Identifying difficulties. Diagnostic techniques for identifying learning difficulties. in a student environment. Explanation

Abdullaev Mirguly Mirkerimovich
Job title: Physical education teacher
Educational institution: FGKOU "Secondary comprehensive school № 13"
Locality: n.p. Borzoi, Chechen Republic
Name of material: article
Subject:"Ways to identify and psychologically correct learning difficulties"
Publication date: 25.03.2016
Chapter: secondary education

ABDULLAYEV MIRGULY MIRKERIMOVICH physical education teacher Federal State Government Educational Institution “Secondary School No. 13” (Borzoy settlement, Chechen Republic)
Methods of identification and psychological correction

learning difficulties

Introduction
Psychological causes of school failure and ways to eliminate them as the subject of the course. The study of internal and external factors that determine the occurrence of various kinds of difficulties in learning, and the formation of an alloy psychological knowledge and the skills of their practical use are two interrelated objectives of the course. Psychodiagnostics of learning difficulties as a scientific and practical activity of a school psychologist. The role of fundamental theoretical and psychological knowledge in ensuring the effectiveness of the work of a practical psychologist. Semiotic, technical and causal-logical components of psychodiagnostic activities to identify psychological causes of school failure. School failure and learning difficulties have long been a serious concern for practicing teachers. This problem has become especially acute in recent years, as the number of children with learning difficulties and disabilities has been steadily growing. The peculiarities of education in a modern school are the increasing volume of information, the constant complication of educational programs, which places the highest demands on the child’s body. Nowadays, the school must ensure that every student has the opportunity to succeed in learning. Currently, the public education system is faced with the problem of an increase in the number of difficulties in teaching schoolchildren. According to
2 different sources Today, from 15 to 40% of primary school students in secondary schools experience learning difficulties for one reason or another. The main directions of modernization of education in Russia for the period up to 2010 are characterized by updating and qualitative changes in the content, methods, means, diagnostics, correction and forms of organizing the learning process, new approaches to its design and practical implementation. Learning difficulties are described in many works of domestic and foreign psychologists. According to the findings of scientists (L.S. Vygotsky, V.V. Davydov, A.R. Luria, N.P. Laskalova, L.S. Tsvetkova, M.S. Neimark, L.S. Slavina, A.I. Zakharov, etc.), they note a complex of difficulties in educational activities, acquiring stability, destabilizing the personality and its inner world, giving rise to intrapersonal contradictions between desires and capabilities, the demands of society and one’s own aspirations. In this regard, the teacher’s activities should be focused not only on the transmission of information, but also on the development of higher mental functions of schoolchildren, and early diagnosis and correction of learning difficulties will solve these problems.
Methods for identifying and psychologically correcting learning difficulties
The reasons causing difficulties in mastering the general education program are very diverse and are determined by the structure of the defect of children with disabilities. When choosing a method of helping a child, we must first of all identify the problem and its causes, otherwise our help will be ineffective. The problem of school failure is very relevant today. Many children fall into the category of underachievers from the very beginning of their education and carry the label of laggards for many school years. Difficulties in children’s assimilation of program material have negative consequences that affect the formation of the child’s personality:
3 - reduce his self-esteem; - make him passive, indifferent to learning or negatively disposed towards any learning. Every parent wants their child to grow up to be a prosperous, successful, happy person. The foundation of such well-being is laid precisely during the school years. Therefore, it is very important to understand the reasons for a child’s underachievement and do everything possible to ensure that the school, with its strict requirements, does not lay pitfalls in his future adult life. It is possible to distinguish two main reasons leading to the immaturity of the child’s psyche: - unfavorable living conditions: negative environmental influences, difficult family relationships, poor living conditions, pedagogical neglect; - the specificity of the maturation of the child’s brain, which consists in the uneven development of individual areas of the brain, the presence of deviations in their work. This may be due to the unfavorable course of the intrauterine period of the child's development and pathological childbirth. Subsequently, difficulties arise with certain functions psyche - memory, attention, thinking, speech and related writing and reading. The majority of underperforming schoolchildren have minor impairments, which are referred to as minimal brain dysfunction. Due to their partiality, these deviations do not manifest themselves in any way in preschool childhood, but reveal themselves with the beginning of schooling. Large intellectual loads, a high pace of learning and strict control of results place an enormous burden on the yet undeveloped brain structures that ensure the state of the psyche. There must be a correspondence between the pedagogical requirements for the child and his capabilities, including the capabilities of the psyche and nervous system.
4 Inconsistency leads to learning difficulties. Mental function is never completely disrupted; many components of the child’s psyche always remain intact. Damaged components of mental function can be compensated by fully functioning links within this function and other healthy ones mental processes. Nemov R.S. highlights general scheme classification of methods:  Psychodiagnostic methods based on observation;  Questionnaire psychodiagnostic methods;  Objective psychodiagnostic methods, including recording and analysis of a person’s behavioral reactions and the products of his activity;  Experimental methods of psychodiagnostics. The means available to diagnostics can be divided according to their quality into two groups: - strictly formalized methods, - poorly formalized methods. Strictly formalized methods include: tests; - questionnaires;  methods of projective technique; - psychophysiological techniques. They are characterized by a certain regulation, strict adherence to instructions, and standardization. Tests are standardized, brief and time-limited tests designed to establish quantitative and qualitative individual psychological differences between people. Their distinctive feature is that they consist of tasks to which the subject needs to obtain the correct answer. Questionnaires are a group of psychodiagnostic techniques in which tasks are presented in the form of questions and statements. They are intended
5 to obtain data from the words of the subject. Unlike tests, questionnaires cannot have “right” or “wrong” answers. They only reflect a person’s attitude to certain statements, the extent of his agreement or disagreement. Projective technique techniques are a group of techniques designed to diagnose personality. They are characterized by a more global approach to assessing personality rather than identifying individual traits. The purpose of projective techniques is relatively disguised, which reduces the ability of the subject to give answers that allow him to make the desired impression about himself. Psychophysiological techniques are a special class of psychodiagnostic methods that diagnose the natural characteristics of a person, determined by the basic properties of his nervous system. Less formalized methods include: - observation; - conversations and interviews;  analysis of activity products. These techniques provide valuable information about the subject, especially when the subject of study is mental processes and phenomena that are difficult to objectify. Observation is the purposeful perception of facts, processes or phenomena, which can be direct, carried out using the senses, or indirect, based on information received from various instruments and means of observation, as well as other persons who conducted direct observation. Conversation, interview is a method of collecting primary data based on verbal communication. One of the most common types of conversation is an interview. An interview is a conversation conducted according to a specific plan, which involves direct contact between the interviewer and the respondent.
6 Analysis of products of activity is a quantitative and qualitative analysis of documentary and material sources, which allows us to study the products of human activity. A full-fledged diagnostic examination requires a harmonious combination of these and other techniques. One of the main forms of pedagogical diagnosis of the causes of school difficulties in learning with disabilities in primary school is the analysis of students’ written work. The identified violations of written speech may indicate the state of the general mental and motor development of children. Neuropsychological methods are currently successfully used to diagnose and correct learning difficulties. These methods allow, firstly, to identify the psychophysiological characteristics that underlie difficulties, secondly, to isolate a system of primary preserved links in children’s mental activity, and thirdly, to determine the optimal ways of an individualized approach to them in the learning process. These methods can be productive in working with children with special needs and mental retardation. The picture of disorders in such children is heterogeneous and is not limited to speech symptoms. Most of them have unformed other higher mental functions. A comprehensive neuropsychological examination, covering both speech and non-speech abilities of the child, allows for high-quality functional diagnostics and development of an effective assistance strategy. The technique is of a test nature, the procedure for its implementation and the assessment system are standardized, which makes it possible to visually present the picture of a speech defect and determine the severity of the violation of different aspects of speech, and is also convenient for tracking the dynamics of the child’s speech development and the effectiveness of correctional interventions.
7 The basic principles of a specialist within the humanistic direction are: A meeting of a specialist is a meeting of two equal people; The resolution of the client’s problem occurs “by itself” if the specialist creates a situation of unconditional acceptance that promotes the client’s awareness, expression and self-acceptance of his true feelings; The client is responsible for choosing his own way of thinking and behavior in life. The basic concepts of the humanistic direction are individuation, self-actualization, self-actualizing personality. In a psychological sense, individuation is thought of as a process of a person’s search for spiritual harmony, integration, integrity, and meaningfulness. Awareness of these moments of existence is important for the individual evolution of man. It is assumed that it is through the process of individuation that a person realizes himself as a unique indivisible whole. In A. Adler’s individual psychology, individuation, one of its main facets, comes into contact with the idea he proposes of a person’s unconscious striving for perfection. In humanistic psychology, this desire finds particular embodiment in a person’s desire for the possible identification and development of his personal capabilities, characterized in different subjects by varying degrees of awareness and defined in this direction by the term self-actualization. In his work “self-actualization,” A. Maslow identified eight modes of behavior leading to self-actualization, which include: Full living and selfless experience with full concentration and absorption; Presentation of life as a process of constant choice;
8 The presence of an “I” that can self-actualize; Be honest, take responsibility; Be a nonconformist; Realize your potential; Be open to higher experiences; Expose your own psychopathology. The object of influence in this direction is the formation of personality. The cause of the problem is understood as a blocked intrapersonal resources. The main task of a consultant is to help in self-awareness and personal growth, integration of the holistic “I” and expansion of the space of being. One of the effective methods in this direction is existential analysis, the scheme of which is the study of what a person knows, feels, desires, and the main goal is the affirmation of human freedom. Thus, based on the analyzed material, we can conclude that psychological correction is an activity aimed at correcting those features of psychological development that, according to the accepted system of criteria, do not correspond to the optimal model. In addition, psychocorrection can be used in situations of overcoming various kinds of difficulties, ultimately ensuring the full functioning of the individual. Psychocorrection classes are closely related to the concept of “norm,” which denotes the main goal of psychocorrection as “returning” or “pulling up” the client to the proper level based on his age and individual characteristics. Psychocorrection is planned and carried out by the psychologist himself. Depending on the form of organization of psychological correction, the following types are distinguished: individual, microgroup, group and mixed.
9 The development and construction of psychocorrection programs is based on the following principles: The principle of unity of diagnosis and correction. Diagnostics not only precedes psychological impact, but also serves as a means of monitoring changes in personality, emotional states, behavior, cognitive functions in the process of correctional work, as well as a tool for its assessment. The principle of “Normativity” requires taking into account the basic patterns of mental development, the sequence of successive age stages. Based on this principle, the age norm is taken into account and a prototype of the child’s future development is built. The “top-down” correction principle formulated by L.S. Vygotsky, is determined by the leading role of education for the psychological development of the child. Psychological research into the personality characteristics and interpersonal relationships of a teenager with developmental disabilities should take into account both the specific characteristics of adolescence and the nature of developmental disorders. The main provisions of the psychodynamic direction: Instinctive impulses, their expression, transformation, suppression are of primary importance in the emergence of problems; The development of the problem is due to the struggle between internal impulses and defense mechanisms. The main provisions of the cognitive-behavioral direction are presented as follows: Most behavioral problems are a consequence of problems in training and education; Behavioral reactions are the body’s response to environmental influences and, therefore, are the result of the “organism-environment” interaction;
10 Behavior modeling is an educational and psychotherapeutic process in which the cognitive aspect is decisive. The basic principles of a specialist within the framework of the humanistic direction are: A meeting of a specialist is a meeting of two equal people; The resolution of the client’s problem occurs “by itself” if the specialist creates a situation of unconditional acceptance that promotes the client’s awareness, expression and self-acceptance of his true feelings; Psychological correction is an activity aimed at correcting those features of psychological development that, according to the accepted system of criteria, do not correspond to the optimal model. In addition, psychocorrection can be used in situations of overcoming various kinds of difficulties, ultimately ensuring the full functioning of the individual. Psychocorrection classes are closely related to the concept of “norm,” which denotes the main goal of psychocorrection as “returning” or “pulling up” the client to the proper level based on his age and individual characteristics. The stages of psychocorrectional work include: - conversation; - psychodiagnostics;  formulation of a forecast;  drawing up a correction plan;  evaluation of the program’s effectiveness. Correction methods depend on which school the specialist belongs to, so they can be fairly “conditionally” divided into existing areas in psychology, which will be described in detail below. Psychocorrection is planned and carried out by the psychologist himself. Depending on the form of organization of psychological correction, there are
11 its following types: individual, microgroup, group and mixed. Individual psychocorrection involves working with a client one-on-one in the absence of strangers, in which case confidentiality, intimacy of relationships, and deeper and more effective work are ensured. The microgroup form of correction involves working in groups of 2 people, who, as a rule, have similar developmental problems. The group form of psychocorrection consists in the targeted use of group dynamics, the entire set of relationships and interactions that arise between group members. When solving some problems, for example those arising in the field of communication and interpersonal interactions, participation in psychocorrectional groups is more effective than individual work. The mixed form combines the advantages of individual and group correction and allows for an integrated approach to solving problems. The psychological correction program is drawn up on the basis of psychological recommendations in collaboration between a psychologist and teachers, educators, class teachers or parents, depending on who will further care for the child. Another form of correctional and developmental work is the actual psychological impact, which includes psychocorrection, advisory work and socio-psychological training. The development and construction of psychocorrection programs is based on the following principles: The principle of unity of diagnosis and correction. Diagnostics not only precedes psychological impact, but also serves as a means of monitoring changes in personality, emotional states, behavior,
12 cognitive functions in the process of correctional work, as well as a tool for its assessment. The principle of “Normativity” requires taking into account the basic patterns of mental development, the sequence of successive age stages. Based on this principle, the age norm is taken into account and a prototype of the child’s future development is built. The “top-down” correction principle formulated by L.S. Vygotsky, is determined by the leading role of education for the psychological development of the child. According to this principle, the main content of psychocorrectional work is the creation of a zone of proximal development of the child’s personality and activity, with the aim of actively shaping what should be achieved by the child in the near future in accordance with the requirements of society. The principle of taking into account the individual and personal characteristics of the child determines the need for an individual approach when choosing goals, objectives, methods and programs of psychocorrectional work. The uniqueness of each individual makes it impossible to apply a single template of psychocorrection to all children. The principle of systematicity, first of all, requires taking into account the complex systemic nature of psychological development in ontogenesis, heterochronicity, different times of maturation of various mental functions with accelerated development of some in relation to others. Operating principle. Reliance on leading activity and variation of various types of activity: procedural, productive, educational, labor, joint, communication as a specific form of activity - makes the process of psychocorrection productive and effective, arousing interest in the child, and determines the motivational aspect of psychocorrection.
13 Methods for diagnosing psychological and pedagogical deviations of a child include: observation method, experimental research, experimental psychological techniques.
Conclusion
The means of psychodiagnostic description of the object of psychodiagnostics, which are represented by: 1) classifications of typical deviations at the phenomenological level and classifications of the most probable causes of these deviations, help the school psychologist to connect together the elements of the phenomenological level and the level of causal grounds; 2) schemes of psychological determination of typical deviations and their causes; 3) psychodiagnostic tables. The first two forms of describing the object of psychodiagnostics have been known for quite a long time. They have been developed by specialists since about the 60s. However, each of them has its own shortcomings: the first, describing the behavioral signs of typical shortcomings and deviations in educational activities and behavior, does not fully reflect all the relationships between the elements of the phenomenological level and the level of causal grounds; the other, reflecting the relationships as much as possible, is cumbersome, confusing and immobile when used in the practice of a school psychologist. The third form of description of the object of psychodiagnostics - psychodiagnostic tables - synthesizes the first two forms. They tie together almost all elements of the diagnostic process - from the request to the issuance of recommendations. In this sense, they act as a guiding basis in the activities of a practical psychologist. The availability of psychodiagnostic tables makes them indispensable assistants in the work of teachers primary classes. Currently, various researchers have already begun the development of psychodiagnostic tables as an effective means of working
14 school psychologist. Thus, N.P. Lokalova developed psychodiagnostic tables based on an analysis of psychological and pedagogical literature and conversations with primary school teachers. The principle of constructing the table was to highlight learning difficulties in writing, reading and mathematics. S.V. Vakhrushev compiled his psychodiagnostic tables based on learning difficulties identified and systematized by L.A. Wenger. The main tasks of this direction are the philosophical ideas of existentialism (M. Heidegger, P. Sartre, A. Camus) and phenomenology (E. Hussel, P. Ricoeur). Accordingly, the main emphasis is placed on studying the problem of time, life and death; problems of freedom, responsibility and choice, problems of communication, love and loneliness, searching for the meaning of existence. The specificity of the outlined range of problems is the uniqueness of the personal experience of a particular person, which is not reducible to general patterns, and its center is the solution to the problem of restoring the authenticity of the individual, that is, the correspondence of his existence in the world to his inner nature. Individualism is seen as an integrative whole. In psychology, the direction is represented by such names as K. Rogers, A. Maslow, G. Allport, V. Frankl.
List of sources used
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15 5. Bart K. Learning difficulties: early warning. – M.: Publishing house. Center "Academy", 2011. 6. Basova L. N. Psychological features of mental development of 9th grade students studying in different educational environments. Abstract of diss… cand. psychol. Sci. – M., 2014. 7. Beskina R. M., Chudnovsky V. E. Memories of the future school. – M.: Education, 2013. – P. 29–30. 8. Blonsky P. P. To the question of measures to combat school failure // P. P. Blonsky. Psychology of junior schoolchildren: Selected psychological works / Ed. A. I. Lipkina, T. D. Martsinkovskaya. – M.: Moscow Psychological and Social Institute; Voronezh: NPO “MODEK”, 2014. – pp. 616–620. 9. Bogoyavlenskaya M. Twice exceptional // School psychologist, 2015. – No. 1. – P. 31–33. 10. Vinogradova N.F., Kulikova T.P. Children, adults and the world around. – M.: Education, 2014.P, 60-63. 11. Wenger L. A., Ibatullina A. A. Correlation of learning, mental development and functional characteristics of the maturing brain // Questions of psychology, 2011. – No. 2. – P. 20–27. 12. Vygotsky L. S. Imagination and creativity in childhood: Psychol. essay: Book. for the teacher. – M.: Education, 2011. 13. Vygotsky L. S. The problem of education and mental development at school age // L. S. Vygotsky. Pedagogical psychology/ Ed. V.V. Davydova. – M.: AST, Astrel, Lux, 2015. – P. 400–419. 14. Gamezo M.V., Petrova E.A., Orlova L.M. “Developmental and educational psychology.” – M.: Pedagogical Society of Russia, 2014. – 511 p. 15. Glazer G. D. Comments on articles by V. A. Sukhomlinsky // Anthology of humane pedagogy. V. A. Sukhomlinsky. – M.: Shalva Amonashvili Publishing House, 2012.
16 16. Gutkina N. I. Psychological readiness for school. – M.: Academic Project, 2010.

Sections: Primary School

Introduction.

Relevance. In the last decade, the state of children's health has caused great concern among specialists. The concept of “school maladaptation” has begun to be used in recent years to describe various problems and difficulties that arise in children of different ages in connection with studying at school.

Currently, only 16% of schoolchildren can be considered completely mentally healthy. (S.N. Enikolopov)

The problem of mental health of the population, especially children, is one of the most pressing problems modern Russia. This is due to the fact that mental health disorders have a significant impact on a wide range of indicators of well-being, both for individual citizens and for the entire country.

How to keep your child healthy? How to form a free, proactive personality, whose position is developed independently, without the excessive influence of external assessments? These questions are very relevant for me, a primary school teacher.

Recruiting the next set of first-graders, involuntarily comparing them, I can say that recently there have been more slow, infantile children.

The problem of school failure with an increase in the number of children who cannot cope with the program and already at the beginning of their education fall into the category of underachievers is very, very relevant today. Its solution requires the development and practical application of new approaches to diagnosing the level of mental development of a child, to analyzing the causes of difficulties in educational activities, to correctional and developmental activities.

Every teacher, in the course of his teaching activities, encounters many students who experience difficulties in mastering educational material. And in most cases, to work with low-performing students, the teacher uses the traditional method: he conducts additional classes, consisting mainly of repetition and additional explanation of educational material. But as the experience of many teachers shows, these activities, to which students have a negative attitude and which require a lot of time and effort from both the teacher and the children, do not always give the desired result. At best, they can only lead to temporary positive changes in learning and do not eliminate the real causes of schoolchildren’s difficulties.

Since in a significant number of cases the causes of these difficulties are psychological in nature, effective assistance to students can only be provided in the following ways: psychological approach to analyze and eliminate the difficulties they encountered during the learning process.

Thus, the teacher’s work with schoolchildren who are lagging behind in their studies must be fundamentally changed.

Based on the above, the following hypothesis is put forward:

Hypothesis. The learning process for low-performing children will be more successful if the following conditions are taken into account:

Taking into account the age and individual characteristics of younger schoolchildren.

Collaboration between teachers and parents.

If, in additional classes, low-performing children are offered special tasks with a diagnostic and correctional-developmental focus using the method of kinesiological correction, rather than an educational nature, then it is possible to ensure positive dynamics in the development of these children.

Goal of the work: updating the content of additional classes for low-performing children in the class.

Tasks:

Study scientific and methodological literature on additional classes with low-performing children and determine methods for diagnosing correction and development of children.
Approximate design of the content of additional classes using the kinesiological correction method.
Providing methodological assistance to teachers in developing a program of additional classes.

Research methods. During the study, the following research methods were used:

studying psychological literature on the research problem;
observation of extracurricular activities in the lower grades;
processing the results of psychological and pedagogical research.

The practical significance of the work lies in the fact that practical methods and techniques can be used by primary school teachers in educational work.

Novelty. School teaching methods train and develop mainly the left hemisphere, ignoring half of the student’s mental capabilities, and do not take into account the peculiarities of the sexual lateralization of the hemispheres, remaining asexual and widespread. To overcome existing disorders in children, prevent pathological conditions, and strengthen mental health, it is necessary to carry out comprehensive psychocorrectional work.

One of the components of such work should be kinesiological exercises. Since they improve attention and memory, form spatial concepts, improve fine and gross motor skills, increase the ability of voluntary control and performance, activate intellectual and cognitive processes, and harmonize the functioning of the brain.

The work is intended for primary school teachers, school psychologists, and students of pedagogical universities. It can also be useful for parents.

Chapter 1. Diagnosis and correction of difficulties in teaching primary schoolchildren.

1.1. Knowledge of the basics of intelligence is a condition for successful learning.

Every teacher, in the course of his teaching activities, encounters many students who experience difficulties in mastering educational material. Without identifying the causes of these difficulties, which in a significant number of cases are psychological in nature, effective work to overcome them and, ultimately, improve school performance is impossible.

According to many studies, the success of children's learning depends on the timely development of interhemispheric interaction and the selection of individual methods that take into account the individual profile of functional asymmetry of the hemispheres and gender dichotomies.

By developing hand motor skills, we create the prerequisites for the development of many

mental processes. The works of V. M. Bekhterev, A. N. Leontyev, A. R. Luria, N. S. Leites, P. N. Anokhin, I. M. Sechenov proved the influence of hand manipulations on the functions of higher nervous activity and speech development. Consequently, developmental work should be directed from movement to thinking, and not vice versa.

Younger schoolchildren quickly remember concepts related to movements, underlining, and palpating. For example,

mental counting by touching objects with fingers
underlining the members of a sentence without voicing the name;
learning multiplication tables by touching the knuckles;
memorization vocabulary words with a figurative pattern;

To understand the impact of kinesiological exercises on the human brain, it is necessary to understand the concepts of functional asymmetry of the hemispheres and interhemispheric interaction.

The unity of the brain is determined by a combination of two fundamental properties: interhemispheric specialization and interhemispheric interaction, which is due to the stability of the transfer of information from one hemisphere to the other and dynamic interhemispheric interference inhibition.

Functional asymmetry of the hemispheres is a property of the brain that reflects the difference in the distribution of neuropsychic functions between its right and left hemispheres. The formation and development of this distribution occurs at an early age under the influence of a complex of biological and sociocultural factors. Functional asymmetry of the hemispheres is one of the reasons for the existence of a certain mental structure in humans. Thus, the phenomenon of bilaterality (right and left hemispheres) is associated with a number of such psychological oppositions as concrete-figurative and abstract-logical thinking, convergent and divergent thinking, first and second signaling systems, syntheticity and analyticity, field dependence and field independence, flexibility and rigidity , extroversion and introversion, etc.

Different degrees of expression of these mental properties form a tendency different people to a predominant reliance on the so-called “left-hemisphere” and “right-hemisphere” thinking with their characteristic abilities, emotional and personal characteristics, and typical features of adaptation processes. There is a hypothesis of effective bilateral interaction as the physiological basis of general talent (“equal-hemisphere” thinking).

Psychophysiologists identify 32 types of functional organization of the brain. Simplifying the diagram of the individual profile of functional asymmetry of the hemispheres, three main types of brain organization are distinguished:

Left hemisphere type - dominance of the left hemisphere determines the tendency to abstraction and generalization, the verbal and logical nature of cognitive processes. The left hemisphere operates with words, conventional signs and symbols; responsible for writing, counting, analytical ability, abstract, conceptual, two-dimensional thinking. In this case, information received in the left hemisphere is processed sequentially, linearly and slowly. The perception of left-hemisphere people is discrete, auditory, intelligence is verbal, theoretical, memory is voluntary. Introverts.

For successful learning activities, the following conditions must be met: an abstract linear style of presenting information, analysis of details, repeated repetition of material, silence in the lesson, working alone, timeless tasks, closed-ended questions. They are characterized by a high need for mental activity. For left-hemisphere students, the most significant is the right hemisphere, the combination of colors on the board: dark background and light chalk, classic seating at desks.

Right-hemisphere type - dominance of the right hemisphere determines the tendency to creativity, the concrete-figurative nature of cognitive processes. The right hemisphere of the brain operates with images of real objects, is responsible for orientation in space and easily perceives spatial relationships. It is believed to be responsible for the synthetic activity of the brain. Its functioning determines visual-figurative, three-dimensional thinking, which is associated with a holistic representation of situations and the changes in them that a person wants to obtain as a result of his activities. Right-brain people are distinguished by visual perception, non-verbal, practical intelligence; fast processing of information; involuntary memory. Extroverts. In addition, the ability to draw and perceive the harmony of shapes and colors, an ear for music, artistry, and success in sports are associated with the functioning of the right hemisphere. Conditions necessary for successful educational activities: gestalt, creative contextual tasks, experiments, musical background in the lesson, speech rhythm, work in groups, open-ended questions, synthesis of new material, social significance of the activity, prestige of the position in the team. For better perception of information from the chalkboard, the color combination should be as follows; light board - dark chalk. To organize nonverbal communication of right-hemisphere students in the classroom, they need to be seated in a semicircle.

Equihemispheric type - the absence of pronounced dominance of one of the hemispheres implies their synchronous activity in the choice of thinking strategies. In addition, there is a hypothesis of effective interaction between the right and left hemispheres as the physiological basis of general talent.

However, innate prerequisites are only initial conditions, and asymmetry itself is formed in the process of individual development, under the influence of social contacts, primarily family ones.

Recently, there has been an increase in the number of children with various developmental disorders, learning difficulties, and adaptation difficulties. Traditional methods of psychological and pedagogical influence on a child do not bring sustainable positive results, since they do not eliminate the root cause of the violations. In contrast, the kinesiological correction method is aimed at the mechanism of occurrence of psychophysiological deviations in development, which allows not only to relieve an individual symptom, but also to improve functioning and increase the productivity of mental processes.

The use of this method makes it possible to improve a child’s memory, attention, speech, spatial concepts, fine and gross motor skills, reduce fatigue, and increase the ability of voluntary control.

Classes should be conducted in a friendly environment, since the most effective is emotionally pleasing activity for the child. Classes taking place in a stressful situation do not have an integrated impact. The effectiveness of classes depends on systematic and painstaking work. Every day classes can become more complicated, the volume of tasks can increase, and the pace of completing tasks can increase. There is an expansion of the child’s zone of proximal development and its transition to the zone of actual development.

1.2. Diagnosis of learning difficulties.

It is quite obvious that effective assistance to students can only be provided through a psychological approach to analyzing and eliminating the difficulties they encounter during the learning process.

The development of various methods for identifying the psychological causes of difficulties in learning should contribute to a fundamental change in the content of additional teacher work with students who are lagging behind in their learning. In additional classes, children should be offered special tasks that are not of an educational nature, but have a diagnostic focus at the first stage in order to identify the psychological reasons that cause certain specific difficulties for schoolchildren. At the second stage, based on the principles of unity of diagnosis and correction, these same tasks can be used as a means of psychological correction of identified deficiencies in the psychological development of students.

To carry out such psychodiagnostic activities, the teacher must have a fairly detailed, systematic description of the difficulties that students encounter during the learning process, listing possible reasons, including psychological ones, underlying the difficulties, and indicating methods of psychological diagnosis and elimination of identified deficiencies .

The teacher faces the need to optimize his psychodiagnostic activities as much as possible in order to quickly and effectively help as many schoolchildren as possible. The majority of specialists solve this problem through the use of psychological diagnostic tools in their practice, which include:

means of measuring and assessing the condition of elements;
means of describing the object of psychodiagnostics;
means of describing the psychodiagnostic process (Anufriev A.F. Psychological diagnosis).

The means of measuring and assessing, as well as changing (correcting) the state of the elements of the object of psychodiagnostics are the most developed among all the means of psychological diagnostics. Indeed, a lot of psychological literature has recently been published, which contains specific psychodiagnostic techniques designed for working with children of different ages.

Now educational psychologists can choose for their work any tests and methods, both foreign and domestic, applicable to some specific elements of a child’s mental development or simultaneously exploring a complex of interrelated elements of the object of psychodiagnostics, involving an individual or frontal examination. In addition, a large number of manuals have been published containing correctional and developmental exercises aimed at overcoming developmental disorders in children that lead to learning difficulties. These are tasks for the development of intellectual functions, the personal sphere, and overcoming anxiety and other negative states.

Meanwhile, the multivariance of cause-and-effect relationships quite often leads to the fact that, when figuring out the cause of difficulties in learning, the educational psychologist experiences difficulties in determining the range of possible psychological disorders (causes) and selecting the necessary ones. this moment adequate psychodiagnostic techniques and effective corrective exercises. The means of psychodiagnostic description of the object of psychodiagnostics, which are presented, help the school psychologist to connect together elements of the phenomenological level and the level of causal grounds:

classifications of typical deviations at the phenomenological level and classifications of the most probable causes of these deviations;
schemes of psychological determination of typical deviations and their causes;
psychodiagnostic tables.

The first two forms of describing the object of psychodiagnostics have been known for a long time. They were developed by specialists starting from about the 60s (Zabrodin Yu. M. Problems of developing practical psychology // Psychological Journal, 1980, vol. 1, no. 2). However, each of them has its own shortcomings: the first, describing the behavioral signs of typical shortcomings and deviations in educational activities and behavior, does not fully reflect all the relationships between the elements of the phenomenological level and the level of causal grounds; the other, reflecting the relationships as much as possible, is cumbersome, confusing and immobile when used in practice.

The third form of description of the object of psychodiagnostics - psychodiagnostic tables - synthesizes the first two forms. They tie together almost all elements of the diagnostic process - from the request to the issuance of recommendations. In this sense, they act as an indicative basis in the activities of an educational psychologist.

The accessibility of constructing psychodiagnostic tables makes them indispensable assistants in the work of primary school teachers.

Currently, various researchers have already developed psychodiagnostic tables as effective tools for the work of a school psychologist. So, N. P. Lokalova psychodiagnostic tables were developed based on an analysis of psychological and pedagogical literature and conversations with primary school teachers (N. P. Lokalova, How to help a low-performing student. - 3rd edition, revised and supplemented - M., 2001). The principle of constructing the table was to highlight learning difficulties in writing (Russian), reading and mathematics. S. V. Vakhrushev compiled psychodiagnostic tables based on learning difficulties identified and systematized by L. A. Wenger (Vakhrushev S. V. Psychodiagnostics of learning difficulties by primary school teachers / Dissertation for the degree of Candidate of Psychological Sciences. - M., 1995 ).

Research conducted by the above authors, using these psychodiagnostic tables when making a psychological diagnosis by a psychologist or teacher, showed that:

this is one of the most effective forms of psychodiagnostics for describing an object;
Establishing a psychological diagnosis using diagnostic tables significantly reduces the complexity of making a diagnosis;

In this regard, it is absolutely clear that the development and equipping of a psychologist or teacher with psychodiagnostic tables is a promising direction for improving the quality of diagnostic activities.

1.3. Educational games and exercises as a method of diagnosis and correction.

Orientation modern school on the humanization of the educational process and the diversified development of the child’s personality presupposes, in particular, the need for a harmonious combination of educational activities themselves, within the framework of which basic knowledge, skills and abilities are formed, with creative activities associated with the development of individual inclinations of students, their cognitive activity, and the ability to independently decide non-standard tasks, etc. The active introduction into the traditional educational process of various developmental activities, specifically aimed at the development of the child’s personal-motivational and analytical-synthetic spheres, memory, attention, spatial imagination and a number of other important mental functions, is in this regard one of the most important tasks of teachers.

One of the main motives for using developmental exercises is to increase the creative and search activity of children, which is equally important both for students whose development corresponds to the age norm or is ahead of it, and for schoolchildren with reduced academic performance. In most cases, they are associated precisely with the insufficient development of basic mental functions.

Activities specifically aimed at developing the basic mental functions of children acquire special significance in the educational process of primary school. The reason for this is the psychophysiological characteristics of younger schoolchildren, namely the fact that at the age of 6-10 years, characterized by increased sensitivity, the physiological maturation of the main brain structures proceeds most intensively and is essentially completed. Thus, it is at this stage that the most effective impact on the intellectual and personal spheres of the child is possible, which can, in particular, compensate to a certain extent for mental development delays that are of an inorganic nature.

Another important reason that encourages more active implementation of specific developmental exercises is the possibility of carrying out effective diagnostics of intellectual and personal development children, which is the basis for targeted planning individual work with them. The possibility of such continuous monitoring is due to the fact that educational games and exercises are mostly based on various psychodiagnostic techniques, and, thus, indicators of students’ performance of certain tasks provide direct information about the current level of their development.

And finally, educational games and exercises reduce the stress factor of testing the level of development and allow children with increased anxiety to more fully demonstrate their true capabilities.

As a basis for constructing developmental tasks, you can use the well-known diagnostic and developmental methods of D.B. Elkonin, A.Z. Zak, L.A. Wenger, etc. In Appendix 3, see the classification of educational games and exercises according to the purposes of their influence, developed by N. V. Babkina (Babkina N.V. Educational games with elements of logic. - M, 1998).

1.4. The use of fairy tale therapy in the psychological and pedagogical correction of children.

The position of an underachiever is, first of all, low social status in class. A teacher who gives low grades and makes comments to a student, in the eyes of other children, has a low assessment of him as a person as a whole. Children fully accept the assessment. They consider underachievers not only stupid, but also endowed with other negative qualities, even ugly.

In addition to the fact that a child who is lagging behind in his studies finds himself at a disadvantage at school, he, as a rule, also loses his usual attitude at home. In the family, his low grades become a source of parental irritation, punishment, and increased demands.

And if the child does not receive the help he needs and does not achieve success in learning, albeit relative, his subjective perception of the situation will gradually change. He will begin to realize his inadequacy compared to his well-performing classmates. By the end of primary school, a feeling of inferiority, and even hopelessness, will arise. And as a result - low self-esteem.

Ideas about one’s low learning abilities and the expectation of further failures lead to the child losing the desire to act, to change something, and his own efforts lose meaning for him.

Thus, targeted work is required to develop an attitude to overcome school difficulties and the ability to receive satisfaction from the learning process. Therefore, in additional classes it is necessary to pay serious attention to ways of developing such an attitude in forms that are close and accessible to children - primarily in the form of fairy tales.

Fairytale therapy has recently become a new technology in the psychological and pedagogical correction of children with intellectual disabilities. But at the same time, fairy tale therapy is the most ancient psychological and pedagogical method.

From time immemorial, knowledge about the world, about the philosophy of life, was passed on from mouth to mouth and rewritten; each new generation reread and absorbed it. Today, the term “fairy tale therapy” is associated with this phenomenon, meaning by it methods of transmitting knowledge about spiritual path soul and social realization of man. That is why fairy tale therapy is called an educational system consistent with the spiritual nature of a person.

Research shows that the fairy tale metaphor directly affects the unconscious. Moreover, the impact of metaphors turns out to be profound and surprisingly stable. Metaphorical, fairy-tale influence activates personal resources and leads the child on the path of independent discovery.

Through fairy-tale images, children gain the opportunity to understand their own difficulties, their causes and find ways to overcome them. The situations in which the heroes of fairy tales find themselves are projected onto real school problems, the child gets the opportunity to look at them from the outside and at the same time identify the hero’s problems with his own.

In the appendix, see therapeutic fairy tales (Khukhlaeva O.V. Path to your Self: a program for developing psychological health in primary schoolchildren. - M., 2001).

Listening to a fairy tale and drawing.

One day a small cloud appeared. They named him Little Cloud. Baby lived without knowing adult worries and worries, and carefreely rejoiced at the Hot Sun, the Cheerful Wind, the Laughing Brook, the Talking Forest.

However, despite the fact that everyone loved Little Cloud, he had no real friends, since he was considered still very small and therefore was not taken seriously.

The kid often walked alone in the sky and thought that he was already big and independent, and not small and stupid, as many people think. Moreover, Little Cloud was already helping his Father Cloud with all the housework. Unfortunately, other older Clouds refused to believe this.

One day, Little Cloud, as usual, was walking across the Blue Sky, dreaming of growing up quickly. Other clouds ran past merrily and, laughing merrily, rushed further, towards the Talking Forest darkening in the distance.

“Hey, Baby!” suddenly it was heard very close, “come fly with us! Today all the birds are celebrating a housewarming in the Talking Forest. Let’s have a lot of fun! Don’t lag behind!”

Little Cloud was so confused by surprise that he could not utter a word and froze in place. When he woke up, there was already no trace of the passing clouds. Hanging his head, the Kid trudged home: “Again, I missed the most interesting thing! So I’ll never grow up!”

But suddenly he noticed that there was some strange silence around. Baby

I looked around and saw that some kind of darkness was creeping from the west. A strange hum was approaching with her. The baby froze.

The darkness was approaching, and a terrible tornado was rushing behind it. They were heading straight for the Talking Forest! The kid remembered that there was a holiday going on there now. This means that many people were in danger. The little cloud became scared, and then he heard a Voice inside him: “Are you really a small, stupid cloud? You really wanted to grow up! You have a kind heart, you love to help everyone. You can help now! YOU CAN HELP !"

And the Kid picked up: “Yes, they need my help! AND I WILL HELP THEM!”

He rushed towards the Talking Forest to warn all its inhabitants about the impending disaster and help them escape.

... Meanwhile, turmoil arose in the Talking Forest. Nobody knew what to do, which way to run. Seeing Little Cloud in the sky, everyone shouted: “Baby,” Run home, otherwise you’ll die!”

“No,” answered the Kid calmly. “I see where the Tornado is moving from, and I know where there is a safe place. Everyone can hide there!”

"Then take us there!" - shouted the Wisest Cloud, blocking the roar of the approaching Storm. And everyone flew after the Kid to the high Rock. All the clouds and birds took refuge in her spacious warm cave. The tornado flew past without harming anyone.

In the evening everyone returned to the Talking Forest, and the celebration continued. And now the hero of the holiday was Little Cloud, who from that time began to be called Fearless Cloud. And, of course, he has many friends, and no one considers him small and stupid anymore.

Issues for discussion

Why did the adult clouds stop calling the cloud a baby?
What voice do you think said to Little Cloud “you can help”?
Have you ever had a situation where you said to yourself “I can”?
How did you manage to prove to yourself that you really can?

Chapter 2. Additional classes as a holistic personality correction and development of the cognitive and emotional spheres of low-performing children.

Methodology.

For underachieving children, the emotional side of organizing the correctional and developmental process is an important condition. The teacher, through his behavior and emotional mood, should evoke a positive attitude towards classes in students. The goodwill of an adult is necessary, thanks to which children have a desire to act together and achieve positive results.

The psychological and pedagogical impact is constructed by creating tasks that are dosed in content, volume, complexity, physical, emotional and mental stress.

Materials offered to children should gradually become more complex, taking into account the children's experience. First of all, the following didactic principles are observed here: accessibility, repetition, gradual completion of the task.

Conditions.

Classes are designed for children of primary school age.

Duration of classes is 40-45 minutes.

Classes are held once a week.

Structure of classes.

The structure of the classes is flexible, it includes kinesiological exercises, material that develops the cognitive sphere and therapeutic fairy tales.

The mood of children, their psychological state at specific moments can cause variations in methods, techniques and structure of classes.

The lessons are structured approximately as follows:

I. Warm-up: psychological mood for the lesson, greeting (3 min.)

P. Kinesiological exercises (5 min.)

Correctional and developmental block: tasks for the development of thinking, memory, attention, etc. (15 minutes)

Motor warm-up (physical minute) (5 min.)

Therapeutic tales (15 minutes)

Parting, homework(2 minutes.)

The goal of such classes should be to provide effective, efficient assistance to students with learning difficulties.

expanding the boundaries of students' brain activity;
development of children's mental abilities;
activating the strength of the children themselves, setting them up to overcome life’s difficulties.

Lesson outline.

I. Greetings.

Standing or sitting in a circle, everyone is invited to learn a greeting that needs to be sung rather than spoken:

Good morning, Sasha (smile and nod your head),

Good morning, Masha... (the names of the children are called in a circle), Good morning, Irina Mikhailovna,

Good morning, sun (everyone raises their hands, then lowers them)

Good morning, sky (similar hand movements),

Good morning to all of us (everyone spreads their arms to the sides, then lowers them)!

1. Exercises for the development of interhemispheric interaction. Complex No. 1. "Ring"

Thanks everyone. Please take your seats.

Now, guys, we will learn exercises for our hands, which develop our mind, memory, and attention. You will have to do them every day for 5 minutes.

So, the first exercise “Ring”...

K-2 "Ladder", K-3 "Eight", K-4 "Patting - stroking", K-5 "Palms fist edge"

2. Corrective and developmental block.

1. "Graphic dictation"to develop attention, self-control, accuracy, and graphic skills.

You did great. Now open your notebooks.

Now we will draw patterns.

Let's start drawing the first pattern.

Place the pencil at the highest point. Draw a line: one cell down. Don't lift your pencil from the paper, now one cell to the right. One cell up. One cell to the right. One cell down. One cell to the right. One cell up. Then continue to draw the same pattern yourself."

- "Now place your pencil on the next point. Get ready! Attention! One cell up. One cell to the right. One cell up. One cell to the right. One cell down. One cell to the right. One cell to the right. One cell up. One to the right. And now continue to draw the same pattern yourself."

- "Three cells up. One cell to the right. Two cells down. One cell to the right. Two cells up. One to the right. Three cells down. One cell to the right. Now continue drawing this pattern yourself."

2. “Blind Fly” for the development of attention, self-control, memory, spatial imagination.

Guys, now we will play the game “Blind Fly”. Look at the board, there is a 3x3 playing field lined up: - And this is the “fly”. Before the start of the game, the “fly” is always on the central square of the field (attached to the board).

Now I will tell the path of movement of the “fly”, but without moving it. Your task is to guess which cell it will be on by the end (from 4 to 15 moves). For example: up - right - down - left - down. So where should the "fly" be? (in the lower central cell).

The following commands can be suggested:

Down - left - up - right - up - right (top right cell).

Up - left - down - right - down - left - up - right (on the original cell).

You can invite the children to give commands to the “fly” themselves, while preventing it from flying out of the playing field.

3. “Complete the ninth” to develop attention and logical thinking. - Guys, look at this drawing. One figure is missing here. Draw it in your notebooks. (Choose one below).

Motor warm-up.

4. "Shake it off."

One of the most difficult obstacles to success in life is the memory of our failures and defeats. Therefore, a simple and very pleasant procedure is proposed, during which children can imagine how they are shaking off everything negative, unnecessary and disturbing.

I want to show you how you can easily and simply put yourself in order and get rid of unpleasant feelings. Sometimes we carry large and small burdens within us, which takes a lot of our strength. For example, one of you may have the thought: “I didn’t succeed in drinking. I don’t know how to draw and I’ll never learn how to do it.” Someone else might think: “In the last dictation I made a bunch of mistakes. In the next dictation I will make no less of them again.” And someone may say to themselves: “I’m not very likable. Why would anyone suddenly like me?” Another may think: “Anyway, I’m not as smart as others. Why should I try in vain?”

Surely each of you has seen how a wet dog shakes itself off. She shakes her back and head so hard that all the water splashes to the sides. You can do much the same. Stand so that there is enough space around you. And start brushing off your palms, elbows and shoulders. At the same time, imagine how everything unpleasant - bad feelings, heavy worries and bad thoughts about yourself - flies off you like water from a dog. Then dust off your feet from your toes to your thighs. And then shake your head. It will be even more useful if you make some sounds while doing this... Now shake off your face and listen to how funny your voice changes when your mouth shakes. Imagine that all the unpleasant burden falls off from you, and you become more cheerful and cheerful, as if you were born again. (Only 30-60 seconds).

Work results:

Many years of experience working with low-achieving children shows good results. If previously we only conducted additional classes with children with delayed development, now at the beginning of classes we conduct motor exercises, exercises for the development of interhemispheric connections, learn tables and vocabulary words, terms and grammatical analyzes with motor manipulations and visual basics.

Thus, with constant training with low-achieving children, you can achieve good results in mental development and an average level of learning.

Conclusion.

Jr school age is a stage of significant changes in mental development. Full life for a child of this age period is possible only with the determining and active role of adults (teachers, parents, psychologists), whose main task is to create optimal conditions for the disclosure and realization of the potential capabilities of younger schoolchildren, taking into account the individual characteristics of each child.

Failure to perform well at school often causes children to have a negative attitude toward school and any activity, and creates difficulties in communicating with others, with successful children, and with teachers. All this contributes to the formation of antisocial behavior, especially in adolescence. Therefore, timely prevention and assistance are required at the primary level, which must be fundamentally changed in connection with the orientation of the modern school towards the humanization of the educational process and the comprehensive development of the child’s personality.

Based on the works of famous scientists, psychologists, psychophysiologists, psychotherapists, such as V. M. Bekhterev, A. N. Leontyev, A. R. Luria, I. M. Sechenov, N. V. Babkina, A. L. Sirotyuk, A. F. Anufriev, T. D. Zinkevich-Evstigneeva, O. V. Khukhlaeva, etc., came to the following conclusion:

Taking into account the knowledge of kinesiology (the science of the development of mental abilities and physical health through certain motor exercises), based on the psychodiagnostic and correctional and developmental activities of the teacher, it is possible to update the content of additional classes with low-performing children. The above methods and methods of work can be effective in eliminating learning difficulties and obtaining positive results from working with low-performing children.

When conducting correctional and developmental classes, it is worth listening to the opinion of the English psychologist and psychotherapist R. Burns:

"The care of teachers and parents for children should be reasonable. It would be wrong to support schoolchildren who do not show great academic abilities with the idea that the highest value and the main factor in any personal assessment is only excellent academic performance. Each child has his own strengths sides, his positive qualities, on which a sensitive adult should help him build a solid foundation of positive self-esteem" (Berne R., 1986, p. 260).

Full name 1st grade 1st grade 2nd grade 3rd grade 3rd grade 23. 01. 07 14. 05. 07. 24. 10. 09 07. 05. 10. 09. 10. 08
Andreev Sasha					(H) 12
Buzikov Yura	(H) 13	(P) 18	(H) 9	(H) 12	(H) 13
Gavrilyeva Alena	(B) 25	(B) 27	(X) 24	(B) 28	(X) 22
Gadzhieva Yulia	(B) 25	(B) 27	(B) 25	(B) 30	(X) 24
Dyakonov Arthur					(H) 12
Kutukova Yulia	(X) 20	(X) 22	(P) 18	(P) 18	(X) 20
Nikiforova Luda					(X) 22
Nikonov Alyosha			(B) 26	(X) 22	(P) 15
Pelinkeeva Milena	(P) 15	(X) 20	(B) 25	(B) 30	(B) 30
Petukhov Tolya	(H) 12	(H) 12	(P) 16	(P) 16	(H) 12
Strekalovsky Stepa	(B) 28	(B) 30	(B) 26	(X) 24	(B) 26
Struchkov Nyurgun	(H) 7	(P) 18	(H) 14	(H) 12	(H) 12
Ushnitsky Andrey	(H) 10	(H) 13	(X) 20	(B) 25	(B) 30
Shakhmatova Nastya	(P) 18	(P) 15	(X) 24	(B) 25	(P) 18
Everestov Vanya			(P) 18	(B) 30	(P) 18
Yadrikhinsky Vitaly			(P) 17	(X) 24	(X) 20

Motivation Research

References:

Anufriev A.F., Kostromina S.N. “How to overcome difficulties in teaching children.” Psychodiagnostic tables. Psychodiagnostic techniques. Corrective exercises. - M., 1998;
Babkina N.V. Educational games with elements of logic / systematic course of educational activities. - M., 1998;
Bukatov V.M., Ershova A.P. I’m going to class. M., 2000;
Volkov M.S. Psychology of junior schoolchildren: study. Manual 30th edition, corrected and supplemented - M., 2000;
Zvereva M. V. Studying the effectiveness of training in primary school. M., 2000;
Korsakova N.K., Mikadze Yu.V., Balashova E.Yu. Underachieving children: neuropsychological diagnosis of difficulties in learning in younger schoolchildren. 2nd ed., add. - M., 2001;
Lokalova N.P. How to help a low-performing student. Psychodiagnostic tables: causes and correction of difficulties in teaching primary schoolchildren the Russian language, reading and mathematics. 3rd ed., revised. and supplemented - M., 2001;
Writing and reading: learning difficulties and correction: textbook. village / Under general ed.. Ph.D. ped. Sciences, Associate Professor O. B. Inshakova. - M., 2001
Sirotyuk A. L. Correction of education and development of schoolchildren. M., 2002;
Khukhlaeva O.V. Path to your Self: a program for developing psychological health in primary schoolchildren. M., 2001;
Khukhlaeva O. V. Ladder of joy. M., 1998.

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Identification and correction of difficulties in younger schoolchildren when developing computational skills

Introduction

The formation of computational skills is the most important task of teaching mathematics to junior schoolchildren, the basis of which is the conscious and solid assimilation of oral and written calculation techniques, which is the foundation in the study of mathematics and other academic disciplines. Difficulties in mastering computational techniques lead to further problems when studying a mathematics course. You should pay attention to the requirements for working on arithmetic operations, under which conditions will be created for the successful development of tabular cases of these actions and bringing them to automatism. Insufficient knowledge of tables quite often turns out to be the main obstacle in mastering the techniques of written calculations, which leads to errors in the calculations of tabular addition and multiplication. Knowledge of oral and written calculation techniques will lay the foundation for further study of mathematics.

The formation of computational skills is a long and complex process, the effectiveness of which depends on the individual characteristics of the child, his level of training and methods of organizing computational activities. It is necessary to choose such ways of organizing the computing activities of younger schoolchildren that contribute not only to the formation of strong conscious computational skills, but also to the comprehensive development of the child’s personality.

The problem of developing computing skills in students has always attracted special attention from psychologists, didactics, methodologists, and teachers. In the methodology of teaching mathematics, the studies of E.S. are known. Dubinchuk, A.A. Stolyara, S.S. Minaeva, N.L. Stefanova, Ya.F. Chekmareva, M.A. Bantova, M.I. Moreau, N.B. Istomina, S.E. Tsareva and many other scientists. Despite the fact that the methodology for primary mathematics teaching, which is based on the formation of computational skills, has been developed for a long time, researchers continue to work on improving the methodology for developing computational skills in primary schoolchildren. In a modern elementary school mathematics course, researchers have succeeded in building a computational system, but students still experience difficulties in developing computational skills.

All of the above led to the choice of the research topic “Identification and correction of difficulties in primary schoolchildren in the formation of computing skills.”

The object is the formation of computing skills in junior schoolchildren.

Subject: difficulties and their correction in developing computing skills in younger schoolchildren.

The goal is to identify difficulties in calculations, their causes and ways to correct them when developing computing skills in younger schoolchildren.

Hypothesis - difficulties in calculations among 4th grade students are individual in nature, and therefore require individual correctional work and have the following reasons:

Ignorance of tabular multiplication cases;

Inability to act according to an algorithm;

Difficulties in applying the rule of order of actions in expressions of complex structure.

The purpose and hypothesis of the study determined the need to solve the following problems:

to study the problem of developing computing skills in younger schoolchildren in the theory and practice of teaching;

analyze the system of developing computing skills among junior schoolchildren;

to identify the nature of mistakes of younger schoolchildren when performing calculations, to select methods of individual correctional work.

Methods: theoretical analysis of psychological-pedagogical and methodological-mathematical literature and other sources, conversation, analysis of the products of the activities of junior schoolchildren, pedagogical observation, pedagogical experiment.

Research base: students of class 4 “B” of MBOU “Gymnasium No. 24”, in which 25 people study: 15 boys and 10 girls aged 1011 years.

1. Methodological basics formation of computing skills among junior schoolchildren

1.1 The essence of the concept of skill, computing skill, criteria

In this section, we will consider the definition of the concepts “skill”, “computing skill”, and also reveal the criteria for the formation of a computing skill.

In Soviet encyclopedic dictionary the concept of skill is considered as the ability to perform purposeful actions, which is brought to automatism during repeated conscious repetition of the same actions or solving standard problems in educational activities.

In the explanatory dictionary of S.I. Ozhegova, N.Yu. Shvedova considers the concept of skill as a skill that is developed through exercise or habit.

M.A. Bantova understands computational skill as a high degree of mastery of computational techniques. Acquiring computational skills means knowing which operations should be performed in what order to find the result of an arithmetic operation, and performing these operations quickly enough.

Computational skill has such characteristics as correctness, awareness, rationality, generalization, automaticity and strength. Let's take a closer look at these characteristics.

Correctness means correctly finding the result of an arithmetic operation on given numbers. The student correctly selects and performs the operations that make up the technique.

Awareness manifests itself when the student realizes with the help of what knowledge the operations were selected and the order of operations was established, which is proof of the correctness of the choice of the system of operations. Based on awareness, the student will be able to explain at any time how he solved the example and why it needs to be solved this way. But this does not mean that the student must always explain the solution to each example. In the process of mastering the skill, the explanation should gradually collapse.

Rationality refers to actions in which the student in each specific case chooses a more rational method. The student considers and makes a choice from possible operations that are easier to perform than others, which quickly leads to the result of an arithmetic operation. This quality of skill can be revealed when for a given case there are different methods for finding the result, and the student, using various knowledge, can construct several methods and choose the more rational one. This shows that rationality is directly related to skill awareness.

Generalization appears when the student can apply the calculation technique to a large number of cases. The student is able to transfer the calculation technique to new cases. Generality, just like rationality, is closely related to the awareness of a computational skill, since a technique based on the same theoretical principles will be common to different cases of computation.

Automaticity is also understood as convolution. With automaticity, the student selects and performs operations at a fast pace and uses a collapsed view, but can always return to the explanation of the choice of system of operations.

Durability is characterized by the retention of computational skills in memory for a long time. The student correctly uses developed computational skills over a long period of time.

Thus, a skill is a skill that has been brought to automaticity. Computational skill is a high degree of ability to master calculation techniques. Computational skill is characterized by a number of criteria, the main of which are awareness, correctness, generalization, rationality, automaticity and strength, which indicates the level of development of computational skill.

1.2 System of computing techniques and computing skills at school

Computational skill is understood as high degree mastering computational techniques. A computational technique is a system of operations, the sequential execution of which leads to the result of the required arithmetic operation. The choice of operations in each computational technique is determined by the theoretical principles that are embedded and used in its theoretical basis.

Let's consider the classification of computational techniques according to M.A. Bantova, the basis of which is the theoretical basis of the computational technique.

1. Techniques whose theoretical basis is the specific meaning of arithmetic operations.

These include such computational techniques as methods of addition and subtraction within 10 for cases of the form a 2, a, a, methods of tabular addition and subtraction with passing through a ten within 20, methods of finding tabular results of multiplication and division (only at the initial stage), and the method of division with a remainder, the method of multiplying one and zero.

These calculation techniques are the first. They are introduced immediately after students are familiarized with the specific meaning of arithmetic operations. Computational techniques provide an opportunity to master the specific meaning of arithmetic operations, since they require its application. Also, the first computational techniques prepare students to master the properties of arithmetic operations. Some techniques contain properties of arithmetic operations, but these properties are not clearly revealed to students. The named techniques are introduced on the basis of performing operations on sets.

2. Techniques whose theoretical basis are the properties of arithmetic operations.

This group of computational techniques includes such techniques as addition and subtraction techniques for cases of the form 28, 5420, 273, 406, 45, 5023, 67.7418; similar computational techniques for cases of addition and subtraction of numbers greater than 100, as well as techniques for written addition and subtraction; methods of multiplication and division for cases of the form 145, 514, 813, 1840, 180: 20; similar techniques for multiplication and division for numbers greater than 100 and techniques for written multiplication and division.

When introducing computational techniques based on the properties of arithmetic operations, it is advisable to follow the following steps: first, the properties corresponding to the techniques are studied, then, based on them, computational techniques are introduced.

3. Techniques whose theoretical basis is the connection between the components and the result of arithmetic operations.

This group of computational techniques includes techniques for cases of the form 9-7, 21:3, 60:20, 54:18, 9:1, 0:6.

When introducing techniques, the connections between the components and the result of the corresponding arithmetic operation are first considered, and then a computational technique is introduced on this basis.

4. Techniques whose theoretical basis is a change in the results of arithmetic operations depending on a change in one of the components.

This group of computational techniques includes techniques such as rounding when performing addition and subtraction of numbers, for example, 46+19, 512 - 298, as well as techniques for multiplying and dividing by 5, 25, 50.

When introducing these computational techniques, it is necessary to first study the corresponding dependencies.

5. Techniques that have a theoretical basis are issues of numbering numbers.

This group of computational techniques includes such techniques for cases of the form a1, 10+6, 1610, 166, 5710, 1200:100; similar techniques for large numbers.

These techniques are introduced after studying the relevant issues of numbering (natural sequence, decimal composition of numbers, positional principle of writing numbers).

6. Techniques whose theoretical basis is rules.

This group of computational techniques includes techniques for two cases: a1, a 0. Since the rules for multiplying numbers by one and zero are consequences from the definition of the action of multiplying non-negative integers, they are simply communicated to students and calculations are performed in accordance with them.

Depending on the choice of the theoretical basis of the technique, a technique is selected in solving the case of the form 46+19 (the possibility of choosing either the fourth group or the second).

A computational technique is built on one or another theoretical basis, and students are aware of the fact of using the relevant theoretical principles that underlie computational techniques, which is a prerequisite for students to master conscious computational skills. The commonality of approaches to revealing the computational techniques of each group is the key to students mastering generalized computational skills. The ability to use different theoretical positions when constructing different techniques for one case of calculation, for example, for the case of addition 46+19, is a prerequisite for the formation of rational flexible computing skills.

The order of introduction of computational techniques is due to the gradual introduction of techniques that include a large number of operations, and previously learned techniques are included as basic operations in new techniques. With such a system, favorable conditions are created for students to develop strong and automated skills.

The methodology for teaching primary schoolchildren oral and written calculations has been most fully and thoroughly studied and presented in the works of N.A. Menchinskaya and M.I. Moro. Basic techniques of oral and written calculations that students must master primary school students are based on the properties of numbers in the decimal number system and the properties of arithmetic operations.

When studying the numbers of the first ten, students become familiar with the formation of numbers by adding one to the number. Addition and subtraction within ten are studied using visual aids.

When studying the topic “The Second Ten,” children master the basic techniques of oral and written calculations (representing a number as a sum of digit units, methods of addition and subtraction without and with transition through a ten). Knowledge of these principles will help students consciously use computational techniques and will also serve as preparation for further consideration of the properties of arithmetic operations. At this stage, knowledge of the connection between multiplication and addition is acquired (multiplication as the addition of equal terms), cases of subtraction when the remainder is zero, the case of multiplication by 1, etc.

At the Sotnya Concentration, work continues to develop and improve mental calculation skills. It is necessary to apply the solution method using visual aids and use verbal explanations. Students easily recognize the similarities between addition (and subtraction) within 20 and within 100. When multiplying and dividing within 100, students learn the corresponding tables and find out what relationships exist between the actions in question, learning to apply this knowledge when compiling the corresponding tables. Students freely use the commutative and combinational property, as well as the distributive property of multiplication relative to addition, etc.

Teaching written calculations leads to students understanding the meaning of those operations that are performed in each specific case.

Thus, the assimilation and formation of computational skills occurs through the development of oral and written calculations. Knowledge of computational techniques is the basis for conscious mastery of computational skills.

1.3 Methodology for developing computing skills in junior schoolchildren

Let's consider the methodology for developing computing skills in junior schoolchildren, developed by M.A. Bantova. In accordance with the approach under consideration, the formation of full-fledged computational skills (having such qualities as correctness, awareness, rationality, generalization, automaticity and strength) is ensured by the construction of an initial mathematics course and the use of appropriate methodological techniques.

To develop conscious, generalized and rational skills, the initial mathematics course is structured in such a way that students master a computational technique after they have mastered the material, which is the theoretical basis of the computational technique. For example, first students learn the property of multiplying a sum by a number, and then this property becomes the theoretical basis for the technique of non-tabular multiplication. Let's consider the multiplication of the numbers 15 and 6, in which the system of operations that make up the computational technique can be traced: 1) we replace the number 15 with the sum of the digit terms 10 and 5; 2) multiply the term 10 by 6, we get 60; 3) multiply the term 5 by 6, we get 30; 4) we add the resulting products of 60 and 30, we get 90. In this example, the property of multiplying a sum by a number is used, which determined the choice of all operations. This proves that the basis for the technique of extra-tabular multiplication is the property of multiplying a sum by a number, or that the property of multiplying a sum by a number is the theoretical basis for the reception of extra-tabular multiplication. This example shows that students apply knowledge not only based on the property of multiplying a sum by a number, but also use other knowledge. Previously developed computational skills are also used: students apply knowledge of the decimal composition of numbers (replacing a number with the sum of digit terms), table multiplication skills and multiplication of the number 10 by single-digit numbers, and skills in adding two-digit numbers. The choice of this knowledge and skills is determined by the application of the property of multiplying a sum by a number.

The techniques are combined into groups in accordance with their general theoretical basis, provided for by the current mathematics program for primary grades, which makes it possible to use general approaches in the methodology for developing relevant skills.

In the course of developing computational skills, work on each individual technique can be developed in a number of stages identified by M.A. Bantova. The following stages are considered: preparation for the introduction of a new technique, familiarization with a computational technique, consolidation of knowledge of a technique and development of a computational skill. Let us present their more detailed characteristics.

At this stage of preparation for the introduction of a new technique, conditions are created for readiness to master a computational technique. Students need to master the theoretical principles that are the basis of a computational technique, and students also master each operation that makes up the technique. To ensure preparation for the introduction of the technique, it is necessary to analyze the technique and determine what knowledge students should master and what computing skills students should already master. For example, students are prepared to perceive the computational technique for cases a2 if they are familiar with the specific meaning of the operations of addition and subtraction, know the composition of the number 2, and have mastered the computational skills of addition and subtraction for cases of type a1. The central link in preparing for the introduction of a new technique is the students’ mastery of the basic operations that will be included in the new technique.

At the stage of familiarization with a computational technique, students learn its essence: what operations must be performed, in what order, and why this is how the result of an arithmetic operation can be found. When a computational technique is introduced, it is necessary to use visualization. For techniques whose theoretical basis is the specific meaning of arithmetic operations, this is operating with sets. Let's look at an example: adding the number 2 to 7, the teacher (students) moves 2 squares (circles, rectangles) one at a time to 7 squares (circles, rectangles). When familiarizing yourself with techniques whose theoretical basis is the properties of arithmetic operations, for clarity, you can use a detailed recording of all operations, which has a positive effect on mastering the technique. For example, when introducing the technique of extra-tabular multiplication, the following entry is made: 145= (10+4)5=105+45=70.

It is important to accompany each operation with explanations out loud. First, students explain them under the guidance of the teacher, then independently. When explaining, it is indicated which operations are performed, in what order, and the result of each of them is called, while previously studied techniques that are included as intermediate (non-main) operations in the example under consideration are not explained. For example, a student adds the number 3 to 6, while explaining the operations: add 1 to six, you get 7; I add 1 to seven, I get 8, I add 1 to eight, I get 9 (how to add 1 is not explained). Explanation of the choice and execution of operations leads to an understanding of the essence of each operation and the entire technique as a whole, which in the future will become the basis for students to master conscious computational skills. When studying addition and subtraction within 100, students can be asked to follow the following plan in their calculations: replace one of the numbers with the sum of convenient terms, name what example you get, and solve this example in a convenient way. The ability to use such a plan leads to the fact that students themselves find various computational techniques even for new cases, and this is a prerequisite for the formation of rational skills and at the same time a manifestation of awareness and generalization of computational skills.

At the stage of consolidating knowledge of a technique and developing a computational skill, students must firmly grasp the system of operations that make up the technique and perform these operations as quickly as possible, that is, master a computational skill.

Let's look at a number of stages in developing students' computing skills. The stages are distinguished: consolidation of knowledge of the technique, partial curtailment of the execution of operations, complete curtailment of the execution of operations, extreme curtailment of the execution of operations.

At the stage of consolidating the knowledge of the technique, students independently perform all the operations that are part of the technique, comment on the implementation of each of them out loud and at the same time make a detailed recording, if it was provided for at the previous stage.

The second stage is a partial curtailment of operations. At this stage, students mentally identify operations in a computational technique and base the choice and order of their execution. Students speak out loud only when performing basic operations (intermediate calculations). Speaking out loud helps to highlight and emphasize the main operations, and performing auxiliary operations silently helps to reduce them (quick execution in terms of internal speech).

The third stage is the complete curtailment of operations. At this stage, students silently perform and highlight all operations (here the main operations are collapsed). Students perform intermediate calculations (basic operations) silently, then name and write down the final result. Updating basic operations and performing them in a compressed plan is the actual computing skill.

The fourth stage is the ultimate reduction in the execution of operations. At this stage, students perform all operations in a collapsed plan extremely quickly (they master computational skills). Mastery of computational skills is achieved by performing a sufficient number of training exercises.

At all stages of the formation of a computational skill, exercises on the use of computational techniques play a decisive role, but the content of the exercises must be subordinate to the goals at the appropriate stages. Exercises should be varied in number and form, and exercises should be offered to compare techniques that are similar in some respects.

In the Zankov system L.V. In developmental education, there are two ways to develop computational skills: direct and indirect. Let's look at them in more detail. The direct path is reproductive. When using it, it is assumed that the sample will be communicated to students during subsequent multiple repetitions. Students memorize the algorithm for performing operations. The indirect path is productive. Here it is assumed that students will independently search for the algorithm.

In the Zankov system L.V. There are three stages (stages) in the formation of computing skills.

At the first stage, students understand the basic principles that underlie the execution of operations and the creation of an algorithm for performing operations. Students' reasoning is translated out loud into a recording using mathematical symbols, and a detailed recording of the execution of operations is also used.

At the second stage, students develop the correct performance of operations with the help of tasks, while students are in an active creative search, which will lead to changes in the components of operations.

At the third stage, students will be able to achieve a high rate of execution of operations, which leads to interest in calculations.

Thus, with the correct identification of stages, the teacher will be able to control the process of students mastering computational techniques, gradually winding down operations, and developing computational skills.

1.4 Typical difficulties

Formation of methods of oral and written calculations is one of the most important tasks in teaching mathematics to primary schoolchildren. Big number errors made by students when solving problems and equations indicate that the developed computational skills and abilities are not strong and conscious. Students make most of the errors in written calculations with large numbers not because they do not know the methods of calculation, but because they cease to keep their attention on the process of calculation itself.

ON THE. Menchinskaya and M.I. Moreau studied the causes of errors and divided them into two groups: errors in the conditions of performing a given operation or as the assimilation of arithmetic knowledge. Errors caused by operating conditions are “mechanical” errors. These errors occur under certain circumstances: fatigue, loss of interest, excitement, distraction, which leads to a weakening of students’ conscious control during calculations, but this does not indicate ignorance or insufficient mastery of the arithmetic operation. Errors such as slips of the tongue and slips are identified; “perseverative” errors (a number is obsessively retained in consciousness, for example, 43+7=70), as well as performing actions that do not correspond to the sign. These mechanical errors are varied and difficult to explain.

The weakening of conscious control due to fatigue is manifested in written calculations: an increase in errors is observed as one moves from lower to higher ranks. A lot of numbers and an abundance of operations on them quickly tires and distracts students' attention.

The second group of errors is associated with insufficient mastery of computing skills. If the calculation skill is based on memorizing certain numerical results and if it is not sufficiently consolidated, then the erroneous answer can be different, and sometimes it can alternate with the correct answer. For example, in case 78, one student had three different answers: 54,56,58.

Skill related errors are based on general rule. The nature of the error is determined in this case by the nature of the assimilation of the rule, the degree of generalization of the rule in accordance with which the operation is performed.

A special group of errors includes errors caused by habit (habitual action, habitual generalization).

Methods of dealing with errors can be used to deal with “mechanical errors”: methods of increasing attention to arithmetic exercises, mobilizing attention, and increasing a sense of responsibility.

When errors occur based on a false understanding of the rule, you need to analyze the error and show the student how it arose. We must strive to ensure that the student realizes the mistake. If an error occurs as a result of insufficient consolidation of a skill (78 = 54), you need to give additional exercise in a poorly consolidated skill, which is effective method to avoid further mistakes.

Let us give a description of the groups of errors identified by M.A. Bantova at the Ten Center.

1. Mixing the action of addition and subtraction (5+2=3, 7-3=10). Errors occur if students do not understand the operations of subtraction and addition or the actions of these signs. The reason may be insufficient analysis of the solved example: students pay more attention to numbers rather than signs.

2. The student gets a result that is one less or more than the correct one (5+3=9, 6-2=5). Such errors occur when counting or counting numbers by one based on the natural series.

3. Obtaining an incorrect result due to the use of irrational techniques. For example, 2+5 uses the method of counting by one, instead of the method of rearranging the terms. This is a difficult trick in this example because Students often forget how much they have already added and how much remains to be added.

4. Name or record in place of the result of one of the components (3+4=4, 5-2=5). IN in this case Students make mistakes due to inattention. It is important to estimate the result to avoid mistakes.

5. The student received a false result due to mixing of numbers. Let's look at the student's entry: 4+3=8. The expression is performed incorrectly, although the correct answer is given when counting verbally. When eliminating errors, individual work is needed, where the student will remember the numbers.

1. The student mixes subtraction techniques, which are based on the properties of subtracting a number into sums and sums from a number. For example, 40-26=40-(20+6)=(40-20)+6=16. To prevent the occurrence of such errors, you need to select similar examples. While solving them, they will compare each step.

2. Performing addition and subtraction on numbers of different digits, as with numbers of the same digit. For example, a student makes a mistake when adding the number of tens to the number of ones (56+4 = 96). To prevent mistakes, it is necessary to discuss incorrect decisions. The teacher can offer examples to students that are solved incorrectly and ask them to find the errors.

3. Errors made in tabular cases of subtraction and addition, included as operations in more complex examples for subtraction and addition. For example, 27+18=46. To prevent mistakes, it is necessary to pay attention to students’ mastery of addition and subtraction tables, especially in cases involving passing through ten.

4. Errors in which an incorrect result is obtained due to skipping operations that are included in the procedure, as well as when the student performs unnecessary operations. For example, 55+30=88, 43-10=30. Students make mistakes due to inattention. To eliminate them, you need to check the solutions of the examples.

5. Mixing the actions of subtraction and addition. For example, 36+20=16. The student makes a mistake due to inattention. To eliminate them, you need to check the solutions of the examples.

Let us describe the groups of errors in the “Hundred” concentration when performing multiplication and division.

1. Identification of errors as a result of finding multiplication by addition.

A) Errors made during the calculation of the sum of identical terms: 39=28. The student, isolating the sum of several terms, made an error in addition.

B) Errors made when setting the number of terms: 76=35. The student found the sum of not six, but five terms, each of which is 7.

C) Errors made due to misunderstanding of the meaning of the multiplication component: 69=51. The student took the number 6 as an addend 10 times to get 60, and then subtracted the number 9 from 60, not 6.

2. Errors caused by difficulties in memorizing multiplication results. Difficult cases:

A) products of numbers greater than five: 67, 68, 77, etc.

B) products with equal values: 29 and 36

C) products whose values are close in the natural series: 69=54

To prevent mistakes in difficult cases, it is necessary to include these cases in oral exercises and written work.

3. The operations of division and multiplication are mixed (63=2, 9:3=27). Errors arise due to the inattention of students. To eliminate them, you need to check the solutions of the examples.

4. Mixing cases of division and multiplication with numbers 1 and 0, for example, 50=5, 0:4=4, 21=0. To prevent errors, an exercise to compare mixed cases will help.

5. Mixing the techniques of off-tabular division and multiplication with the technique of addition. For example, 473=77, 36:3=16. To eliminate errors, it is necessary to use examples 164 and 16+4 in comparison.

6. Mixing methods of extra-tabular division, for example, 66:33=22. To prevent errors, it is necessary to propose solving the examples 66:33 and 66:3 simultaneously, and then compare the examples themselves and the methods for calculating them. It is useful to discuss incorrectly solved examples and consider the mistake made.

7. Students make mistakes in tabular cases of division and multiplication, which are included in cases of off-tabular division and multiplication. For example, 193=(10+9)3=103+93=30+24=54. To eliminate such errors, individual work with students who made a mistake is necessary.

8. Errors when dividing with a remainder, caused by incorrectly entering the number that is being divided by the divisor. For example: 65:7= 8 (remaining 9). The student divided by 7 not 65, but 56, so he received the wrong quotient and a remainder that is greater than the divisor.

Let's list the groups of errors in the Thousand. Multi-digit numbers" when performing addition and subtraction.

1. Errors caused by incorrect recording of examples when writing addition and subtraction. For example: when adding a column 546+43=978.

2. Errors when performing written addition, caused by forgetting the units of one or another category that needed to be remembered, and when subtracting - the units that were occupied. For example, 539+225=754, 692-427=275. To eliminate such errors, it is necessary to solve similar examples.

3. Errors in oral addition and subtraction of numbers greater than one hundred (540300, 1600800).

Let's imagine groups of errors in the “Thousand” concentration. Multi-digit numbers" when performing multiplication and division.

1. Errors in written multiplication by two-digit and three-digit numbers due to incorrect recording of incomplete products: 56432 = 2820. Incorrect recording of multiplication, the second product must be written under tens. To avoid mistakes, it is necessary to ask students for an explanation of the solution to the example.

2. Errors in selecting quotient numbers for written division

A) Obtaining extra digits in a quotient. For example, 1508: 26 = 418. The student divided not 130 tens by 26, but 104 tens, as a result of which he received a remainder of 46, which can be divided by the divisor, which he did, receiving an extra digit in the quotient. To prevent mistakes, it is necessary that students begin division by establishing the number of digits of the quotient; this will be the estimate of the results.

B) Omitting the number zero in the quotient. For example, 30444:43=78. To prevent mistakes, it is necessary that students begin division by establishing the number of digits of the quotient; this will be the estimate of the results.

3. Errors caused by mixing oral techniques for multiplying by two-digit digit and non-digit numbers. For example: 3420=408 (34 multiplied by 2, then 34 multiplied by 10 and added the resulting products 68 and 340). The ability to check a solution by estimating the result and relying on the connection between the components and the result of multiplication will help students identify the error.

4. Errors caused by mixing oral techniques of dividing by digit numbers and multiplying by two-digit non-digit numbers. For example, 420:70=102. The student, by analogy with multiplication by a two-digit non-digit number, performed the division as follows: he divided 120 by 10, then divided 420 by 7 and added the resulting results 42 and 60. To prevent such errors, it is necessary to compare the techniques for the corresponding cases of division and multiplication (420:70 and 4217) and establish the differences (when dividing by two-digit digit numbers, we divide by the product, and when multiplying by two-digit non-digit numbers, we multiply by the sum). It is also useful to analyze examples with errors. schoolboy computing learning

5. Errors in written multiplication and division in tabular cases of multiplication and division. Such errors arise as a result of inattention, or due to poor knowledge of the multiplication table. To eliminate such errors, it is necessary to carry out individual work, memorize the multiplication table, and include cases of multiplication and division in oral exercises.

6. Errors due to the inattention of students: skipping individual operations (7200:9=8, 90007=63), mixing arithmetic operations (320:80=25600). To eliminate errors, it is necessary to analyze examples before solving them, and check the solutions to the examples.

Thus, a number of methodological techniques can be identified to prevent errors in students’ calculations:

1. To prevent mixing of computational techniques, they should be compared under the guidance of a teacher, identifying significant differences in the mixed techniques.

2. To prevent confusion of arithmetic operations, it is necessary to teach students to analyze the expressions themselves and their meanings.

3. Prevention and elimination of errors is helped by discussing incorrect decisions with students, as a result of which the cause of errors is identified.

4. To identify errors and eliminate them by the students themselves, it is necessary to teach children to check calculations in appropriate ways and constantly cultivate this habit in them.

Thus, it can be revealed that the places where students make mistakes are difficult and to prevent them it is necessary to work through them independently, analyzing them with the teacher using similar examples. Grouping errors by concentration helps to navigate in case of an error and select the necessary techniques to prevent students from making mistakes in future work.

2. Experimental work to identify and correct difficulties in younger schoolchildren when developing computational skills

2.1 Identification of difficulties among younger schoolchildren in developing computational skills

This paragraph presents an empirical study with the aim of identifying difficulties among primary schoolchildren in developing computational skills in an experimental class.

The study was conducted on the basis of the municipal budget educational institution municipality"City of Arkhangelsk" "Gymnasium No. 24". The study involved students of grade 4 “B”, which has 25 students: 15 boys and 10 girls, students aged 10-11 years. The class was formed in 2012. It employs a teacher with higher education.

The school has created optimal conditions for the development of students. The environment at school is favorable, teachers try to help students. Students are active in the learning process, and discussions often arise between students during lessons.

Most students cope with learning tasks and have developed cognitive interest. Students complete the amount of mathematics material assigned for study and complete calculation tasks correctly. Children actively take part in school activities; many students go to clubs and sections.

During a conversation with class teacher and personal observations, it turned out that the children interact well with each other when solving any problems, participating in a school event where they need to unite and win. Students are ready to help a classmate and support each other. Parents make a great contribution to the life of the class and invite the teacher to visit various educational and cultural institutions.

25 students from the experimental class took part in the study. Most children successfully cope with independent and test work in mathematics. At the same time, an analysis of the work of 9 people showed that students make mistakes when performing tasks in calculations, and corrective work is necessary with them.

Difficulties among younger schoolchildren in developing computational skills were identified during the analysis of several control and independent work in mathematics, which included calculation tasks. The purpose of checking the proposed tests and independent works in mathematics was to collect information reflecting the difficulties of students in developing computational skills in junior schoolchildren of the experimental class in mathematics lessons, for further correctional work. It should be noted that the collection of empirical material was carried out while checking the work done in class. When checking students' homework, no errors were identified, since many children's errors were corrected at home under the supervision of their parents.

Based on the results of the analysis of tests and independent works in mathematics, various types of errors were identified in primary schoolchildren. Let us present their description and analysis.

1) Error due to incorrect entry during calculations

The original photograph shown shows that the student recorded the calculation incorrectly, but did not make a mistake. The student did not complete the work rationally.

In the first case, the student made an error in the calculations due to inaccurate recording of the second incomplete product, which resulted in an incorrect answer in the expression.

In the second case, the student made an error due to incorrect notation when calculating the second incomplete product (he wrote down the number 8 at the end), but then added it incorrectly (without calculating, he wrote down the correct answer).

On last photo it is clear that the student incorrectly calculated two incomplete products and unconsciously consistently multiplied a four-digit number by a single-digit number. The answer received is seriously different from the correct one in terms of the number of digits received.

2) Error in finding an incomplete product (addition with transition through the digit)

In the first case, the student made a mistake when finding the second incomplete product. When multiplying the number 438 by 6, I correctly found the product of 38 by 6 (hundreds), but “remembered” not 2, but 1 to find tens of thousands. It can be assumed that this error is associated with the difficulty of switching attention. In fact, by multiplying 3 by 6, the student got 18, then added 4 to the result (4 tens from multiplying 8 by 6) and got 22, but “remembered” 1, not 2, focusing on the number 18.

In the second case, the student made a mistake when calculating the second incomplete product. When multiplying the number 324 by 7, he correctly found the product of 24 by 7 (hundreds), but when multiplying 3 by 7, he got 28 and added 1, which he “remembered” when finding tens of thousands. The student found it difficult to calculate 3 7, which led to an error in the calculation and the final result.

In the third case, the student made a mistake in calculating the first incomplete product, multiplying the number 6096 by 6, correctly performed the calculation of 96 by 6, but when multiplying 6 by 6, multiplied not by 6, but by 4 (not by tens, but by hundreds) .

3) Errors associated with the application of rules for the order of actions in expressions of complex structure

The student incorrectly determined the order of actions. We can assume that the student reasoned like this: you cannot subtract 47088 from 720, then from the number 47088 we subtract 720 (we swapped the minuend and the subtrahend). While multiplying the result obtained by subtracting a three-digit number from a multi-digit number by a three-digit number, the student performed the action of addition (replaced multiplication with the action of addition). The student acts formally, although he performed the calculations correctly. This is an individual error.

The student correctly determined the procedure, but in the process of finding the value of the expression when multiplying a three-digit number by a three-digit number ending with zero, she forgot to assign a zero to the answer. When performing the next action (subtraction), seeing that it was impossible to subtract a larger number from a smaller number, she swapped the minuend and the subtrahend. Then she divided the result obtained from subtracting multi-digit numbers by a three-digit number, making an error in the calculations when dividing.

4) Errors associated with difficulty in switching attention

The photograph shows the difficulties of students associated with individual characteristics attention. By performing addition several times, the student automatically replaces the action of subtraction with addition, although he writes down the difference in his notebook.

5) Errors associated with the inability to determine the number of digits in a quotient when dividing

The student performed the division correctly, but, having received zero hundreds when dividing the second incomplete dividend, he forgot to write it down in the quotient. He initially did not determine the number of digits in the quotient, which led to an error.

In the second case, the student made a mistake during division and parallel writing of numbers in quotients. It can be assumed that the child acted like this: having written the division on the left side, he wrote down the resulting answer (zero) in the quotient, then added the answer when dividing the third incomplete dividend.

In the third case, the student used the rounding technique to find the digits of the quotient (dividend and divisor). He wrote down 5 as the number of the quotient, but did not correct it to 4. During the division, 5 did not fit (since 5 58 equals 290, which exceeds the number 266), but he checked for the case with the number 4 in the quotient.

In the fourth case, the student wanted to use a shortened notation where only the remainder is written (dividing 35 by 35), but he rewrote the remainder 0 as a number in the quotient. In the end I got the wrong answer.

It is possible that in children the process of division, writing on the left and right, and the quotient are separated in space and are considered separately.

6) Errors associated with ignorance of tabular multiplication cases

The photograph shows an error in tabular cases of multiplication calculations in which the student was unable to complete the calculation correctly. It turned out that she does not know the table cases with 7, 8 and 9 (the second half of the table) well; this is a traditional mistake.

In the second case, the student correctly calculated 6 by 7, receiving 42. When multiplying 7 by 7, she derived the answer 49, but adding the number 4, which she “remembered,” she received 53 and wrote down the number 3 from it. And when multiplying 8 by 7, she added 4 , not 5 (from the number 53).

After identifying errors and drawing up similar tasks, individual conversations were held with students to clarify the nature of the errors in order to plan correctional work. Students individually explained the course of action and performed computational actions.

In the next paragraph we will present work on correcting difficulties in the formation of computational skills among junior schoolchildren in the experimental class.

2.2 Work to correct difficulties in developing computing skills in younger schoolchildren

This paragraph presents work on correcting difficulties in the formation of computational skills in junior schoolchildren of the experimental class, which was carried out with children who made mistakes in independent and tests in mathematics, individually after classes and during breaks.

An individual conversation was held with a student who made mistakes (see paragraph 2.1 error No. 5) when dividing a multi-digit number by a three-digit number with the omission of a zero in the quotient, during which the technique of determining the numbers in the quotient using dots as a reference signal turned out to be effective. During the calculations, the student said how many numbers should be in the quotient and was guided by the given points. As a result of pronunciation, the student did not make mistakes in calculations and did not miss a zero in the quotient. When checking to find the difference (see paragraph 2.1. error No. 4), the student did not make a mistake and performed the calculation correctly.

During individual work, it turned out (see paragraph 2.1. error No. 6) that the student has difficulty in tabular cases of multiplication (for example, it causes difficulty in calculating the tabular case 7 8). In the expression provided, an incorrect calculation during the multiplication process leads to errors in subsequent calculations of the expression and to an incorrect answer. After identifying an error in the multiplication table case, the student completed the task. During the second individual work, the multiplication table was repeated, which included table cases such as 7 8, 4 7, 8 7 and others. The student coped with checking the tabular cases, and after that she correctly solved the proposed task.

In the process of individual work, the student made mistakes that were caused by ignorance of tabular cases of multiplication and remembering the transition for addition (see paragraph 2.1 error No. 2). The multiplication of two numbers (a four-digit number multiplied by a three-digit number with zero) had to be divided into parts (multiplication of a multi-digit number by a single-digit number), where the first and second incomplete product were found separately. It turned out that the abbreviated recording method is difficult for the student; a step-by-step approach is necessary. There were no difficulties in the process of counting parts by parts. During the second individual work, the multiplication table was repeated, which included table cases such as 4 8, 4 7, 8 7, 9 6 and others. The student coped with checking the tabular cases, after which she correctly solved the proposed task.

During individual work, the student's calculation skills were updated in the following tasks: when multiplying a three-digit number by a three-digit number (see paragraph 2.1, error No. 2), dividing a five-digit number by a two-digit number with zero (see paragraph 2.1, error No. 5). While solving the task, the student found it difficult to calculate when multiplying a four-digit number by a two-digit number (see paragraph 2.1. error No. 1), which led to difficulties in further calculations in the expression. An error was detected when adding parts of an incomplete product (in addition 3 + 5). After correcting the error, the work was completed successfully.

With a student who made a mistake in the formatting of multiplying a five-digit number with zero by a two-digit number (see paragraph 2.1. error No. 1), as well as errors associated with applying the rule for the order of actions (see paragraph 2.1. error No. 3), dividing a five-digit number numbers with zero to three-digit numbers with zero (see paragraph 2.1. error No. 5), individual work was carried out. During the work, the student made a mistake in finding the difference. After re-calculating, the student independently found the error and corrected it. The rest of the work was completed successfully.

Individual work with a student required the development of the ability to multiply a three-digit number by a three-digit number ending in zero (see paragraph 2.1 error No. 2). During the solution, the student performed the actions correctly and spoke out loud. The job was completed without errors.

The student was asked, in the process of individual work, to perform calculations when dividing a six-digit number with zero by a two-digit number (see paragraph 2.1 error No. 5), to use the correct notation when multiplying a four-digit number with zero by a two-digit number (see paragraph 2.1 error No. 1). There were no comments during the work, the student explained the actions well and completed the task successfully.

Individual work was carried out with the student, in which they worked on the correct notation for multiplying a four-digit number by a three-digit number (see paragraph 2.1. error No. 1). There were no comments during the work, the student explained the actions well and completed the task successfully.

With a student who made mistakes (see paragraph 2.1 error No. 5) when dividing. In the process of working on finding an expression with brackets (see paragraph 2.1, error No. 3), the student correctly arranged the order of actions and calculated, observing the order in which the actions were performed (subtraction, multiplication, division).

After conducting individual work with students, we can conclude that students perform work conscientiously, explain the course of actions, pronounce calculations out loud, which contributes to the conscious performance of calculations. After individual lessons Students began to make fewer mistakes.

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MID 70'S OF THE XX CENTURY - PAST	MODERN SITUATION (EARLY XXI CENTURY) - PRESENT
Supersystem - factors influencing the level of development of speech skills: Communication: with adults and children, at home, in kindergarten, in the yard, in everyday life. Communication is active. Parents read books to their children, grandmothers tell fairy tales. The child spends a lot of time outside with friends, both peers and older ones. Their speech serves as a standard for him to follow. Collective games are based on texts spoken in chorus. The leading type of activity is a role-playing game, where children reflect social relations between adults, observed in the surrounding life. Developmental environment (toys, play aids). Designed for team games, board and printed games actively involve speech, for example, various lotto games. MASS MEDIA. Mostly radio. Television has not yet become widespread. Cinema is like occasional entertainment. Fiction. Mainly through listening on the radio or reading to parents.	Supersystem - factors influencing the level of development of speech skills: Communication: with adults and children, at home, in kindergarten, in the yard, in everyday life. Communication is low-active. Parents provide their children with the opportunity to use modern technology (video, tape recorder); grandmothers are often far from the family. The child spends little time outside with friends and more often sits at home. Group games are rare. Role-playing games children prefer educational electronic games, or story-based games based on watched videos. The speech is replete with interjections and onomatopoeia. Developmental environment (toys, play aids). Designed for individual games, the correctness of the task is monitored through self-control. MASS MEDIA. Mainly television, video, computer. Radio and audio are in the background. Fiction. Mainly through video and television as cartoons.
	The analyzed system is the level of development of speech skills
Subsystems - indicators: Imagery, Variety of vocabulary, Connected speech Spoken grammar Sound culture, Mastering literacy.	Subsystems - indicators: Imagery, Variety of vocabulary, Connected speech Creative writing skills, Spoken grammar sound culture, Mastering literacy.

Identifying difficulties. Diagnostic techniques for identifying learning difficulties. in a student environment. Explanation

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