Identification and correction of dyscalculia in students with mental retardation.

Symptoms of dyscalculia

The description of dyscalculia cannot be limited to counting disorders.

“Dyscalculia is a complex of violations of understanding the logic of mathematical operations, patterns of transformation of numbers and their relationships, misunderstanding of the conditions of problems.”

Symptoms of dyscalculia can be grouped into the following groups:

Errors in naming numbers.
Memorizing the order of numbers without understanding their meanings.
Difficulty determining the place of a number among other numbers.
Insufficient knowledge of mathematical terminology.
Difficulties in decomposing a number into terms.
Inability to distribute numbers according to a greater or lesser pattern.
Errors in writing numbers.
Performing only basic arithmetic operations, and exclusively by manual counting.
Thought processes are extremely specific, tasks are perceived only in the presence of an objective condition.
Difficulty performing sequential arithmetic operations.
Significant difficulties or complete inability to perform operations with complex numbers.

Characteristic

Acalculia is a disorder of brain function that is manifested by impaired ability to count and perform arithmetic operations, which complicates the process of learning mathematics in childhood and social adaptation in adult patients. The primary form develops as a consequence of damage to the brain of the left hemisphere (in right-handed people) in the temporo-occipital zone, and is characterized by a violation of the understanding of the structure of numbers and their digits.

The patient does not recognize the division of numbers into single-digit, two-digit, three-digit, etc., has difficulty performing arithmetic operations, and cannot distinguish the signs used in arithmetic. Acalculia of the primary form is often combined with a violation of spatial perception - the ability to perceive an object in a three-dimensional projection with an understanding of the shape, size, and relative position of individual objects.

The secondary form develops against the background of damage to the brain substance in different parts of the cortex due to a stroke, the occurrence of a hemorrhage, a tumor or neurodegenerative process, or neuroinfection. The secondary form is often detected in the structure of a general disorder of higher mental functions.

The secondary form is often combined with other neuropsychological symptoms, for example, agnosia (impaired visual, auditory, tactile perception), amnesia (inability to remember past experiences), and a general disorder of mnestic and intellectual activity. There are types of acalculia of nonspecific (secondary) type:

Optical. Develops against the background of damage to the cortex in the occipital region. With this form, gross misunderstanding of numbers is not revealed. The main defects are associated with impaired visual perception of numbers.
Frontal. Develops as a result of damage to the frontal cortex.
Sensory, acoustic-mnestic. Develops as a consequence of damage to the temporo-parietal cortex. Typically, these forms of acalculia are detected in combination with speech disorders (aphasia) and auditory dysfunction.

The frontal cortex occupies a large area and has diverse connections with different parts of the brain. The frontal cortex regulates and controls the mental activity of the individual. Damage to the cortical layer in the forehead area is accompanied by impaired intellectual activity.

In the acoustic-mnestic form, the patient finds it difficult to perform arithmetic tasks by ear. Sensory acalculia is a violation of the ability to count, often caused by underdevelopment of the temporal gyrus, which leads to sensory aphasia caused by dysfunction of phonemic hearing. Patients experience difficulty recognizing and naming arithmetic signs and numbers.

Acalculia and dyscalculia are similar syndromes. The difference lies in the partial inability to perform arithmetic operations with dyscalculia, while with acalculia this function is impaired at the level of the original, fundamental mechanisms. The mechanism of development of dyscalculia is associated with a violation of the coordinated work of brain analyzers that process numerical data.

Causes of dyscalculia

Dyscalculia can be either a consequence of general mental retardation or the result of exposure to various psychotraumatic factors.

Dyscalculia often occurs in children who have had a negative experience in learning to count - they were forced to learn, punished for poor results, the teacher could not find an approach to this child. All this leads to lack of confidence in one’s abilities, isolation, fear, and, as a result, to poor counting.

Possible organic causes of dyscalculia are difficulties in processing visual information, as a result of which the child cannot recognize the conditions of the task and the inability to remember mathematical formulas and patterns according to which problems are solved.

Dyscalculia often occurs in children from asocial families. In such children, all mechanisms for the formation of dyscalculia are involved.

Causes

The syndrome develops as a consequence of damage to different parts of the brain's cortex. Local damage to an area of the medulla is almost always accompanied by deterioration or loss of the ability to perform arithmetic calculations. Partial acalculia often occurs in combination with numerical amnesia or visual agnosia.

The syndrome occurs in the structure of disorders of the mnestic, speech, and acoustic spheres, and arises as a consequence of the inability to verbally reproduce numbers. In this case, if computational functions are impaired, the core of understanding numbers and performing counting operations is not affected. The main factors involved in the pathogenesis of dyscalculia:

A burdened medical history, the presence of diagnoses such as alcoholism, psychopathy, depression.
Damage to the brain substance in the initial stages of ontogenesis (individual development of the organism).
Underdevelopment of brain structures in the postnatal (from the moment of birth) period.
Diseases of the central nervous system (hydrocephalus, infections - poliomyelitis, encephalitis, meningitis, cerebral palsy, hemiplegia, paraplegia - paralysis of the legs and arms in one half of the body, paralysis of only the upper or lower extremities with complete loss of the ability to make voluntary movements).
Perinatal pathologies (birth injuries, fetal asphyxia, prematurity, slow psychomotor development).
Diseases suffered by the mother during gestation (influenza, viral infections, toxicosis in the first and second trimesters).
Psychotraumatic influences in early childhood (abuse, single-parent family, indifference to the child or excessive care).

The causes of primary acalculia are associated with damage to the brain substance of the cortical layer in the parietal or occipito-parietal region, including in the area of the supramarginal gyrus, which lies in the dominant hemisphere. The pathogenesis is based on defects in spatial gnosis (the process of perceptual categorization - the ability to distinguish objects through visual, auditory, tactile perception).

Primary acalculia is the result of dysfunction of the analytical systems, in particular a violation of spatial perception. In the secondary form, mental arithmetic disorder correlates with local or diffuse damage to the cortical layer in the area of the temples, occiput, forehead, crown due to a disturbance in cerebral blood flow, hemorrhage, abscess, or traumatic brain injury.

Diagnosis of dyscalculia

Parents may independently suspect that their child has a disorder such as dyscalculia. Diagnosis of its specific type is made during a personal conversation between a speech therapist, doctor or psychologist and a child. He is asked to count to 10 or 20, choose larger or smaller numbers, do simple arithmetic operations, arrange numbers in increasing and decreasing order, name various geometric shapes, sort them by color. Further, depending on the identified disorders, an assumption is made about the type of dyscalculia and ways of its correction.

Classification of dyscalculia

The most convenient classification of dyscalculia is:

Practognostic – the inability to count objects or their designations.
Graphic – difficulties when writing numbers and mathematical symbols, difficulty or complete impossibility of reproducing geometric shapes.
Verbal – difficulties when it is necessary to name mathematical operations and concepts.
Dyslexic – impairment of reading mathematical symbols.
Operational – inability to perform arithmetic operations.

The described types of dyscalculia are convenient for developing an optimal strategy for its correction and prevention.

Prevention of dyscalculia

Practognostic dyscalculia is prevented by teaching counting skills, performing arithmetic operations with pronouncing them, naming the result and showing the appropriate number of fingers, developing all types of memory and literate speech, spatial perception and motor coordination, learning to correlate a real object and its image.
Prevention of graphic type dyscalculia is possible with the help of exercises to develop the perception of visual images, fine motor skills, coordination between vision and hand movements, training various types of memory, understanding the connection between an object and its image, and teaching mathematical terms.
Verbal dyscalculia is prevented by teaching the child the names of mathematical operations and their essence, the ability to use them correctly in speech, the development of all types of memory, learning to understand the idea of the shape, color, size of objects, and the use of these concepts in speech.
The dyslexic variant of dyscalculia can be prevented by developing the child’s visual perception, his ideas about color, shape, teaching him to recognize mathematical symbols and correctly name them, the meaning of these signs, developing memory and logical thinking.
Operational dyscalculia for prevention requires learning to count, operate with numbers, use mathematical terms in speech and counting, develop speech, memory and thinking, and various types of perception.

Correction of dyscalculia

Most often, a speech therapist deals with the correction of dyscalculia. Also, if necessary, psychologists, pediatricians, and neurologists are involved. Classes can be held in specialized clinics, kindergartens, specialized groups or classes. For correctional classes, special game exercises are developed that teach counting, while simultaneously developing the child’s speech and thinking, his musical, visual, and learning abilities.

The development of coherent, full-fledged speech is an extremely important area of work for dyscalculia. Correction is carried out by expanding the vocabulary of children in parallel with teaching mathematical terms, their meanings and correct use. At the first stage, the concepts of less-more, the same, names of geometric shapes, generalizing the characteristics of objects are introduced. Next comes training in ordinal counting and the use of numbers in speech, comparison of objects and their quantities, a connection is formed between a number and its appearance in writing, the development of various types of memory, fine motor skills, and thinking.

When stable results in counting and comparison are achieved, the teacher moves on to teaching the simplest arithmetic operations, pronouncing and writing them, understanding the meaning of the problem, and the logic of the solution. Children's vocabulary and speech are expanding, and new ways of comparing objects are being taught. The concept of component parts, breaking an object into parts and putting it together from parts is introduced. Children learn to draw numbers and signs on paper. The development of motor skills, drawing skills, memory and speech continues.

Starting regular classes with a specialist in a timely manner will help eliminate the manifestations of dyscalculia in a child and increase his academic performance.

Identification and correction of dyscalculia in students with mental retardation.

Identification and correction of dyscalculia in students with mental retardation

Students with mental retardation often suffer from some form of dyscalculia. The sooner corrective and developmental measures are taken to prevent this pathology, the easier it will be for the child to go through the process of mastering the school curriculum, taking into account individual characteristics.

When initially mastering the general education program, children with dyscalculia problems experience difficulties in mastering the “exact sciences” and often call mathematics their least favorite subject. Chronic underachievement in mathematics also affects mastery of humanities subjects, which reduces educational motivation and can cause a student’s low social status.

Others, parents, teachers, and peers often perceive such a child as lazy, unwilling to perceive simple concepts.

Dyscalculia in children is a specific disorder of the development of school skills, characterized by a decrease in the ability to study arithmetic and other mathematical sciences. It manifests itself as difficulties or a complete inability to understand digital symbols, compare quantities, and perform addition, subtraction, multiplication and division operations. Children later begin to identify geometric shapes and the sizes of objects. Schoolchildren lag behind in mastering academic subjects that require working with numbers and calculations. Dyscalculia may be a separate disorder that does not affect the overall development of intelligence. But more often combined with dysgraphia, dysorthography

The problem of dyskakulia is also caused by social well-being in the family, emotional problems due to pedagogical failure, when “pressure” from loved ones causes self-doubt and fear of being punished. Organic problems: 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, which greatly complicates the correction of this problem.

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), which is especially typical for children with mental retardation.

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.

Dyscalculia 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 with dyscalculia may experience multiple forms of symptoms. 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.

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.

For initial consultation, parents turn to teachers, school psychologists, speech therapists, and a speech pathologist.

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.

The specialist pays attention to living and upbringing conditions, the presence of neurological and mental illnesses in the patient, dyslexia and dyscalculia in the mother or father. The psychologist performs a number of specific tests:

Classification, comparison, counting. To examine older preschoolers, tests are used to directly count to ten, compare the sizes and number of objects, classify objects, and identify geometric shapes. The development of spatial orientation, the ability to retain instructions, and perform step-by-step operations are taken into account.
Arithmetic operations. Younger schoolchildren are asked to complete tests on arranging numbers in descending and ascending order, comparing numbers, solving examples of addition and subtraction, and determining the right and left sides. The complexity of the tests is selected individually, taking into account age.
Recoding information. Middle and high school students solve problems that require translating verbal structures (“more”, “increase by”, “reduction by”) into mathematical schemes. The ability to carry out complex step-by-step operations, apply formulas, and use fractions is assessed.

For the purpose of differential diagnosis, the general level of intelligence, the degree of development of speech and mnestic functions are examined. The data obtained make it possible to distinguish dyscalculia from mental retardation, mental retardation, pedagogical neglect, and delayed speech development. The key diagnostic sign is an isolated decrease in arithmetic skills with relatively normal development of memory, intelligence, attention, emotional and volitional qualities. After the examination, the form of dyscalculia can be accurately determined and work on its correction can begin. It is important to additionally consult a psychoneurologist or neurologist in order to completely correct existing neurological pathologies.

Methods and exercises for correction:

- sorting figures, chips, cereals, transferring them into various containers, accompany all these tasks with speech, to familiarize yourself with mathematical terms (one-many, numbers, shapes, etc.);

-explanation of how to correctly decompose numbers and objects into parts and assemble them into a single whole;

- learn to correctly name numbers, geometric shapes, their characteristics (size, color) and actions performed on them;

- teaching children to count and perform basic mathematical operations, so that the child understands the sequence of banal operations and actions he performs;

- teach your child to correctly use learned terms and words in everyday life, in conversations with relatives, peers, and friends.

— teach how to write numerical values and arithmetic signs correctly.

It is important to use when correcting:

solving problems close to life situations (in a store, in the family, while walking);
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 problem solving with drawings.

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 child. He must learn to independently control his actions and the ability to correctly distribute personal time.

References

1. Dyscalculia in children: prevention and correction of impairments in mastering counting activities / Baryaeva L.B., Kondratyeva S.Yu. – 2013.

2. The concept of dyscalculia: psychophysiological aspects of development (review) / Rysina N.N., Gribanov A.V.// Arctic Evironmental Research. – 2011.

3. Childhood dyscalculia as a systemic learning problem / Ermolova T.V., Ponomareva V.V., Florova N.B. // Modern foreign psychology. – 2020 – T.5, No. 3.

4. Issues of studying the formation of a culture of knowledge of mathematics in the system of preventing dyscalculia in children with severe speech impairment (SSD)/ Kondratyeva S.Yu.// Theory and practice of social development. – 2020. Source: https://www.krasotaimedicina.ru/diseases/children/dyscalculia

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