Productive and reproductive thinking examples. Thinking productivity. General characteristics of the types of thinking

There are people who amuse themselves with thinking, and for them productive thinking is only boring. For people-creators, productive thinking, where the flow of thoughts, images and sensations is purposeful, where there is an understanding of what is happening, the birth of new life meanings and the solution of life tasks - such thinking is of the highest value.

The orangutan cannot reach the fish in the river, but there is a rather long stick next to it. When an orangutan has understood the connection between a stick and a fish that needs to be reached, this is productive thinking.

Productive thinking - finding a connection between objects and phenomena, solving a vital task. It is the ability to include, to look for a solution to one or another, to do. This is a look at the situation that solves a particular problem. Synonym - think. Productive thinking means thinking about what you need, when you need it and how you need it. And this means:

Train yourself to think concretely.

“Working on yourself”, “Improving yourself”, “Eradicating your shortcomings” are beautiful words, but usually there is nothing behind them. And the one who uses such words, most often marks time in one place.

"Get up, Count! Great things are waiting for you!”, “The morning starts with exercises”, “I got up - I made the bed”, “I left the house - I straightened my shoulders” - these are simple and concrete things. And the benefits of such thoughts, practical orders to oneself, are great.

Avoid thoughts and emptiness. Stop burdening yourself with thoughts that will get you nowhere.

Do not start a conversation about this, do not go to those people where these conversations will arise, do not read what will push you to these thoughts. Keep yourself occupied with something simple and useful. For example, for you in the near future it is: ... What?

Have a plan of your affairs and think about what you need to think about now.

If you have a sheet in front of your eyes where you write down the affairs of the upcoming day, everything becomes easier - this business sheet will organize you. If you have good friends, your friends will organize your thinking. Next to them, you always start to think about the good. About necessary.

Think in such a way as to arrive at results that will please you and will be useful to you and those around you.

Like this? (For example)

Suppose you are thinking about your job.

Are you planning to change something there? Are you really planning to change something there? If yes, then think further, and be sure. If not, then stop thinking and get down to business.

Unfortunately. And upset, of course.

Curious: and why then you thought about it like that? Has it raised your self-confidence, will it help you do the things that lie ahead of you? Think about how you can think differently about yourself so that you believe in yourself and teach yourself at least a small thing that will be useful to you in your work.

Learn to type with ten fingers? Stop making excuses? Something else?

Record this helpful finding in your diary. And you can think even more and make already serious decisions. Life is yours, one, why not? So, "I'm contemplating such a big decision..."

Unproductive thinking

If we single out productive thinking, it means that there is another type of thinking: unproductive. And what is it, what is it? It seems that this is a whole world of the most diverse options for thinking: for example, this is internal chatter - relatively coherent, sometimes even logical, but inappropriate thinking that fills the emptiness of the soul, entertaining and creating the illusion that life is filled with something. These are empty dreams and options for defensive-aggressive thinking, ready to destroy any logic in order to preserve inner comfort.

teacher-psychologist of the highest category,

Ph.D. Yesenzhanova A.A.

Thinking is productive and reproductive.

In thinking, various components are intertwined in a dialectically contradictory unity, in connection with this, the need arises to single out the types of thinking that interest us - productive and reproductive. Although, in its essence, any thinking is always productive to a greater or lesser extent, in a specific mental activity, their share can be different. In Soviet literature, there is an objection to the separation of these types of thinking, since "any process of thinking is productive." But many scientists who dealt with the problem of thinking consider it appropriate to distinguish these types (P.P. Blonsky, D.N. Zavalishina, N.A. Menchinskaya, Ya.A. Ponomarev, V.N. Pushkin, O.K. Tikhomirov) .

The approach to characterizing the thinking of foreign scientists, as a rule, is one-sided: it acts only as a reproductive or productive process. Associationists (A. Bain, I. Herbart, D. Hartley, T. Ribot) characterized thinking from idealistic positions, believing that its essence comes down to isolating dissimilar elements, combining similar elements into complexes, and recombining them. The result, in their opinion, is nothing fundamentally new. Representatives of Gestalt psychology (M. Wertheimer, K. Koffka, W. Keller) expressed an approach to thinking as a purely productive process, considering productivity as a specificity of thinking that distinguishes it from other mental processes. They believed that thinking, arising in a problematic situation (which includes unknown links), leads to a solution, as a result of which something fundamentally new is obtained, which is not available in the knowledge fund. The value of Gestaltist research in the application of problematic tasks, the solution of which caused a conflict among the subjects between the available knowledge and the requirements of the solution (M. Wertheimer, K. Dunker), but, attaching great importance to insight, “aha-experience”, they did not reveal that the insight was prepared past experience of active activity of the subject himself. Those. scientists did not show the very mechanism of the emergence of productive thinking, they sharply opposed it to reproductive processes, believing that past experience and knowledge act as a brake on the development of thinking. It should be noted that over time, the accumulated facts of research forced them to limit the categoricalness of the conclusions, to recognize the positive role of knowledge in productive thinking, considering them as a starting point for understanding and solving the problem.

Domestic scientists believed that reproductive thinking, although characterized by less productivity, plays an important role for a person in cognitive and practical activities, giving him the opportunity to solve problems of a familiar structure. In particular, Z.I. Kalmykova emphasized the importance of reproductive thinking in the educational activities of schoolchildren, believing that it provides an understanding of new material and the application of knowledge in practice when there is no need for their significant transformation. She believed that this thinking is easier to develop (than productive thinking), acting at the initial stage, plays a significant role in solving new problems for the subject, helping him to be convinced of the ineffectiveness of the methods known to him. “Awareness of this leads to the emergence of a “problem situation”, i.e., it activates productive thinking, which ensures the discovery of new knowledge, the formation of new systems of connections that will later provide him with the solution of similar problems.”

Of course, the mixing of types of thinking is quite arbitrary, it cannot be productive without relying on past experience, and at the same time, it involves going beyond it, discovering new knowledge. We adhere to the point of view of Z.I. Kalmykova, who took as the basis for the division into reproductive and productive thinking, the degree of novelty and the degree of awareness for the subject of the knowledge obtained in this process. “Where the proportion of productivity is high enough, they speak of productive thinking proper as a special kind of mental activity. As a result of productive thinking, something original, fundamentally new for the subject, i.e. the degree of novelty here is high.” According to M.V. Glebova, the most important property of mental activity is the derivation of some knowledge from others with the help of reasoning, which leads to the expansion of the original knowledge. "... In such an intensive multiplication of knowledge lies the productive nature of mental activity." It is the productivity of thinking, i.e. focus on the discovery of new knowledge, significantly distinguishes it from other mental processes. In addition to subjective novelty, supporters of this point of view emphasize the originality of this process and the impact on mental development, which is a decisive link, providing a real movement towards new knowledge.

The term "productive thinking" is widely used in pedagogical literature as a synonym for the student's creative activity. In the psychological and pedagogical literature, the following terms are used as a synonym for the concept of "productive thinking": "creative thinking", "heuristic", "independent", "creative"; to reproductive: “discursive”, “rational”, “verbal-logical”, “receptive”, etc. Most researchers prefer to use the term “productive thinking” in relation to the type of thinking of schoolchildren to indicate the difference in the concepts of “productive” and “creative” thinking. , and the term "creative thinking" denotes the highest stage of mental activity. We are close to their point of view, emphasizing that creative thinking is inherent in those who, carrying out mental activity, discover knowledge fundamentally new for humanity, create something original, which has no analogue. They believed that the concept of "creative thinking" is legitimate to use in relation to "persons who make discoveries that are objectively new for mankind" (Z.I. Kalmykova) and it is the highest form of productive thinking.

But we are interested in those indicators by which creative thinking is judged, since elements of creative thinking are inherent in productive thinking. In particular, K. Dunker attributed to them: originality of thought; fluency of thought as the number of associations, ideas that arise per unit of time in accordance with some requirement; the possibility of receiving answers that deviate far from the usual; "susceptibility" to the problem, its unusual solution; the speed and smoothness of the emergence of unusual associative connections; the ability to find new unusual functions of an object or its part (K. Duncker, 1935). The concepts of "creative" and "productive" thinking as synonyms were designated by P. Torrens, believing that it manifests sensitivity to shortcomings in existing knowledge, the ability to formulate problems, the possibility of constructing hypotheses about the missing elements of this knowledge, etc. (P. Torrans, 1964).

Based on research interest, productive thinking includes not only the ability to listen, understand information, speak, read, write, but also “the ability to be motivated and active, the ability to find various options for solving socially significant problems, getting out of various situations, forming general and future professional culture”.

Characterizing productive thinking as different from other mental processes, having its own specifics, we consider it appropriate to proceed to an analysis of the mechanism of action of productive thinking. An effective technique is “analysis through synthesis”, which was used in studies conducted under the direction of S.L. Rubinstein,characterizes the mechanism of thinking precisely as a process. In these studies, the subjectwas included in that system of connections and relations in which he was given the opportunity to most clearly discover the desired property, which in turn contributes to the discovery of a new circle of connections and relations of the object with which he correlates this property. This reflects the dialectic of creative cognition of reality, which can be fully attributed to productive thinking. Such a development of productive thinking leads to the origin and formation of new mental formations - new communication systems, personality traits, abilities, new forms of self-regulation, marking a shift in mental development.

According to Z.I. Kalmykova in a productive thought process there is no fundamental difference between a scientist who discovers objectively new patterns of the world around us that are not known to mankind, and students who make a discovery only of a subjectively new one, since their thinking is based on general patterns. But they are distinguished by the level of mental activity leading to discovery, the conditions for the search for new knowledge. Z.I. Kalmykova believed that productive thinking is inherent in adults and children, since they all make subjective discoveries when solving new problems. “... although, of course, the level of this thinking in the second case is lower, since it is carried out in a learning situation in which teachers are provided for the students to have an initial minimum of knowledge, visual supports that facilitate the search for a solution, etc.”

How we solve life and learning problems depends on many factors. As part of the project "", prepared jointly with the Charitable Foundation of Sberbank "Investment in the Future", psychologist Sergey Yagolkovsky spoke about how our knowledge and experience can affect the thought process during training.

Productive thinking plays a very important role in the learning process. What is productive thinking? This is such a thought process, as a result of which some very valuable, important results appear. It can be ideas, innovations, a new state or a person's worldview. That is, it is thinking that changes something, produces something. And, being tied to the learning process, say, at school, it must be said that productive thinking is largely tied to how the student understands the task.

In the psychology of thinking, the objective and subjective structure of the task is distinguished. The objective structure is what is given in the conditions of the problem: what target situation is required as a result of solving this problem, what means are given to solve it. But with the subjective structure, everything is a little more complicated. This is how a person sees the task within himself. We know from our own experience that it happens that a student immediately grasps the conditions of a problem and then quickly solves it. And there is a slightly different situation when it is difficult to understand the conditions of the problem or the student does not understand the problem quite correctly. This is very important and largely determines the effectiveness of productive thinking.

In the research of productive thinking, there are several mainstream approaches, one of which is the so-called gestalt approach to understanding thinking. It is represented in the works of well-known classics such as Karl Dunker, Max Wertheimer, Wolfgang Köhler. They understood productive thinking primarily in the context of emergence, when a person, as it were, illuminates and as a result of this, a solution to the problem appears. The state of insight they considered the quintessence, the most important element of a productive thought process. But with all this, they also saw a number of problems associated with productive thinking. One of the most important problems is functional fixity, which constantly pushes us to think in stereotypes, look at the world through the usual prism and does not give anything new. This stereotypical thinking is connected with our habit of seeing a certain functional purpose of some object given to us. Let's say, if we see a shovel, then this shovel must certainly dig. But we do not fixate on other possible uses. For example, using its shaft as an electrical insulator, when we need to separate two bare electrical wires so that a short circuit does not occur. A wooden shaft can handle this perfectly.

In Gestalt psychology, numerous studies have been carried out confirming the importance of the state of insight. One such example is Wolfgang Köhler's well-known experiment with chimpanzees. The monkey was placed in a cage and not fed for some time. After that, a branch of tasty, juicy bananas was placed at some distance from the cage. The poor hungry monkey, of course, wanted to reach for the bananas, but she couldn't: the bars of the cage got in the way. The only object that was within her reach was a meter stick. The monkey was furious for a long time, jumping, trying to gnaw the bars of the cage, break them, got angry, but without this stick, she could not get the bananas. Eventually, it dawned on her. She had an insight, as a result of which she guessed that her paws could be lengthened with this stick, get bananas, move them towards her and eat them. Thus, she solved this problem, as if discovering for herself a completely new, unknown way of solving it. This is insight in the full sense, in a vivid form.

Karl Dunker, a very famous researcher of productive thinking, put insight at the heart of his theory, the basis of understanding productive thinking. Insight is good, it helps. But, according to Karl Dunker, there are a number of negative factors that prevent this insight from manifesting itself and make productive thinking less effective, and sometimes block it altogether. These Gestalt approaches to the study and understanding of productive thinking are based on the concept of insight as an unexpected insight that suddenly gives rise to knowledge from ignorance. So what is insight? This is when five minutes or a few moments ago we did not yet know that the problem could be solved, did not know how to solve it, and suddenly it dawns on us. And we already intuitively feel, and then for ourselves we structure, understand and, perhaps, verbalize the process of solving it. Insight - absolutely cool thing - illuminates us. The only problem is that the mechanism itself, the principle itself, the fabric of this insight is not completely clear. And this process is quite difficult to influence.

In this regard, I would like to mention a slightly different approach to understanding thinking, which in many cases also explains very well how new solutions, ideas, inventions are born. This approach was proposed by Otto Selz, a representative, a follower of the well-known Wurzburg school in the psychology of thinking. Unlike Gestalt psychologists, he believed that all our thinking is based on the knowledge and experience that we have. Moreover, he proposed several specific mechanisms, methods of mental activity that can lead to some productive interesting solutions. One of the simplest is an already proven method for solving a problem, which can be applied to another situation. For example, if at school in a lesson a teacher gives students in the lower grades a task: “Mom went to the market, bought five kilograms of apples and cooked compote from two kilograms. How many apples are left? It shows that you need to subtract two from five and you get three. The kids understand this, and they are given a very similar task at home with a similar solution principle: “Dad bought fifteen kilograms of pears, and mother made jam from seven kilograms. How many pears are left? It is quite clear how to solve this problem. It is necessary to apply the already known method of solving it. This is a very simple situation. And it is easy to see that there is very little novelty and productivity here. Although it is, because the situation is different.

A more difficult case is when the method of solving the problem is unknown to its solver. Let's take another example from another area. A ten-year-old schoolboy is faced with a normal life situation when someone close to him was offended. And he does not know how to establish and restore relations with this person. He tries this way and that, but he fails. And if this is a smart child, he begins to analyze the situation and look for possible ways to solve it. And he recalls that five years ago he witnessed a situation in the family, when either mom said a rude word to dad, or vice versa, and the second parent was offended. The parents sulked at each other, and eventually one of them came up and said: "I'm sorry, please, let's make up with you." The second parent broke into a smile, and then everything was fine. This child, solving an actual problem, analyzed past experience and suddenly remembered a certain situation that was once completely unclear. He remembered it from a different perspective, extracting, pulling out of it the principle of the solution. As you can see, this solution method is completely different. It involves the active mental activity of a person when you need to analyze your past experience, existing knowledge and pull out a principle that was still unknown. This is the second level of problem solving.

And finally, Otto Selz came up with an even more sophisticated method that works great for productive thinking as well. I will illustrate it for you on a fairly well-known example with Benjamin Franklin - this is the former president of America, who in his younger years was engaged in scientific research. For a long time he struggled with the problem, which at that time was of great concern to all mankind: how to channel the powerful energy of lightning so that it would not hit ships, carts, buildings, houses; how to protect people from this powerful energy? No one could solve this problem, and neither did he. He fought and suffered until one day he witnessed a very simple and rather banal situation. He saw a father and son flying a kite in the meadow. He looked at the kite as if it were an object that hovered high in the sky and was connected by a thread to a person standing on the ground. And suddenly it dawned on him. He realized that the solution to the problem that worries mankind is to bring some highly conductive object into the sky and connect it to the earth. That is, this kite prompted him to a cool engineering solution, and as a result, the well-known lightning rod appeared. This is a more complex case, when the principle of solving the problem is not presented in finished form in the head of a person. He is not in past experience, but is presented in some kind of current situation, when random circumstances can lead to a brilliant solution.

These problem solving methods proposed by Zelts can be used quite effectively in educational practice. Of course, as it is easy to see, the most developing method is the latter, which involves the random linking of situations and extraction, the selection of the basic principle for solving an actual problem from a picture or situation presented by fate. But the second method is also excellent, because it develops the student's ability to analyze his own experience, some life situations in which this student found himself, and find a solution to the problem there. And the first, simplest method is also good - probably at the elementary school stage, when students must learn to apply the method explained by him and tested to a completely different class of situations. All three of these methods are good, and if used correctly, they will certainly play to the benefit of the effectiveness of the educational process in the school. These two main approaches to research - the Gestalt approach and the approach of Otto Selz - each in their own way describe the specifics of the thought process. In scientific and psychological literature, they are in many respects even opposed to each other. But, as is easy to see, both of these approaches can bring a lot of interesting and new things to the educational process and, of course, can be used both in solving problems and in developing creative, productive thinking.

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PRODUCTIVE THINKING

M. Wertheimer

Max Wertheimer - an outstanding German psychologist, one of the founders of Gestalt psychology - was born on April 15, 1880 in Prague, died on October 12, 1943 in New York. In 1904 he defended his dissertation under the guidance of O. Külpe. For many years he worked at the University of Berlin. In 1933, M. Wertheimer, like other creators of Gestalt psychology, was forced to leave Nazi Germany and continued his teaching and research activities in the United States, working at the New School for Social Research (New York). Apparently, the reaction of the scientist to fascism explains the special attention of M. Wertheimer to the problems of human dignity, personality psychology, to the problems of the theory of ethics, which he developed in the last years of his life while working at this school.

In our country, M. Wertheimer is known mainly as a theorist of Gestalt psychology and an experimental researcher in the field of the psychology of visual perception. Gestalt psychology was formed as an opposition to associative psychology. M. Wertheimer, W. Köhler, K. Koffka, K. Levin and others put forward the principle of integrity as the basic principle of perception (and then other mental processes), opposing it to the associative principle of elements. They proceeded from the position that all processes in nature are initially integral. Therefore, the process of perception is determined not by single elementary sensations and their combinations, but by the entire "field" of stimuli acting on the organism, by the structure of the perceived situation as a whole. That is why this direction began to be called Gestalt psychology.

The approach to studying the perceived image as an integral structure (Gestalt) is the main principle of Gestalt psychology.

Introduction

What happens when thinking is productive? What happens when we move forward in thinking? What actually happens in such a process?

When we turn to books, we often find answers that only seem simple. But in relation to real productive processes - when we, even in connection with the most modest problem, have a creative thought, when we really begin to comprehend its essence, when we experience the joy of the productive process of thinking itself - it turns out that these answers are often instead of to openly admit real problems, carefully hide them. These answers lack the flesh and blood of what is happening.

Throughout your life, of course, you have been interested - sometimes even seriously - in many things. Have you wondered what is the thing called thinking? There are different things in this world: food, thunderstorms, flowers, crystals. Various sciences deal with them; they make great efforts to really understand them, to comprehend what they really are. Are we equally seriously interested in what productive thinking is?

There are excellent examples. They can often be found even in everyday life. Probably, you have experienced for yourself or, watching children, witnessed this amazing event - the birth of a genuine idea, a productive process, a transition from blindness to understanding. If you have not been fortunate enough to experience it yourself, then you may have observed it in others; or maybe you were delighted when something similar flashed before you while reading a good book.

Many believe that people do not like to think and strive to avoid it by all means, they prefer not to think, but to memorize and repeat. But despite the many adverse factors that stifle genuine thinking, people - even children - strive for it.

What actually happens in such processes? What happens when we really think, and think productively? What are the essential features and stages of this process? How does it flow? How does a flash, insight occur? What conditions, attitudes favor or do not favor such remarkable phenomena? What is the difference between good thinking and bad thinking? And finally, how to improve thinking? Your thinking? Thinking in general? Suppose we need to make a list of the main operations of thinking - what would it look like? What, in essence, should be guided by? Is it possible to increase the number of such operations - to improve them and thereby make them more productive?

For more than two thousand years, many of the best minds in philosophy, logic, psychology, and pedagogy have been trying to find answers to these questions. The history of these efforts, brilliant ideas, and enormous labor spent on research and creative discussion is a vivid, dramatic picture. Much has already been done. A solid contribution has been made to the understanding of a large number of particular issues. At the same time, there is something tragic in the history of these efforts. Comparing ready-made answers with real examples of brilliant thinking, great thinkers again and again experienced anxiety and deep disappointment, they felt that, although what was done had merit, it did not, in essence, address the essence of the problem.

And today the situation has hardly changed. Many books deal with these issues as if all the problems had already been solved. The existing opposing views on the nature of thought have serious implications for behavior and learning. When we observe a teacher, we often realize how serious the consequences of such views on thinking can be.

Although there are good teachers who have a taste for genuine thinking, the situation in the schools is often unsatisfactory. The actions of teachers, the nature of teaching, the style of textbooks are largely determined by two traditional views on the nature of thinking: classical logic and association theory.

Both views have their merits. To some extent, they seem to be adequate to certain types of thinking processes, certain types of his work, but in both cases the question remains whether this way of understanding thinking is a serious hindrance, whether it actually harms capable students. .

Traditional logic has approached these problems with great ingenuity. How to find the main thing in a huge variety of problems of thinking? In the following way. Thinking is interested in truth. Truth or falsity are the qualities of statements, judgments, and only them. Elementary propositions affirm or deny some predicate of subjects in the form "all S essence R" , or "none S do not eat R", or "some S essence R" , or "some S not the point R". Judgments contain general concepts - the concepts of classes. They are the basis of all thinking. For a judgment to be correct, it is important to correctly handle its content and volume. Based on judgments, conclusions are made. Logic studies the formal conditions under which conclusions turn out to be right or wrong. Certain combinations of propositions make it possible to obtain "new" correct propositions. Such syllogisms, with their premises and conclusions, are the crown, the very essence of traditional logic. Logic establishes various forms of syllogism that guarantee the correctness of the conclusion.

Although most textbook syllogisms seem completely fruitless, as in the classic example:

All people are mortal;

Socrates is a man;

Socrates is mortal

there are examples of real discoveries that can be considered as syllogisms in the first approximation, for example, the discovery of the planet Neptune. But both formally and essentially, these syllogisms do not differ from each other. The basic rules and characteristics of these stupid, and really meaningful syllogisms are the same.

Traditional logic formulates criteria that guarantee the accuracy, validity, consistency of general concepts, judgments, conclusions and syllogisms. The main chapters of classical logic relate to these topics. Of course, sometimes the rules of conventional logic remind us of efficient rules of the road.

Leaving aside differences in terminology and disagreements on secondary issues, the following characteristic operations of traditional logic can be named:

· definition;

· comparison and distinction;

· analysis;

· abstraction;

generalization;

· classification;

formation of judgments;

inferences;

drawing up syllogisms, etc.

These operations, singled out, defined and used by logicians, have been and are being studied by psychologists. As a result, a lot of experimental research has arisen on abstraction, generalization, definition, inference, and so on.

Some psychologists believe that a person is able to think, that he is smart, if he can correctly and easily carry out the operations of traditional logic. The inability to form general concepts, to abstract, to draw conclusions from syllogisms of certain formal types is considered as a mental disability, which is determined and measured in experiments.

No matter how we evaluate classical logic, it had and still has great advantages:

a clear desire for truth;

focusing on the essential difference between a simple statement, a belief, and an accurate judgment;

· emphasizing the difference between insufficiently clear concepts, vague generalizations and precise formulations;

· the development of a set of formal criteria to detect errors, ambiguities, illegal generalizations, hasty conclusions, etc.;

emphasizing the importance of evidence;

thoroughness of the inference rules;

· the requirement of persuasiveness and rigor of each separate step of thinking.

The system of traditional logic, the foundations of which were laid down in Aristotle's Organon, was considered final for many centuries; and although some refinements were made to it, they did not change its basic character. During the Renaissance, a new field arose, the development of which had a significant impact on the formation of modern science. Its main merit was its introduction as a fundamental new procedure, which had not previously been given much importance due to its insufficient evidence. This is the method of induction, with its emphasis on experience and experimentation. The description of this method reached its greatest perfection in the well-known canon of rules of induction by John Stuart Mill.

The emphasis here is not on rational inference from general propositions, but on the collection of facts, the empirical study of invariant relationships between them, and on observing the consequences of changes occurring in real situations - that is, on procedures that lead to the formulation of general propositions. Syllogisms are seen as tools with which to extract consequences from such hypothetical assumptions in order to test them.

· empirical observations;

careful collection of facts;

Empirical study of problems;

introduction of experimental methods;

correlation of facts;

development of decisive experiments.

The second major theory of thought is based on the classical theory of associationism. Thinking is a chain of ideas (or in more modern terms, a connection of stimuli and reactions or elements of behavior). The way in which thinking is interpreted is clear: we must study the laws governing the sequence of ideas (or, in modern terms, the elements of behavior). An "idea" in the classical associative theory is something like a trace of sensation, in more modern terms, a copy, a trace of stimuli. What is the basic law of succession, connection of these elements? The answer - captivating in its theoretical simplicity - is this: if two objects a and b often occur together, then the subsequent presentation, and will cause in the subject b. These elements are related, entities, in the same way that a friend's phone number is related to his name, or as meaningless syllables are related in experiments to learn a series of such syllables, or as a dog's salivation is related to a certain sound signal.

Habit, past experience, in the sense of the repetition of adjacent elements, is rather inertia than reason - these are the essential factors. That's what David Hume said. Compared to classical associationism, this theory is now very complex, but the old idea of repetition, contiguity, is still its central point. The leading exponent of this approach recently stated unequivocally that the modern theory of conditioned reflexes has, in essence, the same nature as classical associationism.

The list of operations looks like this:

· associations acquired on the basis of communication repetition;

the role of frequency of repetition, novelty;

recollection of past experience;

trial and error with occasional success;

learning based on repetition of a successful trial;

actions in accordance with conditioned reactions and habits.

These operations and processes are now widely studied using well established methods.

Many psychologists will say: the ability to think is a consequence of the work of associative connections; it can be measured by the number of associations acquired by the subject, the ease and correctness of learning and recalling these connections.

Undoubtedly, this approach also has its merits, which relate to the very subtle features observed in this kind of learning and behavior.

Both approaches encountered great difficulty in explaining meaningful, productive thought processes.

Consider first the traditional logic. Over the centuries, again and again, deep dissatisfaction with the way traditional logic has treated such processes has arisen. Compared to genuine, meaningful, productive processes, problems, and even ordinary examples of traditional logic, often look meaningless, flat, and boring. The logical interpretation, although quite strict, still often seems very fruitless, tedious, empty and unproductive. When we try to describe the processes of genuine thinking in terms of traditional formal logic, the result often turns out to be unsatisfactory: we have a number of correct operations, but the meaning of the process and everything that was alive, convincing, creative in it seem to disappear. It is possible to have a chain of logical operations, each of which is quite correct in itself, but taken together they do not reflect a reasonable train of thought. Indeed, there are logically thinking people who, in certain situations, carry out a number of correct operations, but the latter are very far from the true flight of thoughts. The role of traditional logical training should not be underestimated: it leads to the rigor and validity of each step, contributes to the development of a critical mind, but in itself, obviously, does not lead to productive thinking. In short, it is possible to be empty and meaningless, though accurate, and it is always difficult to describe truly productive thinking.

By the way, the realization of the last circumstance - along with others - led some logicians to the following categorical statement: the logic that deals with the problems of correctness and validity has nothing to do with real productive thinking. It has also been pointed out that the reason for this is that logic is not concerned with time and therefore does not deal in principle with the processes of actual thought, which are quite real and exist in time. This division has obviously proved useful in solving certain problems, but from a broader point of view, such statements often resemble the lament of a fox about the unripeness of grapes.

Similar difficulties arise in the associative theory: how to distinguish reasonable thinking from meaningless combinations, how to explain creative side of thinking.

If the solution to a problem is achieved by mere recall, by the rote repetition of what has been learned by rote by accidental discovery in a series of blind trials, then I would hesitate to call such a process intelligent thinking; and it is doubtful whether the accumulation of such phenomena alone, even if in large quantities, will be able to create an adequate picture of thought processes. In order to somehow explain the emergence of new solutions, a number of hypotheses were proposed (for example, the Selz constellation theory, or the concept of a systemic hierarchy of skills), which, by their very nature, turned out to be almost useless.

Parallelogram area

Among the problems I worked on was the problem of determining the area of a parallelogram.

I don't know if you will get the same pleasure from the results of my experiments as I did. It seems to me that you will get if you follow me, understand the essence of the problem and feel the difficulties that arose on the way and for overcoming which I had to find means and methods in order to psychologically understand the problem put forward.

I come to class. The teacher says: "In the previous lesson, we learned how to determine the area of a rectangle. Does everyone know how to do this?"

Pupils answer: "All". One of them shouts out: "The area of a rectangle is equal to the product of its two sides." The teacher approves the answer and then offers several problems with different side sizes, which were all immediately solved.

"Now," says the teacher, "we'll move on." He draws a parallelogram on the board: "This is a parallelogram. A parallelogram is a flat quadrilateral whose opposite sides are equal and parallel."

Here one student raises his hand: "Tell me, please, what are the sides equal to?" "Oh, the sides can be of very different lengths," the teacher replies. "In this case, the value of one of the sides is 11 inches, the other 5 inches." "Then the area is 5x11 square inches." "No," the teacher says, "this is not true. Now you will learn how the area of a parallelogram is determined." He labels the peaks a, b, with, d.

"I drop one perpendicular from the upper left corner and the other from the upper right corner. I continue the base to the right. I designate new points with letters e and f".

With the help of this drawing, he then proceeds to the usual proof of the theorem, according to which the area of the parallelogram is equal to the product of the base and the height, establishing the equality of certain segments and angles and the equality of two triangles. In each case, he gives previously learned theorems, postulates or axioms, with the help of which he justifies equality. Finally, he concludes that it has now been proven that the area of the parallelogram is equal to the product of the base and the height.

"You will find the proof of the theorem that I showed you in your textbooks on p. 62. Learn the lesson at home, repeat it carefully so that you remember it well."

Then the teacher offers several problems in which it is required to determine the areas of parallelograms of various sizes, with different sides and angles. Since this class was "good", the tasks were solved correctly. At the end of the lesson, the teacher assigns ten more tasks of the same type as homework.

A day later, I was back in the same class at the next lesson.

The lesson began with the teacher calling the student and asking him to show how the area of a parallelogram is determined. The student brilliantly demonstrated this.

It was clear that he had learned his lesson. The teacher whispered to me, "And this is not the best of my students. No doubt the others learned the lesson well too." Written test gave good results.

Many will say: "A wonderful class; learning goal achieved." But as I watched the class, I felt some unease. “What have they learned?” I asked myself. “Do they think at all? "Not only could they repeat what the teacher said word for word, there was also some transfer. But did they even understand what was going on? How can I find out? What do I need?" do?" .

I asked the teacher for permission to ask the class a question. "Please," the teacher readily replied.

I went to the blackboard and drew this figure.

Rice. 3 Fig. 4

Some of the students were clearly confused.

One student raised his hand, "Master didn't explain it to us."

The rest took up the task. They copied the drawing, drew auxiliary lines, as they were taught, dropping perpendiculars from the two upper corners and continuing the base (Fig. 4). They were confused, puzzled.

Others didn't seem unhappy at all. They confidently wrote under the drawing: "The area is equal to the product of the base and the height" - a correct, but, apparently, completely blind statement. When they were asked if they could prove it with this drawing, they were quite puzzled.

Others behaved quite differently. Their faces brightened, they smiled and drew the following lines on the drawing or rotated the sheet by 45° and then completed the task (Fig. 5A and 5B).

Rice. 5A Fig. 5 B

Seeing that only a small number of students completed the task, the teacher said to me with a touch of displeasure: "You, of course, offered them an unusual drawing. Naturally, they could not cope with it."

Speaking between us, don't you also think: "It is not surprising that, having received such an unfamiliar figure, many could not cope with it." But is it less familiar than those variations of the original figure that the teacher gave them earlier and with which they coped? The teacher gave problems that varied greatly in terms of the length of the sides, the size of the angles and areas. These variations were obvious, and the students did not find them difficult at all. You may have noticed that my parallelogram is just a rotated original figure suggested by the teacher. With respect to all its parts, it differs no more from the original figure than the variations proposed by the teacher.

Now I will tell you what happened when I gave the problem to determine the area parallelogram to the subjects - mostly children - after briefly explaining to them how the area of a rectangle is determined, without saying anything more, without helping in anything, just waiting for what they would say or do. Among the subjects were adults of various professions, students whose reaction could be judged that they had completely forgotten this theorem, and children who had never heard of geometry at all, even five-year-old children.

Various types of reactions have been observed.

First type. No reaction at all.

Or someone said: "Ugh! Math!" - and refused to solve the problem with the words: "I don't like math."

Some subjects simply waited politely or asked, "What's next?"

Others said, "I don't know; I wasn't taught that." Or: "I went through this in school, but I completely forgot," and that's it. Some expressed dissatisfaction: "Why do you think that I can do this?" And I answered them: "Why not try?".

Second type. Others rummaged vigorously through their memories, trying to remember something that might help them. They blindly searched for some scraps of knowledge that they could apply.

Some asked, "Can I ask my older brother? He probably knows." Or: "Can I see the answer in the geometry textbook?" Obviously, this is also one of the ways to solve problems.

Third type. Some began to talk at length. They talked around the problem, talking about similar situations. Or they classified it in some way, applied general concepts, assigned the task to some category, or carried out aimless trials.

Fourth type. However, in a number of cases it was possible to observe the real process of thinking - judging by the drawings, comments, thoughts aloud.

"Here is this figure; how can I determine the size of the area? The area of \u200b\u200bthe figure of this particular shape?"

"Something needs to be done. I have to change something, change it in such a way that it helps me see the area clearly. Something is wrong here." At this stage, some of the children drew the figure shown in fig. 21.

In such cases, I said: "It would be good to compare the area of a parallelogram with the area of a rectangle." The child helplessly stopped and then resumed attempts.

In other cases the child said, "I must get rid of the difficulty. This figure cannot be divided into small squares."

Here one child suddenly said, "Can you give me a folding ruler?" I brought him such a meter. The child made a parallelogram out of it, and then turned it into a rectangle.

I liked it. "Are you sure it's right?" I asked. "I'm sure," he replied. Only with great difficulty, with the help of an appropriate drawing (Fig. 24), did I manage to make him doubt the correctness of his method.

Then he immediately said: "The area of the rectangle is much larger - this method is not good ..."

4) The child took a sheet of paper and cut out two equal parallelograms from it. Then, with a happy look, he connected them as follows.

In itself, this step was a wonderful find (cf. the solution with the ring, p. 78). I note that in a number of cases I myself gave the children two samples of the figure. Sometimes I encountered such reactions:

Some children even tried to superimpose one figure on top of another.

But there were times when thinking led straight to the goal. Some children, with little or no help, found the correct, reasonable, direct solution to the problem. Sometimes, after a period of extreme concentration, their faces brightened at a critical moment. What a miracle - this transition from blindness to insight, to understanding the essence of the matter!

First, I will tell what happened to a girl of five and a half years old, whom I did not give any help at all in solving the problem with a parallelogram. When, after a brief demonstration of the method for determining the area of a rectangle, she was presented with a parallelogram problem, she said, "Of course I don't know how This do." Then, after a moment of silence, she added: " Not good here- and pointed to the area located on the right, - and here too- and pointed to the area located on the left. "The difficulty is with this place and with this."

Hesitantly said, "Here I can fix it... but..." Suddenly she exclaimed, "Can you give me scissors? What's in the way there is exactly what's needed here. Suitable." She took the scissors, cut the figure vertically and moved the left side to the right.

Another child similarly cut off a triangle.

And she brought the left corner "in order." Then, looking at the other edge, she tried to do the same there, but suddenly she began to consider it not as "an extra part", but as a "missing one".

There were other actions as well. The girl, to whom I gave a long parallelogram cut out of paper (and in the previous examples it is better to start with a long parallelogram), at first said: "The whole middle part is in order, but the edges ..." She continued to look at the figure, clearly interested in its edges, then suddenly she took it in her hands and with a smile turned it into a ring, connecting the edges. When asked why she did this, she, holding the closed edges with her small fingers, replied: “But now I can cut the figure like this,” and pointed to a vertical line located somewhere in the middle, “then everything will be all right ".

My wise friend, whom I told about the scissors solution, exclaimed: "This child is a genius." But many psychologists will say: “So what? Obviously, this is a matter of past experience. Why such complex and difficult explanations? Randomly or through some mechanism of association, the child recalls a past experience associated with scissors.The rest of the children could not solve the problem because they did not remember the past experience, or because they did not have enough experience with scissors.They did not learn the connection , an association that could help them, or they did not remember it. Thus, everything depends on the recall of learned connections. It is memory and recall that underlie this process.

Of course, sometimes the use of scissors comes by chance or as a result of remembering external circumstances. It happens that even in good processes, memory hints are either checked and used, or rejected as useless. There is no doubt that in order for these processes to become possible or probable, in addition to present experience (whatever that may mean), significant past experience is required.

But is it adequate to use only theoretical generalizations to discuss such issues? For example, in our case, it is argued that the decisive factor is that the child remembers the scissors and the actions associated with them.

Suppose a child trying to solve a problem does not think about scissors. This content and related associations are missing. Why not take the theoretical bull by the horns? Let's give the kids everything they need and see what happens. If the most important thing is to remember the experience of using scissors, then we can immediately supply the child with scissors and not burden his memory with the need to remember them. Or you can introduce stimuli to facilitate such recall.

At the beginning of the experiment, I put the scissors on the table or even ask the child to cut a piece of paper. Sometimes this helps (for example, when I show the scissors after a period of hesitation in the child, after some remarks indicating that the child has sensed structural demands).

But in some cases it doesn't help. The child looks at the scissors, then again at the drawing. Seeing them nearby, he clearly begins to experience some kind of anxiety, but does nothing.

I'm stepping up "help". "Would you like to take scissors and cut the figure?" In response, the child sometimes looks blankly at me: he obviously does not understand what I mean. Sometimes children begin to dutifully cut the figure in one way or another:

It happens that the child after this begins to make another parallelogram out of two parts.

In what cases does the presentation of scissors help, and in what cases does it not help? We see that the presentation of the scissors and their ordinary use do not in themselves provide any help; they can lead to completely ridiculous and blind actions. In short, they seem to help if the child is already beginning to recognize the structural requirements of the task, or if they are cleared up with scissors; the latter hardly help in cases where the subject is not aware of the structural requirements, when he does not consider the scissors in connection with their function, their role in the given context, in connection with the structural requirements of the situation itself. In such cases, scissors are just another item along with others. Indeed, in some positive processes there have been attempts that testify to a certain understanding of structural requirements, which then led to such use of past experience or to such trials that were fundamentally different from blind recall of past experience.

Even if the positive procedure can be explained by the combined action of learned connections, on the one hand, and the goal - the idea of a rectangle, on the other, then in our case, apparently, one should take into account not just past experience, but its nature and how it is consistent with the structural requirements of the problem.

The introduction of "help" puts in the hands of the experimenter such a technical tool that helps him come to an understanding of the processes that are taking place. Sometimes it is more useful to give other tasks, which in some details may be even more complex and unusual, but have a more transparent, clearer structure, such as some of our BUT- AT- pairs of tasks. In such cases, the subjects sometimes have insight, they return to the original problem and find its solution. However, they may remain blind despite "help" that actually contains exactly what they need.

The results of such experiments apparently indicate that help should be considered in its functional meaning, depending on its place, role and function within the requirements of the situation.

Now it becomes clear why it is sometimes possible to draw one, two or even all three auxiliary lines as a hint, and this nevertheless does not provide any help. A child who does not understand their role and function may consider them as additional complications, incomprehensible additions. As a result, the situation may become even more complex. By themselves, the lines may not shed light on the problem.

And wasn't the lesson described at the beginning of this chapter an extreme example of such a procedure? The teacher showed exactly and clearly all necessary elements; he trained his students by filling them with knowledge acquired in routine ways, but he never achieved any real understanding, nor the ability to act in changed situations.

You cannot replace a meaningful process with a series of learned connections, even if as a result students can repeat and do what they have been taught.

In short, past experience plays a very large role, but it is important what we have learned from experience - blind, incomprehensible connections or understanding of the internal structural connection. It is important what and how we reproduce, how we apply the reproduced experience: blindly and mechanically or in accordance with the structural requirements of the situation.

The main question is not is not it past experience plays a role, which it is experience - blind connections or structural understanding with subsequent meaningful transfer, as well as how we use past experience: through external reproduction or on the basis of structural requirements, its functional correspondence to a given situation. Referring to past experience thus does not solve the problem, the same problem arises with respect to past experience.

It is very interesting to explore how what has been acquired in the past is being used; but for our problem, as a first approximation, it does not matter whether the material used is extracted from the past or from present experience. What matters is its nature and whether the structure has been understood, and also how this is done. Even if everything, including understanding itself, were explained, in essence, by the repetition of past experience - a hope that some psychologists cherish, but which, in my opinion, is false or at least unfounded - or if we approached from the point of view of the exercise even to meaningful structures, it would still be important to consider and study the described distinction, since it is decisive for the existence of structurally meaningful processes. In ordinary language, "gain experience" means for most people something very different from a simple accumulation of external connections, analogous to those mechanical connections that arose in our last example; meaning that something more meaningful is acquired.

Traditional logic has little interest in the process of finding a solution. It focuses rather on the question of the correctness of each step of the proof. From time to time in the history of traditional logic, hints have been made about how to proceed in order to find a solution. Characteristically, these attempts boiled down to the following: “Find some general judgments known to you, the content of which relates to some of the issues under discussion; select from them such pairs that, due to the fact that they contain a general concept (middle term), allow the construction syllogism", etc.

Teachers strongly recommend the study of geometry as a means of developing mental abilities in an atmosphere of clarity, evidence, consistency, which can help transfer the formed methods and mindsets to more complex and less clear areas.

This is one of the reasons why we have chosen these simple geometric examples for discussion in this book; apparently, it is more useful to first discuss the main theoretical questions on structurally simpler material.

Two boys are playing badminton.The girl describes her office

The main result of the previous chapters is the understanding of the important role of the factor of reasonable reorganization, reorientation, which allows the subject to see the given situation as new, in a broader perspective. This is what leads to discovery, or is discovery in a deeper sense. In such cases, the discovery means not just the achievement of a previously unknown result, the answer to some question, but rather a new and deeper understanding of the situation - as a result of which the field expands and great opportunities open up. These changes in the situation as a whole presuppose changes in the structural meaning of the constituent parts, changes in their place, role and function, which often leads to important consequences.

Before the thinking process has begun, or at its early stages, we often have a certain holistic vision of the situation, as well as its parts, which for some reason does not correspond to the problem, is superficial or one-sided. Such an initial inadequate vision often prevents the solution, the correct approach to the problem. If one adheres to such an initial vision of the situation, then it often turns out to be impossible to solve the problem. When there is a change in our vision, and thanks to this the problem is solved, we are sometimes amazed at how blind we were, how superficially we considered the situation.

Changing the structure of vision in accordance with the properties of the situation plays an extremely important role in the development of science. These changes play the same important role in human life, in particular in public life.

Such a change in the image of the situation is necessary, of course, only when a correct vision of it was absent from the very beginning. Often the first glance is not deep and clear enough; sometimes some property of this or that situation may not be fully realized. In such cases, finding a solution requires further clarification or crystallization of the situation, awareness of those aspects or factors that were only vaguely present at the beginning.

To study these transformations and their implications for the role and function of the parts, I have used special experimental techniques that lead to a radical change in the vision of the situation. Often the subjects react emotionally to the changes that are taking place. These techniques also allow you to study what happens to different parts of the structure when it changes: how the parts are organized and grouped; how the location of the "caesuras", the center, changes, which elements become structurally relevant; how gaps, violations appear; to what extent local conditions can change; in what direction the expectations of the subject, the properties of the whole, the requirements of the situation change.

When such transformations take place in the process of thinking, rational behavior is by no means characterized by the ease of voluntary change as such; it is also not a matter of being able in a given situation to see it at will, one way or another. Something else is more important here - intellectual processes are characterized by a rather decisive transition from a less adequate, less perfect structural vision to a more meaningful one. Indeed, experience seems to show that intelligent people, genuine thinkers (and also children), who are often quite capable of producing intelligent transformations, cannot and do not even want to carry out meaningless changes in these situations.

Sometimes it is necessary to move from a structureless sum of parts to an appropriate structure. But even more important is the transition from one-sided vision, superficial or incorrect structuring, from miscentered, distorted or insufficient vision to an adequate and rightly centered structure.

The main reason for unreasonable, blind behavior seems to be that, through perseveration or habit, a person clings to the old view and ignores or even actively rejects the more reasonable demands of the situation.

In order to show more clearly how such transitions occur, I will now give some simple examples from everyday life that I have studied in various experiments.

Two boys were playing badminton in the garden. I could hear and see them from the window, although they did not see me. One boy was 12 years old, the other was 10. They played a few sets. The younger one was considerably weaker; he lost all the games. productive thinking problem creative

I partially heard their conversation. Loser - let's call him AT- became more and more sad. He didn't stand a chance. BUT often served so skillfully that AT could not even beat off the shuttlecock. The situation got worse and worse. Finally AT threw the racket, sat down on a fallen tree and said: "I won't play anymore." BUT tried to convince him to keep playing. AT didn't answer. BUT sat next to him. Both looked distressed.

Here I interrupt the story to ask the reader a question: "What would you suggest? What would you do if you were the older boy? Can you suggest anything reasonable?"

The advice usually boils down to:

"We need to promise the youngest boy a bar of chocolate."

“You need to start another game, say a game of chess, in which the younger boy is as strong or even stronger than the older one, or offer to play badminton, then another game in which he is much stronger.” "Yes, bring him to his senses, soap his head. You need to be a man, not a sissy. You can't lose heart like that! He must learn to maintain presence of mind. Use your authority to reason with the younger boy,"

"Don't worry about him, he's a sissy. That will teach him a lesson."

"Give him a head start."

"Promise the younger boy that the older boy won't play at full strength."

Now I will continue the story. In addition, I will try to describe how, in my opinion, the boys thought.

1. "What's wrong? Why don't you play anymore?" said the older boy in a sharp, angry voice. "Why did you stop playing? Do you think it's nice to stop playing like that?" He wanted to keep playing. Refusal AT made it impossible. BUT liked to play, liked to win; it was so nice to deceive the enemy with his serve. AT prevented him, he did not allow BUT to do what he so desired.

2. But everything was not so simple. BUT he felt uncomfortable, he was uncomfortable. After some time, during which his expression changed - it is a pity that you could not see how he often looked askance at AT, and then to the side, - he said, but in a completely different tone: "Forgive me." Clearly, something has changed drastically - BUT clearly felt guilty that the second boy was so upset. He understood what was happening AT, how the other boy perceived this situation.

Perhaps this was helped by a sad, calm look. AT.AT turned his head once BUT, and BUT I understood - not immediately, it took some time - why the younger boy was so dejected, why, not knowing how to stand up for himself, he felt like a victim. For the first time BUT felt that his style of play, his cunning serve looked in the eyes AT a nasty trick that AT seemed to be treated dishonestly, BUT treats him unfriendly. And BUT felt that AT he was right about something...

Now he saw himself in a different light. His submission, which did not leave AT not the slightest chance of success, was not just dexterity.

3. "Listen," he said suddenly, "such a game is meaningless." She became meaningless not only for AT, and for BUT, meaningless from the point of view of the game itself. So the difficulty became more serious.

It seemed that he thought - he certainly did not think so, but only felt: "It is pointless for both of us to play in this way. The game requires some kind of reciprocity. Such an inequality does not correspond to the game. The game becomes a real game only if both have hope for success. If there is no such reciprocity, then the game loses its meaning, becomes disgusting for one or the other, and for both; without reciprocity it is no longer a game - just one tyrant drives his victim around the court. "

4. Then his expression changed. He seemed to be struggling to understand something, begins to slowly realize something, and then says: "Our game is somehow strange. I'm quite friendly to you..." He had a vague idea that what an adult would call "the ambivalence of the game": on the one hand, it's so nice to play a good game together, to be good friends; on the other hand, it is the desire to win over the enemy, to defeat him, to make his victory impossible, which in some circumstances may seem or actually become obvious hostility.

5. Then a bold, free and deeply consistent step was taken. He muttered something like: "Really?.." He clearly wanted to address the trouble directly, to discuss it honestly and directly. I interpret it "Really?" like "Is hostility really necessary if it ruins everything good in the game?". There is a practical problem here: "How can I change this? Can't we play not against each other, but..." His face brightened and he said: "I have an idea, let's play like this: let's see how long we can keep the shuttle in the air, and count how many times it will pass from me to you without falling. What can be the score? Do you think 10 or 20? We will start with easy serves, and then we will make them more and more difficult. "

He spoke cheerfully, like a man who has made some kind of discovery. For him, as well as for B it was new.

AT gladly agreed: "Great idea. Come on." And they started to play. The nature of the game has completely changed; they helped each other, acted together, stubbornly and cheerfully. BUT no longer showed the slightest desire to deceive AT; of course, his blows became more and more difficult, but he consciously shouted out in a friendly way: “Will you take a stronger blow?”.

A few days later I saw them playing again. AT played much better. It was a real game. Judging by his subsequent behavior, BUT really gained some life experience. He discovered something beyond the solution of a small problem that arose in the game of badminton.

From the outside, this decision in itself may not seem very significant. I don't know if badminton or tennis experts would approve of it.

It does not matter. For this boy, such a decision was not an easy one. It involved moving from a superficial attempt to get rid of the difficulty to a productive consideration of the fundamental structural problem.

What steps led to this decision? Of course, when one considers a single case, there is still very little factual basis for conclusions. However, let's try to formulate the main points.

At first BUT considered his "I" to be the center of the structure of the situation (Fig. 105). In his thinking and actions, meaning, role, function B, games, difficulties and other elements of the situation were determined in relation to this center. In this case AT was just a face that I needed BUT, to play; so refusing to play, AT turned out to be a violator.

The game was "something where I show my abilities, where I win." AT represents a barrier standing in the way of egocentric impulses, vectors, actions BUT.

BUT did not insist on this one-sided, superficial point of view. He began to understand how he imagined this situation. AT(Fig. 106). In this differently centered structure, he saw himself as a part, as a player who did not treat the other player in the best way.

Rice. 106 Fig. 107

Later, she becomes the center a game, its integral properties and requirements (Fig. 107). Neither BUT, neither AT are now not the center, both are considered from the point of view of the game.

Logically BUT(his self-consciousness) changes with a change in position, other elements become different, dynamic requirements, vectors of the real situation. It is clear that the original game is different from the "good game".

But what in the structure of the game itself is the source of the difficulty? In a good game, there is a delicate functional balance: on the one hand, a pleasant pastime, friendships, on the other hand, the desire to win. Deeper guidelines than the simple outer rules of fair play make this delicate balance possible, distinguishing between a good game and a tough fight or competition, in short, a fragile one that can easily disappear - as it did in this situation.

Moments "against", "desire to win", which take place in a good game, acquire ugly features that no longer correspond to the game situation. Therefore, a vector arose: "What can be done? And done immediately?" Here is the reason for the difficulty. "Can you get to the bottom of the situation?" This leads to the consideration of structure 11.

Structure Ia >

Structure Ib ->

Structure II from rivalry to cooperation;

from "I" to "you" to "we".

BUT and AT as parts of a common structure, they are no longer the same as in structure I, they are not opponents, each of whom plays only for himself, but two people working together for a common goal.

All elements of the situation radically change their meaning. For example, a serve is no longer a means of beating B, of making the return pass impossible. In situation I, the player is happy if he wins and the other loses; but now (II) the players rejoice at every good hit.

The next steps indicate the transition to the consideration of the problem situation from the point of view of her merit, and not in terms of one side or the other, or the simple sum of both sides. The solution arises when a structural breach is recognized; then it takes on a deeper meaning. The tension is not overcome by purely external means, rather the new direction of the vectors is due to basic structural requirements leading to a really good situation. Perhaps you think I have read too much into the minds of boys. I do not think so. Perhaps you know too little about what can go on in the minds of boys.

Let us briefly highlight the following:

operations of re-centering: the transition from one-sided vision to centering dictated by the objective structure of the situation;

changing the meaning of frequent - and vectors - in accordance with their place, role and function in this structure;

considering the situation in terms of a "good structure" in which everything meets the structural requirements;

the desire to immediately get to the point, honestly consider the problem and draw appropriate conclusions.

...

PRODUCTIVE THINKING (STAGES)

Great Psychological Encyclopedia

(eng. productive thinking) - a synonym for "creative thinking" associated with solving problems: new, non-standard intellectual tasks for the subject. The most difficult task facing human thought is the task of knowing oneself. “I'm not sure,” A. Einstein said to the outstanding psychologist M. Wertheimer, “whether one can really understand the miracle of thinking. You are undoubtedly right in trying to achieve a deeper understanding of what happens in the process of thinking ... ”(Productive Thinking. - M., 1987, p. 262). Thinking is akin to art, the miracle of which also resists understanding and cognition. In a paradoxical form, something similar was expressed by N. Bohr. To the question "Can the atom be understood?" Bohr replied that perhaps it was possible, but first we must know what the word "understanding" means. Great scientists, to a greater extent than mere mortals, tend to be surprised at the Great and realize the modesty of their forces. M. Mamardashvili also bowed before the miracle of thinking: “Thinking requires almost superhuman effort, it is not given to man by nature; it can only take place - as a kind of awakening or right-remembering - in the field of force between the person and the symbol. Despite his doubts, Einstein not only sympathized with, but also assisted Wertheimer in understanding M. p. and, beginning in 1916, spent hours telling him about the dramatic events that culminated in the creation of the theory of relativity. The psychologist presented the "titanic thought process" as a drama in 10 acts. Its "participants" were: the origin of the problem; persistent focus on its solution; understanding and misunderstanding, which caused a depressed state, up to despair; findings, hypotheses, their mental playback; identification of contradictions and search for ways to overcome them. All this took place against the background of comprehension, rethinking and transformation of the initial problem situation and its elements and continued until the picture of new physics was built. The process of thinking took 7 years. The main thing during this period was “a sense of direction, of direct movement towards something concrete. Of course, it is very difficult to express this feeling in words; but it was definitely present and must be distinguished from later reflections on the rational form of the decision. Undoubtedly, there is always something logical behind this direction; but I have it in the form of some kind of visual image” (Einstein). The orientation proceeding from the task, ordering the process of thinking, the representative of the Würzburg school, the psychologist N. Akh called it a determining trend, and O. Seltz studied the role of intellectualized (non-sensory) visual representations - images that play the role of plastic tools of mental st. 1. The emergence of the topic. At this stage, there is a sense of the need to start work, a sense of directed tension that mobilizes creative forces. 2. Perception of the topic, analysis of the situation, awareness of the problem. At this stage, an integral holistic image of the problem situation is created, an image of what is and a premonition of the future whole. In modern terms, a figurative-conceptual or sign-symbolic model is created, adequate to the situation that arose in connection with the choice of topic. The model serves as a material (“intelligible matter”) in which the leading contradiction, conflict, is found, i.e., the problem to be solved is crystallized. 3. Stage 3 is the (often painful) work to solve the problem. It is a bizarre mixture of conscious and unconscious efforts: the problem does not let go. There is a feeling that the problem is not in me, but I am in the problem. She captured me. The result of such pre-decision work might be. not only the creation, testing and rejection of hypotheses, but also the creation of special tools for solving the problem. An example is the efforts to visualize the problem, the creation of new versions of the figurative-conceptual model of the problem situation. 4. The emergence of an idea (eidos) of a solution (insight). There are countless indications of the decisive importance of this stage, but there are no meaningful descriptions and its nature remains unclear. 5. Executive, in fact, a technical stage that does not require special explanations. It is often very time consuming when there is no appropriate apparatus for solving. As I. Newton pointed out, when the problem is understood, reduced to a known type, the application of a certain formula does not require labor. Mathematics does this for us. The distinguished stages are very arbitrary, but such descriptions are interesting because they seem to naturally alternate between reflection, visualization (imagination), routine work, intuitive acts, etc.; all this is linked by the focus on solving the problem, its concretization. The above analytical description can be supplemented with a synthetic one. Goethe saw in cognition and thinking "an abyss of aspiration, a clear contemplation of the given, mathematical depth, physical accuracy, the height of reason, the depth of reason, the mobile swiftness of fantasy, the joyful love of the sensual." Let's try for a second to imagine that Goethe owes all this to schooling, and the question immediately arises, what team of teachers could provide such education and development of thinking? It is just as difficult to imagine a scientist who would undertake to study the work of such an incredible orchestra as was the thinking of a great poet, thinker, scientist. Each researcher of thinking chooses to study k.-l. one instrument, inevitably losing the whole. There is no big trouble in this as long as the researcher does not impose the tool he has studied as the only or main tool, for example, on the education system. (V.P. Zinchenko.)...

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