How to increase the level of logical thinking. How to develop logical thinking in children? Have fun with benefits

It is very important to learn to think logically - such skills help not only to calculate your actions in advance, but also quickly find a way out in unforeseen situations. A person who has developed logical thinking will undoubtedly be able to succeed even under not the most favorable circumstances. So, how to develop logical thinking?

Logic and logical thinking

Logic is

The concept of "logic" has its roots in the ancient Greek language, and is translated as thought (reasoning). In general, logic can be called the ability to think correctly, and it can be considered as a science. This is a branch of philosophy that studies intellectual activity. If you are capable of logical thinking, then on the basis of the data you have, you will be able to come to the right conclusion. With the help of logic, you get not only general knowledge about a particular subject, but also comprehend its nuances.

What is logical thinking and its types

It is worth noting that logical thinking is divided into several types, and, having familiarized yourself with their characteristics, you will be able to identify whether you possess any of them. In general, logical thinking is a thought process in which we get a reasonable conclusion from the existing premises. Verbal-logical thinking It uses logical constructions and concepts, acts based on linguistic means and is the highest of the stages in the development of thinking. Using verbal-logical thinking, a person is able to come to general patterns, to generalize different visual material. The formation of such thinking occurs gradually. During training, a person masters the methods of mental activity and analyzes the process of his own reflections. When solving educational problems, it influences the formation of analysis, generalization, synthesis, classification, comparison. Let's understand these concepts in more detail. Analysis- a mental operation in which a person is able to disassemble a complex object into elements. Synthesis- usually acts in unity with the analysis, being carried out simultaneously. Man moves from parts to the whole. Generalization- the union of many elements on a single basis. The comparison reveals something in common. Classification- objects are grouped according to essential features Comparison- comparison of phenomena and objects, as well as the identification of their differences and common features. Verbal-logical thinking People with this type of mindset tend to focus on what they say rather than how they do it. Such logicians have a predisposition to accuracy, show interest in the semantic essence of any information. They try to compare newly acquired knowledge with those they already possessed. It is worth noting that this type of thinking, alas, is not inherent in fast memory. A person needs a certain amount of time to think and analyze everything carefully. We also note that people with this type of thinking are prone to conservatism and a weak manifestation of emotions. The strengths of verbal-logical thinking can be called accuracy, consistency. Of the negative sides - slow switching from one task to another. Mathematical thinking This kind of thinking is characterized by flexibility, originality and depth. Let us consider these concepts in more detail, in the context of mathematical thinking. Flexibility- the ability to vary the options for solving a particular problem, easy transition from one way of solving a problem to another. Also we are talking about the ability to leave the boundaries of the usual ways of action - a person is looking for new solutions, quickly adapting to the changed conditions. Originality- a factor that provides in this case the highest level of unconventional thinking. Depth- the ability to comprehend the essence of all the studied facts, their relationships, hidden features. Associative-figurative thinking It should also be noted that there are people who are characterized by associative-figurative thinking. Their memory is well developed, but it differs from the memory of logicians. Trying to remember something, the lyricist immediately reproduces something else in memory, because he has a predisposition to associative perception of reality. What are the main advantages of this kind of thinking? You can cite as an example emotionality, a rich imagination, the ability to easily switch from one to another. A person wholeheartedly perceives images, connecting them with the existing reality. The disadvantages include inconsistent actions, increased idealization, excessive vulnerability, increased sensuality. Such features do not always make it possible to look at the world objectively, although they make it very exciting.

Developed memory and logical thinking are simply necessary in everyday life - when performing professional tasks, as well as in household chores. Developing memory and logic, you will learn to concentrate your attention, control the train of thought. As a result, it will be easier for you to focus on current tasks and organize your own life. Performing exercises for the development of memory, after a certain period of time you will begin to notice that when solving problems, you use very non-standard and effective methods that you would not have thought of before.

How to develop memory and thinking in adults

Tasks for the development of logical thinking

On the Web, you can easily find a variety of tasks with which you will be able to develop logical thinking. Many sites will offer you different levels of tasks. Try to start with something that is not too difficult and work your way up.

Learn to think logically with games, puzzles and strategies

Also, a variety of games, strategies and puzzles can greatly contribute to the development of logical thinking. To do this, it is not necessary to search for tasks on the Web. Even having bought a box of puzzles, you can not only arrange an entertaining evening for yourself, but also increase the level of logical thinking to a large extent.

10 ways to improve your memory

1.) Read a lot of books Of course, a person who is prone to reading has a better memory than one who does not show any interest in this occupation. So how can this be used. Read a short story, and then immediately retell it to the recorder. After a few hours, try repeating this retelling. Analyze what details you forgot, what was missed by you. Do these exercises regularly. 2.) Say words backwards It is also a very useful method to improve your memory. It is also impossible not to note the convenience of this method - you do not need a voice recorder or other auxiliary devices. Do this task before bed, on the road, in line, and so on. If possible, you can perform the exercise on a piece of paper, in a notebook - so it will be more convenient for you to check yourself. 3.) Learn poetry and new words Memorizing poetry is a great memory trainer. You can also learn new, unfamiliar words. As soon as a similar word catches your eye, at any opportunity, look up its meaning in the dictionary. After that, try to “mentally” make up a few sentences in which the new word will be used. 4.) Remember everything in detail, analyze Get into the habit of replaying the events that happened to you during the past day every evening. Start from the moment you wake up. Remember what you thought about when you woke up, what you ate for breakfast, who you talked to. Next, move on to memories of how your day went, what people you talked to, what tasks you had to face. Then move on to the memories of the evening. Analyze what unpleasant events you could have avoided, what useful things you learned today, what act was senseless, and so on. 5.) Draw images in your head Quite an interesting exercise that perfectly develops the imagination. For example, imagine you are on vacation. Let's say, not just you are sitting on the shore, but in more detail. Imagine that you are sitting on warm sand, you have a glass of lemonade or beer in your hand, a plate of shrimp or corn is next to you - you can smell them. You also hear the sound of sea waves, and sometimes their splashes reach you. You can add more details. Thus, imagine anything. For example, you find yourself in a summer garden: the shadow of trees falls on you, you hear the smell of raspberries, pear fruits periodically fall to the ground. The rays of the sun break through the leaves. 6.) Full sleep Undoubtedly, you have already heard that adequate sleep has an important impact on our memory. If you sleep at least seven hours a night, you can be sure that this has the best effect not only on memory, but also on concentration and even on the rejuvenation of body cells. Good sleep is necessary for the accumulation of energy and health in general. 7.) The Aivazovsky method develops photographic memory This training technique got its name in honor of the famous artist. Being engaged in writing his works, paintings, Ivan Konstantinovich mentally tried to stop the movement of the wave and transfer it to his picture so that it would not look frozen. Aivazovsky devoted many hours to the process of observing water. At the same time, he closed his eyes from time to time, trying to reproduce what he saw in his memory. How to use this technique?

For 5 minutes, study any object, or landscape. Closing your eyelids, try to reproduce the image of this picture in your memory. It is also important that it be in color. The effectiveness of the training can be increased by fixing objects on a piece of paper. If you perform this exercise regularly, you can achieve considerable progress in the development of visual memory.

Such tables are used to determine the degree of attention, which in turn is directly related to memory - you can find them in abundance on the Web. To do this, just drive into the search "Schulte Tables Online", and start training. Note that we are talking about a field divided into squares, and in those, in turn, numbers from 1 to 25 are written in random order. Subsequently, you will need to find all the numbers in order using a stopwatch - over time, the search speed should increase.

9.) Vitaminized healthy food Of course, for a good memory, it is important to eat food that is as rich as possible in vitamins. What products should you pay the most attention to? Eat apples, salmon, blueberries, spinach, various seeds and nuts, and grapes. 10.) Develop your left hand if you are right-handed and vice versa A very useful activity. Set challenging goals for yourself. Train your left hand if you are left-handed, and your right hand if you are right-handed. Using the "unaccustomed" hand will be difficult at first, but over time you will master this skill.

How to develop logic and thinking in a teenager

Quests, puzzles and charades On the Web, you can find many puzzles that you can try to solve with your teenager. Try to look for problems that contain the correct answer - in case the goal is not achieved, you can see how it could have been achieved. Special application with tasks for a smartphone On Google Play, you can easily find an application called "Logic, Tasks, Puzzles" - you can install it on your smartphone. The essence of the application is to develop analytical skills in adults and adolescents. There are also apps like Brain Training, Lumosity, and many more. Many factors influence intelligence and ingenuity. If you are forced to expose your body to constant stress, then it is not surprising that your reactions will leave much to be desired. During peak situations, the human body produces cortisol, which has a detrimental effect on brain cells. If in the morning you have to take on a bunch of things, then you should try to slow down at least a little the usual pace of life. Start by not jumping out of bed immediately after the alarm rings - allow yourself some time (15-25 minutes) to lie still, think about the coming day. How to increase your intelligenceMusic. Periodically take a break from the daily hustle and bustle by listening to music. By the way, scientists believe that classical works are very useful for activating the brain. For example, people who listen to Mozart from time to time are characterized by an increased speed of thinking. Don't waste energy. Don't take on too many tasks at once. In order to do something well, it is important to focus on it. If you have to answer a letter, talk on the phone and listen to the news at the same time, then, of course, attention will begin to disperse to several sources of information. The result will be a decrease in concentration and even the level of intelligence. More positive. Do not deny yourself positive emotions - your performance directly depends on them. Visit parks more often, go to the movies, meet friends. Development. Regularly search the Web for exercises to develop memory and enrich your vocabulary. It is unlikely that unexpected decisions will “illuminate” you if you are the owner of a poor vocabulary that is almost unable to keep anything in your head. To develop memory, learn poetry, just read books.

Online logic test - develop the ability to think logically

So, we propose to mark the time - it is advisable to use no more than a quarter of an hour to pass the test.

Test:

1.) Can a woman marry her widower's brother? 2.) Is there March 2 in Italy? 3.) The girl declares: “The day before yesterday I was 8 years old, and next year I will celebrate my 11th birthday!”. So maybe? 4.) On 2 hands - 10 fingers. So, how many fingers are on ten hands? 5.) You are the driver of a bus that is heading from Yekaterinburg to Ugut. You will have three stops along the way. How old is the driver? 6.) The month ends on the 30th or 31st. What is the month that contains the 28th? 7.) You ended up in a room with two lamps - gasoline and gas. What will you ignite first? 8.) One car left Ufa for Moscow, and the second - from Moscow to Ufa. The cars left at the same time, but the speed of the second car is twice the speed of the first. Which car will be closer to Ufa at the time of the meeting? 9.) A mother and son were involved in an accident. The mother did not survive in the hospital. A nurse comes to my son's room and says, pointing at him: "This is my son." Is it possible? 10.) Found a coin subsidized by the seventy-eighth year BC. So maybe? 11.) The rooster flew onto the roof, the slope of which is 45 degrees on one side, and 30 degrees on the other. When he lays the egg, what slope will it roll down? 12.) The doctor prescribed three injections, which must be done every half hour. So, how long does it take for these three injections? 13.) The weight of a brick is one and a half kilos. Plus another third of the brick. How much does a brick weigh? 1.) Not; 2.) Yes; 3.) Maybe if she was born on December 31st; 4.) 50; 5.) As much as me; 6.) In all; 7.) Match; 8.) Equally; 9.) Yes; 10.) Not; 11.) From none; 12.) One hour; 13.) 1 kg.

If you did: No more than 2 errors Your logical thinking is on top! Surely, you put a lot of effort to achieve such results, but it was worth it! 3 to 5 mistakes It is safe to say that you have a high level of intelligence, despite the fact that, at times, you are prone to mistakes. Be that as it may, you are able to analyze most events correctly. 6 to 7 mistakes Your level of intelligence can be called average. The potential for growth is certainly there, and if you wish, you will succeed in this business. 8 or more errors It is difficult to say that you are often guided by logic in your judgments. Most likely, you act mainly under the influence of emotions.

Books that develop logical thinking

This book can be considered a simple introduction to the world of modern mathematical logic. The textbook was recommended by the State Committee of the Russian Federation for Higher Education, and has become an excellent source of knowledge for many students of higher educational institutions.

This is a book that lays out the basics of logic in an accessible way. The main emphasis is on syllogistic. The textbook contains tasks with the help of which the student is able to learn to apply certain rules in practice in a short time.

A tutorial that talks about how to learn to think logically - who finds it difficult, and who easily overcomes barriers. Contains useful tasks.

Ten-minute exercises for the development of logic for every day

A couple of random words Choose two words at random from any article or story - just poke your finger at the words without thinking about their meaning. Now you need to try to find something in common between the selected words - compare them, find the relationship. Come up with an interesting story that could connect these two concepts. Associations Look around the room you are currently in. Choose an object in the room, such as a chair or a plate. Take a piece of paper and come up with five adjectives that best fit the chosen item. Example: round plate, yellow plate, small plate, clean plate, empty plate. Now write five adjectives that are completely inappropriate for the chosen subject. Example: wooden plate, boiled plate, winter plate, windy plate, silk plate. Undoubtedly, such exercises will benefit you if you perform them daily. Plus, you don't have to spend a lot of time on them! Try to start today, and soon you will notice significant progress in the development of logical thinking and imagination.

Hello dear readers!

So, I did not wait for the questions on the previous one. Although it is the questions that indicate that the topic has affected a person, and he wants to clarify something for himself.

I think that there will be a lot of questions on today's topic. I will answer with pleasure.

How often we lack the ability to logically express our thoughts, especially if the result of this presentation is important to us. It is at this moment that we are overwhelmed with emotions, and our inability to argue only leads to the heat of passion, turning to raised tones. But since this does not lead to a result, insults often come into play, further turning into threats or even a fight.

Mutual understanding did not take place. And the reason is the inability to competently build their thoughts and conduct a discussion.

I think many of you are familiar with this situation. Almost every day we can observe something similar in life, and even more often from TV screens.

Disputes in which there is little logic, but a lot of emotions and aggressiveness.

It is believed that 70% of conflicts arise during communication. And how can we communicate correctly if our emotional competence is not developed (which I wrote about), and no one taught us the logic of statements and the ability of logical thinking.

Development of logic and thinking

What is usually emphasized when it comes to the development of thinking?

The main focus is shifted to the development of creative thinking. Solving creative problems, finding new solutions, generating ideas, of course, requires out-of-the-box thinking.

And this development is devoted to the bulk of the literature.

It's fashionable to think outside the box. True, sometimes this non-standard becomes too shocking and for the sake of attracting attention, elementary logic is neglected.

To splash a bucket of paint on the canvas and call it a work of art, it is possible that this is so, but then it is worth defining in terms - what art is.

It is pointless to argue about this until definitions and concepts are introduced, which is what logic actually does.

Although many people think that Logic is the ability to solve logical puzzles. First of all, logic is the science of correct thinking . Consistent, consistent, reasonable.

We agree that we are missing logical thinking . Yet in life more often it is required. It is not so often to make discoveries and generate ideas, but you have to communicate, convince, prove, think every day.

There are people who are difficult to understand - there is no logic in their reasoning. And, unfortunately, there are more and more of them. Just listen to any talk show.

So today let's talk about development of logical thinking and about Logic as a science and its application in everyday life.

Is it possible to reason logically without knowing the basics of logic?

Yes, you can, because you can decently speak and write without knowing grammar. But by studying logic, we raise the level of our thinking. We learn to express our thoughts more clearly and consistently.

Why do we need it?

We are so accustomed to the bottom line of our efforts, and it takes effort to learn logic. Therefore, I will dwell on this issue in more detail.

Although, as usual, - yeah, the reader thinks - the heading is “Development of logical thinking”, now I’ll jump in for 20 seconds (by the way, there are more than 60% of such visitors), I will see a list of actions from 10 points, and I will begin to think logically.

And the entire Internet is filled with such motivating algorithms, consisting of 7-10 steps. But having run superficially one technique, another, a person is disappointed - how is it, but where are those great changes that are promised. Kindergarten, in a word ….

Unfortunately, this does not work, motivation passes in an hour, at best, and another motivational kick is required. The motive to do something must be stable, conscious, as a necessity, and not as a simple satisfaction of curiosity. Need emotional vector to say "easier".

Therefore, to begin with, I will give a few advantages of studying logic:

1. Logic teaches you to think clearly and express your thoughts clearly. Incoherent speech, when a person cannot connect two words, is common.

2. The ability to convince and defend one's point of view is being formed. A persuasive logically constructed speech is required.

3. The study of logic develops the habit of analyzing one's own and others' judgments. And also to find errors in them and fight against demagoguery. Indeed, often there is nothing to object to except as “the fool himself”.

4. Logic teaches to argue. And do not bring the dispute to a squabble and fight. Helps to find compromises, to refute false reasoning.

5. Logic generally develops the ability to think. Have your own thoughts, not thoughts imposed by an external source.

I think even this is enough to read the article to the end. And suddenly something comes in handy.

Although, as Bertrand Russell said, Many people would rather die than begin to think. And they die without even starting ».

I don't think this applies to my readers.

A bit from the history of the study of logic

Before the 1917 revolution, logic was studied in gymnasiums. But after the revolution, logic was declared a bourgeois subject and excluded from the school curriculum.

The Central Committee of the All-Union Communist Party of Bolsheviks, in its resolution “On the Teaching of Logic and Psychology in Secondary Schools” dated December 3, 1946, considered it necessary to introduce, starting from the 1947/48 academic year, the teaching of these subjects in all schools of the Soviet Union.

There was such a famous textbook of Vinogradov's logic of 1954.

But in 1956, the teaching of logic in high school was canceled. Like this….

Now Logic is studied only in individual universities.

And a little more about the sad.

The study of formal logic does not always contribute to the development of thinking. You can study logical operations, work with judgments, etc., but not everyone succeeds in applying this in life. Students of logic just don't know how to do it.

The problem of most textbooks on logic in abstract examples: all mosquitoes are insects, if autumn comes, leaves fall, and so on. It is logical, yes logical, but some non-life examples, so it is difficult to switch to real situations.

It is even more difficult to use the laws of logic or how to apply the semantics of the language of predicate logic. This is what it takes to have a desire to deal with all this?

How to develop the ability to think logically?

Certainly not by solving logic puzzles and crossword puzzles. The most that can be gained from these activities is to increase the ability to solve puzzles, nothing more. And although this is certainly useful for the brain, the goal is still to learn how to competently build your thoughts, and the exercises should be of a different kind.

First of all, close to those situations when such a need arises: to prove, convince, discuss, etc.

It is in real conditions that one can gain experience, and not by studying the theoretical laws of logic. What you need to learn is how to put theory into practice.

And for this, you should first find out for yourself when the need for logical thoughts arises. I mentioned five such situations above, but there are many more.

To understand in general terms what Logic studies, consider its main sections:
1. Concepts.
2. Definitions.
3. Judgments.
4. Basic laws of logic. The law of identity. The law of contradiction. Law of the excluded middle. Law of sufficient reason.
5. Inductive reasoning
6. Deductive reasoning.
7. Analogies, hypotheses, proofs.

Let's add the basic techniques of logical thinking - comparison, analysis and synthesis, abstraction and generalization. Here are all the sections.

Approach to learning

The problem is how to translate the knowledge of formal logic into practical logic.
I will offer one approach that you may be interested in. In my book "" I mentioned him.

Petr Spiridonovich Agafoshin (1874-1950) is a famous Russian guitarist. In the book "School of the Six-String Guitar" he described one of the basic principles of training as follows:

The student must learn play playing . Those. acquire the necessary playing skills not on dry training material such as exercises and etudes, but on skillfully selected highly artistic material that educates taste and brings aesthetic satisfaction along with practical and technical skills.

Why not use this principle here as well, i.e. solve practical mental problems that arise in reality, where the application of logic is required. These are not educational cases that are solved in ideal conditions, but life situations where there is a place for surprises and manifestations of emotions.

For example, discussion/argument.

In order for various discussions, disputes and just discussions to be logically cultural in nature, it is important that participants equally understand the exact meaning of the terms involved in this discussion.

For example, it is difficult to understand a person - what he is talking about if he has not given a definition on the subject of his conversation. Without specifying the concepts and definitions, each participant in the conversation/dispute can understand something of their own under this concept (to the best of their knowledge). It's not clear what the argument is about.

And if a scientific dispute concerns concepts - infinity, matter, space, etc., then more prosaic things appear in working discussions: for example, margin, strategy, marketing, and in everyday situations - the number of things discussed is much larger.

So the first rule of logic is: the main terms of the statement, theses should be clearly defined, regardless of whether others know them or not. Consistency in understanding is important.

From here first practical logic skill – ability to operate with concepts.

Knowing the importance of this, one can study in more detail the theoretical part of the section of logic - “ Definitions". Here are its subsections (for example, according to Vinogradov's textbook):

1. Content and scope of concepts.
2. The relationship between the content and scope of the concept.
3. Restriction and generalization of the concept.
4. Generic and specific concepts.
5. Main classes of concepts.
6. Relations between concepts.
7. The essence of the definition of the concept.
8. Rules of definition.
9. Genetic definition.
10. Nominal definition.
11. Meaning of definitions.
12. Techniques that replace the definition.
13. The essence of the division of the concept.
14. Division rules.
15. Dichotomous division.
16. Techniques similar to division.
17. Classification.

By studying this issue theoretically, you already imagine how this knowledge can be used in practice.

Another important skill is the ability to ask questions.. As I said earlier, our thinking consists of questions and the search for answers to them.

But in order to correctly pose questions and answer them, you need to know what a correctly posed question is. This is already in the field of Logic.

Every question has premise question, i.e. information about the object about which the question arose.

For example: a question - do you like articles on my benefit?
The question assumes the existence of a blog and articles posted on it, as well as the author. Those. premise.

What is the right question?

First, it requires the availability of the necessary amount of information and the ability to use this information.

It is also necessary to check all the premises of the question - they must be true, if at least one premise is false, then the question is wrong.

For example, if there is only one article on the blog and the question is about "articles". The premise is not true, so the question is wrong.

In general terms, the question is correct if, in principle, there can be an answer to it.

After all, there is this: One fool can ask a question that even a hundred wise men cannot answer.».

Knowing that the question must satisfy the formal rules of logic, we study this part of the Logic more closely.

Consider another logical form - reasoning .

Reasoning is a mental activity (i.e. our thinking) when interaction of separate judgments and on their basis new judgments appear. This whole process is a discussion.

We can talk about the structure of reasoning: i.e. some judgments are known to us, others are not. They are connected by a logical operation.

There are several types of reasoning. If from a known judgment (called premise ) comes out previously unknown proposition ( conclusion ), then this is called inference e.

known deductive reasoning and inductive reasoning.

What logical laws the reasoning is based on can also be found in the textbook of logic.

But it is better to do this after visually, in a real situation, highlight the reasoning and try to understand how it is being built now, without knowledge of formal logic. Then turn to the textbook.

So the sequence is:

1. Getting to know the main sections of Logic.
To do this, you will need the complex business reading skills that I described in the book "", in particular synoptic reading and techniques for reading business literature.
Result: a general idea of ​​formal logic.

2. Areas of use. You already know the areas where logic will be useful. We have defined this above, in general terms.
The next thing to do is to gradually introduce logical forms into these situations, i.e. practical use of individual elements of the theory of Logic.

To begin with, you should choose situations that are not too critical for you - after all, there is no experience yet. We learn from simple everyday situations where failure will not affect you personally. Gradually increase the complexity of the situation.
There are a lot of such opportunities in life - starting from the store, ending with visiting government institutions.

It can be useful to notice the logical tricks that come our way. For example, advertising "Today - on credit, tomorrow - for cash." It is required to eliminate the logical uncertainty: today is when, and tomorrow - when? Ask the advertiser why the laws of logic are violated. And there are many such examples.

3. We introduce logical forms gradually, step by step, element by element.

Task: to analyze individual logical forms and try to use them in practice.
First, we introduce definitions and concepts. Those. starting any discussion, we define the concepts involved in it. To do this, we carefully study the theoretical part of logic - Definitions and Concepts.

In any communication, try to find the subject of discussion, formulate definitions and try to apply the knowledge gained.

Then there is the wording of the questions. We try to ask the right questions.

Then we try to reason. We study the theory of reasoning. And so on, including the rest of the logic elements.

To some extent, we can say that this approach uses logical methods of thinking, such as analysis and synthesis, abstraction and generalization.

By using analysis we have singled out separate parts of the Logic. Learned and applied.

abstraction helped us eliminate minor, unimportant features of logical forms. By using synthesis and generalization - united separate parts into a single one. And now we can use all logical elements in our communication.

This is how, gradually moving from simple to complex, Logic will take an important place in your thinking.

At the same time, we study not only theoretical, but also popular literature on Logic.
The main thing is to start.

It is not necessary to become a great mathematician whose mathematical logic comes first. Enough level of logical thinking required in everyday life.

You can talk about logic for an infinitely long time, but you won’t cover everything in one article.

Therefore, I will offer you a list of literature for study, but this is not an easy subject.

It is better to study theory from textbooks, and from old textbooks. Yet the previous generation had a better command of Logic. So the list might look like this:

1. V.G. Chelpanov. Logic textbook. 1915
2. V.F. Asmus. Logics. 1947
3. S.N. Vinogradov, A.F. Kuzmin. Logics. Textbook for high school. 1954
4. A. D. Getmanova. Logic textbook. 1995
5. D.A. Gusev. A short course in logic. The art of right thinking. 2003
6. V.I. Kirillov, A.A. Starchenko. Logics. 2008
7. A.L. Nikiforov. Logic book. 1998
8. D. Halpern. Psychology of critical thinking. 2000

And more useful books:

9. A.I. Uyomov. Logic errors. How do they get in the way of thinking? 1958
10. Yu.A. Petrov. ABC of logical thinking. 1991
11. A.A. Ivin. The art of thinking right. 1986

You can get acquainted with the book M. Cohen, E. Nagel. An introduction to logic and the scientific method. 2010 (656 pages). For a long time it was the main textbook for universities in the United States.

can be studied and Aristotle the father of formal logic. His Organon.

Organon (instrument, method) is the traditional name of Aristotle's philosophical writings devoted to logic.

Organon includes:
1. Categories.
2. About interpretation.
3. First analytics.
4. Second analytics.
5. Topeka.
6. Sophistical rebuttals.

Aristotle calls logic " Analytics”, and in the treatise “Analyst” (First and Second), he outlined its main teachings: on inference and on proof.

I think this will be enough. Next time we will continue to consider other approaches to the development of thinking.

I look forward to your comments and questions.

If you liked the article, please click on the social buttons. Thank you!

Sincerely, Nikolai Medvedev.

6 comments on the entry “Formation of logical thinking”

Surprising features of Russian education: to ask what was not taught. On the exam in the Russian language, even the logical coherence of the text was included in the essay criteria, who else would have taught this graduate. Only a talented teacher will combine a very superficial teaching of his subject and logic. Therefore, children, except for screaming, have nothing to learn from adults, and sometimes it is a shame to watch programs of a discussion plan.

And now the question is: "Why did they exclude the study of logic and psychology in schools and do not study at some universities? How many grievances from misunderstanding by interlocutors do you need to get in order to acquire the skills of logical thinking, or are they given by nature and inherited?" Thank you for your content, it's very important.

• Thanks Lana for your comment!

  Why was logic excluded from the school curriculum?

  The official version is the fight against overload of schoolchildren. At this time, there were many changes in the education system, textbooks were rewritten, the management system changed, and so on.

  Although logic was introduced in 1948, the level of teaching is ? Who taught, as a rule, these were not specially trained teachers, but more often teachers of literature.

  Similarly, now - the teaching of the foundations of religion is in question - and who will teach this discipline.

  Skills of logical thinking, unfortunately, are not inherited. At the level of everyday logic, we learn from real life examples.

  But this is not enough. In addition, the logical thinking is not only the knowledge of logical forms, but also a general outlook. Without it, there will simply be nothing to connect logically.

Where is the logic in the fact that they do not teach Logic?

After the change of the tsarist regime, the abolition of the Logic was dictated, most likely, as its replacement with the code of the builder of communism, and this was an underestimation of its significance in everyday life. Now its absence is the result of a thoughtless reform of education under the influence of the West.

Not only Aristotle is a pleasure to read, but any ancient book in which there is no double meaning, unnecessary complications of speech, and everything is stated simply and clearly. There is no more magical and meaningful language on earth than Russian, from which other languages ​​actually originated, which is easy to see in the example of English, if you are attentive to words. The ease of reading ancient literature also speaks of the author's complete understanding of what he writes, in contrast to modern books and especially textbooks (everything that the author of this blog Medvedev writes does not apply here), filled with completely unnecessary complexity of presentation, coming from a lack of understanding of the subject. And now take the Russian word "difficult", what does it mean? Difficult = false. And vice versa - "simple, like everything ingenious." While studying at school in the 60s and 70s, I didn’t really like to write essays, although everything was fine with the Russian language. And, once I took old textbooks from my mother, a Russian language teacher, both pre-war and post-war, I was amazed how much better they were than ours - everything was explained in them so simply and clearly. These textbooks were a godsend for me, it was a nice thing to write essays on them. And already in those on which I studied, the widespread prevalence of formalization over simplicity and clarity of presentation began. Why do we need formalization, especially for children? At home, we speak with them not in a formalized language, but in a simple one. And remember what Lenin took in his speeches. He spoke to people in an understandable, accessible language for ordinary people, although at that time the theory of Marxism-Leninism was considered very complex and few people could understand it. By the way, in the library, where I was a regular weekly visitor, I somehow came across Lenin's article on the correct organization of labor. Otherwise, no matter how brilliant you can call it, I still regret that I did not rewrite it then.

The most important value of logic, I see the ability to create your own opinion on any issue, and not use the mental "gum" of other people. And I understand the main property of logic as a sequence of thoughts to achieve a certain result, in which each subsequent thought follows from the previous one. Those. Logic is the structure by which we organize our thoughts in order to achieve a specific goal.

For example, I need to create my own opinion about an object, phenomenon or situation. I start collecting information, then I separate facts, objective information from subjective information. I consider the subject of study in its development, evolution, determining the patterns and trends of development. And based on these objective factors, I build my opinion. If my opinion is different from the other, then I will try to determine what the other opinion is based on, on what premises, facts or subjective things.

It was this main feature of logic - the sequence of thoughts - that the famous Socrates used in his disputes and convictions, when, starting from some indisputable fact recognized by both sides, he began a consistent movement from one indisputable statement to another, finally coming to his opponent. to be convinced that you are right.

Today, I too, using logic, namely, showing the bank employee the lack of consistency between their declarations of good service and the real state of affairs, convinced him of the need to take appropriate measures.

Thank you, Nikolai, for a good, relevant topic and, as always, an interesting article!

• Thanks Konstantin for the excellent continuation of the article!

  In one of my articles, I mentioned 10 questions of a systematic approach to studying a subject, so I completely agree with you on the technology of creating your own opinion on the subject that you described.

  I also prefer earlier editions, and I usually read the creators of ideas, teachings, and not their subsequent interpretations and “chewing”.

  In the next article, I will provide practical tips for using logical forms. Let's talk about critical thinking, especially important for the present time.

  I already see that this article is too voluminous, so I will take the format of 3,000 characters as a basis (this one has 17,000 characters).

  I will also add a few old publications on the organization of labor, but before they knew how to organize:

  1. G.F. Popov. Technique of personal work.

  2. A.K. Gastev. How to work. 1972

  3. P.M. Kerzhentsev. Organization principles. 1968

  4. M.A. Shtremel. Engineer in the laboratory. Organization of labor. 1983

Good day, dear friends! Do you remember what grades you got in school? I remember. There are no triples in my certificate. But during any year of study there were triples, deuces, and even cola sometimes happened. So I think, who is Alexandra, my daughter, like? Excellent student, hangs on the honor roll! Apparently those additional exercises that we do with her are bearing fruit.

Lesson plan:

Exercise 1

A very interesting exercise! Useful not only for children, but also for adults. This exercise is used as a test at the casting of radio hosts. Imagine, you come to the casting, and they say to you: “Come on, my friend, connect us a chicken with a pole.” In all seriousness, they say so!

The meaning is precisely in this, you need to combine two completely unrelated concepts. Radio presenters need this in order to quickly and beautifully compose lead lines to songs during live broadcasts, for easy transitions from one topic to another.

Well, the kids are suitable for the development of creative, creative, quick thinking.

So how do you connect a chicken with a pole? Lots of options:

1. The chicken walks around the post.
2. The chicken was blind, walked and crashed into a pole.
3. The chicken was strong, hit the pole, and it fell.
4. The pillar fell right on the chicken.

Do you want to work out? Good. Connect:

• chamomile with milk;
• headphones with a jellyfish;
• moon boots.

Exercise 2. Word Breakers

If in the previous exercise we connected, then in this we will break one long word into many short ones, consisting of letters of a large word. According to the rules, if a letter occurs once in a long word, then it cannot be repeated twice in short words.

For example, the word "switch" breaks down into:

• tulle;
• key;
• beak.

I don't see any more options, do you?

You can break any long words, for example, “holiday”, “picture”, “towel”, “polar explorer”.

Exercise 3. Puzzles

Solving puzzles helps to think outside the box, creatively. Teaches the child to analyze.

Rebuses may contain images, letters, numbers, commas, fractions, placed in a very different order. Let's try to solve some simple puzzles together.

1. On the first we see the syllable "BA" and "barrel". Connect: BA + Barrel = Butterfly.
2. On the second, the principle is the same: Baran + KA = Bagel.
3. The third is more difficult. Cancer is drawn, and next to it is “a = y”. So in the word cancer, the letter "a" must be replaced with the letter "y", we get "hands". To this we add one more "a": hands + a = hand.
4. The fourth rebus with a comma. Since the letter “A” is the first, the guess word begins with it. Next, we see the “fist”, after the picture there is a comma, which means that the last letter must be subtracted from the word “fist”. Let's get "cool". Now we combine everything together: A + kula = shark.
5. The fifth rebus is only at first glance difficult. It is necessary to remove the letter “and” from the word “saw”, and read the word “cat” backwards. As a result, we get: pla + current = handkerchief.
6. The sixth, fully alphabetic rebus. Everything is clear with the first and last letters, but what about the middle? We see the letter "o" drawn in the beech "t", so let's say "in t o". We connect: A + WTO + P \u003d AUTHOR.

Have you trained? Now try to solve the puzzle yourself.

You can share your answers in the comments. You will find many puzzles in children's magazines and.

Exercise 4. Anagrams

Can an orange be turned into a spaniel and vice versa? "Easily!" - anagram lovers will answer. You don't even need a magic wand.

An anagram is a literary device that consists in rearranging the letters or sounds of a certain word (or phrase), which results in another word or phrase.

Just as easily, a dream turns into a nose, a cat into a current, and a linden into a saw.

Well, shall we try? Let's make it so:

• the "carriage" flew to the stars;
• "word" grew on the head;
• "lace" learned to fly;
• "atlas" became edible;
• "pump" settled in the forest;
• "mote" became transparent;
• the “roller” was placed on the table before dinner;
• "bun" learned to swim;
• "chamomile" was spinning by the lantern on summer evenings;
• "Park" could not live without water.

Exercise 5. Logic problems

The more logic puzzles you solve, the stronger your thinking becomes. After all, it is not for nothing that they say that mathematics is gymnastics for the mind. Indeed, when solving some of them, you directly feel how the brain moves.

Let's start with the simpler ones:

1. Kolya and Vasya solved problems. One boy decided at the blackboard, and the other at the desk. Where did Vasya solve problems if Kolya did not solve them at the blackboard?
2. Three old grandmothers live in the same entrance, on the third, fifth and seventh floors. Who lives on what floor, if grandmother Nina lives above Valya's grandmother, and Galya's grandmother lives below Valya's grandmother?
3. Yura, Igor, Pasha and Artem finished in the top four in the running competition. Who took what place? It is known that Yura ran not the first and not the fourth, Igor ran after the winner, and Pasha was not the last.

And the next three problems Sashulya brought from the Mathematical Olympiad. These are tasks for the third grade.

“The gardener planted 8 seedlings. Of all but four, pear trees have grown. All but two pear trees grow pears. Pears from all fruit-bearing pear trees except one are not tasty. How many pear trees have tasty pears?”

“Vasya, Petya, Vanya wear ties of only one color: green, yellow and blue. Vasya said: "Petya does not like yellow." Petya said: "Vanya wears a blue tie." Vanya said: "You are both deceiving." Who prefers what color if Vanya never lies?

And now attention! A task of increased difficulty! "On the backfill," as they say. I couldn't solve it. I suffered for a long time, and then I looked at the answers. She is also from the Olympics.

“The traveler needs to cross the desert. The transition lasts six days. The traveler and the porter who will accompany him may take with him a supply of water and food for one person for four days each. How many porters will the traveler need to realize his plan? Enter the smallest number."

If you still fall asleep on any task, then contact me, I will help)

Exercise 6. Match puzzles

Matches are not toys for children! A tool for training thinking. For safety reasons, I suggest replacing matches with counting sticks.

These simple little sticks make very complex puzzles.

First, let's warm up:

• fold two identical triangles from five sticks;
• of seven sticks, two identical squares;
• remove three sticks to make three identical squares (see picture below).

Now more difficult:

Move three sticks so that the arrow flies in the opposite direction.

The fish also needs to be turned in the other direction, while shifting only three sticks.

After shifting only three sticks, remove the strawberry from the glass.

Remove two sticks to make two equilateral triangles.

The answers can be found at the end of the article.

Exercise 7

And now let's work as Sherlock Holmes! Let us seek the truth and discover lies.

Show the child two pictures, on one of which depict a square and a triangle, and on the other a circle and a polygon.

And now offer cards with the following statements:

• some figures on the card are triangles;
• there are no triangles on the card;
• there are circles on the card;
• some of the figures on the card are squares;
• all shapes on the card are triangles;
• there are no polygons on the card;
• There are no rectangles on the card.

The task is to determine whether these statements are false or true for each picture with figures.

A similar exercise can be carried out not only with geometric shapes, but also with images of animals. For example, put a cat, a fox and a squirrel on the picture.

Statements can be as follows:

• all these animals are predators;
• there are pets in the picture;
• all the animals in the picture can climb trees;
• all animals have fur.

Pictures and statements to them can be selected independently.

Exercise 8. Instruction

We are surrounded by a variety of things. We use them. Sometimes we do not pay any attention to the instructions that are attached to these items. And it also happens that there are simply no instructions for some very necessary items. Let's fix this misunderstanding! We will write the instructions ourselves.

Take, for example, a comb. Yes, yes, the usual comb! That's what we got with Alexandra.

So, instructions for using the comb.

1. A comb is a device for making hair smooth and silky, made of plastic.
2. Use a comb should be with increased shaggy and curly.
3. In order to start combing, approach the comb, gently take it in your hand.
4. Stand in front of a mirror, smile, bring the comb to the roots of your hair.
5. Now slowly move the comb down to the ends of your hair.
6. If there are obstacles in the form of knots on the way of the comb, then run the comb over them several times with slight pressure, while you can scream a little.
7. Each strand of hair is subject to processing by a comb.
8. Combing can be considered finished when the comb does not meet a single knot on the way.
9. After combing, it is necessary to rinse the comb with water, put it in a place specially designated for it.
10. If a tooth has broken off a comb, you need to throw it in the trash.
11. If all the teeth of the comb have broken off, send it after the tooth.

Try writing instructions for a pot, or slippers, or a glasses case. It will be interesting!

Exercise 9. Making up a story

Stories can be composed in different ways, for example, based on a picture or on a given topic. By the way, this will help. And I suggest you try to compose a story based on the words that must be present in this story.

As always, an example.

Words are given: Olga Nikolaevna, poodle, sequins, turnip, salary, gray hair, castle, flood, maple, song.

Here's what happened to Sasha.

Olga Nikolaevna walked down the street. On a leash, she led her poodle Artemon, the poodle was all shiny. Yesterday he broke the lock on the locker, got to the box of glitter, and poured it all over himself. And Artemon gnawed through the pipe in the bathroom and made a real flood. When Olga Nikolaevna came home from work and saw all this, gray hair appeared in her hair. And now they were going for turnips, as turnips calm the nerves. And the turnip was expensive, worth half the salary. Before entering the store, Olga Nikolaevna tied the poodle to a maple tree and, singing a song, went inside.

Now try it yourself! Here are three sets of words:

1. Doctor, traffic light, headphones, lamp, mouse, magazine, frame, exam, janitor, paper clip.
2. First grader, summer, hare, button, gap, bonfire, Velcro, shore, plane, hand.
3. Konstantin, jump, samovar, mirror, speed, sadness, trip, ball, list, theater.

Exercise 10

We have already worked as detectives. Now I propose to work as a police officer. The fact is that the words in well-known proverbs and sayings violated the order. We will deal with violators of the order. Try to arrange the words the way they are supposed to stand.

1. Food, comes, time, in, appetite.
2. You will pull out, not, labor, from, a fish, a pond, without.
3. Measure, one, a, one, seven, cut, one.
4. And, ride, sled, love, carry, love.
5. Waiting, no, seven, one.
6. Word, cat, and, nice, kind.
7. One hundred, a, rubles, have, don't, have, friends, a hundred.
8. Falls, not, apple trees, far, apple, from.
9. Flowing, stone, not, water, recumbent, under.
10. Autumn, consider, by, chickens.

I want to clarify. We don't do this on purpose. That is, it doesn’t happen that I say: “Come on, Alexandra, sit down at the table, let’s develop thinking!” No. All this in between times, if we go somewhere, we go, before going to bed instead of books. It is very interesting to do it, so you don’t have to force anyone.

Well, now the promised answers to matchstick puzzles!

Puzzle Answers

About two triangles of five matches.

About two squares out of seven.

We get three squares.

Expand the arrow (watch the color of the sticks).

We turn the fish.

And about two equilateral triangles.

I recently found this video on the internet. It has completely different exercises. We tried, until it turns out with difficulty. Well, let's practice. See if you can use it too.

Dare! Get busy! Develop with your children. Try these "golden" exercises. Show off your results in the comments!

Thank you for your attention!

And I look forward to visiting again! Here you are always welcome!

Some people have logical thinking, they can calculate the necessary moves and actions, predict what might happen in the near future.

If a person does not have developed logical thinking, it will be difficult for him to calculate the necessary steps forward and make the right decision.

How can logic be developed? What can you do to make logical thinking work for you?

You can develop logic in many ways using different exercises, games, using tips, and so on. Logic is translated as thought and the ability to reason. If you want to reason and think intelligently, then you need to start doing it with reasoning.

Take some information and try to reason about it, look at this situation from different angles, draw a few conclusions and try to find the right and right choice. Then take another situation and try to reason about it and find the right solutions.

Thus, you will learn to reason and determine how you act in different situations.

Now you can deal with logic, this quality is possessed by people who discover something in life, but logic is also needed by any person, no matter if he is young or old, works as a leader or a simple worker.

In any simple business, logic is needed, for example, a manager must think logically so that the work process moves in a planned manner and the enterprise works stably.

Let's take another profession, for example, a person who washes the floor, he should also have logic on how to stand up correctly and in which direction to move and wash the floor, if this person does it without logic and wash the opposite, then he will simply stomp on the clean floor, and trample on your work.

If you learn to think logically, you will be able to:

avoid mistakes at work and at home;

always find the right way out of any situation;

correctly formulate your thoughts and convey them to the audience;

to get ahead of liars and deceivers among people;

find the right arguments and win over most of the people;

see your mistakes and the mistakes of the people around you and you can prevent a bad situation;

quickly and correctly find the right answers.

Development of logic through games and exercises

Checkers

A simple and uncomplicated game that helps develop attention, concentration, improves memory and develops logic.

Chess

The game of chess is more difficult than checkers, but it teaches you to think logically and make the right moves.

Scanwords, puzzles

By solving puzzles and puzzles, you develop memory, attention and logic.

Associations

Come up with any word and associate it with different associations, the more you come up with different associations for this word, the better your logic will develop.

Anagrams

Solve anagrams more often, they help develop logic and thinking.

Come up with 10 different ways to use an item

Take any item and come up with 10 ways to use this item.

For example, a pencil.

You can draw, draw, loosen the ground with a pencil, use it as a bookmark, use it as a pointer, you can rewind a cassette in a cassette recorder, and so on.

Look at the following words and think of ten ways to use them: vase, axe, water, flower, carpet.

Come up with different phrases

This exercise can be used everywhere without being distracted by it specifically, for example, when you are preparing a meal or going to work, come up with a variety of phrases.

For example, a ball.

A ball flew in, a ball was scored, a blue ball, a favorite ball, and so on.

Try to come up with as many phrases as possible.

Learn to write with the other hand

If you are right-handed, then you can practice writing with your left hand, and if you are left-handed, then write with your right hand.

Then try writing numbers and letters with both hands at the same time.

This is a very interesting exercise and it is not easy to perform, it will take practice and patience to complete.

Educational games for the development of logic

Game 1 "Anagrams"

The game "Anagrams" develops thinking and memory.

The main essence of the game is to quickly decipher the anagram.

In this game, a word is given on the screen and four anagrams are given below the word. You need to quickly read and find the anagram you need. If you answered correctly, then you score points and continue to play on.

Game 2 "Visual Geometry"

The game "Visual Geometry" develops thinking and memory.

In this game, blue squares are shown on the screen, they must be quickly counted, then they close. Four numbers are written below the table, you must select one correct number and click on it with the mouse. If you answered correctly, then you score points and continue to play further.

Game 3 "Letters and numbers"

The game "Letters and Numbers" develops thinking and memory.

The main essence of the game on the field is the object, you must quickly specify its property using the "yes" and "no" buttons.

In this game, an object is placed on the field and a question is asked. Read the question carefully. You can answer the question using the yes and no buttons below. If you answered correctly, you score points and continue playing.

Game 4 "Operations"

The game "Operations" develops thinking and memory.

The main essence of the game is to choose a mathematical sign so that the equality is true.

In this game, examples are given, look carefully at the example and put the correct “+” or “-” sign so that the equality is correct. If you answer correctly, then you score points and continue to play on.

Game 5 "Complex Geometric Switching"

The game "Complex Geometric Switching" develops thinking and memory.

The main essence of the game on the field is an object whose property must be specified.

In this game, a geometric figure or other object appears on the screen. Read the question on the screen and answer it using the yes or no buttons located at the bottom of the screen. If you answer correctly, you score points and continue playing.

Game 6 "Matrices of color"

The game "Color Matrix" develops thinking and memory.

The main essence of the game is shown a matrix consisting of multi-colored cells, it is necessary to indicate which color cells are larger.

In this game, a matrix is ​​shown on the screen, it consists of multi-colored cells. Look carefully and say which cells are more. With the mouse, you can click on the box of the color that is larger. If you answer correctly, you score points and play on.

Game 7 Simplify

The game "Simplify" develops thinking and memory.

The main essence of the game is to quickly perform a mathematical operation.

A student is drawn on the screen at the blackboard, and a mathematical action is given, the student needs to calculate this example and write the answer. Below are three answers, count and click the number you need with the mouse. If you answer correctly, you score points and play on.

Game 8 "Fast Addition"

The game "Quick Addition" develops thinking and memory.

The main essence of the game is to choose numbers, the sum of which is equal to a given number.

This game is given a matrix from one to sixteen. A number is given above the matrix, you must select the numbers, the sum of which will be equal to the given number. If you answered correctly, you score points and continue playing.

Game 9 "Geometric Switching"

The game "Geometric switching" develops thinking and memory.

The main essence of the game on the field is the object, you need to define its properties using the "yes" and "no" buttons.

In this game, there is an object on the field, you need to determine the properties of this object and answer using the buttons located at the bottom “yes” or “no”. If you answered correctly, you score points and play on.

Game 10 "Letters and Numbers Plus"

The game "Letters and Numbers Plus" develops thinking and memory.

The main essence of the game on the field is an object, you must specify its properties.

In this game, there is an object on the field and a question is written, read this question and answer using the buttons “yes” or “no” located at the bottom. If you answered correctly, you score points and continue playing.

Courses for the development of intelligence

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

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

The course includes 30 lessons with useful tips and exercises for the development of children. Each lesson contains useful advice, some interesting exercises, a task 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.

The secrets of brain fitness, we train memory, attention, thinking, counting

If you want to overclock your brain, improve its performance, pump up memory, attention, concentration, develop more creativity, perform exciting exercises, train in a playful way and solve interesting puzzles, 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, a powerful 30-day training for the development of super-memory and brain pumping will begin for you.

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

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

Money and the mindset of a millionaire

Why are there money problems? In this course, we will answer this question in detail, look deep into the problem, consider our relationship with money from a psychological, economic and emotional point 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.

Speed ​​reading in 30 days

Would you like to read interesting books, articles, mailing lists and so on very quickly.? 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 starts to work many times faster, which opens up many more possibilities. Attention, concentration, perception speed amplify many times over! Using the speed reading techniques from our course, you can kill two birds with one stone:

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

We speed up mental counting, NOT mental arithmetic

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

Conclusion

Develop logic, think logically and learn to possess logic and apply it in life. We wish you good luck.

The very concept of figurative thinking implies operating with images, carrying out various operations (thinking) 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 for the formation of such a skill are described in sufficient detail in the section on memory development. Here we will supplement them with a few more tasks for visualization.

Visualization exercises.

Task: you need to come up with as many associations as possible for each picture. The quantity and quality (originality) of the images are evaluated. It is good to carry out the exercise with a group of children in the form of a competition.

Exercise number 2. "Fill in the gap" task.

You can find additional tasks for the development of visualization and visual-figurative thinking in the "Diagnostics of the development of thinking" section.

After the process of visualization is sufficiently well mastered by children, one can proceed to the direct operation of images, i.e. to solving the simplest mental problems based on representations.

Exercise number 3. Game Cubes.

The material consists of 27 ordinary cubes - glued together so that 7 elements are obtained:

This game is mastered in stages.

The first stage is examining the elements of the game and finding their similarities with objects and forms. For example, element 1 is the letter T, 2 is the letter G, element 3 is a corner, 4 is a lightning zigzag, 5 is a tower with steps, 6 and 7 are a porch. The more associations are found, the better and more effective.

The second stage is the development of ways to attach one part to another.

The third stage is the folding of three-dimensional figures from all parts according to the samples, indicating the constituent elements. It is advisable to carry out the work in the following sequence: invite the children to first consider the sample, then divide it into its constituent elements and fold the same figure.

The fourth stage is the folding of three-dimensional figures according to the representation. You show the child a sample, he carefully examines it, analyzes it. Then the sample is removed, and the child must make the figure that he saw from the cubes. The result of the work is compared with the sample.

Counting sticks can also be used as material for solving mental problems based on figurative thinking.

Exercise number 4. "Problems for composing a given figure from a certain number of sticks."

Problems for changing figures, for the solution of which it is necessary to remove the specified number of sticks. Given a figure of 6 squares. It is necessary to remove 2 sticks so that 4 squares remain.

"Given a figure that looks like an arrow. You need to shift 4 sticks so that you get 4 triangles."

"Make two different squares of 7 sticks."

Tasks, the solution of which is to shift the sticks in order to modify the figure.

"In the figure, shift 3 sticks so that you get 4 equal triangles."

"In a figure consisting of 4 squares, shift 3 sticks so that you get 3 of the same squares."

"Make a house of 6 sticks, and then shift 2 sticks so that you get a flag."

"Shift 6 sticks so that the ship turns into a tank."

"Shift 2 sticks so that the cow-like figure looks the other way."

"What is the least number of sticks you need to move to remove the garbage from the scoop?"

Exercises aimed at developing visual-figurative thinking.

Exercise number 5. "Continue the pattern."

The exercise consists of a task to reproduce a drawing about a symmetrical axis. The difficulty in doing this often lies in the inability of the child to analyze the sample (left side) and realize that the second part of it should have a mirror image. Therefore, if the child finds it difficult, at the first stages you can use a mirror (attach it to the axis and see what the right side should be).

After such tasks no longer cause difficulties in reproduction, the exercise is complicated by the introduction of abstract patterns and color designations. The instructions remain the same:

"The artist drew part of the picture, but the second half did not finish. Finish the drawing for him. Remember that the second half must be exactly the same as the first."

Exercise number 6. "Handkerchief".

This exercise is similar to the previous one, but is a more difficult version of it, because. involves the reproduction of a pattern with respect to two axes - vertical and horizontal.

"Look carefully at the picture. It shows a handkerchief folded in half (if there is one axis of symmetry) or four times (if there are two axes of symmetry). What do you think, if the handkerchief is unfolded, what does it look like? Draw the handkerchief so that it looks unfolded. "

Patterns and options for tasks can be invented independently.

Exercise number 7. "Make a figure."

This exercise, like the previous one, is aimed at developing figurative thinking, geometric ideas, constructive spatial abilities of a practical plan.

We offer several options for this exercise (from the easiest to the most difficult).

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 it is possible to make a layout out of paper and work with the child in a visual-active way, i.e. when he can manipulate the parts of the figure and thus compose the whole.

b) "Look carefully at the picture, there are two rows of figures. In the first row there are whole figures, and in the second row these same figures, but broken into several parts. Mentally connect the parts of the figures in the second row and the figure that you have this will work, find it in the first row. The figures of the first and second rows that fit together, connect with a line. "

c) "Look carefully at the pictures and choose where the details are located, from which you can make the figures shown on the black rectangles."

Exercise number 8. "Fold the figures."

The exercise is aimed at developing the ability to analyze and synthesize the ratio of figures to each other in color, shape and size.

Instruction: "What do you think the result will be 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 the difficulty (the disguise of relations in form), the tasks are distributed in this way: when a larger figure is superimposed on a smaller figure, which provokes the child to not suggest covering a larger figure with a smaller one and chooses the result of mixing 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 plan (mental imposition), but in a visual-effective one, i.e. direct imposition of geometric shapes.

Exercise number 9. "Find a pattern."

a) The exercise is aimed at developing the ability to understand and establish patterns in a linear series.

Instruction: "Look carefully at the pictures and fill in the empty cell without breaking the patterns."

b) The second version of the task is aimed at developing the ability to establish patterns in the table. Instruction: "Look at the snowflakes. Draw the missing ones so that all types of snowflakes are represented in each row."

Similar tasks can be created independently.

Exercise number 10. "Traffic light".

"Draw red, yellow and green circles in the cells so that there are no identical circles in each row and in each column."

Exercise number 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 images of five different cubes in the first row. The cubes are arranged in such a way that only three of the six faces of each of them 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 dice, new icons may appear on those faces that were not visible before the rotation. Each cube from the top row must be connected with a line with its rotated image in the bottom row.

This exercise is very effective in terms of developing visual-figurative thinking. If the operation of images causes great difficulties for the child, we advise you to glue such cubes and carry out exercises with them, starting with the simplest - "find a correspondence between the picture shown and the same position of the cube."

Exercise number 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 set for the child: for example, arrange objects (or figures) so that all rounded figures (and only them) are inside the hoop.

After the arrangement of the figures, it is necessary to ask the child: "What figures lie inside the hoop? What 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 the child to designate the property of the 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 shaded (red, green), and only they, are inside the hoop." "Arrange objects (pictures) so that all denoting animate objects, and only they, are inside the hoop", etc.

"Game with two hoops".

Formation of a logical operation of classification by two properties.

Before starting the exercise, four areas are set, defined on the sheet by two hoops, namely: inside both hoops (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 circled with a pencil.

Then the rule for classification is reported: "It is necessary to arrange the figures so that all the shaded figures are inside the hoop of the black line, and all the charcoal ones are inside the circle of the dashed line."

The difficulty encountered in completing this task is that some children, starting to fill in the inside of the circle from a broken line, place the shaded charcoal figures outside the hoop from the black line. And then all the other shaded shapes outside the broken line hoop. As a result, the common part (intersection) remains empty. It is important to bring the child to the understanding 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 dashed 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.

For the game, not only figures, but also subject pictures can be used. In this case, the variant of the game may be as follows: "Arrange the pictures so that in a circle of black lines there are pictures of wild animals, and in a hoop of broken lines - all small animals, etc."

"Game with three hoops" (classification according to three properties).

The work is built similarly to the previous one. First you need to find out into which areas the hoops divide the sheet. What is this area where hoops of black and dashed 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 figures: for example, inside a circle from a black line should be all round figures; inside a hoop of broken lines - all small, inside a circle of wavy lines - all shaded.

A set of figures.

If a child finds it difficult to assign a figure to the desired hoop according to a certain class, it is necessary to find out what properties the figure has and where it should be 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 such conditions under which individual regions turn out to be empty; for example, if you arrange the figures so that inside the hoop of the black line are all round, inside the hoop of the dashed line - all triangles, inside the hoop of the wavy line - all shaded, etc. In these variants of the task, it is important to answer the question: why did certain areas turn out to be empty?

Exercise number 13. "Classification".

Just like the previous exercise, this is aimed at developing the ability to classify according to a certain attribute. The difference lies in the fact that when performing this task, the rule is not given. The child needs to independently choose how to divide the proposed figures into groups.

Instruction: "There are a number of figures (objects) in front of you. If it were necessary to divide them into groups, how can this be done?"

A set of figures.

It is important that the child, completing this task, find as many reasons for classification as possible. For example, it can be a classification by shape, color, size; division into 3 groups: round, triangles, quadrilaterals, or 2 groups: white and non-white, etc.

Exercise number 14. "Traveling Animals".

The main purpose of this exercise is to use it to form the ability to consider different ways or options to achieve the goal. By operating with objects mentally, imagining different options for their possible changes, you can quickly find the best solution.

As the basis of the exercise, there is a playing field of 9 (at least), and preferably 16 or 25 squares. Each square contains some kind of schematic drawing that is understandable to the child and allows you to identify this square.

"Today we will play a very interesting game. This is a game about a squirrel that can jump from one square to another. Let's see what squares-houses we have drawn: this square is with an asterisk, this one is with a mushroom, this one is with an arrow etc.

Knowing what the squares are called, we can say which of them are next to each other, and which are one after the other. Tell me, which squares are next to the Christmas tree, and which are one through from it? How are the squares with a flower and the sun, a house and a bell, next to each other or through one?

After the playing field is mastered by the child, a rule is introduced: how can the squirrel move from one house to another.

"A squirrel jumps around the field according to a certain rule. She cannot jump into neighboring squares, because she can only jump through one cell in any direction. For example, from a cell with a Christmas tree, a squirrel can jump into a cell with a bell, a cell with a leaf and a cell with a house ", but nowhere else. Where do you think a squirrel can jump if it is in a cage with a tree? Now you know how a squirrel can jump, tell me how to get from a cage with a star to a cage with a window?" While working on the task, we immediately teach the child to record:

"In an empty cell, we fill in the same pattern as on the cell through which the squirrel jumps." For example, in order for it to get from a cell with an asterisk to a cell with a window, the squirrel must first jump into the cell with an arrow looking to the right, and we draw it 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 you need to draw a tree.

Next, the adult offers the child various options for tasks in which you need to guess how the squirrel can get into the right cage by jumping according to its own rule. In this case, tasks can consist of two, three or more moves.

Task options.

You can come up with options for tasks on your own, outlining the first and final point of the journey, at which it is possible to comply with the rule. It is very important that when thinking through the moves, the child can find several ways to get from one square to another.

The Animal Journey exercise using this game board can be modified in a variety of ways. For another lesson, an adult offers a game with another animal (this is a bunny, a grasshopper, a neuk, etc.) and according to a different rule, for example:

1. The beetle can only move obliquely.
2. 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 another version of the exercise, on a different playing field.

An alphanumeric field is used for work in the same way as a picture field. You can train on it according to the same rules or according to others invented by yourself. In addition, these may include the following rules:

1. The goose can only walk on neighboring cells and only straight ahead.
2. A ladybug can fly only to the next cell and only with the same letter or the same number.
3. A fish can only swim to an adjacent cell with a mismatched 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 reverse type: “From which cell should the beetle crawl out so that, crawling according to its rule (call the rule), it gets into the cell, for example, GZ or with a mushroom (for a picture playing field).

Verbal-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 number 15. "Systematization".

The exercise is aimed at developing the ability to systematize words according to a certain attribute.

"Tell me, what berries do you know? Now I will name the words, if among them you hear the word for a berry, then clap your hands."

Presentation words - 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 to fruits - twice." (Words can be used the same, you can come up with others.)

As a basis for systematization, there may be a topic - tools, furniture, clothes, flowers, etc.

"Tell me, how are they similar in taste? Color? Size?
lemon and pear
raspberries and strawberries
apple and plum
currant and gooseberry
How are they different in taste? color? size?"

Exercise number 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 up of these words: dove, sparrow, carp, tit, pike, bullfinch, pike perch."

Exercise number 17. "Choose the words."

1) "Pick up as many words as possible that can be attributed to the group of 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. Task: Use arrows to match the words that make sense.

Such tasks develop the child's ability to distinguish generic and specific concepts, form inductive speech thinking.

Exercise number 18. "Find a common word."

This task contains words that are united by a common meaning. It is necessary to try to convey this general meaning in one word. The exercise is aimed at developing such a function as generalization, as well as the ability to abstract.

What is the common word for 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, sense organs)
c) apple and strawberry (fruits)
d) clock and thermometer (measuring instruments)
e) whale and lion (animals)
f) 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 in terms of developing a generalizing function.

Exercise number 19. "Unusual Domino".

This exercise is aimed at the gradual (level-by-level) teaching of the child to look for signs by which generalization can occur.

Empirically, three spheres of such signs are distinguished.

The first sphere is a generalization by an attributive property (the lowest level). This includes: the shape of an object, its size, the parts from which it is made, or material, color, i.e. everything that is some kind of external qualities, or attributes of the subject. 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 a generalization on a situational basis (a higher level). Transitional to this area is the generalization of objects on the basis of "property - action", i.e. the child singles out as a general property the action produced by objects.

For example, "A frog approaches a squirrel because they can jump." In addition, this area includes generalizations on the situation of using "pears and carrots, because both are eaten ..."; situations of place and time of stay - "a cat and a mouse, because they live in the same house"; situations of communication, games - "a puppy and a hedgehog, because they play together ...".

The third sphere is a generalization on a categorical basis (the highest). This is a generalization on the basis of the class to which the objects belong. For example, a ball and a bear are toys; spider and butterfly, the common thing is that they are insects.

The domino exercise allows the child to choose the basis for generalization (thus, an adult can get an idea of ​​the level of development of this function in the child), as well as to guide and help the child look for more significant, high-grade 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 contains two pictures.

1. tractor - deer
2. bucket - zebra
3. puppy - mouse
4. cat - doll
5. girl - bear
6. elephant - 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 - chick
18. hedgehog - windmill
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. trolley - cup
29. kettle - pencil
30. dog - birch
31. kitten - orange
32. kennel - beetle

Each player is dealt the same number of cards. After that, the right of the first move 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 an image .... It is necessary, in order to make a move, to pick up one of your cards, but with the condition that the picture you choose has something in common with the one to which you picked her."

(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 there be in common between the selected pictures?", To choose different grounds 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 of you will again select a picture for one of the two that are at stake, explaining your choice."

Thus, as a result of the game, a chain of pictures is built, logically related to each other. We remind you that, as in a regular domino, the double-sidedness of the pictures provides the possibility of moving both in one direction and in the other.

Points are awarded for each move. If the generalization was made on an attributive property - 0 points, on a situational basis - 1 point, on a categorical basis - 2 points. The one with the most points wins.

The cards that the players receive during the distribution, the guys do not show each other.

Logic tasks.

Logical tasks are a special section on the development of verbal and logical thinking, which includes a number of various exercises.

Logical tasks involve the implementation of a thought process associated with the use of concepts, logical structures that exist on the basis of language tools.

In the course of such thinking, there is a transition from one judgment to another, their correlation 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. Rubinshtein noted, "in the conclusion ... knowledge is obtained indirectly through knowledge without any borrowing in each individual case from direct experience."

Developing verbal-logical thinking through the solution of logical problems, it is necessary to select such tasks that would require inductive (from the singular to the general), deductive (from the general to the singular) and traductive (from the singular to the singular or from the general to the general, when the premises and conclusion are judgments of the same generality) inferences.

Traductive reasoning can be used as the first step in learning to solve logical problems. These are tasks in which, based on the absence or presence of one of the two possible features in one of the two objects under discussion, a conclusion follows about the presence or absence of this feature in the other object, respectively. 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?"

Tasks to solve.

1. Sasha ate a large and sour apple. Kolya ate a large and sweet apple. What is the same about these apples? different?

2. Masha and Nina looked at the pictures. One girl was looking at pictures in a magazine, and the other girl was looking at pictures in a book. Where did Nina look at the pictures if Masha did not look at the pictures in the magazine?

3. Tolya and Igor drew. One boy drew a house, and the other a branch with leaves. What did Tolya draw if Igor did not draw a 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 read books. One boy read about travel, another about the war, the third about sports. Who read about anything if Kolya did not read about the war and about sports, and Vanya did not read about sports?

6. Zina, Liza and Larisa embroidered. One girl embroidered leaves, another - birds, the third - flowers. Who embroidered what, if Lisa did not embroider leaves and birds, and Zina did not embroider leaves?

7. The boys Slava, Dima, Petya and Zhenya were planting fruit trees. Some of them planted apple trees, some - pears, some - plums, some - cherries. What did each boy plant if Dima did not plant plums, apple trees and pears, Petya did not plant pears and apple trees, and Slava did not plant apple trees?

8. Girls Asya, Tanya, Ira and Larisa went in for sports. Some of them played volleyball, some swam, some ran, some played chess. What sport was each girl fond of if Asya did not play volleyball, chess and did not run, Ira did not run and did not play chess, and Tanya did not run?

These eight tasks have three degrees of difficulty. Tasks 1-3 are the simplest; to solve them, it is enough to operate with one judgment. Tasks 4-6 are of the second degree of complexity, since when solving them, it is necessary to compare two judgments. Tasks 7 and 8 are the most difficult, because To solve them, you need to correlate three judgments.

Usually, the difficulties that arise when solving problems 4 to 8 are related to the inability to keep in the internal plan, in the representation, all the circumstances indicated in the text, and they get confused because they do not try to reason, but strive to see, present the correct answer. In this case, a technique is effective when the child has the opportunity to rely on visual representations that help him keep all the textual circumstances.

For example, an adult can make pictures of houses (task 4). And then, relying on them, conduct a reasoning of the following type: “If Alik and Borya lived in different houses, then in which of the drawn ones could they live? And why not in the first two? Etc.

For tasks 7 and 8, it is more convenient to make a table that will be filled in as you reason.

"It is known that Dima did not plant plums, 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 graphical reflection of the structure of the reasoning process helps the child to 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 problem contains the following starting point: if three objects and two features are given, one of which two objects have, and the other one, then, knowing which two objects differ from the third in terms of the specified features, it is easy to determine what feature the first two have. . When solving problems of this type, the child learns to perform the following mental operations:

Make a conclusion about the identity of two objects out of three according to the specified feature. 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;

Make a conclusion about what is the sign by which these two objects are identical. For example, if the problem says that Olya embroidered a flower, then Ira also embroidered a flower;

Make a final conclusion, i.e. Based on the fact that two out of four objects are already known that are identical in one of the two data in the feature problem, it is clear that the other two objects are identical in 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.

Tasks 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 one animal. What did Asya draw if Katya and Asya and Lena and Asya drew different animals?

3. Two boys bought stamps, one a badge and one 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 the other. Where did Petya and Kolya live if Oleg and Petya and Andrei and Petya lived on different streets?

5. Two girls played with dolls, and two - 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 - a house. What did Natasha embroider if Ira with Natasha and Natasha with Olya embroidered different pictures, and Oksana embroidered 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 fast 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 - potatoes. What did Serezha plant if Volodya planted potatoes, Valera and Sasha and Sasha and Volodya planted different vegetables, and Valera and Serezha also planted different vegetables?

Comparison tasks.

This type of problem is based on such a property of the ratio of object sizes as transitivity, which consists in the fact that if the first member of the relation is comparable with the second, and the second with the third, then the first is comparable with the third.

You can start learning to solve such problems with the simplest ones, in which you need to answer one question and which 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 most cheerful 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 each girl's hair. Sign their names. Answer the question, who is the lightest of all?"

3. "Tolya is taller than Igor, Igor is taller than Kolya. Who is taller than everyone? Show the height of each boy."

The graphic representation of the transitive ratio of quantities greatly simplifies the understanding of the logical structure of the problem. Therefore, when a child finds it difficult, we advise using the method of depicting the ratio of magnitudes 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 built as follows: "Look carefully at this line.

On the one hand, the children are the fastest, on the other - the slowest. If Katya is faster than Ira, then where will we place Katya, and where will Ira? That's right, Katya will be on the right, where are the fast children, 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 will we place Lena in relation to Ira then? That's right, even more to the left, because. she is slower than Ira.

Look closely at the drawing. Who is the fastest? and slower?"

Below we give options for logical tasks, which are divided into three groups according to the degree of complexity:
1) tasks 1-12, in which it is required to answer one question;
2) problems 12-14, in which you need to answer two questions;
3) problems 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, a question posed in different ways. Of particular importance are "fabulous" problems, in which the relationships between quantities are built in a way that does not happen in life. It is important that the child be able to distract himself from life experience and use the conditions that are given in the task.

Task options.

1. Sasha is sadder than Tolik. Tolik is sadder than Alik. Who is the funniest of all?

2. Ira is neater than Lisa. Lisa is neater than Natasha. Who is the most careful?

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. A fox is slower than a turtle. The fox is faster than the deer. Who is 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 the highest?

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 lighter than Katya. Who is the brightest?

11. Lyosha is weaker than Sasha. Andrey is stronger than Lesha. Who is stronger?

12. Natasha is more fun than Larisa. Nadia is sadder than Natasha. Who is the saddest?

13. Sveta is older than Ira and lower 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 lower 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, lowest and 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 of all, who is the strongest?

All the variants of logical problems we have considered are aimed at creating conditions in which there is or would be the possibility of forming the ability to single out significant relationships between objects and quantities.

In addition to the tasks that were indicated above, it is advisable to offer the child tasks in which some of the necessary data is missing or, conversely, there are unnecessary data. You can also use the technique of self-composing tasks by analogy with this one, but with different names and a different attribute (if the task has the attribute "age", then it can be a task about "growth", etc.), as well as tasks with missing and redundant data. It makes sense to turn direct problems into inverse ones and vice versa. For example, a direct task: "Ira is higher than Masha, Masha is higher than Olya, who is higher than everyone?"; in the inverse problem the question is: "Who is the lowest of all?".

If the child successfully copes with all types of tasks proposed to him, it is advisable to offer tasks related to the 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 problem that would be easier than the sample problem, etc.

Exercise number 20. "Anagram".

This exercise is based on combinatorial problems, i.e. those in which the solution is obtained as a result of creating certain combinations. An example of such combinatorial tasks are anagrams - letter combinations from which it is necessary to compose meaningful words.

Invite the 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 learns the principle of composing words from letter combinations, complicate the task. To this end, enter a new condition: "Decipher what words are hidden here, and say which word from the data is superfluous."

The task can be of another type: "Decipher the words and say what common word they can be combined with."

Another version of the task with anagrams: "Decipher the words and say what groups they can be divided into."

This exercise is very similar to the puzzles we are used to.

Of course, the rebus is the same combinatorial task that can be effectively used to develop verbal and logical thinking: crossword puzzles teach the child to focus on the definition of a concept according to the characteristics described, tasks with numbers - to establish patterns, tasks with letters - to analyze and synthesize various combinations. Let's take another similar exercise.

Exercise number 21. "Twin words".

This exercise is connected with such a phenomenon of the Russian language as homonymy, i.e. when words have different meanings but are spelled the same. What word means the same as the words:

1) a spring and what opens the door;
2) the girl's hair and a grass cutter;
3) a branch of grapes and a tool for drawing.

Think of words that sound the same but have different meanings.

Additional tasks for the exercise:
4) a vegetable that makes one cry and a weapon for shooting arrows (a burning vegetable and small arms);
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 a construction site and a mechanism that needs to be opened so that water flows.

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. Usually this type of thinking only begins to develop at primary school age, however, the program already includes tasks that require solutions in the abstract-logical sphere. This determines the difficulties that arise in children in the process of mastering educational material. We offer the following exercises, which not only develop abstract-logical thinking, but also correspond in their content to the main characteristics of this type of thinking.

Exercise number 22. "Formation of concepts on the basis of abstraction and selection of essential properties of specific objects".

“A car runs on gasoline or other fuel; a tram, trolleybus or electric train is powered by electricity. All this together can be classified as a group of “transport.” Seeing an unfamiliar car (for example, a truck crane), they ask: what is it? Why?

Similar exercises are performed with other concepts: tools, utensils, plants, animals, furniture, etc.

Exercise number 23. "Formation of the ability to separate the form of a concept from its content."

“Now I will speak words to you, and you will answer me, which is more, which is less, which is longer, which is shorter.
- Pencil or pencil? Which one is shorter? Why?
- Cat or whale? Which one is more? Why?
- A boa constrictor or a worm? Which one is longer? Why?
- Tail or ponytail? Which one is shorter? Why?"

The teacher can come up with his own questions, focusing on the above.

Exercise number 24. "Formation of the ability to establish relationships between concepts."

The exercise below involves establishing the relationships in which the given words are found. An approximate pair of words serves as a key to revealing these relationships. Knowing them, you can pick up a pair to the control word. Work with this exercise is carried out jointly by an adult and a child. The task of an adult 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, examples of such analogies are given. Only when a stable and consistent ability to establish logical associations has been formed in children can one proceed to tasks for independent work.

Exercise number 25. "Formation of the ability to identify essential features to maintain the logic of judgments when solving a long series of similar tasks."

An adult says to the children: “Now I will read you a series of words. Of these words, you will have to choose only two, denoting the main features of the main word, that is, without which this subject 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, a garden ... What do you think, which of these words are the main ones: plants, gardener, dog, fence, earth, i.e. without which there can be no garden? Can there be a garden without plants? Why?.. Without a gardener... a dog... a fence... land?.. Why?"

Each of the proposed words is analyzed in detail. The main thing is that children understand why this or that word is the main, essential feature of this concept.

Sample tasks:

a) Boots (laces, sole, heel, zipper, bootleg)
b) River (shore, fish, angler, 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 (aircraft, guns, battles, guns, soldiers)

This exercise allows you to purposefully direct the search for a solution, activate thinking, create a certain level of abstraction.

Work on the formation in children of the ability to highlight the essential features of concepts, to establish various relationships prepares fertile ground for the development of the ability to form judgments as a higher level in the development of abstract-logical thinking. The purposefulness of judgments, the degree of their depth depend on the child's ability to operate with meaning, to understand figurative meaning. For this work, you can use various literary material, proverbs, sayings, containing the possibilities of verbalization and transformation of the text.

Exercise number 26. "Formation of the ability to operate with meaning."

"Now I will 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, cut once

a) If he himself cut off incorrectly, then you should not blame the scissors

b) Before doing, you need to think carefully

c) The seller measured seven meters of fabric and cut

The correct choice here is "Before you do, you need to think carefully", and the scissors or the seller are just details and do not reflect the main meaning.

Sample tasks:

1. Less is better.
a) It is more useful to read one good book than seven bad ones.
b) One delicious cake is worth ten bad ones.
c) It is not the quantity that matters, but the quality.

2. Hurry - make people laugh.
a) The clown makes people laugh.
b) To do a job better, you need to think about it well.
c) Haste can lead to ridiculous results.

3. Strike while the iron is hot.
a) A blacksmith forges hot iron.
b) If there are favorable opportunities for business, you should immediately use them.
c) A blacksmith who works slowly often gets more done than one who is in a hurry.

4. There is nothing to blame on the mirror if the face is crooked.
a) You should not blame the cause of failures on circumstances, if the matter is in you.
b) The good quality of a mirror does not depend on the frame, but on the glass itself.
c) The mirror hangs crooked.

5. The hut is not red with corners, but with pies.
a) You can’t eat only pies, you have to eat rye bread.
6) The case is judged by the results.
c) One delicious cake is worth ten bad ones.