What is abstract thinking and why is it needed?
In the scientific concept, abstraction is the mental separation of some properties and characteristics of an object from the object itself, as it is written in the explanatory dictionary of the Russian language” (edited by D.N. Ushakov). Remember the film “Chapaev”: where should the commander be during an attack? Potatoes laid out on the table symbolize the location of the troops. They are completely different from a commander going on an attack or an army, but nevertheless they successfully cope with their task - they symbolize the properties and characteristics of certain objects.
The object and the symbols that designate or define it are different things, and yet, when you hear the word “cow,” you imagine a large, horned, cloven-hoofed, “milk-bearing” animal, and not a gray, striped, clawed, meowing animal.
Abstract thinking is inseparable from mathematicians and physicists, poets and writers, musicians and composers. Any creativity requires abstract thinking, that is, manipulation with symbols. And if you want to develop your child’s creative abilities, then you need to start with the development of abstract thinking.
Some are inclined to believe that abstract thinking is like an ear for music: it either exists or it doesn’t. An innate gift. And its development is practically impossible, just as it is impossible for someone who is deprived of musical ear.
In extreme cases, persistent exercises for the development of abstract thinking can give some temporary results, but as soon as you stop them, everything immediately returns to normal.
But here’s the thing: it turns out that all children are born with an excellent ear for music. And if a five-year-old child is found to lack it, then it was not a bear who stepped on his ear at birth, but throughout the five years of his life, musical development occurred in the opposite direction: from excellent musical ear to “bear-like.” And if you concentrate almost immediately after the birth of a child on the development of his musical abilities, then by the age of five he will be a potential Chaliapin or Caruso.
So abstract thinking can be developed; every child has its germs, and they are absolutely viable. But they are like plants. Without proper care they will simply wither away. But everyone knows that if the plant is completely dry, then no amount of watering or care will produce results.
The simplest game to develop abstract thinking is to imagine what a cloud looks like. Clouds, fortunately, are absolutely accessible and free. And they offer many different pictures without requiring any effort (well, except maybe raising your head). A cloud can look like a dragon, a knight, a castle, puffs of smoke, a piece of cotton candy, a flower... There are an infinite number of forms. By looking at clouds in terms of symbols and their manipulation, rather than in terms of meteorology (it looks like it's going to rain!), the child develops abstract thinking.
By the way, the dialogue between Winnie the Pooh and Piglet from the Soviet cartoon is also shining example abstract thinking. The bees were offered a magnificent logical chain of the symbols: a “cloud” in the face of Winnie the Pooh, Piglet’s umbrella, and even corresponding statements (“I am a cloud, a cloud, a cloud, and not a bear at all...”, “It seems like it’s going to rain!”). The only problem is that the bees refused to think in symbols and preferred specifics. But that is another story.
There is a game that children almost never get tired of, and at the same time develops abstract thinking perfectly: shadow theater. What is a shadow if not a real abstraction? She is not an object, but only its symbol. But you can play with this symbol, unlike clouds - you can only watch them.
All you need for this game: a lamp, a sheet and a set of cardboard figures. You can make the figures yourself, it’s not too difficult.
Various shadow plays are performed. Any children's fairy tale is ready script, requiring only "actors". Moreover, “actors” can be multifaceted. The bear from the fairy tale about Masha and the Three Bears will perfectly cope with the role in the fairy tale about Teremka. The tower itself will perfectly depict a hut in any other fairy tale. The wolf is Little Red Riding Hood, the Seven Little Goats, and the dog in “Turnip.”
Another interesting exercise is shadows on the wall. The symbol and what it symbolizes. The shadow cast by the hands takes on the shape of completely different objects. The child no longer sees hands, but a flying bird, barking dog, hare and so on.
This shadow “theater” can be continued on the street. What kind of shadow will you get if you raise your arms above your head? How to make a shadow-hare? Shadow tree? Chinese pagoda?
Offer your child abstractions, invite him to create abstractions himself. Play with clouds and shadows. Maybe your future Pushkin is growing up. Or Lobachevsky. Help him grow up.
This is something incomprehensible at first glance. You look, for example, at a picture and don’t understand what these figures, lines, dots mean... Somehow they are scattered everywhere. But after taking a closer look, you begin in your imagination to connect circles, triangles, strokes into separate areas... and notice that one area is human face is somewhat similar, another is like the sun, and the third is like a cow... This is an example of an abstract painting. Images from our ordinary life are drawn in individual details.The term "abstraction" does not only apply to images. Words (concepts) can also be abstract - these are words that mean something that cannot be seen, heard, touched, smelled, that is, touched. It is these words that our encyclopedia mainly consists of.
Even the concept of color is an abstract concept. We see not a color, but an object of a certain color. Color by itself does not exist - it is a property of an object.
What is abstract thinking and why is it needed? " Dictionary Russian language" (edited by D.N. Ushakov) states that in the scientific concept, abstraction is the mental separation of some properties and characteristics of an object from the object itself. Remember the film “Chapaev”: where should the commander be during an attack? Potatoes laid out on the table symbolize the location of the troops. They are completely different from a commander going on an attack or an army, but nevertheless they successfully cope with their task - they symbolize the properties and characteristics of certain objects.
The object and the symbols that designate or define it are different things, and yet, when you hear the word “cow,” you imagine a large, horned, cloven-hoofed, “milk-bearing” animal, and not a gray, striped, clawed, meowing animal. Abstract thinking is inseparable from mathematicians and physicists, poets and writers, musicians and composers. Any creativity requires abstract thinking, that is, manipulation with symbols. And if you want develop in a child creative abilities, then you need to start with the development of abstract thinking.
Some are inclined to believe that abstract thinking is like an ear for music: it either exists or it doesn’t. An innate gift. And its development is practically impossible, just as it is impossible for someone who lacks an ear for music to become a composer. In extreme cases, persistent exercises for the development of abstract thinking can give some temporary results, but as soon as you stop them, everything immediately returns to normal.
But here’s the thing: it turns out that all children are born with an excellent ear for music. And if a five-year-old child is found to lack it, then it was not a bear that stepped on his ear at birth, but all five years of his life musical development happened in the opposite direction: from an excellent ear for music to a “bearish” one. And if you concentrate almost immediately after the birth of a child on the development of his musical abilities, then by the age of five he will be a potential Chaliapin or Caruso.
So abstract thinking can be developed; every child has its germs, and they are absolutely viable. But they are like plants. Without proper care they will simply wither away. But everyone knows that if the plant is completely dry, then no amount of watering or care will produce results.
The simplest game that develops abstract thinking is what a cloud looks like. Clouds, fortunately, are absolutely accessible and free. And they offer many different pictures without requiring any effort (well, except maybe raising your head). A cloud can look like a dragon, a knight, a castle, puffs of smoke, a piece of cotton candy, a flower... There are an infinite number of forms. By looking at clouds in terms of symbols and their manipulation, rather than in terms of meteorology (it looks like it's going to rain!), the child develops abstract thinking.
By the way, the dialogue between Winnie the Pooh and Piglet from the Soviet cartoon is also a vivid example of abstract thinking. The bees were offered an excellent logical chain of symbols: a “cloud” in the face of Winnie the Pooh, Piglet’s umbrella, and even corresponding statements (“I am a cloud, a cloud, a cloud, and not a bear at all...”, “It seems like it’s going to rain!” ). The only problem is that the bees refused to think in symbols and preferred specifics. But that is another story.
There is a game that children almost never get tired of, and at the same time develops abstract thinking perfectly: shadow theater. What is a shadow if not a real abstraction? She is not an object, but only its symbol. But you can play with this symbol, unlike clouds - you can only watch them.
All you need for this game: a lamp, a sheet and a set of cardboard figures. You can make the figures yourself, it’s not too difficult.
Various shadow plays are performed. Any children's fairy tale is a ready-made script that requires only “actors”. Moreover, “actors” can be multifaceted. The bear from the fairy tale about Masha and the Three Bears will perfectly cope with the role in the fairy tale about Teremka. The tower itself will perfectly depict a hut in any other fairy tale. The wolf is Little Red Riding Hood, the Seven Little Goats, and the dog in “Turnip”.
Another interesting exercise is shadows on the wall. The symbol and what it symbolizes. The shadow cast by the hands takes on the shape of completely different objects. The child no longer sees hands, but a flying bird, a barking dog, a hare, and so on.
This shadow “theater” can be continued on the street. What kind of shadow will you get if you raise your arms above your head? How to make a shadow-hare? Shadow tree? Chinese pagoda?
Offer your child abstractions, invite him to create abstractions himself. Play with clouds and shadows. Maybe your future Pushkin is growing up. Or Lobachevsky. Help him grow up.
The very concept of figurative thinking implies operating with images, carrying out various operations(mental) based on ideas. Therefore, efforts here should be focused on developing in children the ability to create various images in their heads, i.e. visualize. Exercises to develop such a skill are described in sufficient detail in the section on memory development. Here we will supplement them with a few more visualization tasks.
Visualization exercises.
Assignment: you need to come up with as many associations as possible for each picture. The quantity and quality (originality) of images is assessed. The exercise is good to do with a group of children in the form of a competition.
Exercise No. 2. "Fill in the blank" type task.
Additional tasks on the development of visualization and visual-figurative thinking you can find in the section "Diagnostics of the development of thinking."
After the visualization process has been sufficiently well mastered by children, they can move on to directly operating with images, i.e. to solve the simplest mental problems based on ideas.
Exercise No. 3. Game "Cubes".
The material consists of 27 ordinary cubes, glued together so that 7 elements are obtained:
This game is mastered step by step.
The first stage is examining the elements of the game and finding their similarities with objects and shapes. For example, element 1 is the letter T, 2 is the letter G, element 3 is a corner, 4 is a zigzag lightning bolt, 5 is a tower with steps, 6 and 7 is a porch. The more associations are found, the better and more effective.
The second stage is mastering ways to connect one part to another.
The third stage is the folding of three-dimensional figures from all parts according to samples indicating the constituent elements. It is advisable to carry out the work in the following sequence: invite children to first examine the sample, then dismember it into its component elements and put together the same figure.
The fourth stage is folding three-dimensional figures according to the idea. You show the child a sample, he carefully examines it and analyzes it. Then the sample is removed, and the child must make the figure he saw from the cubes. The result of the work is compared with the sample.
Counting sticks can also be used as a material for solving mental problems based on imaginative thinking.
Exercise No. 4. "Tasks on making a given figure from a certain number of sticks."
Problems involving changing figures, to solve which you need to remove a specified number of sticks. Given a figure of 6 squares. You need to remove 2 sticks so that 4 squares remain."
“Given a figure that looks like an arrow. You need to rearrange 4 sticks so that you get 4 triangles.”
"Make two different squares from 7 sticks."
Problems whose solution involves rearranging sticks in order to modify a figure.
“In the figure, rearrange 3 sticks so that you get 4 equal triangles.”
“In a figure consisting of 4 squares, rearrange 3 sticks so that you get 3 identical squares.”
“Make a house out of 6 sticks, and then rearrange 2 sticks so that you get a flag.”
“Arrange 6 sticks so that the ship turns into a tank.”
“Move 2 sticks so that the cow-shaped figure faces the other way.”
“What is the smallest number of sticks that need to be moved to remove debris from the dustpan?”
Exercises aimed at developing visual-figurative thinking.
Exercise No. 5. "Continue the pattern."
The exercise consists of a task to reproduce a drawing relative to a symmetrical axis. The difficulty in performing often lies in the child’s inability to analyze the sample ( left side) and realize that its second part must have a mirror image. Therefore, if the child finds it difficult, in the first stages you can use a mirror (put it on the axis and see what the right side should be like).
After such tasks no longer cause difficulties in reproduction, the exercise is complicated by the introduction of abstract patterns and color symbols. The instructions remain the same:
“The artist drew part of the picture, but didn’t have time to do the second half. Finish the drawing for him. Remember that the second half should be exactly the same as the first.”
Exercise No. 6. "Handkerchief."
This exercise is similar to the previous one, but is a more complex version of it, because involves reproducing a pattern relative to two axes - vertical and horizontal.
“Look carefully at the drawing. It shows a handkerchief folded in half (if there is one axis of symmetry) or in four (if there are two axes of symmetry). What do you think, if the handkerchief is unfolded, what will it look like? Complete the handkerchief so that it looks unfolded.”
You can come up with patterns and options for tasks yourself.
Exercise No. 7. "Make a figure."
This exercise, like the previous one, is aimed at developing imaginative thinking, geometric concepts, and practical constructive spatial abilities.
We offer several variations of this exercise (from the easiest to the more complex).
a) “On each strip, mark with a cross (x) two such parts from which you can make a circle.”
This type of task can be developed for any shapes - triangles, rectangles, hexagons, etc.
If it is difficult for a child to focus on a schematic representation of a figure and its parts, then you can make a model from paper and work with the child in a visually effective way, i.e. when he will be able to manipulate the parts of the figure and thus compose the whole.
b) “Look carefully at the drawing, there are two rows of figures. In the first row there are whole figures, and in the second row the same figures, but broken into several parts. Mentally connect the parts of the figures in the second row and the figure that you have This will work, find in the first row the figures of the first and second row that fit each other, connect them with a line.”
c) “Look carefully at the pictures and choose where the parts are located from which you can make the shapes depicted on the black rectangles.”
Exercise No. 8. "Fold the figures."
The exercise is aimed at developing the ability to analyze and synthesize the relationship of figures to each other by color, shape and size.
Instructions: “What do you think will be the result when the figures are superimposed sequentially on each other on the left side of the picture. Choose the answer from the figures located on the right.”
According to difficulty (disguised relationships by form), tasks are distributed in this way: when a larger figure is superimposed on a smaller figure, which provokes the child to not assume that a larger figure will be covered by a smaller one and chooses the result of mixing the smaller and larger figures. Indeed, if a child finds it difficult to determine relationships, it is better to superimpose objects on each other not in a visual-figurative way (mental superimposition), but in a visual-effective way, i.e. direct superposition of geometric shapes.
Exercise No. 9. "Find a pattern."
a) The exercise is aimed at developing the ability to understand and establish patterns in a linear series.
Instructions: “Look carefully at the pictures and fill in the empty cell without breaking the pattern.”
b) The second version of the task is aimed at developing the ability to establish patterns in the table. Instructions: “Look at the snowflakes. Draw the missing ones so that all types of snowflakes are represented in each row.”
You can come up with similar tasks yourself.
Exercise No. 10. "Traffic light".
“Draw red, yellow and green circles in the boxes so that there are no identical circles in each row and column.”
Exercise No. 11. "We play with cubes."
The exercise is aimed at developing the ability not only to operate with spatial images, but also to generalize their relationships. The task consists of pictures of five different cubes in the first row. The cubes are arranged so that out of the six faces of each of them, only three are visible.
In the second row the same five cubes are drawn, but rotated in a new way. It is necessary to determine which of the five cubes of the second row corresponds to the cube from the first row. It is clear that in inverted cubes new icons may appear on those faces that were not visible before the rotation. Each cube from the top row must be connected by a line to its rotated image in the bottom row.
This exercise is very effective from the point of view of developing visual and figurative thinking. If operating with images causes great difficulty for a child, we recommend gluing such cubes together and doing exercises with them, starting with the simplest one - “find a correspondence between the picture depicted and the same position of the cube.”
Exercise No. 12. "Game with hoops"
The exercise is aimed at developing the ability to classify objects according to one or more properties. Before starting the exercise, a rule is established for the child: for example, arrange objects (or figures) so that all rounded figures (and only them) are inside the hoop.
After arranging the figures, you need to ask the child: “Which figures lie inside the hoop? Which figures are outside the hoop? What do you think the objects lying in the circle have in common? outside the circle?” It is very important to teach a child to designate the properties of classified figures.
The game with one hoop must be repeated 3-5 times before moving on to the game with two or three hoops.
Rules for classification: “Arrange the objects (figures) so that all the shaded ones (red, green), and only they, are inside the hoop.” “Arrange the objects (pictures) so that all denoting animate objects, and only they, are inside the hoop,” etc.
"Game with two hoops."
Formation logical operation classification according to two properties.
Before starting the exercise, four areas are established, defined on the sheet by two hoops, namely: inside both hoops (the intersection); inside the black line hoop, but outside the broken line hoop; inside the broken line hoop, but outside the black line hoop; outside of both hoops. Each of the areas can be outlined with a pencil.
Then the rule for classification is given: “It is necessary to arrange the figures so that all the shaded figures are inside the circle of the black line, and all the coal ones are inside the circle of the broken line.”
The difficulties encountered when completing this task are that some children, starting to fill the inner part of the circle from the broken line, place the shaded charcoal figures outside the circle from the black line. And then all the other shaded shapes outside the hoop from the broken line. As a result, the common part (intersection) remains empty. It is important to lead the child to understand that there are figures that have both properties at the same time. For this purpose, questions are asked: “What figures lie inside the black line hoop? outside it? What figures lie inside the broken line hoop? outside it? inside both hoops?” etc.
It is advisable to carry out this exercise many times, varying the rules of the game: for example, classification by shape and color, color and size, shape and size.
Not only figures, but also object pictures can be used for the game. In this case, a variant of the game could be as follows: “Arrange the pictures so that in a circle made of a black line there are pictures with images of wild animals, and in a hoop made of a broken line there are all small animals, etc.”
“Game with three hoops” (classification according to three properties).
The work is structured similarly to the previous one. First you need to find out into which areas the hoops of the sheet are divided. What is this area where the hoops of black and broken lines intersect; intermittent and wavy; wavy and black; the area of intersection of all three hoops, etc.
A rule is established regarding the arrangement of the figures: for example, all round figures must be inside a circle of black line; inside a hoop made of broken lines - all small, inside a circle made of wavy lines - all shaded.
Set of figures.
If a child finds it difficult to assign a figure to the desired hoop in a certain class, it is necessary to find out what properties the figure has and where it should be located in accordance with the rules of the game.
The game with three hoops can be repeated many times, varying the rules. Of interest are also the conditions under which individual regions turn out to be empty; for example, if you arrange the figures so that inside a hoop made of a black line there are all round ones, inside a hoop made from a broken line - all triangles, inside a hoop made from a wavy line - all shaded ones, etc. In these versions of the task, it is important to answer the question: why were certain areas empty?
Exercise No. 13. "Classification".
Just like the previous exercise, this is aimed at developing the ability to classify according to a certain criterion. The difference is that when performing this task, no rule is given. The child must independently choose how to divide the proposed figures into groups.
Instructions: “In front of you is a number of figures (objects). If it were necessary to divide them into groups, how could this be done?”
Set of figures.
It is important that the child, when completing this task, finds as many grounds for classification as possible. For example, this could be a classification by shape, color, size; division into 3 groups: round, triangles, quadrangles, or 2 groups: white and non-white, etc.
Exercise No. 14. "Animal Travels"
The main goal of this exercise is to use it to develop the ability to consider different ways or options for achieving a goal. Operating with objects mentally, imagining different variants their possible changes, you can quickly find a better solution.
As a basis for the exercise, there is a playing field of 9 (at least), and preferably 16 or 25 squares. Each square depicts some kind of schematic drawing that is understandable to the child and allows him to identify this square.
"Today we will play very interesting game. This is a game about a squirrel who can jump from one square to another. Let's see what little house squares we have drawn: this square with a star, this one with a mushroom, this one with an arrow, etc.
Knowing what the squares are called, we can tell which ones are next to each other and which ones are one apart from each other. Tell me, which squares are next to the Christmas tree, and which ones are one step away from it? How do the squares with the flower and the sun, the house and the bell stand, side by side or one after the other?”
After the child has mastered the playing field, a rule is introduced: how the squirrel can move from one house to another.
"The squirrel jumps across the field according to a certain rule. She cannot jump into adjacent squares, because she can only jump through one square in any direction. For example, from a cage with a Christmas tree, a squirrel can jump into a cage with a bell, a cage with a leaf and a cage with a house , and nowhere else. Where do you think a squirrel can jump if it is in a cage with a tree? Now you know how a squirrel can jump, tell me how to get from a cage with a star to a cage with a window? While working on the task, we immediately teach the child the following notes:
“In the empty cage we fill in the same pattern as on the cage that the squirrel is jumping through.” For example, in order for it to get from a cage with a star to a cage with a window, the squirrel must first jump into the cage with an arrow pointing to the right, which we draw in an empty square. But the squirrel could jump in another way: first into a cage with a tree, and then into a cage with a window, then in an empty cage it is necessary to draw a tree.
Next, the adult offers the child various options tasks in which you need to guess how a squirrel can get into the right cell by jumping according to its own rule. In this case, tasks can consist of two, three or more moves.
Options for tasks.
You can come up with variants of tasks yourself, outlining the first and final destination of the journey at which it is possible to comply with the rule. It is very important that when thinking through moves, the child can find several paths from one square to another.
Exercise "Animal Travels" using this playing field subject to change different ways. For another activity, an adult offers a game with another animal (this is a bunny, a grasshopper, a nook, etc.) and according to a different rule, for example:
1. The beetle can only move diagonally.
2. The bunny can only jump straight.
3. The grasshopper can only jump straight and only through one cell.
4. A dragonfly can only fly to a non-neighboring house, etc.
(We remind you that the number of cells on the playing field can be increased.)
And one more version of the exercise, on a different playing field.
The alphanumeric field works in the same way as the picture field. You can train on it according to the same rules or according to others you come up with yourself. In addition, these may be the following rules:
1. The goose can only walk on adjacent cells and only straight.
2. A ladybug can only fly to an adjacent cell and only with the same letter or the same number.
3. The fish can only swim to the adjacent cell with a mismatching letter and number, etc.
If the child copes well with solving problems, you can invite him to come up with a task about the journey of an animal or a task of the opposite type: “Which cell should a beetle crawl out of so that, crawling according to its rule (name the rule), it ends up in the cell for example, GZ or with a mushroom (for a picture playing field).
Verbal and logical thinking.
Verbal-logical thinking is the performance of any logical actions (analysis, generalization, highlighting the main thing when drawing conclusions) and operations with words.
Exercise No. 15. "Systematization".
The exercise is aimed at developing the ability to systematize words according to a specific feature.
“Tell me, what berries do you know? Now I will name the words, if among them you hear a word that means berry, then clap your hands.”
Words for presentation - cabbage, strawberry, apple, pear, currant, raspberry, carrot, strawberry, potato, dill, blueberry, lingonberry, plum, cranberry, apricot, zucchini, orange.
“Now I will name the words, if you hear a word related to berries, clap once, if related to fruit, clap twice.” (You can use the same words, you can come up with others.)
The basis for systematization can be a theme - tools, furniture, clothes, flowers, etc.
“Tell me, how are they similar in taste? color? size?
lemon and pear
raspberries and strawberries
apple and plum
currants and gooseberries
How do they differ in taste? color? size?"
Exercise No. 16. "Divide into groups."
“What groups do you think these words can be divided into? Sasha, Kolya, Lena, Olya, Igor, Natasha. What groups can be made from these words: pigeon, sparrow, carp, tit, pike, bullfinch, pike perch.”
Exercise No. 17. "Choose your words."
1) “Choose as many words as possible that can be classified as wild animals (pets, fish, flowers, weather conditions, seasons, tools, etc.)".
2) Another version of the same task. We write two columns of words that can be attributed to several groups of concepts. Assignment: connect words that match the meaning with arrows.
Such tasks develop the child’s ability to identify generic and specific concepts and form inductive verbal thinking.
Exercise No. 18. "Find a common word."
This task contains words that have a common meaning. We must try to convey this general meaning in one word. The exercise is aimed at developing a function such as generalization, as well as the ability to abstract.
"What in general terms The following words can be mentioned:
1. Faith, Hope, Love, Elena
2. a, b, c, c, n
3. table, sofa, armchair, chair
4. Monday, Sunday, Wednesday, Thursday
5. January, March, July, September."
Words for finding a generalizing concept can be selected from any groups, more or less specific. For example, the general word may be “spring months”, or it may be “months of the year”, etc.
A more complex version of the exercise contains only two words for which you need to find a common concept.
"Find what the following words have in common:
a) bread and butter (food)
b) nose and eyes (parts of the face, sensory organs)
c) apple and strawberry (fruits)
d) clock and thermometer (measuring instruments)
e) whale and lion (animals)
e) echo and mirror (reflection)"
Such exercises stimulate the child’s thinking to search for a generalizing basis. The higher the level of generalization, the better developed the child’s ability to abstract.
The following exercise is very effective from the point of view of developing the generalizing function.
Exercise No. 19. "Unusual Domino"
This exercise is aimed at gradually (level-by-level) teaching the child to search for signs by which generalization can occur.
Empirically, three areas of such signs are distinguished.
The first sphere is generalization according to the attributive property (the most low level). This includes: the shape of the object, its size, the parts from which it is made, or material, color, i.e. everything that is some external qualities or attributes of an object. For example, “a cat and a mouse fit together because they have four paws” or “an apple and a strawberry, they have in common that they are red...”. In addition, it can be the use of the name of the object, for example, "... a plate and a basin, the common thing is that both objects begin with the letter "t".
The second area is generalization on a situational basis (more high level). The transition to this area is the generalization of objects according to the attribute “property - action”, i.e. The child identifies the action produced by objects as a general property.
For example, “the frog approaches the squirrel because they can jump.” In addition, generalizations regarding the situation of use “pear and carrot, because both are eaten...”; situations of place and time of stay - “a cat and a mouse, because they live in the same house”; communication situations, games - “a puppy and a hedgehog, because they play together...”.
The third sphere is generalization on a categorical basis (the highest). This is a generalization based on the class to which objects belong. For example, a ball and a bear are toys; spider and butterfly, what they have in common is that they are insects.
The “domino” exercise allows the child to choose the basis for generalization (thus the adult can get an idea of the level of development of this function in the child), as well as guide and help the child look for more significant, higher-level signs for generalization.
Two or more children can take part in the game. In addition, an adult himself can be a participant in the game.
The game consists of 32 cards, each of which shows two pictures.
1. tractor - deer
2. bucket - zebra
3. puppy - mouse
4. cat - doll
5. girl - bear
6. elephant - Christmas tree
7. fungus - carrots
8. pear - snail
9. spider - duckling
10. fish - month
11. monkey - flower
12. butterfly - pig
13. squirrel - pyramid
14. ball - poppy
15. bird - vase
16. calf - plane
17. helicopter - chicken
18. hedgehog - mill
19. house - apple
20. rooster - strawberry
21. hare - cherry
22. strawberry - stork
23. penguin - frog
24. sun - caterpillar
25. leaf - fly agaric
26. plums - lion
27. lion cub - boat
28. cart - cup
29. teapot - pencil
30. dog - birch
31. kitten - orange
32. kennel - beetle
Each participant in the game is dealt the same number of cards. After this, the right to move first is played.
The one who walks lays out any card. Then the organizer of the game says: “In front of you lies a card with a picture.... In order to make a move, it is necessary to pick up some of your cards, but with the condition that the picture you choose has something in common with the one to which you picked her up."
(In order to avoid the child completing the task in only one way, it is necessary to explain how the selection can be made. In addition, during the game, it is necessary to constantly stimulate the child with questions like “What else can be common between the selected pictures?”, to choose different bases for generalization) .
“At the same time, you must explain why such a choice was made, say what is common between the selected pictures. The next one of you will again match the picture to one of the two on the line, explaining your choice.”
Thus, as a result of the game, a chain of pictures is built that are logically connected to each other. We remind you that, as in regular dominoes, the double-sidedness of the pictures provides the possibility of moving in both one and the other direction.
Points are awarded for each move. If the generalization is made on an attribute basis - 0 points, on a situational basis - 1 point, on a categorical basis - 2 points. The one who scores the most points wins.
The guys do not show the cards that the players receive during distribution to each other.
Logic problems.
Logical tasks are a special section for the development of verbal and logical thinking, which includes a number of different exercises.
Logical tasks involve the implementation thought process associated with the use of concepts and logical constructions that exist on the basis of linguistic means.
In the course of such thinking, a transition occurs from one judgment to another, their relationship through the mediation of the content of some judgments by the content of others, and as a result, a conclusion is formulated.
As S.L. Rubinstein noted, “in inference... knowledge is obtained indirectly through knowledge without any borrowing in each individual case from direct experience.”
When developing verbal-logical thinking through solving logical problems, it is necessary to select tasks that would require inductive (from individual to general), deductive (from general to individual) and traductive (from individual to individual or from general to general, when premises and conclusion are judgments of the same generality) inferences.
Traductive reasoning can be used as the first stage of learning the ability to solve logical problems. These are tasks in which, due to the absence or presence of one of two possible signs for one of the two objects under discussion, a conclusion follows about, respectively, the presence or absence of this feature in the other object. For example, “Natasha’s dog is small and fluffy, Ira’s is big and fluffy. What is the same about these dogs? What is different?”
Problems to solve.
1. Sasha ate a large and sour apple. Kolya ate a large and sweet apple. What is the same about these apples? miscellaneous?
2. Masha and Nina looked at the pictures. One girl looked at pictures in a magazine, and another girl looked at pictures in a book. Where did Nina look at the pictures if Masha didn’t look at the pictures in the magazine?
3. Tolya and Igor were drawing. One boy drew a house, and the other a branch with leaves. What did Tolya draw if Igor did not draw the house?
4. Alik, Borya and Vova lived in different houses. Two houses had three floors, one house had two floors. Alik and Borya lived in different houses, Borya and Vova also lived in different houses. Where did each boy live?
5. Kolya, Vanya and Seryozha were reading books. One boy read about travel, another about war, a third about sports. Who read what if Kolya didn’t read about war and sports, and Vanya didn’t read about sports?
6. Zina, Lisa and Larisa were embroidering. One girl embroidered leaves, another - birds, the third - flowers. Who embroidered what if Lisa didn’t embroider leaves and birds, and Zina didn’t embroider leaves?
7. The boys Slava, Dima, Petya and Zhenya planted fruit trees. Some of them planted apple trees, some - pears, some - plums, some - cherries. What did each boy plant if Dima didn’t plant plum trees, apple trees and pears, Petya didn’t plant pears and apple trees, and Slava didn’t plant apple trees?
8. The girls Asya, Tanya, Ira and Larisa went in for sports. Some of them played volleyball, some swam, some ran, some played chess. What sports was each girl interested in if Asya didn’t play volleyball, chess or run, Ira didn’t run or play chess, and Tanya didn’t run?
These eight problems have three levels of difficulty. Problems 1-3 are the simplest; to solve them, it is enough to operate with one judgment. Problems 4-6 are of the second degree of difficulty, since solving them requires comparing two judgments. Problems 7 and 8 are the most difficult, because To solve them, three judgments must be correlated.
Usually, the difficulties that arise when solving problems from 4 to 8 are associated with the inability to retain in the internal plan, in the mind, all the circumstances indicated in the text, and they get confused because they are not trying to reason, but strive to see and present the correct answer. An effective technique in this case is when the child has the opportunity to rely on visual representations that help him retain all the textual circumstances.
For example, an adult can make pictures of houses (task No. 4). And then, based on them, carry out reasoning of the following type: “If Alik and Borya lived in different houses, then in which of those drawn could they live? Why not in the first two? Etc.
It is more convenient to make a table for problems 7 and 8, which will be filled in as the reasoning progresses.
“It is known that Dima did not plant plum trees, apple trees and pears. Therefore, we can put a dash next to these trees next to Dima. Then what did Dima plant? That’s right, there was only one free cell left, i.e. Dima planted cherries. Let’s put in this cell there is a "+" sign, etc."
A graphic reflection of the structure of the course of reasoning helps the child understand general principle constructing and solving problems of this type, which subsequently makes the child’s mental activity successful, allowing him to cope with problems of a more complex structure.
The next version of the problems contains the following starting point: if three objects and two characteristics are given, one of which is possessed by two objects, and the other by one, then, knowing which two objects differ from the third according to the specified characteristics, one can easily determine which characteristic the first two have . When solving problems of this type, the child learns to perform the following mental operations:
Draw a conclusion about the identity of two objects out of three based on the specified criterion. For example, if the condition says that Ira and Natasha and Natasha and Olya embroidered different pictures, then it is clear that Ira and Olya embroidered the same one;
Draw a conclusion about what is the characteristic by which these two objects are identical. For example, if the problem says that Olya embroidered a flower, therefore, Ira also embroidered a flower;
Draw a final conclusion, i.e. Based on the fact that two out of four objects are already known that are identical according to one of the two data in the feature task, it is clear that the other two objects are identical according to the other of the two known features. So, if Ira and Olya embroidered a flower, then the other two girls, Natasha and Oksana, embroidered a house.
Problems to solve.
1. Two girls planted trees, and one - flowers. What did Tanya plant if Sveta and Larisa and Larisa and Tanya planted different plants?
2. Three girls drew two cats and one hare, each with one animal. What did Asya draw if Katya and Asya and Lena and Asya drew different animals?
3. Two boys bought stamps, one bought a badge and one bought a postcard. What did Tolya buy if Zhenya and Tolya and Tolya and Yura bought different items, and Misha bought a badge?
4. Two boys lived on one street, and two on another. Where did Petya and Kolya live, if Oleg and Petya and Andrey and Petya lived on different streets?
5. Two girls played with dolls, and two played with a ball. What did Katya play if Alena and Masha and Masha and Sveta played different games, and Masha played ball?
6. Ira, Natasha, Olya and Oksana embroidered different pictures. Two girls embroidered a flower, two girls embroidered a house. What was Natasha embroidering if Ira and Natasha and Natasha and Olya were embroidering different pictures, and Oksana was embroidering a house?
7. The boys read different books: one - fairy tales, the other - poetry, the other two - stories. What did Vitya read if Lesha and Vitya and Lesha and Vanya read different books, Dima read poetry, and Vanya and Dima also read different books?
8. Two girls played the piano, one the violin and one the guitar. What did Sasha play if Yulia played the guitar, Sasha and Anya and Marina and Sasha played different instruments, and Anya and Yulia and Marina and Yulia also played different instruments?
9. Two girls swam quickly and two slowly. How did Tanya swim if Ira and Katya and Ira and Tanya swam at different speeds, Sveta swam slowly, and Katya and Sveta also swam at different speeds?
10. Two boys planted carrots and two boys planted potatoes. What did Seryozha plant, if Volodya planted potatoes, Valera and Sasha and Sasha and Volodya planted different vegetables, and Valera and Seryozha also planted different vegetables?
Comparison problems.
This type of problem is based on such a property of the relationship between the quantities of objects as transitivity, which consists in the fact that if the first member of the relation is comparable to the second, and the second to the third, then the first is comparable to the third.
You can start learning to solve such problems with the simplest ones, which require answering one question and are based on visual representations.
1. “Galya is more fun than Olya, and Olya is more fun than Ira. Draw Ira’s mouth. Color the mouth of the funniest girl with a red pencil.
Which girl is the saddest?
2. “Inna’s hair is darker than Olya’s. Olya’s hair is darker than Anya’s. Color the hair of each girl. Sign their names. Answer the question, who is the fairest?”
3. “Tolya is taller than Igor, Igor is taller than Kolya. Who is taller than everyone? Show the height of each boy.”
A graphical representation of a transitive relation of quantities greatly simplifies the understanding of the logical structure of the problem. Therefore, when a child finds it difficult, we advise using the technique of depicting the ratio of quantities on a linear segment. For example, given the task: “Katya is faster than Ira, Ira is faster than Lena. Who is the fastest?” In this case, the explanation can be structured as follows: “Look carefully at this line.
On one side are the fastest children, on the other - the slowest. If Katya is faster than Ira, then where do we place Katya and where do we put Ira? That's right, Katya will be on the right, where the fast children are, and Ira will be on the left, because... she is slower. Now let's compare Ira and Lena.
We know that Ira is faster than Lena. Where do we then place Lena in relation to Ira? That's right, even further to the left, because... she is slower than Ira.
Look carefully at the drawing. Who is the fastest? and slower?"
Below we present options for logical tasks, which are divided into three groups according to the degree of complexity:
1) tasks 1-12, which require answering one question;
2) tasks 12-14, in which you need to answer two questions;
3) tasks 15 and 16, the solution of which involves answering three questions.
Task conditions differ not only in the amount of information that needs to be sorted out, but also in its observable features: types of relationships, different names, a question posed differently. Of particular importance are “fairytale” problems in which the relationships between quantities are constructed in a way that does not happen in life. It is important that the child is able to escape from life experience and use the conditions given in the task.
Task options.
1. Sasha is sadder than Tolik. Tolik is sadder than Alik. Who's the most fun?
2. Ira is more careful than Lisa. Lisa is more careful than Natasha. Who is the neatest?
3. Misha is stronger than Oleg. Misha is weaker than Vova. Who is the strongest?
4. Katya is older than Seryozha. Katya is younger than Tanya. Who is the youngest?
5. The fox is slower than the turtle. The fox is faster than the deer. Who's the fastest?
6. The hare is weaker than the dragonfly. The hare is stronger than the bear. Who is the weakest?
7. Sasha is 10 years younger than Igor. Igor is 2 years older than Lesha. Who is the youngest?
8. Ira is 3 cm lower than Klava. Klava is 12 cm taller than Lyuba. Who is tallest?
9. Tolik is much lighter than Seryozha. Tolik is a little heavier than Valera. Who is the lightest?
10. Vera is a little darker than Luda. Vera is much brighter than Katya. Who is the brightest?
11. Lesha is weaker than Sasha. Andrey is stronger than Lesha. Who is stronger?
12. Natasha is more fun than Larisa. Nadya is sadder than Natasha. Who's the saddest?
13. Sveta is older than Ira and shorter than Marina. Sveta is younger than Marina and taller than Ira. Who is the youngest and who is the shortest?
14. Kostya is stronger than Edik and slower than Alik. Kostya is weaker than Alik and faster than Edik. Who is the strongest and who is the slowest?
15. Olya is darker than Tonya. Tonya is shorter than Asya. Asya is older than Olya. Olya is taller than Asya. Asya is lighter than Tonya. Tonya is younger than Olya. Who is the darkest, the shortest and the oldest?
16. Kolya is heavier than Petya. Petya is sadder than Pasha. Pasha is weaker than Kolya. Kolya is more fun than Pasha. Pasha is lighter than Petya. Petya is stronger than Kolya. Who is the lightest, who is the most fun, who is the strongest?
All the variants of logical tasks we have considered are aimed at creating conditions in which there is or would be the possibility of developing the ability to identify significant relationships between objects and quantities.
In addition to the tasks listed above, it is advisable to offer the child tasks that lack some of the necessary data or, conversely, contain unnecessary data. You can also use the technique of independently composing problems by analogy with this one, but with other names and a different attribute (if the problem has the attribute “age”, then it can be a problem about “height”, etc.), as well as problems with missing and redundant data. It makes sense to transform direct problems into inverse ones and vice versa. For example, a direct task: “Ira is taller than Masha, Masha is taller than Olya, who is taller than everyone?”; in the inverse problem the question is: “Who is the lowest?”
If a child successfully copes with all types of tasks offered to him, it is advisable to offer tasks related to a creative approach:
- come up with a task that is as different as possible from the sample task, but is built on the same principle as it;
- come up with a task that would be more difficult, for example, would contain more data than the sample;
- come up with a task that would be simpler than the sample task, etc.
Exercise No. 20. "Anagram".
This exercise is based on the following problems: combinatorial type, i.e. those in which the solution is obtained as a result of creating certain combinations. An example of such combinatorial problems are anagrams - letter combinations from which it is necessary to form meaningful words.
Invite your child to make a word from a certain set of letters. Start with 3 letters, gradually increasing the number to 6-7, and maybe 8 or even 9 letters.
After the child has mastered the principle of making words from letter combinations, complicate the task. To this end, introduce a new condition: “Decipher what words are hidden here, and tell me which word from the data is the odd one out.”
The task can be of another type: “Decipher the words and tell me what common word they can be combined with.”
Another version of the task with anagrams: “Decipher the words and tell me into what groups they can be divided.”
This exercise is very similar to our usual puzzles.
Of course, the rebus is the same combinatorial task that can be effectively used for the development of verbal and logical thinking: crosswords teach the child to focus on defining a concept based on the described features, tasks with numbers - to establish patterns, tasks with letters - to analyze and synthesize various combinations. Let's give another similar exercise.
Exercise No. 21. "Twin words"
This exercise is associated with such a phenomenon of the Russian language as homonymy, i.e. when words have different meaning, but identical in spelling. "Which word means the same thing as the words:
1) a spring and what opens the door;
2) a girl’s hairstyle and a tool for cutting grass;
3) a branch of grapes and a tool used for drawing.
Come up with words that sound the same but have different meanings."
Additional tasks for the exercise:
4) a vegetable that makes people cry and a weapon for shooting arrows (a burning vegetable and a small weapon);
5) part of a gun and part of a tree;
6) what they draw on, and greenery on the branches;
7) a lifting mechanism for construction and a mechanism that needs to be opened for water to flow.
Abstract logical thinking.
The functioning of this type of thinking occurs based on concepts. Concepts reflect the essence of objects and are expressed in words or other signs. Typically this type of thinking only begins to develop in childhood school age, however, the program already includes tasks that require solutions in the abstract-logical sphere. This determines the difficulties that children have in the process of mastering educational material. We offer the following exercises, which not only develop abstract logical thinking, but also, in their content, meet the basic characteristics of this type of thinking.
Exercise No. 22. "Formation of concepts based on abstraction and identification of essential properties of specific objects."
“A car runs on gasoline or other fuel; a tram, trolleybus or electric train runs on electricity. All of this together can be classified as “transport.” When they see an unfamiliar car (for example, a truck crane), they ask: what is it? Why?”
Similar exercises are performed with other concepts: tools, dishes, plants, animals, furniture, etc.
Exercise No. 23. “Developing the ability to separate the form of a concept from its content.”
“Now I will tell you words, and you will answer me, which is more, which is smaller, which is longer, which is shorter.
- Pencil or pencil? Which one is shorter? Why?
- Cat or whale? Which one is bigger? Why?
- Boa constrictor or worm? Which one is longer? Why?
- Tail or ponytail? Which one is shorter? Why?"
The teacher can come up with his own questions based on the ones above.
Exercise No. 24. "Developing the ability to establish connections between concepts."
The exercise below involves identifying the relationships in which these words are found. An approximate pair of words serves as a key to identifying these relationships. Knowing them, you can match the control word. Work with this exercise is carried out jointly by an adult and a child. The adult’s task is to lead the child to a logical choice of connections between concepts, the ability to consistently identify essential features to establish analogies. Each task is thoroughly analyzed: a logical connection is found, transferred to the word given next to it, the correctness of the choice is checked, and examples of such analogies are given. Only when children have developed a stable and consistent ability to establish logical associations can they move on to tasks for independent work.
Exercise No. 25. “Formation of the ability to identify essential features to maintain logical judgments when solving a long series of similar problems.”
The adult says to the children: “Now I will read you a series of words. From these words you will have to choose only two, denoting the main features of the main word, i.e., something without which this object cannot exist.
Other words are also related to the main word, but they are not the main ones. You need to find the most important words. For example, garden... Which of these words do you think are the main ones: plants, gardener, dog, fence, earth, i.e. something without which a garden cannot exist? Can there be a garden without plants? Why?.. Without a gardener... a dog... a fence... land?.. Why?"
Each of the suggested words is analyzed in detail. The main thing is for children to understand why this or that word is the main, essential feature of a given concept.
Sample tasks:
a) Boots (laces, sole, heel, zipper, shaft)
b) River (shore, fish, fisherman, mud, water)
c) City (car, building, crowd, street, bicycle)
d) Barn (hayloft, horses, roof, livestock, walls)
e) Cube (corners, drawing, side, stone, wood)
f) Division (class, dividend, pencil, divider, paper)
g) Game (cards, players, fines, penalties, rules)
h) Reading (eyes, book, picture, print, word)
i) War (plane, guns, battles, guns, soldiers)
This exercise allows you to focus your search for a solution, activate your thinking, and create a certain level of abstraction.
Work on developing in children the ability to identify essential features of concepts and establish various relationships prepares favorable soil for the development of abilities to form judgments as a higher stage in the development of abstract logical thinking. The purposefulness of judgments and the degree of their depth depend on the child’s ability to operate with meaning and understand figurative meaning. For this work, you can use various literary materials, proverbs, sayings, which contain the possibility of verbalization and transformation of the text.
Exercise No. 26. "Formation of the ability to operate with meaning."
“Now I’ll read you a proverb, and you try to find a suitable phrase for it that reflects the general meaning of the proverb, for example:
Seven measure it once and cut once
a) If you cut it incorrectly, you shouldn’t blame the scissors
b) Before you do, you need to think carefully
c) The seller measured seven meters of fabric and cut it
Right choice here - “Before you do, you need to think carefully,” and the scissors or the seller are only details and do not reflect the main meaning.”
Sample tasks:
1. Less is more.
a) One good book reading is more useful than seven bad ones.
b) One tasty pie is worth ten bad ones.
c) It is not quantity that matters, but quality.
2. If you hurry, you will make people laugh.
a) The clown makes people laugh.
b) To do a job better, you need to think carefully about it.
c) Haste can lead to absurd results.
3. Strike while the iron is hot.
a) A blacksmith forges hot iron.
b) If there are favorable opportunities for business, you must immediately take advantage of them.
c) A blacksmith who works slowly often gets more done than one who is in a hurry.
4. There is no point in blaming the mirror if your face is crooked.
a) You shouldn’t blame the reason for failure on circumstances if it’s about you.
b) Good quality The beauty of a mirror depends not on the frame, but on the glass itself.
c) The mirror hangs crookedly.
5. The hut is not red in its corners, but red in its pies.
a) You can’t eat pies alone; you must also eat rye bread.
6) A case is judged by its results.
c) One tasty pie is worth ten bad ones.
Teachers have to deal with at different levels intellectual development of children. Some of them are “stuck” at the stage of visual-effective thinking. Therefore, in learning they can only use rote learning and relatively accurate reproduction of the information received from the teacher. This is largely the fault of parents who do not want to be educated in matters of child development. We cannot come to terms with this situation, and therefore we present our judgments about COGNITION to the readers.
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Abstract thinking - highlighting some features and abstracting from others that are insignificant in this moment or for this person. Without the development of this type of thinking, it is impossible to become a successful person.
Success here means the personal feeling that a person manages to build his life according to his own goals and with his own strength for the benefit of himself and others. Success should not be confused with prestige. Prestige is a socially determined idea of a decent life. It may conflict with a person's spiritual needs. The right to choose is up to the person himself.
Abstract thinking in creativity involves going beyond real data, finding new connections and relationships between objects, and a broad but targeted mobilization of knowledge and experience.
Stages of developing a child’s thinking:
Visually effective (up to 3 years),
- visual-figurative (up to 9 years),
- verbal-logical (abstract) (by the age of 14).
The development of a child’s thinking begins with information presented in the form of a question or task. Parents will find many reasons to communicate with their child in this regard if they realize the importance of abstract thinking for the child’s fate.
Until the age of nine, children live in a magical world; they cannot be rushed into realizing reality; everything has its time. And this period is necessary for the development of imagination, fantasy - the basis creative activity person. It is very interesting for a child to “pick mushrooms on the asphalt”, imagining that he is in the forest; “to feed mother, according to her order, with various foods from river sand,” his ideas will flow if his parents support him in play activities.
By the way, a child under 9 years old is not yet ready for the freedom to choose his actions and responsibility for his choice. His actions are often impulsive or dictated by fear of punishment. If adults create such difficult circumstances of choice for a child, the child experiences psychological anxiety and uncertainty.
The need for protection is strongest at this age, so the child needs “strong” parents to guide him.
To develop a child’s thinking, an adult should not rush to answer some “why?” child, but ask “What do you think?”, and guide his “thinking”. As a result, children preschool age They show an early interest in games that develop intelligence; they like to solve riddles, answer tricky questions and write them themselves.
There is no need to overload a child with different information; it is better to teach him to think about what is available to him at his age. At this age, abstract thinking should be based on visual-figurative thinking, on the child’s acquired life experience.
Starting from the age of nine, you can directly ask about his moods, desires, teach him to correlate needs with opportunities and the consequences of their implementation - this is how the experience of freedom of choice is acquired.
Teenagers from 12 to 14 years old, it’s time to ask what they think about any problem and what ways they see to solve it. At this age it is already possible to make decisions on your own. You just need to make it clear to the teenager that making mistakes is normal. By correcting them, a person becomes wiser. This is the norm mental development personality.
Ideal in knowledge - WISDOM , and not erudition, which is based, rather, on memory as a property of the natural mind. Wisdom combines all the spiritual qualities of a person (sometimes in the absence of an official certificate of education).
