for mathematical activities, scientific and technical creativity, in the profession of a teacher, actor, writer, in decorative and fine arts, in the process of reading a work of art (M M. Bakhtin, L. I. Bozhovich, I. A. Breus, N. V. Goncharenko, E. A. Klimov, A. M. Korshunov, V. T. Kudryavtsev, I. I. Lapshin, A. K. Markova, Ya. A. Ponomarev, B. M. Rebus, I. O. Yakimanskaya and others).

Imagination is not given to a person at birth, it arises in the course of activity, including cognitive. Imagination allows us to cognize the reality around us. In order for the imagination to manifest itself, assisting in the process of acquiring new knowledge, it is necessary to provide a person with actual experience. Imagination will be the richer, the more extensive is the person's available experience, regarding the individual parts and elements of the object or phenomenon that is to be studied. In the course of cognitive activity, as can be seen from practice, imagination plays a significant role, because without it, the learning process would be very difficult, and in graphic disciplines almost impossible.

Spatial imagination is the ability to mentally model and "imagine" various projects or structures, to see them with inner vision in color and detail.

The images that a person operates on are not limited to the reproduction of what is directly perceived. Before a person in images can appear both that which he did not directly perceive, and that which did not exist at all, and even that which in such a concrete form in reality cannot exist. Thus, not every process that takes place in images can be understood as a process of reproduction. Actually, each image is to some extent both a reproduction - albeit a very distant, mediated, modified one - and a transformation of the real. These two tendencies of reproduction and transformation, the data are always in some unity, at the same time, in their opposite, they diverge from each other. And if reproduction is the main characteristic of memory, then transformation becomes the main characteristic of imagination. According to R.S. Nemov's imagination is a special form of the human psyche, standing apart from other mental processes and at the same time occupying an intermediate position between perception, thinking and memory.

Imagination significantly expands and deepens the process of cognition of the objective world. So, for example, G.I. Salamatova emphasizes that when studying mathematics, physics, chemistry and other subjects, imagination helps students to revive abstract concepts, fill the formulas with concrete content. And often the difficulties in mastering scientific concepts, in solving educational problems are due to the fact that students do not have the appropriate images. So, for example, an incorrect representation of the drawing of a geometric problem makes it generally unsolvable. In order to solve a particular problem, it is necessary not only to comprehend the content, but also to create an adequate image. And this is the function of the imagination.

In this regard, one of the main tasks of the school is to develop the spatial imagination of schoolchildren, which consists in the ability to create images in three-dimensional space. Spatial imagination is an important component of human mental development, the importance of which has been repeatedly emphasized by teachers and psychologists.

Without a well-developed spatial imagination, it is impossible to successfully study geometric material, especially stereometric material, which constantly requires the ability to read images of figures, mentally imagine the necessary configuration, hold several objects in the visual field at once and operate with them.

In middle and high school, when the study of stereometry implies that schoolchildren have elementary spatial imagination skills, a misfire occurs, teachers are faced with the fact that their students cannot read images of spatial figures, they do not perceive a flat drawing in volume, students are often unable to determine the relationship between the individual elements of the image, mentally change their relative position, dismember the figure into parts or glue it from the existing parts. That is why every opportunity should be sought and every reserve of time should be used to develop the spatial imagination of students during the first years of schooling, both in the classroom and outside of school hours.

The low level of spatial imagination of students requires greater clarity when solving geometric problems. At the same time, the question often arises of the ease of operating with spatial images of figures and by the teacher himself. The most effective means of developing students' spatial representations, as you know, are: demonstrating figures, comparing the positions of geometric figures relative to each other, modeling, competently depicting figures, reading a drawing. These tools lead to the best results if they are used systematically and in combination. The creation of graphic images or graphic modeling is necessary not only for the successful teaching of the basics of science, but is also of considerable importance in visual, design, technical activities, and is implemented in everyday life.

When studying the foundations of geometry by younger students, relying only on direct contemplation is not enough. Motor skills and the muscular feeling associated with it play a fundamental role in the development of the psyche of intellect and personality, visual and practical teaching of geometry should provide the opportunity to operate with object models, to identify geometric facts. This means that any new knowledge should be obtained in the process of active actions of the child himself, and not be limited to observing the actions of others.

Organized on this basis, cognitive activity allows you to practically transform the subject of study in accordance with the goal. Thus, in the formation of a geometric image, the activity of the tactile and visual analyzers is very important. Tactile analyzers are also one of the most important sources of knowledge about the space and mechanical properties of objects.

2. Geometric material as a means of developing the spatial imagination of younger students

The topic "Geometric figures" occupies a significant place in modern programs and is studied during the entire period of primary education. As a rule, individual questions related to the topic are not separated into separate blocks, but are intertwined with the study of the main - arithmetic - material. The measurement of the area, angles, volume of spatial figures and geometric models of the number series (numerical (coordinate) ray) is presented separately.

We list the main tasks of studying geometric material:

- refinement and generalization of geometric representations obtained in preschool age;

- enrichment of geometric representations of schoolchildren, the formation of some basic geometric concepts (figure, planar and spatial figures, the main types of planar and spatial figures, their hierarchical relationship with each other, etc.);

- development of planar and spatial imagination of schoolchildren;

- preparation for the study of a systematic course of geometry in the main link of the school.

The study of geometric material in modern elementary school pursues mainly practical goals, accompanying the course of arithmetic. So, consideration of the properties of figures, the formation of initial geometric representations is mainly aimed at acquiring by students practical skills related to solving practical problems for calculating (length or area).

Geometry from the first years of education contributes to the cognitive and intellectual activity of schoolchildren and is the way to achieve a new quality of education.

Mathematics as an academic subject, or rather its geometric component, has ample opportunities for the development of figurative components of thinking. Working in geometric space requires the creation and operation of images in which the form, location in space, the relative position of elements are highlighted, that is, spatial images; the study of geometry requires predominantly emotional-figurative cognitive strategies that are organic for younger students, and therefore is extremely important for the full-fledged intellectual, emotional and aesthetic development of children.

3. Methodology for the development of spatial imagination in mathematics lessons in elementary school

In the first grade, the study of geometric material begins with the deepening of children's knowledge of space. Seven-year-old students have a developed sense of shape, volume, the ability to notice some distinctive features of objects and geometric shapes (the ball is smooth, round, easy to roll, it is convenient to catch it; you can build a fortress from cubes - they are stable, etc.). Interest in visual activity formed the first experience of operating with a geometric form among students.

In order to form spatial imagination, it is advisable to study geometric material in the form of didactic blocks. Didactic blocks have a single principle of construction and form a certain system of activity. In general, the didactic block looks like this:

1. Form - properties of objects of the world.
2. A three-dimensional figure is the shape of an object.
3. Elements of a three-dimensional figure, their number.
4. A flat figure as a graphic "trace" of the elements of a three-dimensional figure.
5. Mutual arrangement of figures. A figure as a special case of the mutual arrangement of other figures.
6. Distinctive features and properties of geometric shapes.
7. Measurement, graphic representation, modeling, graphic combination of geometric shapes. Reading drawings.

Consideration of the objects of the surrounding world and their opposition to each other allows us to distinguish the form among other properties of objects (color, size, material quality, etc.). Comparison and juxtaposition of objects of the same shape contributes to the transition to a geometric form in the form of a three-dimensional material model of a geometric figure.

Analysis of the shape of the model with the involvement of the sensory experience of the child allows you to highlight the elements of a three-dimensional geometric figure using the graphic “trace” method, to put them in line with a flat figure. The graphic combination of flat figures allows you to move on to the mutual arrangement of geometric shapes. Comparison of flat figures, three-dimensional figures, flat and three-dimensional figures among themselves helps to form an idea of ​​their properties.

The practical part in the first grade is based on the design and modeling of materials known to children: sticks, plasticine, wire, which makes it possible to fix a stable image of a figure in the memory of students. At the same time, there is an acquaintance with the details of the designer, simple connections of parts to each other. Acquaintance with the origami technique allows students to form the ability to raise questions about the world and look for answers to them, develop curiosity and creativity, and teach the basic skills of reading drawings and technological maps.

The formation of the concept occurs in the following stages:

I. Preparatory stage.

II. Introduction to the concept.

III. Consolidation.

IV. Generalization.

Acquaintance with volumetric bodies in mathematics lessons can occur in the following sequence:

I. Acquaintance with the ball, its properties.

II. Introduction to the cylinder and its properties.

III. Introduction to the cone and its properties.

IV. Generalization on the topics "Ball", "Cylinder", "Cone".

V. Acquaintance with the prism, its properties; familiarity with the parallelepiped and the cube.

VI. Acquaintance with the pyramid, its properties.

VII. Generalization on the topics "Prism", "Pyramid"; introduction of the concept of "Polyhedron".

VIII. Generalization and consolidation of knowledge on the topics "Ball", "Cylinder", "Cone" and "Polyhedron".

In the formation of these concepts, creative tasks are used. When forming each concept, historical material is given; “relationships” between concepts are clarified: which is generic, i.e. which is "older", "more important"; element names are given.

On a specific example, we will present a system of tasks for the formation of the concept of "Ball".

I. Purpose: to introduce the ball. Introduce the concept of "form".

Equipment: spherical objects, a set of photographs and drawings of spherical objects, a cylinder, a cone, a circle.

Consideration of a group of objects. What is it? (Globe, tennis ball, balloon, ball, beads, peas. See how all these items differ from each other?

• by color;
• to size;
• according to the material from which they are made;
• made by man or created by nature;
• by appointment;
• by gravity;
• for transparency, etc.

What do they have in common, how are they similar? (If “round”, then show a circle. The circle is round, and these objects?) These are balls. So what do all these items have in common? (The form)

What else? (Compare the drawn ball and the ball). You can grab the ball with your hands, look at it from all sides, that is, the ball is voluminous, you can “hug” it.

What else do these items have in common? Look, they don't want to lie on the table. They all (roll. The ball rolls? So it is a ball. The pea rolls? This is also a ball. Show a cylinder and a cone. Roll? So, balls too?

Try it, ride it. How do these pieces roll and how does the ball roll? (The ball rolls in all directions.)

Make a conclusion. What do all these items have in common? (Spherical shape, volume, the ability to ride in different directions.) How can you call all these objects in one word? (Ball).

Look around you. Are there balls in the class? Remember where you saw spherical objects at home, on the street? (Christmas tree decorations in the form of a ball, lampshades, berries, balls, etc.) Look at the photographs and drawings.

What else have you forgotten?

Let's draw a ball in notebooks and sign it. To prevent the ball in the drawing from turning out flat, draw a shadow and paint over the dark places. Like this.

Do you know why a ball is called a ball? The word "ball" comes from the Greek word [fatra], which means "ball".

Homework - write down in notebooks the names of spherical objects that we did not remember in class.

II. Purpose: consolidation of the concept of "ball", its properties.

Equipment: a set of objects of various shapes for playing the "Black Box"; geometric bodies and flat figures made of colored paper, balls, plasticine.

What geometric figure are you familiar with? (Ball.) What properties does it have?

Let's play the game "Silence". You must silently show me, depict the ball with your hands, show all its properties. Who's better?

Take plasticine and mold each of your balls. Did everyone get balls?

See how the balls turned out different. What is the difference? (Color, size.) What is common?

Place the largest ball on the right and the smallest on the left. Put a green ball, and after it - red, in front of it - blue.

At the board are objects of various shapes, figures cut out of colored paper. Show only balls.

Divide the objects into two groups: in one - balls, in the other - all other objects. How to name all the objects of the first group? (balls, or objects having a spherical shape).

The board has two spherical objects, a cone, a cylinder and a circle made of paper. Children close their eyes, the teacher removes one object. Children open their eyes if the ball has disappeared, clap their hands.

Let's play the black box game. There is a black box in front of you. It contains many different items. Your task is to get the ball, determining that it is a ball by touch.

When forming concepts, various creative tasks can be used. This can be writing a fairy tale, poems, various crafts, drawings, mathematical newspapers, etc.

One of the types of creative tasks when working with concepts is the compilation of a "Geometric Dictionary" by children. When compiling a dictionary, children give a definition of the concept (in their own words, as they understand it), independently identify essential properties, select interesting material, draw up a dictionary, compose fairy tales, poems, riddles, and perform drawings.

The following points are reflected in the geometric dictionary:

1. Term (Children write the name)
2. Definition (Children answer the question "What is it?", describe the figure, list its properties)
3. The content of the concept (Properties are listed due to which this figure can be distinguished from other geometric shapes)
4. The scope of the concept (Species are listed, answer the question “What are there?”, “How can I do it?”)
5. Connection with life (Where is it found, what objects or parts of them have the same shape?)
6. Creative design (poems, fairy tales, riddles, interesting tasks, drawings, etc.)

In the second grade, work continues on the formation of design skills in schoolchildren using the most general geometric knowledge, technical and mathematical methods of action, mathematical and technical ways of describing these actions and their results. Any work will give its positive result only when it is carried out systematically and purposefully. Therefore, it is necessary to continue the study of geometric material in the form of extended didactic blocks. An example of one of them will be the work on the topic "Cube-Square".

1. Cube - the shape of objects: boxes, rooms, drawers, etc.
2. Cube elements: vertices, edges, faces. Their number.
3. Point, segment, square - graphic trace of the vertex, edge and face of the cube, respectively.
4. Line as a graphic "trace" of a continuously moving point. Closed, open lines.
5. A point as a result of the intersection of lines.
6. Straight. Mutual arrangement of a point and a line. Ray. Graphic representation of a beam.
7. Mutual arrangement of two beams. Injection. Graphic representation of an angle. Right angle.
8. Square. Elements of a square, their number, relative position.
9. cube. Geometric features of the cube shape. Modeling a cube from sticks and plasticine.
10. Cut length. Section measurement. Diagonals of a square, their properties. Finding the perimeter of a square.

By the same principle, the study of the blocks "Parallelepiped - rectangle", "Pyramid - triangle", "Ball - circle" is carried out. Thus, studying the geometric material of the first block, students firmly master a variety of techniques and methods of activity, which they reinforce and then use in the study of each subsequent block, but already as learning tools for acquiring new knowledge.

At the end of the study of each block, practical exercises are held, where students apply the acquired knowledge in practice, combine them on the basis of common patterns. Performed individual, group and collective creative work in the technique of origami.

The study of the geometric material of the third class is carried out not so much along the path of expanding the volume of knowledge about new figures, but along the path of revealing properties, relationships between figures and increasing the quality level of mastering the techniques of constructive geometric, creative and mental activity. In this regard, third grade students improve their skills in graphic representation of figures, learn the rules for constructing geometric figures, patterns and rosettes with a compass and ruler, as well as the rules for depicting three-dimensional figures (cube, parallelepiped, pyramid, sphere). The stock of existing knowledge about three-dimensional figures is expanded by acquaintance with projection drawings (views from above, left, front) and scale (reduction of natural size).

In the 3rd and 4th grades, children get acquainted with various methods of depicting three-dimensional objects on a plane, creating the illusion of three-dimensionality. Through a system of tasks, children independently come to the conclusion that artists, graphic artists, draftsmen use for this. For this, painters use the play of chiaroscuro or perspective, graphics - the curvature of lines, draftsmen - an orthogonal projection.

In addition to these techniques, children get acquainted with the image of three types of objects (front, top, side). This method is especially important for the development of spatial imagination.

Comparison of models of various names can be used as an effective method for developing spatial imagination. All this material is studied at an introductory level. For example, comparing models of a ball, cylinder, cone, children note that what they have in common is the ability to roll (rolls). The difference is that the ball rolls arbitrarily, the cylinder - in a straight line, the cone - in a circle, in the center of which is its top. The differences between these bodies are also that the ball has neither tops nor bases, the cylinder has two bases, but no tops, the cone has one base and one top. Similarly, a prism and a pyramid, a cylinder and a prism, a pyramid and a cone, etc. are considered and compared.

A variant of such work is a comparison of three-dimensional figures of the same name. For example, children are encouraged to compare several different prisms. When performing the task, signs of similarities and differences are revealed.

Signs of similarity: all prisms have two polygon bases, edges and vertices, their side faces are rectangles (in elementary school we consider only straight prisms).

Signs of differences: the bases are different polygons, the number of vertices and edges is different, the lengths of the edges are different.

You can invite students to find prisms that have only one or the other number of features of difference and discuss why this is so.

In the fourth grade, the formation of an idea of ​​​​the shape and relative position of the figures ends with an acquaintance with regular polyhedra and regular polygons, modeling paper polyhedra. The measuring activity of students is reaching a qualitatively new level. They learn to use measurements when building, measure models of figures and objects on the ground. Modeling of polyhedra includes almost all the techniques of constructive geometric activity, therefore, the ability of a student to make a model of a three-dimensional figure serves, along with the ability to read drawings and technological maps, one of the main criteria for his ability to design in a representation, operate with spatial images and use them as a support in mental activity.

Participation in the creative process by creating collective works in the origami technique on a chosen topic, the ability to draw up a plan of one's actions, to select material and tools for one's activities allow one to develop independence, stimulate cognitive activity, create an atmosphere of collective search activity for each individual student and the team as a whole .

4. Planned results

The formation of spatial imagination is characterized by the ability to mentally construct spatial images or schematic models of the objects under study and perform various operations on them.

Study of the level of development of spatial imagination

(Cognitive UUD)

So, given that tasks that reveal the level of spatial imagination are practically not included in the complex final work, it is legitimate to use additional tasks, for example:

1. Show the child a scan of the figure and ask him to mentally identify the three-dimensional figure that can be obtained from it if the scan is bent along the marked dotted lines.
2. Divide the round cheese in three cuts into eight pieces.
3. Each of the figures shown in the following figure consists of a certain number of cubes. Look carefully at the figures and count how many cubes each figure is made up of.

Conclusion

Spatial imagination is a type of mental activity that ensures the creation of spatial images and their operation in the process of solving various practical and theoretical problems. Spatial imagination is such a psychological formation that is formed in various types of activity (practical and theoretical). For its development, productive forms of activity are of great importance: design, pictorial (graphic). In the course of mastering them, skills are purposefully formed to represent the results of their actions in space and embody them in a drawing, drawing, construction, crafts. Mentally modify them and create new ones on this basis, in accordance with the created image, plan the results of your work, as well as the main stages of its implementation, taking into account not only the temporal, but also the spatial sequence of their implementation.

Spatial imagination in its developed form operates with images, the content of which is the reproduction and transformation of the spatial properties and relations of objects: their shape, size, mutual position of parts. Operating with spatial images in visible or imaginary space is the content of spatial imagination.

The content of the geometric material selected for study should be diverse (in the sense of simultaneously introducing students to two-dimensional and three-dimensional figures), ensure continuity (avoid periods of inactivity and gaps) and uniformity (avoid overload at some stages) of the process of forming spatial representations and imagination at students.

When selecting content, it must be taken into account that the formation of image manipulation skills is fundamental for working in geometric space. The activity of figurative thinking is a priority at the age of 6-11 years. Therefore, spatial imagination as a kind of figurative thinking must be developed already in elementary school. Purposeful work with images is necessary at primary school age and for the development of creativity in a child (figurative thinking associated with the creation of multi-valued contexts underlies creative activity).

List of sources used

1. How to design universal learning activities in elementary school: from action to thought: a teacher's guide / [A.G. Asmolov, G.V. Burmenskaya, I.A. Volodarskaya and others]; ed. A.G. Asmolov. - M. : Education, 2008. - 151 p.
2. Maklakov A.G. General psychology: Textbook for universities. - St. Petersburg. : Peter, 2004.
3. Geometry teaching technique. Tutorial. Edited by Gusev V.A. - M .: Publishing Center "Academy", 2004.
4. Nemov R.S. Psychology. In three books. Book. 1. General foundations of psychology.-M. : Vlados, 1998.
5. Salamatova G.I. Imagination as a component of creativity in the study of mathematics / / Primary school + before and after, 2004, No. 9, p. 47-48
6. Tsukar A.Ya. Development of spatial imagination. - St. Petersburg: SOYUZ Publishing House, 2000.
7. Yakimanskaya I.S. Methods for the study of non-verbal thinking Sat. test methods of I.S. Yakimanskaya, V.G. Zarkhin, O.S. Zyablova, X.M.Kh. Kadayas, A.Yu. Lebedev; [ed. I.S. Yakimanskaya] M. 1993.
8. Yakimanskaya I.S. Psychological foundations of mathematical education. - M .: "Academy", 2004. - 320 p.

Answer to the cheese circle problem:

Answer to the cube problem:

1 figure - 55 dice

2 figure - 27 dice

3 figure - 60 cubes

4 figure - 27 dice

5 figure - 27 dice

6 figure - 60 dice