Modern man, due to various circumstances, often suffers from various mental disorders. According to statistics, approximately 35% of Europeans have such disorders. This may be not just widespread depression, but also a more rare pathology - acalculia (loss of a person’s ability to count). The problem is indeed incredibly serious, but it can be solved.

We’ll talk more about what acalculia is and how to get rid of it in this article.

Why is acalculia confused with dyscalculia?

Acalculia and dyscalculia should not be confused, although they are very similar neuropsychiatric diseases. Their main difference is in the causes of the disorders.

The first syndrome is acquired as a consequence of other brain injuries, and the second is congenital.

In addition, acalculia can be partial, and dyscalculia is complete absence ability to study even the simplest arithmetic, because a person does not have the function of estimating the number of objects. The manifestation of dyscalculia is observed in 5% of first-graders. With the help of special techniques you can successfully get rid of it.

Causes of the syndrome

The cause may be failure different parts cerebral cortex: traumatic brain injury, neurological pathologies, infections, intoxications, neoplasms.

Because of this, cognitive processes are disrupted. Very rarely, the syndrome is inherited or appears as a result of the influence of a negative social environment.

Types of disease

Depending on the manifestation, there are many types of acalculia.

Verbal

Characterized by difficulties in denoting mathematical terms, concepts and operations verbally. It is quite possible that the patient is fluent in arithmetic, but cannot express it.

Apraxic

A person is not able to independently determine the number of objects that are nearby.

Dyslexic

It manifests itself in the fact that the patient suffers defeats in attempts to read some arithmetic sign or symbol. It is believed that this type disorders can be transmitted at the genetic level.

Graphic

In this case, the name speaks for itself; graphic acalculia deprives a person of the ability to display mathematical operations in writing. Such a person will not even be able to draw a basic geometric figure.

operating room

During the operational type of disorder, it will be almost impossible for the patient to perform arithmetic operations: add, subtract, divide and multiply. Perhaps this will manifest itself partially. For example, a person copes well with subtracting numbers, but cannot multiply them.

Primary

Scientists believe that the disease of primary acalculia has no connection with disorders of other mental functions. It appears due to damage to the left hemisphere different zones cerebral cortex: frontal or parietal.

Frontal

Impaired functioning of the frontal lobes of the brain leads to loss of conscious activity in a person. Thus, the individual cannot perform precise mathematical operations.

Parietal

Occurs as a loss of spatial thinking. Accordingly, the patient cannot understand the concept of “numbers” and everything connected with them.

Secondary

It is part of a neuropsychiatric syndrome that already exists in the individual. It appears as a result of a lack of ability for purposeful mental functions. Secondary acalculia has several subspecies.

Optical

A variety that appears due to problems with vision receptors. The patient literally cannot distinguish one number from another.

Sensory

As a consequence of problems with the temporal areas of the cerebral cortex, sensory acalculia develops. Because of this, the patient loses the ability to count verbally.

Acoustic-mnemonic

If the prefrontal areas of the brain are affected, then an acoustic-mnemonic type of disorder may begin. It is expressed in the fact that the person cannot perceive any arithmetic terms or commands by ear.

Symptoms of acalculia

• Problems recognizing numbers that are externally similar or the number “0”;
• inability to independently perform arithmetic calculations;
• violations in understanding what a number is and its rank;
• difficulties in perceiving mathematical information aurally/visually;
• inability to reproduce numbers/operations verbally.

Features of acalculia in children

In children, most often, it is the primary type of acalculia that is observed. This happens between the ages of 5 and 11 years.

The child does not perceive any arithmetic information that they try to convey to him at school. He does not understand how it is possible to carry out any operations with incomprehensible signs, calling them numbers.

Neuropsychiatric disorders can lead to the fact that the baby will not be able to distinguish between “left” and “right”.

Usually this disease is treated up to 12 years of age.

Diagnosis of the syndrome

If you suspect the appearance of acalculia, you should urgently contact a psychologist, speech pathologist or neurologist. The doctor will conduct an examination; if clinical symptoms are detected, an additional examination will be prescribed. These are tests for counting, speech, and writing. If the results are very low, the diagnosis will be confirmed.

Treatment method

The technique depends on the stage of acalculia, its type and, of course, the age of the patient.

In adults

Correction of the syndrome in a sexually mature person may include classes with a specialist and various computer programs. The doctor will gradually lead the patient to understand the concept of “number”. After this, he will be taught mathematical operations: from the simplest to the more complex. Regular exercise will lead to good results. For auditory problems with number perception, there is no need for a special technique.

In children

I often use visualization. Restoring the counting function is carried out using various pictures, drawings, and arithmetic sticks. The main thing is that the baby is interested and perceives it as a game.

What complications can the syndrome cause?

The manifestation of acalculia syndrome significantly inhibits personality development. She becomes poorly trained, because she perceives the material worse. A specialist with this syndrome quickly loses his qualifications. In addition, having such a disease, many feel inferior. This is where mental disorders appear.

This section briefly describes two other forms of nonspecific acalculia - sensory and acoustic-mnestic. If optical acalculia occurs in the syndrome of disturbances in the process of optical perception, then these two forms of counting disorders occur in the syndrome of disturbances in acoustic perception and speech. Therefore, one of them can be conditionally called "auditory acalculia", in which only the oral form of counting and counting by ear is violated, and the other - "amnestic acalculia"- associated with impairment of auditory-speech memory and the volume of auditory perception.

Damage (or underdevelopment in children) of the superior temporal gyrus (Wernicke's 22nd area) is known to lead to sensory aphasia, which is based on impaired phonemic hearing. ...

Impairments in phonemic hearing, oral expressive and impressive speech in patients with sensory aphasia also lead to impaired understanding of words denoting numbers and numbers, and their recognition. Instead of the sounding number “six”, patients can hear the word “seven”, instead of “sixteen” - “seventeen”, instead of “nine” - “ten”, etc. The same and other difficulties arise when naming, and all this leads to great difficulties in counting operations, in their understanding and implementation. These defects are not a violation of the account, they only complicate it, and they can be overcome if the account and counting operations are transferred to internal operations- without the participation of speech, and even better if we exclude internal speech. As for children, in them these defects in the temporal region and unformed speech lead to gross primary violations of counting, counting operations and the formation of the concept of number. In this case, other methods of examining and restoring the account are necessary.

Thus, sensory acalculia has the following characteristics:

clinical picture- patients do not understand by ear the meaning of numbers and numbers; they make many attempts to perform oral arithmetic operations, but all of them are unsuccessful;

neuropsychological picture- sensory acalculia occurs in the syndrome of sensory aphasia, agraphia, alexia (symptoms - impaired understanding of numbers by ear, naming numbers due to speech defects; factor- violation of acoustic perception and, above all, phonemic hearing);

psychological picture- in this case, a violation of counting leads to a violation of speech, but primarily counting, the concept of number and counting operations are not impaired.

This form of counting disorder is also nonspecific, secondary, and counting defects are associated with disorders of speech and acoustic perception and occur in the syndrome of acoustic-mnestic aphasia, the main mechanisms (factors) of which are defects in the volume of acoustic perception and disturbance of object images and representations. This form of acalculia is poorly understood and needs further understanding. The fact is that with this form of acalculia there were often symptoms of failure to recognize numbers presented in loud noise or in large quantities simultaneously for their consistent recognition and naming, i.e. Symptoms of secondary agnosia and, as it were, amnesia for the name of a figure or number arose. Under these sensitized conditions, perceptual difficulties, defects in perception, recognition and naming of numbers arose, due to defects in image representations and the volume of perception. When asked to quickly write a series of figures or numbers, patients also made many mistakes, completed the task slowly and highest degree arbitrarily and consciously, they tried to name what they wrote, as if helping themselves with speech.

Clinical picture. When asked to name a number or perform an arithmetic operation, patients perform everything extremely consciously and slowly, are constantly asked to repeat the numbers or the task itself, often refuse to complete the task, and become upset.

Neuropsychological picture. This acalculia is of secondary origin and occurs in the syndrome of a very specific acoustic-mnestic aphasia, which is characterized by a violation of the volume of acoustic perception, the replacement of simultaneous perception with a successive one, a violation of image-representations, which leads to naming defects. All these symptoms also manifest themselves in acalculia: the volume of perception of the named number is reduced, patients require repetition of the number in parts, the images (perception and representation) of numbers are also defective - patients cannot isolate the essential features of similar numbers and figures.

Factors - a decrease in the volume of acoustic perception, a violation of the visual image of numbers due to defects in the speech organization of perception.

2.3. Frontal acalculia... Neuropsychological analysis of counting disorders in lesions frontal systems brain

The frontal region of the cerebral cortex occupies more than a third of the total mass of the cortex in humans. Along with the inferior parietal region, the frontal lobes are the most complex and historically the newest formation of the cerebral hemispheres. This area differs from others in that it has the finest structure and the most diverse and numerous systems of connections with other areas of the brain. They mature later than other parts of the brain and represent special zones, the way they work and functions are also very different from all other areas of the brain.

... Damage to the frontal lobes of the brain leads to changes in a person’s mental activity, to behavioral disturbances, which in some cases manifests itself in a decrease in activity, and in others in a tendency to impulsive, uncontrolled acts. These disturbances also affect the course of intellectual activity.

Counting, as one of the types of ID, is impaired when the frontal lobes of the brain are damaged. In the literature, there is often an opinion that with these brain lesions a nonspecific, secondary disorder of counting occurs. Our experimental data give grounds to consider “frontal acalculia” a much more complex disorder, in which both primary and secondary counting disorders occur, and this depends on the factors (mechanisms) that underlie each variant of the frontal syndrome. Therefore, “frontal acalculia” cannot be attributed entirely to the nonspecific forms that we described above. Here we encounter a complex “knot” of counting violation, which occurs as a violation of ID.

... In patients with “frontal syndrome,” the concept of number is impaired due to defects in understanding the abstract and generalized essence of number, impaired understanding of the meaning of numbers, the meaning and meaning of zero in the structure of a number and in numerical operations. These disorders occur against the background of the primary preservation of the positional-bit principle of number construction, based on the intactness of spatial perception in these patients.

Patients in this group retain intact recognition and naming of simple numbers, and the processes of automated counting (multiplication tables, addition and subtraction within one ten, etc.) are preserved. Number and counting operations are violated in them as purposeful selective activity; these violations are manifested in the instability of the task, in defects in active orientation-research activity, in the creation of a program of activity and action, in the simplification of the program of action (sometimes in inert stereotypes) and, finally, in the violation of comparison of the effect with the initial data, i.e. in violation of control. These calculation defects are detected primarily in solving arithmetic examples, consisting of several links and requiring a sequence of operations, holding intermediate results, and comparing the results obtained with the original data. Violation of these components of ID leads to disruption of counting function with complete preservation of visual, acoustic and spatial gnosis, as well as speech.

A completely different picture of counting disorders is revealed in case of defeat basal and medio-basal parts of the frontal lobes of the brain, which is known to lead to significant changes emotional sphere behavior of the patient, without greatly affecting the course of his intellectual processes. ID defects arise based on impulsiveness and manifest themselves in a violation of the orienting basis of action due to a decrease in attention. There are no primary violations of either counting operations and actions with numbers, or the concept of number. Errors arise due to a disruption in the dynamics of nervous and mental processes in the direction of their acceleration, impulsiveness, and due to defects in inhibitory processes. Patients in this group retain the recognition and naming of simple numbers, and the processes of automated counting (multiplication tables, addition and subtraction within one ten, etc.) are preserved.

In case of defeat posterior frontal brain systems counting disorders usually occur in a syndrome of pronounced speech and motor perseverations, which are the result of a violation dynamics of mental processes, inertia of their course. And, finally, ID disorders and, in particular, counting disorders can arise in the syndrome of damage to the posterior frontal parts of the brain (and primarily to the posterior frontal parts of the leading hemisphere). Operations for solving intellectual problems can acquire a disautomated, detailed character here. Damage to this part of the brain leads to increased inertia of emerging stereotypes, which complicate the flow of thinking. In cases of massive lesions in this area, all these phenomena of deautomation, inertia of stereotypes, and inactivity manifest themselves especially clearly in speech sphere, which makes ID even more difficult: the patient deforms the task, perseverates the data (numbers, name of the action, etc.). These counting defects, which most often occur together with efferent motor aphasia, do not affect the counting structure, however, perseverations and echolalia make it difficult to carry out this function and can sometimes lead to gross disturbances in numerical operations.

The described “frontal” syndromes cause specific violations of counting and counting operations. Counting disorders in patients with different variants of frontal syndrome manifest themselves in different forms, but it is typical for all of them primary violation of the concept of number(structure of number and its bit structure) and counting arithmetic operations, but for different reasons, in contrast to parietal acalculia. This is especially true for damage to the polar parts of the frontal zone of the brain. Patients in this group can formally compose the number given to them from combinations of other numbers, but when organizing their activities from the outside, they can also decompose the number into a number of combinations of other numbers (cf. 15 = 5 and 10; 10 and 5; 9 and 6; 6 and 9; 7 and 8, etc.), they can read multi-digit numbers, but also when organizing their actions.

Given the formal possibility of performing these operations with numbers in this group of patients violated not only the organization and management of activities, but also understanding the meaning of the interaction of numbers, their internal composition, the systematic nature of the number. And this is a primary violation of counting, but it is based on other mechanisms, in contrast to parietal acalculia: 1) violation understanding the meaning and meaning numbers; 2) violation of the activity itself: the indicative link, the planning and control link; 3) violation of the regulatory function of speech. Counting operations are also not initially preserved in these patients: they do not understand the essence of arithmetic operations, the system of mathematical relations between numbers. They have no difficulties in spatial counting schemes, but their understanding and comprehension of these operations is impaired. Counting violations here are of a heterogeneous nature: in some cases they are based on phenomena of inertia of stereotypes and perseveration, inactivity in the course of higher mental processes; in others - impaired attention and impulsivity; thirdly - The main factor in the calculation defects may be a gross violation of the motivational side of the activity, instability of goals and intentions. The general picture of counting disorders in this group of patients is as follows.

When performing tasks to compose a given number from various combinations of other numbers, some patients (with damage to the posterior frontal regions), as a rule, name a limited number of possible combinations of numbers. ...

A slightly different picture of counting violations opens up to us in the event of a defeat. basal sections frontal systems. In this case, counting defects proceed much smoother and are easier to overcome. The cause of defects in this case is a violation of orientation in a task, failure to retain a task, etc., resulting from impulsiveness and instability of attention. The counting process in this case is not significantly disrupted...

In this case, the calculation is disrupted for the second time due to defects in the dynamics of the process. At the psychological level, this defect manifests itself in symptoms of a violation of general behavior and activity: in impulsive uncontrolled actions, in violation of the programming of activities and its purposefulness, etc. However, these symptoms are secondary, they are not associated with a primary disorder of ID, as we saw in patients with the lesion prefrontal convexital regions of the frontal areas of the brain. Here it is necessary to control the dynamics of the process, restore the inhibition of impulsive actions, and this will be enough to obtain the correct course of the counting process. Elementary assistance from the teacher, aimed at strengthening the patient’s orientation in the task conditions, as well as transferring the process to the level of awareness, lead to the correct execution of counting operations.

Damage to the posterior frontal parts of the brain leads to disruption of the dynamics of mental processes, manifested in pathological inertia of once established stereotypes, switching defects, and perseverations...

Counting defects are especially clearly detected when performing tasks that take place under conditions of maximum mobility of computational operations, for example, in a task where the patient is required to sequentially subtract from 100 by 7 or add 7 by 7, starting from 5. The difficulties of this operation lie primarily in that the account here is subject to internal conditions, which represent a constantly changing dynamic field.

We see a difference in the clinical, neuropsychological and psychological pictures of counting disorders when different areas of the frontal systems are affected. Naturally, the methods for restoring counting in prefrontal, basal and posterior frontal syndromes will be different. They will also differ from recovery methods for other forms of acalculia, since in all these cases there are different mechanisms (factors) for the violation of counting.

Let's briefly summarize. Lesions of the frontal areas of the brain lead, in the same way as lesions of the parieto-occipital regions, to a violation of counting and numerical operations. In contrast to existing ideas about a secondary violation of counting when the frontal areas of the brain are damaged, our study allows us to conclude that when the frontal systems of the brain are damaged, there is a primary violation of counting - the concepts of number and counting operations. This defect manifests itself especially clearly when lesions of the prefrontal convexital regions. In this case, the semantic component of counting, understanding of the structure of a number, and the dependence of the value of a number on the positional principle are disrupted. All these defects occur in the syndrome of personality disorder, motivation, on the one hand, and the collapse of the ID structure, on the other. With this syndrome, orientational research and search activity is grossly disrupted, replaced by familiar patterns, and planning of counting activities is also disrupted. All activities of patients in this case are unfocused, unregulated and uncontrollable. In this syndrome, defects arise in the concept of number, its composition, understanding of the interaction of numbers within one number and understanding of the essence of arithmetic signs and operations with them. Let us briefly clarify the clinical and neuropsychological picture of counting disorders in different options"frontal" acalculia.

In the clinical picture violations, counting defects appear in some cases in impulsive actions sick, in others - in slowness and difficulties in switching from one type of action to another, in the third option

In “field behavior” that has nothing to do with the task (for example, the task is to solve the arithmetic example 9 + 5 =; the patient looks around and says: “Ah, that means 9 chairs, but there aren’t nine here... one, two, three... just three"). Children with insufficient function of the frontal lobes are also distracted from the task: they begin to draw or get up and walk around the room, etc. All behavior in the situation of performing a task is inadequate; patients are uncritical of their actions.

Neuropsychological picture violations. Counting disorders occur in the syndrome of disruption of activity, its purposefulness, regulation, control, disturbance of motives and needs for behavior in the absence of organization of activity and destruction of the regulatory role of speech. Factor

- violation of selectivity and focus of activity. Symptoms: a) lack of ability to independently act with numbers, without external control; b) lack of understanding of the relationship between numbers within the composition of a number; c) narrowing the scope of number connections, i.e. decreased generalization and violation of the concept of number; d) violation of accounting operations; e) loss of intermediate links in counting operations; f) emergence of side connections; g) perseveration. Recognition and naming of numbers and simple numbers, multiplication tables, addition and subtraction within the first ten, and automated operations are preserved.

Psychological picture counting disorders with damage to the frontal areas of the brain are, first of all, characterized by a violation of the voluntary level of this process. The involuntary level of counting, especially numerical operations, is often preserved, which often leads to an erroneous conclusion about the preservation of the ability to count and counting operations in these patients, while in fact, as our experimental data show, only skills are preserved; conscious and meaningful actions with numbers are grossly violated.

Methods of restorative learning to count in cases of damage to the frontal systems of the brain

In the field of problems of restoring human mental activity, methods for restoring higher mental functions, including counting, in patients with damage or dysfunction of the frontal lobes of the brain are the least developed. This equally applies to the state of methods for restoring HMF in children with underdevelopment (delayed maturation, etc.) of the frontal systems of the brain. This is especially true for children's acalculia. This area of ​​restorative learning needs theoretical and experimental study.

Here we will describe the methods that we developed through experiment and have undergone extensive practice. Our methods meet a number of requirements and conditions. The first and most important requirement to the methods of rehabilitation training for patients with frontal syndrome is their influence on the organization of the general behavior of patients and behavior in a training situation. Second requirement refers to the correct setting of tasks for remedial training. Third requirement involves the use of methods adequate to the structure and mechanism of acalculia, and fourth appeals to the content of the methods, their psychological essence.

The practice of teaching this group of patients has shown that the most effective direction in these cases is programming activities of patients, which is also the leading method. The psychological essence of this method lies in the fact that the program: a) divides the integral action into its constituent operations; b) brings this structure of action outside; c) makes the action voluntary and conscious.

First condition restorative learning appeals to personalities the patient and his emotional-volitional sphere. This means that all types of work, solving any problems and tasks must begin with establishing contact with the patient, from clarifying (and creating) the interests of patients, the system of their relationships, from creating motive of activity and its understanding by the patient. Second condition assumes skillful use of speech - the patient’s own speech and the teacher’s speech. In some cases, speech acts as an organizer and regulator of the patient’s activity (and later as a means of self-regulation), in other cases, speech records the completion of a task and connects speech with the actions of patients. But in some cases, namely in cases of damage to the posterior frontal zones of the cerebral cortex of the right and left hemispheres, as well as the mediobasal regions, speech may be a hindrance, and work must be carried out with speech turned off.

In modern psychology, thinking is considered in close connection with action, and vice versa. “At every step in life we ​​see the transition of thought into action and action into thought. These systems are not isolated from each other” 1. An action refracted through the prism of thought is a different action, meaningful, conscious. This is different highest level implementation of the action. It is this level in the structure of ID and, in particular, in counting that is disrupted when the frontal systems are damaged. As we saw above, this factor underlies frontal acalculia, which should be taken into account in remedial training.

Objectives of rehabilitation training for this group of patients:

1. Restoration of the processes of understanding as an integral part of thinking.

2. Restoring not formal operations and actions with numbers, but conscious and meaningful ones.

3. Restoring the connection between thought and action (and action and thought).

4. Restoring not isolated actions and operations with numbers, but system ones, i.e. restoration of understanding of the integrity of an arithmetic operation and the connection of operations with each other in the structure of an arithmetic operation. For example, in action 35-17: a) 17+3=20, b) 35-20=15 c) 15+3=18 - all operations, the sequential execution of which leads to the solution of the task, are interconnected and represent a holistic formation or “ system of operations."

5. Restoring understanding meaning and meaning numbers.

Before you start working on actually restoring your account, you should work over the organization of the patient's behavior, using for this purpose not numerical material, but picture, verbal, and then only numerical.

Methods for organizing the behavior and activities of patients are numerous and varied; we will describe some of them. Picture classification method(and words): a) according to given characteristics, b) free classification. Nonverbal method of oppositions(opposites): the patient is given a picture (rain, night, etc.), he needs to find a picture with the opposite meaning. Verbal method of antonym words: The patient’s task is to find antonyms for a given series of words (for example, fat - ...; smart -...; rainy - ...; sit - ... etc.).

A method of organizing, distributing and concentrating attention. Method procedure:

1. Patients are offered one stack of cards on which numbers from 1 to 10 are written and a classification task: a) put even numbers to the left, odd numbers to the right; b) put 2 odd numbers and 2 even numbers to the left.

2. Then another stack of cards is offered, on which the numbers of the second and third tens are written (11, 12, 13, etc., 21, 22, 23, etc.) and a number of tasks are given for various types of classification of these numbers For example, a) put the numbers of the 2nd ten to the left, and the 3rd to the right; b) alternately put one number from the 2nd ten, the next from the 3rd, etc. c) find and put the numbers 11; and 21, say how these numbers differ, etc.

3. Schulte table. This table allows you to carry out a variety of exercises for patients with numbers. For example, a) find and consistently show numbers from 1 to 25 (children from 1 to 10 or 15) and, conversely, from 25 to 1; b) find and show even numbers; c) find and show odd numbers; d) show all numbers that are greater (less than) 10, etc.

All these and a number of other similar methods and techniques contribute to:

Organization of patient behavior;

Restoring voluntary understanding;

Inhibition of impulsive actions;

Intensification of activities;

Programming activities;

Restoring awareness of one's own actions.

In children, these methods also work to restore knowledge of numbers and their sequential series. All these methods and exercises are used on / stages training and are aimed at updating (disinhibition) general knowledge about the number.

OnIIstages You can move on to solving special problems of counting restoration and, above all, to restoring an understanding of the composition of a number and the relationship between numbers. In this case it is good to use method of programmed remedial training number of patients. As a material, you can again use the Schulte table and numbers written on cardboard cards, and as techniques - the actions of addition and subtraction. ...

After working together on the first written program, an attempt is made to transfer the patient to work with the program using loud spoken language, reproducing and performing operations from memory, and in the end - at the level of internal speech, i.e. "to myself." After this, they move on to the next program, which solves other problems. Instructions: I will read, and you listen carefully, and then complete the task I read, then repeat the task and complete it again. Below we describe several programs for number operations.

Program No. 1

1. Show the first two numbers in the table (1 and 2).

2. Write them down in your notebook.

3. Add them up (1+2) and write down the sum.

4. Show the next two numbers (3 and 4).

5. Write them down in your notebook.

6. Add them up and write down the sum.

7. Continue working until number 10.

Program No. 2

1. Look at the first sum written down (3) and at the table of numbers; tell me from what numbers this amount was obtained.

2. Perform this action again: add these numbers and write

write the amount.

3. Look at the following sum (7) and also say,

What numbers did the number 7 come from?

4. Perform this action again: add these numbers and write

write the amount. Etc.

After working on these programs multiple times, and making sure that patients understand and are aware of the actions, you can move on to the next program.

Program No. 3

1. Write down from which numbers you got the number 3. Write it down. Perform the addition action.

2. Write what other numbers this number can be obtained from. Now fold it.

3. Write down from which numbers you got the number 7. Write it down, and now add it up. Etc.

After prolonged work with materialized visual supports (tables, cards with numbers, etc.), you need to gradually move on to working in terms of oral speech and always with the numbers that you have already worked with in previous programs. ...

In one stack of cards in the patient’s field of vision there are numbers from 1 to 10, in the other - from 10 and beyond. The patient is given the task of making up the number 25 and finding the necessary numbers for this. A sample is given: 5=3 and 2; 4 and 1; 1, 1, 1, 1, 1. The task is to find the composition of other numbers. It is necessary to work a lot and for a long time with variant techniques with numbers to restore the understanding of number, its composition and the interaction of numbers. ...

Method for analyzing the bit structure of a number. The work begins with the numbers of the 2nd ten. In front of the patient there should be cards with numbers from 1 to 9 and cards with numbers of the second ten (11, 12, 13, 14, etc.) and a program. The program should be written in large letters, highlighting the main words indicating the operation to be performed. ...

After long-term cooperation with the patient, the teacher transfers the patient to independent activity, in which he must strictly carry out all the operations of the program. Subsequently, the programs are assimilated by the patient, reduced in the number of operations, many of which are eliminated (that is, they are already performed “in the mind” and are automated). Similar work is carried out on all categories and classes with a gradual transition to them.

Rehabilitation education for children is carried out according to the same programs (or their variants), but the program is read by a teacher, sequentially giving a task (operation) to the child, explaining it. It's good to give all this work game character, and it is better to work not individually with each child, but with a group (2-3 people). It is useful to use methods such as competition method, assistance method one child to another, cross-check method(when each participant checks his work and the work of other group members). Bit grid method is used to restore understanding of the role of zero in a number, understanding its quantitative essence - zero means the absence of something (some digit). Long-term work with the digit grid, the placement of zero in different digits with the same digit and with different digits helps to restore understanding of its place and role in the number.

For younger children (senior preschoolers and junior schoolchildren), it is good to use another method first - specific quantity transfer method objects into an abstract number by playing with objects and the numbers that represent them. For this, 2 matchboxes are given (later 3, etc.); in the first of them there are always 10 matches (or buttons, etc.), and in the other the number of matches changes - sometimes one, then five, etc. The number 1 is pasted on the first box, and cards with different numbers are placed on the other box each time. First, the child must open the box, look at its contents, count the matches, feel them and close the box. After this action, the child already knows what and how much is in this box (10 matches) and that we denote this quantity with the number 1. This means that here 1 = 10. To this box we add a second box, on which is written 5, then 3, etc. units, and the child must name the numbers obtained by folding the boxes. First the work goes conjugate with the teacher, then conjugate-reflected and at the end reflected and independently. After working for a long time using this method, you can move on to working with the bit table, i.e. from the material form of work to that materialized in the form of diagrams. These methods form in the child the concept of number - its composition and digit capacity, understanding of the dependence of the number on its place in the digit grid (table). ...

Igroup of methods. Classification method(its different variants) - directed and free classification based on verbal and non-verbal (picture) material; analogy search method- “The fourth wheel.”

IIgroup of methods. These methods relate to the restoration of the activity planning process: retelling method story pictures and texts, planning method to the retelling, essay planning method(oral and written), method of series of plot pictures(laying out, telling a story, making a plan), story writing method as specified and own plan etc.

These and a number of other methods, described in detail by us in other works, precede the beginning of account restoration, and then are used in parallel with the work of account restoration.

A smooth transition from this group of methods is method for solving arithmetic problems. In this method, firstly, the condition of the problem (its content) is the semantic background for working with numbers. Secondly, the numbers in the problem are objectified. This is good for restoring understanding of concrete numbers and can serve as a transition to restoring symbolic activity with abstract numbers. This method should be used with gradual complication, ...

…. Psychological essence This method is that in an arithmetic problem the numbers are in a semantic context, represent quantitative characteristics of objects(objects, phenomena) and are inextricably linked with the subject. This type of everyday experience is reinforced and occurs on an involuntary level. The method of translating an arithmetic problem into arithmetic operations (examples) is a series of programs consisting of sequential operations. Work according to the programs is first performed by the patient in collaboration with the teacher, and later independently.

Program No. 1

Instructions: You will solve the problem, but first gradually read the program and complete each task.

1. Read the problem.

2. Repeat it.

3. Tell me how many (apples)... were in the problem

4. Tell me how many (pears)... there were.

5. Say what you need to know.

6. Write down the condition of the problem - write down only the numbers (a sample is given).

7. Solve the problem.

8. Explain why you decided this.

9. Check the correctness of the solution. …..