Introduction to abstract logical thinking. Stages of development of thinking. We develop imaginative, abstract and logical thinking

Abstract thinking is of great importance to all people. The high level of its development allows not only to improve the quality of life, but also to achieve much greater success. You should develop this type of thinking already in childhood, but you should not stop training as you grow up. Only regular exercise will improve and maintain your intellectual abilities. Knowing how to develop abstract thinking in adults and children will help with this. All methods can be put into practice independently, without resorting to outside help.

Forms

Abstraction is the abstraction of some properties of objects from others in order to identify their features. The definition of abstract thinking is almost the same. This phenomenon refers to a type of intellectual activity during which a person thinks about a situation, separating it from some details. Abstractness has a significant impact on the physiology of thinking and allows you to cross certain boundaries, discovering new knowledge.

This type of thinking develops in parallel with ontogenesis from an early age. It first appears at the moments when the child begins to fantasize, composing his own stories or acting out unusual situations, and abstracts himself from toys, preferring to think about their certain properties.

Abstract thinking is divided into forms, each of which corresponds to the characteristics of the thought process accompanied by abstraction. There are 3 of them in total:

1. Concept. Involves defining one common property for different objects. A very important point is the significance of this unifying feature. For example, the legs of tables or green leaves of different trees.
2. Judgment. In judgment, an affirmation or denial of a certain event occurs. Everything is usually described in a phrase or short sentence. Judgments can be simple or complex. In the first case, they relate to one active object or person (for example, “the boy bought milk”). In the second, the judgment affects several sides at once (“clouds appeared, it became dark outside”). It can also be true, based on subjective conclusions, or false, based on personal interest.
3. Conclusion. Inference is understood as a thought, the formation of which occurs on the basis of several judgments. It consists of premises, conclusion and conclusion. All three processes occur sequentially in the human head. It all starts with initial judgments (premises), then moves to the stage of reflection (conclusions), and ends with the formation of a new judgment (conclusion).

Abstract thinking can be used in any of these three forms. An adult uses them all in everyday life. Nevertheless, it is imperative to develop them even for those who are good at abstraction.

Modern artificial intelligence is endowed with abstract thinking that is superior in quality to human thinking.

Peculiarities

Abstract thinking is used by children from the first years of life. It begins to appear along with the development of articulate speech. A younger child fantasizes, thinks about unusual things, explores the world, compares his toys, using abstraction skills. They are underdeveloped, but you can still use them.

School age is combined with an increase in the importance of abstract thinking. The student will need to think outside the box when faced with solving various problems. This is especially true in mathematics, where abstraction plays a big role. Later, when the teenager is in high school, the importance of such thinking will become even greater.

Abstract thinking is also used in philosophy, writing, engineering, managerial psychology, time management and many other areas. Its good development allows you to achieve success in any field.

Signs

Thinking with abstraction has its own characteristic features. They allow us to distinguish it from other thought processes and better understand why abstraction is so useful for a person.

Signs:

1. Reflection of the surrounding world without using the senses. A person does not need to use his senses or contact an object to obtain information about it. It is abstraction that allows you to use old existing knowledge to solve a particular problem.
2. Generalization of phenomena. By summarizing various objects and identifying their characteristic features, a person is able to quickly access his knowledge. If he is able to identify certain patterns and similarities, then in the future it will be much easier to remember and find the necessary information in memory.
3. Linguistic expression. All thoughts are easily expressed in the form of internal dialogue, which can be translated into real life. In this case, abstract concepts can be thought through in the head without the use of linguistic expression at all, and the result will be a final judgment that will be easy to express in speech.

The development of abstract thinking allows you to improve all of the characteristics listed above, which are also useful skills, without which it is difficult to achieve success.

Impact on humans

It is difficult for the average person to imagine exactly what someone with highly developed abstract thinking looks like. Such people, as a rule, always achieve their goals, they are successful and happy. At the same time, something is always happening in their heads: they reason, think about events, imagine the future figuratively, and solve difficult problems. Most often, they speak a complex language, which causes difficulties in communication. Their high efficiency allows them to occupy high positions, and their developed intelligence makes them very important for any company.

Such people may face a number of problems. They are often too selfish, which makes it difficult for them to find true friends. At the same time, people with developed abstract thinking cannot show enough physical activity and are passive in practical work. Sometimes they are careless in appearance, which alienates others.

Most often, men in technical professions have developed abstract thinking.

Exercises for adults

It is quite difficult for an adult to develop abstract thinking, because... his intellect has long been formed. However, with the help of some exercises you can still achieve results. It is recommended to perform them daily for several weeks.

The most effective exercises:

1. Representation of emotions. You need to mentally imagine exactly how different emotions manifest themselves in a certain person. It is recommended to use the full range of people's possible feelings.
2. Reverse reading. You need to turn the book over and read it in reverse order. In parallel with this, it is necessary to establish logical connections between various events. It is best to choose simple works written in easy language.
3. Analysis of communication. You should remember all the people with whom you had to communicate during the day. It is necessary to analyze not only the conversation itself, but also the facial expression, gestures and voice of the interlocutor. It is recommended to do this with your eyes closed.
4. Inventing contradictions. You just need to come up with different phrases that seem contradictory. They can be absolutely anything (hot ice, bitters, etc.).
5. Compiling abbreviations. It is enough to come up with any phrase, shorten it to the first letters, and then decipher it throughout the day. For example, independent development of thinking (SDM).
6. Listing the functions of objects. You need to select any existing item and list all its functions. You can even come up with unusual purposes that are not usually used.
7. Brainstorm. You need to choose any letter of the alphabet and write it on a piece of paper. The task is to remember the maximum number of words starting with this letter in a limited amount of time, writing them all down on paper.
8. Combination of words. You need to write nouns on one piece of paper, and adjectives on the second. This does not need to be done right away. It's best to start with just one noun. You will need to select suitable, as well as completely incompatible adjectives for it. All of them should be written down in different columns.
9. Title of a painting from life. It is required to visually record any event that happened in reality and give it an unusual name. It should be what an artist might call a painting.
10. Painting. You need to paint any pictures using colored paints. During the process, the characteristics of all present items should be presented. If it is not possible to use paints, you can start with regular pencil drawing.

The listed methods will help develop abstract thinking also in a teenager or an elderly person. You just need to apply them on a regular basis, without missing regular classes.

Exercises for children

It is easiest to develop in childhood. At this time, the brain is open to external influences and can undergo any changes. Exercises for children differ from those offered to adults, but are no less effective.

Best exercises:

1. Reverse reading of inscriptions. Parents should invite their child to play a game in which they read the signs they see in reverse order. It will be very difficult to do this with all the advertising posters. Therefore, additional conditions should be negotiated (for example, read only red signs).
2. Drawing unusual animals. The child must draw an animal consisting of parts of other animals. When the drawing is ready, you need to come up with an unusual name for the new species.
3. Shadow play. With the help of his hands, on which the light from a lamp falls in the dark, the child must create unusual shadows depicting certain things. You can even invite him to act out his favorite fairy tale using shadows.
4. Mental arithmetic. The child will be required to calculate simple examples using special abacus called an abacus. Such training will also develop perseverance and general intelligence.
5. Puzzles. You need to choose puzzles, rebuses, anagrams, etc. games, taking into account the baby's preferences. His task will be to solve all the problems provided. At an older age, you can add crosswords to them.
6. Studying clouds. The child should look at the clouds together with his parents and name what exactly he sees. The ability to visually evaluate each cloud for its similarity to different objects or animals increases the chances of successful development.
7. Construction. Parents need to give their baby a task, which involves building certain objects from toy blocks. This will help develop imaginative thinking and creativity.
8. Associations. The baby needs to come up with associations for everything he sees or feels. You can also ask him to imagine animals by hearing the sounds they make.
9. Classification. The child needs to sort all available things or toys according to certain criteria. For example, by shape, weight or purpose. Parents should monitor the process and give hints if necessary.
10. Questions. Parents should ask their child “why?” and “what if?” questions. etc. to make him think and analyze the situation. You can ask at any time.

Such simple exercises will allow you to achieve good results in a few weeks of training. It is recommended to combine them with other activities that will be aimed at developing general intelligence.

Thinking- a tool that every person has who solves various problems in life. Thinking can be developed, its speed, depth, freedom, and meaningfulness can be changed. Also, thinking can become more interesting and positive.

Development of logical thinking

Logical thinking very useful for every person. It will facilitate the understanding of any laws in science or society. Logic is often needed in everyday life.

The brain needs constant training to maintain its mental activity, to have good thinking and memory. Regular exercise can improve your thinking skills.

Have fun with benefits

1. Start solving logic puzzles for children and adults (puzzles, find 10 differences, attention riddles).
2. Find games that develop attention and logic that you can play with friends and no matter how old you are, it will be fun and have a good time with friends.
3. Use IQ tests. There are interesting tasks that require quite a bit of logical thinking. Although there are many others besides IQ tests.

Educate yourself

For example, you can start with the mega-useful course “Money and the Millionaire Mindset.”

Development of critical thinking

Critical thinking is a step towards active, creative methods. What is critical thinking?

1. Thinking is independent, and the owner puts his own ideas, evaluates the situation, has his own beliefs independently of others.
2. Receiving information is just the beginning, and the end will be processing, that is. generating a complex thought as a conclusion. Another thought is subjected to critical reflection.
3. This kind of thinking starts with asking questions and identifying problems.
4. Critical thinking is convincing arguments, evidence, conclusion.
5. This kind of thinking helps to exchange opinions and points of view.

How to develop critical thinking?

1. Evaluate reality. Reality is a world independent of your desires. Your thinking will be most effective if you learn to understand and “translate” this reality.
2. Mass hobbies. A concept becomes popular, a large number of people accept it, that is, they create a crowd. And there can be no talk of critical thinking there, but only of consistency. Think before you join.
3. Draw parallels between observation and inference.
4. Don't judge a situation or person until you are sure of your information.
5. Don't lose your sense of humor.
6. Be curious. There are many unknown, interesting, shocking things in the world. Having curiosity indicates intelligence. A curious person looks for new ways, ways to solve problems, for example, which gives him new opportunities.
7. Do not give free rein to your emotions, because they can cloud your mind. A striking example is anger, under the influence of which you can do things that you will regret.
8. Don't overestimate your self-esteem.
9. Learn to listen to people.
10. Use your intuition, don't ignore it. Because such thoughts may come to your mind on a subconscious level. This is the result of information that was once received, which you probably no longer remember.

Tasks for the development of thinking

1) What number is hidden under the car?

2) Find the extra figure. Only 15% of people can cope with this task.

3) Where is the bus going?

1. 87, just turn the photo over.
2. The answer is -1, because it is the standard, because the rest of the figures are modifications of it, either the shape, or the color, or the frame has been changed.
3. Even though the bus is moving forward and moving on the right side, as is customary, it is moving to the left. Because the door is not visible.

Development of speed reading

Reading quickly will always allow you to read more interesting and useful books, as well as excellent will develop thinking. Sign up for our Speed ​​Reading course in 30 days. We will teach you not only to read faster, but also to think faster, understand and remember text, as these are the basic requirements for the reading process.

Verbal counting

Learn to quickly and correctly add, subtract, multiply, divide, square numbers, and even take roots. I will teach you how to use easy techniques to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.

Money and the Millionaire Mindset

Knowledge of the psychology of money and how to work with it makes a person a millionaire. 80% of people take out more loans as their income increases, becoming even poorer. On the other hand, self-made millionaires will earn millions again in 3-5 years if they start from scratch. This course teaches you how to properly distribute income and reduce expenses, motivates you to study and achieve goals, teaches you how to invest money and recognize a scam.

Development of creative thinking

Creative thinking is thinking in which the owner finds unusual, improved or shorter, better solutions. Creative thinking will allow you to generate new ideas.

Creative thinking will give you the opportunity to try your hand at art. You might be able to find yourself in music or drawing, poetry or something unusual. For example, creating sculptures from scrap materials and so on.

We offer several interesting exercises for developing creative thinking:

1. Find a drama or horror film and remake it as a comedy.
2. Also try the opposite. Turn the comedy into a drama.
3. Come up with a script for the film. Take 2-3 pairs of people who have disagreements with each other and develop this plot.
4. Imagine any person or animal or object that could become a serial killer.

In this way, scripts for films and books can appear. And the process of such a game itself will be fun for you and the circle of people with whom you will try to discuss it. This exercise is more interesting to perform in the company of friends and acquaintances.

Development of thinking in children

The mental activity of a child has a special structure of cognition. When a baby is born, he begins to study everything around him, draw parallels, and look for connections between his discoveries. Gradually developing, the child begins to reason, imagine, a fantasy world appears, and speech not only appears, but also becomes more literate over time.

Anagrams

Gorbov-Schulte tables

Color matrix game

The “color matrix” game will be an excellent trainer for your thinking. A field of cells will open in front of you, each of which will be painted in one of two colors.

Your aim: determine which color is greater. The game, of course, is for a while and therefore you have to try. As the game progresses, the field will expand if the answers are correct or narrow if the answers are incorrect.

Game "Quick Count"

The game "quick count" will help you improve your thinking. The essence of the game is that in the picture presented to you, you will need to choose the answer “yes” or “no” to the question “are there 5 identical fruits?” Follow your goal, and this game will help you with this.

Game "Simplification"

The game “Simplification” is a wonderful simulator, not only for mental arithmetic, but also for logic. You will come across examples both simple and complex. But not everything is so complicated in reality, you just need to figure out how to simplify or find the answer from the proposed answers. To do this, you will have to think logically!

Game "Number Reach: Revolution"

An interesting and useful game “Numerical Reach: Revolution” that will help you improve and develop memory. The essence of the game is that the monitor will display numbers in order, one at a time, which you should remember and then reproduce. Such chains will consist of 4, 5 and even 6 digits. Time is limited. How many points can you score in this game?

Game "Memory Matrix"

"Memory Matrices" is a great game for training and developing memory. In the presented game you will need to remember the placement of the colored cells, and then reproduce them from memory. How many levels can you complete? Remember, time is limited!

Lessons in the development of thinking

A good exercise for creativity, as you finally fill out the field, you will understand how highly developed your thinking is. Below you will see a field of crosses. Your goal is to add a picture to each cross. Thinking, creativity and imagination come into play:

When you fill it out, pay attention to this picture (below), maybe you will find some drawing from the ones you just drew.

Also try a field not with crosses, but with other figures or, simply, with a different blank. These can be triangles, circles, squares, and so on. For example:

And another example:

Exercise - Architect

Imagine that you are an architect. Your goal is to design a house. It doesn’t matter whether you can draw or not, whether you can draw, it doesn’t matter. The essence is completely different and no less interesting. Place a piece of paper in front of you and write ten nouns on it. They can be absolutely anything: Orange, water, tomato, cloud, smoke, and so on... Then the fun begins. These ten words become the customer's terms and conditions. If it's orange, then you can paint the roof of the house orange. Water? Make a river behind the house. Tomato? Paint the floors in your house red. Here your imagination and thinking are unleashed. Try to make it as interesting as possible, make up words as complex as possible.

Technologies for the development of thinking

The technology for developing critical thinking is presented in three stages:

1. Challenge. A gap is sought in previously acquired knowledge or experience, which is now the goal of elimination. That is, a goal is set to close this knowledge gap.

2. Understanding. A person who has a serious goal of developing critical thinking must realize that it is necessary to keep a diary and draw tables in order to determine the level of understanding of a certain topic or information.

3. Reflection. At the stage of reflection, a person forms his attitude towards the text, information, book, picture. This attitude is often written down or discussed with someone. This method will help not only in developing critical thinking, but also in developing communication skills.

Development of thinking in children 4-5 years old

There are good exercises for children to help them develop and train their thinking. These are the simplest exercises that will surely help them think and apply thinking to answer the question. If the child finds it difficult, just push him.

Examples of exercises to develop thinking

Exercise 1. The child’s goal is to find the extra word. Below are rows of 4 words, and one of them is extra and your child must determine which one. Ask him the question “why did he choose this word?”

Birch, pine, linden, apple tree.
Bed, table, chest of drawers, spoon.
Oak, chamomile, rose, tulip.
Fork, spoon, chair, knife.
Candy, soup, halva, jam.
Skirt, hat, dress, slippers.
Apple, beets, pears, grapes.

Exercise 2. You come up with a word for the child, and he answers what this person needs from things. It may not be a person at all, but an animal or a bird, and the child names their elements. For example:

Sparrow - branches, grains, puddle.
Doctor - gown, mask, syringe.
Janitor - broom, bucket, rake.
Small baby - rattle, diaper, pacifier.
Dog - booth, bone, leash.
Seller - cash register, goods, calculator.
Bee - flowers, nectar, hive.
Artist - paints, brushes, canvas.
Mother - ...?
And you will learn a lot of interesting things about your status :)

Exercise 3. Name the components of certain items and objects. The task is very difficult. During the exercise, the child’s vocabulary will be replenished, since not all words are known to him yet, and you will help him with this. So:

Car - wheels, body, headlights, steering wheel (let the child name as many elements as possible) ship - ...
airplane - ...
train - ...
bike - ...
trolleybus - ...
table - ...
armchair - ...
book - ...
computer - ...
guitar - ...
piano - ...
drum - ...
house - ...
fence - ...
flower - ...
tree - ...
mushroom - ...
bug - ...
butterfly - ...
dog - ...
Human - ...
apple - ...
watermelon - ...

Development of thinking in children 6-7 years old

Exercise 1: Which vehicle is the odd one out of the four?

Exercise 2: Logical problem. Petya is stronger than Misha, but weaker than Kolya. Which of the guys is the weakest?

Exercise 3: There are three buckets: green, yellow, blue. Grandfather, grandmother and grandson carried water in different buckets (each with its own color). Grandfather's was neither green nor blue. Grandmother's is neither green nor yellow. What was the grandson's?

It would also be helpful to teach your child how to play chess. This game perfectly develops the sense of thinking, logic, mental calculation and many other senses.

For the game “chess” a lot of problems are constantly being written and invented. For example: checkmate in 1 move or checkmate in 2 moves, this can also happen in 4. The problems are very interesting, and being able to solve them means having good thinking.

Development of thinking in children 8-9 years old

The older the child gets, the more difficult the tasks should be for him. Below are exercises that will help your child tense up, think, reflect and give reasons for his answer:

Exercise 1: What can be common and what is the difference between the following pairs of words?

1. table chair
2. Bird, plane
3. Heaven, earth
4. Day Night
5. Slide, hole
6. skis, skates
7. Tree, bush

Let them explain their position.

Exercise 2: How can you seat 6 children on 2 sofas? How to seat 3 sofas? The answer should be given in numbers, and all possible answer options should be used.

Exercise 3: The child is called a series of words, and the child’s goal is to combine the words into one concept:

1. perch, crucian carp, pike (fish)
2. elephant, giraffe, ant (animals)
3. autumn, summer, winter (seasons)
4. shovel, rake, broom (tools)
5. cheese, sour cream, butter (dairy products)
6. hand, ears, legs (body parts)

Properties of thinking

There are several properties of thinking, which we discussed below:

Speed ​​of thinking

Each person has his own speed of thinking, and therefore each person copes with a task differently. There are techniques for increasing your thinking speed:

1. Do facial exercises, that is. normal warming up of the facial muscles.
2. Stop being lethargic, sleepy and with an expressionless face. The more alive you and your facial expressions, the more alive your thinking!
3. Increase the speed of internal reasoning and thoughts. This will help speed up your thinking.
4. Try to massage your head regularly. Massage stimulates the blood vessels in the brain, which improves their functioning, and at this moment great thoughts may come to your mind.
5. Speed ​​reading training. By perceiving text faster, you not only improve your reading speed, but also your thinking speed. Indeed, if you read faster and remember what you read, then your thoughts also speed up.

Meaningful thinking

The most common type of thinking is internal chatter - this is negative thinking, it “seems to fill” the spiritual emptiness, it is an illusion. Such thinking is a problem, an obstacle to concentration on any task. To keep your thinking clear, you need to perform actions with full understanding of them. It is also advisable to write down thoughts, draw, tell stories to friends, acquaintances, and relatives.

Take Notes and Drawings Get into the habit of expressing your thoughts in writing or drawings. Some people, when explaining or telling something, not only speak, but also draw, that is, they give you a picture and clarify the situation.

Tell your thoughts It will be useful to express your thoughts to others who will be really interested in it. Telling this to someone will help you get feedback. Another plus is that the more you tell your thoughts, the more clear they will be for you (if there were any points that were not clear).

DiscussDiscussing thoughts is an effective thing. One head it's good, but two better. The main thing is that the discussion does not turn into a quarrel. If you suddenly do not agree with your interlocutor’s thesis, then make up your own, but do not start a heated argument, but have a calm conversation.

Watch your speech Thinking and speech are closely related to each other. Therefore, in order to contribute to the development of thinking, it is worth constructing your speech correctly. Advice: exclude the words “problems”, “horror”, “difficult”, include “interesting”, “goal”.

Why are speech and thinking closely related? Thinking is fleeting and difficult to remember, but speech is a different story. Speech is memorable and easier to follow. Do you want to improve your thinking? Pay attention to your speech.

Pay attention to other people's speech It is easier to monitor someone else's speech than your own. Because someone else’s speech is something new and all the shortcomings and failures in logic can be heard in it. Studying the mistakes of other people's speech will help you find mistakes in your own speech.

Improve your skills in working with texts Text analysis can be compared to listening to someone else's speech. In both cases, you look for mistakes, roughness and take notes. Improved thinking depends on word processing skills.

Depth and freedom of thinking

People use their thinking in different ways and with varying degrees of freedom. It all depends on the position of perception. Depth and freedom of thinking can be represented in the form of several criteria:

1. Template thinking, as a rule, this is the view of an egoist: “Forgot - it means he doesn’t respect”, “Didn’t kiss - it means he doesn’t love” and so on.
2. My interests: Does this concern me and my plans? “I was cooking dinner, but he didn’t distract me - oh well. If I wanted to kiss, then that’s exactly what I wanted, which means I’ll kiss when he comes.”
3. Interests of loved ones: "He was in such a hurry that he even forgot to kiss me. I love him :)"
4. Objectivity: “The world is a stream of neutral events, nothing serious happened, it was just in a hurry.”
5. Systemic view: He ran to work, takes care of us! My love!
6. Angel Position: My husband works for people, and this is very important. I'm proud of him!

Efficiency of thinking

To create more effective thinking, you need to master meaningful thinking, and then master areas for increasing the efficiency of thinking:

1. Move from your worries to specifics.
2. Replace negative thinking with positive thinking.
3. Find the bridge from right thinking to productive thinking.

Thinking control

Control of thinking is primarily related to the development of thinking and higher functions of human psychology, the development of will and attention.

It happens that useless and unnecessary thoughts are spinning in your head that you want to discard. Don't bother trying to eradicate them, but try:

1. Think positively and constructively
2. Do something so that your thoughts are involved in this activity.
3. Start remembering funny moments, positive stories and pleasant things that will create a good atmosphere.

Courses for the development and training of thinking

In addition to games, we have interesting courses that will perfectly pump up your brain and improve memory, thinking, and concentration:

Money and the Millionaire Mindset

Why are there problems with money? In this course we will answer this question in detail, look deep into the problem, and consider our relationship with money from psychological, economic and emotional points of view. From the course you will learn what you need to do to solve all your financial problems, start saving money and invest it in the future.

Development of memory and attention in a child 5-10 years old

The course includes 30 lessons with useful tips and exercises for children's development. Each lesson contains useful advice, several interesting exercises, an assignment for the lesson and an additional bonus at the end: an educational mini-game from our partner. Course duration: 30 days. The course is useful not only for children, but also for their parents.

Secrets of brain fitness, training memory, attention, thinking, counting

If you want to speed up your brain, improve its functioning, improve your memory, attention, concentration, develop more creativity, perform exciting exercises, train in a playful way and solve interesting problems, then sign up! 30 days of powerful brain fitness are guaranteed to you:)

Super memory in 30 days

As soon as you sign up for this course, you will begin a powerful 30-day training in the development of super-memory and brain pumping.

Within 30 days after subscribing, you will receive interesting exercises and educational games in your email that you can apply in your life.

We will learn to remember everything that may be needed in work or personal life: learn to remember texts, sequences of words, numbers, images, events that happened during the day, week, month, and even road maps.

Speed ​​reading in 30 days

Would you like to quickly read books, articles, newsletters, etc. that interest you? If your answer is “yes,” then our course will help you develop speed reading and synchronize both hemispheres of the brain.

With synchronized, joint work of both hemispheres, the brain begins to work many times faster, which opens up much more possibilities. Attention, concentration, speed of perception intensifies many times over! Using the speed reading techniques from our course, you can kill two birds with one stone:

1. Learn to read very quickly
2. Improve attention and concentration, as they are extremely important when reading quickly
3. Read a book a day and finish your work faster

We speed up mental arithmetic, NOT mental arithmetic

Secret and popular techniques and life hacks, suitable even for a child. From the course you will not only learn dozens of techniques for simplified and quick multiplication, addition, multiplication, division, and calculating percentages, but you will also practice them in special tasks and educational games! Mental arithmetic also requires a lot of attention and concentration, which are actively trained when solving interesting problems.

Bottom line

In this article, we analyzed the features of thinking, learned how to develop thinking, what browser and board games and exercises help develop thinking.

Bubnova Ksenia Alexandrovna

Now your baby has become a first grader. Or maybe he will go to school next year, but now you are worried about the question: “Will it be difficult for my child to study? What should I pay attention to when preparing for school?” In this article I will talk about how to help your child develop abstract logical thinking. After all, good abstract logical thinking is the key to successful mastery of the school curriculum. A simple test will help you determine whether it is sufficiently developed in your child (we are talking about preschoolers and children of primary school age).

Test "Increased or decreased."
Conservation of mass.

Take two plasticine balls, 5 cm in diameter. Show them to your baby, let him make sure that each has the same amount of plasticine: “Imagine that this is pie dough. If we bake two pies from these balls, and you eat one and I eat the other, will we eat equally? Or will you eat more?” ? Or me?"

After that, take one of the balls and make a biscuit out of it (a flat oval) approximately 8 cm long: “And now the ball and the biscuit have the same amount of plasticine? Or is there more plasticine in the ball? Or in the biscuit? (Play up the situation with food). Depending on the answers You can try to confuse your child: “Look at the biscuit, it’s flat, very thin. Don't you think you can eat more in a ball?" Before you roll the biscuit into a ball again, as in the beginning, ask your child: "If I make a ball out of this biscuit, will I have as much as I do now?" Make a ball out of the biscuit and show that there is the same amount of substance left. Third procedure with plasticine: divide one of the balls into small pieces (approximately 8-10 “crumbs”), and then ask the child to compare all the resulting pieces with the ball.

Abstract logical thinking is poorly developed.
Here are the answers and explanations the child gives: “There is more in the ball because the sausage is thinner” or “There is more in the biscuit because it is longer.” This means that the baby is focused on one of the dimensions, sometimes moves from one to another, but does not connect them with each other. Reminding him of the initial amount of the substance does not change his opinion. Sometimes children suggest the possibility of returning to the same number of balls.

Abstract logical thinking is not very well developed.
The child hesitates between affirmation and denial. If you confuse him by suggesting the wrong answer, the baby does not resist.

Abstract - logical thinking is well developed. The child reasons approximately like this: “Both here and there are the same, because if you make a ball again, it will be the same.” Or: “After all, nothing was taken away or added, so it’s the same here and there.”

Test "Which word is the odd one out?"

Let your child know that you are going to play now. The extra word is hidden among words that “suit” each other in meaning. The task is to find the “inappropriate” word. Then read the first row of words.

Tulip, lily, bean, chamomile, violet.

If the child answered incorrectly, give him a chance to correct the mistake. If the answer is correct, ask the question: “Why?” The same work is carried out with the remaining rows of words. The question "Why?" is set from rows 1 to 9.

Rows of words:

1. River, lake, sea, bridge, pond.
2. Doll, jump rope, sand, ball, spinning top.
3. Table, carpet, chair, bed, stool.
4. Poplar, birch, gooseberry, linden, aspen.
5. Chicken, duck, eagle, goose, turkey.
6. Circle, triangle, pointer, square.
7. Sasha, Vitya, Stasik, Petrov, Kolya.
8. Cheerful, fast, sad, tasty, careful

If the child is not mistaken in most cases and can answer the question “Why?” (for tasks 1 - 9), his level is assessed as high, if he successfully completed half of the tasks - as average. If the level is low (the child couldn’t cope with half the tasks), you shouldn’t worry - you just need to work with the baby. Try another test.

"What do they have in common?"

It is assessed in the same way as the previous one.
Ask your child how to describe what you read in one word.

1. Perch, crucian carp - ...
2. Cucumber tomato - …
3. Wardrobe, sofa -…
4. June July - …
5. Elephant, ant - ...

First, you read these rows to the baby, then give the task (name it in one word). Ask your child to answer as you read the words again. If the task is not clear, tell your child and think together about how to, say, call a rose and a daisy in one word. Ask if you can say: “Rose and daisy are flowers”?

There are several more tests (awareness test using the Amthauer method, analogy test) with a point system for assessing the level of development of abstract logical thinking. You can familiarize yourself with them by reading the wonderful book “How to Prepare a Child for School” (authors - A. A. Rean and S. N. Kostromina), based on the materials of which this article was prepared. However, based on the results of the proposed tests, you can determine whether your baby has problems and how serious they are.
And now - a little theory. Abstract logical thinking is largely based on concepts. Concepts reflect the essence of objects and are expressed in words or other signs. Typically, in a preschool child this type of thinking is just beginning to develop, but the first grade curriculum includes tasks that require solutions in the abstract-logical sphere. It's better to start training early.

Exercise "What and why?"

Psychologists call it this way: “The formation of concepts based on abstraction and identification of essential properties of specific objects.”
You explain to your child: “A car runs on gasoline or other fuel; a tram, trolleybus or electric train runs on electricity. All this together is transport.” When you see an unfamiliar machine (for example, a crane truck), ask "What is this? Why?" Similar exercises can be performed with other concepts: tools, utensils, utensils, plants, animals, furniture, etc.

Exercise "Cards"
(Formation of artificial concepts)

You will need to make three sets of cards (nine cards in each set). The cards should depict geometric shapes (one on each card): triangle, square, circle. Each figure is depicted against a background of three degrees of saturation: pale pink, pink, red. In the first set, all the figures are black. In the second - white, in the third - gray. On the back of the cards are written meaningless combinations of three letters. For the first set - PAK, for the second - BRO. For the third - VIL. You need to divide the cards into groups and invite the children to guess the intended combination of figures.

The child must identify the signs that unite the figures into a group. At the same time, he can sometimes use meaningless words written on the back of the cards: figures belonging to the same group have the same inscriptions on the back. It is very important to ensure that the child looks at the back of the card as little as possible. Thus, the child, willy-nilly, will have to form artificial concepts using two rows of stimuli: one row performs the function of the object to which the child’s activity is directed, the other row serves as the function of signs organizing this activity.

Exercise "Bigger, Longer and Shorter"
(Formation of the ability to separate the form of a concept from its content)

Tell your child: “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?
You can come up with your own questions based on the ones above.

Exercise "What is this all called?"

You read the given series of words to the child and then ask how these objects can be called in one word. You can invite your child to continue the row. Example: duck, chicken... All these are birds. And also a dove, a crow, a turkey.
Rows of words:

1. Perch, crucian carp - _______________
2. Cucumber tomato - ____________
3. Wardrobe, sofa - ________________
4. June July - _________________
5. Butterfly, ant - ____________
6. Tree, flower - _______________
7. Coat, skirt - ________________
8. Teacher, doctor - ________________
9. Bus, tram - _____________
10. Monday Tuesday - ________
11. Spring Summer - __________________
12. Morning evening - __________________
13. Pan, spoon - _____________
14. Doll, ball - ___________________
15. Boots, shoes - ________________

Exercise "Difference and Similarity"

The child must determine how the concepts are different and similar:

1. Morning evening
2. Cow - horse
3. Tank pilot
4. Skis - skates
5. Tram - trolleybus
6. Lake - river
7. Rain - snow
8. Train - plane
9. deception is a mistake
10. Little girl - big doll
11. Apple - cherry
12. Crow - sparrow
13. Milk - water
14. Gold Silver
15. Sleigh - cart
16. Sparrow - chicken
17. Evening - morning
18. Oak - birch
19. Fairy tale - song
20. Painting - portrait

Exercise "Who can't do without what"
(Helps the child learn to identify essential features to maintain logical judgments if he solves a long series of similar problems.)

You explain the task like this: “Now I will read a series of words. From these words you need to choose only two, meaning something that the main subject cannot do without. Other words are also related to the main word, but they are not the main ones. You need to find the most important ones words. For example, garden... Which of these words do you think are the most important: plants, gardener, dog, fence, earth, that is, something without which a garden cannot exist? Can there be a garden without plants? Why?.. Without a gardener ... dogs... fence... land?.. Why?"
Each of the suggested words is analyzed in detail. The main thing is for the child to understand why this or that word is the main, essential feature of a given concept.

Sample tasks:

1. Boots (laces, sole, heel, zipper, shaft)
2. River (shore, fish, fisherman, mud, water)
3. City (car, building, crowd, street, bicycle)
4. Barn (hayloft, horses, roof, livestock, walls)
5. Cube (corners, drawing, side, stone, wood)
6. Division (class, dividend, pencil, divider, paper)
7. Game (cards, players, fines, penalties, rules)
8. Reading (eyes, book, picture, print, word)
9. War (plane, guns, battles, guns, soldiers)

The next stage of your studies should be the formation of judgments, and for this the child must learn to understand the figurative meaning of the phrase. For this training, you can use various literary material, proverbs, sayings that can be understood both literally and figuratively.

For example, work on explaining the following proverbs:
"Measure twice and cut once"
"Less is better"
"If you hurry, you'll make people laugh"
"Strike while the iron is hot"
"Business before pleasure"
"Don't sit in your own sleigh"

Work on proverbs is carried out as follows.
Tell your child: “Now I’ll read you a proverb, and try to find a suitable phrase for it from those that I offer you.”

For the proverb “Measure twice, cut once”, offer three options:

1. If you cut it incorrectly, you shouldn’t blame the scissors.
2. Before you do it, you need to think carefully.
3. The seller measured seven meters of fabric and cut it.

Good luck to you and your child!

In children starting school, “memory becomes thinking, and perception becomes thinking.” The statement of the outstanding child psychologist, author of original methods, D. B. Elkonin means the main thing: in the mental development of children of primary school age, an active transformation of the entire cognitive sphere (memory, attention, perception, speech) occurs. Psychologists emphasize that such improvement of the psyche is possible only with abstract logical thinking. Experts authoritatively state that abstract thinking is necessary not only for the further mental development of a child, but also for mastering such complex academic subjects as mathematics, natural history, and later, physics, geometry, and astronomy. It is important for parents to understand the diversity of their child’s mental development in order to come to the rescue in time.

What is abstract thinking

What do we know about abstract thinking? Is it really so important in a person’s life or can you do without it just fine, just using something visual! Abstract (abstract) thinking, that is, the formation of abstract concepts and operating with them, is inherent in each of us. From time to time a person should abstract (mentally distract himself) from the particular and operate with general concepts in order to see the world around him as a whole, without touching on the details. Such an action is necessary in order to concentrate on a specific goal, make discoveries, develop abilities, and fulfill one’s aspirations. When an event is viewed as if from the outside, abstractly, then original ways to solve it are sure to be found.

The clearest example of how abstract thinking works is in the exact sciences. For example, in mathematics we do not see a number as such, but we see its components (numbers), we can count or group different objects according to some characteristic and call their quantity. Abstraction is needed even when a person plans his future. It is still unknown, but each of us sets goals, has desires, makes plans, and all this happens thanks to abstract logical thinking.

About forms of abstract thinking

The main characteristic features of abstract thinking are its forms, since those surrounding phenomena that are inaccessible to the human eye are still actively present in human life. Like any phenomenon, they must have their own design, so psychologists distinguish three main forms:

Concept

The concept means a thought or a system of thoughts that identifies and generalizes various objects according to their general and specific characteristics. The concept conveys a common property of different objects in the surrounding world. For example, “furniture” unites into its group those objects that we need in everyday life and have a common property - to provide comfort to a person: table, chair, sofa, wardrobe, etc. Another concept “school supplies” generalizes a pen, pencil, notebook, eraser, that is, those items that are necessary for writing. Basic publicly available concepts are transmitted to children already in preschool age, since otherwise it will be simply impossible to understand the world around us in its entirety.

Judgment

The basic form of abstraction, which is present in the assertion or denial of something about an object, its qualities or relationships with other objects. In other words, the judgment shows some connection between objects and phenomena of the surrounding reality. Simply put, a judgment (simple or complex) serves us when we need to confirm or refute something, for example: “the child is playing” (simple judgment). The complex expression also has a more complex form: “autumn has come, the leaves are falling.” In addition, a proposition can be true or false, it all depends on what it is based on. If a person reasons objectively, in accordance with reality, then the judgment will be true. And if he is interested in his statement and relies on his own thoughts that contradict the real thing, then the judgment becomes false.

Inference

Expressed by a thought that is formed on the basis of several judgments. In order to draw a conclusion, you need to go through three stages: premise (initial judgment), conclusion (new judgment) and conclusion (logical transition from premise to conclusion). Usually, inference is expressed in complex sentences (“if all angles of a triangle are equal, then this triangle is equilateral”). A well-known fan of making inferences is the literary character Sherlock Holmes.

Signs of abstract-logical thinking in children

The presence of such signs can already be detected in preschoolers, since experts consider senior preschool age to be the most optimal period of transition from visual to abstract thinking. It is believed that by school the mental development of children reaches a fairly high level. A seven-year-old child already knows and can do a lot, acquires some life experience, for example, navigates the world around him, easily remembers information, knows literary works well, understands the meaning of riddles, solves problems whose conditions are clear, coherently expresses his opinion about various events, and is interested in computer, loves to do creative work (sculpting, drawing, designing). At the same time, the thinking of a primary school student is at a turning point in development; abstract-logical thinking is still imperfect. To understand what level of mental development your child is at, you can use a simple test that psychologists often use when examining primary school children.

Diagnosis of the ability to think abstractly

Cross out the extra word

• Lamp, lantern, Sun, candle.
• Boots, boots, laces, felt boots.
• Dog, horse, cow, wolf.
• Table chair, floor, sofa
• Sweet, bitter, sour, hot.
• Glasses, eyes, nose, ears.
• Tractor, combine, machine, sled.
• Soup, porridge, pot, potato.
• Birch, pine, oak, rose.
• Apricot, peach, tomato, orange.

Fill in the missing letters in the words

• d...r...in... (tree); k...m...n (stone); r...b... (fish); k...r...v... (cow); b...r...z... (birch)

Choose the word that makes sense

• 1) wolf: mouth = bird: ? a) air b) beak c) nightingale d) egg e) singing
• 2) library: book = forest: ? a) birch b) tree c) branch d) log e) maple
• 3) bird: nest = person: ? a) people b) worker c) chick d) house d) reasonable
• 4) school: training = hospital: ? a) doctor b) patient c) treatment d) establishment

Choose the opposite word

• Beginning -... (end). Day Night). Evil -... (good).
• High Low). Young -... (old). Strong -... (weak).
• Cry - ... (laugh). Make peace -... (quarrel). Find -... (lose).

Unscramble the words

• naul - (moon); maiz - (winter); aker - (river); toel - (summer).

Analysis of results

Each correct action is worth 1 point. The number of maximum points is 29.

• 29 - 26 - increased level of logical thinking
• 25 - 22 - high level
• 21 - 18 - average level
• 17 - 14 - level of logical thinking below average
• 13 - 10 - low level
• 9 - 0 - critical level.

Why develop abstract thinking in children

Are you convinced that a certain level of abstract thinking is necessary for success in school? Have you realized that your child has problems in the ability to think logically and find non-standard solutions? Do you want to form forms of abstraction in your little schoolchild? Then you need to listen to the opinion of experts. Thus, psychologists warn that the development of thinking is a rather long process and requires daily work. One child may not be able to quickly and efficiently master abstract operations. Therefore, parents need to help him develop abstraction skills. In psychological and pedagogical practice, many methods have been developed for the formation of abstract processes in primary schoolchildren. Parents can focus on the one that seems most accessible and acceptable to them for homeschooling.

Exercises and games for logical thinking

Gaming activities still remain important for younger schoolchildren, so games and exercises are successfully used in the development of abstract thinking. This method is accessible and interesting for children; with its help, you can do complex work to improve forms of abstraction. Each adult can come up with game tasks independently for their child. The main thing is your creativity and ingenuity! To prevent games from getting boring, they can be easily “revitalized” with elements of outdoor games (running, jumping, clapping) or sports objects (ball, skittles, rope). A competitive moment (who can name it faster...) and forfeits are good options. What can you offer for home use?

Synonyms - antonyms

The classic game of matching synonyms and antonyms always attracts children. They enjoy the competition of “who can come up with the first word (synonym or antonym).” You can play verbally, or you can throw the ball to each other with the chosen word. Approximate synonyms (close in meaning): stingy - greedy, throw - throw, dog - dog, slacker - lazy, friend - buddy, damp - wet, lie - not true.

A simpler task for children is to select antonyms (words with opposite meanings). It is carried out similarly to the previous one, for example: friend - enemy, brave - cowardly, future - past, good - evil, grief - joy, beautiful - ugly. Interest in the game can be maintained by introducing game moments: for an incorrect answer, the player gives a forfeit, and then redeems it with the help of a certain task: sing, dance, say a tongue twister, guess a riddle.

Finish the sentence

Similar to the previous game, an exercise is carried out to complete sentences. Players must catch the ball with the beginning of the phrase, and return it with the ending, for example: dogs bark, and cats... (meow), in winter there is frost, and in summer -... (heat), the car drives, but the plane... (flies). A more complex option - you need to end a complex sentence with a subordinate clause, for example: in winter it’s cold, ... (because it’s frost); the student received an A, ... (because he learned the lessons) and the like.

Decipher it!

Such an exercise must be prepared in advance; at first, pictures or words written on cards are used. Subsequently, when the student learns to divide a word into syllables mentally, it can be carried out in the form of a word game. The essence of the exercise is the following:

• highlight the first syllables of each word and compose a new one (decipher): de lo, re ka, in yes (tree); si la, Neither on the, tsa ritsa (tit); ma ma, shi py, On tasha (car);
• highlight the last syllables and create a new word: itself years, me chick(pilot); bar ban, ut ka(jar); dere in, laban Yes(water).

Three effective methods for developing abstract thinking

Association game

Associations (connections between phenomena and concepts) are considered the most accessible and simple method of developing abstract thinking in children. It is easy to use in everyday life if you invite your child to find various connections between objects and phenomena that surround him. For example, during a walk together, or while traveling to the country, or over evening tea, you can play a word association game. The point of the game is that one concept or image entails another. An adult pronounces a concept, and children must choose words that are in any way related to it. For example, umbrella - rain - puddles - boots - roof; car - trip - passenger - truck - motor - wheel; summer - sun - warm - fun - swim - sunbathe - holidays. The player can name any word, the main thing is to prove that the words are related. It is interesting to involve all family members in the action and reward the winner who has found and proven the most associations.

As a variant of such a game, you can invite participants to create an associative chain based on a given characteristic, for example, yellow and warm - sun - lantern - lamp, etc. Or original associations, for example, hedgehog - Christmas tree - needles - burdock - brush.

The older the child, the more complex the concepts from which associations are built should be. These can be words denoting various relationships in the world around us: between people (family, mom, dad, sister, brother, society, friendship, school); in living and inanimate nature (winter, summer, water, thunderstorm, any animals, forest, tree, fruit, vegetables); emotional processes (joy, grief, love, success, envy, sympathy); phenomena of social life (homeland, peace, war, country) and other concepts that make up the world around us.

Shadow play

The most popular and interesting way to develop abstract thinking, somewhat similar to an association game. With its help, various images are created, by playing with which the child uses all mental processes (memory, attention, thinking, imagination, speech). Shadow theater is easy and simple to organize at home and make it a family tradition. To organize, you will need a sheet, a table lamp, character figures cut out of cardboard or plywood, or a variety of hand movements. The lamp is installed so that it creates a shadow. You can act out any works familiar to children, but not only - performances can be improvised. The main thing is that the child must see the image depicted and be able to act out it. Shadow theater promotes the development of abstract thinking in the child, develops the ability to use and understand symbols: hand movements are concrete, real, and an image is created from shadows on the screen. You have to imagine that these are no longer fingers, but animals that move.

Mental arithmetic

Experts consider mental arithmetic a more effective way to develop abstract thinking - a program for developing mental abilities and creative potential using arithmetic calculations on special accounts (soroban). The technique is designed for children and schoolchildren from four to sixteen years old. Instructions for this technique can be found in more detail on the Internet, in special courses for schoolchildren.

As you can see, it is not so difficult to form abstract thinking in a child at home if you follow the recommendations of specialists. And most importantly, show parental love, care, and attention. Help your little schoolchild see the world around him from all sides and show his abilities.

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 for the development of visualization and visual-figurative thinking can be found 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 this task often lies in the child’s inability to analyze the sample (the left side) and realize that its second part should 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 If this works, find it in the first row. Connect the figures of the first and second row that fit each other with a line.”

c) “Look carefully at the pictures and choose where the parts are located from which you can make the figures 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 of a logical classification operation based on 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. By handling objects mentally, imagining different options for their possible changes, you can quickly find the best 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 a very interesting game. This is a game about a squirrel who can jump from one square to another. Let’s see what kind of house squares we have drawn: this square is with a star, this one is with a mushroom, this one is 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 it can 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 for tasks in which he needs to guess how the squirrel can get into the desired cage 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.

The Animal Journeys activity using this game board can be modified in a variety of 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 phenomena, 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 general word can be used to describe the following words:

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 by attributive property (the lowest 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 (higher 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 of a 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.”

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, based on the absence or presence of one of two possible features in 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 the general principle of 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.

The conditions of the tasks 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, questions 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 combinatorial type problems, 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 meanings but are spelled the same. "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 at primary school age, but the program already includes tasks that require solutions in the abstract-logical sphere. This determines the difficulties that children encounter 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:

Measure seven times 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

The correct choice here is “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) It is more useful to read one good book 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) The good quality of a mirror does not depend 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.