In other words: "I" is only possible because there is "we"

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Municipal Institution "Methodical Cabinet"

Rtishchevsky municipal district of the Saratov region

Municipal preschool educational institution

"Kindergarten No. 12 "Zvezdochka", Rtishchevo, Saratov Region"

“Individually differentiated approach of the teacher in the organization of the educational process of MDOU. Algorithm of the work of the teacher.

S.E. Lysenkova,

senior caregiver

MDOU No. 12 "Asterisk"

Rtishchevo, 2014

"To educate a man in all respects,

you need to know it well."

K.D.Ushinsky.

GEF DO defines one of the qualities of the basic principles of preschool education:building educational activities based on the individual characteristics of each child, in which the child himself becomes active in choosing the content of his education, becomes the subject of education (hereinafter - the individualization of preschool education).

Individualization is the implementation of the principle of an individual approach, it is the organization of the educational process, taking into account the individual characteristics of children, which allows you to create optimal conditions for the realization of the potential of each child.

It is important to note that every child really needs an individual approach, because this is an indispensable condition and prerequisite for the formation of a harmonious and comprehensively developed personality, the formation of the personality itself as a unique individuality.More K.D. Ushinsky noted: “upbringing should not only develop a person’s mind and give him a full amount of knowledge, but also kindle in him a thirst for serious work, without which his life cannot be either useful or happy.”That is, the main thing in education is not the transfer of knowledge and skills, but the development of the ability to acquire knowledge and skills and use them in life, providing a sense of psychological security for the child, taking into account his capabilities and needs, in other words, a student-centered model in learning is, first of all, individualization of education, creation of conditions for the development of the child as a person.

However, in the current conditions (a large number of children in groups, lack of qualified personnel, etc.), the implementation of an individual approach is very difficult. It is possible to carry out the pedagogical process taking into account the individual characteristics of children only by grouping children according to any of these characteristics. This approach is often calledindividually differentiated, although in essence it corresponds simply todifferentiated.A differentiated approach occupies an intermediate position between frontal educational work with the entire team and individual work with each child. A necessary condition for a differentiated approach is the study of interpersonal relationships. A differentiated approach makes it possible to influence the relationship between the individual and the group, the group and the team, children and adults.In other words:"I" is possible only because there is "we".

With a differentiated approach, the teacher is not engaged in the formation of a personality with predetermined properties, but creates conditions for the full manifestation and, accordingly, the development of personal functions of the subjects of the educational process. Offers help to a preschooler in becoming aware of himself as a person, in identifying, revealing his capabilities, in the formation of self-awareness, in self-determination regarding personally significant and socially acceptable goals, self-realization and self-affirmation. Children are not only, and not so much the object of pedagogical influence, but the subject of their own activities.

Therefore, speaking about the development of the child, we must first of all keep in mind his self-development.

Basic rules for using an individually differentiated approach:

work carried out with a group of children should focus on the development of each child, taking into account his individual qualities.
a constant search for ways to correct the behavior of each child is necessary.
the success of educational influence when working with one child should not negatively affect the development and upbringing of others.

Our institution has been working under the Kindergarten 2100 program since 2009. The main goal of this educational system is to create conditions for the development of a functionally literate personality - a person who is able to decide any life tasks (problems), using for this the knowledge, skills and abilities acquired throughout life and remaining a person at the same time. All children are different, you can not focus on either the weak or the strong. There can be no "middlemen" here. Orientation towards the "average" child leads to the fact that the development of children with high intelligence is artificially inhibited and they are deprived of the opportunity to fully realize their abilities. Children with a lower level of development are forced to constantly experience failure, which negatively affects their emotional well-being. In both cases, this leads to the appearance of such undesirable personality traits as unjustified self-confidence, aggressiveness, anxiety, insecurity, excessive shyness, constant dissatisfaction with oneself, etc. The organization of educational work is based on the minimax principle., which teaches to determine the need for information and independently find it.The minimax principle - the child can learn the maximum, but must (under the guidance of the educator) learn the minimum.

The standard of preschool education is aimed at solving a number of tasks, one of which is the creation of favorable conditions for the development of children in accordance with their age and individual characteristics and inclinations, the development of the abilities and creative potential of each child as a subject of relations with himself, other children, adults and the world.

“Creating conditions for the formation of a harmonious, physically healthy, aesthetically developed personality of a preschool child under the conditions of the introduction of the Federal State Educational Standard” is a problem that the teaching staff of the preschool educational institution is working on in 2013-2014.

The organization of the object-spatial environment is the main aspect of the implementation of an individually differentiated approach to the child. The environment is one of the main means of developing the child's personality, the source of his individual knowledge and social experience. The object-spatial environment not only provides different types of activity for preschoolers (physical, playful, mental, etc.), but also underlies his independent activity, being a kind of self-education.The adult's duty in this case is to open up to the children the full range of possibilities of the environment and to direct their efforts towards the use of its individual elements.

When creating the subject-spatial environment of group rooms, we proceeded from the need to take into account the following factors:

individual socio-psychological characteristics of the child;
originality of his emotional and personal development;
individual interests, inclinations, preferences and needs;

curiosity, research interest and creativity;

Age and gender characteristics.
Let us consider how each of these factors is concretized in the construction of the object-spatial environment.

Socio-psychological featurespreschool age children suggest a desire to participate in joint activities with peers and adults, as well as an occasional need for privacy. At the same time, to ensureoptimal balance of joint and independent actions of childrenin each age group, zones have been created for different types of children's activity: motor, play, visual, constructive, theatrical, etc., as well as conditions for frontal, subgroup and individual classes.

Accounting for individual characteristicsemotional and personal development of the childrequires the design of a kind of "privacy zones" - special places where each child keeps his personal property: a favorite home toy, a postcard, badges, decorations, gifts from friends, etc. Great importance is attached to the organization of exhibitions of photographs of children and their families.

In order to implementindividual interests, inclinations and needs of preschoolersthe object-spatial environment provides right each child to their favorite activity. To do this, when zoning the premises of a preschool educational institution, periodic updating of the material and equipment is provided, focused on the interests of different children.

Development curiosity, research interest and creativitychild is based on creationrange of possibilities for modeling, searching and experimentingwith various materials. In this case, various constructors, natural and waste materials, etc. are used.

Accounting age featuresrequires a child when creating a subject-spatial environmentage-specific equipment and materials.So, in the group for children 5-6 years old, the constructive zone is widely represented.

For accounting purposes sex role featureschildren object-spatial environmentserves the interests of both boys and girls.For example, for boys of 5-6 years old, samples of various equipment are widely presented, for girls - samples of handbags, etc.

The design of the subject-spatial environment creates the basis for the implementation of an individual approach to the child, implies the observance of the following principles:

ensuring a balance between the joint and individual activities of children;

organization of "privacy zones";
providing truth and freedom of choice;

creating conditions for modeling, search and experimentation;
polyfunctionality of the use of premises and equipment;
age and gender-role addressing of equipment and materials.

Our educators pay a lot of attention to teaching children to be more independent in the implementation of routine processes. Therefore, when organizing them (dressing for a walk, washing, going to bed), preference is given to subgroup forms of work. The composition of subgroups is not random, but is formed by the teacher, based on the most favorable circumstances for children. Teachers specifically create situations in which preschoolers gain the experience of friendly communication, attention to their peers.

A feature of the individually differentiated approach is the presence of certain conditions, without which its implementation is impossible, namely, monitoring the individual development of children's abilities. and based on the monitoring results, the zone of educational needs of each pupil is determined: the zone of increased educational needs corresponds to the high level, the zone of basic educational needs corresponds to the average level, the zone of risk corresponds to the low and lowest level. Accordingly, the planning of the educational process is carried out on the basis of the integration of educational areas, taking into account its individualization. Individually differentiated approach allows us to use different types of activities. For examplespeech developmentI want to tell you about the differentiated approach in working with children of teachers of our institution. In recent years, there has been a sharp decline in the level of speech development of preschool children. First of all, this is due to the deterioration in the health of children. Another reason is the passivity and ignorance of parents in matters of speech development of children. Acting on intuition, they do not help their child, and often doom him to serious difficulties in the subsequent teaching of written forms of speech. Most modern parents replace the development of speech with literacy, for them the main thing is to teach the child to read. Therefore, the kindergarten program provides for serious work on the development of speech, which is carried out in the system, covers all its aspects (dictionary, grammatical structure, sound culture of speech, coherent speech).

A good result in the speech development of a child can be achieved only if the coordinated actions of parents, educators, narrow specialists.

Educational psychologistconducts a psychological examination of children and, based on the results obtained, carries out developmental and corrective work. At preschool age, most mental functions are in the formative stage, so more attention is paid to preventive and developmental work. In order to create conditions for the full-fledged mental development of the child, the pedagogue-psychologist provides assistance to children, parents and teachers, draws up recommendations for the prevention of emotional overload in children. educators groups monitor the observance of a single speech mode throughout the day, work on the development of fine motor skills, in special cases, conduct individual classes with children.

Musical directorin his classes, he forms the tempo-rhythmic side of speech and contributes to the automation of sound through specially selected chants and songs. Speech therapist deals with the determination of the complexity and severity of speech deficiencies, the production and automation of sounds, the prevention of violations of written speech. Provides advisory assistance to parents, methodological assistance to employees of preschool educational institutions.

To implement a competent differentiated approach, the main provisions necessary for teaching preschoolers to develop speech are highlighted:

* Knowledge of the age characteristics and capabilities of children.

* Diagnosis and accounting of the level of speech development of each child.

* Close connection with speech therapy technologies.

* Balanced coverage of all aspects of the child's speech.

* The conscious attitude of teachers and parents to the speech development of children.

* Interaction between the kindergarten and the family on this issue.

The division into subgroups is not the distribution of prizes, but a normal working moment that helps to develop the speech of each child more effectively and efficiently. With such a distribution of children, both teachers can deal with all subgroups, however, the intensity of work with each of them is different. The intensity of work with subgroups is determined by the teachers themselves, depending on the results of the examination of children's speech at the beginning of the school year.

The most acute problem for educators is the organization of individual work with children. There is not enough time to cover all children and work with them in all areas of speech development. To determine the real time possibilities in each group, at the beginning of the school year, a timekeeping of the day and week was carried out, which made it possible to draw up a real plan for individual and subgroup work, to develop an algorithm for pedagogical influence and independent speech activity of each child. On the basis of timing, an approximate scheme for the distribution of various forms of work on speech development was developed. So, children who are always the first to come to kindergarten are offered individual tasks and exercises that take into account their speech shortcomings and difficulties. Those who come later are offered individual tasks or are connected to already working children (the latter option is possible if the speech defects of the children coincide). So individual work gradually turns into subgroup work. When almost all the children of the group gather, the teacher offers to see who did what and what results they achieved, after which they move on to frontal events. By analogy, work takes place in the afternoon, only in the reverse order: from the front to the subgroup and then to the individual (depending on how the children go home).

Cognitive development - mathematics (training group).The use of a differentiated approach in teaching mathematics to older preschoolers begins with the identificationthe level of mathematical development of children, which is based on the following indicators:

* the amount of mathematical knowledge and skills in accordance with the current program in kindergarten;

* the quality of mathematical knowledge: awareness, strength, memorization, the ability to use in independent activities;

* the level of skills and abilities of educational activities;

* the degree of development of cognitive interests and abilities;

* features of the development of speech (learning mathematical terminology);

* level of cognitive activity.

In accordance with the diagnostic results and the individual characteristics of the children in this group, we conditionally divided them into several subgroups. TOIn the first subgroup, we assigned children who showed great activity and interest in mathematics classes,as well as the creative nature of the application of the acquired knowledge and skills in practical activities.

The second subgroup included those pupils whose activity is not outwardly manifested.They do not raise their hands, but, as they are always attentive, they answer correctly and know how to find the right solution to the proposed problem.

The third subgroup consisted of children who did not show interest in mathematics classes, they not only have no desire to answer, but even when called, they prefer to remain silent.As practice shows, the passivity of children in mathematics classes is caused, first of all, by gaps in their knowledge, the difficulties they experience in the learning process, sometimes the reason was long absences due to illness.

The fourth group - risk group , children who experience difficulties in learning math. The teachers thought over the system of correctional and developmental work in the process of frontal, subgroup and individual lessons. It is in these classes that educators have the opportunity to work with preschoolers in a differentiated way, explaining the material in an accessible way, correlating the pace of the lesson with the possibilities of learning activities and the individual capabilities of each child. We thought over and made an individual plan of work with each child, aimed at the development of mathematical (quantitative, geometric, temporal, spatial, magnitude) representations, the logical sphere, cognitive activity and interest, etc.

During the lesson, teachers offer options for differentiating tasks:

- according to the level of difficulty,for example, a didactic exercise with counting sticks, in which there are three options: for one group of children, compose and name a geometric figure consisting of 3 sticks; the second - from 4 sticks; the third - from 6 sticks. This exercise arouses interest, great activity in children. One group tried to help the other, and vice versa.

– in terms of creativityfor example, tasks with geometric shapes (counting sticks) for the development of recreative and creative imagination, didactic games “Tangram”, “Magic Circle”, “Columbus egg”, etc.

When selecting games of mathematical content, the educator observes a certain sequence, taking into account that games with more difficult mathematical tasks should be preceded by games with tasks of a lesser degree of difficulty, serving as a kind of preparation for their implementation. Children show particular interest in games that contain an element of expectation or surprise, for example, the games “What has changed?”, “Which number?”, “Wonderful bag”, etc. If a child has difficulty mastering certain mathematical concepts and concepts, then, a day or two before the lesson, the teacher shows, for example, a figure and says to the child: “Soon we will get acquainted with a new figure. No one yet knows what it is called, but I’ll tell you now, just try to remember - it’s a rhombus (square, triangle). On the eve of the lesson, it once again reminds you of the name of the figure and how it differs from those already familiar. After such preparation, the child copes with tasks more easily and, as a rule, is active in the classroom. Performing a small task inspires confidence, activates the child to perform more complex tasks. Children who successfully acquire mathematical knowledge and skills should be given a more difficult task in the game so that they also maintain interest in the game.

With lagging behind children, in addition to frontal classes, additional individual lessons are conducted, widely using visualization (small counting material, pictures, models of numbers and geometric shapes, etc.), and notebooks for individual work are also offered. If some task is not given today, you should not try to achieve an immediate result from the child, you should move on without focusing on this. Then, after a while, you should return to this “difficult” task and try to complete it again. It is important to remember that only those activities that the child coped with on his own bring benefits. Parents should also be involved in working with children, who receive advice from a teacher on the mathematical development of preschoolers or narrow specialists, if necessary.

An individual approach to children, of course, cannot be turned into individual learning, when the teacher works with several children, leaving others as passive observers. Education in quantity is based on the fact that the educator sets common tasks for all, interests children in each other's work (the work of a strong child with a weak one), directs their common work, uses the comments and suggestions of individual children to achieve success for all. An individual approach is used in order to create conditions for the maximum development of each of the children and to prevent the influence of adverse circumstances. So children with impaired vision and hearing are placed closer to the educator, closer to visual aids, so that they better listen to the educator's explanations and see the display of the sample. Shy, timid children usually do not take an active part in the course of classes, and if they are not called to talk, do not ask them questions, do not encourage success, they themselves do not show activity and may not be noticed. A passive role in the classroom is an unfavorable condition for the development of such children. The educator somewhat restrains impulsive children with weak inhibitory abilities so that by their activity they do not bring disorganization into the course of the lesson, without “overshadowing” other children.

Thus, the implementation of a differentiated approach in the process of teaching elementary mathematics in kindergarten makes it possible not only to help children learn program material, but also to develop an interest in mathematics. At the present stage of development of pedagogical science, the implementation of an individually differentiated approach is considered a necessary condition for solving many pedagogical problems , including the readiness of older preschoolers to study at school.

Algorithm of the teacher's work with a differentiated approach

Establishment of a monitoring working group.
Selection of diagnostic tools
Carrying out diagnostics
Determination of the zone of educational needs of each pupil
Formation of small subgroups according to similar indicators
Planning the educational process
Familiarization of parents with the results of the diagnosis (individually)
Tracking the results of work, in the form of control slices, according to problematic indicators
Correction or continuation of work with children in the chosen direction.
Final diagnostics
Registration of monitoring results and evaluation of the results of the work of the teaching staff.

A differentiated approach is the ability to teach everyone!

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Introduction
1.1 Psychology of learning
1.2 Learning process
ChapterII. Using a differentiated approach to teaching in mathematics lessons in elementary school
Conclusion

Introduction

We are concerned about the same questions and problems: what needs to be done to give students high-quality knowledge in 45 minutes, how to rationally use time, how to increase students' interest, how to teach them to work independently.

And among the huge number of these problems, painfully solved by the national school and pedagogy, perhaps the most acute is: the problem of differentiation of education, which is the most relevant today.

A differentiated approach to students in the process of collective learning is one of the important principles of didactics, the implementation of which must overcome many contradictions inherent in the classroom system. The classroom system, which has withstood the test of time, remains the main system of education due to the fact that its structure optimally meets the requirements of a unified general education school, the conditions of collective and systematic learning with the rational use of material resources. The classroom system "averages" the knowledge, skills and abilities of students. The problem of differentiated learning was dealt with by Guzik N.P., Firsov V.V., Selevko G.K., Und Inge, Loshnova O.B. and many educators are innovators.

It should be noted that, despite the abundance of work on the implementation of the principle of a differentiated approach, the problem of differentiated learning remains unresolved. Its sharpness is due to the lack of sufficiently clear positions among the researchers involved in its development. Firstly, the principle of differentiated teaching in most cases is studied in isolation from other principles of didactics, which leads to a certain disregard for the latter in the course of the implementation of practical recommendations by teachers. Secondly, the search for optimal ways to implement the principle of a differentiated approach to teaching is often carried out without taking into account the level of qualifications of teachers and the specific conditions of their activities. This circumstance is one of the main obstacles to the differentiation of the educational process. Separating the educational process from the personality of the teacher, researchers often give such recommendations, the implementation of which is generally impossible in school practice.

As observations of the work of teachers show, it is possible to fully implement a differentiated approach only for master teachers with a rich complex of knowledge, skills and pedagogical abilities, teachers with a pronounced professional orientation.

Purpose: to consider the influence of various differentiated tasks on the formation of students' mental activity.

Tasks: to analyze the psychological and pedagogical literature on this topic, to consider tasks, exercises that contribute to the formation of interest in learning.

Chapter 1. Implementation of the principle of a differentiated approach to teaching

1.1 Psychology of learning

Educators and psychologists are constantly solving the question of how to build the learning process so that it is interesting and "affordable" for everyone. When we talk about learning, we emphasize the role of the teacher teaching, which, however, is not limited to the transfer of knowledge from teacher to student. The teacher does not just transfer knowledge, does not shift it into the head of the student. In the conditions of interaction between the teacher and the student, under the influence of the activity of both the teacher and the student, the student acquires knowledge, skills and abilities. The teacher manages this process.

With admission to school, the leading activity of children becomes educational activity. Its essence lies in the mastery of knowledge and skills, ways of their practical implementation. Educational activity does not form by itself. If a student goes to school, conscientiously listens to the teacher and does his homework, this does not mean that he is engaged in learning activities. The teacher forms the learning activity of schoolchildren (teaches them to learn).

Educational activity is complex in its structure, there are three main components:

- motivational;

- operational;

- control and evaluation.

It is also worth noting that learning depends, firstly, on the material to be learned, on its content and the system in which it is presented. Secondly, the nature of teaching depends on the methodological skill and experience of the teacher, his personal characteristics, on the specific teaching methodology that the teacher uses in each individual case.

The main aspects of the learning process are as follows:

- the formation of a positive attitude towards learning, social motives for learning among students;

- assimilation of the knowledge system;

- formation of methods (techniques) for performing the relevant activity - skills and abilities;

- mental development of students - the formation of their need and ability to independently replenish and improve knowledge, the development of active, independent, creative thinking;

- education in the learning process.

In this regard, let us consider the features of the cognitive activity of a younger student, which are taken into account when constructing a lesson.

Assimilation of knowledge. Assimilation as an organized cognitive activity of a student includes the activity of perception, memory, thinking and imagination.

There are four main parts of the learning process:

direct perception, observation (obtaining information);

comprehension of the material, its mental processing (processing of the information received);

memorization and preservation of material (storage of received and processed information);

application of knowledge in practice (application of information).

Of course, this division is to a certain extent arbitrary, since these links are not isolated from each other, but are closely intertwined and interconnected.

Perception. Educational activity in the primary grades stimulates, first of all, the development of mental processes of direct knowledge of the surrounding world - sensations and perception. Younger students are distinguished by sharpness and freshness of perception. A child with lively curiosity perceives the life around him, which every day reveals more and more new sides to him. However, perception in grades 1 and at the beginning of grade 2 is still very imperfect and superficial. Younger schoolchildren make inaccuracies and errors in differentiation when perceiving similar objects. Sometimes they do not distinguish and mix letters and words similar in style or pronunciation, images of similar objects and similar objects themselves. For example, they confuse the letters "sh" and "u", shown in the picture of rye and wheat, pentagons and hexagons. Often children highlight random details, while they do not perceive the essential and important. In a word, younger students do not know how to consider objects.

The next feature of perception at the beginning of primary school age is its close connection with the actions of the teacher. Perception at this level of mental development is associated with the practical activities of the child. To perceive an object for a student means to do something with it, to change something in it, to perform some action, to take it, to touch it.

A characteristic feature of students in grades 1-2 is a pronounced emotionality of perception. First of all, children perceive those objects or their properties, signs, features that cause a direct emotional response, an emotional attitude. Visual, bright, alive is perceived better, more distinctly. However, the teacher should also strive to ensure that the children clearly perceive the less vivid, less exciting and significant, specifically drawing their attention to this.

Thinking. The thinking of a younger student, especially a first-grader, is visual-figurative. It constantly relies on perceptions and ideas. A verbally expressed thought that does not have support in visual impressions is difficult for younger students to understand.

What categories of signs are distinguished by younger students? Here, too, there is a definite pattern. For example, in class 1, the most visible visual signs are those related to the actions of the object (“what it does”) or its purpose (“what it is for”), i.e. utilitarian and functional signs ("The moon is shining", "Cherries are delicious, they are eaten").

Approximately from the 2nd grade, schoolchildren are noticeably freed from the inspiring influence of visual signs and rely more and more on signs that reflect the connections and relationships between objects and phenomena.

Grade 3 students are capable of a higher level of generalization associated with the establishment of subordination of concepts: children isolate broader and narrower concepts.

The student develops the ability for verbal-logical thinking, reasoning, conclusions, conclusions. If students of the 1st and partly 2nd grade often replace argumentation and proof by simply pointing to a real fact or rely on an analogy (which is far from always legitimate), then students of the 3rd grade, under the influence of training, are able to give a reasonable proof, expand the argument, build a deductive conclusion.

Imagination. A feature of the imagination of younger students is its reliance on perception. It is sometimes quite difficult for students in grades 1-2 to imagine something that does not find support in nature or in a picture. But without a recreative imagination it is impossible to perceive and understand the educational material. The main trend in the development of imagination in primary school age is the improvement of the recreative imagination. It is associated with the presentation of previously perceived or the creation of images in accordance with a given description, diagram, drawing, etc.

Of great importance is the inclusion of the student in creative work (drawing, craftsmanship, folk art circle). The role of special methodological techniques is important here - stories and compositions based on pictures, drawing illustrations for texts, a mental journey along a geographical map with a visual description of nature, a journey into the past with a visual representation of that era.

Memory. In life, one can observe significant individual differences in the field of memory. Different types of memory are distinguished depending on what a person remembers more successfully and how he prefers to remember.

First, people remember different material in different ways. Some people remember pictures, faces, objects, colors, sounds most well. These are representatives of the visual-figurative type of memory. Others better remember thoughts and verbal formulations, concepts, formulas, etc. These are representatives of the verbal-logical type of memory. Still others remember both visual-figurative and verbal-logical material equally well. These are representatives of the harmonic type of memory.

Secondly, people prefer to remember in different ways. Some remember better visually, others - by ear, others - with the help of motor sensations, and fourth - with a combined method.

A person's memory can also be characterized depending on how developed his individual memory processes are. We say that a person has a good memory if he is different:

memorization speed

strength of preservation

fidelity

the ability to extract from memory reserves.

Far from often there are people who quickly memorize, and remember for a long time, and accurately reproduce, and remember at the very moment when it is needed.

Among schoolchildren, there are often children who, in order to memorize the material, only need to read or listen carefully to the teacher's explanations once. Moreover, these children not only memorize quickly, but also retain what they have learned for a long time, easily and fully reproduce it. Such students stand out among other students by their success in mastering knowledge.

The most difficult case is slow memorization and quick forgetting of educational material. Such children spend a lot of time and effort memorizing material, reproduce it inaccurately and quickly forget. The poor performance of their memory is due to various reasons. As a rule, poor memorization is observed in schoolchildren who often miss classes, do not systematically complete learning tasks, and do not master memorization techniques. These children should be regularly helped, patiently taught the methods of rational memorization.

Very often, insignificant results of memorization do not depend on poor memory, but on poor attention.

When organizing the educational activities of a younger student, it is necessary to take into account the impact on the success of memorizing interests, emotional attitude to educational material, and active work with it. The teacher must always remember that in each class there are students of different types of memory, and therefore he needs to turn to different analyzers (motor, visual, auditory). And, finally, it is important for the teacher to know the individual characteristics of the memory of his students: this gives him the opportunity, on the one hand, to rely on the stronger aspects of their memory, and on the other hand, to purposefully work to improve the weaknesses of the memory of students.

Skills skills. While studying at school, students acquire a variety of skills and abilities through exercise and training.

An exercise, as a necessary condition for the formation and consolidation of skills, must meet the following conditions:

you should know exactly the purpose of the exercise, what results should be achieved;

it is necessary to monitor the accuracy of the exercise in order not to reinforce mistakes if they occur, monitor the results of the exercises, compare your actions with the standard, realize what successes have already been achieved and what shortcomings should be fixed in order to eliminate them;

exercises should not be a random set of the same type of actions, they should be based on a certain system, it is necessary to plan their correct sequence, constantly complicate them;

exercises should not be interrupted for a long time, since in these cases the skill is formed slowly;

exercises must be differentiated, since a weak student needs help with some exercises, although a strong one performs it without difficulty.

Peculiaritiesbuildingprocesslearningatjuniorschoolboy.

At each age stage of human development, both general properties inherent in a social group and specific, individual characteristics are formed. Children of the same age differ from each other in typological features of higher nervous activity, physical and spiritual development, abilities, interests, etc. Thus, the class consists of students with different development, different readiness, different academic performance and attitude to learning, different features of attention and memory. From the first grade, the teacher often conducts training in relation to the average level - to average development, average readiness, average academic performance. This often leads to the fact that "strong" students are artificially restrained in development, lose interest in teaching, which does not require mental effort from them: "weak" students, on the contrary, are often doomed to chronic lag and also lose interest in teaching, which requires too much mental stress from them. The question arises of how to build a learning process so that a "weak" student would be able to do it and be interesting, and a "strong" student would not lose the desire to work because of the ease and simplicity of teaching.

Students with learning disabilities are especially in need of a differentiated approach in order to prevent their transition to the category of chronically underachieving or to overcome their underachievement. In the primary grades, there may be children with a lack of sufficient cognitive activity, intellectually passive, as psychologists call them.

These children show normal intellectual development, which is manifested in games and practical activities. But in educational activity they are not yet accustomed to and do not know how to think; they are characterized by the desire to avoid active mental activity.

Psychologists have substantiated the optimal ways of teaching children with low learning ability and intellectually passive children. Training must be built on the basis of the peculiarities of their psyche - a slow type of formation of generalized knowledge, intellectual passivity, increased fatigue during mental activity. At first, for this category of schoolchildren, it is optimal to study at a somewhat slower pace, with a wider visualization and verbal concretization of general provisions with a large number of exercises, the implementation of which relies on a direct demonstration of decision techniques, with constantly decreasing outside help and also a constantly increasing degree of difficulty of tasks.

The implementation of the principle of a differentiated approach in teaching means attention not only to those who find it difficult to study, but also to those who show a high level of mental development, show pronounced interests, inclinations and abilities for any kind of activity.

differentiated approach mathematics learning

1.2 Learning process

The learning process is a purposeful, consistently changing interaction between teachers and students, during which the tasks of education, upbringing and general development of students are solved. The learning process is part of the whole pedagogical process.

Basic learning functions.

Based on the overall goal of the school, the learning process is designed to carry out three functions: educational, upbringing, developing. Modern didactics emphasizes that the tasks of the educational process cannot be reduced only to the formation of knowledge, skills and abilities. It is designed to have a complex effect on the individual. The conditional allocation of these functions is useful for the practical activities of teachers, especially when planning learning tasks in the classroom.

The unity of these functions is carried out by combining a variety of methods, forms and means of teaching.

The structure of the learning process

When considering the structure of the learning process, it is necessary to identify its structure and main components.

The learning process consists of two interrelated processes - teaching and learning

Learning is impossible without the simultaneous activity of the teacher and students, without their didactic interaction. No matter how actively the teacher strives to convey knowledge, if there is no active activity of the students themselves in mastering knowledge, if the teacher does not provide motivation and accessibility of learning, didactic interaction does not really function. Therefore, in the learning process, it is not just the influence of the teacher on the student, but precisely their interaction, the unity of the trainees and the personal influences of the teacher is realized, the emergence of independent efforts of the student to master knowledge, skills and abilities.

Based on the characteristics of the process of activity, we can holistically imagine the constituent elements of the learning process:

- target;

- stimulating and motivational;

- operational and activity;

- control and regulation;

- evaluative and effective.

The content of training is determined by the curriculum and programs. The content of the lessons is specified by the teacher, taking into account the tasks set, the need to reflect the specifics of the school, the level of preparedness, and the interests of students in the content of the subjects.

1.3 The essence of learning differentiation

L.S. Vygotsky noted: “According to his characteristics, a child is capable of some new cycle of learning, inaccessible to him before. interests, according to the level of his thinking, he can assimilate it to the extent that it is his own program.

The requirement to take into account the individual abilities of the child in the learning process is a very old tradition. The need for this is obvious, because students are very different from each other.

One of the requirements of the teacher's activity and the condition for the effective organization of the educational process is to ensure the complete assimilation of knowledge by all students. Can you imagine how many more lessons the teacher needs to give in order for the students of the second, and especially the third group, to learn new material? The teacher may be happy to work with them, but driven by the program, he goes further, starts studying a new topic.

The individual development of students is also manifested in the level of working capacity. On this basis, students can be divided into three groups:

The first one is characterized by high working capacity (there are 36% of such students)

The second - medium (50-55%)

Third - low (8-17%)

It is noteworthy that students with low working capacity are more likely than others to fall into the ranks of those who do not succeed, although most of them do not suffer from mental insufficiency or lack of interest in learning at all. No, they just need a different pace of work.

It is the working capacity, both low and high, that is an indicator of the student's belonging to a certain type of nervous system. Students with a weak nervous system work slowly, but very thoroughly. They, of course, need much more time. They are pedantic, very sensitive and vulnerable. Therefore, their learning failures should be assessed very carefully, avoiding harsh expressions, insulting reproaches.

Individual differences are also manifested in the types of thinking: in some children, practically effective thinking prevails, in the second - visual-figurative, and in others - verbal-logical. In real life, all three types of thinking are interconnected, and the learning process should be aimed at the formation of each of them.

The influence of the type of thinking on the strength of the assimilation of knowledge was proved in the experiment. Students of mathematical and art schools were asked to memorize a series of numbers written in different fonts and colors. Some time later, they were asked to reproduce these figures. "Mathematicians" reproduced the numbers themselves, while their "artist" peers paid attention to the color and font of the numbers.

The traditional education system and the proposed approaches to its modernization affect the main contradiction in education - between the high needs of society for the quality of education of all its members and the psycho-physiological characteristics of children. At present, world pedagogy is increasingly aware that the crisis caused by the above contradictions cannot be resolved within the framework of the old system and requires a change in teaching technology.

It is necessary to create optimal conditions for the development of the personality of the most complete account of the individual differences of students. The way to create these conditions is the differentiation of learning

Differentiation in translation from the Latin "difference" means division, stratification of the whole into various parts, forms, steps.

Differentiated learning:

- this is a form of organization of the educational process, in which the teacher, working with a group of students, takes into account the presence of any qualities that are significant for the educational process (homogeneous group);

- it is also part of the general didactic system, which provides specialization of the educational process for different groups of students.

Differentiation of learning (differentiated approach to learning):

- this is the creation of a variety of learning conditions for various schools, classes, groups in order to take into account the characteristics of their contingent.

- This is a set of methodological, psychological, pedagogical, organizational and managerial measures that provide training in homogeneous groups.

The purpose of differentiation is to teach everyone at the level of their capabilities, abilities, to adapt learning to the characteristics of different groups of students.

According to the characteristic individual psychological characteristics of children, which form the basis for the formation of homogeneous groups, differentiation is distinguished:

- by age composition (school classes, age parallels, different age groups);

- by gender (male, female, mixed classes, teams);

- by personal-psychological types (type of thinking, temperament);

- according to the level of health (physical education groups, groups of impaired vision, hearing);

- according to the level of mental development (level of achievement);

- by area of interest (humanitarian, historical, mathematical).

Differentiation according to the level of mental development does not receive an unambiguous assessment in modern didactics; It has some negative aspects as well as positive ones.

Positive aspects of level differentiation:

- unjustified and inappropriate for society "equalization" and averaging of children are excluded;

- the teacher has the opportunity to help the weak, pay attention to the strong;

- the absence of lagging behind in the class eliminates the need to reduce the overall level of teaching;

- there is an opportunity to work more effectively with difficult students who do not adapt well to social norms;

- the desire of strong students to move faster and deeper in education is realized;

- the level of "I - the concept" rises: the strong are affirmed in their abilities, the weak get the opportunity to experience educational success, get rid of the inferiority complex;

- increases the level of learning motivation in strong groups;

- in a group where the same children are gathered, it is easier for a child to learn.

Negative aspects of level differentiation:

- the division of children according to the level of development is inhumane;

- the weak are deprived of the opportunity to reach out for the stronger, to teach help from them, to compete with them;

- socio-economic inequality is highlighted;

- transfer to weak groups is perceived by children as a humiliation of their dignity;

- the imperfection of diagnostics sometimes leads to the fact that extraordinary children are transferred to a number of weak ones;

- the level of "I-concept" goes down: in elite groups there is an illusion of exclusivity, an egoistic complex; in weak groups, the level of self-esteem decreases, an attitude towards the fatality of one's weakness appears.

1.4 Lesson organization with a differentiated approach to teaching

The principle of learning differentiation itself is not new.

Even Pestalozzi warned teachers against trying to "cut all children with the same brush" and pedagogy has always declared the need for a differential approach to children, taking into account individual developmental characteristics, inclinations, etc. However, without denying the need for differentiation, pedagogy suggests two extreme options:

First, each child is individual, which means that his upbringing is unique, and each child needs his own special approach to upbringing and education. It is extremely difficult or impossible to implement this option in practice in the specific conditions of the school, which means it remains available. The second option is universal equality, uniformity in the approach to different children and differentiation only for certain groups of children with pronounced developmental features (impairment, giftedness, etc.).

In direct dependence on the accepted approach to differentiation is the organization of the educational process and its main form - the lesson.

In elementary school, a lesson is practically the only form of study, regardless of programs and approaches. The content and methods of work in the lesson can be different and even varied, but in form it is a traditional lesson, when all students perform the same types of work at the same time.

The traditional lesson, when the teacher works for everyone, with everyone, asks everyone (a rare exception is independent work, work on cards, but still with strict time regulation for everyone), fetters the teacher more and more. Each teacher realizes and experiences in practice the difficulty of working with everyone as "with one", understands that children have a different pace of activity, "get involved in work" in different ways, and switch to a new type of activity in different ways.

However, realizing these problems, many believe that it is impossible to change the system of work in the classroom.

Is it so? Perhaps differentiation does not seem so necessary, but then it is worth asking other questions - is it possible without differentiation, is such frontal learning effective?

Let's try to figure it out. For example, it is well known that a frequently ill child is usually characterized by low and unstable working capacity, increased fatigue, difficulties in organizing activities, etc., in addition, he has to "catch up" with classmates after illness. And if this does not cause serious problems in reading or work, then it is impossible to "catch up" while mastering new material in mathematics or literacy, so it is worth turning the child off from the system of general work and working with him (not after school, when he is no longer able to study ) at the lesson. At the same time, it is not difficult to find three or four more students who also need to parse the same material.

The elementary school program is available to all children (without pronounced deviations). However, effective learning is possible only when "it makes sufficiently high demands on the more capable and does not violate the trust and attitude to learning among the less capable." (J. Bruner)

The need for individualization and differentiation of education is undeniable, but then it is required to find options for organizing work in the classroom that are acceptable in the conditions of a modern school.

One option may be to create three groups and work individually with each (the size and composition of the group may vary).

How can the lesson be organized in this case?

Lesson work is carried out in small groups of 6-8 people. Each of the groups works in any lesson with a teacher from 7 to 10 minutes (this is the optimal duration of effective intensive work). Thus, in 45 minutes, each group (and therefore each child) has a chance to work with a teacher.

The advantage of this option is that the teacher gets the opportunity to more evenly distribute his attention between the students of each group. At that moment, when the teacher works with the next group, the rest either independently prepare to work with the teacher, or also independently perform tasks.

The advantage of such an organization of classes is the development of independent work skills and ample opportunities to help those children who need extra attention. From observations, we can conclude that children highly appreciate the opportunity to work with the teacher "eye to eye", ask their questions, get clarifications, and even more they like to do written work without rushing: if they are not urged, they get used to such a system of work .

For convenience, you can assign a specific symbol, color to each group, make an activity wheel with the group and hang it in a conspicuous place. The arrow shows which group is working with the teacher. The circle can be rotated by combining a certain symbol (color) with the arrow. You can attach a task to the circle for each group. Each teacher can find their own options for work.

It is important to note that the composition of the group can and should change, it will be different in different classes, since differentiation can be carried out according to different criteria. An indispensable condition for successful work in groups is the teacher's good knowledge of the characteristics of each child, the ability to build an individual training program.

Those. working with each group, which is made up of students of the same level of learning (level of development, etc.), the teacher can work with each student individually.

Differentiation of education covers the education of the individual in the broad sense of this concept. It creates the prerequisites for the development of the interests and social abilities of the child, while trying to take into account existing cognitive interests and encourage new ones. Differentiation preserves and develops the individuality of the child, brings up such a person who would be a unique personality. Purposeful differentiated work mitigates the shortcomings of home education, it is especially necessary for those students who grow up in unfavorable families. In this sense, a mission of great social significance falls on differentiation.

Differentiation is applied in various parts of the learning process

Study of new material

In preparing for the passage of new material, differentiation is necessary, since the skills and abilities of students are different. Some students need simple tasks, others can receive tasks that, from the point of view of a particular problem, included in the topic being studied, successfully integrate with the students' prior knowledge on the topic.

- When passing a new topic, it is necessary to take into account the differences between students, primarily in learning skills and mental abilities. These properties determine what kind of guidance they need and how difficult the task they can choose for independent work.

- Compared to other parts of the learning process, differences in students' knowledge can be less taken into account here. But this account becomes relevant when a student has a much more extensive knowledge than his classmates.

- When presenting new material, one should, if possible, address various analyzers (visual, auditory, motor, etc.), because this favors better comprehension and consolidation.

Orientation on the finite result

Orientation to the final result determines the differentiated attitude of the teacher to the input material. Weak students should be given enough time to work out new material, and strong students, after explaining the topic, can be given training exercises to complete on their own.

Anchoring passed.

The need for differentiation is especially great when consolidating and applying knowledge. Therefore, students need reinforcement and exercises not at the same level and not in the same amount. For stronger students at this stage of work, time is freed up to perform additional tasks that expand and deepen their knowledge and skills.

It is during the performance of educational tasks that the assimilation of theoretical knowledge takes place, practical skills are formed, therefore, at the stage of consolidation, the efforts of the teacher should be concentrated. At the same time, it is very important to organize educational work in such a way that each student does the work that is feasible for himself, getting the opportunity to experience educational success at each lesson.

Didactic support for a differentiated approach to students at the stage of consolidating the material is the selection of a system of exercises. Such a system of tasks should include:

- a wide range of tasks of a mandatory level;

- a task to prevent common mistakes;

- tasks of increased complexity, designed for students who are rapidly advancing in the assimilation of the material.

Control

Based on the main goals of developmental education, Abasov Z.V. provisions were formulated on the issue of monitoring and evaluating the educational activities of students.

Position 1: The pedagogical activity of teachers at the stage from the first to the third (fourth) grades is aimed at developing the ability to learn in students, which includes two actions.

a. The ability of a child at different stages of learning (at the beginning together with the teacher, then in cooperation with peers, then individually) to determine the limit of his ignorance.

b. To make meaningful a targeted request to various sources of knowledge (to a teacher, to peers, to parents, to literary sources, etc.).

To implement this very important skill, it is necessary to focus the teacher's attention on the formation of children's abilities for mutual and self-control, mutual and self-esteem. The absence of these educational actions on the part of children leads to the destruction of all educational activity: it turns into a formal "farce" that does not give the final result.

Position 2: Control and evaluation by the teacher of the activities of each student is present without fail in pedagogical activities. However, the teacher needs to take into account a number of features.

Monitoring and evaluation are aimed not only, and this is very important, at identifying a certain result in knowledge and skills, but, above all, at the process of forming this knowledge among students to ensure targeted and timely correction.

When monitoring the activities of students, the child himself determines the level of his abilities and chooses the tasks with which he can cope, therefore, the assessment of the student's work is determined based on the level of complexity of the tasks he has chosen.

The main function of control is seen in the constant monitoring of the progress of the implementation of educational activities, the timely detection of various errors in their implementation.

In pedagogy, the following forms of control are distinguished:

- test work,

- Independent work,

- Test papers,

- Checking robots,

- final work,

- Starting work.

When conducting independent work, the goal here is to identify the level of mathematical training of children and to eliminate the existing knowledge gaps in a timely manner. At the end of each independent work, there is a place for working on mistakes. At first, the teacher should help the children in choosing knowledge that allows them to correct their mistakes in a timely manner.

Control works sum up the result of this work. Their main function is knowledge control. From the first steps, the child should be taught to be especially attentive and precise in his actions during the control of knowledge. The results of the tests are not corrected - you need to prepare for the knowledge control before it, and not after. At the same time, preparatory work, timely correction of errors during independent work gives a certain guarantee that the test will be written successfully.

Independent work is designed, as a rule, for 7-10 minutes. If the child does not have time to complete the task within the allotted time, then after checking the work by the teacher, he finalizes these tasks at home.

The assessment for independent work is put after the work on the bugs has been carried out. It is not so much what the child managed to do during the lesson that is evaluated, but how he eventually worked on the material. Therefore, even those works that are not written very well in the lesson can be evaluated with an excellent and good score. In independent work, the quality of work on oneself is fundamentally important and only success is evaluated.

30-40 minutes are allotted for examinations. If one of the children does not fit into the allotted time, then at the initial stages of training, some additional time can be allocated for him to give him the opportunity to calmly finish the work. The assessment for the control work is corrected in the next control work.

Independent work is offered approximately 1-2 times a week, and control 2-3 times a quarter. At the end of the year, children first write a translation paper that tests their ability to continue their education in the next grade in accordance with the State Standard of Knowledge, and then a final test. The main goal of the final work is to reveal the real level of knowledge of children, their mastery of general educational skills and abilities, to enable children themselves to realize the result of their work, to experience the joy of victory.

Home Work

Particularly great opportunities for differentiation open up in homework.

In pedagogy, the following ways of differentiating homework are known:

- additional tasks for students;

- development of special tasks for different students (differentiation of tasks);

- explanation of the meaning and content of the task, briefing.

There are many ways to help students prepare for homework:

- point to analogies,

- explain with examples

- to understand the difficult aspects of tasks.

- explain the content of the work,

- give an algorithm,

- inform the methods of performing tasks,

Some teachers practice flashcards and homework charts that they give weak students to help them highlight the main points in the material. The younger the students, the more specific the teacher's instructions should be.

The problem of homework is closely connected with the ways of further development of the school, the improvement of all its links. The first step in improving homework is to optimize it. The second, more distant stage is the embodiment of ideas about the voluntariness of doing homework, its differentiation and individuality.

Chapter II. Using a differentiated approach to teaching in mathematics lessons in elementary school

2.1 Level differentiation in teaching mathematics to younger students

Level differentiation can be organized in a variety of forms, which significantly depend on the individual approaches of the teacher, the characteristics of the class, and the age of the students. As the main way to implement differentiation in training, we choose the formation of mobile groups. The division into groups is carried out on the basis of reaching the level of compulsory training. The teacher plans to work with leveling groups and with advanced level groups. Level differentiation gives the teacher clear guidelines for the selection of content, allows you to make it purposeful.

The peculiarity of using a differentiated approach is that for independent work the student is offered three options for tasks of varying degrees of complexity:

Option 1 is the most difficult

Option 2 - less difficult

Option 3 is the easiest.

Each student has the opportunity to choose the most optimal option for himself when compiling educational tasks of varying degrees of difficulty, teachers Fomenkova M.V., Khaustova N.I. suggest considering the following:

1) The first step actions (addition, multiplication) are easier to perform compared to the second step actions (subtraction, division).

2) Expressions containing several actions are more complex than expressions containing only one action (for example, 48+30, 32+13-10).

3) Actions containing a large number of elementary operations require a higher level of development of students

Another set is cards, the peculiarity of which is that, in addition to the material with tasks for independent work, additional cards are given for each series (C-1A C-1B; C-2A C-2B, etc.)

Additional cards contain drawings, drawings, instructions and tips that should help the student if he cannot cope on his own with the main task. In this case, you should always remember that cards with indices A and B have no independent meaning. They are additional to the cards of the main series. Children need to be taught how to work with cards of this type. Having received one (or two) additional cards, the student should read the main task, and then cards A and B. Students should clearly imagine that they should use the additional instructions and tasks contained in the cards when completing the main task. More prepared students do not need additional guidance. For the same students whom the teacher deems necessary to provide some help, he will give an additional card with index A, on which the children will see a schematic drawing illustrating the condition of the problem and the task. For many children, obviously, such help will be enough, since by examining the drawing and answering the question posed, they receive the key to solving the problem. Children who are less prepared for work than others may not be able to cope with the task even under such conditions. For them, the teacher has another additional card (with index B). Such a task, of course, largely deprives the independence of solving the task, since there is not much left for the student to do, but still, in this case, the task requires awareness of the method of solving, the particularity of the issue of the problem. For students who easily and quickly completed the main task, a number of cards also contain tasks marked with an asterisk (as a rule, these tasks are more difficult, deepening the knowledge of children).

Among the reasons that determine the insufficient level of formation of students' ability to solve problems, the following can be distinguished:

The first is in the teaching methodology, which for a long time oriented the teacher not to the formation of generalized skills in students, but to "learning" ways to solve problems of certain types.

The second reason lies in the fact that students objectively differ from each other in the nature of mental activity carried out in solving problems.

Many teachers are familiar with the difficulties that are associated with the organization of frontal work on a text task in a lesson. Indeed, at a time when most of the students in the class are just starting to comprehend the content of the problem together with the teacher, the other, albeit a smaller part, already knows how to solve it. Some students are able to see different ways of solving, others need a lot of help in order to simply solve the problem. At the same time, a certain part of the students in the class remains underloaded, since the proposed tasks are too simple for them. In this regard, the question arises: "How to organize the work on the task in the lesson so that it corresponds to the abilities of the students?" To do this, it will be necessary to study the analysis of the work of psychologists, which will make it possible to highlight the levels of ability to solve problems by younger students.

Low level. The perception of the task is carried out by the student superficially, incompletely. At the same time, he singles out disparate data, external, often insignificant elements of the task. The student cannot and does not try to foresee the course of her decision. A typical situation is when, having not properly understood the task, the student already proceeds to solve it, which most often turns out to be a random manipulation of numerical data.

Average level. The perception of the task is accompanied by its analysis. The student strives to understand the task, highlights the data and what is being sought, but at the same time is able to establish only separate connections between them. Due to the lack of a unified system of relationships between quantities, it is difficult to predict the subsequent course of solving the problem. The more developed this network, the greater the probability of an erroneous decision.

High level. Based on a complete comprehensive analysis of the problem, the student identifies an integral system (complex) of relationships between the data and the desired. This allows him to carry out a holistic planning of solving the problem. The student is able to independently see different ways of solving and select the most rational of the possible.

It is obvious that the educational influence that is appropriate for high-level mental activity will be inaccessible for understanding and assimilation at a low level. Therefore, in order to increase the effectiveness of teaching problem solving, it is necessary to take into account the initial level of formation of this skill in the student (this is intuitively done by an experienced teacher).

In order to organize multi-level work on a task at the same time allotted for this in the lesson, you can use individual task cards that are prepared in advance in three versions (for three levels). These cards contain task systems related to the analysis and solution of the same problem, but at different levels. In a duplicated form, they are offered to students in the form of a printed basis. The student completes the task in writing in a specially designated place. Offering the student a variant of the optimal level of complexity for him, we carry out the differentiation of search activity in solving the problem.

Here are some examples of such cards. Note that for ethical reasons, the level offered to the student is not indicated in the card, and the difference in options is indicated by circles of different colors in the upper corner of the card.

Task. (III class.). From two piers, the distance between which is 117 km, two boats set off simultaneously towards each other along the river. One walked at a speed of 17 km/h, the other - 24 km/h. What is the distance between the boats 2 hours after the start of the movement?

1 level.

Consider the drawing for the task and complete the tasks:

a) draw a line with a blue pencil indicating the distance traveled by the first boat in 2 hours. Calculate this distance.

b) draw a line with a red pencil indicating the distance traveled by the second boat in two hours. Calculate this distance.

c) consider the segments denoting the distance traveled by two boats during this time. Calculate this distance.

d) read the question of the problem and mark the segment corresponding to the desired one with an arc in the drawing. Calculate this distance.

If the problem is solved, then write down the answer.

Answer:

Consider again task I and write down a plan for solving this problem (without calculations).

Test yourself! Answer: 35 km.

This problem has a more rational way to solve it. But it is usually more difficult for weak students, since it involves operating with a less specific concept of "speed of convergence." Therefore, you can invite students to consider this way of solving and explain it. This task is designated in the card as an additional one.

Additional exercise.

Consider another way to solve this problem. Write explanations for each action and calculate the answer.

17+24=

…х2=

117-…=

Answer: ... km

2 level.

Finish the drawing for the task. Mark on it the data and the desired:

Consider the "reasoning tree" from the data to the question. Indicate on it the sequence of actions and the arithmetic signs of each action.

Using the "reasoning tree", write down a plan for solving the problem.

Write down the solution to the problem:

a) by actions

b) an expression.

Answer

Additional task.

Using the drawing, find another way to solve the problem and write it down. (because the other solution is more obvious, students can find it on their own, without aids).

by action with explanation

expression.

Answer.

Test yourself! Compare the answers obtained in different ways.

3 level.

Complete the drawing for the task.

Using the drawing, find a more rational way to solve. Make up a "reasoning tree" for this method (children independently compose a "reasoning tree" as in the second option).

Write down a plan for solving the problem in accordance with the "reasoning tree".

Using the plan, write down the solution to the problem:

by actions;

expression.

Answer:

Test yourself! Answer of the problem: 35 km.

Additional exercise.

Find out what distance will be between the boats at the same speed and direction of movement after 3 hours? 4 hours?

In tasks, the solution plan is deliberately isolated from computational actions (in practice, "step-by-step" planning prevails as more accessible). This is done in order to form the ability to carry out a holistic planning of solving the problem. Its advantage over "step by step" is seen in the fact that in this case the attention of students is concentrated on the search for a generalized way of solving the problem, regardless of specific numerical data, being distracted from them.