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Clinical and psychological characteristics of acalculia and dyscalculia in childhood. Symptoms of dyscalculia in children and methods for correcting the disorder Primary acalculia

Dyscalculia is the inability to operate with mathematical categories, the inability to understand the essence of arithmetic operations, the concepts of “number”, “sum”, “triangle” and the like. As a rule, this disorder appears in children of preschool and primary school age, but it can also occur in adults. Dyscalculia is difficult to diagnose for a non-specialist, so children with this pathology often end up in specialized classes for schoolchildren with mental development disorders.

Approximately 10% of schoolchildren suffer from some form of dyscalculia. Not all parents know that with timely diagnosis even in preschool age, effective measures can be taken to prevent this pathology and make it easier for the child to master the school curriculum.

If a child suffers from manifestations of dyscalculia, he experiences a negative attitude towards the “exact sciences”. Chronic underachievement can also affect mastery of humanities subjects, as well as cause a student’s low social status. He does not have good relationships with his peers, and teachers and parents often put unjustifiably strong pressure on him because of his perceived laziness and lack of diligence. In the future, such children experience difficulties with choosing a profession and self-realization.

Fear of arithmetic - the violation is based on the negative experience of learning to count through coercion and punishment. This unusual phobia is due to the fact that when solving arithmetic examples, especially problems, the child had difficulties or was often scolded and punished. Over time, he developed fear and self-doubt for fear of being punished.
Social problems. They most often occur in children who are brought up in conditions of pedagogical neglect, in a dysfunctional family.
Damage to the parietal lobe of the cerebral cortex due to the pathology of pregnancy and childbirth, brain injuries and neuroinfections, tumors and genetically determined defects.

In adults, this problem often appears due to disruption of the brain. Its occurrence can be caused by hemorrhages, organic lesions in the temporal region, tumors, blood clots, cysts and traumatic brain injuries. Various psychological traumas can also provoke the occurrence of dyscalculia. If you have problems using mathematical knowledge, you should contact a neuropsychiatrist.

Dyscalculia in children often occurs due to disorders of mental activity. These include:

disturbance in the processing of visual information;
decreased concentration;
violation of logical thinking;
problems with assimilation and memorization of information.

Dyscalculia can be combined with reading and writing disorders such as dysgraphia and dyslexia, as well as ADHD (attention deficit hyperactivity disorder).

Symptoms of the problem

Children suffering from dyscalculia are not able to understand what a number is and on what principle the number series is built; they cannot distinguish and remember numbers. They cannot perform operations with numerical values and do not know how to decompose them into terms. It is difficult for them to compare the number of objects, perform simple arithmetic operations and carry out calculations according to the internal plan, that is, to count “in their minds”.

Symptoms of dyscalculia:

difficulty recognizing and writing numbers;
inability to tell time and navigate hours, minutes, seconds;
impaired coordination of fine movements;
inability to determine the distance traveled or measure the length of a segment;
difficulty in perceiving the concepts “less” and “more”;
the impossibility of solving problems without illustrative support;
difficulties in solving logical problems and performing actions with abstract categories;
inability to visually determine the number of objects, putting them into groups without counting them one by one.

As soon as relatives discover the above symptoms in a child, you should immediately seek advice from a speech therapist or psychotherapist. The specialist will conduct a differential diagnosis, determine the form of the disorder, identify the causes of its occurrence and develop an effective correction method.

Due to a violation in the processing of visual information, the child can solve examples only if their objective component is present. The child cannot independently imagine what is written in the task conditions. In addition, schoolchildren in primary grades are unable to rationally calculate their free time, which leads to poor academic performance and behavior problems in the future. This aspect is described quite fully in the video below:

Forms of dyscalculia

It can be congenital or acquired, primary or secondary. Experts identify the following forms:

Practognostic – the inability to keep an abstract count, to classify objects by shape, size, quantity.
Verbal – the inability to name numbers, geometric figures and the actions that are performed with them.
Graphic – problems with converting numbers into digit form, depicting mathematical symbols, and geometric figures.
Lexical - characterized by errors in reading arithmetic signs and numbers, in understanding the terms of the problem, the essence of mathematical operations, and violations of spatial visualization.
Operational – the child has difficulty performing simple arithmetic operations and solving basic examples and problems.
Arithmeria is the inability to learn computational operations.
Pseudodyscalculia is a violation of the mastery of mathematics due to reduced motivation for learning and poorly organized learning process.

In some cases, children suffering from dyscalculia may experience symptoms of several forms of this disease. After determining the type, the specialist develops therapy aimed at correcting the disorder and further preventing the development of other forms in the child.

There is such a thing as acalculia - this is a neuropsychological symptom that manifests itself in a violation of counting and counting operations due to damage to various parts of the cerebral cortex. It should not be confused with dyscalculia.

Test tasks for diagnostics

You can suspect dyscalculia in a child even before school starts. It is enough to ask a 5-7 year old child to count something, after which you can see that performing basic mathematical operations causes him significant difficulties.

Test tasks for children of primary school age:

count from 10 to 20 (counting up to 10 can be perfect);
arrange numbers in ascending and descending order;
compare two numbers;
determine the name of geometric shapes, classify them by color, size;
perform arithmetic operations (addition and subtraction);
analyze the human body diagram;
determine the direction left and right.

After the examination, the specialist can accurately determine the form of dyscalculia and begin work on its correction.

How is dyscalculia corrected?

Correction (treatment) is carried out in a clinic or specialized medical center. The following specialists are involved in this: psychoneurologist, neuropathologist, child psychologist, speech therapist. The main treatment is carried out in a playful way; specialized computer programs and interactive sessions between the child and a specialist can be used.

On average, 30–90 sessions are required to eliminate the problem; in severe cases, their number reaches 250.

Methods and exercises for correction:

solving problems close to life situations (in a store, in the family, on a walk);
imitation of objects with sticks, matches, buttons and other improvised materials;
creation by the teacher of diagrams and memos containing an algorithm for completing tasks;
transition from verbal pronunciation of one’s actions to the internal plan;
measuring objects with a ruler, determining values by eye, weighing bulk objects, measuring the volume of liquids;
training in automatic perception of groups of objects up to five pieces, all components of the group must have a different color and size;
accompanying the solution of problems with a drawing performed by the child.

Various games for young patients suffering from this pathology are aimed at teaching counting and performing basic mathematical operations. The baby is taught to sort objects according to various characteristics. After this, the specialist helps the child master simple mathematical problems and operations. During the training, it is necessary to ensure that the little patient understands the sequence of banal operations and actions he performs. Next, the child is explained how to correctly separate numbers and objects into parts and assemble them into a single whole.

To get rid of this pathology, it is necessary to work with the child from an early age, sort shapes, seeds, cereals, transfer them into various containers, accompany all these tasks with speech, and also introduce them to mathematical terms (one-many, numbers, shapes, etc.). d.). You need to teach your child to correctly name numbers, geometric shapes, their characteristics (size, color) and the actions performed on them.

Next, the child learns to correctly use the learned terms and words in everyday life, in conversations with relatives, peers, and friends. Particular attention must be paid to translating spoken symbols into written form. The child must definitely learn to write numerical values and arithmetic signs correctly.

Along with the correction of dyscalculia, it is also necessary to develop abstract and logical thinking, visual memory, spatial orientation and musical abilities in the baby. He must learn to independently control his actions and the ability to correctly distribute personal time. Here is an example of several exercises:

To treat this disorder in a child or adult, doctors can prescribe certain medications, such as Glycine, Cortexin and B vitamins. It is doctors, but not speech therapists or speech pathologists (unfortunately, they often prescribe medications, although they do not have the right to do so ).

Prevention methods

Precautionary measures to prevent dyscalculia can be carried out in early preschool childhood. First of all, the most complete correction of existing neurological pathologies should be carried out. At an early age, you can start learning basic mathematics in a playful way.

Parents should clearly demonstrate to their child how to count objects, shapes and perform basic mathematical tasks, for example, while swimming, you can ask your child to count blue balls or catch three red balls with a net. When teaching a child to count, it is necessary to carefully pronounce the names of numbers, and then arithmetic operations. You can show the number of objects to the child on your fingers or using small toys and objects. Gradually, you need to teach your child to correlate the number of objects with a specific number.

To prevent a child from developing operational dyscalculia, he must be taught the rules of counting and the order of mathematical operations. To prevent verbal and lexical forms, it is necessary to ask the child to say the name of the numbers when counting, and when examining various figures and other objects - their color and shape. Parents should monitor the correct use of certain symbols and, if their child makes mistakes, calmly correct them, without using harsh punishments.

To prevent the occurrence of dyscalculia in graphic form, it is necessary to pay special attention to the development of the child’s visual memory, fine motor skills, coordination of movements through finger and outdoor games, collecting cut pictures, cubes, puzzles, playing with small parts of the construction set, stringing beads on a cord, identifying them shape and color. The productive activities of children are very effective in this regard - modeling, drawing, appliqué, making crafts, origami.

Moms and dads must pay attention to the development of thinking and memory in the child, and then, in the future, the occurrence of dyscalculia can be avoided.

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The authors of the program emphasize that the formation of mathematical knowledge and skills should be carried out taking into account the complex structure of the student’s mathematical activity (motivational-target, operational stage, control stage).

The program defines the directions in which mathematical skills are formed: concept of number – counting operations – problem solving. The prerequisites for mastering counting operations and the ability to solve mathematical problems is the development of all types of thinking, taking into account their evolutionary development (visual-effective, visual-figurative, verbal-logical).

In this regard, the formation of counting operations as complex mental actions is carried out in the following stages (taking into account the stage-by-stage formation of mental actions (according to P. Ya. Galperin):

– performing a mathematical action based on objective actions with specific objects (action materialization stage), first with the help of a teacher, then independently;

– performing a mathematical operation based on clarity and loud speech, but without using practical actions with specific objects;

– performing mathematical operations only in speech terms;

– performing mathematical operations mentally, in terms of internal speech.

Schoolchildren with SLI experience particular difficulty in learning mathematics when understanding and solving mathematical problems. The creators of the program believe that the leading role in learning to solve problems is played by modeling techniques, building a specific model, and mastering an algorithm for solving a certain type of problem.

Speech occupies a special place in the development of a child’s mathematical activity. Taking this fact into account, it is necessary to include speech notations as much as possible at all stages of the formation of mathematical actions, starting from the stage of materialization, i.e., performing counting operations using practical actions.

The creators of the program emphasize the important role of correctional work aimed at preventing difficulties in mastering mathematics by schoolchildren with SLI in preparatory and first grade.

Questions and tasks for independent work

1. List the tasks of mathematical education for preschoolers, having analyzed the educational area “Cognition” (Formation of mathematical concepts) in the Program for the education and training of preschoolers with severe speech impairments.”

2. Determine the tasks of mathematical education for junior schoolchildren in type V secondary educational institutions.

3. Formulate the principles of construction and basic requirements for methods of teaching mathematics in primary school.

4. Define “learning activity.”

5. List the methods of educational activity of younger schoolchildren in the mathematics course.

1. Akhutina T.V., Obukhova L.F., Obukhova O.B. Difficulties in mastering the initial course of mathematics by children of primary school age and their causes // Psychological Science and Education. – 2001. – No. 1. – P. 65–78.

2. Istomina N. B. Methods of teaching mathematics in primary classes. – M.: Academy, 2000.

3. Kapustina G. M.. Corrective techniques for teaching mathematics to junior schoolchildren // Education and training of children with developmental disorders. – 2005. – No. 2. – P. 63–72.

4. Moro M. I., Pyshkalo A. M. Tools for teaching mathematics in primary school: A manual for teachers. – M.: Education, 1981. – 144 p.

5. Program for the education and training of preschoolers with severe speech impairments. – St. Petersburg: CDK prof. L. B. Baryaeva, 2009.

6. Spirova L. F. Features of speech development of students with severe speech impairments. – M.: Pedagogy, 1980.

7. Stoilova L. P. Mathematics. – M.: Academy, 1997.

8. Elkonin D. B. Psychology of teaching primary schoolchildren / Selected psychological works. – M., 1989.

Topic 3. Acalculia and dyscalculia: symptoms, mechanisms, classifications

Plan

1. Brief information about acalculia.

2. The concept of “dyscalculia”.

3. Symptoms of dyscalculia.

4. Mechanisms of dyscalculia.

5. Classifications of dyscalculia.

Violations of counting operations are defined by the terms “acalculia” and “dyscalculia”. At the same time, counting disorders in patients with local brain lesions are acalculia, and disorders in mastering counting operations in children are dyscalculia.

The term “acalculia” was proposed by S. F. Henschtn in 1919 to designate violations of counting operations due to local brain lesions. The scientist differentiated between impairments in reading and writing numbers, which he called “acalculia” in the broad sense of the term, and impairments in mental counting operations, which he designated as “acalculia” in the narrow sense of the term.

The concept of “dyscalculia” is an integral part of the concept of “acalculia”. Therefore, let us first analyze the manifestations of violations of counting operations in people that arise as a result of local brain damage.

So, the first mention of counting disorders due to local brain lesions was recorded at the beginning of the 20th century. J. Gerstman described a syndrome associated with left-sided parieto-occipital localization, in which finger agnosia was combined with inability to distinguish between right and left, with agraphia, with constructive apraxia and with impaired counting function. The author emphasized the intimate correlation between finger skills and elementary counting operations.

Differential diagnosis between various forms of counting disorders that occur with local brain lesions was carried out in 1934 by K. Kieist. The author identified: acalculia as a violation of mental calculation operations, alexia of numbers, which he considered as a residual disorder in aphasia, agraphia of numbers associated with apraxia and agraphia of words.

In the case of digit agraphia, the spatial organization of numbers is absent, but patients do not experience difficulties in mental calculation operations.

Alexia and agraphia of numbers were noted in the majority of patients with aphasia by S. Henschen, who associated agraphia of numbers with apraxia and agraphia of words. In the first form, the patient does not find accurate movements when writing numbers - the numbers are either distorted or replaced by another. In the second form, the idea of the arrangement of digits in a number disintegrates. In this case, the sequence of numbers when designating a number is confused, spatial orientation in the number is disrupted, but the patients do not experience difficulties in mental calculation operations.

Thus, an analysis of the literature of the 20th century showed that during this period there were two different types of counting disorders. In the first type of acalculia, the main difficulties were the inability to identify the position of numbers when perceiving and writing a number, while patients are not able to implement a counting plan, make mistakes when adding and subtracting numbers, because the columns of numbers are incorrectly placed by them, at the same time, mental arithmetic them saved. Most authors associate this type of acalculia with a defect in spatial perception.

With the second type of acalculia, a connection can be traced with the collapse of the quantitative system, with a violation of the concept of number.

In the future, one of the problems in studying acalculia in adults is to consider counting disorders in isolation or in combination with other disorders.

Most authors have established a correlation between acalculia and visual agnosia, based on the fact that counting disorder is the most common disorder in lesions of the occipital region. In 1930, J. Lange assessed acalculia as the inability to use categories of direction in space.

A. R. Luria and L. S. Tsvetkova made a significant contribution to the study of violations of counting operations in local brain lesions. Acalculia, according to A. R. Luria, is combined with semantic aphasia, the central symptom of which is a violation of the understanding and use of complex logical and grammatical structures. Both of these disorders are a consequence of the collapse of simultaneous, mainly spatial syntheses, and are included in the syndrome that A. R. Luria called “spatial apraktoanosia.” Its symptoms are characterized by: a violation of the perception of spatial relationships, synthetic spatial patterns stored in memory and corresponding movements and actions requiring spatial organization.

A. R. Luria characterized the violation of counting operations as a particular manifestation of forms of mental activity. Most people suffering from acalculia are proficient in simple ordinal counting, the operation of recalculation and the correlation of object sets, but they do not understand the principle of place value and do not operate with generalized quantities. A number, as a complex mental image, including components that are heterogeneous in structure and function, must be formed according to laws that reflect its structure.

In the studies of L. S. Tsvetkova, based on a syndromic approach to the analysis of disorders of higher mental functions with local brain damage, primary and secondary acalculia are distinguished.

Primary acalculia is caused by a violation of spatio-temporal structures, and secondary ones are associated with difficulties in operating with numerical symbols.

Primary acalculia occurs as a result of damage to the parieto-occipital lobes of the cortex of the dominant hemisphere and manifests itself as a disturbance in perception and orientation in space.

The main disturbances in acalculia are: the disintegration of the concept of number, disturbances in the awareness of the digit structure of a number, in the awareness of the meaning of arithmetic signs, the “loss” of a number from a complex decimal number system.

With secondary acalculia, the main core of the psychological structure of number and counting operations is preserved, that is, it does not disintegrate. These acalculia are divided into optical and frontal.

Optical acalculia occurs when the occipital systems of the brain are damaged and is associated with amnesia for numbers, visual agnosia, and a violation of the verbal designation of numbers. The main mechanism is a disorder of optical and sometimes optical-spatial perception. A. R. Luria, S. S. Mnukhin, L. S. Tsvetkova and other scientists believe that the consequence of this is difficulties in perceiving the optical image of a number, violations of the differentiation of numbers, which include graphically similar numbers, along with this, specific violations are identified tasks.

With frontal acalculia, there are no disturbances in visual perception or spatial patterns. The main mechanism of counting disorders is the disintegration of programs of mental actions, which lose such properties as selectivity and purposefulness. Frontal acalculia manifests itself in the inability to perform actions in several operations, in the inability to retain intermediate information and the final question of the task. People suffering from frontal acalculia recognize and name numbers; they have retained automated counting. But at the same time, there is a violation of counting operations as targeted electoral activities. This is reflected in the process of solving arithmetic problems, examples consisting of several links. In the process of solving them, the impossibility of creating mental action programs, difficulties in maintaining intermediate results, and a violation of the sequence of actions are noted. It has been established that in patients, as a rule, the orienting basis of action completely disintegrates; they begin to solve the problem without attempting to analyze the condition.

Studies by A. R. Luria, S. S. Mnukhin, L. S. Tsvetkova and other scientists indicate that the results are not compared by calculators with the original data, errors are not noticed and are not corrected, and all activity when solving an arithmetic problem becomes uncontrolled chaotic character.

A number of studies have found that acalculia is combined with semantic aphasia, the main symptom of which is a violation of the understanding and use of complex logical and grammatical structures.

Attention is drawn to the fact that most people suffering from acalculia know simple ordinal counting, the operation of recalculation and the correlation of object sets, but they do not understand the principle of place value and do not operate with generalized quantities.

Dyscalculia in children is a specific, complex and persistent disorder in mastering counting operations, which negatively affects the child’s school adaptation, the formation of his personality, and, in general, the formation of a culture of knowledge of mathematics.

In the studies of A. Germakovsk, Yu. G. Demyanov, M. V. Ippolitova, A. N. Kornev, R. I. Lalaeva, S. S. Mnukhin, S. L. Shapiro, L. S. Tsvetkova, attention is paid to the fact that dyscalculia, like other disorders leading to school failure (dyslexia, dysgraphia), is most often a consequence of mental deficiency, sensory impairments, speech disorders, especially in children with minimal brain dysfunction (MCD), cerebral palsy (CP) , mental retardation (MDD).

It should be noted that scientists’ ideas about dyscalculia in children are ambiguous. At the initial stage of research into this problem, the prevailing opinion was that difficulties in mastering numeracy are not specific, but are rather associated with improper training or non-attendance at school, which at present could be characterized as pedagogical neglect. Another approach to dyscalculia is described, based on highlighting the difficulties in learning to count. Based on this, cases of “pure” dyscalculia and cases of dyscalculia associated with dysgraphia were identified. In cases of “pure” dyscalculia, the main difficulties are observed in mental counting operations: children find it difficult to compare the number of beats, count the number of beats in a given rhythm, simultaneously determine the number of objects, etc.

A. Germakovska, R. I. Lalaeva, A. R. Luria, L. S. Tsvetkova consider dyscalculia in connection with dysgraphia, when children make mistakes in writing numbers and mix up the positions of numbers when carrying out written counting operations.

In general, it can be noted that increased attention to this disorder has followed the path of expanding psychological and neuropsychological research on children with dyscalculia. This made it possible to identify not only the symptoms, but the etiology and mechanisms of violations in mastering counting activities, that is, the violations began to be considered from the perspective of a syndromic approach.

The studies of A. Germakovsk, Yu. G. Demyanov, T. V. Egorova, R. I. Lalaeva, S. S. Mnukhin and other scientists draw attention to the role of heredity in the occurrence of dyscalculia in children. Many parents of the studied children with dyscalculia were found to have psychopathological burdens: alcoholism, depressive states, psychopathy, psychological imbalance.

R. Berkow, T. A. Vlasova, G. S. Gumennaya, M. V. Ippolitova, M. S. Pevzner and other scientists found that various types of mental development anomalies in most cases are associated with organic brain damage in early stages of ontogenesis and secondary underdevelopment of brain structures that form in the postnatal period. This was confirmed by the fact that a number of children with dyscalculia had a history of pathology of the central nervous system.

Among the “risk factors” for dyscalculia are: prematurity, toxicosis of the first and second half of pregnancy, asphyxia during childbirth, malnutrition, impaired early psychomotor development, previous infections, chronic diseases, somatic weakness of children.

In the works of N. F. Berezhnaya, R. Berkow, Yu. G. Demyanov, V. A. Ilyukhina, V. Levy, Levy Harold B, M. S. Pevzner, A. N. Sokolov, G. E. Sukhareva and Other researchers draw attention to the fact that in children with school failure, the etiology of these disorders comes first from diseases suffered before the age of three (chronic diseases, severe infections, etc.), as well as birth injuries and brain injuries in early childhood. age.

Interesting is the information presented by E. Gruszczyk-Kolczynska E., Yu. G. Demyanov, V. Levi, Harold B. Levi that the microsocial environment plays an important role in school performance. A child’s unfavorable microsocial environment affects children’s poor performance at school, including in mathematics. In most cases, children with dyscalculia have a “distorted” family situation: an incomplete family, significant deviations in the manifestation of maternal feelings.

The study of dyscalculia has made it possible to identify conceptual approaches, symptoms, and develop a classification of dyscalculia.

As a symptom of dyscalculia ( violations of counting operations) in children are distinguished:

– insufficient mastery of mathematical vocabulary;

– incorrect naming of numbers;

– inaccurate understanding of the graphic structure of numbers;

– mechanical reproduction of the order of numbers;

– difficulties in determining the place of a number in a series of natural numbers;

– insufficient knowledge of the composition of numbers;

– difficulties in mastering the rules of number formation;

– difficulties in establishing the relationship of a number to its neighbors;

– lack of formation of quantitative relationships between numbers;

– an elementary way of performing arithmetic operations (children rely not on rules, but on external actions, use the “manual” method of execution);

– mental operations are predominantly concrete in nature.

As mechanisms of dyscalculia consider a variety of factors that are the basis for different conceptual approaches to this problem.

Several concepts are conventionally distinguished.

According to with the first concept, gnostic-praxic disorders are distinguished as mechanisms of dyscalculia. In this case, dyscalculia is correlated with a violation of finger gnosis and praxis in combination with an unformed body diagram and constructive apraxia. It should be noted that gnostic-praxic disorders are considered only as possible pathogenetic factors, i.e., as one of the possible, but not the dominant mechanisms of dyscalculia. This is indicated by A. Germakovska, R. I. Lalaeva, S. S. Mnukhin and others.

According to with the second concept, considered within the framework of general school failure, highlight the psychological concepts of dyscalculia. G. M. Kapustina, K. S. Lebedinskaya, S. S. Mnukhin and others associate this violation with with immaturity of mental operations, memory, attention, thinking. A. Germakovska, R. I. Lalaeva, S. S. Mnukhin, L. S. Tsvetkova confirm this fact by studying children with reading, writing and counting disorders, which revealed they had disorders of series formation and reproduction of automated series (violation of ordinal counting, naming days of the week, months, etc.), lack of formation of complex actions that consist of a number of sequential operations, inferior development of spatial functions: spatial orientation, spatial perception.

A. V. Kalinchenko, T. V. Rozanova, E. J. Skiotis note that in children who fail in mathematics, the processes of logical and mathematical thinking are significantly impaired. Yu. G. Demyanov, E. S. Ivanov, N. G. Poddubnaya and other scientists pay attention to the difficulties students have at the level of basic mental operations - analysis, synthesis, classification, generalization, abstraction, inference, etc.

T. V. Akhutina, E. M. Mastyukova, N. A. Menchinskaya, M. I. Moro, L. F. Obukhova, O. B. Obukhova, A. M. Pyshkalo state the fact that students with dyscalculia disturbances of attention, visual and auditory memory are observed.

A. Germakovska, R.I. Lalaeva highlight the characteristics of not only cognitive activity, but also the emotional-volitional sphere in students with dyscalculia. Yu. G. Demyanov, E. S. Ivanov consider mental exhaustion, low performance, and inertia of mental processes in students with dyscalculia.

Based on the neuropsychological concepts of A. Germakovska, Yu. G. Demyanov, A. N. Kornev, R. I. Lalaeva, they identify connections between dyscalculia and the immaturity of a number of speech and non-speech mental functions. This third concept, which is based on neuropsychological concepts. The authors believe that systemic speech disorders, immaturity of phonemic functions, underdevelopment of the lexico-grammatical aspect of speech, reading and writing disorders have a significant negative impact on the process of mastering counting operations. This leads to difficulties in mastering mathematical concepts, mathematical vocabulary, disturbances in the perception of the text of the problem, incorrect recording of examples and problems, and other symptoms.

Based on the analysis of symptoms and conceptual approaches, the following are distinguished: classifications of dyscalculia:

– congenital and acquired (S. S. Mnukhin);

– primary and secondary (N. Granjon-Galifret, J. Ajuriaguerra, L. S. Tsvetkova);

– classification by L. Kosch.

Let us consider in more detail the classification of L. Kosch. The scientist highlights:

– verbal dyscalculia, which manifests itself in a violation of the verbal designation of mathematical concepts;

– practical-gnostic dyscalculia, manifested in disorders of the number system of concrete and visual objects or their symbols;

– dyslexic dyscalculia, which is based on a violation of reading mathematical signs;

– graphic dyscalculia, manifested in a violation of the recording of mathematical signs or symbols and the correct reproduction of geometric figures;

– operational dyscalculia associated with the inability to perform mathematical operations.

The identification of certain types of dyscalculia is relative, since in most cases its mechanisms and symptoms are complex and are caused by not one, but several pathogenetic factors. Children most often exhibit symptoms of various types of dyscalculia.

To select the most effective correctional work for the prevention and correction of dyscalculia, it is necessary to identify and understand the mechanisms and symptoms of dyscalculia that cause children difficulties in mastering mathematical skills, knowledge and skills.

Based on the conclusions drawn from the consideration of modern approaches to the development of numeracy skills in preschool children, it becomes necessary to identify risk factors for the occurrence of dyscalculia in preschool age and conduct speech therapy work to prevent it.

About 5% of school-age children suffer from such a rare disease as dyscalculia. It manifests itself in the inability to perform any computational operations, misunderstanding of counting and inability to distinguish between numbers. If a person did not have any difficulties with counting, was mentally developed, but as a result of some illness or injury lost this ability, then here we are talking about acalculia. First of all, acalculia is characterized by a counting disorder, and dyscalculia is characterized by the ability to master it.

Acalculia is an acquired brain disorder, in which the ability to perform simple arithmetic operations is lost, while dyscalculia is different in that any ability to teach a child mathematical operations is lost, and the problem is often compounded by the inability to recognize letters.

As a rule, acalculia is accompanied by a mental disorder, as a result of which in an adult some areas of the brain responsible for numbers and counting are affected. There are two forms of acalculia.

The first form is primary acalculia. It is observed when the parieto-occipital-temporal parts of the cerebral cortex are damaged, while the person experiences difficulties in the simplest mathematical operations, does not understand the structure of numbers, and may confuse the arithmetic sign.

Secondary acalculia can occur against the background of a mental disorder. For example, amnesia, in this case a person may confuse numbers, since they will be similar in spelling to him. Or the calculation in his mind will be upset; he cannot perform the counting operation correctly.

Also, acalculia occurs after a serious injury, as a result of which all mathematical abilities acquired previously are lost. People with acalculia cannot be called mentally retarded, they just experience some problems in calculations, they have a very difficult time counting money and remembering numbers.

Dyscalculia, unlike acalculia, is a problem that begins at a young age. Dyscalculia in children is expressed in the fact that it is almost impossible to teach them mathematics; the brain simply does not accept this information. This is a congenital problem that remains for life. Very often, this disorder occurs in children with a genetic predisposition to the disease, resulting in mental retardation. Not only can they not count, but it is difficult for them to determine where is right and where is left; therefore, they cannot tell the time on the clock, they do not recognize geometric shapes well, and some letters are similar in writing.

Common signs of dyscalculia:

Often this disease requires correction in children, namely the participation of specialists who will examine the child’s skills: memory, speech, writing, reading, arithmetic using special tests and draw conclusions about the possibility of achieving any result in treatment. In correction, it is very important to choose a set of activities that will be aimed at eliminating disorders and activating the brain.

Dyscalculia is a disorder expressed in a person’s inability to count and solve mathematical problems. Most often, this condition manifests itself in preschool and primary school age. Often children suffering from dyscalculia are considered either mentally retarded or lazy, and they are placed in special classes for the retarded. For the further full development and successful education of the child, it is important to carry out timely diagnosis and correction of this disorder.

ICD-10 code

F81.2 Specific arithmetic disorder

Causes of dyscalculia

Dyscalculia in adults occurs as a result of disruption of normal brain function. Organic lesions of the temporal part of the brain can lead to this disease. This can result from hemorrhages and blood clots, brain tumors and cysts, and traumatic brain injuries.

The development of dyscalculia in an adult requires immediate contact with a neurologist!

Psychotraumatic factors include:

Fear of mathematics. This psychological factor significantly affects children's ability to count. Perhaps the child has bad memories of learning math when he was unable to solve problems correctly and was punished or scolded for it. In this case, self-doubt and fear of repeated punishment reduces the child’s ability to count.
General violation of the child’s psychological health. This disorder is often observed in children raised in dysfunctional families.

Disorders of mental activity that lead to dyscalculia:

Impaired visual processing—children are unable to visualize what is described in the task.
Problems with abstract logical thinking.
Memory problems, inability to learn formulas and rules for solving mathematical problems.
Low concentration.

Symptoms of dyscalculia

Dyscalculia is not only a violation of the ability to count, it is a complex disorder of mental activity that manifests itself in various symptoms.

The child does not understand what a number is and does not know the names of the numbers.
He does not understand the principle by which the number series is built, and is not able to determine the place of the number in the sequence.
The child is not able to perform operations with complex numbers and does not understand how to decompose a number into terms.
The child's ability to compare numbers is impaired. He doesn't understand what a higher or lower number means.
Comparisons of the number and size of items are also difficult.
It is difficult for a child to perform arithmetic operations on numbers; he does not understand the meaning of these actions. He is only capable of performing basic arithmetic operations using manual rather than mental arithmetic.
The child does not know the sequence of arithmetic operations and is not able to solve examples of several operations.
He cannot remember the names of numbers and mathematical terms and does not know what they mean.
The child is unable to write numbers correctly.
Due to impaired visualization ability, the child is able to solve problems only if they have an objective component. He is not able to imagine what is described in the problem.

In general, dyscalculia in children manifests itself as an inability to understand and solve mathematical and logical problems. The child is not able to remember and understand the conditions of the problem and develop an algorithm for solving it. Dyscalculia in schoolchildren is often associated with the fact that they are also unable to correctly calculate their time. All this leads to poor performance at school.

Forms

Depending on the pathogenesis, the following types of this disease are distinguished:

Practognostic. The child is unable to count objects, determine how many there are, or compare the numbers of one and another group.
Verbal. The child makes mistakes when he names numbers, the actions that are performed on them, and geometric figures.
Graphic. The child is unable to write down numbers, symbols of mathematical operations, or draw geometric shapes.
Dyslexic. The child makes mistakes when reading numbers and arithmetic signs in the problem statement.
Operating room. It is difficult for a child to perform mathematical operations with numbers or solve simple or complex examples. A child may experience several groups of symptoms. After determining the type of disease, specialists develop therapy aimed at correcting existing disorders and preventing the development of other types of dyscalculia.

Complications and consequences

The consequences and complications of dyscalculia manifest themselves in the child’s inability to master the school curriculum and refusal to further education. The inability to count is accompanied by a weak ability to master the humanities. As a result, such a person is not able to master any profession and experiences difficulties in life.

Differential diagnosis

The first signs of dyscalculia appear in preschool age, when the child first encounters the need to count, and basic mathematical operations cause him difficulty. If parents have identified such problems in their child, they should contact a speech therapist or child psychologist. Specialists carry out differential diagnosis of the type of disorder, identify its causes and develop a correction method.

For an accurate diagnosis, the child is asked to perform a number of mathematical operations:

count from 10 to 20;
compare numbers with each other;
arrange the proposed numbers in descending or ascending order;
perform basic arithmetic operations on numbers;
name and sort different geometric shapes by color and size.

A child’s ability or inability to perform certain groups of mathematical actions allows us to make a clear diagnosis and determine the type of dyscalculia. Further treatment directly depends on this.

Treatment of dyscalculia

Correction of the disorder is carried out in speech therapy centers, as well as in clinics and specialized treatment centers. Effective correction requires the joint work of a speech therapist, a neurologist and a child psychologist. The therapy uses special computer games for children with dyscalculia and interactive sessions with a specialist.

Therapeutic games for dyscalculia are aimed at teaching the child to count and perform mathematical operations. He is taught to compare objects, sort them according to various characteristics. After the child achieves success in this, you can begin to teach him simple arithmetic operations. At the same time, it is important to ensure that the child understands the logic of the operations performed and the simplest mathematical operations. Then he is taught to decompose a whole object or number into parts and assemble them into a whole.

To correct the disorder, it is very important to develop the child’s literate and rich speech and enrich his vocabulary, including mathematical terms. To begin with, the child must correctly name the numbers and the actions that are performed with them, geometric shapes and their characteristics: color, size. The child is then taught to use the learned words correctly in spoken language. Close attention is paid to written literacy: the ability to correctly write down numbers and mathematical symbols.

In parallel with the correction of the inability to count, it is important to carry out the general development of the child’s mental abilities: the development of abstract logical thinking, visual memory, spatial orientation, the ability to predict, and musical abilities. Children are taught self-control and the ability to evaluate and manage their time.

A number of drugs, for example, B vitamins, glycine, cogitum, cortexin, are used for dyscalculia to improve cerebral circulation and activate higher nervous activity.

Prevention

To prevent violations of the practical-gnostic type, it is recommended to teach children counting skills in preschool age. The child needs to be shown how objects are counted and how simple arithmetic operations are performed. When learning, it is important to pronounce the names of numbers and mathematical operations and accompany this with visualization (show the number of fingers or objects). It is important to develop in a child the ability to correlate a real object and its image. At the same time, the child remembers the names of objects, numbers and arithmetic operations.

To avoid the development of operational dyscalculia, it is important to teach the child the rules of counting and the order of arithmetic operations.

To avoid verbal and dyslexic dyscalculia, it is important to ask the child to pronounce the names of numbers and actions, color, size and shape of geometric figures and objects. At the same time, the parent must control the correct use of certain words and gently correct errors.

To prevent graphic dyscalculia, it is important to develop the child’s visual memory and the ability to recognize and operate with visual images. Fine motor skills and coordination of movements, the ability to calculate hand movements based on visual information, for example, estimate the distance to an object, have time to grab a moving object, are important.

For the prevention of all types of disease, it is important to develop spatial and abstract logical thinking, all types of memory, competent and clear speech, and clear coordination.

This disorder is acquired; acalculia is expressed in a malfunction of the brain. In this case, the patient has difficulty performing simple mathematical tasks, for example, subtraction and addition, multiplication, and comparison of simple numbers are difficult. Acalculia differs from dyscalculia in that it is acquired by the patient during life, as the person receives neurological injuries, and this is especially true for stroke. As for dyscalculia, it occurs in children with impaired brain development during the acquisition of mathematical knowledge. That is, the child is practically deprived of the opportunity to receive such knowledge.

As is known, the ability to count is the integration of several different cognitive skills. A person suffering from acalculia experiences significant difficulties in four areas. The same can be said for people with dyscalculia. One area is understanding what each number is, what it represents, immediately registering that meaning in the mind. Another area to consider is number comparison, that is, understanding a numerical value in relation to another number. The association of the number designation with the name pronounced orally is also important. Basically, acalculia is related to damage to the frontal and parietal lobes and is often an early sign of dementia.

In rare cases, acalculia can be observed as a single disease; most often, the disease is detected as a whole series of diseases. In this case, we can call agnosia, agraphia, and sometimes even aphasia. A person suffering from acalculia, or having dyscalculia, generally lives a full, normal life. They have problems when they have to calculate something in their head.

The basis of this violation is various mechanisms, and the main determining factor is the violation of counting operations. It all depends on where the lesion is located. It is known that if the disorder occurs in the left hemisphere, the occipito-parietal regions are affected, or there is a bilateral focus, then primary acalculia occurs. If the occipital region is affected, the optical image of the number disappears, and the number ceases to be a sign for the patient, reflecting a specific quantity. A person does not recognize numbers well; in his perception they are mixed. This is especially true for those that are close in design, for example, six and nine.

Experts note that such a disorder is optical-gnostic in nature, therefore there is a similarity with optical alexia, or a combination of both is observed. Another type of acalculia is based on an impaired representation of the perception of numbers in space. For example, seeing a multi-digit number, a person can read it as individual numbers. Problems also arise with multi-digit numbers containing the same digits. For example, the numbers one hundred eighty-seven and seven hundred eighty-one may seem the same. In addition, a major difficulty with acalculia is the evaluation and recognition of the elements contained in Roman numerals. Patients are unable to identify the difference, evaluate them incorrectly, or simply confuse them.

When writing Roman numerals, the same errors occur. According to scientists, the basis for this manifestation of acalculia is the presence of general apraktoagnostic disorders, which are typical for the left hemisphere of the parietal lobe.

Features of the types of acalculia

The third type of acalculia deserves special attention. It is related to the violation of counting described above, but at the same time it can also arise in the case when the meaning of simple number symbols is preserved. In this case, the patient loses the ability to perform simple arithmetic operations; it is difficult for him to perform basic mental calculations. The most serious violations are observed if the patient conducts counting operations that go to tens. Also, a person cannot count in columns; operations with fractions are extremely difficult for him.

Secondary acalculia is detected in various forms of aphasia, and is closely related to speech disorders. Treatment of acalculia, primary and secondary, primarily involves eliminating the patient’s underlying disease. The causes of impaired brain activity are always different. These are hemorrhages, traumatic lesions, neoplasms. To choose the right therapy, a consultation with a neuropsychologist is required.

In case of acalculia, corrective action should begin without delay, especially if the problem arose after a stroke or injury. With an early start of rehabilitation training, it is possible to prevent the occurrence of a number of complications and prevent the pathological state of speech symptoms. In particular, this refers to agrammatism, paraphasia, speech embolus. The work of a speech therapist for acalculia can last up to three years.

Disease prevention

To overcome acalculia, a neuropsychologist and speech therapist carry out labor-intensive and lengthy work with the patient. The attending physician must cooperate not only directly with the patient, but also with his relatives. The sooner such treatment is started, the better the prognosis for recovery will be, which is determined by the size of the affected area. In addition, a significant role is played by the patient’s age and the degree of speech disorder. It is known that young patients demonstrate better dynamics. In addition, if the disease occurs at a young age, then a severe disturbance in speech development may subsequently occur, since acalculia is often combined with aphasia.

Preventive measures primarily consist of preventing brain injuries and preventing vascular accidents. If tumors are present, they must be identified immediately. Acalculia can be treated if you address this problem in a timely manner without delaying a visit to a specialist.