Independent work in mathematics lessons. Maintaining a basic outline

The role of independent work is quite large:

Allows students to form the skills of self-education and self-realization of the individual;
Provides continuous education throughout a person's life;
Regular and systematic updating of any aspects of education that reflect changes in the field of culture, economics, science, technology, etc.

Independent work is not aimed at giving knowledge. It is aimed at teaching students the correct independent search for this knowledge.

The main goal of independent work

The educational system is imperfect. There is a huge gap between what the student should know and what the teacher thinks he really knows and can do.

This is why education faces a controversial task: one side use any resources at our disposal to develop the student's cognitive processes and help him reach a new level of knowledge, with another- make the material taught as accessible as possible.

How can this problem be solved? By compiling competent, carefully thought out and systematized, logical tasks and exercises for independent work. It turns out that with the consistent solution of each task, students actively and consciously acquire some knowledge, and also learn to use this knowledge creatively in life.

Additional goals for self-study

There are a number of secondary goals that independent work is designed to achieve:

Systematize and consolidate the theoretical knowledge and practical skills of students;
Deepen and expand theoretical knowledge;
To form the skills of using educational literature to find answers to the task;
To develop the student's cognitive activity, their creative initiative, organization and responsibility;
Develop independence of thinking, identify the ability to self-development, self-realization and self-improvement;
To form practical skills and abilities;
Contribute to the development of research skills;
To help develop the skills of productive independent professional work at the level of generally recognized world standards;
To form the skills and abilities of generalization and isolation of the particular;
To teach to identify common features, compare these features and create generalizations based on the data obtained;
To teach to compare by common and distinctive properties;
Learn to build evidence based on the main features.

All this is typical both for the performance of independent work in the SPO, and for universities.

But still, the main task of this type of work is to create in students the need to study and learn.

Have you noticed that each time the tasks in independent work become more and more difficult? So the teacher tries to stimulate your cognitive interest, activate and develop your thought processes, form a scientific worldview and communication skills.

Methods of independent work of students

In the literature with guidelines for the implementation of independent work of students, you can find the following classification of the types of this type of work:

Observation of students;
Comparative analytical observations;
Actually the classes themselves;
Solving professional and educational problems;
Work with different sources of information;
Research activity.

Structure of independent work

Independent work includes the following types of work:

Preparing for a classroom lesson (lecture, seminar, laboratory work, practical lesson) and completing assignments for it.
Independent study of individual topics of the subject according to the educational and thematic plan.
Preparing for practice and completing assignments for it.
Creation of written control and presentations.
Drawing up diagrams, diagrams, graphs.
Preparation for any kind of work.
Preparation for the final certification, writing final qualifying works.
Work at seminars, circles, scientific communities.
Participation in symposia, conferences, congresses and other activities.

As for the time for the process of doing independent work outside the classroom, the teacher speaks about this. You can also read the working curriculum for the chosen discipline. As a rule, this is at least 30% of the total time of the entire full-time study.

Types of independent work

Before proceeding with the instructions for doing independent work, you should determine the type of work. So, the following types of this type of work are distinguished:

Reproductive (or reproducing) independent work

This work involves performing tasks according to the algorithm - similar to the situation described (filling in tables, drawing diagrams, etc.). In the course of this type of work, comprehension, memorization, recognition develop. All this helps to strengthen knowledge and build skills.

Reconstructive independent work

Here we are talking about the use of accumulated knowledge and the use of a known type of action, only the conditions are slightly changed. In the course of this work, decisions are restructured, a plan, theses, annotations, etc., are drawn up.

Partial search (heuristic) independent work

It consists in the accumulation of new experience and its application in non-standard situations.

Creative independent work

Helps develop students' research skills. Here it is necessary to apply the analysis of problematic situations and obtain new data. At the same time, recommendations on the implementation of independent work by students indicate that the student should, if possible, independently seek means and ways to solve the problem.

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Independent work: target areas

Different types of independent work (for example, reading, collecting material for a report, working with notes, etc.) are designed to develop different skills and abilities. Here is a table that will help you understand what certain types of independent work are for:

The basis of independent work: student aids

There are many teaching aids for the student to help him achieve optimal self-study:

Didactic tools (documents, primary sources, collections, magazines, newspapers, tables, maps, films). They themselves can be a source of knowledge acquisition.
Technical means (audio and video equipment, computers). It is a means of providing educational information.
Various manuals for independent work (manuals, cards, etc.).

Types of independent work

Working with textbooks

To help students assimilate the material as fully as possible, it is necessary to take into account not only the complexity of the subject, but individual characteristics. Teachers can offer the following types of work with textbooks:

Taking notes;

Development of a text plan;

Drafting of abstracts;

Compilation of annotations;

Determining the problem and finding ways to solve it;

Bringing algorithms of practical actions (schemes, plans) to automaticity.

Maintaining a basic outline

Usually, the teacher presents the material sequentially, from point to point, topic by topic. And only at the very end he tries to tie together the material presented. Although it would have made more sense to do this in an introductory lesson, then giving the students a baseline on which they could repeat and study the topics. Such a summary is useful not only for weak students, but also for excellent students. With a baseline to study well in the moment, there is no need to repeat yesterday and prepare for tomorrow.

The reference summary is given in the process of studying new material and provides invaluable assistance in repeating what has been covered. With it, you can easily summarize what you have learned. And the teacher wins time, because there is no need to waste time on repetitions.

Testing

Students treat tests more friendly, perceiving them rather as a kind of game. This helps to eliminate a lot of psychological problems (stress and fears that accompany the usual types of knowledge control).

The biggest advantage of tests for students is the simplicity and speed of execution, and for the teacher - the speed of assessing the level of knowledge on the topics studied. They are often used to determine whether students are ready for final control or to correct certain elements of a topic.

There are two levels of tests:

Level 1 Tests– choice of one or more correct answers from the proposed ones:

To check the quality of acquired knowledge and its application in practice (select one of the listed answers…);
For correlation (find similarities and differences in the studied objects ...);
To test reflection (match...).

Level 2 Tests- tasks using own knowledge:

For substitution: selection and addition of phrases, formulas, graphics, diagrams, etc. (definition with a missing word);
To design an answer (fill in the table, diagram, graph, write a formula);
To solve specific situations.

When compiling tests, a number of requirements must be taken into account:

The typicality of tasks for a given subject;
The ability to complete the task for a certain time period (no more than an hour);
Feasibility for students to perform in terms of structure and complexity for students at this stage of learning;
Having only one correct answer standard per answer;
Uniform increase in complexity as you learn and master the profession;
Clarity of the wording and its relevance to the task.

Self-employment is hard work. But having mastered these skills, you will be able to achieve incredible heights in the future. After all, the skills of competent independent work are very useful in life. However, not all teachers can adequately teach this skill. And if you really need to do some work, but do not have enough time, energy or resources for this, contact those who are ready to help you at any time of the day or night.

Independent work in the system of the educational process should be considered both as a means of teaching, and as a form of educational and scientific knowledge, and as a teaching method.

Therefore, independent work is a learning tool that:

In each specific situation, assimilation corresponds to a specific didactic goal and task;

Forms the student at each stage of his movement from ignorance to knowledge the necessary volume and level of knowledge, skills and abilities to solve a certain class of cognitive tasks and, accordingly, move from lower to higher levels of mental activity;

Develops in the student a psychological attitude towards independent systematic replenishment of his knowledge and the development of skills to navigate the flow of scientific information when solving new cognitive problems;

It is the most important condition for self-organization and self-discipline of the student in mastering the methods of cognitive activity;

It is the most important instrument of pedagogical guidance and management of independent cognitive activity of the student in the learning process.

As a teaching method, independent work was more often used in the classroom and at home in order to consolidate knowledge and develop skills. However, the experience of teachers and experiments convincingly prove its effectiveness in achieving other goals. So, before studying a new topic in the classroom, students can complete preliminary tasks related to observations, setting up simple experiments, reading the text. New material available for self-study, children can successfully learn in the classroom, working with a textbook, map or other teaching aids. Independent work is also used for the purpose of repetition, systematization and testing of knowledge.

Student independent work is a method of learning where 1) students are offered learning tasks and guidance for their implementation; 2) the work is carried out without the direct participation of the teacher, but under his guidance; 3) performance of work requires mental effort from the student (51).

From the point of view of organizational foundations, independent work can be divided into: 1) independent work at school and 2) independent work performed outside the school, including at home. Independent work at school can be carried out as part of a lesson, test, seminar, practical lesson, etc. On the basis of another logical division, two more types of independent work can be distinguished: 1) individual and 2) group.

Pidkasty P.I. speaks of independent work as a means of learning, with the help of which the teacher organizes the student's activities in the classroom, and when doing homework.

Speaking about the role of independent work, one cannot fail to emphasize that modern society needs people who are capable of independent judgments and assessments, actions and actions. Needs are expressed in the ability and opportunity to show independence.

Independent work should be distinguished from independent activity.

Independent activity is characterized by the following components: purpose; motive; content; subject actions; result.

Independent work acts in the learning process as a specific pedagogical means of organizing and managing students' independent activities.

Consider each of the components of independent activity.

The attitude of the student towards the goal is important. In some cases, the goal is assigned in a ready-made form, in others the student joins the formation of the goal, in the third, the student himself sets the goal.

Motives may vary. But in order to get a result, the student must be guided by a cognitive motive. There must be a desire to learn something new. To do this, you need to interest the student in new material. The content of independent activity should be made interesting and varied, as well as appropriate for the age of the student.

When performing various objective actions, the student himself chooses the methods of performing these actions that are adequate from his point of view, performs many operations, and controls them in accordance with the goal.

Independent activity always ends with a result. It is much more important than the result obtained through joint activities. Students get much more satisfaction from the results in independent activity.

Psychologists and educators identify the following skills that characterize independence:

the ability to highlight the main thing, highlight the general pattern and draw generalized conclusions;

the ability to consistently and logically justify their actions and control them;

the ability to apply knowledge in new conditions, often complicated, with elements of a creative and non-standard approach to achieving the goal;

the ability to reach the truth without turning to others for help.

Hometasks

Home independent work of students is an important and integral part of the educational process. Its goal is to expand and deepen the knowledge, skills acquired in the lessons, prevent them from being forgotten, develop individual inclinations, talents and abilities of students. Home independent work is built taking into account the requirements of the curriculum, as well as the interests and needs of schoolchildren, their level of development. It relies on the self-activity, consciousness, activity and initiative of the children themselves. Properly organized home independent work weighs in the development of students no less than work in the classroom.

Home independent work performs important didactic functions, namely:

Consolidation of knowledge, skills acquired in the classroom;

Expansion, deepening of the educational material worked out in the classroom;

Formation of skills and abilities to perform exercises independently;

Development of independent thinking by performing individual tasks in a volume that goes beyond the scope of the program material, but meets the abilities of students;

Implementation of individual observations, experiments; collection and preparation of teaching aids, such as herbaria, natural specimens, postcards, illustrations, newspaper and magazine clippings, etc., for the study of new topics in the lessons.

Usually home independent work of schoolchildren is made out in the form of educational tasks. Types of homework:

Working with the text of the textbook (reading, understanding, writing out incomprehensible words, expressions);

Performing exercises, solving problems;

Performing graphic works (drawing, filling in contour maps, etc.);

Practical work on observing animals, plants, natural phenomena;

Carrying out simple independent experiments;

Learning by heart.

The last decades have been marked by a revision of the expediency of home independent work of schoolchildren. Calls to work without homework spread, which were seen by many teachers as a progressive step in the humanization of school relations. However, there is no serious evidence of the futility of homework. On the contrary, there are centuries-old practice and pedagogical laws that prove that if the knowledge acquired in the lesson is not repeated at home, then they are forgotten. Refusal from home independent work necessarily entails a decrease in the quality of education. Do not refuse, but skillfully manage this work will be a teacher. He will not give homework to first-graders - they have lessons in subjects every day and knowledge is not forgotten. It will make it easier for students in grades 2-4 to do homework, and strictly observe the maximum workload standards for schoolchildren.

Maximum load standards

In addition, by practicing homework, teachers will:

Persistently stimulate its independent and thorough implementation;

Give homework with the full attention of the whole class;

Conduct homework assignments;

Practice more creative work that will arouse the interest of schoolchildren;

Individualize and differentiate tasks;

Consider the feasibility of tasks;

Systematically check the completion of homework in the classroom;

Keep in touch with parents on this matter.

A common drawback is that in the classroom teachers pay little attention to issues of independent learning. There is often not enough time to explain homework assignments, they are communicated hastily. Teachers rarely guide students to the difficulties that they may encounter when doing homework, do not indicate ways to overcome them. As a result, home independent work often turns out to be unmanageable and ineffective.

The best teachers ensure that children learn the rules of working at home:

1. After returning from school, have lunch, relax in the fresh air, or run errands for your parents around the house.

2. Do your homework at the time set by the daily routine.

3. Have a permanent job. Remove from the workplace everything that is not related to homework. Prepare your writing materials.

4. Think over a work plan.

5. Do more difficult tasks first, and do easy ones later.

6. Repeat the rules first, and then proceed to the exercises, problem solving and examples.

7. Work according to the plan, take your time.

8. Take small breaks to rest, ventilate the room.

9. At the end, check if you did everything right.

10. Collect books, notebooks in a bag - everything you need for school.

Without carefully thought out, regularly and systematically performed independent work of students, it is impossible to achieve a high quality of education. Homework in the primary grades allows students to form the ability to work independently, develop cognitive interests. The teacher will adhere to the rules for managing home independent work, making it necessary and attractive for students.

In innovative technologies, there is a type of homework designed for long-term work, for example, during the year. The task is given - to solve problems from the collection chosen by the teacher (many of them are offered in stores), fixing the solution in notebooks, and information about the work done on special sheets. This helps the teacher to quickly exercise control, and the student is interested, since the sheet shows some figure that he “fills in”. This work is of great educational value.

Introduction………………………………………………………………….……….. ...3

Independent work as a kind of learning activity.

1.1. The concept of independent work. Analysis of different approaches…………...5

1.2. Didactic principles of organizing independent work………...11

1.3. The value of independent work for the development of cognitive abilities of students……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

2. Classification of types and forms of independent work……………………….17

2.1. Homework of students………..………………………………..19

2.2. Working with the book….………….…………………………………………………….22

2.2.1. Traditional forms of working with a book…………………………………………23

2.2.2. Unconventional forms……………………………………………………28

2.3. Exercises - as an independent type of educational activity………….32

Practical part…………………………………………………………...37

Conclusion…………………………………………………………………….46

Literature……………………………………………………………………….48

Applications

Introduction

The relevance of this problem is indisputable, because. knowledge, skills, beliefs, spirituality cannot be transferred from a teacher to a student, resorting only to words. This process includes acquaintance, perception, independent processing, awareness and acceptance of these skills and concepts.

And, perhaps, the main function of independent work is the formation of a highly cultured personality. Man develops only in independent intellectual and spiritual activity.

The organization of independent work, its management is a responsible and difficult work of every teacher. The education of activity and independence must be considered as an integral part of the education of students. This task appears before every teacher among the tasks of paramount importance.

Speaking about the formation of independence among schoolchildren, it is necessary to keep in mind two closely related tasks. The first of them is to develop students' independence in cognitive activity, to teach them to acquire knowledge on their own, to form their own worldview; the second is to teach them to independently apply the existing knowledge in teaching and practical activities.

Independent work is not an end in itself. It is a means of fighting for deep and solid knowledge of students, a means of forming their activity and independence as personality traits, and developing their mental abilities. A child crossing the threshold of a school for the first time cannot yet independently set the goal of his activity, is not yet able to plan his actions, correct their implementation, and correlate the result obtained with the goal set.

In the process of learning, he must achieve a certain sufficiently high level of independence, which opens up the opportunity to cope with various tasks, to get something new in the process of solving educational problems.

The purpose of this qualification work is to study the organization of independent work of schoolchildren and the conditions for their successful implementation. To address this goal, we put forward the following tasks:

To analyze various directions in the study of the nature of students' independence in learning,

Get acquainted with a variety of definitions and find out what functions the independent cognitive activity of students performs and why it is so necessary for the formation of a mature personality,

To test some types of independent work in practice.

Hypothesis: The use of various types of independent work in the informatics lesson forms the ability of students to independently acquire knowledge and apply it in practice.

The object of study is the student's independent activity. The subject is the conditions for its implementation.

1. Independent work as a kind of learning activity.

The concept of independent work. Analysis of different approaches.

Analysis of monographic works devoted to the problem of organizing independent work of schoolchildren, P.I. Pidkasistoy, I.A. Zimney, showed that there are several definitions for the concept of independent work. P.I. Pidkasty gives such a definition of independent work.

Independent work is such work that is performed without the direct participation of the teacher, but on his instructions, at a time specially provided for this, while students consciously strive to achieve their goals, using their efforts and expressing in one form or another the result of mental or physical (or both) actions.

By definition A.I. In winter, independent work is presented as purposeful, internally motivated, structured by the object itself in the totality of the actions performed and corrected by it according to the process and result of the activity. Its implementation requires a sufficiently high level of self-consciousness, reflectivity, self-discipline, personal responsibility, gives the student satisfaction as a process of self-improvement and self-knowledge.

A.I. Zimnyaya emphasizes that the independent work of a student is a consequence of his properly organized learning activities in the classroom, which motivates its independent expansion, deepening and continuation in his free time. For the teacher, this means a clear awareness not only of his plan of educational activities, but also the conscious formation of it among schoolchildren as a certain scheme for mastering a school subject in the course of solving new learning tasks. But in general, this is a parallel existing employment of a schoolchild according to a program chosen by him from ready-made programs or by himself, developed by him for the assimilation of any material.

In my opinion, this definition is the most extended and affects both the activities of the student and the teacher.

The effectiveness of the educational process of cognition is determined by the quality of teaching and the independent cognitive activity of students. These two concepts are very closely related, but independent work should be singled out as a leading and activating form of learning due to a number of circumstances. Firstly, knowledge, skills, abilities, habits, beliefs, spirituality cannot be transferred from a teacher to a student in the same way as material objects are transferred. Each student masters them through independent cognitive work: listening, understanding oral information, reading, parsing and understanding texts, and critical analysis.

Secondly, the process of cognition, aimed at revealing the essence and content of what is being studied, obeys strict laws that determine the sequence of cognition: acquaintance, perception, processing, awareness, acceptance. Violation of the sequence leads to superficial, inaccurate, shallow, fragile knowledge, which practically cannot be realized.

Thirdly, if a person lives in a state of the highest intellectual tension, then he will certainly change, form as a person of high culture. It is independent work that develops a high culture of mental work, which involves not only the technique of reading, studying a book, keeping records, but above all the mind, the need for independent activity, the desire to delve into the essence of the issue, go into the depths of problems that have not yet been solved. In the process of such work, the individual abilities of schoolchildren, their inclinations and interests are most fully revealed, which contribute to the development of the ability to analyze facts and phenomena, teach independent thinking, which leads to creative development and the creation of their own opinions, their views, ideas, their position.

Thus, independent work can be given the following definition: independent work is the highest work of a student’s educational activity and is a component of a holistic pedagogical process, therefore, it has such functions as upbringing, educational, and developmental.

The fundamental requirement of society for a modern school is the formation of a person who would be able to independently creatively solve scientific, industrial, social problems, think critically, develop and defend his point of view, his convictions, systematically and continuously replenish and update his knowledge through self-education, improve skills, creatively apply them to reality.

Experts in this field emphasized that it is important for students to be given a method, a guiding thread for organizing the acquisition of knowledge, which means equipping them with the skills and abilities of the scientific organization of mental labor, i.e. the ability to set a goal, choose the means to achieve it, plan work in time. For the formation of a holistic and harmonious personality, it is necessary to systematically include it in independent activity, which in the process of a special type of educational tasks - independent work - acquires the character of problem-search activity.

There are many different directions in the study of the nature of activity and independence of students in learning. The first direction originates in antiquity. Its representatives can be considered even the ancient Greek scientists (Socrates, Plato, Aristotle), who deeply and comprehensively substantiated the importance of the child's voluntary, active and independent mastery of knowledge. In their judgments, they proceeded from the fact that the development of human thinking can proceed successfully only in the process of independent activity, and the improvement of the personality and the development of its ability through self-knowledge (Socrates). Such activity gives the child joy and satisfaction and thereby eliminates passivity on his part in acquiring new knowledge. They are further developed in the statements of Francois Rabelais, Michel Montaigne, Thomas More, who, in the era of the dark Middle Ages, at the height of prosperity in the practice of the school of scholasticism, dogmatism and cramming, demand to teach the child independence, to educate in him a thoughtful, critically thinking person. The same thoughts are developed on the pages of the pedagogical works of Ya.A. Kamensky, Zh.Zh. Russo, I.G. Pestalozzi, K.D. Ushinsky and others.

In pedagogical work, scientists theorists, in unity with philosophers, psychologists, sociologists and physiologists, explore and theoretically substantiate this aspect of the problem in the light of the main personality traits of a representative of the modern era - initiative, independence, creative activity - as the main indicators of the comprehensive development of a person of our days.

Studying the essence of independent work in theoretical terms, there are 3 areas of activity in which the independence of learning can develop - cognitive, practical and organizational and technical. B.P. Esipov (60s) substantiated the role, place, tasks of independent work in the educational process. In the formation of students' knowledge and skills, the stereotypical, mostly verbal way of teaching becomes ineffective. The role of independent work of schoolchildren is also increasing in connection with a change in the purpose of education, its focus on the formation of skills, creative activity, as well as in connection with the computerization of education.

The second direction originates in the works of Ya.A. Comenius. Its content is the development of organizational and practical issues of involving schoolchildren in independent activities. At the same time, the subject of theoretical substantiation of the main provisions of the problem is teaching, the activity of the teacher without a sufficiently deep study and analysis of the nature of the activity of the student himself. Within the framework of the didactic direction, the areas of application of independent work are analyzed, their types are studied, the methodology for their use in various parts of the educational process is steadily improved. The problem of the relationship between pedagogical guidance and the independence of the student in educational cognition is becoming and to a large extent being solved in the methodological aspect. The practice of teaching was also enriched in many respects by informative materials for organizing independent work of schoolchildren in the classroom and at home.

The third direction is characterized by the fact that independent activity is chosen as the subject of research. This direction originates mainly in the works of K.D. Ushinsky. The studies that developed in line with the psychological and pedagogical direction were aimed at identifying the essence of independent activity as a didactic category, its elements - the subject and purpose of activity. However, with all the achievements in the study of this area of independent activity of the student, its process and structure have not yet been fully disclosed.

However, there are some structural principles for analyzing the meaning, place and function of independent activity. There are 2 options, close in essence, but having their own content and specifics: they determine (under the condition of their unity) the essence of the independent coloring of activity.

First group:

2) operational component: a variety of actions, operating skills, techniques, both externally and internally;

3) the effective component: new knowledge, methods, social experience, ideas, abilities, qualities.

Second group:

2) procedural component: selection, definition, application of adequate methods of action leading to the achievement of results;

3) motivational component: the need for new knowledge that performs the functions of word formation and awareness of activity.

The actual process of independent activity is represented as a triad: motive - plan (action) - result.

So, in social terms, independent activity can be considered in a very wide range. In any relation of the individual to the world around him, in any form of his concrete interaction with the environment.

Introduction…………………………………………………………………………….. 3

I. Independent work as the highest type of learning activity.

1.1. Student's independent activity in teaching: analysis of different approaches. Structure……………………………………………………………….. 5

1.2. The concept of independent work and its functions……………………………... 9

1.3. Management of independent activities of schoolchildren……..………….. 12

II. The system of independent work of students.

2.1. Didactic principles of organizing the independent work of students ……………………… .. ……………………………………………………………………………………………………

2.2. Classification of types of independent work of students………..………….….. 19

2.3. Organization of independent work in the classroom……………….…………..…….. 22

2.4. The influence of independent work on the quality of knowledge and the development of cognitive abilities of students ………………………………………………………………. 27

Conclusion………………………………………………………………………... 28

Literature ………………………….……………………………………………. thirty

Introduction

The purpose of this course work is to study the organization of independent work of students and the conditions for their successful implementation. To consider this goal, we resorted to the analysis of various directions in the study of the nature of students' independence in learning, got acquainted with a variety of definitions and found out what functions students' independent cognitive activity performs and why it is so necessary for the formation of a mature personality.

The object of study is the student's independent activity, and the subject is the conditions for its implementation.

And, perhaps, the main function of independent work is the formation of a highly cultured personality. Man develops only in independent intellectual and spiritual activity.

1.1. Student's independent activity in teaching: analysis of different approaches. The structure of independent activity.

Any science sets as its task not only to describe and explain this or that range of phenomena or objects, but also in the interests of man to control these phenomena and objects, and, if necessary, transform them. It is possible to manage and even more so to transform phenomena only when they are sufficiently described and explained. In science, the functions of control and transformation fulfill the prescriptions, which include the principles and rules for the transformation of phenomena. Thus, cognizing an object or phenomenon, we must first of all get acquainted with it, consider it as a whole. Identify the functional relationship of its parts, and only then describe. Having described an object or phenomenon, we must explain them (the functional relationship of their parts and structure as a whole), formulate the law of their existence, and then prescribe how to control them, how to transform these objects and phenomena with the help of certain operations.

Independent work is not a form of organizing training sessions and not a teaching method. It is legitimate to consider it rather as a means of involving students in independent cognitive activity, a means of its logical and psychological organization. (10, p. 279)

There are many different directions in the study of the nature of activity and independence of students in learning. The first direction originates in antiquity. Ancient Greek scientists (Aristoses, Socrates, Plato, Aristotle) can be considered its representatives, who deeply and comprehensively substantiated the importance of the voluntary, active and independent acquisition of knowledge by a child. In their judgments, they proceeded from the fact that the development of human thinking can proceed successfully only in the process of independent activity, and the improvement of the personality and the development of its ability through self-knowledge (Socrates). Such activity gives the child joy and satisfaction and thereby eliminates passivity on his part in acquiring new knowledge. They are further developed in the statements of Francois Rabelais, Michel Montaigne, Thomas More, who, in the era of the dark Middle Ages, at the height of prosperity in the practice of the school of scholasticism, dogmatism and cramming, demand to teach the child independence, to educate in him a thoughtful, critically thinking person. The same thoughts are developed on the pages of the pedagogical works of Ya.A. Kamensky, Zh.Zh. Russo, I.G. Pestalozzi, K.D. Ushinsky and others.

First group:

2) operational component: a variety of actions, operating skills, techniques, both externally and internally;

3) effective component: new knowledge, methods, social experience, ideas, abilities, qualities.

Second group:

2) procedural component: selection, definition, application of adequate methods of action leading to the achievement of results;

3) motivational component: the need for new knowledge that performs the functions of word formation and awareness of activity.

The actual process of independent activity is represented as a triad: motive - plan (action) - result.

1.2. The concept of “independent” work and its functions.

Analysis of monographic works devoted to the problem of organizing independent work of schoolchildren, P.I. Pidkasistoy, I.A. Zimney, showed that the concept of independent work is interpreted ambiguously:

Independent work, in our opinion, is most fully defined by A.I. Winter. According to its definition, independent work is presented as purposeful, internally motivated, structured by the object itself in the totality of the actions performed and corrected by it according to the process and result of the activity. Its implementation requires a sufficiently high level of self-consciousness, reflectivity, self-discipline, personal responsibility, gives the student satisfaction as a process of self-improvement and self-knowledge. (4, p. 335)

First, this definition takes into account the psychological determinants of independent work: self-regulation, self-activation, self-organization, self-control, etc.

Let's try to define more precisely what is essentially included in the concept of "independent activity".

“Independence” is a very multifaceted and psychologically difficult phenomenon, it is rather a meaning-forming, qualitative characteristic of any sphere of activity and personality, which has its own specific criteria. Independence - as a characteristic of the student's activity in a specific learning situation, is a constantly manifested ability to achieve the goal of the activity without outside help. (8, p. 47)

“Amateur activity” is a subjective, actually individual self-governed activity, with personally conditioned components: a goal, a leading need, motivation and ways of implementation.

“Self-activation” is a subjectively correlated internal motivation of activity.

“Self-organization” is the property of a person to mobilize himself, purposefully, actively use all his abilities to achieve intermediate and final goals, rationally using time, effort, and means.

“Self-regulation” is initially a psychological support of activity, in the subsequent development it acquires a personal meaning, i.e. actual psychic content.

“Self-control” is a necessary component of the activity itself, which carries out its execution at the personal level.

Secondly, attention is focused on the fact that independent work is connected with the work of the student in the classroom and is a consequence of the correct organization of educational and cognitive activity in the classroom.

Thirdly, independent work is considered as the highest type of educational activity, requiring a sufficiently high level of self-awareness, reflexivity, self-discipline, responsibility from the student, and giving the student satisfaction, as a process of self-improvement and self-awareness.

From all that has been said above, it can be seen that independent work is the highest work of the student's educational activity and is a component of a holistic pedagogical process, therefore, it has such functions as upbringing, educational, and developmental.

1.3. Management of independent activity of schoolchildren.

The management process should ensure the implementation of the teaching, educational, developmental functions of independent work of students in the classroom and at home.

Most researchers believe that control is inherent only in complex dynamic systems of biological and social types. Their functioning under the influence of external conditions can change, be disturbed if timely adjustment or restructuring of the system is not provided. Therefore, it is necessary to manage, which counteracts the disorganization of the system, maintains the necessary order. In the most general form, control can be defined as the ordering of the system, i.e. bringing it into line with the objective laws operating in the given environment. (7, p. 25)

The need for management follows from the structure of the pedagogical system. The components of the pedagogical system are goals, subjects that realize these goals, activities, relationships that arise between its participants and unite their management, ensuring the unity of the system. The loss of any component leads to the destruction of the system as a whole.

For a complete understanding of the problem, we need to identify the general and particular in the concepts of "management", "pedagogical leadership", "organization", which are often used as synonyms.

Based on the structure of activities, the management of independent work includes goal-setting, planning, organization, adjustment and evaluation of students' activities, diagnostics of its results.

Pedagogical guidance is the management of the student's independent activity at the stage of its direct implementation: presenting the educational task to the student, instructing how to complete it, motivating its resolution, monitoring and correcting the student's independent actions, evaluating the results of independent work.

The organization of independent work is the selection of means, forms and methods that stimulate cognitive activity, the provision of conditions for efficiency.

So, we found out that in the process of managing independent activity, not the last place belongs to the teacher, since he takes a direct (then indirect) participation in the organization of the pedagogical process. In this regard, the following management principles should be listed:

1) a differentiated approach to students in compliance with the feasibility of educational tasks;

2) a systematic increase in intellectual loads and a gradual transition to more inaccurate and incomplete instructions for performing independent work;

3) the gradual distance of the teacher and the occupation of the position of a passive observer of the process;

4) the transition from teacher control to self-control.

II. The system of independent work of students

2.1. Didactic principles of organizing students' independent work

In various lessons, with the help of a variety of independent work, students can acquire knowledge, skills and abilities. All these works only give positive results when they are organized in a certain way, i.e. represent the system.

Under the system of independent work, we mean, first of all, a set of interconnected, mutually conditioning each other, logically following from one another and subordinate to common tasks, types of work.

Every system must satisfy certain requirements or principles. Otherwise, it will not be a system, but a random set of facts, objects, objects and phenomena.

When building a system of independent work, the following were put forward as the main didactic requirements:

1. The system of independent work should contribute to the solution of the main didactic tasks - the acquisition by students of deep and solid knowledge, the development of their cognitive abilities, the formation of the ability to independently acquire, expand and deepen knowledge, and apply them in practice.

2. The system must satisfy the basic principles of didactics, and, above all, the principles of accessibility and systematicity, the connection of theory with practice, conscious and creative activity, the principle of teaching at a high scientific level.

3. The works included in the system should be varied in terms of educational purpose and content in order to ensure the formation of a variety of skills and abilities in students.

4. The sequence of doing home and class independent work logically followed from the previous ones and prepared the ground for the next ones. In this case, not only "near", but also "distant" links are provided between individual works. The success of solving this problem depends not only on the pedagogical skill of the teacher, but also on how he understands the meaning and place of each individual work in the system of work, in the development of students' cognitive abilities, their thinking and other qualities.

However, one system does not determine the success of the teacher's work on the formation of students' knowledge, skills and abilities. To do this, you also need to know the basic principles, guided by which you can ensure the effectiveness of independent work, as well as the methodology for managing certain types of independent work.

The effectiveness of independent work is achieved if it is one of the integral, organic elements of the educational process, and special time is provided for it in each lesson, if it is carried out systematically and systematically, and not randomly and episodically.

Only under this condition, students develop stable skills and abilities in performing various types of independent work and increase the pace in its implementation.

When selecting types of independent work, when determining its volume and content, one should be guided, as in the entire learning process, by the basic principles of didactics. The most important in this matter are the principle of accessibility and systematicity, the connection between theory and practice, the principle of gradualness in increasing difficulties, the principle of creative activity, as well as the principle of a differentiated approach to students. The application of these principles to the management of independent work has the following features:

1. Independent work should be purposeful. This is achieved by a clear statement of the purpose of the work. The task of the teacher is to find such a wording of the task that would arouse the students' interest in the work and the desire to do it as best as possible. Students should be clear about what the task is and how it will be checked. This gives the work of students a meaningful, purposeful character, and contributes to its more successful implementation.

Underestimation of this requirement leads to the fact that students, not understanding the purpose of the work, do not do what is necessary, or are forced to repeatedly turn to the teacher for clarification in the process of its implementation. All this leads to an irrational waste of time and a decrease in the level of independence of students in their work.

2. Independent work should be really independent and encourage the student to work hard when doing it. However, extremes should not be allowed here: the content and volume of independent work offered at each stage of education should be feasible for students, and the students themselves should be prepared to perform independent work theoretically and practically.

3. In the first couples, students need to form the simplest skills of independent work (execution of diagrams and drawings, simple measurements, solving simple problems, etc.). In this case, independent work of students should be preceded by a visual demonstration of the methods of work with the teacher, accompanied by clear explanations, notes on the board.

Independent work performed by students after showing the methods of work by the teacher has the character of imitation. It does not develop independence in the true sense of the word, but is important for the formation of more complex skills and abilities, a higher form of independence in which students are able to develop and apply their own methods for solving problems of an educational or industrial nature.

4. For independent work, it is necessary to offer such tasks, the implementation of which does not allow actions according to ready-made recipes and a template, but requires the application of knowledge in a new situation. Only in this case, independent work contributes to the formation of initiative and cognitive abilities of students.

5. In organizing independent work, it must be taken into account that different students need different time to master knowledge, skills and abilities. This can be done through a differentiated approach to students.

Observing the progress of the work of the class as a whole and individual students, the teacher must timely switch those who successfully completed the tasks to perform more complex ones. For some students, the number of training exercises can be reduced to a minimum. Others are given much more of these exercises in various variations so that they learn a new rule or a new law and learn how to independently apply it to solving educational problems. The transfer of such a group of students to more complex tasks should be timely. Excessive haste is harmful here, as well as excessively long “marking time”, which does not move students forward in learning new things, in mastering skills and abilities.

6. Tasks proposed for independent work should arouse the interest of students. It is achieved by the novelty of the tasks put forward, the unusualness of their content, the disclosure to students of the practical significance of the proposed task or method that needs to be mastered. Students always show great interest in independent work, in the course of which they explore objects and phenomena.

7. Independent work of students must be systematically and systematically included in the educational process. Only under this condition will they develop solid skills and abilities.

The results of work in this matter are more tangible when the whole team of teachers is engaged in instilling the skills of independent work in schoolchildren, in classes in all subjects, including classes in educational workshops.

8. When organizing independent work, it is necessary to carry out a reasonable combination of the presentation of the material by the teacher with the independent work of students to acquire knowledge, skills and abilities. Extremes should not be allowed in this matter: excessive enthusiasm for independent work can slow down the pace of studying program material, the pace of students moving forward in learning new things.

9. When students perform independent work of any kind, the leading role should belong to the teacher. The teacher thinks over a system of independent work, their systematic inclusion in the educational process. It defines the purpose, content and volume of each independent work, its place in the lesson, teaching methods for various types of independent work. He teaches students the methods of self-control and exercises quality control, studies the individual characteristics of students and takes them into account when organizing independent work.

2. 2. Classification of types of independent work of students

Under the independent work of students, we mean such work that is performed by students on the instructions and under the control of the teacher, but without his direct participation in it, at a time specially provided for this. At the same time, students consciously strive to achieve the goal, using their mental efforts and expressing in one form or another (oral answer, graphic construction, description of experiments, calculations, etc.) the result of mental and physical actions.

Independent work involves active mental actions of students associated with the search for the most rational ways to complete the tasks proposed by the teacher, with an analysis of the results of the work.

In the learning process, various types of independent work of students are used, with the help of which they independently acquire knowledge, skills and abilities. All types of independent work used in the educational process can be classified according to various criteria: by didactic purpose, by the nature of the students' learning activities, by content, by the degree of independence and the element of students' creativity, etc.

All types of independent work for didactic purposes can be divided into five groups:

1) the acquisition of new knowledge, mastering the ability to independently acquire knowledge;

2) consolidation and refinement of knowledge;

3) development of the ability to apply knowledge in solving educational and practical problems;

4) formation of practical skills and abilities;

5) the formation of a creative character, the ability to apply knowledge in a complicated situation.

Each of these groups includes several types of independent work, since the solution of the same didactic task can be carried out in different ways. These groups are closely related. This connection is due to the fact that the same types of work can be used to solve various didactic problems. For example, with the help of experimental, practical work, not only the acquisition of skills and abilities is achieved, but also the acquisition of new knowledge and the development of the ability to apply previously acquired knowledge.

Consider the content of the works in the classification according to the main didactic purpose.

1. Acquiring new knowledge and mastering the ability to independently acquire knowledge is carried out on the basis of working with a textbook, performing observations and experiments, and works of an analytical and computational nature.

2. Consolidation and refinement of knowledge is achieved with the help of a special system of exercises to clarify the features of concepts, limit them, and separate essential features from non-essential ones.

3. The development of the ability to apply knowledge in practice is carried out by solving problems of various types, solving problems in a general form, experimental work, etc.

4. The formation of creative skills is achieved when writing essays, essays, preparing reports, assignments when looking for new ways to solve problems, new options for experience, etc.

2.3. Organization of independent work of students in the classroom.

The content of the educational material is assimilated by students in the process of learning activities. The result of training depends on what this activity is. The attitude of students to their own activities is determined to a large extent by how the teacher organizes their learning activities. The decrease in interest in learning largely depends on the actions of the teacher. For example, incorrect selection of the content of educational material by him, causing an overload of schoolchildren; teacher's lack of knowledge of modern teaching methods and their optimal combination; inability to build relationships with students and organize the interaction of students with each other; personality traits of the teacher.

In the history of pedagogy, attempts have been made more than once to create an ideal education system that would meet all the requirements put forward for the organization of the cognitive process.

But the most successful, in our opinion, is the system of individualized learning. It gained its popularity in the beginning of the 20th century. and is considered as an objective necessity to take into account the individual differences of children in the established, already traditional classroom system. At the beginning of the century, it developed in three directions: the organization of an individual mode of educational activity; combination of individual mode and content with group work of students; organization of individual work on specially developed educational materials.

The first direction found its development in the "Dalton Plan": the annual volume of educational material was divided into "contracts", which consisted of daily tasks. The student entered into an “agreement” with the teacher on the independent study of certain material at the appointed time. The material was studied in subject laboratories, where he could receive teacher's advice on this subject. The Dalton Plan taught students to be independent, developed initiative, responsibility for their obligations, encouraged them to find rational ways to complete tasks.

The second direction - the combination of individual mode and content with the group work of students - most clearly found its expression in the Howard Plan and the Jena Plan. The main provisions of the systems: instead of classes of the same age - groups of different ages, variable in composition; the schedule of classes, the choice of subjects depended on the interests of each child; the educational material was divided into "departments", the study of which, mainly, took place through individual independent work in combination with mutual assistance in a small group (4-5 people); one teacher could deal with different subjects in different groups.

The third direction can be considered a prototype of programmed learning. It represents a departure from the class-lesson system in the main "academic" disciplines; independent study of these disciplines according to specially prepared teaching aids; these materials were worked out at an individual pace for each student; individual work was carried out in the first half of the day; the training was accompanied by diagnostic testing, which established the degree of the student's approach to the tasks set and revealed the need to introduce additional and auxiliary material; in the second half of the day, group activities of students were organized to accustom them to collective work; groups arose on the basis of common interests.

In our time, a class-lesson teaching system is used, which involves grouping students into classes in accordance with age and condition of knowledge, the main organizational structure is the lesson; the content of education in each class is determined by curricula and programs; based on the curriculum, a lesson schedule is drawn up. An important element of this system is the planning of educational work by the teacher, on which the quality of training sessions largely depends. There are 2 types of planning:

1) prospective - carried out in thematic plans, the topics of lessons, laboratory work, excursions are determined, written control work, general repetition and test classes are outlined. The number of study hours allocated for the study of the topic is determined, but these plans are not detailed.

2) current - is to develop plans, individual lessons. Developing the content of the lesson, the teacher offers a brief plan for the conversation, story, lecture; forms questions for the student, tasks for independent work, lists the numbers of exercises, determines ways to test knowledge.

An equally important role in the organization of independent work is played by a selection of educational material, because. with its help we scoop information of the content of training. However, the information itself outside the needs of the child has no meaning for him and does not have any effect. If the information is consonant with the needs of the student and is subjected to emotional processing, then he receives an impulse to follow-up activities. To do this, the content of the educational material should be accessible to the student, should be based on the knowledge he has and be based on them and on the life experience of children, but at the same time, the material should be quite complex and difficult.

However, it should be noted. That the successful organization of independent cognitive activity of students depends on the method of solving problems. Let's consider some of them.

An analysis of the practice of using problems has shown that the most common way to organize problem solving is an unmotivated requirement to solve problems without formulating an educational goal for solving them, when it all comes down to the fastest search for a solution and getting the right answer, which completes the solution process.

Only a small part of teachers indicate that they always form the goal of solving problems. Some teachers not only formulate themselves, but also involve students in this, because they believe that this makes it possible to better understand the problem, to solve it more consciously, to realize its purpose, and thereby creates conditions for its better assimilation. This method is called the target requirement method.

Finally, a very small part of the teachers not only formulate the goal of solving the problem, but build a process for solving it, as a process of solving the problem, achieving the goal, and after the solution they discuss with the students how the problem was solved, the goal of the solution was realized. This method is called educational-problem.

Thus, the data convincingly show that it is not enough just to formulate the goal of solving the problem, it is necessary to construct the entire solution process as a process of solving a specific problem. Therefore, if we want to find the most effective way to form internal motives for independent cognitive activity, then the analysis of the pedagogical practice of teachers shows that this way is associated with the use of an educational-problem method of organizing problem solving in teaching. Psychologists have studied learning activities and found that the study of each independent section or topic of the curriculum should consist of the following three main stages:

1) Introductory-motivational stage.

At this stage, students should realize the main goal of the upcoming study of the educational topic, its place and role in general education, its practical and theoretical significance. In necessary cases, the teacher indicates what knowledge and skills of the previously studied material will be especially needed when studying this topic. Then the teacher reports how many lessons are allotted for studying the topic, the approximate time for its completion and lists the main elements of the topic, i.e. knowledge, skills and abilities that students should master as a result of studying this topic.

2) Operational-cognitive stage.

At this stage, students learn the knowledge included in the content of this topic, while using different types and forms of educational work: a story or lecture, frontal work on the study of the concept. Collective work on the assimilation of educational material, solving problems, conducting experiments and experiments, individual work on solving problems, etc.

The presentation of the educational material is carried out mainly by the teacher, but as the students grow older, part of the educational material is transferred for presentation by the speaker or for individual study and elaboration according to the textbook.

3) Reflective-evaluative stage.

Here is a summary of what has been learned and a summary of the work on this topic. At the same time, the main goal of this stage is the development of students' reflective activity (introspection), the ability to generalize and the formation of adequate self-esteem. To summarize the material covered, various methods can be used: generalizing lessons, student reports, compiling generalizing schemes in groups.

We found out that the most difficult thing for a teacher in this system is to learn how to organize the independent activities of the class team, gradually transfer many of their functions and roles to students, and, without suppressing the initiative, manage students' independent work. As experience shows, if this system is introduced starting from the first grade, then students quickly get used to it and it becomes familiar to them, and students will be able to fully experience feelings of emotional satisfaction from what they have done, the joy of victory over overcome difficulties, the happiness of learning new, interesting things. . Thus, students will develop an orientation towards experiencing such feelings in the future, which will lead to the emergence of a need for creativity, cognition, and persistent independent study.

2.4. The influence of independent work on the quality of knowledge and the development of the cognitive ability of students

Independent work has a significant impact on the depth and strength of students' knowledge of the subject, on the development of their cognitive abilities, and on the pace of assimilation of new material.

The practical experience of teachers in many schools has shown that:

1. Systematically conducted independent work (with a textbook on solving problems, performing observations and experiments), with its proper organization, helps students to obtain deeper and more solid knowledge compared to those that they acquire when the teacher communicates ready-made knowledge.

2. The organization of the implementation by students of various independent works in terms of didactic purpose and content contributes to the development of their cognitive and creative abilities, the development of thinking.

3. With a carefully thought-out methodology for conducting independent work, the pace of formation of practical skills and abilities in students is accelerated, and this, in turn, has a positive effect on the formation of cognitive skills and abilities.

4. Over time, with the systematic organization of independent work in the classroom and its combination with various types of homework on the subject, students develop stable skills for independent work. As a result, students spend much less time to perform work of approximately the same volume and degree of difficulty compared to students in classes in which independent work is not organized at all or is carried out irregularly. This allows you to gradually increase the pace of studying the program material, increase the time for solving problems, performing experimental work and other types of creative work.

Conclusion

The school, giving students the knowledge necessary to continue their studies at the university, and at the same time should orient the youth towards socially useful work in the national economy and prepare for this. Therefore, it is useful to improve the scientific level of teaching and the quality of students' knowledge and at the same time overcome their overload. In accordance with these requirements, it is necessary to raise the level of teaching, to aim it at the formation of a modern scientific picture of the world among the younger generations, as well as knowledge about the practical application of sciences. It is necessary that the theory of the subject contribute to a greater extent to the development of the positive abilities of schoolchildren and their practical training.

This is achieved by a whole range of means: improving the content of education, improving the quality of textbooks and other teaching aids, developing the heuristic activity of schoolchildren in the learning process based on problems, developing the current laboratory experiment and the final physical workshop of a creative nature.

In the process of considering this problem, it turned out that in order to effectively organize the student's independent work, the teacher must be able to plan the student's cognitive process and choose the right way to solve the problem, while great importance is given to the selection of educational material.

Improving the quality of education is closely related to improving the methods of organizing classes in the classroom.

To improve the quality of education, the development of students' cognitive enthusiasm and interest in the subject is of particular importance. Students should understand what is the meaning of studying the proposed material. Moreover, modern schoolchildren have the right to wish that educational activities be interesting and satisfying.

The development of cognitive activity of schoolchildren is facilitated by the use of text and illustrations in the lesson from their textbook, reader, reference book, from scientific and popular science magazines and newspapers, as well as interesting demonstration experiments, fragments from films, transparencies and other visual aids.

However, it is not enough to provide motivation for learning and arouse the cognitive interest of the student. It is further necessary, firstly, to clearly understand the goals of training and, secondly, to show how these goals can be achieved.

List of sources used

1. Gornostaeva Z.Ya “The problem of independent cognitive activity” // Opened. school. - 1998. - No. 2

2. Yosipov B.P. "Independent work of students in the classroom." – M.: Uchpedgiz, 1961.

3. Zharova L.V. “Management of independent activities of students” - L., - 1982.

4. Zimnyaya I.A. “Fundamentals of educational psychology” - M, 1980.

5. Kralevich I.N. “Pedagogical aspects of mastering generalized methods of independent learning activity.” / Mn. - 1989.

6. Nilson O.A. “Theory and practice of independent work of students” - Tal., 1976.

7. Novik N.B. "Cybernetics. Philosophy and sociological sciences.” - M., 1963.

8. Orlov V.N. “Activity and independence of students” - 1998.

9. Pidkasisty P.I., Goryachev B.V. “The learning process in the conditions of democratization and humanization of the school.” - M, 1991.

10. Pidkasy P.I. “Independent cognitive activity of schoolchildren in learning.” - M, 1980.

11. Podlasy I.P. "Pedagogy" - M., 1996.

12. Stolyarenko L.D. "Pedagogy" - Rostov, 2000.

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14. Kharlamov I.F. “Pedagogy” - Mn., 2002.

INTRODUCTION……………………………………………………….…………………3

CHAPTER I. Independent work in mathematics lessons in primary

classes…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

1. Independent work as a teaching method. Its importance in the development and

educating younger students…………………………………………….8

2. Types of independent work:…………………………………...……….10

Frontal independent work;

Individual independent work;

Group independent work;

Home independent work;

1.3 Methodology for organizing independent work……………..……….14

A differentiated approach to independent work.

With the help of cards;

CHAPTER II ………………………….……………………………22

1. Ascertaining experiment…………………….……………….…….23

2. Formative experiment………………….…………………………..27

3. Control experiment………….…………………………………….32

CONCLUSION………………………………………………………………………34

LITERATURE……………………………………………………………………..36

APPENDICES……………………………………………………………………....38

INTRODUCTION

On the basis of the choice of topic.

It is independent work that is the most important condition for self-regulation of the personality, its

creative possibilities. But why are so many people dependent,

unable to timely, without looking back at others, to take the necessary

solutions. This question again and again confronts society, does not stop

a long-standing dispute between educators from different countries. Independent work

the student is the main way of educating independence. Years of experience

schools are the best proof of that.

But independent work, attracting modern schoolchildren, causes

At the same time, many people have serious difficulties. It requires emotional and

mental stress, gives rise to a lot of unexpected questions and errors,

doubts and worries. It has been observed that there are many difficulties

children at the initial stage of developing certain skills and abilities,

Therefore, this work must begin in the primary grades. If you miss it

then it will be too late to do this work in middle and high school. In his

work, I want to highlight questions about the correctness of the organization of independent

work, as I believe that independent work serves as an effective

means of personality formation, encourages

mental independence in children. It disciplines thought, gives rise to

schoolchildren have faith in themselves, in their strengths and capabilities. Everyone in primary school

depends on the teacher: how he will teach children to perform independent

Relevance of the topic.

In the process of teaching mathematics, the task of the teacher is not only to

to ensure the sound knowledge provided by the program, but also in

to develop independence and active thinking of students. The thing is

is not easy and it is necessary to start it from the first days of schooling.

Independent work is such a cognitive training

activity, when the sequence of thinking of the student, his mental and

practical operations and actions depend and are determined by the student himself.

The presence of independent work is necessary in the classroom, including

mathematics lessons, as they train the will, educate

efficiency, attention, discipline students. teacher in class

mathematics must be based on the independent work of students,

independent reasoning, conclusion.

Self-study is a method that is very helpful for the teacher to

evaluating student abilities. Working independently, the student must

gradually master such general techniques of independent work as

a clear idea of the purpose of the work, its implementation, verification, correction

More and more widely independent work is included in the practice of the school, various

her types. Teachers strive to equip students with relevant skills,

using both classroom and extracurricular activities, and

homework.

Object of study.

Organization of the educational process in mathematics in elementary

Subject of study.

Organization of independent work. Methodology for performing independent

work in 4th grade.

Purpose of the study.

Prove that with the right methodology for organizing

independent work activates the mental activity of children.

Hypothesis

If children are taught the skills of doing independent work and

use its various types in the classroom, then children develop

independence and thinking develops, they strive to perform more

difficult tasks.

Research objectives.

1. Study the literature on the research problem

2. Determine the level of formation of independent work skills in

subject under study.

3. Determine the system of exercises for work on the formation of skills

independent work in 4th grade.

Research methods.

The study of literature on the topic of term paper, conversations, modeling

lessons, and classes, control tasks, interviewing, studying

documentation.

Chapter 1 THEORETICAL PART

1.1 Independent work is an active learning method. An example can be given in the discussion of the lesson. Some teachers said that there was independent work in the lesson, others argued that there was none, because there was nothing to think about. So what is self-employment? For some, this is a form and method of organizing learning, for others, it is special tasks intended for independent fulfillment, for others, it is the activity of students that takes place without direct participation.

teachers. However, the main features of independent work in mathematics lessons are the presence of a teacher's task, student independence, teacher guidance,

performance of the task without the direct participation of the teacher, activity and

student effort, special time to complete the task.

So, s/r. in mathematics lessons is a method of teaching in which

students, on the instructions of the teacher and under his guidance, independently decide

learning task, showing effort and activity. Often specific

a sign of s / r. consider the activity of children, lack of teacher assistance.

This view is wrong and counterproductive. Holding on to it

the teacher excludes the possibility of cooperation in those situations where it

there is a need. The teacher does not really take part in the implementation

tasks, in solving problems, but he organizes activities. C / r. always

ends with some results, as the student comes to them

on one's own. Their value and significance are more acutely realized in comparison with

those who achieve in joint activities. As a result of work

not only the level of knowledge is always revealed, but also independence

schoolchild, individual style of his activity, creativity and

non-standard approach.

As a method of teaching s/r. often used in the classroom and at home for the purpose of

consolidation of knowledge and formation of skills. However, the experience of teachers and

experiments convincingly prove its effectiveness and, when it is achieved,

other purposes. Material available for self-study children can

learn in class. C / r. are used for the purpose of repetition, systematization,

knowledge checks. an essential role in the organization of independent

activities are played by technical means and equipment. On the lessons

mathematicians can use such technical means as educational

manuals (counting material, geometric shapes, etc.), collections of problems

and exercises, textbook.

A big role in s / p. textbook plays in mathematics lessons. Years of experience

teachers and special studies have shown that the textbook as a means

organizations with / r. in mathematics lessons. Has large shaping

opportunities. Teacher at the organization of s / r. in the lesson, along with d. / Z. maybe

use a textbook from which tasks for s / r can be selected.

Pedagogical value s/r. also depends on how it is organized.

student activities. The form of organization is a certain arrangement

participants in the educational process, ways of interaction between the teacher and students,

the students themselves.

In the process of teaching, the mathematical task of the teacher is not only to

to provide solid knowledge provided by the program, but also in

to develop independence and active thinking of students. students

when performing s / p. not always able to get timely assistance from

teachers, so it is necessary to carefully consider lesson plans, determine