The mental activity of people is carried out with the help of mental operations: comparison, analysis and synthesis, abstraction, generalization and concretization. All these operations are different aspects of the main activity of thinking - mediation, i.e. disclosure of more and more significant objective connections and relationships between objects, phenomena, facts.

Comparison- this is a comparison of objects and phenomena in order to find similarities and differences between them. K.D. Ushinsky considered the operation of comparison to be the basis of understanding. He wrote: “... comparison is the basis of all understanding and all thinking. We know everything in the world only through comparison ... If you want the ka-176

any object of the external environment was clearly understood, then distinguish it from the objects most similar to it and find in it a similarity with the objects most distant from it: then only find out for yourself all the essential features of the object, and this means understanding the object.

Comparing objects or phenomena, we can always notice that in some respects they are similar to each other, in others they are different. Recognition of objects as similar or different depends on what parts or properties of objects are essential for us at the moment. It often happens that the same objects are considered similar in some cases, and different in others. For example, a comparative study of domestic animals from the point of view of their usefulness to humans reveals many similar features between them, but a study of their structure and origin reveals many differences.

Comparing things, phenomena, their properties, comparison reveals identity and difference. Revealing the identity of some and the differences of other things, comparison leads to their classification. Classification is carried out according to some feature that turns out to be inherent in each subject of this group. So, in a library, books can be classified by authors, by content, by genre, by binding, by format, etc. The attribute by which the classification is made is called the basis of classification.

Comparing, a person identifies, first of all, those features that are important for solving a theoretical or practical life task.

Analysis and synthesis- the most important mental operations, inextricably linked. In unity, they give a complete and comprehensive knowledge of reality.

Analysis- this is a mental division of an object or phenomenon into its constituent parts or a mental selection of individual properties, features, qualities in it. Perceiving an object, we can mentally single out one part after another in it and thus find out what parts it consists of. For example, in a plant we single out the stem, root, flowers, leaves, etc. In this case, analysis is the mental decomposition of the whole into its constituent parts.

Analysis can also be a mental selection as a whole of its individual properties, features, aspects. For example, mental selection of color, shape of an object, individual features of behavior or character traits of a person, etc.

Analysis is possible not only when we perceive an object or any whole in general, but also when we remember it, imagine it to ourselves. It is also possible to analyze concepts, when we mentally single out their various features, analysis of the course of thought - proof, explanations, etc.

Synthesis - this is a mental connection of individual parts of objects or a mental combination of their individual properties. If analysis provides knowledge of individual elements, then synthesis, based on the results of analysis, combining these elements, provides knowledge of the object as a whole. So, when reading in the text, individual letters, words, phrases stand out and at the same time they are continuously connected with each other: letters are combined into words, words - into sentences, sentences - into certain sections of the text. Or let's remember a story about any event - individual episodes, their connection, dependence, etc.

So as well as analysis, synthesis can be carried out with the direct perception of objects and phenomena or with their mental representation. There are two types of synthesis: as a mental union of parts of the whole (for example, thinking through the composition of a literary and artistic work) and as a mental combination of various features, properties, aspects of objects and phenomena of reality (for example, a mental representation of a phenomenon based on a description of its individual features or properties).

Analysis and synthesis often arise at the beginning of practice. We actually dismember or assemble an object, which is the basis for developing the ability to perform these operations mentally. Developing on the basis of practical activity and visual perception, analysis and synthesis should also be carried out as independent, purely mental operations. Every complex thought process involves analysis and synthesis. For example, by analyzing individual actions, thoughts, feelings of literary heroes or historical figures, and as a result of synthesis, a holistic description of these heroes, these figures is mentally created.

Abstraction. Often, when studying a phenomenon, it becomes necessary to highlight some feature, property, one part of it for more in-depth knowledge, distracting (abstracting) for a while from all the others, not taking them into account. For example, to

to assimilate the proof of a geometric theorem in a general form, it is necessary to abstract from the particular features of the drawing - it is made with chalk or a pencil, what letters indicate the vertices, the absolute length of the sides, etc.

Abstraction is the mental selection of essential properties and features of objects or phenomena while simultaneously abstracting from non-essential features and properties.

The attribute or property of an object singled out in the process of abstraction is thought independently of other attributes or properties and become independent objects of thinking. So, for all metals, we can distinguish one property - electrical conductivity. Observing how people, cars, planes, animals, rivers, etc. move, we can single out one common feature in these objects - movement and think about movement in general, study movement. With the help of abstraction, we can get abstract concepts - courage, beauty, distance, heaviness, length, width, equality, cost, etc.

Generalization and specification.Generalization closely related to abstraction. Man could not generalize without being distracted by the differences in what he generalizes. It is impossible to mentally unite all the trees, if you do not abstract from the differences between them. When generalizing, objects and phenomena are connected together on the basis of their common and essential features. The signs that we obtained during abstraction are taken as a basis, for example, all metals are electrically conductive. Generalization, like abstraction, occurs with the help of words. Every word refers not to a single object or phenomenon, but to a set of similar single objects. For example, in the concept that we express by the word “fruit”, similar (essential) features are combined that are found in apples, pears, plums, etc.

In educational activities, generalization is usually manifested in definitions, conclusions, rules ... It is often difficult for children to generalize, since they are not always able to single out not only general, but essential general features of objects, phenomena, facts.

Specification - this is a mental representation of something single, which corresponds to a particular concept or general position. We are no longer distracted from various signs or properties of objects and phenomena, but,

on the contrary, we strive to imagine these objects or phenomena in a significant wealth of their features. Essentially, the concrete is always an indication of an example, some kind of illustration of the general. Concretization plays an essential role in the explanation we give to other people. It is especially important in the explanations given by the teacher to children. Careful consideration should be given to the choice of example. Leading by example is sometimes difficult. In general, the thought seems clear, but it is not possible to indicate a specific fact.

Pupils and students often find it difficult to give examples illustrating their answer. This occurs during the normal assimilation of knowledge, when the formulation of general provisions is assimilated (or memorized), and the content remains unclear. Therefore, the teacher should not be content with the fact that students correctly reproduce the general provisions, but should seek to specify these provisions: giving an example, an illustration, a specific particular case. This is especially important at school, and especially in the elementary grades. When a teacher gives an example, he reveals, shows how in this particular case the general is found, which is illustrated by an example. Only under this condition does the particular provide significant assistance to the understanding of the general.

6.5. Concepts and their formation

Generalizations that a person makes in the process of thinking are fixed in concepts. concept is a form of thinking that reflects the general and essential properties of objects and phenomena. In other words, a concept is a set of essential properties of an object. For example, a chair has many characteristics: color, material, size, softness. But only those that make a chair a chair are essential. They are: a piece of furniture designed to sit, it has a back support. This is the most essential features of this concept, its content. The concept of "tree" includes all the features inherent in a tree, and does not include what is characteristic only of birch, or spruce, or oak, etc.

Reflecting the general, essential, natural in objects or phenomena of reality, the concept acts as the highest stage of reflection of the world. A concept is denoted by a word, which is a sensual, material object.

concept box. To think in terms is to think in words. The word replaces the subject, but in a certain sense. After all, you won’t sit down on the word “chair”, and you won’t be full of the word “bread”. In sensory cognition, a person gets acquainted with the objects and phenomena of reality themselves, which he then generalizes with this concept. To own a concept means to own the entire body of knowledge about the objects and phenomena to which this concept refers.

Most of the concepts we have are assimilated ready-made from other people. However, mastery of a concept is not a simple “transfer” of knowledge, for example, from an adult to a child. Assimilation of concepts, mastering them is a complex process. It has the most direct relation to the development of thinking both of all mankind and of each individual person. Here, all generations of people receive most of the concepts from previous generations, assimilate these concepts, deepen, clarify, enrich and, on the basis of their own experience and knowledge, create new concepts about those objects and phenomena of reality about which previous generations have not yet created concepts.

In children, the acquisition of a concept largely depends on the experience on which they rely. Significant difficulties arise when a new concept denoted by a certain word does not agree with what is already associated with this word in the child, i.e. with the content of the given concept (often incorrect or incomplete), which he already owns. Most often this happens in cases where a strictly scientific concept, assimilated by children at school, diverges from the so-called worldly, pre-scientific concept, already learned by them outside of special education, in the process of everyday communication with other people and the accumulation of personal sensory experience (for example, a bird - this is an animal that flies, so butterflies, beetles, flies are birds, but chicken, duck are not, they do not fly Or: predatory animals are "harmful" or "terrible", such as rats, mice, and a cat is not a predator , she is a pet, affectionate).

In the assimilation of concepts, the correct organization of the sensory experience of students is especially important. The more abstract the concept, the more difficult it is to rely on material that can be shown to children, the more one has to use a story about things that can help the assimilation of an abstract concept.

Thus, the formation of concepts, the transition to it from sensory forms of cognition is an established process in which comparison, analysis, synthesis, abstraction, generalization, and more or less complex forms of inference take part. An important role in the assimilation of concepts belongs to definition. The definition contains an indication of the most essential features of an object or phenomenon that make up the essence of this concept, reveals its relation to other, more general concepts. The definition fixes the most important thing that must be learned when mastering the concept. For example, the definition of the concept of "proverb" is given. A proverb is one of the types of oral folk art: a common figurative expression that aptly defines any life phenomenon. Unlike proverbs, sayings are devoid of a direct instructive meaning and are limited to a figurative, allegorical definition of a phenomenon. Examples of sayings: “No candle to God, no poker to hell”, “By the ear and the sun”, “All cats are gray at night”, “Neither give nor take, “Neither cold nor hot”, “Not two, not one and a half” , "Neither light nor dawn."

Once again, let us recall that the essential features of concepts are properties and relations, in the event of the loss, absence or change of which, an object or phenomenon becomes by its nature or in some important respect different. Insignificant signs entail the appearance of only external, particular characteristics and differences without changing the essence of the object or phenomenon.

Basic mental operations

The process of thinking consists of a number of mental operations and their various combinations; it is analysis, synthesis, comparison, generalization, classification, systematization, abstraction, concretization.

Analysis is the mental division of an object or phenomenon into its constituent parts, the selection of individual parts, features and properties in it.

For the development of the mental operation of analysis, it is advisable to offer students tasks with missing or redundant data. The student is faced with a deadlock (with a lack of information) or a problem (with an excess of information).

Analysis can be practical and mental. In the first case, the thought process is directly included in the practical (manual) activity of a person. In the second case, it is performed only as a mental activity. Examples of practical analysis are the dismantling (dismantling) of the mechanism, filtering, sorting grain before sowing, determining chemical composition soil, etc. Of course, producing practical analysis something, a person thinks, is guided by a certain principle in highlighting parts of the whole. Mental analysis is not included directly in practical activity, but is an independent thought process. Mental analysis is also called theoretical. In theoretical analysis, a person only perceives an object, or represents it, or only thinks about it. Perceiving the artist's picture, one can distinguish in it the idea, the originality of the composition, the main characters, the features of the background, artistic techniques in depicting the characters and the general mood of the picture, etc. When analyzing a historical event, a person only imagines this event and thinks about it; in this case, the analysis is aimed at identifying the main stages in the course of an event, its causes and consequences.

There are several types of analysis for the intended purpose: for the purpose

A) revealing the structure, i.e. what the object consists of, what are its parts;

B) determining the components that form a set of properties;

C) finding the functions of the object.

Synthesis is a mental combination of individual elements, parts and features into a single whole. Analysis and synthesis are inextricably linked, they are in unity with each other in the process of cognition: we always analyze what is synthetically whole, and we synthesize what is analytically dissected.

Analysis and synthesis are the most important mental operations, in unity they provide a complete and comprehensive knowledge of reality. Analysis provides knowledge of individual elements, and synthesis, based on the results of the analysis, combining these elements, provides knowledge of the object as a whole.

Any analysis begins with a preliminary general acquaintance with an object or phenomenon and then proceeds to a deeper and more detailed analysis. The processes of analysis and synthesis often arise first in practical action. To disassemble or assemble a motor in your mind, you need to learn how to disassemble and assemble it in practice.

In the process of cognition, it becomes necessary not only to analyze any object or phenomenon, but also to single out for a more in-depth study of any one feature, one property, one part, distracting (abstracting) for a while from all the others, not taking them into account. As a rule, not just some signs and properties are distinguished, but important, essential signs.

The interrelation of analysis and synthesis in the processes of thinking cannot be understood in such a way that first analysis must be carried out, and then synthesis: any analysis presupposes synthesis and vice versa. The relationship between analysis and synthesis in the processes of thinking cannot be understood in such a way that first an analysis must be carried out, and then a synthesis: any analysis presupposes a synthesis and vice versa of its elements that were known in the process of its analysis. Thanks to synthesis, we get a holistic concept of a given object or phenomenon, as consisting of naturally connected parts. As in analysis, synthesis is based on the possibility of practically performing such a reunion of an object from its elements.

In the analysis, not all parts are singled out, but only those that are essential for a given subject. In such a physical exercise as a jump, many different elements can be noted: the movement of the hands, the movement of the head, facial expressions, etc. All of these elements are related to this exercise to one degree or another, and we highlight them. However, in the process of scientific analysis, we rely not on these, but on the essential parts of the whole, without which this whole cannot exist. Essential for the jump are not facial expressions or movements of the head and hands, but the run and push.

The selection of essential elements in the analysis of a complex phenomenon does not occur mechanically, but as a result of understanding the significance of individual parts for the whole. Before mentally isolating the essential features or parts, we must have at least a vague general synthetic concept of the entire object as a whole, in the aggregate of all its parts. Such a concept arises as a result of a preliminary, formed even before a detailed analysis general idea about the subject based on practical knowledge of it.

Comparison is a comparison of objects and phenomena in order to find similarities and differences between them. K.D. Ushinsky considered the operation of comparison to be the basis of understanding. He believed that we cognize any object only by equating it to something and distinguishing it from something.

The comparison is based on analysis. In order to reflect with the help of thinking any connections and relations between objects or phenomena of the objective world, it is necessary, first of all, to single out these phenomena in perception or representation. For example, in order to understand the reason for the failure of an athlete to complete a given exercise, it is necessary to focus your thought on this exercise and on the conditions under which it was performed. This selection is always associated with the awareness of the task, it involves a preliminary statement of the question, which determines the selection of the objects of interest to us.

In the educational activity of a schoolchild, comparison plays a very important role. Comparing, for example, an adjective and a verb, the operations of multiplication and division, oxygen and hydrogen, a triangle and a rectangle, a forest, a steppe and a desert, a slaveholding and a feudal system, the student learns more deeply the features of these objects or phenomena.

A successful comparison of objects and phenomena is possible when it is purposeful, i.e. occurs from a certain point of view, for the sake of answering a question. It can be directed either to establish the similarity of objects, or to establish differences, or both at the same time.

Studies have shown that younger students will be more successful in finding similarities between objects if, when comparing, give additional item different from those being compared. Pupils compare images of domestic animals - cows and sheep, and there are not so many similar signs. If, however, to demonstrate three pictures - a cow, a sheep and a dog, then students find much more similar features in a cow and a sheep.

Concepts are formed in a person as a result of the process of generalization, i.e. mental association of objects and phenomena that have common properties. Generalizations will be correct when objects and phenomena are combined according to an essential feature. So, to think about the concept of "metal" means to single out the common features that iron, steel, cast iron, copper, etc. have, and combine them in one generalizing word - "metal". But not always an essential feature is taken as the basis of generalization. Sometimes the association occurs on random grounds. Such mistakes are often made by children.

The writer resorts to generalization, taking some features from individual people and combining them in one person, thus creating a typical image of a literary hero. A.M. Gorky said that it is necessary to take a very good look at a hundred people of any class in order to approximately correctly paint a portrait of one of its representatives.

Generalization is one of the basic mental operations. It consists in identifying common features, properties, qualities, trends in a number of objects, phenomena, events.

There are 2 types of generalizations: empirical and theoretical.

Empirical generalization - a generalization based on a comparison of objects in the selection and designation through the word of their common properties. The use of such properties as classifiers provides a person with the opportunity to work with a much larger volume of objects than is possible in the preceptive plan. With the help of classification schemes, each new item recognized as belonging to a particular class. The ability for empirical generalization is formed even in preschool age, but the most sensitive age is primary school age.

For example, in physics there is a group of problems united by such a common feature: in them it is necessary to find the characteristics of the movement of bodies, without delving into the causes that cause the movements; these tasks are related to kinematics.

When we perform laboratory work, then after a series of experiments of the same type, we draw a conclusion, the essence of which is to identify a common property in the results obtained.

The examples given convince us that the operation "generalization" is not so rare, that it is associated with analysis, comparison, classification and abstraction.

Theoretical generalization - a generalization based on the identification of significant links between the phenomena of the surrounding world, indicating their genetic relationship. It is carried out with the help of a concept in which only the most essential is fixed, and the private is omitted. The ability for theoretical generalization is formed most intensively in adolescence and youth.

Theoretical generalization is carried out by analyzing the totality and highlighting the general in its composition. Usually this selection occurs as a result of a transformation.

Teachers and didacticians came to the conclusion that in middle age it is expedient for students to deal only with empirical generalizations, and in older age - sometimes with theoretical ones.

Classification is a complex mental operation that requires the ability to analyze the material, compare (correlate) its individual elements with each other, find common features in them, generalize on this basis, distribute objects into groups based on those identified in them and reflected in the word - name groups - common features. Classification, therefore, contains such operations as correlation, generalization and designation.

In life, we often perform this operation or observe it. In problem books, we see collections of problems related to one specific issue, for example, free fall of bodies, friction.

Classification also takes place in public life. For example, those who go in for sports join sports sections, those who love fishing join the Fisher-Sportsman society, those who adhere to certain political views form a party.

The classification is widely used in botany, zoology. For example, there is a class of vertebrates - "Reptiles"; it is divided into subclasses: "Pervolizards", "Scaly", "Turtles", "Crocodiles".

Considering ionization (i.e. the process of transformation of atoms and molecules into ions) from the point of view of the cause that causes this process. Scientists have identified the following types of ionization: thermal ionization (occurs as a result of gas heating), photoionization (reason - absorption of light), ionization by impact (reason - mechanical collision), ionization generated by exposure to a) electric field, b) radioactive decay, c) cosmic flow rays.

With the help of a separator, the extracted ore can be divided into fractions according to the mass of particles of the same composition: in one there will be grains that are heavier, in the other - lighter.

Systematization is a procedure for creating or compiling a whole from separate parts and identifying the relationships between them.

There is another definition of the concept of "systematization". To systematize means to bring into the system, i.e. arrange in some order the individual components, establishing their sequence on the basis of the chosen principle.

It is with this (second) definition that the world-famous work of the great chemist D.I. Mendeleev. Taking as a basis, i.e. choosing for the main feature that determines the properties chemical elements, relative atomic weight, the scientist arranged all the elements in ascending order of atomic weights and received the Periodic Table of Elements. Further, in connection with the development of science, the main system-forming feature was changed: it became a charge atomic nucleus; Fortunately, the system itself has not changed from this.

How to proceed if we want to systematize in accordance with the second definition (for example, create a link diagram of formulas from some section of physics, a chronological table scientific discoveries in some area of physics)?

In the second chapter, we present the systematization algorithm.

Abstraction is the mental selection of essential properties and features of objects or phenomena while simultaneously abstracting from non-essential features and properties.

The attribute of an object, singled out in the process of abstraction, is thought independently of other attributes and becomes an independent object of thinking. So, observing various transparent objects: air, glass, water, etc., we single out a common feature in them - transparency and can think about transparency in general; observing the movement of celestial bodies, machines, people, animals, we single out a common feature - movement and think of movement in general as an independent object. In the same way, with the help of abstraction, concepts of length, height, volume, triangle, number, verb, etc. are created.

Abstraction is the basis of generalization - the mental association of objects and phenomena into groups according to those common and essential features that stand out in the process of abstraction.

V academic work schoolchildren generalization usually manifests itself in conclusions, definitions, rules, classification. It is sometimes difficult for schoolchildren to make a generalization, since it is far from always possible for them to independently identify not only common, but also essential general features.

Some domestic psychologists (D.B. Elkonin, V.V. Davydov) distinguish two types of generalization: formal-empirical and meaningful (theoretical). Formal-empirical generalization is carried out by comparing a number of objects and identifying outwardly identical and common features. A meaningful (theoretical) generalization is based on a deep analysis of objects and the identification of hidden common and essential features, relationships and dependencies.

abstraction process

Any process of cognition is aimed at achieving complete, comprehensive knowledge about the object, therefore, “naked”, abstracted knowledge should gradually “grow” with specifics, which is inseparable from synthesis. The concretization of abstractions can be considered as another stage of cognition. In life, science always ascends from the abstract - the main, but simplified, one-sided, as it were "rectilinear", "naked" knowledge to concrete, more complete, "branched" knowledge.

Abstraction is used to study new objects, phenomena, processes, events. It is widely used when considering complex problems, which simplifies the solution. Gradually, a solution with one specific condition is added to the solution with an abstract object, then with the second, and so on.

Types of abstractions

Abstraction is of three types:

Isomerating (singling out) - highlighting the phenomenon under study from a certain integrity,

Generalizing - giving a generalized picture of the phenomenon,

Idealizing - replacing reality, an existing object or phenomenon with an idealized one, with a scheme.

Concretization is a mental transition from the general to the individual, which corresponds to this general.

In educational activity, to concretize means to give an example, an illustration, a specific fact that confirms a general theoretical position, a rule, a law (for example, a grammatical, mathematical rule, a physical, socio-historical law, etc.). In the educational process, concretization has great importance: it connects our theoretical knowledge with life, with practice and helps to correctly understand reality. The lack of concretization leads to the formalism of knowledge, which remains bare and useless abstractions, divorced from life.

Stages of the instantiation process

Concretization involves recreating the most complete picture of knowledge about a real object. Thanks to this, the knowledge contained in the abstract concept in an abbreviated form becomes complete. This process and its steps are illustrated in the figure below.

If you think about the drawing, then concretization can be imagined as the creation of branches to the main trunk of a tree identified with abstraction. And the more branches there are, the more complete the specification of the tree is.

Concretization is one of the ways of knowledge. The ability to carry it out necessary condition formation of thinking. Specification is carried out in two forms:

Sensory-visual - through models, tables, maps, plans, diagrams, experiments;

Verbal - through verbal explanations. As stated in the Russian Pedagogical Encyclopedia, concretization differs from illustration and examples, which only explain some property or some regularity with a separate private fact. We tend to consider examples - the most simple view concretization, but on the condition that each example reveals one of the properties or qualities of the object, one of the relationships.

We deal with concretization in its scientific understanding in cases like the following. To master a new concept, for example, “friction” (friction is the force of resistance to movement that occurs at the point of contact of bodies pressed against each other, this is an abstraction), you need to organize the work in such a way that students see: friction appears when:

a) the movement of bodies relative to each other,

b) sliding and rolling,

c) friction can be large and small,

d) it can increase and decrease,

e) depends on the material of the contacting surfaces.

All these facts and the experiments that reveal them make it possible to create a fairly complete image of the phenomenon, to reveal both the main, typical features, and private ones.

It becomes clear why in empirical thinking (that is, based on experience) concretization acts as a means of implementing the principle of visibility in teaching.

Practice has shown: visual concretization is available to students of junior and secondary school age, and verbal - mainly older.

Let us note once again: to concretize means to connect a concept, a term with reality, to explain it, but the main thing is to present it in detail and with many connections.

Mental operations are actions that we carry out in our thinking on material, real or imagined. Mental operations are separate "bricks" or stages of our thinking. The main types of mental operations include:

Comparison,

abstraction,

concretization,

induction,

Deduction.

Comparison

Comparison is a mental operation that consists in establishing similarities and differences between individual objects or phenomena of the real world.

When a person observes two objects, willy-nilly or not, he begins to notice how these objects are similar or how they differ. Outwardly simple, this operation includes a number of complex elements. There is no "comparison in general", it always depends on what properties of the compared objects are essential for us, what interests us. Depending on the situation, on our needs (sometimes very subtle) there are different bases for comparison.

Example. There are four people. Three of them are interested in books, the fourth is not. The former is interested in books insofar as he is interested in, say, science fiction. When he encounters a book, he pays attention to those details that can show that it belongs specifically to science fiction. On the cover you can find the name of a familiar author, if the author is unknown, then the title of the work or the characteristic design of the cover can give out that the book belongs to a particular genre. Therefore, when meeting two books, a fan of science fiction will compare them with each other in terms of authors, titles, and design. And, without even looking inside, he can give preference to one or another book.

Another person is also interested in books, but his interest is professional: he is engaged in publishing. Such a person is likely to compare books with each other on other grounds: paper quality, cover design methods, book sizes, and some other technical characteristics.

The fourth person is not at all interested in books, at least in their paper versions. If he reads books, then only from a computer screen or mobile device. Paper books occupy almost no place in the life of this person. And therefore, interestingly and importantly, the grounds for comparing books among themselves are temporary and unstable: today two books seem similar / different because of color, tomorrow they are compared in size, the day after tomorrow in the year of publication, etc. .

The comparison operation is carried out either directly or indirectly. When we perceive two things directly, we use direct comparison. Otherwise, we use an indirect comparison. In an indirect comparison, we can use inferences based on indirect signs.

Indirect comparison generally relies on the full power of our intellect; both, for example, imagination and visual actions can be used as a "mediator" in the comparison. The child cannot find out if he has become taller by comparing himself directly with his present self and his former self (for example, a month ago). However, he can use a visual trick and mark his height on the door frame. And then by the marks he will be able to find out the desired information.

Strictly speaking, in nature there are no two identical objects at all. Any two stones differ from each other, heavenly bodies differ, there are no two absolutely identical birds or insects. It must be assumed that even two identical atoms or electrons do not exist. Our thinking makes objects the same. For this, in fact, there is a comparison operation.

Moreover, the human mind has come up with objects that are always the same, under all circumstances. This, of course, is about mathematical - exclusively invented - objects. So in mathematics, all equilateral triangles with a side length of 7 centimeters are always equal to each other.

The operation of comparison is extremely important for the work of the psyche. And in any comparison, as we have already said, there is one or another basis, one or another essential feature. It is interesting that in the comparison operation there are individual differences not only in terms of bases, but also in the comparison algorithm.

Example. There are four people (A, B, C, D) and two stones (b and b). The test subjects are tasked with comparing the stones and making a verdict: are these stones the same or different. For all subjects, the main comparison criterion is the shape, but there are also secondary ones - color, size. A and B started their reasoning like this: "Suppose b and b are the same..." C and D started their reasoning differently: "Suppose b and b are different..." Then they continued their reasoning. Subject A stated: "The shape of the stones is the same, so the hypothesis is fully confirmed." Subject B decided differently: "The shape of the stones is the same, but I have not yet compared in color and size; if it turns out that they are different in some way, then the stones will be different." Subject B argues differently: "The shape of b and b is the same, so my hypothesis was not confirmed, and this means that the stones are not different, but the same." And the last subject, G: "The shape, of course, is the same, and this somewhat contradicts my hypothesis; I will have to compare more in color and size; maybe they will confirm my hypothesis."

Unlike abstract reasoning in philosophy, formal or mathematical logic in real life in most cases we have several bases for comparison. In this case, some grounds are usually somewhat more important than others. Therefore, all four comparison algorithms given in the example make sense. Depending on the number of bases, on their equal or different significance, there are profitable talk one way or another.

The comparison operation is carried out by our thinking so often and in most cases so quickly that we simply do not have time to reflect on the algorithms by which we compare. Algorithms are very different and specific, not only such simple logical ones as in our example. Comparison can be multi-criteria, when in our head we formulate a number of comparison criteria, and then, as it were, putting points in our minds to the compared objects. Some comparison algorithms are inherent in us by nature and have not yet been fully studied by science.

Such, for example, is auditory perception, entirely built on comparisons. Listening to another popular motive, we relatively easily and not without pleasure seek out a recurring chorus in a musical opus. We can say with certainty what other opuses this opus is similar to. But we are not able to clearly describe the algorithm for comparing two pieces of music with each other, or at least separate short sections, because we control this intellectual comparison process very weakly with our consciousness.

The comparison operation is inherent not only to people, but also to animals and birds. Females of many animals, for example, having the opportunity to compare two potential marriage partners among themselves, prefer a larger and more physically developed male. When meeting each other, geese stand on tiptoe and stretch their beak upwards, comparing their height and competing in this indicator.

The comparison operation is the base for many other mental operations. Abstracting from some properties and circumstances, focusing on others provides a primary structuring, ordering of the material.

Analysis and synthesis

Analysis is the mental division of something into parts or the mental selection of individual properties of an object. The essence of this operation is that, perceiving or imagining an object or phenomenon, we can mentally select one part from another in it, and then select the next part, etc.

Through analysis, we can find out what parts are in what we perceive. Analysis allows us to decompose the whole into parts, i.e. allows us to understand the structure of what we perceive. Not always, however, there is only one way of this decomposition of the whole into parts. If the system is very complex, then there can be a lot of these methods. Therefore, as in the case of the comparison operation, the analysis can also have reasons.

Example. Suppose we are given the task of dividing the city in which we live into several separate parts. As a basis for decomposition (analysis), we can take the already established administrative-territorial division (by districts). We can divide the city into functional parts: residential areas, industrial areas, landscape gardening areas. We can distinguish the historical part (with houses built, say, before 1917), the modern part, and the area of new buildings. It can be divided into right bank and left bank.

It is possible to analyze not only those objects that are presented to us visually. You can analyze, for example, processes. If a position was established in some organization, for example, an economist-analyst or a marketer, then the specialist who occupied it will begin his work with an analysis: he will find out what structural and functional divisions exist in the organization in general, what specific tasks the organization faces, who her partners, etc. Without a preliminary analysis in his work, such a specialist will poke around like a blind kitten.

When analyzing visual objects, we highlight:

Essential parts of the subject (structure),

Color, shape, material properties and other properties.

Analysis of objects, of course, can be carried out not only in a visual mode, but also from memory.

Synthesis is an operation opposite to analysis, a mental combination of parts of objects or phenomena into a single whole, a mental combination of their individual properties.

Suppose we come across a new radio-controlled toy car and we really want to understand how it works. At first we will just play and observe the behavior of the machine. Then we can disassemble it together with the remote control and conduct an analysis, that is, carefully study the structure of the toy, understand what parts it consists of. After that, we can assemble the machine (that is, carry out the synthesis) and continue studying the behavior of the machine. We can disassemble the machine again, change something in its device and assemble it, see what comes of it.

The very fact that we managed to assemble the machine again already shows that we have a good understanding of its device.

Synthesis, as well as analysis, is characterized by mental operation of the properties of an object. However, it cannot be argued that synthesis and analysis are exclusively mental (non-material) operations. It is possible to assemble and disassemble the machine, as in our example, not only in the mind, but also in a mixed form: that is, on visual material. Analysis and synthesis are not some "mystically incomprehensible" operations, they are literally the decomposition and assembly of an object. And it's often more rewarding to take apart a typewriter or something literally than mentally. By the way, the human hand is represented in the cerebral cortex by very large areas and, by manipulating this or that object, the "smart hand" can "explain" a lot.

Throughout life, a person constantly, daily and even hourly uses analysis and synthesis. Arriving, for example, in a new supermarket, the buyer in his mind divides the store area into departments, analyzes the assortment by manufacturers, highlights the strengths and weaknesses in the work of the staff, determines which goods are profitable to buy and which are not.

Both analysis and synthesis can pursue purely practical goals, and can also be theoretical. In the latter case, a person is only interested in "truth for the sake of truth", that is, he is engaged in the development of a single, scientific picture (model) of the world.

Regardless of the practical or theoretical nature of reflection, analysis and synthesis are closely related to other mental operations, such as comparison. Comparison of two objects with each other can serve as an impetus for the analysis of one of these objects or both. Having learned, for example, that not all products are equally useful, a curious person will begin to inquire why and will begin to sort products into components in his mind. Within the analysis operation itself, a comparison may be required: having met two identical gears in the design of a machine, a person may be interested in whether they are exactly the same, and if they are different, then how significant this difference is.

Analysis and synthesis are closely related. In everyday life, we usually don’t notice how in our mind we first “sort things out” and then put them together into one whole. By themselves, analysis for the sake of analysis and synthesis for the sake of synthesis practically do not occur. If we have "taken apart something brick by brick", then later we want to make something out of these "bricks". And having done something, I want to take it apart again.

Abstraction and Concretization

Abstraction is a mental distraction from some parts or properties of an object in favor of other, more significant features. You can abstract from any features or properties of the object. To abstract from something means not to attach importance to it, to ignore this circumstance.

You can ignore the age, gender and character of your colleagues. Then it will be possible to evaluate colleagues more objectively, according to business qualities.

You can ignore the fact that the Earth is round and build a football field flat instead of convex.

You can disregard the temperature of ice cream and consider melted ice cream to be ice cream as well.

Abstraction is weak and strong. In the first case, we abstract from one or two signs, circumstances. In the second case, we abstract from everything else, except for one or two signs or circumstances.

If we abstract from everything except age, gender and character, then we can make a small personality portrait: "An elderly grumpy woman" or "A brave but arrogant young man."

If we abstract from all other circumstances except that the Earth is round, then we can say that the planet Earth is one big football field.

If we abstract from everything except temperature, then we can say that all cold objects are ice cream.

The beauty of abstraction lies not only in the fact that we can talk about such concepts as "a sexless person" or " flat earth", but also in the fact that we can talk about strong abstractions - features abstracted from carrier objects. We can judge such abstract things as temperature, gender, age, round shape, rectangular shape, shape, color, democracy , psychology.

What gives us the ability to abstract? For example, it is widely used in the formation and assimilation of new concepts, since the concepts reflect only essential features common to a whole class of objects. Having said "table", we abstract from other, seemingly secondary, features, such as color, dimensions, material, functionality, and present a certain image of a whole class of objects. In the word "table" we present only an abstract characteristic: a rather large object with a flat surface, at which one can sit and on which one can perform certain manual actions, a third or half the height of a person.

Not every person can define a table, but all people are well aware of this concept and use it competently. Some abstract concepts cannot be explained directly at all, only indirectly. So, for example, without the use of a scientific apparatus, it is impossible to explain to another person what is different green color from red. It is possible only in examples, through concretization, to say that green is the color of plants, and red is the color of ripe tomatoes or ketchup.

It is even more difficult to explain the meaning of words denoting non-visual objects. How to define love? Or democracy? A feeling of deep sympathy? What is sympathy? Deep attachment to another person or object? How can you tell a deep attachment from a shallow one? People power? Over whom?

This is very interesting feature of the human psyche: we can speak for hours in abstract words, but to give a definition to these words is given to us by significant efforts.

Among the types of abstraction are sometimes distinguished:

Practical (directly included in the process of activity),

sensual (external)

Higher (mediated, expressed in concepts).

Pure abstraction, abstraction for the sake of abstraction, can take you very far in reasoning. In contrast to it, there is concretization - the representation of something single, which corresponds to a particular concept or general position. In concrete representations, we do not seek to abstract ourselves from the various features or properties of objects and phenomena, but, on the contrary, we strive to imagine these objects in all their diversity of properties and features, in a close combination of some features with others.

If abstraction is the breaking of links between features, the transition from consideration of isolated cases to general ones, then concretization always acts as an example or as an illustration of something in common. Specifying general concept we understand it better.

Examples. There was an abstract concept "a piece of furniture" - the concept "table" became less abstract (more concrete). To be specific, you can go to "desk", "my home desk", "my home desk, as it was ten years ago."

"Activity" - "Professional activity" - "Healing" - "Pulling out teeth."

"Animal" - "Predator" - "Representative of the cat family" - "Domestic cat" - "My cat Musya".

Induction and deduction

An important feature of our mental activity is that as a result of it we receive (can receive) new knowledge. The acquisition of new knowledge is directly followed by a conclusion, which is also referred to as mental operations. There are usually two main types of inference:

Inductive reasoning (induction),

Deductive reasoning (deduction).

Induction - the transition from special cases to a general position, which covers special cases.

Examples. Suppose we have made a series of observations. We saw bears in several zoos. All of them were brown. From this we concluded that all bears are brown.

We have seen many birds in our lifetime. All of them had feathers, except for those sold in the store. From this we concluded that all living birds have feathers.

I went through a lot of different numbers in my mind. It turned out that no matter how big a number is, there will always be even more. From this they concluded that there is no largest number in the world.

As in any mental operation, in induction we can make certain mistakes, the conclusion made may turn out to be insufficiently reliable or completely false. The reliability of inductive reasoning is achieved not only by increasing the number of cases on which it is based, but also by using a variety of examples in which insignificant features of objects and phenomena vary.

Inferences like "Some bears are brown" are also inductive. And it's not hard at all to make them. It is enough just to watch a few brown bears. Much more difficult with strong statements like "All bears are brown." Even after observing a thousand bears, among which all turned out to be brown, it cannot be argued that all bears are brown, because we do not know if we have seen all possible bears in the world.

Having polled 1200 respondents during sociological research it can be found out that all respondents support the politician Vasisualy Lokhankin. It will be true. However, the inductive conclusion "All the inhabitants of our city (country) support Vasisualy Lokhankin" will remain conjectural and unproven. It will only be proven that some residents support the said politician. And you can't get away from this fact.

Although inductive reasoning is not precise in a strict, logical sense, it is of course of great use in everyday life. Having bought spoiled products several times in the same store, one can come to the inductive conclusion that all (many) products from this store are spoiled. Observing how often a person lies, one can inductively conclude that he usually tells lies in general.

The mental operation opposite to induction is deduction - a conclusion made in relation to a particular case on the basis of a general position. For example, knowing that all numbers are divisible by three, the sum of the digits of which is a multiple of three, we can say that the number 412815 is divided by three without a remainder. At the same time, knowing that all birches shed their leaves for the winter, we can be sure that any individual birch will also be without leaves in winter.

Induction through generalizations of varying degrees of accuracy and reliability helps us to enrich our knowledge about the world around us. We can say that the picture (model) of the world consists of many different inductive conclusions. In adolescence, when a person is studying, he uses the induction operation much more often. In mature years, when it is time to act, deduction is needed more often, because it is it that helps in solving specific life problems.

The doctor, having made a definite diagnosis to the patient, based on knowledge general patterns the course of this disease, concludes how to treat a particular patient. An experienced auto mechanic, knowing the typical problems of cars of a given model and observing certain symptoms, draws a conclusion about the alleged problems. The buyer, knowing that all ripe bananas are yellow, does not buy green ones.

Like induction, deduction is a rather risky inference. Knowing, for example, that the majority of engineers are men, a school graduate may change her mind about entering a technical university, although she had success in mathematics and physics at school.

In addition to induction and deduction, traduction is also distinguished in logic - a conclusion that is not accompanied by a transition from the particular to the general or vice versa. The most typical example of traduction is analogy. Having a rather vague idea (model) of the object in question, we can turn to an analogy, that is, take another object, or rather its model, correct something in this model and use it on the current object. If students, for example, do not really understand how the earth's crust works, then the teacher can give an analogy with a layer cake.

Literature

Maklakov A. G. General psychology. St. Petersburg: Peter, 2001. Consideration, study of something, based on the dismemberment (mental, and often real) of an object, phenomenon into its constituent parts, determination of the elements included in the whole, analysis of the properties of an object or phenomenon. The reverse procedure of A. is synthesis, with which A. is often combined in practical or cognitive activity. Synthesis consists in the fact that knowledge about the subject is obtained by combining its elements and studying their connection. One of the logical operations thinking. Tasks on S. objects, images, concepts are widely used in psychological research development of thinking and its disorders. The grounds for S. that a person uses, the ease of transition from one of them to another, etc. are analyzed.

To solve problems, a person uses many mental operations: analysis, synthesis, generalization, comparison, etc. Without them, it is impossible cognitive activity, learning, productive thinking in general. Today we will look at the essence of basic mental operations and find out how to teach them to a child.

Types of mental operations

mental operations or theoretical methods research is one of the tools of mental activity aimed at solving problems. The main function of these operations is the awareness of the essence of processes, phenomena or objects. Simply put, everything that we mean by the word "think".

There are many theoretical research methods. The main ones are:

Analysis. The decomposition of the whole into parts, the selection of individual features, properties, qualities of objects / phenomena.
Synthesis. Combining parts into a whole based on the semantic relationships of objects / phenomena among themselves.
Comparison. Comparison of objects / phenomena with each other, finding similarities and differences between them.
Generalization. The combination of various objects / phenomena into one group based on common features (based on similarity).
Specification. Filling some generalized scheme with a particular meaning (features, properties).
Analogy. Transfer of knowledge about one subject/phenomenon to another (less studied or inaccessible for study).

These operations are indispensable in the process of learning, assimilation of new knowledge. Many of them are used by a person unconsciously and intuitively. However, in order to effectively apply these mental operations, it is necessary to develop and improve them already from primary school age.

Analysis

For younger students

Name the properties. Offer the child a number of concepts (apple, table, dog, etc.) and ask them to name the essential features of each of them. For example, an apple is round, green and grows on a tree. The more properties the student names, the better. To complicate the task, you can ask the child to highlight a certain number of signs (at least five, seven, ten).
Divide by feature. The student is offered a set of different shapes (small/large, red/blue/green/yellow squares/circles/triangles), which must be divided according to a certain attribute: first by shape, then by color and, finally, by size.

Analysis of a literary work. The student's task is to read a poem or a story and explain how he understands its meaning, to guess what the author wanted to say with one or another part of the work.
Analysis of the situation. The child is offered a situation that he needs to consider from all sides, to offer some solution to the problem, a possible development of events. For example, studying at a university. It can be paid and free. Paid education costs 80,000 rubles, for free education you need to score at least 200 USE points. For admission to one faculty, Russian language, mathematics and biology are needed, to the other - mathematics, Russian language and physics. In physics, the student has a five, and in biology - a four. Etc.

IMPORTANT! The student should not only make assumptions, but also explain them. I think so because...

Synthesis

For younger students

Draw the missing figure. The child is offered several figures, united according to some attribute (color, shape, size). One object is missing in the row - the student must name it and finish it.
Lay out the figure. From a set of elements, the child needs to fold an object: a square, a triangle, a rhombus, a house, a chair, etc.