Analytical-synthetic ability and ways of its development in schoolchildren. Formation of analytical and synthetic activity of a preschooler as a prerequisite for teaching literacy

The processes of education and upbringing become more complicated as the student matures. Instead of the total perception of the explained, associated with the irradiation of excitation, there appears the ability to isolate in the perception of individual aspects of objects and phenomena, followed by an assessment of its integral state. Thanks to this, the mental activity of the student goes from the particular to the general. The physiological mechanism of such changes is due to the analytical and synthetic activity of the cerebral cortex.

Analysis(analytical activity) is the ability of the body to decompose, dismember the stimuli acting on the body (images of the outside world) into the simplest constituent elements, properties and signs.

Synthesis(synthetic activity) is a process opposite to analysis, which consists in highlighting among the simplest elements, properties and features decomposed in the analysis, the most important, essential in this moment and combining them into complex complexes and systems.

The unity of the analytical-synthetic activity of the brain lies in the fact that the body, with the help of sensory systems, distinguishes (analyzes) all existing external and internal stimuli and, based on this analysis, forms an idea about them.

GNI is the analytical and synthetic activity of the cortex and the nearest subcortical formations of the GM, which manifests itself in the ability to isolate from environment its individual elements and combine them in combinations that exactly correspond to the biological significance of the phenomena of the surrounding world.

Physiological basis of synthesis make up the concentration of excitation, negative induction and dominant. In turn, synthetic activity is the physiological basis for the first stage in the formation of conditioned reflexes (the stage of generalization of conditioned reflexes, their generalization). The stage of generalization can be traced in the experiment if a conditioned reflex is formed to several similar conditioned signals. It is enough to strengthen the reaction to one such signal in order to be convinced of the appearance of a similar reaction to another, similar to it, although a reflex has not yet formed to it. This is explained by the fact that each new conditioned reflex always has a generalized character and allows a person to form only an approximate idea of the phenomenon caused by it. Consequently, the stage of generalization is such a state of the formation of reflexes in which they appear not only under the action of reinforced, but also under the action of similar unreinforced conditioned signals. In humans, an example of generalization is the initial stage of the formation of new concepts. The first information about the subject or phenomenon being studied is always distinguished by a generalized and very superficial character. Only gradually does a relatively accurate and complete knowledge of the subject emerge from it. The physiological mechanism of generalization of the conditioned reflex consists in the formation of temporary connections of the reinforcing reflex with conditioned signals close to the main one. Generalization is of great biological importance, because. leads to a generalization of actions created by similar conditional signals. Such a generalization is useful, because it makes it possible to assess the general significance of the newly formed conditioned reflex, for the time being without regard for its particulars, the essence of which can be dealt with later.

The physiological basis of the analysis make up the irradiation of excitation and differential inhibition. In turn, analytical activity is the physiological basis for the second stage in the formation of conditioned reflexes (the stage of specialization of conditioned reflexes).

If we continue the formation of conditioned reflexes to the same similar stimuli with the help of which the generalization stage arose, then we can see that after a while conditioned reflexes appear only to the reinforced signal and do not appear on any of the similar ones. This means that the conditioned reflex has become specialized. The stage of specialization is characterized by the appearance of a conditioned reflex to only one main signal with the loss of the signal value of all other similar conditioned signals. The physiological mechanism of specialization consists in the extinction of all secondary conditional connections. The phenomenon of specialization underlies the pedagogical process. The first impressions that a teacher creates about an object or phenomenon are always general and only gradually they are refined and detailed. Only that which corresponds to reality and turns out to be necessary is strengthened. Specialization, therefore, leads to a significant refinement of knowledge about the subject or phenomenon being studied.

Bakirov Ruzil Floritovichteacher of mathematics and computer science, "Aktanysh secondary comprehensive school No. 2 in-depth study of individual subjects”, Republic of Tatarstan, Aktanysh district, Aktanysh village [email protected]

Analytic-synthetic ability and ways of its development in schoolchildren

Annotation.In scientific work such a question as the study of ways of development of analytic-synthetic abilities in schoolchildren is being studied. In the course of the study, a detailed description of the concepts of analysis and synthesis is given. Further, their interrelation and interdependence, as well as the development of analytic and synthetic abilities in schoolchildren, are considered.

It should be noted that the analytic-synthetic ability is the most important tool of the personality in both its cognitive and creative activities. And at school, teachers need to teach students to apply the techniques of "synthesis" and "analysis", "analysis through synthesis", "synthesis through analysis". This work must be carried out constantly and purposefully.Key words.Analysis, synthesis, analytical-synthetic ability, cognitive activity.

Analysis and synthesis constitute the thought process of any reasonable person This is what distinguishes him from other representatives of the animal world of our planet. Analysis is the division of the whole into parts, the presentation of complex in the form of simple components, changing these parts, adding new ones or eliminating some of them for more efficient activity or convenience of research. Synthesis is a connection, a union (mental or real) of an updated set of simple components of an object into a single whole, harmonization of their activities for more efficient activity or convenience of research. The purpose of this work is to study such a question as the study of ways of developing analytic and synthetic abilities in schoolchildren. Tasks:  Disclosure of the concepts of analysis and synthesis. The study of analytic-synthetic abilities in schoolchildren. Analysis is the dismemberment, decomposition of an integral object and phenomenon into its component parts or sides. Dismemberment, decomposition of the object is carried out ideally, "in the mind." Of course, sometimes such a decomposition can be carried out in practice. Moreover, in all cases, at first the object had to be divided into separate parts, tested in its individual properties in order to find out these parts and properties of it. The main functions of analysis: 1. Analysis replaces practical activity on objects with ideal "mental" activity on meanings. This is achieved by replacing practical action speech actions. And the objects themselves - words that designate these objects.2. Analysis is the starting point in the cognition of meanings.3. Analysis allows you to dismember an object without killing it, preserving its own properties. Analysis puts an object into a network of categories. He cuts it not at random, but along the lines of certain basic relations with other things.

Any analysis from this point of view is at the same time the establishment of a connection between some object and a certain property. But such a process is already called synthesis. After all, “synthesis is any correlation, comparison, any establishment of a connection between various elements.” The difference between analysis and synthesis is conditional. It is itself a product of analysis and implies connection as much as difference. To use Goethe's expression, analysis is connected with synthesis, like inhalation with exhalation. Synthesis also has an ideal character, is carried out in the form of mental actions and with the help of words. It also has a categorical character: different properties are not just combined in an object, but are connected by certain relations from the category set.

Synthesis is only an ideal reflection of the practical operation of binding, connecting, as an analysis of the operation of distinguishing, separating. So, the properties of things or phenomena established by analysis, and their connections established by synthesis, are ultimately discovered from the study of the things and phenomena themselves, from the results of practical actions over them, that is, ultimately, from practical experience. “Analysis and synthesis are the “common denominators” of the entire cognitive process. They refer to sensory knowledge and perception. In terms of sensory cognition, analysis is expressed in the selection of some sensory property of an object that had not previously been properly distinguished. The cognitive significance of analysis is due to the fact that it singles out and “emphasizes”, highlights the essential. The core of various mental abilities is the quality of the processes of analysis (and, therefore, synthesis) and generalization, especially the generalization of relations. - "common denominators" of the entire cognitive process and any kind of abilities. Ability is a property of a person on which the effectiveness of an activity depends and which is a condition for the successful implementation of each type of activity. There are an incredible amount of abilities. Abilities should not be confused with knowledge, skills and abilities. Although abilities and knowledge are interconnected, they are essentially different. “In the European project “Adjustment educational structures”, aimed at realizing the goals of the Bologna Agreement, a list of general competencies is given. The list is divided into three categories: instrumental, interpersonal and systemic. Among the instrumental ones, the first place is occupied by "the ability to analyze and synthesize." This quote contains an important idea that the analytic-synthetic ability is the most important tool of the personality both in its cognitive and creative activity, and in self-development. For the development of analytic-synthetic abilities, one must learn to form the methods of mental activity of synthesis and analysis. At the same time, understanding their inextricable connection, do it separately, taking into account the importance of the didactic tasks being solved. The formation of these techniques should permeate all schooling, since it is important and useful to constantly answer the questions: “We have some statement, what consequences can be obtained from it ? We want to prove some statement, what do we need to know for this?”. It can be assumed that in practice this always happens, but it is enough to analyze the system of exercises in almost any textbook in mathematics to be convinced of the opposite. It should also be emphasized that these techniques should be formed taking into account the individual characteristics and capabilities of students. It is important to demand that the system of questions and exercises for the formation of these techniques be differentiated according to their degree of complexity, so that each student can always find a question that he would have to think about. And one more important note. The student will have to perform such work constantly both in solving problems and in proving theorems, but very effective tool in this work is a system of oral exercises, the so-called oral differentiated survey. The formation of methods of synthesis and analysis develops the thinking of students, and during oral survey, oral conversation, all students are involved. Note that this form of work in the classroom is actively used only in elementary school during oral counting, and in the systematic study of mathematics, it is clearly underestimated. This work, being collective, at the same time allows to identify the individual characteristics and capabilities of students. Let's move on to the description of the practical implementation of recommendations for the formation of methods of mental activity "synthesis" and "analysis". To do this, we can consider a system of exercises related to the study of the basic concepts of the geometry course, from which the study of geometric material in 56 classes begins and which are then refined and deepened. Starting from grade 7.1. The elementary school, working according to a specially designed program, provides for a fairly wide acquaintance of students with the elements of geometric knowledge, skills, and ideas. Note that it is still difficult to fix the level of geometric training of this category of students, it will not develop soon and can be quite different in their results. One thing is clear - Primary School can and should contribute to the formation of the geometric culture of students, and the minimum of these ideas should be clearly fixed. At this age, there should already be a serious impact on the formation of methods of mental activity (most importantly, on the formation of synthesis and analysis, but also on the formation of other methods). If we take into account the essence techniques of synthesis and analysis, one can imagine how these techniques should be developed during the four years of study in elementary school.2. Over the past decades, a stage of teaching mathematics has appeared in the school - 56 classes. It is difficult to imagine how this stage will be transformed in the conditions of a twelve-year school, but one thing is clear that here there are some peculiarities of including geometric material in the general course of mathematics: − highlighting a certain propaedeutic path; − systematic study of geometry from grades 5 to 12 important idea that is currently being worked out). In the first case, from the standpoint of the formation of methods of mental actions, this is a continuation of the work begun in primary school(it should be somewhat systematized and subjected to strict control). In the second case, this is a large, long-term, planned work, which, of course, should have practical results. I will give examples of the problem for the formation of methods of synthesis and analysis from the first sections of the textbooks "Geometry 511" Task 1. The perimeter of an isosceles triangle is 1 m, and the base is 0.4 m. Determine the length of the side. Solution. From the condition of the problem we have: 1. ΔABC - isosceles (according to this);

2. PΔABC \u003d AB + AC + BC \u003d 1m (according to this); 3. AB \u003d 0.4 m (according to this). 4. AC = BC = ? (required to find). From the task data, you can write: 5. AC = BC (1, definition of an isosceles triangle); 6. 0.4 + 2AC = 1m (2, 5); 7. AC \u003d 0.3 m (6). So, in this problem, obtaining consequences from the condition, we come to the answer. At the same time, analysis consists only in the fact that we remember what we need to find. This is the simplest example of using the "synthesis through analysis" technique, where the analysis is not related to the advancement of a new original mathematical idea. Problem 2. In an isosceles triangle ABC, straight lines are drawn through the ends of the base AC, which make equal angles with the base and intersect at point K. Prove that triangles ABK and SVK are equal. Solution. From the condition of the problem we have: 1. ΔABC - isosceles (according to this); 2. KAS = KSA (according to this, Fig. 1);

rice. 13. ΔABK = ΔSVK (required to prove). The main question arises: we need to prove equality 3, what should be done (prove) for this? It is clear that we must apply one of the signs of equality of triangles, in this case, the third ). Consider the triangles we need. In them: 4. AB \u003d CB (1, definition of an isosceles triangle); 5. VC is the common side of triangles ABK and SVK (1, 2). It would be nice to prove that AK = CK.6. ΔAKS - isosceles (2, a sign of an isosceles triangle); 7. AK = KS (5, definition of an isosceles triangle); 8. ΔABK = ΔSVK (4, 5, 6, the third sign of equality of triangles). We attribute this decision to the use of the “synthesis through analysis” technique. Here the idea of a solution is connected with the application of a well-known mathematical fact - a sign of the equality of triangles. Task 3. Solve the equation in natural numbers: 1. 1 + x + x2+ x3= 2y. Solution. From the condition we have: 1. 1 + x + x2+ x3= 2y, x and y are natural numbers (given). Let's try to transform this equation:

2. 1 + x + x2(1 + x) = 2y(1)3. (1 + x2)(1 + x) = 2y(2). What can follow from this notation? Let's read it like this: the product of two natural numbers (x is a natural number, which means that x + 1 and x2 + 1 are also natural) is equal to the power of 2. When does this happen? We can draw such a conclusion.4. The product of two natural numbers will be a power of two if each of the factors is also a power of two (3, the property of powers). Based on item 4, we can introduce the following notation.5. x + 1 = 2m, m is a non-negative integer; 6. x2+ 1 = 2n, n is a non-negative integer; 7. х = 2m–1(5);8. (2m–1) + 1 = 2n(6, 7);9. 22m–2 2m+ 2 = 2n(8);10. 22m1

22m+ 1 = 2n1(9);11. 2m(2m1–1) + 1 = 2n1(10). All the transformations that we have done seem to be clear, but why we were striving for equality 11 may not seem clear. Here, “analysis through synthesis” took place, which led to the fact that the expression was even on the right, and odd on the left. Note that it is difficult to teach such an activity, it comes with development, with experience. Let us consider for what m and n this is true.12. If n>1, then 2n1 is an even number (11, power property).13. With n = 0 and n = 1, we get two solutions: x = 0, y = 0 and x = 1, y = 2. Thus, in this example, the “analysis by synthesis” technique was used three times. I have only touched on some questions that help teach students apply the techniques of "synthesis" and "analysis", "analysis through synthesis", "synthesis through analysis". This work must be carried out constantly and purposefully. When solving any problem, it is important to pay attention to the very organization of analytic and synthetic activity. As for the implementation options this activity, then, for example, from this process you can make some kind of competition game, which, on the one hand, will interest students, and on the other hand, will help them to find out their capabilities, assess the level of their knowledge. This is the manifestation of differentiation in teaching mathematics. Thus, the analytic-synthetic ability is the most important tool of the individual in both his cognitive and creative activities. Indeed, studying different sources, one can cite the following characteristics for the methods of "analysis" and "synthesis": two interrelated mental operations; constructive elements of thinking; powerful means human knowledge; forms of thinking; two sides of the same process, and so on. Considering the formation of students' thinking, it is necessary first of all to think about the formation of methods of mental activity, about analysis and synthesis.

Links to sources 1. Itelson L.B. Lectures on General Psychology. Moscow-Minsk, Ast Harvest. 2002.S.6682. Rubinstein S.A. Problems of General Psychology, M: Pedagogy. 1976.S.410.3. Quote from the book: Dmitry Ivanov. Competencies and competency-based approach in modern education. M., 2007.S.11.

Bakirov Ruzil is a teacher of mathematics and informatics in “Aktanysh secondary school № 2 with profoundly studying of separate subjects” in the Tatarstan Republic, Aktanyshsky region, village Aktanysh

Analytics-synthetic ability and ways of its development in students

Annotation.In scientific work such question is studied as research of ways of development of analyticsynthetic abilities in students. During the study the detailed characteristic is given to concepts of analysis and synthesis. Further, their interrelation and interdependence, and also the development of analyticsynthetic skills in students is consideredIt should be noted that analyticsynthetic ability is the most important tool of the personality and his cognitive and creative activity. And teachers should teach students to apply the receptions "synthesis" and "analysis", "the analysis through synthesis", "synthesis through the analysis". This work is necessary for conducting constantly and purposefully at school.Keywords: analysis, synthesis, analyticsynthetic ability, cognitive activity

Novoselova Olga Pavlovna, teacher of mathematics, MBOU "Berdnikovskaya School"

Theoretical basis development of analytical and synthetic thinking of schoolchildren

Today there is a serious problem associated with the reassessment of values in the field of education. Comes to the forethe formation of a diversified creative personality capable of realizing creative potential both in their own vital interests and in the interests of society.

Until today, educational activity is the most important basis for the development of abilities, motives and other mental properties of the individual, therefore, the most acute question is that training should be directed not only to equip students with the necessary knowledge, skills, skills, but also to form the ability to acquire new knowledge. , that is, the purposeful formation of thinking. This need is also indicated by the program in mathematics: “... the development logical thinking and preparation of the apparatus necessary for the study of related disciplines (physics, drawing, etc.) and the course of stereometry in the upper grades, "as well as" ... the further development of students' logical thinking "in the geometry course of grades 10-11." However, analyzing psychological and pedagogical research and methodological literature, we can conclude that the problem of the development of thinking and specific mental operations by means of mathematics is complex and far from being solved. This is due to many reasons.

First, the organization learning activities, aimed at developing the thinking of students, psychologists and teachers are most actively involved, but little is said about the concept of mathematical thinking, since psychologists and didactics do not know the specifics of mathematical activity well, and mathematicians and methodologists are not specialists in psychology and didactics.

Secondly, many teachers consider mathematics to be a science that in itself contributes to the mental and mental development of students, that is, thinking develops when establishing the characteristic properties of a mathematical object, when it is necessary to build chains of logical inferences, and when solving a large number of problems, therefore, purposeful activity no teacher needed.

The third problem is related to age characteristics students. In adolescence, discovering wide cognitive interests, students strive to check everything on their own, thereby personally verifying the truth. By the beginning of adolescence, such a desire decreases somewhat, there is more confidence in someone else's experience, while students accept only what they personally think is reasonable, useful and expedient.

Another significant problem in the development of thinking is that many problems are solved according to the model considered in the classroom, thereby turning the solution of a certain type of problem into the study of a kind of theory, because students do not have an awareness of the connection between mathematics and the real world, with practical human activity.

But the problem of the unified state exam (USE) remains the most relevant for this period. Often, familiarization with testing procedures is in the nature of coaching students to perform a specific test. Training, coaching lead to a decrease in the validity of this measurement procedure. The practice of teaching how to pass a test focuses only on a specific set of knowledge and skills covered by a given test. Conditions are no longer created for students to study a wide area of knowledge that they are trying to assess with the help of this test, namely, students are not taught the methods of effective problem solving, the ability to analyze problems and questions, and carefully choose an answer.

All these problems can be solved by means of mathematics, but subject to a properly developed methodology for teaching it, since mathematics has great opportunities for shaping the mental activity of all students.

Let us dwell on the consideration of analysis and synthesis as the most important methods of mental activity that contribute to the formation of analytical and synthetic thinking, without which the formation of a full-fledged personality is not possible.

The content of mathematics, in particular geometry, provides a great opportunity for the formation of analysis and synthesis, which have long been used in teaching mathematics as two aspects: as logical operations of thinking (studying the properties of mathematical concepts - to bring under concepts and derive consequences from the belonging of an object to a concept) and as proof methods (in solving problems and proving theorems).

If you systematically and purposefully teach students analysis and synthesis as logical operations, and analytical and synthetic methods of reasoning, this will contribute to the development of their thinking, and hence the improvement of the quality of their mathematical knowledge.

Speaking of development of thinking in the process of teaching mathematics, often think of intellectual development or creativity. This is how I.O. defines the development of intelligence and creative abilities. Kon: "... The development of cognitive functions and intelligence has two sides: quantitative and qualitative ...".

Quantitative changes are changes in the level of development. A teenager solves intellectual problems easier, faster and more efficiently than a child younger age. And qualitative changes are shifts in the structure of thought processes, since it is important how a person solves the tasks.

The task of the math teacher is the process of tracking these changes and transforming them into more optimal ones. To do this, he needs to represent their structure and features, and on this basis, select the appropriate teaching methodology.

At the first stage, in the presence of a problem, the child must directly transform the existing situation into a given one. Here such mental operations are formed as setting a goal, analyzing these conditions, correlating the results of transformations with the goals set, etc. Thus, we can talk about the formation and developmentvisual action thinking. Its main feature is that the object of direct mental transformations is the real situation. This form of thinking is the main and first step for the development of other forms of mental activity.

In the future, when the problems facing the child become more and more complex, more advanced forms of thinking are required, which make it possible to transform the situation not in practical, but in mental terms. Now, in the process of solving the problem, the role of the transformed object should be played by the image of the problem situation, which is formed either at the stage of trial and error, or in the process of purposeful inspection, feeling, listening, etc. A new form of mental activity is emerging -visual-figurative thinking .

Over time, the child becomes aware of the presence of internal, hidden connections between various phenomena, and on the basis of visual-figurative thinking, he begins to form and developlogical thinking, which appears in the form of abstract concepts and judgments.

But the development of logical thinking does not mean at all that visual-effective and imaginative thinking is not capable of further development. S. L. Rubinshtein wrote that "genetically earlier types of visual thinking are not being supplanted, but are being transformed, moving on to higher forms of visual thinking."

Solving a variety of tasks that a person faces is most often associated with the need to plan the results of certain transformations of a problem situation. The decision process has to be built first in mental images, and then to translate it into reality, i.e. a person in the process of thinking operates with some mental model of a real situation. Therefore, figurative thinking is laid as the basis for studying the school geometry course, because. promotes the arbitrary creation of images based on some given visual material, stores and reproduces them in memory, mentally transforms them in a given or independently chosen direction, and on this basis creates new images that may differ significantly from the original ones. The ability to act in accordance with the idea, the ability to freely operate with images is considered as one of the professionally important qualities necessary for the successful implementation of a wide variety of activities.

The problem of the development of mathematical thinking in general is very complex and extensive.

One of the first characteristics of mathematical thinking isthe clarity of the formulation of the problem, task, task, whichis provided by the teacher and passed on to the student, since posing a question in the process of teaching mathematics is a very crucial moment. First of all, the content of the question must be perfectly clear. For example, after reading the text of the problem, the vast majority of teachers ask students: “Did you understand the condition of the problem?” or "Do you understand?" This is a tribute to tradition, since neither the teacher nor the student can give answers to these questions. You can ask about a lot of other reasonable things, for example: “What is given in the condition of the problem? What do you need to find? Where should a decision start? Have you solved a similar problem? etc. The question should be posed in such a way that it suggests in which direction the answer should be sought, what should be found. When looking for a method for solving a problem, it is especially important for a teacher to learn how to ask leading questions, since at present in the lesson we often get out of the situation by formulating various hints in the problem statement: “Solve the problem by the vector method”, “Use the first sign of equality of triangles”, etc. e. The question should guide the activity of the student, and not force him to do just that. Even more responsible is the formulation of the question-assistance in the search for different ways of solving problems.

Thus, the first of the most important stages in solving a mental problem is the isolation and formulation of the question and the analysis of the condition of the problem.

It is with the question that the process of thinking begins, at the same time, the correctness, accuracy, completeness and depth of the question are determined by the level of development of a person’s thinking, the student’s understanding of what is being discussed in the lesson. Therefore, the next characteristic of mathematical thinking is the understanding of the mathematical material offered to the student.

A mathematical object cannot be correctly understood if it is considered in isolation, without its connection with other objects. To understand any mathematical phenomenon means to reveal the essential in it, to realize the causes of its occurrence, its relationship with other phenomena, its place in the system of surrounding phenomena.

It is very important to teach the student how tosome consequences from the study fact. The number of such consequences, the level of significance and complexity depend on the individual abilities and characteristics of the students. It is the process of obtaining such consequences that ensures the understanding of the fact itself.

We constantly adhere to this rule, this is how all our mathematical courses are built. At the same time, practice shows that where this principle is violated, understanding of the material is not obtained. This also happened when the abstract level of presentation of the beginnings of geometry was overestimated, when supplements were suddenly introduced into the school in the form of vector algebra, the beginnings of mathematical analysis, elements of probability theory and mathematical statistics, when the topics of the courses turned out to be poorly or insufficiently connected with other educational material.

Organize like this educational process not easy, but the provision of such an organization should be constantly thought of. The teaching of mathematics should give rigorous conclusions, teach logical thinking, and develop creative thinking.

Creative thinking is denounced by the fact that the subject, with the help of special procedures, achieves new results in the process of independent search.

Creative search usually begins with understanding, awareness of the problem and then its formulation. The solution of the problem becomes the content of creativity.

The concept of mathematical thinking is also often adjacent to the concept"memory".Sometimes people who are far from mathematical activity confuse the concept of memory with the assessment of the abilities of some students, whose memory sometimes replaces some parameters of mathematical abilities. The unity of these activities is due to the unity of all the functions of thinking.

With regard to the category of "memory", psychology has accumulated a lot useful information: for successful memorization of educational material, it is necessary not so much to repeatedly read and repeat the same material as the desire to remember, to realize the importance of remembering it. It is meaningful, memorization is stronger than mechanical; The best and most durable material is remembered by the student on which the student independently actively creatively thought and with which he independently worked, even if he did not intend to memorize it.

Analysis and synthesis as the main operations of thinking

According to Rubinstein, "The process of thinking is, first of all, the analysis and synthesis of what is distinguished by analysis ... The patterns of these processes and their relationship with each other are the main internal patterns of thinking."

It is clear from the above quotation that"analyzing Andsynthesizing" should be considered among the most important methods of thinking. Therefore, considering the formation of students' thinking, it is necessary first of all to think about the formation of methods of mental activity, about analysis and synthesis.

DI. Bogoyavlensky and N.A. Menchinskaya write that “... we single out analysis and synthesis as the leading processes in cognitive activity. Thus, the main patterns that help reveal the essence of the transition from the lower stages of assimilation to the higher ones are the patterns of analysis and synthesis.

Analysis -this is a mental, as well as real, dismemberment of an object, the properties of an object, a phenomenon, a situation and the identification of its constituent elements, parts; by analysis we isolate phenomena from those random, unimportant connections in which they are often given to us in perception. Everything can be the subject of analysis: a psychological act, sensation, perception, idea, thought, logical device, any scientific theory.

Analysis is often presented as a multi-step process. What is achieved as a result of the initial analysis then becomes the subject of a deeper analysis. This transition from one level of analysis to another, deeper one, is determined by the requirements and nature of the new tasks that arise in the course of cognition.

And synthesis is understood as “a mental combination of parts of objects, phenomena or a mental combination of their features, properties or sides”. There are two types of synthesis: synthesis as a mental union of parts of the whole and synthesis as a mental combination of various features, properties, aspects of objects and phenomena of reality.

Synthesis always reproduces the analyzed subject, but at the same time it is always associated with clarifying, enriching, deepening the knowledge about the subject as a whole that we had before the analysis. As a result of the analysis and synthesis, the subject is reproduced in its essential and necessary connections.Synthesisrestores the whole dissected by the analysis, revealing more or less significant connections and relationships of the elements identified by the analysis.

Thus, synthesis is a procedure opposite to analysis, but with which analysis is often combined in practical or cognitive activities.

Analysis and synthesis arise first on the plane of action, are formed first in practice, then become operations or aspects of the theoretical thought process.

Analysis dismembers the problem; synthesis combines data in a new way to resolve it. Analyzing and synthesizing, thought goes from a more or less vague idea of the subject to a concept in which the main elements are revealed by analysis and the essential connections of the whole are revealed by synthesis.

In the original understanding, analysis was considered as a method of thinking from the whole to parts of this whole, and synthesis as a path from parts to the whole, therefore analysis and synthesis are practically inseparable from each other. They accompany each other, complement each other, making upunified analytic-synthetic method. Analysis presupposes synthesis, and synthesis is impossible without analysis, therefore, attempts at a one-sided application of analysis outside of synthesis lead to a mechanistic reduction of the whole to the sum of parts, and it is unacceptable to use synthesis without analysis, since synthesis must restore the whole in thought in the essential interconnections of its elements that analysis highlights .

If in the content of scientific knowledge, in order for it to be true, analysis and synthesis, as two sides of the whole, must strictly cover each other, then during the thought process they continuously pass into each other, and can alternately come to the fore. The dominance of analysis or synthesis at a particular stage of the thought process may be due, first of all, to the nature of the material. If the material, the initial data of the problem are not clear, their content is unclear, then at the first stages it is inevitable that more or less long time the thinking process will be dominated by analysis. If, on the contrary, at the beginning of the thought process all the data appear before thought with sufficient distinctness, then thought will at once go predominantly along the path of synthesis.

In the very warehouse of some people there is a predominant tendency - in some to analysis, in others to synthesis. There are predominantly analytical minds, whose main strength is in accuracy and clarity, and others, predominantly synthetic.

S.L. Rubinstein singled out an important form of analysis - analysis, which is carried out through synthesis. Its essence is that “in the process of thinking, the object is included in more and more connections, and because of this, it appears in all new qualities that are fixed in new concepts. From the object, as it were, more and more new content is drawn, it seems to turn every time with its other side, more and more new properties are revealed in it.

In the process of mental activity, a person never deals with an object that would be completely unfamiliar to him or, on the contrary, completely known. One and the same object in different systems of relations appears both as old and as new. Such unity naturally determines the general strategy of cognition of this object and the initial mechanism of thinking - analysis through synthesis.

Analysis through synthesis contributes to the identification of new qualities, aspects and properties of the object by concluding them in such a system of connections and relations in which these desired properties are manifested. Possession of this method of mental activity is highest level mathematical development.

It was emphasized that analysis and synthesis are interrelated and do not work without each other, but for educational purposes they need to be separated, and at the first stages of mathematical education they should be formed separately. This is necessary to understandanalytical and synthetic activity of students in teaching mathematics .

The content of the concepts of synthesis and analysis was revealed in heuristic methods of mathematical activity, i.e. in the methods by which the accumulation of facts and the formulation of hypotheses are carried out. Yu.M. Kolyagin, V.A. Oganesyan note that "analysis began to be understood as a method of thinking, in which one passes from the effect to the cause that gave rise to this effect, and synthesis - as a method of thinking, in which one goes from the causes to the effect generated by this cause."

Analysis and synthesis can be seen as methods of reasoning in the processes of hypotheses.

For example, when studying the topic "Perpendicularity of a line and a plane", the problem arises of the impossibility of determining the perpendicularity of a line and a plane using only the definition.

In this situation, the teacher can offer to use life experience: remember how a pole is installed or what is used to install a Christmas tree. The analysis of these situations leads to the hypothesis that "if a line is perpendicular to two intersecting lines lying in a plane, then it is perpendicular to this plane" - synthesis.

Also, analysis and synthesis are considered as methods of reasoning in processes in the definitions of concepts.

For example, when studying the topic "Perpendicularity of a straight line and a plane", the teacher simulates a situation where a straight line intersects a plane.

It can be seen that in this case, various angles are formed with straight lines lying in the plane α.

Are there any lines on the plane α that form a right angle with the line a?

Students will answer yes.

It can be concluded that in the plane α there are lines that are perpendicular and not perpendicular to the line a.

Rotating the triangle shows that the linemis perpendicular to any line lying in the plane α.

In this case, the line is said to be perpendicular to the plane.

Consideration of all these cases is analysis.

Then the students are able to independently formulate the definition of a straight line perpendicular to the plane - synthesis.

At each lesson, it is necessary to think over a system of questions that purposefully forms methods of analysis and synthesis. When working with didactic units, analysis will act as a logical action "deriving a consequence", and synthesis - "bringing under a concept".

For example, possible questions when studying the topic "Perpendicularity in space".

Given a plane and a point not lying in the given plane. Is it possible to draw a line perpendicular to a plane through a point? How? How many lines can be drawn? Why?

There is a straight line and a plane. How can they be located? And how can planes and two parallel lines be arranged?

We want to draw a plane passing through a given point and perpendicular to some line. How can I do that?

How can two planes and a line be located? What can be said about planes if the line is perpendicular to them?

These are questions-tasks, the answers to which teach to draw conclusions, i.e. obtain consequences from the conditions of the problems. With the help of these questions, it is possible to check whether the students have mastered the main theoretical material, and each student must answer them. Questions of this type are important in that they not only form in students a method of mental activity - synthesis, but also teach them to find the properties of an object and the necessary conditions for its existence.

But the questions may be different. For example:

Given a plane. How many lines can be perpendicular to this plane?

The figure shows several planes and straight lines.

Through which lines do the planes α, β, γ pass?

Which lines are perpendicular to the plane α? What are the β planes? What are the γ planes?

Which of the planes are perpendicular?

These questions-tasks are more complex, since in them it is necessary not only to obtain consequences from the condition, but to find out the reason for the appearance of these consequences. These questions form the analysis, and also lay down the possibilities of such important concepts for mathematics as the attribute of an object and sufficient conditions for its existence.

It is useful to develop a system of such questions-tasks at each lesson, because they allow students to master the content of the material being studied, and the teacher to evaluate the successes and failures of students.

Analysis and synthesis as methods of evidence

Analysis and synthesis in the methodology of teaching mathematics are traditionally called two types of reasoning that are opposite in the direction of thought, which can be used not only as logical operations, but also as methods of proving theorems, as well as in solving problems by complete induction. Analysis is a reasoning going from what needs to be found or proved to what is given or already established earlier, and synthesis is a reasoning going in the opposite direction.

AI Markushevich believes that one of the main goals of teaching mathematics at school is the development of deductive thinking skills. Those. the ability to deduce logical consequences from given premises, to cultivate the ability to analyze an object, to isolate special cases from it, and it is important to distinguish when these special cases in the aggregate cover all possibilities, and when they are only examples and do not exhaust all possible cases.

V. A. Gusev singles out in the process of personality qualities formation those that make up mental education, one of which is deductive thinking (logical development of students), namely the ability to abstract, generalize, specialize, define concepts, make judgments, find ways to solve the problem . The ability to deduce logical consequences from given premises (the ability to draw conclusions). The ability to analyze an object, isolate its essence, abstract from non-existent details, single out special cases from it, etc.

Among many tasks, there are those where the use of analysis was the promotion of some idea. The solution of these problems can be attributed to the use of the "analysis through synthesis" technique. It is used when, after analyzing the condition of the problem,receive some consequences, but from which nothing can be obtained directly, and there are no other data. There is a need for analysis, and the analysis is quite difficult - this is, for example, an additional construction or application of a well-known theorem in a non-standard situation. When solving complex problems, the “analysis through synthesis” technique can work more than once.

The methodology for teaching students to perform additional constructions when solving geometric problems should be specially developed. At the same time, it is not necessary to prompt students about additional construction immediately, but only after appropriate work.

There are tasks where pure synthesis is used, but analysis is still invisibly present. In this case, we can talk about the activity of the type "synthesis through analysis". Most often, these are problems in which consequences are obtained from the condition and proceed to the answer. Analysis consists only in the fact that we remember what we need to find. Also, the “synthesis through analysis” technique can include tasks, the idea of solving which is associated with the use of a well-known mathematical fact.

As a result of using the methods of mental activity of "analysis", "synthesis", "synthesis through analysis" and "analysis through synthesis", a special type is born, which is commonly calledanalytic-synthetic.

Most often, analysis, synthesis, analysis through synthesis and synthesis through analysis are used inproofs of theorems.

Proof is understood as a logical action, in the course of which the truth of a certain proposition is established by bringing other propositions, the truth of which has already been established and from which the truth of what is being proved necessarily follows.

The deductive method of proof is the most reliable way to obtain true knowledge. Deductive reasoning - obtaining from one or more true judgments a new judgment based on correct application logical laws.

The main laws of logic are:

The law of identity: a statement, repeated in a conclusion, must have the same truth value;

Law of Contradiction: A proposition and its negation cannot both be true;

Law of the excluded middle: one of two contradictory statements is true;

Law of sufficient reason: every true statement must be justified by other statements, the truth of which is established.

The proof has 3 parts:

Thesis is a proposition, the truth of which must be proved;

Reason (argument, argument) - a judgment, the truth of which is established and which is used to substantiate or refute the thesis;

Demonstration is a logical reasoning, during which the truth or falsity of the thesis is derived from the basis.

When constructing a chain of valid inferences that represents a proof, one can start with the condition , and it is possible from the conclusion . The method of reasoning in the first case is called synthesis or synthetic method, in the second - analysis or analytical.

Essence synthetic method of proof is as follows. Suppose we need to prove the truth of the hypothesis "If , That ". From the condition and previously substantiated theoretical positions deduce a consequence . If does not match with or , then from deduce a consequence (this can be used And ). This continues until the result is received. , which either coincides with or contradicts .

If the consequence matches the conclusion , then the truth of the hypothesis “If , That » installed, i.e. we have a theorem and we can write "
».

If the consequence - a statement that contradicts , then the hypothesis "If , That » is incorrect, i.e. this is not a theorem. However, it is obvious that the theorem is the sentence "If , That ».

For example, one can synthetically prove the three perpendiculars theorem.

"A straight line drawn in a plane through the base of an inclined plane perpendicular to its projection onto this plane is also perpendicular to the inclined one itself."

It is given from the condition that
- perpendicular to the plane,
- inclined,
- projection of the inclined plane
.

↓ on the basis of perpendicularity of a straight line and a plane

, because it is perpendicular to two intersecting lines and
(
by condition,
, because
)

The advantages of the method include the exhaustive completeness and impeccability of the proof, its conciseness and brevity in presentation.

The disadvantages of the method include that when using it, it is difficult to choose the initial statement, it is impossible to motivate additional constructions, the choice of consequences, etc. Also, reading ready-made proofs in a synthetic presentation without appropriate explanations does little to develop the creative thinking abilities of schoolchildren, forcing them to memorize proofs.

At analytical method of reasoning sent from what is required to prove. There are two possible chains of inference:

Let it be required to prove the theorem "
". For conclusion choose a sufficient condition, i.e. such a judgment , What
. At the same time they say: “In order for it to be true , enough to be true ". If about truth nothing is known, then select a sufficient condition , i.e. such that
. This continues until they receive
sufficient condition , i.e.
And true. When constructing a chain, they are used as a condition , as well as the theoretical , Related And , the truth of which was previously established.

The obtained sequence of reliable conclusions is the proof of the theorem "
". This method is calledbottom-up analysis .

Let us show how the method of bottom-up analysis can be used to prove the theorem on three perpendiculars.

To prove that
, Where
, A
- oblique toα, it is enough to prove that
or
. To prove the assertion
there are no preconditions. To prove
enough to find in the plane
two intersecting lines perpendicular to a line . Such lines can be found using the conditions of the problem:
- perpendicular to the planeα,
- projection of the inclined plane,
.

The proofs of the method of bottom-up analysis include a lower degree of uncertainty and ambiguity compared to synthesis. In addition, the method creates favorable conditions for creative activity and promotes the development of independent thinking. But sometimes it is difficult to immediately get to the condition that will lead to the goal, in some cases it is impossible to find a sufficient condition at all, i.e. bottom-up analysis cannot be applied. There are disadvantages in this.

In the learning process, bottom-up analysis is used to find evidence. It is effectively combined with a heuristic conversation, with a problematic method in teaching mathematics.

When looking for proof of the truth of hypotheses, synthesis and bottom-up analysis are rarely used in pure form. Often in proofs there are, and more than once, transitions from analysis to synthesis and vice versa, until the proof is completed. This method of proving and searching for evidence is called analytic-synthetic.

When proving the validity of the hypothesis "If , That » you can start with a conclusion , but the reasoning is carried out differently than in the previous case. In a bottom-up proof for a conclusion looking for a sufficient condition. In another kind of analysis is itself a sufficient condition for some judgment.

The construction of the chain begins with the words: “Suppose that true." Coming from make a logical conclusion . If about truth nothing can be said, deduce a consequence . This continues until the judgment is received. which is known to be true or false. When deriving consequences, use the elements of the condition and theoretical propositions, the truth of which has previously been established.

This kind of analytical method is calledtop-down analysis.

According to the truth value of the statement In top-down analysis, two cases are possible: - false and - true. If - a false statement is also false, because from a true judgment, according to the rules of logic, it is impossible to obtain a false judgment. But if - a true statement, then about the truth , and hence the truth of the hypothesis "If , That ', nothing can be said. The sentence may turn out to be both true and false, because According to the rules of logic, anything can be obtained from a lie. there are two intersecting lines that are perpendicular to the line

The resulting chain of reasoning can be reversed, that is, a synthesis can be carried out, which means that the hypothesis is true that
.

Although top-down analysis is not a method of proof (if one obtains true), but with its help one finds the starting point and plan of proof for the synthetic method. But this method is good for refuting hypotheses mistaken for being true. And also, by conducting a top-down analysis, in fact, we prove the truth of the proposition that is the opposite of the one being proved. If the top-down analysis can be reversed, two mutually inverse theorems are in fact true.

But this method is cumbersome, because the discussion has to be repeated twice. It is also not always possible to turn top-down analysis into synthesis.

In turn, top-down analysis has two varieties: imperfect analysis and the method of proof by contradiction.

Imperfect analysis is reduced to finding consequences that follow from the assumption of the validity of the conclusion, which leads to obtaining correct consequences or incorrect judgments. If the arguments with all their conclusions are correct, and the consequence turned out to be false, then what is being proved is false.

This method prompts students for a synthetic solution to the original problem. It is applicable when students would hardly be able to come up with such a synthetic solution on their own.

The method of "proof by contradiction" is such a kind of top-down analysis, in which the solution of a problem occurs by obtaining the necessary conditions for the validity of a position that contradicts the conclusion of a theorem or problems.

There is another form of the analytical method - this is the algebraic method of solving problems. To solve problems with this method, you must perform the following steps:

Study the condition of the problem;

Select the main unknown quantity and enter its designation;

Express other unknowns in terms of the chosen unknown and the data in the condition of the quantity problem;

Write an equation (or system of equations) and solve it (her).

Problem solving activities are explicit, so the teacher needs to think carefully about how to teach problem solving, whichmost effective in the process of finding their solution. At the same time, the accumulation of experience in solving problems by students also gives positive results. However, learning to search not only reveals the mechanisms of mental and practical activities students, but also develops their creative thinking.

The search for solutions to problems is carried out mainly with the help of the analytic-synthetic method, which in this case is purposeful. Analysis underlies a general approach to solving problems (meaning non-standard problems for which there is no corresponding algorithm), known as reduction (reduction) of a problem to a set of subtasks. The idea of this approach is precisely in the “thinking backwards” characteristic of analysis from the problem to be solved to subtasks, then from these subtasks to subsubtasks, and so on, until the original problem is reduced to a set of elementary problems. What is meant by "elementary tasks"? These are, firstly, problems that can be solved in one search step, and secondly, more complex problems (i.e., not solved in one search step), the solution of which is already known from the existing experience in solving problems.

We single out three stages of analytic-synthetic reasoning:

Let's assume that the problem is solved;

Let's see what conclusions can be drawn from this;

Drawing up the obtained conclusions (synthesis), we will try to find a way to solve the problem.

It is possible to single out a system of actions and operations that are part of the analytical search for their solution. Generalizing these actions and operations, one can obtain one of the methods of analytical search for a solution to the problem.

Since this process of analysis at all stages of the search for a solution is associated with synthesis, we are dealing with an analytic-synthetic search for a solution to the problem.

The system of operations for performing one or another action included in the technique constitutes an indicative basis for performing the action. Therefore, for the effective use of techniques in teaching, it is necessary that students know the content of the orienting basis of each action as a condition for its implementation.

Consider the methods of finding solutions to problems of a school mathematics course using the example of geometric computational problems.

Distance from point M to each of the vertices of an equilateral triangleABCequal to 4 cm. find the distance from point M to the planeABC if AB = 6 cm.

Analysis: the completed drawing, according to the condition and requirement of the problem, that MA=MB=MC, allows us to put forward the assumption that M is projected into O - the center of the circumscribed circle near the triangle ABC. Since ABC is correct, then O is the point of intersection of the medians.
.

It is advisable to search for MO based on the equality of right-angled triangles AMO, VMO and CMO (the hypotenuses AM=VM=CM and the common leg OM are equal) and from the triangle ABC.

The search for a solution to this problem is over. Justification for each step is not needed, because. they are obvious, and special attention is paid to what is unknown in each formula and what to look for. In order to solve the problem, it is enough to carry out the reverse (opposite) transition from the last (second) action to the first. To facilitate the implementation of the actions indicated in the search for a solution, you can sequentially perform the corresponding calculations.

Analysis in the process of finding a solution to a problem or proving a theorem can be either top-down or bottom-up in form.

Top-down analysis requires synthesis - the opposite way of reasoning. The bottom-up analysis also contains synthesis, so it does not require an opposite line of reasoning. It has certain methodological advantages: it provides a conscious and independent search for evidence; promotes the development of logical thinking; provides understanding and purposefulness of actions at each stage of reasoning.

The scheme is simple - clarification of two questions: what is required to find, prove, and what is enough to know for this?

The method of applying bottom-up analysis to finding a solution to geometric computational problems contains the following sequence of actions:

Write down the formula (in the notation of the drawing) to find the desired problem;

In this formula, identify unknown quantities that are sufficient to determine to find what you are looking for;

For each unknown quantity included in the original formula, select formulas for finding these quantities (successively for each value);

The search process is terminated at the moment when:

For a sequence of unknown quantities involved in the search for a solution to the problem, the formulas for finding them will be indicated;

For the last unknown quantity (in this sequence), a formula is given in which the unknown quantities are determined by the problem data.

Techniques for the formation of analytical and synthetic thinking by means of mathematics .

The formation of methods of analysis and synthesis should permeate all teaching at school, since it is important and useful to constantly answer the questions: “what consequences can be obtained from the statement? We want to prove some statement, what do we need to know or prove? It is necessary to calculate the value of a certain quantity, what needs to be calculated for this?

In practice, this is not always the case. Therefore, the teacher needs to competently compose a system of questions and exercises that allows the formation of methods of analysis and synthesis, both of logical operations (deriving consequences, summing up under a concept), and as methods of proof. At the same time, the questions and exercises of these systems should be differentiated according to their degree of complexity, so that each student can always find a question that he would have to think about.

To be able to choose a way to solve problems, you need to have a sufficient stock of knowledge and ideas. This reserve is created by the practice of solving problems. It is necessary to teach schoolchildren to use the stock of basic ideas for solving various problems, to teach them to choose and apply the right idea.

The most difficult thing in organizing a solution to a problem different ways is the teacher's help in finding these ways. At the same time, the teacher should come up not with the idea of a new version of the proof, but with a question or a series of questions that contribute to the emergence of the corresponding idea.

For students to firmly assimilate the analytic-synthetic search for a solution to geometric computational problems, it is necessary to work it out on specific tasks in the conditions of organizing schoolchildren's collective forms of activity in teaching. The transition to an individual form of student activity through the organization independent work is possible only after they have realized the essence of this technique.

The analysis of the evidence given by the teacher, after the synthesizing has been completed, must be a well-considered device. It is conducted in the form of questions to which the answer is given not by the students, but by the teacher himself. This is necessary because students can give reasons that are not as convincing as those that the teacher gives after having thought them over well. It is desirable that after the analysis, either the teacher himself again or the student again conducts the entire proof.

Speaking of mental activity, one can keep in mind its role in the formation of a comprehensively developed personality, by which mental development is understood.

It can be said with certainty that mathematical education in the processes of forming thinking or mental development students should be given and given a special place, because it is the means of teaching mathematics that most effectively affect many of the main components of a holistic personality, and above all - on thinking. But considering the development of thinking in the context of student-centered learning, it should be remembered that a necessary condition for the implementation of such development is the individualization of learning. It is she who takes into account the peculiarities of the mental activity of students of various categories.

Synthesis(synthetic activity) is a process opposite to analysis, which consists in highlighting among the simplest elements, properties and features decomposed during the analysis, the most important, essential at the moment and combining them into complex complexes and systems.

GNI is the analytical and synthetic activity of the cortex and the nearest subcortical formations of the GM, which manifests itself in the ability to isolate its individual elements from the environment and combine them in combinations that exactly correspond to the biological significance of the phenomena of the surrounding world.

Analysis and synthesis are inextricably linked. Analytical-synthetic (integrative) activity of the nervous system is the physiological basis of perception and thinking.

The connection of the organism with the environment is the more perfect, the more developed the property of the nervous system to analyze, to isolate from external environment signals that act on the body, and synthesize, combine those of them that coincide with any of its activities. Abundant information coming from the internal environment of the organism is also subjected to analysis and synthesis.

On the example of sensation and perception by a person of parts of an object and the whole object as a whole, even I.M. Sechenov proved the unity of the mechanisms of analytical and synthetic activity. A child, for example, sees an image of a person in a picture, his entire figure, and at the same time notices that a person consists of a head, neck, arms, and so on. This is achieved thanks to his ability "... to feel every point of a visible object separately from others, and at the same time all at once."

In each analyzer system, three levels of analysis and synthesis of stimuli are carried out:

1) in receptors - the simplest form of isolating signals from the external and internal environment of the body, encoding them into nerve impulses and sending them to the overlying departments;

2) in subcortical structures - a more complex form of isolation and combination of stimuli of various kinds of unconditioned reflexes and signals of conditioned reflexes, which are realized in the mechanisms of the relationship between the higher and lower parts of the CNS, i.e. analysis and synthesis, which began in the receptors of the sense organs, continue in the thalamus, hypothalamus, reticular formation, and other subcortical structures. So, at the level of the midbrain, the novelty of these stimuli will be assessed (analysis) and a whole series of adaptive reactions will arise: turning the head towards the sound, listening, etc. (synthesis - sensory excitations will be combined with motor ones);

3) in the cerebral cortex - the highest form of analysis and synthesis of signals coming from all analyzers, as a result of which systems of temporary connections are created that form the basis of GNI, images, concepts, semantic distinction of words, etc. are formed.

Analysis and synthesis are carried out according to a specific program, fixed by both congenital and acquired nervous mechanisms.

For understanding the mechanisms of the analytical and synthetic activity of the brain, I.P. Pavlov’s ideas about the cerebral cortex as a mosaic of inhibitory and excitatory points and, at the same time, as a dynamic system (stereotype) of these points, as well as cortical systemicity in in the form of a process of combining "points" of excitation and inhibition into a system. The systematic nature of the brain expresses its ability to higher synthesis. The physiological mechanism of this ability is provided by the following three properties of GNI:

a) the interaction of complex reflections according to the laws of irradiation and induction;

b) the preservation of traces of signals that create continuity between the individual components of the system;

c) fixing the emerging bonds in the form of new conditioned reflexes to the complexes. Consistency creates integrity of perception.

Finally, the well-known general mechanisms of analytic-synthetic activity include the “switching” of conditioned reflexes, first described by E.A. Asratyan.

Conditioned reflex switching is a form of variability of conditioned reflex activity, in which the same stimulus changes its signal value from a change in the situation. This means that under the influence of the situation there is a change from one conditioned reflex activity to another. Switching is a more complex type of analytical and synthetic activity of the cerebral cortex compared to a dynamic stereotype, chain conditioned reflex and tuning.

The physiological mechanism of conditioned reflex switching has not yet been established. It is possible that it is based complex processes synthesis of various conditioned reflexes. It is also possible that a temporal connection is initially formed between the cortical point of the conditioned signal and the cortical representation of the unconditioned reinforcer, and then between it and the switching agent, and finally between the cortical points of the conditioned and reinforcing signals.

In human activity, the switching process is very important. In pedagogical activity, a teacher who works with younger students. Students in these classes often find it difficult to move both from one operation to another in line with one activity, and from one lesson to another (for example, from reading to writing, from writing to arithmetic). Insufficient switching of students by teachers is often qualified as a manifestation of inattention, absent-mindedness, and distractibility. However, this is not always the case. Switching violation is very undesirable, because it causes the student to lag behind the teacher's presentation of the content of the lesson, in connection with which there is a weakening of attention in the future. Therefore, switchability as a manifestation of flexibility and lability of thinking should be educated and developed in students.

In a child, the analytical and synthetic activity of the brain is usually underdeveloped. Young children learn to speak relatively quickly, but they are completely unable to distinguish parts of words, for example, to break syllables into sounds (weakness of analysis). With even greater difficulty, they manage to compose separate words or at least syllables from letters (weakness of synthesis). These circumstances are important to consider when teaching children to write. Usually, attention is paid to the development of the synthetic activity of the brain. Children are given cubes with the image of letters, they are forced to add syllables and words from them. However, learning progresses slowly because the analytical activity of the brain of children is not taken into account. For an adult, it doesn’t cost anything to decide what sounds the syllables “yes”, “ra”, “mu” consist of, but for a child this is a lot of work. He cannot separate a vowel from a consonant. Therefore, at the beginning of training, it is recommended to break words into separate syllables, and then syllables into sounds.

Thus, the principle of analysis and synthesis covers the entire GNI and, consequently, all mental phenomena. Analysis and synthesis are difficult for a person due to the presence of verbal thinking. Main component human analysis and synthesis is motor speech analysis and synthesis. Any kind of analysis of stimuli occurs with the active participation of the orienting reflex.

Analysis and synthesis occurring in the cerebral cortex are divided into lower and higher. The lowest analysis and synthesis is inherent in the first signal system. Higher analysis and synthesis is an analysis and synthesis carried out by the joint activity of the first and second signal systems with the obligatory awareness of the subject relations of reality by a person.

Any process of analysis and synthesis necessarily includes as an integral part its final phase - the results of action. Mental phenomena are generated by brain analysis and synthesis.

dynamic stereotype- this is a system of conditioned and unconditioned reflexes, which is a single functional complex. In other words, a dynamic stereotype is a relatively stable and long-term system of temporary connections formed in the cerebral cortex in response to the implementation of the same types of activities at the same time, in the same sequence from day to day, i.e. . this is a series automatic actions or a series of conditioned reflexes brought to an automatic state. DC can exist for a long time without any reinforcement.

The physiological basis of the formation initial stage dynamic stereotype are conditioned reflexes for a while. But the mechanisms of the dynamic stereotype have not yet been deeply studied.

DS plays an important role in the education and upbringing of children . If a child goes to bed at the same time every day and wakes up, has breakfast and lunch, performs morning exercises, conducts hardening procedures, etc., then the child develops a reflex for a while. The consistent repetition of these actions forms in the child a dynamic stereotype of nervous processes in the cerebral cortex.

It can be considered that the reason for what is called student overload is of a functional nature and is caused not only by dosing and difficulty learning tasks, but also negative attitude teachers to the dynamic stereotype as the most important physiological basis of learning. Teachers do not always succeed in constructing a lesson in such a way that it represents a dynamic stereotype system. If the content of each new lesson were organically connected with the previous and subsequent ones into a single mobile system that would allow, if necessary, to make changes to it, as a dynamic stereotype, and not as a simple addition, then the work of students would be so facilitated that it would no longer would cause overload.

The strengthening of a dynamic stereotype is the physiological basis of a person's inclinations, which have received the designation of habits in psychology. Habits are acquired by a person in various ways, but, as a rule, without sufficient motives and often quite spontaneously. However, according to the mechanism of a dynamic stereotype, not only such, but also purposeful habits are formed. Among them can be attributed the daily routine developed by the student.

Each habit is developed and strengthened by training on the principle of a conditioned reflex. At the same time, external and internal irritations serve as trigger signals for them. For example, we do morning exercises not only because we are used to it, but also because we see sports equipment that in our minds are associated with morning exercises. The reinforcement of this habit is both the morning exercise itself and the feeling of satisfaction that comes after it.

From a physiological point of view, skills are dynamic stereotypes, in other words, chains of conditioned reflexes. A well-developed skill loses connection with the second signaling system, which is the physiological basis of consciousness, only if a mistake is made, i.e. a movement is carried out that does not achieve the desired result, an orienting reflex appears. The excitations that arise in this case disinhibit the inhibited connections of automatic habit, and it is again carried out under the control of the second signal system, or, in psychological terms, consciousness. Now the error is corrected and the necessary conditioned reflex movement is carried out.

The dynamic stereotype of a person includes not only a large number of a variety of motor skills and habits, but also the habitual way of thinking, beliefs, ideas about surrounding events.

Modernity requires a reworking of habitual views, and it happens that strong convictions, i.e. a situation is created when it is necessary to move from one dynamic stereotype to another. And this is associated with the appearance of corresponding unpleasant feelings. In this case, our nervous system not always easy to cope with life's task. The difficulty lies in the fact that before developing a new attitude towards reality (a new stereotype of life), it is necessary to destroy the old attitude towards it. Therefore, some people find it quite difficult to restructure any element of their life stereotype, not to mention the restructuring of ideas and beliefs. It is difficult to remake stereotypes in childhood.

IP Pavlov came to the conclusion that emotional states may depend on whether a dynamic stereotype is supported or not. When maintaining a dynamic stereotype, positive emotions are usually manifested, and when the stereotype is changed, negative ones.

It should be noted that in the implementation of complex stereotypes importance belongs to the setting, i.e. such a state of readiness for activity, which is formed by the mechanism of temporary connection. The emergence of a conditioned reflex setting can be seen in students who divide school subjects into favorite and unloved. A student goes to a lesson with a teacher who teaches his favorite subject with a desire, and this can be seen in his good mood. A student often goes to a lesson with a teacher of an unloved subject, and perhaps even with an unloved teacher, in a bad, sometimes even depressed mood. The reason for this behavior of the student lies in the conditioned reflex attunement from the complex environment of the classes, the essence of the subject, the behavior of the teacher. A dissimilar situation causes a different setting.

THINKING

Thinking- a cognitive mental process, which consists in generalizing and indirectly reflecting the connections and relationships between phenomena and objects of the surrounding world.

Thinking arises on the basis of practical activity from sensory cognition and goes beyond it. . Thought activity receives all its material from sensory cognition. Thinking correlates the data of sensations and perceptions - compares, compares, distinguishes, reveals relations, and through the relations between directly sensually given properties of things and phenomena reveals their new abstract properties.

Any mental activity arises and develops inextricably linked with speech. It is only with the help of speech that it becomes possible to abstract one or another property from a cognizable object and fix the idea or concept of it in a special word. The thought acquires the necessary material shell in the word. The deeper and more thoroughly this or that thought is thought out, the more clearly and accurately it is expressed in words, in oral and written speech.

Thinking is a socially conditioned mental process of mediated and generalized reflection of reality, which is inextricably linked with speech, is of a problematic nature and arises on the basis of practical activity from sensory cognition and goes far beyond its limits.

Clarifications should be made to this definition:

1. Thinking is closely connected with such processes as sensation and perception, which provide sensory knowledge. In the process of sensation and perception, a person learns the world as a result of its direct, sensual reflection. However, internal laws, the essence of things cannot be reflected in our consciousness directly. . No regularity can be perceived directly by the senses. Whether we determine, looking out the window, on wet roofs, whether it was raining or establish the laws of planetary motion - in both cases we are performing a thought process, i.e. we reflect the essential links between phenomena indirectly, comparing the facts. Man has never seen an elementary particle, has never been to Mars, but as a result of thinking, he received certain information about elementary particles matter, and about the individual properties of the planet Mars. Cognition is based on identifying connections and relationships between things.

2. Sensory cognition gives a person knowledge about individual (single) objects or their properties, but thanks to thinking, a person is able to generalize these properties, therefore thinking is a generalized reflection of the external world.

3. Thinking as a process is possible thanks to speech, since thinking is a generalized reflection of reality, and it is possible to generalize only with the help of a word, a person’s thoughts appear in speech. Another person's thinking can be judged by their speech.

4. Thinking is closely connected with practical activity. Practice is the source of thinking: “Nothing can be in the mind if it was not previously in external practical activity” (A.N. Leontiev).

5. Thinking is closely connected with the solution of a particular problem that arose in the process of cognition or practical activity. . The process of thinking is most clearly manifested when a problem situation arises that needs to be solved. A problem situation is a circumstance in which a person encounters something new, incomprehensible from the point of view of existing knowledge. . This situation is characterized by the emergence of a certain cognitive barrier, difficulties to be overcome as a result of thinking. In problem situations, goals always arise, for the achievement of which the available means, methods and knowledge are not enough.

6. Thinking is socially conditioned, it arises only in the social conditions of human existence, it is based on knowledge, i.e. on the socio-historical experience of mankind. Thinking is a function of the human brain and in this sense is natural process. However, human thinking does not exist outside of society, outside the language and knowledge accumulated by mankind. Each individual person becomes the subject of thinking only by mastering the language, concepts, logic, which are a product of the development of socio-historical practice. Even the tasks that a person sets before his thinking are generated by the social conditions in which he lives. Thus, the human mind is public nature(A.N. Leontiev).

Hence, thinking is the highest form of human reflection and cognition of objective reality, the establishment of internal connections between objects and phenomena of the surrounding world. Based on the emerging associations between individual representations, concepts, new judgments and conclusions are created. In other words, thinking in its expanded form is an indirect reflection of not visually given relations and dependencies of real world objects. In the process of thinking, a number of conscious operations are performed, with the aim of resolving specially set tasks by revealing objective connections and relationships.

The physiological basis of thinking is the integral analytical and synthetic activity of the cerebral cortex, carried out in the interaction of signal systems.

KINDS THINKING

In psychology, there are basically three types of thinking: visual-effective (concretely visual), figurative and abstract-logical (theoretical). The first two types are united by the name of practical thinking. Visual-effective thinking is realized mainly in external actions, and not in verbal forms, which are woven into it only as separate elements. Visual-effective thinking, as a rule, is chained to a specific situation and largely relies on the activity of the first signal system, although its connection with the second signal system is undeniable. However, her signals - words - here only ascertain, and do not plan. The beginnings of visual-effective (and figurative) thinking are also characteristic of higher animals. Here is an example of visual action thinking taken from experiments with monkeys. The experiment consists of two stages. First, fruit is placed at some distance from the monkey, and a fire is made between the animal and the fruit. It is impossible to take a delicacy without extinguishing the fire. An empty bucket is placed next to the monkey, a vessel with water is located on the side, and to get water. Repeatedly reproduced environment of the experiment teaches the monkey to use a bucket and water to extinguish the fire. Then it becomes possible to finally get the bait. The situation of the second stage of the experiment: a fire is made between the animal and the fruit, the bucket is in the same place, there is no water in the jar, but the experiment is carried out on a small area, surrounded on all sides by water. The monkey repeatedly performs a series of actions described above, runs around the island with an empty bucket, comes into a state of excitement, etc., but due to the inability to think abstractly, it does not<догадывается>scoop up water from the pool. Imaginative thinking is<мышление через представление>. With this form, a person (usually these are children of primary school age) has a series of images built in his mind - successive stages of the upcoming activity. The plan for solving the mental problem is worked out in advance, it is known how to start work, what to do in the future. In the construction of a plan for solving a problem, logic is also necessarily involved, although it has not yet reached perfection. Figurative thinking has a direct connection with speech, and its grammatical forms play a planning role.

Abstract-logical thinking operates with concepts, judgments, symbolic and other abstract categories. The meaning of concepts comes through especially clearly in the example of the thinking of the deaf and dumb. It has now been experimentally established that deaf-mutes from birth usually do not rise to the level of conceptual thinking. They are limited to reflecting predominantly visually given signs, i.e. use the means of visual-effective thinking. Only under the condition of mastering speech, i.e. from the time when concepts arise and the deaf-mutes have the opportunity to operate with them, their thinking becomes conceptual - abstract-logical. Abstract-logical thinking is characteristic of an adult and is based on the activity of the second signal system. Characterizing certain types and the whole process of human thinking as a whole, it should be emphasized that if the most simple form- visual-effective thinking - gives way in the future to figurative, and it, in turn, to abstract-logical, then everyone? of these three species is fundamentally different from the others and is characterized by its own characteristics. All three species are genetically related and from a dialectical point of view they represent the degree of transition of quantity into a new quality. Once having arisen, a new quality, however, not only does not exclude the properties of the previous type of thinking, but, on the contrary, involves their use, albeit in the form of an auxiliary, subordinate means. Only the joint work of all kinds of thinking will lead to a real knowledge of the goals and objectives of surgical intervention.

In other words, the content, character, and success of the fulfillment of a mental and, consequently, a practical task depend on the level of a person’s development, the degree of his practical training and the nature of the flow of thought processes. All this finds its concrete expression in various correlations of sensations, perceptions, ideas, concepts and words, external and internal actions that take place in the course of solving the task. Individual features of thinking are manifested in the qualities of the mind: independence, depth, flexibility, inquisitiveness, speed, creativity.

Thinking Options

· Slenderness- is expressed in the need to think in accordance with logical requirements, reasonably, consistently, reflecting the internal patterns between phenomena and objects, and grammatically correctly formulate thoughts.

· Productivity- the requirement to think so logically that the associative process leads to new knowledge. This is the final property of mental activity, as a result of which there is an adequate reflection of the essential aspects of the objective world and its interrelations.

· Purposefulness- the need to think for some real purpose.

· Pace- the speed of the associative process, conditionally expressed in the number of associations per unit of time.

· Evidence- the ability to consistently justify one's opinion or decision.

· Flexibility and mobility- the ability to quickly give up earlier decisions taken if they no longer meet the changed situation or conditions, and find new ones.

· economy- fulfillment of a certain mental task with the help of the smallest number of associations.

· Latitude- horizons, the ability to use a range of various facts and knowledge in the thought process and the ability to introduce important and new things into them.

· Depth- the ability to delve into the essence of phenomena, not limited to stating the facts lying on the surface, the ability to assess the observed phenomena.

· criticality- the ability to adequately evaluate the results of one's own mental activity, i.e. the extent to which we identify flaws in our judgments and the judgments of others.

· Independence- the ability to independently identify a question requiring a solution and, regardless of the opinions of others, find an answer to it.

· inquisitiveness- the desire to find out the main causes of the observed phenomena and facts, to study them comprehensively.

· Curiosity- the desire to learn something new with which a person meets in life.

· Resourcefulness- the ability to quickly find a way to solve a mental problem.

· Wit- the ability to unexpected, unconventional conclusions that arise on the basis of semantic connections hidden from others. In wit, such qualities of the mind as depth, flexibility, speed, etc. are manifested.

· Originality- the individual quality of the thought process, which leaves an imprint on all its manifestations, lies in the ability to come to the right conclusions in an unconventional way.

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Analytical-synthetic ability and ways of its development in schoolchildren. Formation of analytical and synthetic activity of a preschooler as a prerequisite for teaching literacy

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