Ministry of Education and Science of the Russian Federation

federal state budgetary educational institution of higher professional education

KRASNOYARSK STATE PEDAGOGICAL UNIVERSITY named after V.P. Astafieva

(KSPU named after V.P. Astafiev)

Faculty of Primary School

Department of Music and Art Education

Direction (specialty) music

Final qualifying work on the methodology of music education

The development of figurative thinking of younger students through listening to music

Made by a student of the MZK group

Correspondence form of education

Ponomareva K.A. I.P.

(Last name, first name) (Signature, date)

Scientific adviser:

Kharchenko L.E.

(Last name, first name) (Signature, date)

Date of protection ___________________

Grade_________________________

Krasnoyarsk, 2015

The title page must be looked at and properly formatted

Introduction ................................................ ................................................. .. 3

1. Theoretical part ............................................... .................................................. 5 1.1 Psychological characteristics of younger students, main activities ........ ................................................. ................................................... 5 1.2 Thinking. Creative thinking................................................ ........ 9 1.3 Activities in the music lesson. “Listening” to music .............................. 14 1.4 Means for the development of imaginative thinking .............................. .................................. 20 2. Practical part .............................. ................................................. .25

2.1 Analysis of the situation............................................... ................................... 25

2.2 Description of practical work experience.................................................... ..28

Conclusion................................................. ................................................... 38

Bibliography............................................... ............. 40

Applications ................................................. ............................................. 43

INTRODUCTION

Currently, as you know, the sphere of the educational system of the Russian Federation is going through a period of various reforms that are aimed at improving the quality of education and the knowledge and competencies of schoolchildren. Also, modern society understands the need to humanize learning, in connection with this, there is an increase in the importance of subjects, for example, such as "Music". Why is it so ugly? As you know, "Music" is a rather specific subject that requires a special approach. Updating the content and methods of music education is a constant orientation towards an ideal that is both in the future and in the past, which means not overcoming traditions, but understanding them from the standpoint of today. And where is at least something about the Federal State Educational Standard? A form of reflection of the world, specific to art, is figurative thinking. Like any mental process, figurative thinking needs to be developed and corrected. Therefore, the idea of ​​developing figurative thinking in music lessons is relevant for the modern school. In particular, the development of figurative thinking is relevant for primary school age, because. this age has a predisposition to the knowledge of the world through images. Target this research work - the development of figurative thinking of younger students through listening to music. object of this study is the development of figurative thinking. Subject of this study is listening to music. In accordance with the purpose of the study, the following tasks: 1. To study the psychological and pedagogical characteristics of primary school students; 2. Consider the features of the development of figurative thinking in music lessons for younger students; 3. Develop methodological and practical techniques (recommendations for "Listening") that contribute to the development of figurative thinking in music lessons; 4. Test these techniques in practice.

This study uses such methods how: 1. Analysis of psychological and pedagogical literature; 2. Empirical methods: Observation, conversation with students; 3. Method of peer review (conversation with a music teacher); 4. Studying the products of student creativity. Experimental-practical The work was carried out on the basis of the comprehensive school No. 17 in Krasnoyarsk.

1. THEORETICAL PART

1. 1. Psychological characteristics of younger students, main activities

It’s better not to start a sentence with a surname. Ya. A. Kamensky, an outstanding Czech teacher, wrote: “Everything to be mastered should be distributed according to age levels so that only what is available for perception at each age is offered for study.” Therefore, accounting age features, according to Ya. A. Kamensky - one of the fundamental pedagogical principles. Primary school age is determined by the moment the child enters school at the age of 6-7 and continues until the age of 10-11 - this is a period of positive changes and transformations. The most important neoplasms arise in all spheres of mental development: the intellect, personality, social relations(10, p.50). In elementary school, all cognitive processes develop, but D.B. Elkonin, following L.S. Vygotsky, believes that changes in perception and memory are derived from thinking. It is thinking that becomes the center of development during this period of childhood. Because of this, the development of perception and memory follows the path of intellectualization. Students use mental actions when solving problems of perception, memorization and reproduction (24, p. 123). As mentioned above, primary school age is characterized by intensive intellectual development. During this period, there is an intellectualization of all mental processes and the child's awareness of his own changes that occur in the course of educational activities. L. S. Vygotsky believed that the most significant changes occur in the sphere of thinking. The development of thinking becomes the dominant function in the development of the personality of younger schoolchildren, which determines the work of all other functions of consciousness. “Thanks to the transition of thinking to a new, higher level, a restructuring of all other mental processes takes place, memory becomes thinking, and perception becomes thinking. The transition of thinking processes to a new stage and the restructuring of all other processes associated with this constitute the main content of mental development in primary school age” (25, p. 65). The cognitive activity of a younger student is characterized, first of all, by the emotionality of perception. A picture book, a bright presentation, a visual aid - everything causes an immediate reaction in children. Younger schoolchildren are in the grip of a vivid fact: the images that arise on the basis of a description during a teacher's story or reading a book are very vivid. Imagery is also manifested in the mental activity of children. The music teacher must use a large number of visual aids, reveal the content of abstract concepts and figurative meaning words on a number of specific examples, since younger students initially remember not what is most significant in terms of learning tasks, but what made the greatest impression on them: what is interesting is brightly emotionally colored. According to the age periodization of L. S. Vygotsky, the leading activity of primary school age (from 6-7 to 10-11 years of age I-IV) is educational activity, in the process of its implementation, the child, under the guidance of a teacher, systematically masters the content of developed forms public consciousness(science, art, morality, law) and the ability to act in accordance with their requirements. However, the leading, educational activity will be only at this age; also at this age, only the foundations of theoretical consciousness and thinking are formed (10, p. 87). Why are there so many commas in unexpected places?

The thinking of a younger student is characterized by an active search for links and relationships between different events, phenomena, things, objects. It differs markedly from the thinking of preschoolers. Preschoolers are characterized by involuntariness, low controllability, they often think about what interests them. And younger students, who, as a result of studying at school, need to regularly complete assignments, are given the opportunity to learn how to control their thinking, to think when they need to, and not when they like it. When studying in the primary grades, children develop awareness, critical thinking. This is due to the fact that the class discusses ways to solve problems, considers solutions, children learn to substantiate, prove, and tell their judgments. Of course, other types of thinking develop further at this age, but the main burden falls on the formation of methods of reasoning and inference. At the same time, it is known that the thinking of children of the same age is quite different. Some children are easier to solve problems of a practical nature, when it is required to use the methods of visual-effective thinking, for example, tasks related to design and manufacture in labor lessons. Others are more easily given tasks related to the need to imagine and imagine any events or some states of objects and phenomena, for example, when writing essays, preparing a story from a picture or determining an image conveyed in music, etc. The third group of children argues more easily, builds conditional judgments and conclusions, which allows them to solve mathematical problems more successfully than other children, derive general rules and use them in specific cases.

There are such children for whom it is difficult to think practically, and to operate with images, and to reason, and those for whom it is easy to do all this. Differences in the thinking of children require individualization of the selection of tasks, exercises performed in the process of cognitive activity, taking into account their specificity and focus on the development of one or another function of thinking. Systematization, accumulation and testing of such tasks in a certain logical sequence, their integration and focus on fulfilling the tasks of developing intellectual abilities, creating an environment that allows the student to realize not only the system of reasoning proposed to him, but also his own thinking process, the formation social intelligence tasks on which the author of the experiment is working. Thus, since every time we help a child, we set different tasks, there must be different approaches, techniques, and means (exercises, tasks, trainings, etc.) in the implementation of this assistance, which can be effective and lesson, and in the organization of extracurricular activities. So, during the primary school age, significant changes occur in the psychophysiological and mental development of the child: the cognitive sphere is qualitatively transformed, inclusion in new activities occurs, a personality is formed, and a complex system of relationships with peers is formed.

1. 2. Thinking. Creative thinking

Figurative thinking is a process of cognitive activity aimed at reflecting the essential properties of objects (their parts, processes, phenomena) and the essence of their structural relationship. O.m. represents a single system of forms of reflection - visual-effective, visual-figurative and visual thinking - with transitions from the signification of individual units of the subject content of reflection to the establishment of constitutive links between them, generalization and construction of a figurative-conceptual model and then, on its basis, to identifying the categorical structure of the essential function of the reflected . In this type of thinking, the means of isolating, forming, transforming and generalizing the content of the reflection of a figurative form are mainly used. Whose definition?

Thinking is the highest form of projection of the surrounding world by the brain, the most complex cognitive process of cognition of the world, peculiar only to man; consequently, it is very important to develop and study the development of thinking in children at the entire stage of their education at school, and especially during the period of primary school age. A feature of a healthy psyche of a child is cognitive activity. The curiosity of the child is constantly directed to the knowledge of the world around him and the construction of his own picture of this world. The child strives for knowledge, he is forced to operate with knowledge, imagine situations and try to find a possible way to answer. He imagines a real situation and, as it were, acts in it in his imagination. Such thinking, in which the solution of the problem occurs as a result of internal actions with images, is called visual-figurative. Whose definition? Figurative thinking is the main type of thinking in primary school age. Of course, a younger student can think logically, but it should be remembered that this age is sensitive to learning based on visualization (16, p. 122). It is possible to speak about the child's thinking from the time when he begins to reflect some of the simplest connections between objects and phenomena, and to act correctly in accordance with them. The ability to think is gradually formed in the process of development of the child, the development of his cognitive activity. Cognition begins with the brain's reflection of reality in sensations and perceptions, which form the sensory basis of thinking. Figurative thinking differs from other types of thinking in that the material that a person uses here to solve a problem is not concepts, judgments or conclusions, but images. They are mentally retrieved from memory, or creatively recreated by the imagination. Such thinking is used by workers in literature, art, in general, people of creative work who deal with images. This kind of thinking is special influence on the mental development of a person, the formation of his creative "I" and the development of high moral principles. It forms a generalized and dynamic idea of ​​the world around and allows you to develop a social and value attitude to this world, its ethical and aesthetic assessment. Creating images and operating with them is one of the main fundamental features of the human intellect. Without this, a person is not able to analyze, not able to plan his actions, anticipate their results and, if necessary, make changes to his actions. It has long been proven that the most complex processes of figurative thinking are the result of sensory perception of the real world. These results are conceptually processed and mentally transformed depending on the task that a person faces and depends on his experience. Despite the undoubted success of science in the field of studying the nature and specifics of figurative thinking, many researchers note contradictions and inconsistencies in its definition (V. V. Medushevsky, O. I. Nekiforova, G. M. Tsypin). An analysis of the scientific literature on this issue leads to the conclusion that there is no consensus on the role of figurative thinking in the artistic and figurative activity of a person. For a long time in science, thinking was understood as exclusively cognitive activity, therefore it is no coincidence that abstract-logical thinking was determined as a priority in the process of cognizing the surrounding reality, and special attention was paid to its study. The role of figurative thinking was often considered as a kind of age stage in the development of the student's personality, and the stage was auxiliary, transitional (from visual-figurative to conceptual-logical thinking). And the very concept of “imaginative thinking” raised doubts about the appropriateness of using this term in scientific dictionary, since psychology already has a suitable term “imagination” to denote the operation of images” (5, p. 69). Since the image was considered as the main means of "operational unit" of figurative thinking, the very concept of "image" in psychology, most often, was used in a narrow sense - only as sensory-visual elements in the reflection of reality. Formed figurative thinking is a simultaneous and intuitive process, and therefore it displaces parallel logical operations. Figurative thinking should be considered as a complex process of transformation of sensory information. This transformation is provided by perceptual actions that make it possible to create images in accordance with the source material, operate with them, solve problems for comparing images, their recognition, identification, transformation, taking into account the originality of subjective experience” (26, p. 65). I. S. Yakimanskaya considers imagination as a “mental process, in complex unity” with perception, memory and representation, functioning in figurative thinking. Figurative thinking cannot be regarded as a primitive mental activity dying off in the process of child development. On the contrary, in the course of development, figurative thinking becomes more complex, diverse and flexible, and as a result, it is able to create figurative generalizations in the human mind that are not inferior in depth to conceptual generalization in reflecting essential connections. From the foregoing, we can conclude that figurative thinking directly depends on such a concept as perception. And if we are talking about the development of imaginative thinking through listening to music, then this connection is obvious. Porridge, everything is unclear in what logic. There should be a next section, perhaps? The development of figurative thinking is impossible without the development of musical perception. The role of music perception in musical culture is multifaceted and comprehensive: firstly, it is the ultimate goal of music-making, to which the creativity of the composer and performer is directed; secondly, it is a means of selecting and fixing certain compositional techniques, stylistic finds and discoveries - what is accepted by the perceiving consciousness of the public becomes part of musical culture, takes root in it; and finally, musical perception is what unites all types of musical activity from the first steps of the student to the mature works of the composer: every musician is inevitably his own listener (12, p. 75). Musical perception is a complex process, which is based on the ability to hear, experience musical content as an artistic and figurative reflection of reality. Students should, as it were, “get used to” the musical images of the work. Musical perception-thinking "is aimed at comprehending and comprehending the meanings that music has as an art, as a special form of reflection of reality, as an aesthetic artistic phenomenon" (17, p. 153). Perception - thinking is determined by a system of several components - a piece of music, a general historical, life, genre and communicative context, external and internal conditions of human existence - both an adult and a child. Despite the fact that musical perception as a direct object of study appeared in musicological works not so long ago, the invisible presence of the perceiving consciousness is felt in all musicological works, especially those of a general theoretical nature. It is impossible to think of music as a means of artistic communication and not try to see "the direction of the musical form towards perception", and hence the methods that the mind uses to comprehend the musical form. This psychological tendency, present in the works of B. Yavorsky, B. Asafiev, L. Mazel, naturally led to the summation, generalization of the ideas about the perception of music that had developed in the depths of classical musicology. Such a generalized concept was "adequate perception" - a term proposed by V. Medushevsky (15, p. 56). “Adequate perception” is the reading of the text in the light of the musical, linguistic, genre, stylistic, spiritual and value principles of culture. The more fully a person absorbs the experience of musical and common culture, the more adequate (ceteris paribus) is its inherent perception. Just as in relative truths the absolute shines through, and in concrete acts of perception one or another degree of adequacy is realized. So, the main function of figurative thinking is to ensure the process of cognition of the most significant aspects and regular connections of objects of reality in the form of visual images.

1. 3. Types of activities in the music lesson. "Listening" to music.

Currently, in the theory and practice of music education, there are different approaches to the interpretation of the term "types of musical activity of students in music lessons". In the very general plan they can be reduced to different positions depending on the level of generalization at which the issue is considered. If we turn to the traditions of Russian pedagogy of music education, then it is customary to refer to the types of musical activity of students:

· Listening to music;

· Choral singing;

· Game on musical instruments;

· Rhythmic movements to music;

Improvisation and composition of music by children (children's musical creativity).

The musical culture of schoolchildren is formed in the process of active musical activity. So, in singing, while listening to music, in rhythm classes, playing children's musical instruments, students get acquainted with the works, learn to understand them, acquire knowledge, acquire the skills and abilities necessary for their emotionally conscious perception and expressive performance. Therefore, the more varied and active the activities of children in the lesson, the more successfully the development of their musical and creative abilities, the formation of interests, tastes, and needs can be carried out.

However, by itself, the number of types of musical activities in a school lesson does not yet determine success in solving problems. musical education. This requires an integrated approach to its organization, when all elements of the lesson are subject to its theme, the theme of the quarter, year, and the lesson itself provides targeted musical development of students (9, p. 115).

One of the important and necessary sections of the lesson is listening to music.

This type of musical activity - listening to music - makes it possible to acquaint children with the music of famous composers available to them, to obtain the necessary knowledge about music, its expressive means and musicians. In the process of perceiving music, children are instilled with a love for highly artistic music, a need is formed to communicate with it, their musical interests and tastes are brought up, an idea is formed that music tells about the life around them, expresses feelings and thoughts, moods of a person.

In elementary school, the teacher teaches children:

Listen carefully to music from beginning to end, perceive music;

· Be imbued with its emotional content;

· To make a feasible analysis of the work (emotionally - figurative content, means of musical expression, structure, performance);

· Recognize the sound of studied musical works, remember their names and the names of composers.

The main task of the listening activity is the formation of the listener's musical culture of students. This is primarily: a) the accumulated experience of communicating with highly artistic samples of folk, classical and modern domestic and foreign music; b) the ability to emotionally and deeply perceive the figurative and semantic content of music on the basis of acquired knowledge about various musical styles, genres, forms, etc.; c) the need for listening activities.

When organizing the process of developing the student's listening culture, one should keep in mind the existence of different approaches to understanding the meaning and content of musical art. The first method is based on the understanding of music as a reflection of reality in a figurative form. D. B. Kabalevsky said: “To understand a musical work means to understand its life plan, to understand how the composer melted this idea in his creative mind, why he embodied this particular form, in a word, to find out how, in what atmosphere this work was born” . At the same time, the main thing is the behavior of students to understand the various relationships between music and life. The basis for establishing these connections are such basic categories of musical art as the genre basis of music, intonation, musical image, musical dramaturgy, style, as well as the relationship of music with other art forms. The second way is that the meaning of music must be found in the music itself. According to L. Bernstein, “music is never about something. Music just exists. Music is a mass of beautiful notes and sounds so well connected that they give pleasure when you listen to them” (2, p. 45). The term "musical perception" in musical pedagogy has two meanings. One, more capacious, is understood as the development by students of various types of musical activities in the lesson - choral singing, playing musical instruments, musical and rhythmic movement. Another meaning of the term, narrow, implies direct listening to music: acquaintance with musical works of various genres and roles, composers, performers. At the same time, the two sides of the musical development of younger schoolchildren - the perception of music and creativity itself - are inextricably linked and mutually complement each other. The basis of musical perception is a complex psychological process of isolating in works of musical art, properties and qualities that evoke aesthetic feelings. Hearing music means not only emotionally responding to it, but also understanding and experiencing music, its content, storing its images in your memory, internally representing its sound. Therefore, the perception of music is the ability to hear, emotionally experience the content of musical images, artistic unity, artistic and figurative reflection of reality, and not a mechanical sum of different sounds. Just listening to music doesn't do much, understanding music needs to be taught. Beginning the formation of the process of musical perception in younger students should be from the sensual aspect, with the awakening of emotions, the formation of emotional responsiveness, as part of the musical and aesthetic culture, which implies a shift in emphasis from the technical side of musical art to the spiritual - suggestive - emotional. In order for listening to become hearing, what is the term and what does it mean? needed: musical analysis, analysis of what they heard, a conversation with students about what they heard, i.e. artistic and pedagogical analysis. Children should receive correct information about the musical genre, the structure of the work, the elements of musical speech, the life and work of the composer. Already in the lower grades, attention should be paid to the fact that the lullaby should be calm, affectionate, its melody is soft and smooth, and the dance is usually cheerful, its melody is fast and loud. In elementary school, children learn by ear accessible two- and three-part forms, get acquainted with the methods of music development: repetition, contrast, variation.

Conventionally, the following stages are distinguished in the organization of the process of listening to music:

1. Acquaintance with a piece of music in the form introductory remarks teachers (it is necessary to direct the attention of students, to interest them, to tell about the composer);

2. Performance of a work by a teacher or listening to music on a recording (initial listening to music in complete silence);

3. Analysis - analysis of the work (perception of individual episodes, concentration of students' attention on expressive means, comparison of the work with others already known). The difficulty of this stage is in maintaining an emotional attitude to the listened work;

4. Repeated listening to the work in order to remember it, to enrich it with new observations. The perception of the work during repeated listening is carried out at a higher level, based on the received musical experience;

5. Listening to a piece of music in subsequent lessons in order to repeat, consolidate, compare it with new works (comparison of musical images).

Listening to music is one of the important and necessary sections of the lesson. A modern child is surrounded by a rich world of sounds, which is created, first of all, by television, radio, and cinema. He listens to music that is accessible and inaccessible to his understanding, close and interesting in terms of subject matter, and music designed for adults. Achieving the main task - raising interest, love, the need to communicate with art - is possible only if children acquire the necessary skills to perceive music, which, in turn, is impossible without the systematic musical and auditory development of the child. Therefore, by developing the necessary skills for perceiving music through the systematic musical and auditory development of the child, we also develop his imaginative thinking. Properly organized listening to music, various methods of activating perception (for example, through movement, playing the simplest musical instruments, as well as vocalization of themes) contribute to the development of students' interests and tastes, the formation of their musical needs. So, the perception of musical images occurs as a result of a kind of creative activity of the listener, as it includes his own experience (musical-auditory and life). The idea of ​​the work is perceived by him as something secret. That is why musicologists say that you need to listen to music in such a way that you can hear it, this is hard work of the heart and mind, and special creativity. Influencing, music is able to excite, delight, arouse interest. Joy and sadness, hope and disappointment, happiness and suffering, all this gamut of human feelings conveyed in music, the teacher must help children hear, experience and understand. The teacher creates all the conditions for the manifestation of the emotional response of students to music. Only then does he bring them to the realization of the content of the work, the expressive elements of musical speech and the complex of expressive means. Thanks to this, the work has a stronger impact on the feelings and thoughts of children. They develop the skill of cultural listening (listen to the work to the end, in complete silence), the ability to talk about music, that is, to give an aesthetic assessment of its content.

1. 4. Means of development of figurative thinking

The objective material form of figurative thinking and thinking in general is speech, in the mechanism of thinking it is hidden, silent: inner speech. I. Z. Postalovsky in his writings writes that verbal definitions, judgments and conclusions are also used in the formation of the image. But, as far as we know, the word in figurative thinking is not the main thing. It can be argued that the same task can be solved by constant transitions of figurative thinking and verbal expressions of thought. Each of them separately cannot fulfill the task of cognition. Their interaction and mutual transition is a condition for successful learning activity, a condition for any creativity (22, p. 4). Consequently, the material form of thinking is language. During the period of primary school age, the development of speech is very intensive. It takes place in two main directions: firstly, the vocabulary is intensively recruited and the morphological system of the language spoken by others is assimilated; secondly, speech provides a restructuring of cognitive processes (attention, perception, memory, imagination, as well as thinking) (16). Thanks to the language, people's thoughts are not lost, but are transmitted in the form of a system of knowledge from generation to generation. A thought becomes a thought both for oneself and for others only through the word - oral and written. Thinking is an ideal reflection of reality, has a material form of its manifestation. The mechanism of human thinking is hidden, silent, inner speech. Naturally, the thinking of younger schoolchildren develops in conjunction with speech, therefore, arguing, discussing the listened works, which have vivid imagery, emotionality, we touch on several areas. Thus, in order to develop the figurative thinking of younger students, you first need to try to expand their vocabulary, introduce into it a large number of definitions that more accurately and vividly convey the nature of the works. In this study, the enrichment of the vocabulary of younger students will be the first and main means of developing figurative thinking. Revealing the specifics of music, Asafiev emphasized that "musical intonation never loses its connection with either the word, or the dance, or the facial expressions and plasticity of the human body ...". “Any musical-plastic sign or intonation is simultaneously breathing, muscle tension, and heartbeat,” V. Medushevsky develops this idea and emphasizes that “intonations focused on musical and speech experience are captured by the real, or folded mental ... co-intonation. The listener responds to the plastic signs encoding the gesture with a sympathetic pantomimic movement. “A simple gesture - a wave of the hand,” writes Neuhaus, “can sometimes explain and show much more than words” (13, p. 163). The organic unity of music and movement is necessary and natural. Movements should reveal the content of music, correspond to it in composition, character, dynamics, tempo, metro-rhythm. At the same time, movements encourage conscious perception of a piece of music. Vivid examples of the relationship between music and movement are demonstrated by ballet performances and sports such as figure skating and rhythmic gymnastics. The system of musical and rhythmic education was one of the first developed in late XIX in. Swiss teacher and musician Emile Jacques - Dalcroze. The basis of musical and rhythmic education is the development of children's perception of musical images and the ability to reflect them in motion. Moving in accordance with the temporal course of a piece of music, the child also perceives pitch movement, i.e. melody in connection with all expressive means. It reflects the character and tempo of a piece of music in movement, reacts to dynamic changes, starts, changes and ends movement in accordance with the structure of musical phrases, reproduces a simple rhythmic pattern in movement. Consequently, the child, perceiving the expressiveness of musical rhythm, holistically perceives the entire piece of music. It conveys the emotional nature of a musical work with all its components (development and change of musical images, changes in tempo, dynamics, registers, etc.) (11, p. 132). Reproduction of an artistic image in plastic, the ability to maintain a certain speed of movement, switching from one tempo-rhythm to another, excites and develops the emotional memory and feeling of children. Thus, musical-rhythmic movements are a means of developing emotional responsiveness to music and a sense of musical rhythm, and hence figurative thinking. D. B. Kabalevsky believed that from the very first steps of a small person, music should enter his world as part of the spiritual culture of mankind, connected by thousands of threads with literature, fine arts, theater, plasticity, where the concept of the artistic image is integral. The integrative principle of the interaction of arts in the educational process, allows you to combine the knowledge and skills of artistic activity through artistic culture through music. The principle of the interaction of the arts, proposed in the integrative course by D. B. Kabalevsky for younger students, allows a new approach to the problem of art synthesis in the music lesson. It is this approach to conducting listening to music that allows solving the problem of developing creative abilities and imaginative thinking. G. S. Rigina, in her book for music teachers, offers some methodological techniques and recommendations for conducting listening with elements of integration. G. S. Rigina claims that perception is helped by such techniques as: 1. Engaging texts and poems. So, if we are talking about a major musical work, for example, music from ballets, operas, cantatas, the teacher talks to the children about their content, time and history of creation; or gives explanations for the name of the play (for example, "Rondo in the Turkish style" by W.A. Mozart); 2. Attracting reproductions of paintings and drawing on the theme of the music heard. For example: to listening to the theme from the “Bogatyr Symphony” by A.P. Borodin, a painting by V. Vasnetsov "Three Heroes" is offered, etc.; 3. Children draw on the topics of the music they listened to. For example: "Winter" by M. Krutitsky, "Disease of the Doll" by P.I. Tchaikovsky (23, p. 24). People of art have always been concerned about the problem of synthesis of music and painting. This synthesis was realized most organically in operas and ballets. Everyone is well aware of the importance of good costumes and decorations in the theater that correspond to the music. There are many musical works in which composers convey their impressions of the visual arts. Such is the piano cycle of M.P. Mussorgsky "Pictures at an Exhibition", dedicated to the memory of his friend, architect and artist V.A. Hartmann and inspired by his work. Plays by F. Liszt "Betrothal" to the painting by Raphael and "The Thinker" to the sculpture of Michelangelo. "Sea" and "Prints" by C. Debussy, "Painting" by the Soviet composer E. V. Denisov.

The relationship between painting and music exists from ancient times to the present day. It manifests itself in all spheres of human activity, emotionally enriching his spiritual world. Also, there is a direct connection between music and literature. A lot of vocal music is based on the works of famous poets. The plots of operas and ballets are also taken from literature.

2. PRACTICAL PART

2.1. Analysis of the situation

Based on the analysis of scientific and theoretical works and the pedagogical situation on the problem of the development of figurative thinking of younger schoolchildren, a study was organized. The study was conducted on the basis of a comprehensive school No. 17 in Krasnoyarsk, with students of the 3rd "B" class, in the amount of 25 people. As a result of applying the observation method, what was observed, under what conditions, what parameters of observation? How were the results recorded? It has been established that during the educational process in this general education school, unfortunately, little attention is paid to the development of figurative thinking (as opposed to abstract - logical). Also, as a result of the analysis of the pedagogical situation and scientific and methodological literature, the following problems were identified: 1. The absence of clear criteria for determining the level of development of figurative thinking, and their diagnosis; 2. The possibilities for the development of figurative thinking, through the diverse connections of music with other types of art, are used sporadically, within a limited framework; 3. A certain limitation exists in the use of specific methods of activating figuratively - emotional perception of music. In accordance with the goal of this experimental and practical research, an attempt will be made to develop ways to develop figurative thinking in children of primary school age by means of listening to music. Within 4 weeks, work on the development of figurative thinking will be carried out in a comprehensive manner mainly in three areas: speech, "painting", emotional embodiment through plasticity.

When implementing the developed techniques, we take into account that the imaginative thinking of a child of 6-11 years old in the process of perceiving life or musical and artistic phenomena is able to change and form intensively. On the initial stage development of figurative thinking, before the next listening to a particular musical work, we will rely on an introductory conversation about this work and its author, in order to adjust the perception of students. Moreover, all the musical works that we offer for listening will be necessarily programmatic, i.e. have a name that corresponds to the musical image embedded in it, this facilitates the figurative perception of younger students, and gives them the opportunity to imagine something specific. As criteria the development of figurative thinking of children, in this study everything will need to be written in the past tense: 1. The ability to give a verbal description of the musical image in the proposed work, expressing one's own associations and feelings; 2. The ability to establish emotional, thematic, figurative and expressive connections between several works of various types of art; 3. Maturity of musical-figurative associations and the degree of their correspondence to the content of music; 4. The ability to express one's own feelings and emotions to this work (while listening) through plastic movements. 5. The ability to depict the presented image in your own drawing. The processing of the results will be carried out according to the following parameters: the accuracy of the musical characteristics, the brightness of the images, as well as the ability to correlate the given definitions for the characteristics of the musical image and the proposed music, images of works of art and music, literary works (poems), quotations from literary works (fairy tales) and music, plastic movements and music.

2.2 Description of practical work experience

In the first week of classes, an entrance control was carried out in order to identify and establish the actual level of development of figurative thinking among younger students. This was how some practical methods were used to develop figurative thinking.

The level of formation of figurative thinking of students is monitored each student , according to E.P. Torrance.

In the methodology of E.P. Torrens, the subtest "Circles" allows you to assess the level of development of imaginative thinking of students.
I suggest that students should do it impersonally!! 1 draw on the basis of circles (2 rows of identical contour images, 8 pieces each) as many different drawings as possible: objects, things. At the same time, you can add any details to the figures and combine the figures into one drawing.
The task is given from 15 to 20 minutes. Students should draw as many images as possible related to the theme of the semester.
The main indicator of figurative thinking in this subtest is the number of ideas reproduced by the child. Counting them, you need to pay attention to the number of subject topics depicted. Each image is evaluated with a new score.
The final result is evaluated according to the table

Table - The level of development of figurative thinking of schoolchildren

The level of development of figurative thinking

Scheme - "Circles"

First lesson. For the formation of figurative thinking, the following stages of work were carried out:

· Development of figurative thinking through the choice of proposed paintings (selection of paintings with discussion).

At this, the first lesson, the theme of the music lesson in grade 3 "B" was as follows: "Music of winter." To conduct the hearing, the students were divided into 4 groups of four and five people. The following work was chosen for the hearing: Antonio Vivaldi "The Seasons" - "Winter" I part of Allegro molto.

First hearing.

An epigraph was read before the first hearing:

A frosty surface spreads the road,
And a man with cold feet.

Trampling the path, chattering teeth,
Runs to keep warm.

characterize the work, describe the proposed image. How does the composer reveal this image?

After that, the students were offered the following reproductions of paintings with winter landscapes: A. Solomatkin "Snowstorm", Sviridov "Snowstorm", I.I. Shishkin "In the wild north", I.I. Shishkin "Winter in the forest. Hoarfrost”, “Snow-covered Park” Isaac Levitan.

Exercise: choose which of the reproductions correspond to the image of the listened work, and explain your choice.

Before completing this assignment, I again read the epigraph to this work.

After completing the task, together with all the students, we once again examined the reproductions, revealed the image of each, and identified those that fully corresponded to the musical image of the work.

Rehearing:

Before the second hearing, I again read the epigraph to this work.

Exercise: choose from the definitions offered on the interactive board those that correspond to the musical image of the work and reveal it.

For this task, I selected 10 definitions, 5 of them fully correspond to the character and image of the work, the remaining 5 absolutely do not correspond. This was done in order to assess how adequately children perceive the image of the work.

Homework: draw a picture for the listened work, try to display the image proposed by the composer. Be able to present it, give an oral description of the image. As a result of the incoming control, it was revealed: 30% (7 people) of students - are able to give a verbal description of the musical image, but the vocabulary is not sufficiently developed for complete characteristics musical image, are able to establish emotional, thematic, figurative and expressive connections between a piece of music and the proposed paintings. The remaining 70% (18 people) are poorly able to give a verbal description of the musical image, a small vocabulary, which is not enough to characterize the musical image, can establish emotional, thematic, figurative-expressive connections between the piece of music and the proposed paintings, but they are poorly substantiated ( App.1). From the results of the incoming control, we see that, in 7 students of grade 3 "B", imaginative thinking is developed quite well, in the remaining 18 students, figurative thinking is poorly developed or not developed at all.

Second lesson. For the development of figurative thinking in the second week, the following stages of work were carried out:

· The development of figurative thinking through the choice of the proposed (Dictionary of aesthetic emotions that exist in music, as signs of the nature of the sound of V. Razhnikov).

· Development of figurative thinking through the choice of proposed verses.

· Development of figurative thinking through plasticity.

The topic of the lesson in the second lesson was as follows: “Fairy-tale ballet of P.I. Tchaikovsky "The Nutcracker". Tchaikovsky from the ballet The Nutcracker.

At the beginning of the lesson, we held a second listening to the work of Antonio Vivaldi "The Seasons" - "Winter" I part of Allegro molto from the previous lesson. The students then presented their homework.

First hearing.

Before the first hearing, I had a conversation about P.I. Tchaikovsky's "The Nutcracker", its content is disclosed. Appropriate illustrations for the ballet were selected.

Task after the first hearing: choose poems corresponding to the musical image of this work, from those proposed by me (Appendix 2).

Exercise: choose definitions corresponding to the musical image of the work.

As for the first lesson, I selected 10 definitions, 5 of them fully correspond to the nature and image of the work, the remaining 5 absolutely do not correspond. This was done in order to assess how adequately children perceive the image of the work.

Before the second hearing, I worked on plastic movements. Together with the students, we came up with what plastic movements can show one or another part of the work, more precisely, with the help of what plastic movements it is possible to convey the musical image of the work.

Rehearing.

Work on plasticity: students in their movements reflect the changing nature of the work, change movements (impulsive whirling of snowflakes, singing of the choir, waltz-like movements).

Homework: draw a picture for the piece and verbally substantiate the drawn musical image.

From the results of the second lesson, we see that the students become more active in their answers, they can more fully substantiate their answer, using the new definitions that they acquired during the first and second lessons.

40% (10 people) give a good verbal description of the musical image, substantiating their answer, quite accurately select poems corresponding to the work, and can embody the musical image through plastic movements.

60% (15 people) give a verbal description of the musical image (sometimes they get confused in definitions, there are repetitions), make mistakes in conveying the image through plasticity (they do not feel the change in the musical image during the work), select verses corresponding to the musical work, but poorly substantiate their answers (Appendix 3).

Third lesson. For the development of figurative thinking, the following stages of work were used:

· The development of figurative thinking through a choice from the proposed (“Dictionary of aesthetic emotions”, which exist in music, as signs of the nature of the sound of V. Razhnikov).

· Development of figurative thinking through the choice of quotes from the fairy tale by A.S. Pushkin "The Tale of Tsar Saltan".

Lesson topic: “Fairy tales in music.” Works proposed for listening: N.A. Rimsky-Korsakov, The Tale of Tsar Saltan, Three Miracles.

At the beginning of the lesson, I again held a second hearing of the work passed at the last lesson “Waltz of the Snow Flakes” by P.I. Tchaikovsky from the ballet The Nutcracker.

The guys presented their homework, substantiating their ideas about the musical image of the work presented in the picture.

First hearing. Before the hearing, I had a conversation about the tale of A.S. Pushkin "The Tale of Tsar Saltan". Appropriate illustrations have been selected. Together with the students, we recalled the content of the fairy tale and the miracles that took place there. "the first miracle" is the theme of the squirrel. You need to choose the right definitions for it:

Exercise:

“The Second Miracle”, the theme of the swan princess, you also need to choose the correct definitions for this passage:

Exercise: find a quote from A.S. Pushkin to this passage (Appendix 4).

“The Third Miracle”, the theme of heroes, you also need to choose the correct definitions for this passage:

Exercise: find a quote from A.S. Pushkin to this passage (Appendix 4).

Rehearing. Before the second listening, the students and I remembered everything we talked about in this lesson, once again identified the three musical images that the composer offered us, and tried to describe them.

As a result of the intermediate control, it was revealed that 20% (6 people) of students cope with the tasks perfectly, adequately and fully substantiate their answer, define the musical image well, use various definitions, accurately select quotes for works.

70% (17 people) of students cope well with tasks, define the musical image well, use different definitions, but not enough, there are repetitions in the answers, select the right quotes for fragments of musical works. They do their homework well, they do not fully substantiate their work (there are repetitions in the answers).

10% (2 people) also cope well with tasks, satisfactorily define the musical image, sometimes get confused in definitions. They do their homework, but they poorly substantiate their answers (Appendix 5).

Homework: the students were divided into groups of five and four, they were offered a list of fragments of the works (the fragments were recorded by the students on flash drives and disks), which they could listen to at home and during the after-school (Appendix 6). The works were selected in such a way that both positive and negative characters were present in them, as well as works that could correspond to the environment. All works are software. Those. have a name.

Exercise: Come up with a short story, a fairy tale, based on the proposed fragments of works, illustrate your stories according to musical images. You also need to verbally justify your answer (present a story).

The guys present their stories, showing illustrations, justifying the choice of this or that image, and revealing the image.

Fourth lesson. This lesson is a control. In order to see the final results of the effectiveness of our practical methods for the development of figurative thinking, in the third lesson the children were given an unusual homework.

The presentation of this homework is a control event for the development of figurative thinking of younger students while listening to music.

The guys include a fragment of the work, show the corresponding drawing and explain it. And so it goes throughout the story.

Results:

40% (10 people) of the students did an excellent job with the task, gave a good and complete verbal description of the musical images of the selected works, expressed their own associations and feelings, substantiated them. They demonstrated the maturity of musical-figurative associations and the degree of their correspondence to the content of music. They depicted very bright illustrations corresponding to musical images.

70% (15 people) of students coped with the task, made illustrations for the musical images of the selected works. But not always their answers-justifications were complete, accurate and detailed. Sometimes there were discrepancies between the musical image of the work and the drawing (Appendix 7).

Comparing the results of the incoming diagnostics and the control lesson, we see that the level of development of figurative thinking among students of the 3rd "B" class has increased, but not as much as we would like, most likely, this is due to the limited number of pre-diploma practice classes. Therefore, we can conclude that the use of these practical and methodological techniques is indeed a fairly productive way to develop the figurative thinking of younger students.

In general, in practice: the experiment is not clearly described. No histogram input, no summary totals, no comparison of results.

CONCLUSION

The need for a multifaceted study of the sphere of figurative thinking in children is recognized as an urgent problem of modern musical pedagogy. The most favorable for the development of figurative thinking by means of listening to music is the younger school age, since it is during this period that thinking becomes the center of development, and the basic culture of a person is laid and organized, the so-called foundation of all types of thinking. To date, music pedagogy has accumulated a fairly rich and extensive material related to the problems of the development of figurative thinking. In these scientific and methodological works, the need for careful preparation for listening in music lessons is noted, namely, it is recommended to use additional practical methods and techniques during listening that would contribute to a better perception of musical images, improve emotional reactions and internal responsiveness to musical works. Thus, developing the imaginative thinking of younger students. However, after analyzing the scientific and methodological literature, we did not find detailed methodological recommendations for listening to music for the development of imaginative thinking, as well as discussions of the results of extensive experimental studies. this issue. In this study, the relevance determined the main areas of work, including: the development of practical recommendations, sample tasks and their testing for active listening, in order to develop the imaginative thinking of younger students. To nurture creative imaginative thinking means to put the student in front of the need to make their own decisions. The problem of musical figurative thinking will not be adequately elucidated if we do not touch upon one of the aspects of musical abilities, such as musical and auditory representations. In the process of teaching music, these ideas develop in conjunction with the development of emotional susceptibility, attention, imagination, and creative initiative. Thus, musical and auditory representations are the basis for the emergence of both musical thinking and figurative thinking, respectively, the guarantee of its embodiment in music. The experimental and practical work carried out confirmed the legitimacy of the chosen path for the development of figurative thinking. In the course of this study, it was found that listening in music lessons has a direct impact on the development of figurative thinking, and in this work it was proved that the use of these methodological techniques allows for a more perfect development of figurative thinking by means of listening to music.

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Introduction

Chapter I. Development of visual-effective and visual-figurative thinking in integrated lessons of mathematics and labor training.

Clause 1.1. Characterization of thinking as a mental process.

Clause 1.2. Features of the development of visual-effective and visual-figurative thinking of children of primary school age.

Clause 1.3. Studying the experience of teachers and methods of work on the development of visual-effective and visual-figurative thinking of younger students.

Chapter II. Methodological and mathematical foundations for the formation of visual-effective and visual-figurative thinking of younger schoolchildren.

Clause 2.1. Geometric figures on the plane.

Clause 2.2. The development of visual-effective and visual-figurative thinking in the study of geometric material.

Chapter III. Experimental work on the development of visual-effective and visual-figurative thinking of younger students in integrated lessons of mathematics and labor training.

Clause 3.1. Diagnosis of the level of development of visual-effective and visual-figurative thinking of younger students in the process of conducting integrated lessons in mathematics and labor training in grade 2 (1-4)

Clause 3.2. Features of the use of integrated lessons in mathematics and labor training in the development of visual-effective and visual-figurative thinking of younger students.

Clause 3.3. Processing and analysis of experimental materials.

Conclusion

List of used literature

Application

Introduction.

Creation of a new system primary education follows not only from the new socio-economic conditions of life in our society, but is also determined by the great contradictions in the system of public education, which have developed and clearly manifested themselves in recent years. here is some of them:

For a long time, there was an authoritarian system of education and upbringing in schools with a strict management style, using coercive teaching methods, ignoring the needs and interests of schoolchildren, cannot create favorable conditions for introducing ideas for reorienting education with the assimilation of ZUNs to the development of the child's personality: his creative abilities, independence thinking and sense of personal responsibility.

2. The teacher's need for new technologies and the developments that pedagogical science gave.

For many years the attention of researchers has been focused on the study of learning problems, which have yielded many interesting results. Previously, the main direction in the development of didactics and methodology followed the path of improving individual components of the learning process, methods and organizational forms of learning. And only recently, teachers have turned to the personality of the child, began to develop the problem of motivation in learning, ways of forming needs.

3. The need for the introduction of new educational subjects (especially aesthetic subjects) and limited scope curriculum and learning time for children.

4. The fact that modern society stimulates the development of selfish needs (social, biological) in a person can also be attributed to the number of contradictions. And these qualities contribute little to the development of a spiritual personality.

It is impossible to resolve these contradictions without a qualitative restructuring of the entire system of primary education. The social demands placed on the school dictate the search for new forms of education for the teacher. One of these urgent problems is the problem of integration of education in primary school.

A number of approaches have been outlined to the question of the integration of education in primary school: from conducting a lesson by two teachers of different subjects or combining two subjects into one lesson and conducting it by one teacher to creating integrated courses. The fact that it is necessary to teach children to see the connections of everything that exists in nature and in everyday life, the teacher feels, knows and, therefore, integration in learning is the imperative of today.

As a basis for the integration of learning, it is necessary to take, as one of the components, the deepening, expansion, clarification of non-fast general concepts that are the object of study of various sciences.

The integration of education has the goal: in elementary school to lay the foundations for a holistic view of nature and society and to form an attitude towards the laws of their development.

Thus, integration is a process of rapprochement, connection of sciences, occurring along with processes of differentiation. integration improves and helps to overcome the shortcomings of the subject system and is aimed at deepening the relationship between subjects.

The task of integration is to help teachers integrate separate parts of different subjects into a single whole with the same goals and learning functions.

An integrated course helps children combine the knowledge they gain into a single system.

The integrated learning process contributes to the fact that knowledge acquires the qualities of a system, skills become generalized, complex, all types of thinking develop: visual-effective, visual-figurative, logical. The personality becomes comprehensively developed.

The methodological basis of an integrated approach to learning is the establishment of intra-subject and inter-subject connections in the assimilation of sciences and understanding the patterns of the entire existing world. And this is possible under the condition of repeated return to the concepts in different lessons, their deepening and enrichment.

Therefore, any lesson can be taken as the basis for integration, the content of which will include that group of concepts that relates to a given academic subject, but in an integrated lesson knowledge, analysis results, concepts from the point of view of other sciences, other scientific subjects. In elementary school, many concepts are cross-cutting and are considered in the lessons of mathematics, the Russian language, reading, fine arts, labor education, etc.

Therefore, at present it is necessary to develop a system of integrated lessons, the psychological and creative basis of which will be the establishment of links between concepts that are common, cross-cutting in a number of subjects. The purpose of educational preparation in elementary school is the formation of personality. Each subject develops both general and special qualities of the individual. Mathematics develops intelligence. Since the main thing in the activity of a teacher is the development of thinking, the topic of our thesis is relevant and important.

Chapter I . Psychological and pedagogical foundations of development

visual-effective and visual-figurative

thinking of younger students.

clause 1.1. Characterization of thinking as a psychological process.

Objects and phenomena of reality have such properties and relations that can be known directly, with the help of sensations and perceptions (colors, sounds, shapes, placement and movement of bodies in visible space), and such properties and relations that can be known only indirectly and through generalization. , i.e., through thinking.

Thinking is a mediated and generalized reflection of reality, a type of mental activity, which consists in knowing the essence of things and phenomena, regular connections and relationships between them.

The first feature of thinking is its indirect character. What a person cannot cognize directly, directly, he cognizes indirectly, indirectly: some properties through others, the unknown through the known. Thinking is always based on the data of sensory experience - sensations, perceptions, ideas, and on previously acquired theoretical knowledge. indirect knowledge is indirect knowledge.

The second feature of thinking is its generalization. Generalization as knowledge of the general and essential in the objects of reality is possible because all the properties of these objects are connected with each other. The general exists and manifests itself only in the individual, the concrete.

People express generalizations through speech, language. Verbal designation refers not only to a single object, but also to a whole group of similar objects. Generalization is also inherent in images (representations and even perceptions). But there it is always limited by visibility. The word allows you to generalize without limit. Philosophical concepts matter, movement, law, essence, phenomenon, quality, quantity, etc. - the broadest generalizations expressed by the word.

Thinking is the highest level of human cognition of reality. Sensual basis of thinking are sensations, perceptions and representations. Through the sense organs - these are the only channels of communication between the body and the outside world - information enters the brain. The content of information is processed by the brain. The most complex (logical) form of information processing is the activity of thinking. Solving the mental tasks that life puts before a person, he reflects, draws conclusions and thereby cognizes the essence of things and phenomena, discovers the laws of their connection, and then transforms the world on this basis.

Our knowledge of the surrounding reality begins with sensations and perception and moves on to thinking.

Thinking function- expanding the boundaries of knowledge by going beyond the limits of sensory perception. Thinking allows, with the help of inference, to reveal what is not given directly in perception.

The task of thinking- disclosure of relationships between objects, identifying connections and separating them from random coincidences. Thinking operates with concepts and assumes the functions of generalization and planning.

Thinking is the most generalized and mediated form of mental reflection, establishing connections and relationships between cognizable objects.

Introduction

To date, there is a tendency towards an increase in the number of children with deviations in mental and physical development. According to research conducted by the Research Institute of Hygiene and Health Protection of Children and Adolescents of the SCCH RAMS, over the past 10 years the number of children with mental retardation has doubled.

At primary school age, children with mental retardation experience certain difficulties in the learning process, since they are characterized by a significant degree of lagging behind the norm in the development of mental cognitive processes, slow learning.

The relevance of the study is due to the growing need to expand and modernize the pedagogical conditions and methods of teaching children with mental retardation, in particular, methods for the formation of visual-figurative thinking.

A theoretical analysis of existing psychological and pedagogical approaches to the definition of visual-figurative thinking allows us to identify its main components: hand-eye coordination, basic mental operations (analysis, comparison, abstraction, synthesis, generalization, classification) and imagination.

Many prominent scientists of the past and present (R. Arnheim, A.V. Bakushinsky, L.S. Vygotsky, V.S. Mukhina, E.A. Flerina, K.D. Ushinsky and others) substantiated the positive effect of visual-figurative thinking on the formation of children's intelligence.

The problem of the study is due to the fact that in the scientific and methodological literature there is a lack of works devoted to the study of the conditions for the development of visual-figurative thinking of younger schoolchildren with mental retardation. Weakly developed scientific base studying the process of development of visual-figurative thinking of children with mental retardation in the conditions of the primary link of a general education school.

The study of the problem of the development of visual-figurative thinking of younger schoolchildren in a general education school, the study of the theory and practice of educating younger schoolchildren with mental retardation give grounds for highlighting the contradiction between the possibility of purposeful and effective development of visual-figurative thinking of younger schoolchildren with mental retardation in a general education school and insufficient development of methodological support.

The object of the study is visual-figurative thinking of children with mental retardation.

The subject of the study is the psychological and pedagogical aspects and methodological foundations for the development of visual-figurative thinking of younger schoolchildren with mental retardation.

Research hypotheses: it is assumed that the development of visual-figurative thinking in children of primary school age with mental retardation will be more successful if:

Timely diagnose the thinking of children in this category;

To carry out correctional and developmental work with children of primary school age with mental retardation, taking into account the results of a diagnostic examination, as well as age and individual characteristics of development.

The purpose of the study is to determine the effectiveness of the conditions for the development of visual-figurative thinking of younger schoolchildren with mental retardation.

In accordance with the goal, the following research objectives are formulated:

1. To study and analyze the psychological, pedagogical and special literature on the problem of the development of visual-figurative thinking in children of primary school age with mental retardation.

2. Use a diagnostic program aimed at identifying the level of development of visual-figurative thinking in children of primary school age with mental retardation.

3. Taking into account the results of diagnostics, to test a psycho-corrective program that promotes the development of visual-figurative thinking in children of primary school age with mental retardation.

4. Analyze the effectiveness of the work done (compare the results before the program and after the program).

The methodological and theoretical basis of the study was the ideas of personality-oriented and humanistic pedagogy (Sh.A. Amonashvili, V.V. Serikov, I.S. Yakimanskaya, etc.), the activity approach to personality development (L.S. Vygotsky, A. N. Leontiev, S.L. Rubinshtein and others), the theory of cognitive activity (A. Binet, N.A. Menchinskaya and others), psychological and pedagogical concepts of the development of creative thinking (D.B. Bogoyavlenskaya, I.Ya. Lerner, Ya.A. Ponomarev and others) and imagination (O.M. Dyachenko, E.I. Ignatiev and others), the importance of figurative thinking in the process of solving practical and cognitive problems (B.G. Ananiev, A.V. Zaporozhets, V.P. Zinchenko, N.N. Poddyakov, I.S. Yakimanskaya and others), the theory of visual perception (J. Gibson, A.V. Zaporozhets, J. Piaget and others), ideas about the essence visual perception (R. Arnheim, V.M. Gordon, V.P. Zinchenko, V.M. Munipov, etc.) and its role in cognitive activity (V.I. Zhukovsky, D.V. Pivovarov, I.S. . Yakimanskaya and others).

The theoretical significance of the results of the study lies in the development of the theoretical provisions of psychology and pedagogy, considering the possibilities of developing visual-figurative thinking of younger students with mental retardation according to the new Federal State Educational Standards.

The practical significance of the study lies in the use of diagnostic tools that allow us to investigate the dynamics of the development of visual-figurative thinking of younger schoolchildren with mental retardation; guidelines for teachers on the development of visual-figurative thinking in elementary school.

Sample: primary school age, 9-10 years old.

Methods and techniques: theoretical, mathematical and statistical methods. Ascertaining, forming and control experiments. Diagnostic tools I.S. Yakimanskaya. The program for the development of visual-figurative thinking "I draw the world" I.A. Serikova.

Method indicators

Average

T-test

Significance level

methodologies

meaning

Student

Visual motor skills

3,07

Visual motor skills

4,47

15,39

0,000

Distinguishing a figure against a background_before

1,67

Distinguishing the figure on the background_after

2,17

5,39

0,000

Attention volume_before

1,37

Attention volume_after

2,00

7,08

0,000

Capacity of short-term visual memory_up to

1,30

The amount of short-term visual memory_after

1,97

7,62

0,000

visuo-spatial functions_before

1,50

visuo-spatial functions_after

2,00

5,39

0,000

Planning and Orientation_before

1,13

Planning and orientation_after

2,00

10,93

0,000

Memory and attention to detail

4,10

Memory and attention to detail

4,87

8,33

0,000

Classification_before

1,20

Classification_after

2,10

16,16

0,000

Short-term and working memory_up to

1,27

Short-term and working memory

1,97

8,23

0,000

Analysis and generalization_before

1,03

Analysis and generalization_after

1,93

16,16

0,000

Switching and distribution of attention_before

1,07

Switching and distribution of attention_after

1,93

13,73

0,000

verbal fantasy_before

2,53

verbal fantasy_after

3,73

9,89

0,000

Figurative flexibility_to

2,40

figurative flexibility_after

3,87

9,34

0,000

figurative fluency_before

2,33

figurative fluency_after

3,53

7,76

0,000

Originality of images_before

2,30

Originality of images_after

3,17

8,31

0,000

Image manipulation_before

2,47

Image manipulation_after

3,53

16,00

0,000

The results of the identified differences are shown in Fig. 1:

Fig.1. Differences in indicators of the level of development of visual-figurative thinking of younger schoolchildren at the stage of ascertaining and control experiment

From Table 2, Fig. 1, it can be seen that after the junior schoolchildren completed the program for the development of visual-figurative thinking, their indicators noticeably increased, in particular:

1) indicators of the first block (the ability to perform tasks for hand-eye coordination: visual-motor skills, visual-spatial functions, distinguishing a figure against the background, attention span and short-term visual memory) after the program are at an average level (at the stage of the ascertaining experiment, the results were low and below average).

That is, after completing the program classes, the younger schoolchildren surveyed by us have developed the skills of developing fine motor skills of the hand and coordination of movements to a greater extent; they can maintain proportionality when copying or playing a pattern from memory. In the process of distinguishing figures against the background, children make fewer mistakes in tracing the indicated geometric figures with one solid line without lifting the pencil from the paper, while the number of figures found and the accuracy of the task is average.

It can also be said that the level of attention and the volume of short-term visual memory of younger schoolchildren with mental retardation has increased. Children easily and quickly memorize cards with dots, broken lines on a demonstration card and reproduce them.

2) in the second block (the ability to perform tasks for basic mental operations: planning and orientation, short-term and working memory, attention to detail, classification, analysis and generalization, switching and distribution of attention) the degree of formation of mental operations: the ability to concentrate, plan the sequence of one's actions , navigate the scheme, quickly switch and distribute their attention - after the program they are at an average level (at the stage of the ascertaining experiment, the results were low and below the average level). Children are characterized by an increase in the ability to classify objects, carry out operations of analysis and generalization, memorize material and reproduce it.

3) in the third block (the ability to perform tasks for imagination: verbal fantasy, figurative fluency and flexibility, originality of images and operating with them), an average level was revealed in younger students with mental retardation (at the stage of ascertaining experiment, the results were low and below the average level). It became easier for children to come up with and draw an illustration for the given sentences, the originality of the interpretation of the plot and images after completing the classes became higher. Indicators of flexibility, the ability of younger students to produce a wide variety of associations, the ability to combine them into one holistic image; originality and thoroughness in the development of ideas, abstraction from familiar images are also at an average level.

The revealed results of diagnostics of younger schoolchildren with mental retardation indicate the effectiveness of the program for the development of the level of visual-figurative thinking of students.

Conclusion

In this work, according to the purpose and objectives of the study, we studied the psychological and pedagogical aspects and methodological foundations for the development of visual-figurative thinking of younger schoolchildren with mental retardation.

In the theoretical part of the study, such aspects of the topic under study as the problem of visual-figurative thinking in psychology and pedagogy, the development of visual-figurative thinking in primary school age, the pedagogical conditions for the development of visual-figurative thinking, and the features of visual-figurative thinking of younger students with mental retardation were considered.

The results of experimental work showed that at the initial stage, younger schoolchildren with mental retardation have poorly developed skills in developing fine motor skills of the hand and coordination of movements; it is difficult for them to maintain proportionality when copying or playing a pattern from memory. In the process of distinguishing figures against the background, children make mistakes in tracing the indicated geometric figures with one solid line without lifting the pencil from the paper, while the number of figures found and the accuracy of the task is low. The level of attention and volume of short-term visual memory of younger schoolchildren with mental retardation is low. Children have difficulty remembering cards with dots, a broken line on a demonstration card and reproducing them. In younger schoolchildren with mental retardation, an insufficient degree of formation of mental operations was revealed: the ability to concentrate, plan the sequence of their actions, navigate the scheme, quickly switch and distribute their attention. Children are also characterized by a reduced level of ability to classify objects, carry out analysis and generalization operations, memorize material and reproduce it. Children find it difficult to come up with and draw an illustration for the given sentences, the originality of the interpretation of the plot and images is low. Difficulties in flexibility, the ability of younger students to produce a variety of different associations, the ability to combine them into one holistic image were also identified; originality and thoroughness in the development of ideas, abstraction from familiar images is low.

After completing the program for the development of visual-figurative thinking, the indicators for all three blocks are at an average level of formation, which indicates the effectiveness of the program.

Summing up the work done, we can say that the research hypothesis put forward by us has found its empirical confirmation. Namely, the development of visual-figurative thinking in children of primary school age with mental retardation will be more successful if the diagnosis of thinking in children of this category is carried out in a timely manner; to carry out correctional and developmental work with children of primary school age with mental retardation, taking into account the results of a diagnostic examination, as well as age and individual characteristics of development.

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Applications

Attachment 1

Methodology for diagnosing the level of development of visual-figurative thinking of younger schoolchildren I.S. Yakimanskaya

Testing conditions:  test material, demonstration cards and registration sheets of students, in which the surname, name, class and school are entered;  simple (M or 2M) and colored pencils, pen, felt-tip pens; - a table or desk of proper height with a sufficiently large and even surface. If the surface is uneven, the child, drawing a line, will circle the unevenness of the table. Lighting of the workplace and ventilation of the room, noise isolation and the absence of distractions are very important. Researcher's instructions: “Now we will draw. Listen carefully to the task and do it as I say. Start each task only on my command. When finished, put the pencil on the table and wait for the next instruction. If someone does not understand the task, ask right away so as not to make mistakes.

Block 1. Visual-motor coordination: development of fine motor skills of the hand and coordination of movements; visual-motor skills and visual-spatial functions (observance of proportionality when copying or reproducing a sample from memory); distinguishing the figure against the background; attention and short-term visual memory.

Test 1. Visual-motor skills. Instructions for all test tasks: “Do not take the pencil off the paper when completing the task. Do not turn the test sheet.

Task 1. Draw a straight horizontal line between the dot and the cross.

Task 2. Mark the midpoints of two vertical lines with dots, connect them with a straight horizontal line.

Task 3. Draw a straight line in the middle of a given path.

Task 4. Draw a straight vertical line from the dot to the cross.

Task 5. Mark the midpoints of two horizontal lines with dots, connect them with a straight vertical line.

Task 6. Draw a straight vertical line in the middle of the track.

Tasks 7-12. Outline the drawn figure along a dashed line in the given direction, starting from a dot and ending at a cross. Draw a line on a free field of the sheet, keeping the shape, size and given direction.

Tasks 13-16. Outline the drawing along a dashed line, following the direction indicated by the arrow.

Groups of tasks 1-6, 7-12, 13-16 are evaluated by 3 points. The maximum score is 9 points.

Test 2. Distinguishing a figure against a background. Stepping back slightly, circle the indicated geometric shapes with one solid line, without lifting the pencil from the paper. Find in tasks 5-8 and circle in different colors 5) hexagonal stars, 6) pentagonal stars, 7) rhombuses, 8) ovals, in task 9 find and circle all squares in one color, and triangles in another. In the fourth grade: in task 10, find and circle all circles in one color, triangles in another, ovals in a third. The number of figures found and the accuracy of the task are taken into account. Time - 2 minutes. The maximum score is 3 points.

Test 3. The amount of attention. For 10-15 seconds, sequentially show cards with dots. Over the next 15 seconds, children mark these points on their card from memory. Cards 1-3 are used, for the second - 1-4, for the third - 1-6, for the fourth - 1-8. The maximum score is 3 points.

Test 4. The amount of short-term visual memory For 15 seconds, the children examine the broken line on the demonstration card, and then reproduce it from memory on their sheet. With age, the complexity of the line increases. The direction and proportionality of the given line segments are evaluated. The maximum score is 3 points.

Test 5. Visual-spatial functions. Draw (slightly enlarged) a perspective drawing of a house, a fence, and a tree onto a piece of paper. You have 3 minutes to complete the task. When scoring, the presence of all elements of the image and proportionality are taken into account. The maximum score is 3 points. Block 2. Possession of basic mental operations: the ability of students to concentrate, their attention to detail; planning the sequence of their actions and the ability to navigate the scheme, quickly switch and distribute their attention; the amount of short-term and operative memory; skills of classification, analysis and generalization.

Test 6. Planning and orientation. Find your way through the maze, showing your movement with a clear line, trying not to tear the pencil from the paper. The execution time is 1 minute. A clear thoughtful path with a minimum number of deviations into dead ends is evaluated. The maximum score is 3 points.

Test 7. Memory and attention to detail. Draw a tree, a house and a person on a horizontal sheet. Images may not be related to each other. Run time - 3 minutes. A well-executed image is considered fairly large in size, with good muscle control when drawing lines. The drawing should reflect the main features of objects: the tree has a clear trunk, branches and crown; the house shows the walls, roof, windows and door; in a person - a figure is drawn, there are clothes, movement is conveyed, and emotion is reflected on the face. In the absence or incorrect representation of details (neck and fingers - in a person; branches near a tree; a roof with additional details, doors, window arrangement) - 2 points. For small images, conventionality and non-observance of proportions - 1 point, in the absence of basic details - 0 points. The maximum score for each of the three images is 3 points, the total score is 9 points.

Test 8. Classification. There are ten lines in the assignment. In each row of six items, two are logically related to each other. Find them and circle them in 1 minute. Criteria: 9-10 correct lines - 3 points, 7-8 lines - 2 points, 4-6 lines - 1 point, 0-3 lines - 0 points.

Test 9. Short-term and working memory. For the first class: the picture shows two rugs, and pieces of cloth that can be used as patches. From the proposed samples, choose and circle the most suitable for the pattern of the rug, for the second class - identical gnomes, for the third - the correct shadow of the king, for the fourth - two identical bugs. The execution time is 1 minute. The maximum score is 3 points. 82

Test 10. Analysis and generalization. In each line, one of the items is redundant. In 1 minute, cross out all unnecessary items in the task. Criteria: 15-16 lines - 3 points, 10-14 lines - 2 points, 6-9 lines - 1 point, 0-5 lines - 0 points.

Test 11. Switching and distribution of attention. Geometric shapes are set on the sheet: squares, triangles, circles and rhombuses. In each of them, sequentially put down the sign that is given on the sample. In the first grade, students work only with squares, in the second - with squares and triangles, in the third grade, circles are added to these figures, in the fourth - the task is completed in full. The time to complete the task is 2 minutes. Geometric figures not marked with the appropriate signs are considered errors.

Criteria: 0-1 mistake - 3 points, 2-3 mistakes - 2 points, 4-5 mistakes - 1 point, more than 5 mistakes - 0 points. Block 3. Imagination: looseness and level of development of verbal fantasy, visual-effective and visual-figurative thinking; originality of interpretation of a given plot and images in an independently executed illustration; figurative fluency and flexibility, originality of images and free operation with them; the ability to produce a wide variety of associations and create a new image, the source of which is objective reality.

Test 12. Verbal fantasy. Think up and draw an illustration for the words: “Autumn bathes in the rays of the sun; the worm liked the mushroom very much ... ". The originality of the interpretation of the plot and images is evaluated. Time - 2 minutes, maximum score - 6 points.

Test 13 In two minutes, complete the elements given in the form of a bean, depicting something specific. The sheet can be rotated, the drawings are not related to each other in meaning. The repetition of the same element allows you to test the ability of the subject to produce a variety of different associations. The number (or the ability to combine them into a coherent image) and the variety of drawings are evaluated. The maximum score is 6 points.

Test 14 There is a set of twelve identical circles on the sheet. In two minutes, turn them into thematically related drawings, for example: fruits and vegetables, domestic or wild animals, birds, food, household items, etc. The number and variety of images is taken into account. The maximum score is 6 points.

Test 15. Originality of images. Having considered the given "doodles" (there are 5 in total), draw each one to a specific image. Finished figures are judged on the originality and thoroughness of the development of the idea. The task is completed in 2 minutes. Maximum score - 6 points

Test 16 Having a sheet of paper and felt-tip pens (at least six different colors), come up with and draw a fantastic creature in 2 minutes. Elaboration and abstraction from familiar images are evaluated. The maximum score is 6.

A high level of development of visual thinking corresponds to a total number of points from 65 to 75 (i.e., from 86% of completed tasks and above), an average level - from 52 to 64 points (from 69% to 85%), a low level - from 32 to 51 points (from 43% to 68%), risk group - 31 points or less (up to 42%).

Annex 2

Initial data table

(stating experiment)

Appendix 3

Initial data table

(control experiment)

Appendix 4

Benchmarking table by Student's t-test

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Introduction

The study of the mechanisms of the formation of figurative thinking in ontogenesis is of great importance for developmental and pedagogical psychology, in which the idea that the development of thinking occurs as a kind of change in its forms, as the displacement of lower forms during the transition to more advanced ones (from visual-effective to visual-figurative and from it to abstract, theoretical thinking). Such an idea, which has been preserved in psychology for a long time, determined to a certain extent the attitude to the development of problems of figurative thinking, since the latter was often identified only with sensual forms of reflection of reality, described in terms of "empirical", "concrete", "contemplative" and opposed to theoretical, abstract , scientific thinking.

For example, at school, under the influence of the assimilation of knowledge, circle work on interests, there is an intensive formation of figurative thinking of students. However, the features of its development, indicators, conditions of formation are set based on the content of each academic subject (type of activity). The school still does not have scientifically based recommendations on building a general logic for the development of figurative thinking of students from grades I to XI, a description of age standards and individual characteristics of its functioning, which, of course, makes it difficult for the harmonious development of the student's personality.

Figurative thinking is not a given from birth. Like any mental process, it needs development and adjustment. According to psychological research, the structure of figurative thinking is the intersection of five main substructures: topological, projective, ordinal, metric, compositional. These substructures of thinking exist non-autonomously, but intersect. Therefore, a tempting idea arises to develop the imaginative thinking of children in such a way as not to "break" its structure, but to use it as much as possible in the learning process, making the latter humanized.

The relevance of the topic is undeniable, since visual-figurative thinking is the basis for conceptual (verbal-logical) thinking, and the further cognitive person and the development of the personality as a whole depend on its development.

Object: features of the cognitive sphere of younger students.

Subject: figurative thinking.

Thus, the purpose of our course work: to study the development of figurative thinking in schoolchildren.

Analysis and generalization of psychological and pedagogical sources on the problem;

To study the concepts: types of thinking, image and figurative thinking;

Choose methods for studying the development of figurative thinking;

Conduct a study to study the development of figurative thinking;

Analysis of the obtained results.

Hypothesis - first-grade students have an average and above average level of development of figurative thinking.

Chapter 1. Thinking as a psychological process

1.1 Main types and properties of thinking

Our knowledge of the surrounding reality begins with sensations and perception and moves on to thinking. The function of thinking is to expand the boundaries of knowledge by going beyond the limits of sensory perception. Thinking allows, with the help of inference, to reveal what is not given directly in perception.

The task of thinking is to reveal the relationships between objects, to identify connections and separate them from random coincidences. Thinking operates with concepts and assumes the functions of generalization and planning.

Thinking is the most generalized and mediated form of mental reflection, establishing connections and relationships between cognizable objects.

With the development of society, thinking evolves and more and more moves to a generalized, theoretical level, to concepts. Abstractions of number, space and time appear and develop. Just as the development of the technical potential of society leads to the operation physical phenomena, which are not amenable to perception by our senses, and thinking proceeds to operate with concepts that do not have not only sensory, but in general any representations. good example to illustrate this are many concepts of modern nuclear physics.

There are several classifications of types of thinking. The most common classification characterizes thinking in terms of the use of substitutes for reality, building material for one kind of thought or another. Therefore, this classification presents three types of thinking. The first is object-effective (visual-effective), the tool of which is the object, the second is visual-figurative (sometimes called simply figurative thinking), operates with images of the real world, and the last is verbal-logical (conceptual), in which we use the word ( concept).

These types of thinking in the history of mankind (phylogeny) can be analyzed as forms of knowledge developing on the basis of each other. For the ontogenetic development of each individual, this approach is applicable only in general terms. For example, figurative thinking in a particular person is not supplanted by a verbal-logical type of thinking, but develops intensively, which later makes it possible to successfully implement such types of professional activities as technical, pictorial, graphic, subject-artistic, etc.

Figurative thinking (visual-figurative). Visual-figurative thinking was the second type in the history of development after objective-active thinking. It allowed (and allows) to know the real world without the participation of practical action, can only be realized in the ideal plan. Figurative thinking "grasps" a visual situation simultaneously (at the same time), often intuitively, that is, without detailed analysis and reasoning. At the same time, it has the ability to display in a sensual form of movement, the interaction of several objects at once.

If a verbal response is not required, then the conclusions are not formulated verbally. In general, the word in figurative thinking is only a means of expression, interpretation of the transformations performed in images. The process of figurative thinking, carried out in the form of images, proceeds quickly, rather curtailed. The decision comes, as it were, suddenly, in the form of insight, a kind of mental spatial picture. Therefore, in addition to simultaneity (simultaneity), it is necessary to add impulsiveness and syntheticity to the distinctive features of figurative thinking. The specificity of figurative thinking is the filling of its results with personal content and meaning.

Images are much more closely connected than the word with the sensual attitude of a person to the world around him, to his experiences. The image presents not only the perceptual features and properties of the object, but also the emotional and personal attitude towards them, which often cannot be detected when operating with concepts.

Visual-figurative thinking - thinking, which is based on the modeling and resolution of a problem situation in terms of representations. Acting as the next stage in the development of the intellect after visual-effective thinking, this type of thinking is based on the use of certain preceptive standards, on the basis of which it is possible to reveal perceptually non-obvious connections between objects. Thus, in the representations that visual-figurative thinking operates, not only situationally arising connections are expressed, but also deeper, hidden essential properties that are not represented in a visual situation. The basis for the functioning of visual-figurative thinking is the translation of the perceptual structure of a problem situation into a system of semantic features that form certain values, thereby achieving a sufficiently large latitude for modeling possibilities.

In concepts, especially scientific ones, the social and generic experience of a person is fixed. And in this sense, they are impersonal. This difference between the concept and the image is one of the factors that determine the great difficulties in the initial assimilation of concepts and the preference for using examples when studying new educational material. At the same time, the images that we offer to other people do not always contribute to the clarification of the truth, and at times even complicate this process.

There are several reasons for this. First, it is the poverty of the resulting image. Indeed, there are many situations when the image in the resulting expression (drawing, object design, schematic representation, verbal description, etc.) turns out to be much poorer than it was at the time of its creation, operating on it. This phenomenon is due to the fact that a person does not possess sufficiently accurate means to express the content of the image he has. Therefore, there should be a stock of created images. The more and richer they are, the more opportunities a person has for their modification, transformation, that is, successful operation with them.

Secondly, the understanding of the presented image is significantly influenced by the proximity of personal meanings that fill the corresponding images of the transmitting and receiving information.

Thirdly, people differ in their ability to create and operate with images. For some, representations are enough to easily and freely create images and operate with them. This ability is associated with the development in an adult of the arbitrariness of all mental processes. But there are people who, according to their individual characteristics, require the presence of a visual basis for the ease and freedom of creating an image.

Visual-figurative thinking is the basis for conceptual (verbal-logical) thinking. The foundations of logical analysis are already laid in it, but only the initial ones.

1.2 Theoretical foundations for the study of figurative thinking

In psychology, the varieties of figurative thinking, which are formed under the influence of different systems of knowledge, methods of cognition, the conditions for the development of figurative thinking, the role of figurative thinking in the formation of concepts, have been little studied.

In particular, figurative thinking is understood as the process of thought working with external and internal systems of a person, operating with mental, dynamic signs, models, images and creating new ones (signs, models, images) addressed to oneself and others with the aim of interacting and gradually changing the outside world. as well as human self-change.

L.B., Itelson notes that the mechanisms of figurative thinking have a three-link character:

1) a certain stimulus-irritant (external, internal, symbolic);

2) reintegration (activation of the entire system of excitations associated with it in the past);

3) isolation, disintegration. The whole chain of emerging associative images obeys a certain principle.

The younger school age is characterized by intensive intellectual development. During this period, there is an intellectualization of all mental processes and the child's awareness of his own changes that occur in the course of educational activities. The most significant changes are taking place, as L.S. Vygotsky, in the sphere of thinking. The development of thinking becomes the dominant function in the development of the personality of younger schoolchildren, which determines the work of all other functions of consciousness.

As a result, the "serving thinking" functions are intellectualized and become arbitrary. The thinking of a younger student is characterized by an active search for links and relationships between different events, phenomena, things, objects. It differs markedly from the thinking of preschoolers. Preschoolers are characterized by involuntariness, low controllability, they often think about what interests them.

And younger students, who, as a result of studying at school, need to regularly complete assignments, are given the opportunity to learn how to control their thinking, to think when they need to, and not when they like it. When studying in the primary grades, children develop awareness, critical thinking. This is due to the fact that the class discusses ways to solve problems, considers solutions, children learn to substantiate, prove, and tell their judgments.

There are such children for whom it is difficult to think practically, and to operate with images, and to reason, and those for whom it is easy to do all this. Differences in the thinking of children require individualization of the selection of tasks, exercises performed in the process of cognitive activity, taking into account their specificity and focus on the development of one or another function of thinking.

In the real process of thinking (acquisition of knowledge) there are both<образная>, and<понятийная>logic, and these are not two independent logics, but a single logic of the flow of the thought process. The mental image itself, with which thinking operates, is by its nature flexible, mobile, reflecting a piece of reality in the form of a spatial picture.

There are different ways to create subject images according to drawings, diagrams. Some students rely on visualization, looking for a kind of sensory support in it. Others operate easily and freely in the mind. Some students quickly create images based on visualization, keep them in memory for a long time, but get lost when it is necessary to modify the image, since under these conditions the image expands, as it were, and disappears. Others operate well with images.

The following regularity has been found: where the originally created images are less visual, bright and stable, their transformation, operation with them is more successful; in those cases when the image is objectified, burdened with various details, it is difficult to manipulate it.

The main function of figurative thinking is the creation of images and operating them in the process of solving problems. The implementation of this function is provided by a special representation mechanism aimed at modifying, transforming existing images and creating new images that are different from the original ones.

The creation of an image according to the idea is carried out in the absence of an object of perception and is provided by its mental modification. As a result, an image is created that is different from the visual material on which it originally arose. Thus, the activity of representation, at whatever level it is carried out, ensures the creation of something new in relation to the original, i.e., it is productive. Therefore, the division of images into reproductive and creative (productive) is not correct.

Spatial thinking is also a kind of figurative.

Chapter 2

2.1 Cognitive sphere of a primary school student

The cognitive sphere is the sphere of human psychology associated with its cognitive processes and consciousness, which includes a person's knowledge about the world and about himself.

Cognitive processes - a set of processes that ensure the transformation of sensory information from the moment the stimulus affects the receptor surfaces to the receipt of a response in the form of knowledge.

In early school age, a child experiences many positive changes and transformations. This is a sensitive period for the formation of a cognitive attitude to the world, learning skills, organization and self-regulation.

The main feature of the development of the cognitive sphere of children of primary school age is the transition of the mental cognitive processes of the child to more high level. This is primarily expressed in the more arbitrary nature of the flow of most mental processes (perception, attention, memory, ideas), as well as in the formation of abstract-logical forms of thinking in the child and teaching him written speech.

At first, visual-effective thinking prevails (grade 1.2), then abstract-logical thinking (grade 3.4) is formed.

Arbitrary memory becomes the main type of memory in a child, the structure of mnemonic processes changes.

The age of 7-11 years in its psychological content is a turning point in the intellectual development of the child. The development of logical thinking. The mental operations of the child become more developed - he is already able to form various concepts himself, including abstract ones.

In the process of schooling, all spheres of a child's development are qualitatively changed and restructured. Thinking becomes the dominant function in primary school age. The transition from visual-figurative to verbal-logical thinking, which was outlined in preschool age, is being completed.

2.2 The development of figurative thinking in younger students

The development of imaginative thinking means a person's transition to a higher level of intellectual development compared to the level at which he was previously.

One of the most famous theories of the development of human thinking is the theory developed by J. Piaget.

The development of figurative thinking can be processes of two kinds. First of all, these are the natural processes of the emergence and progressive change of figurative thinking that take place in ordinary, everyday conditions of life. It can also be an artificial process that takes place in a specially organized learning environment. This takes place when, for one reason or another, figurative thinking is not formed at the proper level.

If a child lags behind his peers in terms of the development of figurative thinking, it is necessary to develop it specially.

Exist different types developmental learning. One of the training systems developed by D.B. Elkonin and V.V. Davydov gives a significant developmental effect. In elementary school, children receive knowledge that reflects the regular relationships of objects and phenomena; the ability to independently obtain such knowledge and use it in solving various specific problems; skills that are manifested in a wide transfer of the mastered action to different practical situations. As a result, visual-figurative thinking and, consequently, verbal-logical thinking in their initial forms develop a year earlier than in traditional programs.

Special studies G.I. Minska showed that the experience gained by a child in solving visual-effective tasks (the formation of orientation mechanisms in the conditions of the task and the activation of speech forms of communication) can have a decisive influence on the transition to visual-figurative and verbal thinking. In other words, the organization of attention, the formation of speech, etc. are important for the development of a child's thinking.

The well-known psychologist J. Piaget distinguishes four stages in the development of a child's intellect. At the stage of sensorimotor, or practical thinking (from birth to 2 years), the child learns the world as a result of their actions, movements, manipulations with objects (visual-effective thinking). With the advent of speech, the stage of preoperative thinking begins (lasting from 2 to 7 years), during which speech develops, the ability to mentally (internally) imagine external objective actions (visual-figurative and verbal-logical thinking) is formed.

Of greatest interest to us is the stage of pre-operational thinking, namely, visual-figurative thinking.

One of the important signs of the development of visual-figurative thinking is how much the new image differs from the initial data on the basis of which it is built.

The degree of difference between the new image being formed and the original images reflecting the conditions of the problem characterizes the depth and radicalness of the mental transformations of these initial images.

The development of a figurative reflection of reality in younger schoolchildren proceeds mainly along two main lines: a) improving and complicating the structure of individual images that provide a generalized reflection of objects and phenomena; b) the formation of a system of specific ideas about a particular subject. Individual representations included in this system have a specific character. However, being combined into a system, these representations allow the child to carry out a generalized reflection of the surrounding objects and phenomena.

The main line of development of visual-figurative thinking is the formation of the ability to operate with images of objects or their parts. The basis of such an operation is the ability of children to arbitrarily update these images. Such skills arise in children in the course of assimilation of two closely interconnected systems of actions. First, a system of analyzing actions is formed, during which the child is taught to sequentially identify the main and then the derivative parts of the subject, that is, they are taught to go from the general to the particular.

Then, in productive activity, a system of reproducing actions is formed, during which the child is taught to recreate, first, the main parts of objects, and then derivatives. The logic of reproduction corresponds to the logic of the analysis of the subject and unfolds from the general to the particular.

In the course of such training, children develop the ability to arbitrarily actualize the idea of ​​the perceived object and then embody this idea in a design or drawing.

An essential moment in the development of visual-figurative thinking is the formation in children of a certain technique for operating with images. The basis of such an operation is the use by children of a special group of means of mental activity, with the help of which various kinds of mental movements of objects in space are carried out.

Our analysis of both domestic and foreign studies shows that the development of visual-figurative thinking is a complex and lengthy process. N.N. Poddyakov showed that the development of the internal plan in children of preschool and primary school age goes through the following stages:

1st stage. The child is not yet able to act in the mind, but is already capable of manipulating things on a visual-active plane, transforming the objective situation directly perceived by him with the help of practical actions. At this stage, the development of thinking consists in the fact that at first the situation is given to the child visually, in all essential features, and then some of them are excluded, and the emphasis is placed on the child's memory. Initially, the development of intellect proceeds through the development of recall of what they have seen, heard, felt, done by them, through the transfer of once found solutions to the problem to new conditions and situations.

2nd stage. Here speech is already included in the statement of the problem. The task itself can be solved by the child only on the external plane, by direct manipulation of material objects or by trial and error. Some modification of the previously found solution is allowed when it is transferred to new conditions and situations. The solution found in verbal form can be expressed by the child, so at this stage it is important to get him to understand the verbal instructions, formulate and explain in words the solution found.

3rd stage. The problem is solved already in a visual-figurative plan by manipulating the images-representations of objects. The child is required to be aware of the methods of action aimed at solving the problem, their division into practical - the transformation of the objective situation and theoretical - awareness of the way the requirement is made.

4th stage. This is the final stage, at which the task, after finding its visual-effective and figurative solution, is reproduced and implemented in an internally presented plan. Here, the development of intelligence is reduced to the formation in the child of the ability to independently develop a solution to the problem and consciously follow it. Thanks to this learning, there is a transition from the external to the internal plan of action.

So, visual-figurative thinking acquires the main significance in the knowledge of the surrounding world by younger students. It gives the child the opportunity to assimilate generalized knowledge about the objects and phenomena of reality, becomes a source of children's creativity.

In order to find out how visually-figurative thinking is developed among younger students, it is necessary to conduct an examination, that is, to diagnose, in order to provide timely assistance if necessary.

Chapter 3. Practical part

An ascertaining experiment is an experiment that establishes the existence of some immutable fact or phenomenon. An experiment is ascertaining if the researcher sets the task of identifying the current state and the level of formation of a certain property or parameter under study, in other words, the actual level of development of the studied property in the subject or group of subjects is determined.

The research procedure took place in several stages:

1 selection of research methods;

2 planning and conducting the study;

3 analysis of the results of the study.

The organization on the basis of which the study was conducted is the Municipal General Education Boarding School "General Education Boarding School of Secondary (Complete) General Education No. 17" Young Rescuers of the Ministry of Emergencies. "Children from the first to the eleventh grade, both boys and girls, study at this educational institution .

We have chosen the following methods:

- "Nonsense", aimed at the study of visual-figurative thinking and elementary figurative representations of the child about the world around him;

- "A series of plot pictures", which allowed us to directly assess the level of development of visual-figurative thinking;

The study was conducted on an individual basis.

To study the formation of elementary figurative ideas about the world around us, we used the diagnostics of "Nepitsy" (see Appendix No. 1). The study was conducted individually with each child. Children were offered pictures depicting animals in ridiculous situations (a cat sitting on a tree, a goose on a chain, etc.). The child worked according to the instructions for 3 minutes. During this time, the child should notice as many ridiculous situations as possible and explain what is wrong, why it is wrong and how it really should be. At the time the child completed the task, we recorded the time it took to complete, the number of correctly marked absurdities, and the correctness of their explanation.

We evaluated the results on a 10-point system and correlated with the standards:

	Indicators	State of the art
	In the allotted time (3 minutes), the child noticed all the absurdities in the picture, managed to satisfactorily explain what was wrong, and, in addition, say how it really should be.	Very tall
8-9 points	The child noticed and noted all the available absurdities, but 1-3 of them failed to fully explain or say how it should really be.
6-7 points	The child noticed and noted all the available absurdities, but 3-4 of them did not have time to fully explain and say how it really should be.
4-5 points	The child noticed all the existing absurdities, but 5-7 of them did not have time to fully explain and say how it should really be in the allotted time.
	During the allotted time, the child did not have time to notice 1-4 of the 7 absurdities in the picture, and the matter did not come to an explanation.
	During the allotted time, the child managed to detect less than 4 of the 7 available absurdities.	Very low

Conclusions about the level of development:

10 points - very high

8-9 points - high

4-7 points - average

2-3 points - low

0-1 point - very low

At the next stage of our study of visual-figurative thinking, the children were offered the "Series of plot pictures" method (see Appendix No. 2).

The plot pictures are laid out in front of the child and they are offered to consider them and put them in order: "Decompose what happened first, what then and how it all ended. Now tell me what is drawn there." An adult does not interfere in the process of laying out pictures. The child can correct his own mistakes.

1 point - does not understand the task, acts inadequately to the instructions (very low level).

2 points - the task understands, lays out the pictures without taking into account the sequence of events depicted in the picture, perceives each picture as a separate action, without combining them into one plot (low level).

3 points - accepts the task, lays out the pictures, confusing the actions, but eventually lays them out sequentially, but cannot compose a coherent story about this event (intermediate level).

4 points - accepts the task, lays out the pictures in a certain sequence, combining them into one event and can make up a story about it (high level).

The study was conducted in the 1st grade, 25 people study in it. We have chosen exactly the 1st grade, since it is the first in elementary school and is transitional from visual-figurative thinking to verbal-logical. At this age, one can most accurately trace the success of the formation of visual-figurative thinking.

As a result of the analysis of the results obtained by the method of "nonsense" were obtained following results:

Very high level - 8% (2 people);

High level - 32% (8 people);

Average level - 48% (12 people);

Low level - 12% (3 people).

Based on these data, a diagram was compiled that clearly shows the diagnostic results:

As a result of the analysis of the results obtained using the "Series of plot pictures" method, the following results were obtained:

High level - 72% (18 people);

Average level - 16% (4 people);

Low level - 12% (3 people).

Thus, according to the results of the study, a comparative analysis can be made.

Of all students in grade 1, we can identify 22 people with a high and medium level of development of figurative thinking, which confirms our hypothesis.

Also revealed 3 people with a low level of development of figurative thinking. Consequently, these children will develop verbal-logical thinking much worse than the rest of the students in this class. These students need special classes aimed at developing figurative thinking.

Conclusion

Both domestic and foreign studies show that the development of visual-figurative thinking is a complex and lengthy process. Analyzing the views of representatives of various approaches and schools regarding the dynamics of thinking in primary school age, we note significant age-related changes in this most important systemic function that ensures the child's adaptation to the conditions of life in the subject and social environment. The main change in the process of thinking in primary school age is the transition from visual-figurative thinking to verbal-logical. This means that the visual-figurative thinking of a younger student should be well developed.

In the process of schooling, all spheres of a child's development are qualitatively changed and restructured. Thinking becomes the dominant function in primary school age. The transition from visual-figurative to verbal-logical thinking, which was outlined in preschool age, is being completed.

In this work, after analyzing various literature on developmental psychology and pedagogy, the following were considered: the concept of thinking as a mental process, visual-figurative thinking and the development of figurative thinking in younger students.

The conducted theoretical and practical research gives grounds to conclude that figurative thinking is not a given from birth. Like any mental process, it needs development and adjustment.

The practical part of the work presents the results of the study, which, in turn, confirmed the hypothesis put forward by us that in the first grade, figurative thinking should not be developed below the average level.

Based on the results obtained, we have developed recommendations for parents on the development of visual-figurative thinking in younger students.

The recommendations are aimed at developing in children the ability to mentally regroup the elements of an object; navigate in a simple plan-scheme of space; the ability to navigate in a schematic representation of an object and the ability to design; the ability to mentally transform an object, "read" and create simple schematic images of various objects; plan your actions in your mind.

student visual figurative thinking

Bibliography

1. Vygotsky L. S. Questions of child psychology. - St. Petersburg, 2006.

2. Galperin P. Ya., Zaporozhets A. V., Karpova S. N. Actual problems of developmental psychology. M., 2007.

3. Dubrovina I. V. Working book of a school psychologist. - M., 2003.

4. Ilyasova I. I., Lyaudis V. Ya. Reader on developmental and pedagogical psychology. Works of Soviet psychologists of the period 1946 - 1980. - M., 2008.

5. Kulagina I. Yu. Developmental psychology. M., 2005

6. Luskanova N.G. Ways of psychological correction of anomalies in personality development. In: Health, development, personality. M.: Medicine, 2000.

7. Mukhina B. C. Developmental psychology - M., 2003

8. Nemov R. S. Psychology: Dictionary reference book: at 2 pm - M., 2005.

9. Nemov R. S. Psychology. Volume 2. - M., 2001.

10. Ovcharova R. V. Reference book of a school psychologist. - M., 2006.

11. Pavlova Yu. A. Psychological and pedagogical conditions for the formation of skills and abilities. M., 2008.

12. Rogov E. I. Handbook practical psychologist in education. - M., 2001.

13. Fridman L. M., Kulagina I. Yu. Psychological reference book of the teacher. Minsk, 2001.

14. Kharlamov I. F. "Pedagogy", Minsk, 2003.

15. Reader in general psychology. Psychology of thinking // Ed. Yu.B. Gippenreiter - M., 2004

16. Elkonin D. B. Selected psychol. works. Irkutsk. 2002

17. Yakimanskaya I. S. The main directions of research of figurative thinking. - Minsk, 2004.

Application

With the help of this technique, elementary figurative representations of the child about the world around and about the logical connections and relationships that exist between some objects of this world: animals, their way of life, nature are evaluated. With the help of the same technique, the child's ability to reason logically and grammatically correctly express his thoughts is determined. The procedure for carrying out the technique is as follows. First, the child is shown the picture below. It has some rather ridiculous situations with animals. While looking at the picture, the child receives instructions with the following content: "Look carefully at this picture and say if everything here is in its place and drawn correctly. If something seems wrong to you, out of place or drawn incorrectly, then point to this and explain why it is not so. Next, you will have to say how it really should be."

Note. Both parts of the instruction are executed sequentially. At first, the child simply names all the absurdities and points them out in the picture, and then explains how it really should be.

The exposure time of the picture and the execution of the task is limited to three minutes. During this time, the child should notice as many ridiculous situations as possible and explain what is wrong, why it is wrong and how it really should be.

Evaluation of results

10 points - such an assessment is given to the child if, in the allotted time (3 minutes), he noticed all 7 absurdities in the picture, managed to satisfactorily explain what was wrong, and, in addition, say how it should really be .

8-9 points - the child noticed and noted all the available absurdities, but from one to three of them he was not able to fully explain or say how it should really be.

6-7 points - the child noticed and noted all the existing absurdities, but three or four of them did not have time to fully explain and say how it really should be.

4-5 points - the child noticed all the existing absurdities, but 5-7 of them did not have time to fully explain and say how it should really be in the allotted time.

2-3 points - in the allotted time, the child did not have time to notice 1-4 out of 7 absurdities in the picture, and the matter did not come to an explanation.

0-1 point - in the allotted time, the child managed to detect less than four of the seven available absurdities.

Comment. A child can get 4 or more points in this task only if, in the allotted time, he completely completed the first part of the task, determined by the instruction, i.e. found all 7 absurdities in the picture, but did not have time to either name them or explain how it should actually be.

Technique "A series of plot pictures"

Purpose: to identify the level of formation of visual - figurative thinking of children 5-7 years old.

Stimulus material: plot pictures depicting a sequence of events.

Conducting a survey: plot pictures are mixed up in front of the child and they are offered to consider them and put them in order: "Decompose what happened first, what then and how it all ended. Now tell me what is drawn there." An adult does not interfere in the process of laying out pictures. The child can correct his own mistakes.

Processing instruction: acceptance and understanding of the task, the child's ability to understand that one event is shown in all the pictures, and also that the event has a certain temporal sequence, the child's ability to compose a coherent logical story.

1 point - does not understand the task, acts inadequately to the instructions.

2 points - the task understands, lays out the pictures without taking into account the sequence of events depicted in the picture, perceives each picture as a separate action, without combining them into one plot.

3 points - accepts the task, lays out the pictures, confusing the actions, but eventually lays them out sequentially, but cannot compose a coherent story about this event.

4 points - accepts the task, lays out the pictures in a certain sequence, combining them into one event and can make up a story about it.

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Introduction

Chapter I. Development of visual-effective and visual-figurative thinking in integrated lessons of mathematics and labor training.

Clause 1.1. Characterization of thinking as a mental process.

Clause 1.2. Features of the development of visual-effective and visual-figurative thinking of children of primary school age.

Clause 1.3. Studying the experience of teachers and methods of work on the development of visual-effective and visual-figurative thinking of younger students.

Chapter II. Methodological and mathematical foundations for the formation of visual-effective and visual-figurative thinking of younger schoolchildren.

Clause 2.1. Geometric figures on the plane.

Clause 2.2. The development of visual-effective and visual-figurative thinking in the study of geometric material.

Chapter III. Experimental work on the development of visual-effective and visual-figurative thinking of younger students in integrated lessons of mathematics and labor training.

Clause 3.1. Diagnosis of the level of development of visual-effective and visual-figurative thinking of younger students in the process of conducting integrated lessons in mathematics and labor training in grade 2 (1-4)

Clause 3.2. Features of the use of integrated lessons in mathematics and labor training in the development of visual-effective and visual-figurative thinking of younger students.

Clause 3.3. Processing and analysis of experimental materials.

Conclusion

List of used literature

Application

Introduction.

The creation of a new system of primary education stems not only from the new socio-economic conditions of life in our society, but is also determined by the great contradictions in the system of public education that have developed and clearly manifested themselves in recent years. here is some of them:

For a long time, there was an authoritarian system of education and upbringing in schools with a strict management style, using coercive teaching methods, ignoring the needs and interests of schoolchildren, cannot create favorable conditions for introducing ideas for reorienting education with the assimilation of ZUNs to the development of the child's personality: his creative abilities, independence thinking and sense of personal responsibility.

2. The teacher's need for new technologies and the developments that pedagogical science gave.

For many years the attention of researchers has been focused on the study of learning problems, which have yielded many interesting results. Previously, the main direction in the development of didactics and methodology followed the path of improving individual components of the learning process, methods and organizational forms of learning. And only recently, teachers have turned to the personality of the child, began to develop the problem of motivation in learning, ways of forming needs.

3. The need for the introduction of new educational subjects (especially subjects of the aesthetic cycle) and the limited scope of the curriculum and the time of teaching children.

4. The fact that modern society stimulates the development of selfish needs (social, biological) in a person can also be attributed to the number of contradictions. And these qualities contribute little to the development of a spiritual personality.

It is impossible to resolve these contradictions without a qualitative restructuring of the entire system of primary education. The social demands placed on the school dictate the search for new forms of education for the teacher. One of these urgent problems is the problem of integration of education in primary school.

A number of approaches have been outlined to the question of the integration of education in primary school: from conducting a lesson by two teachers of different subjects or combining two subjects into one lesson and conducting it by one teacher to creating integrated courses. The fact that it is necessary to teach children to see the connections of everything that exists in nature and in everyday life, the teacher feels, knows and, therefore, integration in learning is the imperative of today.

As a basis for the integration of learning, it is necessary to take, as one of the components, the deepening, expansion, clarification of non-fast general concepts that are the object of study of various sciences.

The integration of education has the goal: in elementary school to lay the foundations for a holistic view of nature and society and to form an attitude towards the laws of their development.

Thus, integration is a process of rapprochement, connection of sciences, occurring along with processes of differentiation. integration improves and helps to overcome the shortcomings of the subject system and is aimed at deepening the relationship between subjects.

The task of integration is to help teachers integrate separate parts of different subjects into a single whole with the same goals and learning functions.

An integrated course helps children combine the knowledge they gain into a single system.

The integrated learning process contributes to the fact that knowledge acquires the qualities of a system, skills become generalized, complex, all types of thinking develop: visual-effective, visual-figurative, logical. The personality becomes comprehensively developed.

The methodological basis of an integrated approach to learning is the establishment of intra-subject and inter-subject connections in the assimilation of sciences and understanding the patterns of the entire existing world. And this is possible under the condition of repeated return to the concepts in different lessons, their deepening and enrichment.

Therefore, any lesson can be taken as the basis for integration, the content of which will include that group of concepts that relates to a given academic subject, but in an integrated lesson knowledge, analysis results, concepts from the point of view of other sciences, other scientific subjects are involved. In elementary school, many concepts are cross-cutting and are considered in the lessons of mathematics, the Russian language, reading, fine arts, labor education, etc.

Therefore, at present it is necessary to develop a system of integrated lessons, the psychological and creative basis of which will be the establishment of links between concepts that are common, cross-cutting in a number of subjects. The purpose of educational preparation in elementary school is the formation of personality. Each subject develops both general and special qualities of the individual. Mathematics develops intelligence. Since the main thing in the activity of a teacher is the development of thinking, the topic of our thesis is relevant and important.

Chapter I . Psychological and pedagogical foundations of development

thinking of younger students.

clause 1.1. Characterization of thinking as a psychological process.

Objects and phenomena of reality have such properties and relations that can be known directly, with the help of sensations and perceptions (colors, sounds, shapes, placement and movement of bodies in visible space), and such properties and relations that can be known only indirectly and through generalization. , i.e., through thinking.

Thinking is a mediated and generalized reflection of reality, a type of mental activity, which consists in knowing the essence of things and phenomena, regular connections and relationships between them.

The first feature of thinking is its indirect character. What a person cannot cognize directly, directly, he cognizes indirectly, indirectly: some properties through others, the unknown through the known. Thinking is always based on the data of sensory experience - sensations, perceptions, ideas, and on previously acquired theoretical knowledge. indirect knowledge is indirect knowledge.

The second feature of thinking is its generalization. Generalization as knowledge of the general and essential in the objects of reality is possible because all the properties of these objects are connected with each other. The general exists and manifests itself only in the individual, the concrete.

People express generalizations through speech, language. Verbal designation refers not only to a single object, but also to a whole group of similar objects. Generalization is also inherent in images (representations and even perceptions). But there it is always limited by visibility. The word allows you to generalize without limit. The philosophical concepts of matter, motion, law, essence, phenomenon, quality, quantity, etc., are the broadest generalizations expressed in words.

Thinking is the highest level of human cognition of reality. Sensual basis of thinking are sensations, perceptions and representations. Through the sense organs - these are the only channels of communication between the body and the outside world - information enters the brain. The content of information is processed by the brain. The most complex (logical) form of information processing is the activity of thinking. Solving the mental tasks that life puts before a person, he reflects, draws conclusions and thereby cognizes the essence of things and phenomena, discovers the laws of their connection, and then transforms the world on this basis.

Our knowledge of the surrounding reality begins with sensations and perception and moves on to thinking.

Thinking function- expanding the boundaries of knowledge by going beyond the limits of sensory perception. Thinking allows, with the help of inference, to reveal what is not given directly in perception.

The task of thinking- disclosure of relationships between objects, identifying connections and separating them from random coincidences. Thinking operates with concepts and assumes the functions of generalization and planning.

Thinking is the most generalized and mediated form of mental reflection, establishing connections and relationships between cognizable objects.

Thinking- the highest form of active reflection of objective reality, consisting in a purposeful, mediated and generalized reflection by the subject of essential connections and relations of reality, in the creative creation of new ideas, forecasting events and actions (speaking in the language of philosophy); higher function nervous activity(speaking the language of physiology); a conceptual (in the system of the language of psychology) form of mental reflection, characteristic only of a person, establishing connections and relationships between cognizable phenomena with the help of concepts. Thinking has a number of forms - from judgments and conclusions to creative and dialectical thinking and individual characteristics as a manifestation of the mind using existing knowledge, vocabulary and an individual subjective thesaurus (i.e.:

1) a dictionary of the language with complete semantic information;

2) a complete systematized set of data about any field of knowledge, allowing a person to freely navigate in it - from the Greek. thesauros - stock).

The structure of the thought process.

According to S. L. Rubinshtein, any thought process is an act aimed at solving a specific problem, the formulation of which includes goal and terms. Thinking begins with a problem situation, a need to understand. Wherein the solution of the problem is a natural completion of the thought process, and its termination when the goal is not achieved will be perceived by the subject as a breakdown or failure. The emotional well-being of the subject is connected with the dynamics of the thought process, tense at the beginning and satisfied at the end.

The initial phase of the thought process is the awareness of the problem situation. The very formulation of the problem is an act of thinking, often it requires a lot of mental work. The first sign of a thinking person is the ability to see the problem where it is. The emergence of questions (which is typical for children) is a sign of the developing work of thought. A person sees the more problems, the wider the circle of his knowledge. Thus, thinking presupposes the presence of some initial knowledge.

From understanding the problem, thought moves to its solution. The problem is solved in different ways. There are special tasks (tasks of visual-effective and sensorimotor intelligence) for the solution of which it is enough to correlate the initial data in a new way and rethink the situation.

In most cases, a certain base of theoretical generalized knowledge is needed to solve problems. The solution of the problem involves the involvement of existing knowledge as means and methods of solution.

The application of the rule involves two mental operations:

Determine which rule needs to be involved for the solution;

Application of general rules to particular conditions of the problem

Automated schemes of action can be considered skills thinking. It is important to note that the role of thinking skills is great precisely in those areas where there is a very generalized system of knowledge, for example, in solving mathematical problems. When solving a complex problem, a solution path is usually outlined, which is realized as hypothesis. Awareness of the hypothesis generates the need for verification. Criticality is a sign of a mature mind. An uncritical mind easily takes any coincidence as an explanation, the first solution that comes up as the final one.

When the test ends, the thought process moves to the final phase - judgment on this issue.

Thus, the thought process is a process that is preceded by awareness of the initial situation (conditions of the task), which is conscious and purposeful, operates with concepts and images, and which ends with some result (rethinking the situation, finding a solution, forming a judgment, etc.). )

There are four stages of problem solving:

Training;

Solution maturation;

Inspiration;

Checking the found solution;

The structure of the thought process of solving the problem.

1. Motivation (desire to solve a problem).

2. Analysis of the problem (highlighting "what is given", "what needs to be found", what redundant data, etc.)

3. Search for a solution:

Finding a solution based on one well-known algorithm (reproductive thinking).

Finding a solution based on choosing the best option from a variety of known algorithms.

Solution based on a combination of individual links from various algorithms.

Search for a fundamentally new solution (creative thinking):

a) based on in-depth logical reasoning (analysis, comparison, synthesis, classification, inference, etc.);

b) based on the use of analogies;

c) based on the use of heuristic techniques;

d) based on the use of an empirical trial and error method.

4. Logical substantiation of the found idea of ​​the solution, logical proof of the correctness of the solution.

5. Implementation of the solution.

6. Verification of the found solution.

7. Correction (if necessary, return to stage 2).

So, as we formulate our thought, we form it. The system of operations that determines the structure of mental activity and determines its course is itself formed, transformed and consolidated in the process of this activity.

Operations of mental activity.

The presence of a problematic situation, from which the thought process begins, always aimed at solving some problem, indicates that the initial situation is given in the representation of the subject inadequately, in a random aspect, in insignificant connections.

In order to solve the problem as a result of the thought process, it is necessary to come to a more adequate knowledge.

To such an increasingly adequate cognition of its subject and the solution of the problem facing it, thinking proceeds through diverse operations that make up various interrelated and mutually transitioning aspects of the thought process.

These are comparison, analysis and synthesis, abstraction and generalization. All these operations are different aspects of the main operation of thinking - "mediation", that is, the disclosure of more and more essential objective connections and relationships.

Comparison, comparing things, phenomena, their properties, reveals identity and differences. Revealing the identity of some and the differences of other things, comparison leads to their classification . Comparison is often the primary form of knowledge: things are first known by comparison. It is also an elementary form of knowledge. Identity and difference, the basic categories of rational cognition, appear first as external relations. Deeper knowledge requires the disclosure of internal connections, patterns and essential properties. This is carried out by other aspects of the thought process or types of mental operations - primarily by analysis and synthesis.

Analysis- this is a mental dismemberment of an object, phenomenon, situation and the identification of its constituent elements, parts, moments, sides; by analysis we isolate phenomena from those random, unimportant connections in which they are often given to us in perception.

Synthesis restores the whole dissected by the analysis, revealing more or less significant connections and relationships of the elements identified by the analysis.

Analysis dismembers the problem; synthesis combines data in a new way to resolve it. Analyzing and synthesizing, thought proceeds from a more or less vague idea of ​​the subject to a concept in which the main elements are revealed by analysis and the essential connections of the whole are revealed by synthesis.

Analysis and synthesis, like all mental operations, first arise on the plane of action. Theoretical mental analysis was preceded by a practical analysis of things in action, which dismembered them for practical purposes. In the same way, a theoretical synthesis was formed in a practical synthesis, in production activities of people. Formed first in practice, analysis and synthesis then become operations or aspects of the theoretical thought process.

Analysis and synthesis in thinking are interconnected. Attempts at one-sided application of analysis outside of synthesis lead to a mechanical reduction of the whole to the sum of its parts. In the same way, synthesis without analysis is also impossible, since synthesis must restore the whole in thought in the essential interconnections of its elements, which are distinguished by analysis.

Analysis and synthesis do not exhaust all aspects of thinking. Its essential aspects are abstraction and generalization.

Abstraction- this is the selection, isolation and extraction of one side, property, moment of a phenomenon or object, in some respect essential and its abstraction from the rest.

So, considering an object, you can highlight its color without noticing the shape, or vice versa, highlight only the shape. Starting with the selection of individual sensible properties, abstraction then proceeds to the selection of non-sensory properties expressed in abstract concepts.

Generalization (or generalization) is the rejection of single features while maintaining common ones with the disclosure of significant relationships. Generalization can be made by comparison, in which common qualities are distinguished. This is how generalization is carried out in elementary forms of thinking. In higher forms, generalization is accomplished through the disclosure of relationships, connections and patterns.

Abstraction and generalization are two interrelated sides of a single thought process, through which thought goes to knowledge.

Knowledge takes place in concepts , judgments and inferences .

concept- a form of thinking that reflects the essential properties of the connection and relationship of objects and phenomena, expressed by a word or a group of words.

Concepts can be general and singular, concrete and abstract.

Judgment- this is a form of thinking that reflects the relationship between objects or phenomena, it is the affirmation or denial of something. Judgments can be false and true.

inference- a form of thinking in which a certain conclusion is made on the basis of several judgments. There are inductive, deductive, and analogical inferences. Induction - a logical conclusion in the process of thinking from the particular to the general, the establishment of general laws and rules based on the study of individual facts and phenomena. Analogy - a logical conclusion in the process of thinking from particular to particular (based on some elements of similarity). Deduction - a logical conclusion in the process of thinking from the general to the particular, the knowledge of individual facts and phenomena based on the knowledge of general laws and rules.

Individual differences in mental activity.

Individual differences in the mental activity of people can manifest themselves in the following qualities of thinking: the breadth, depth and independence of thinking, the flexibility of thought, the speed and criticality of the mind.

Latitude thinking- this is the ability to cover the whole issue as a whole, without losing at the same time the parts necessary for the case.

Depth thinking expressed in the ability to penetrate the essence difficult questions. The quality opposite to the depth of thinking is the superficiality of judgments, when a person pays attention to the little things and does not see the main thing.

Independence thinking It is characterized by the ability of a person to put forward new tasks and find ways to solve them without resorting to the help of other people.

Flexibility thoughts is expressed in its freedom from the shackling influence of methods and methods of solving problems fixed in the past, in the ability to quickly change actions when the situation changes.

Rapidity crazy- the ability of a person to quickly understand a new situation, think over and make the right decision.

criticality crazy- the ability of a person to objectively evaluate his own and other people's thoughts, carefully and comprehensively check all the propositions and conclusions put forward. The individual features of thinking include the preference for a person to use a visual-effective, visual-figurative or abstract-logical type of thinking.

There are individual styles of thinking.

Synthetic the style of thinking manifests itself in creating something new, original, combining dissimilar, often opposite ideas, views, and carrying out thought experiments. The motto of the synthesizer is "What if ...".

Idealistic the style of thinking manifests itself in a tendency to intuitive, global assessments without detailed analysis of problems. The peculiarity of idealists is an increased interest in goals, needs, human values, moral issues, they take into account subjective and social factors in their decisions, strive to smooth out contradictions and emphasize similarities in various positions. "Where are we going and why?" is a classic idealist question.

Pragmatic style of thinking is based on direct personal experience, on the use of those materials and information that are readily available, striving to get a concrete result (albeit limited), a practical gain as soon as possible. The motto of the pragmatists: "Something will work", "Anything that works"

Analytical the style of thinking is focused on a systematic and comprehensive consideration of an issue or problem in those aspects that are set by objective criteria, it is inclined to a logical, methodical, thorough (with an emphasis on details) manner of solving problems.

Realistic the style of thinking is focused only on the recognition of facts, and “real” is only that which can be directly felt, personally seen or heard, touched, etc. Realistic thinking is characterized by concreteness and an attitude towards correcting, correcting situations in order to achieve a certain result.

Thus, it can be noted that the individual style of thinking affects the way the problem is solved, the line of behavior, and the personal characteristics of a person.

Types of thinking.

Depending on what place the word, image and action occupies in the thought process, how they relate to each other, three types of thinking are distinguished: concrete-active or practical, concrete-figurative and abstract. These types of thinking are also distinguished on the basis of the characteristics of the tasks - practical and theoretical.

Visual Action Thinking- a type of thinking based on the direct perception of objects, real transformation in the process of actions with objects. The type of this thinking is aimed at solving problems in the conditions of production, constructive, organizational and other practical activities of people. practical thinking is primarily technical, constructive thinking. The characteristic features of visual-effective thinking are pronounced observation, attention to details, particulars and the ability to use them in a particular situation, operating with spatial images and schemes, the ability to quickly move from thinking to action and vice versa.

Visual-figurative thinking- a type of thinking characterized by reliance on representations and images; the functions of figurative thinking are associated with the representation of situations and changes in them that a person wants to receive as a result of his activity that transforms the situation. A very important feature of figurative thinking is the establishment of unusual, incredible combinations of objects and their properties. In contrast to visual-effective thinking, in visual-figurative thinking, the situation is transformed only in terms of the image.

Verbal-logical thinking It is aimed mainly at finding common patterns in nature and human society, reflects common connections and relationships, operates mainly with concepts, broad categories, and images and ideas play a supporting role in it.

All three types of thinking are closely related to each other. Many people equally developed visual-effective, visual-figurative, verbal-logical thinking, but depending on the nature of the tasks that a person solves, one, then another, then a third type of thinking comes to the fore.

Chapter II

visual-effective and visual-figurative

thinking of younger students.

clause 2.2. The role of geometric material in the formation of visual-effective and visual-figurative thinking of younger students.

The mathematics program in the elementary grades is an organic part of the mathematics course in the secondary school. Currently, there are several programs for teaching mathematics in primary grades. the most common is the three-year elementary school mathematics program. This program assumes that the study of relevant issues will be carried out during the 3 years of primary education, in connection with the introduction of new units of measurement and the study of numbering. In the third grade, the results of this work are summed up.

The program includes the possibility of implementing interdisciplinary connections between mathematics, labor activity, speech development, fine arts. The program provides for the expansion of mathematical concepts on concrete, life material, which makes it possible to show children that all those concepts and rules that they get acquainted with in the lessons serve the practice, were born from its needs. This lays the foundation for the formation of a correct understanding of the relationship between science and practice. The mathematics program will equip children with the skills necessary to independently solve new educational and practical problems, instill in them independence and initiative, habits and love for work, art, a sense of responsiveness, perseverance in overcoming difficulties.

Mathematics contributes to the development in children of thinking, memory, attention, creative imagination, observation, strict sequence, reasoning and its evidence; gives real prerequisites for further development visual-effective and visual-figurative thinking of students.

This development is facilitated by the study of geometric material associated with algebraic and arithmetic material. The study of geometric material contributes to the development of cognitive abilities of younger students.

According to the traditional system (1-3), the following geometric material is studied:

¨ In the first grade, geometric material is not studied, but geometric shapes are used as didactic material.

¨ In the second grade, they study: a segment, right and indirect angles, a rectangle, a square, the sum of the lengths of the sides of a rectangle.

¨ In the third grade: the concept of a polygon and the designation of points, segments, polyhedra with letters, the area of ​​a square and a rectangle.

In parallel with the traditional program, there is also an integrated course "Mathematics and Design", the authors of which are S. I. Volkova and O. L. Pchelkina. The integrated course "Mathematics and Design" is a combination in one subject of two subjects that are diverse in the way they are mastered: mathematics, the study of which is theoretical in nature and not always equally complete in the process of studying, it is possible to realize its applied and practical aspect, and labor training, the formation of skills and skills, which is of a practical nature, not always equally deeply supported by theoretical understanding.

The main provisions of this course are:

A significant strengthening of the geometric line of the elementary course of mathematics, which ensures the development of spatial representations and imaginations, including linear, planar and spatial figures;

Intensification of the development of children;

The main goal of the course "Mathematics and Design" is to ensure the numerical literacy of students, give them initial geometric representations, develop visual-effective and visual-figurative thinking and spatial imagination of children. To form elements of design thinking and constructive skills in them. This course provides an opportunity to supplement the subject "Mathematics" with the design and practical activities of students, in which the mental activity of children is reinforced and developed.

The course "Mathematics and Design" on the one hand contributes to the actualization and consolidation of mathematical knowledge and skills through the targeted material of logical thinking and visual perception of students, and on the other hand, creates conditions for the formation of elements of design thinking and design skills. In the proposed course, in addition to traditional information, information is given about lines: a curve, a broken line, a closed one, a circle and a circle, the center and radius of a circle. The idea of ​​​​angles is expanding, they are getting acquainted with three-dimensional geometric shapes: a parallelepiped, a cylinder, a cube, a cone, a pyramid and their modeling. There are various types of constructive activities for children: construction from sticks of equal and unequal lengths. Planar construction from cut out ready-made figures: triangle, square, circle, plane, rectangle. Volumetric design using technical drawings, sketches and drawings, designing according to the image, according to the presentation, according to the description, etc.

The program is accompanied by an album with a printed basis, which contains tasks for the development of visual-effective and visual-figurative thinking.

Along with the course "Mathematics and Design" there is a course "Mathematics with the strengthening of the line on the development of the cognitive abilities of students", authors S. I. Volkova and N. N. Stolyarova.

The proposed mathematics course is characterized by the same basic concepts and their sequence as the current mathematics course in elementary school. One of the main goals of developing a new course was the creation of effective conditions for the development of cognitive abilities and activities of children, their intellect and creativity, and the expansion of their mathematical horizons.

The main component of the program is the purposeful development of the cognitive processes of younger students and the mathematical development based on it, which includes the ability to observe and compare, notice the common in the different, find patterns and draw conclusions, build the simplest hypotheses, test them, illustrate with examples, and classify objects. , concepts on a given basis, develop the ability to make simple generalizations, the ability to use mathematical knowledge in practical work.

The fourth block of the program in mathematics contains tasks and assignments for:

Development of cognitive processes of students: attention, imagination, perception, observation, memory, thinking;

Formation of specific mathematical methods of action: generalizations, classifications, simple modeling;

Formation of skills to practically apply the acquired mathematical knowledge.

The systematic implementation of purposefully selected content-logical tasks, the solution of non-standard tasks will develop and improve the cognitive activity of children.

Among the programs discussed above, there are developmental education programs. The developmental education program of L.V. Zanyukov was developed for a three-year elementary school and is an alternative education system that has been and is still in practice. Geometric material permeates all three elementary school courses, i.e. it is studied in all three classes compared to the traditional system.

In the first grade, a special place is given to acquaintance with geometric shapes, their comparison, classification, and identification of the properties inherent in a particular figure.

"It is this approach to the study of geometric material that makes it effective for the development of children," says L. V. Zanyukov. Its program is aimed at developing the cognitive abilities of children, so the math textbook contains many tasks for the development of memory, attention, perception, development, and thinking.

Developing education according to the system of D. B. Elkonin - V. V. Davydov provides for cognitive functions (thinking, memory perception, etc.) in the development of the child. The program aims to form mathematical concepts in younger students based on meaningful generalization, which means that the child moves in the educational material from the general to the particular, from the abstract to the concrete. The main content of the presented training program is the concept of a rational number, which begins with the analysis of genetically initial relations for all types of numbers. Such a relation that generates a rational number is the ratio of magnitudes. With the study of the quantities and properties of their relations, the course of mathematics begins in the first grade.

Geometric material is associated with the study of quantities and actions with them. Crossing out, cutting out, modeling, children get acquainted with geometric shapes and their properties. In the third class, methods for directly measuring the area of ​​figures and calculating the area of ​​a rectangle on given sides are specially considered. Among the available programs there is a program of developmental education by N. B. Istomina. When creating her system, the author tried to take a comprehensive account of the conditions that affect the development of children, Istomina emphasizes that development can be carried out in activities. The first idea of ​​Istomina's program is the idea of ​​an active approach to learning - the maximum activity of the student himself. Both reproductive and productive activities affect the development of memory, attention, perception, but thought processes develop more successfully with productive, creative activities. "Development will go on if the activity is systematic," Istomina believes.

The textbooks of the first and third grades contain many tasks of geometric content for the development of positive abilities.

1.2. Features of the development of visual-effective and visual-figurative thinking of children of primary school age.

Intensive development of the intellect occurs in primary school age.

A child, especially of 7-8 years of age, usually thinks in specific categories, while relying on the visual properties and qualities of specific objects and phenomena, therefore, at primary school age, visual-effective and visual-figurative thinking continues to develop, which involves the active inclusion of models in teaching different types (subject models, diagrams, tables, graphs, etc.)

"A picture book, a visual aid, a teacher's joke - everything causes an immediate reaction in them. Younger students are in the grip of a vivid fact, the images that arise from the description while the teacher is talking or reading the book are very bright." (Blonsky P.P.: 1997, p. 34).

Younger students tend to understand literally the figurative meaning of words, filling them with specific images. Students solve this or that mental problem more easily if they rely on specific objects, ideas or actions. Given the figurative thinking, the teacher accepts a large number of visual aids, reveals the content of abstract concepts and the figurative meaning of words in a number of specific examples. And primary schoolchildren remember not what is most significant in terms of educational tasks, but what made the greatest impression on them: what is interesting, emotionally colored, unexpected and new.

Visual-figurative thinking is very clearly manifested when understanding, for example, complex pictures, situations. To understand such complex situations requires a complex orienting activity. Understanding a complex picture means understanding its inner meaning. Understanding the meaning requires complex analytical and synthetic work, highlighting the details of comparing them with each other. Visual-figurative thinking also involves speech, which helps to name a sign, to compare signs. Only on the basis of the development of visual-effective and visual-figurative thinking, formal-logical thinking begins to take shape at this age.

The thinking of children of this age differs significantly from the thinking of preschoolers: so if the thinking of a preschooler is characterized by such a quality as involuntariness, low controllability both in setting a mental task and in solving it, they more often and easily think about what is more interesting to them, what they captivates, then younger students as a result of studying at school, when it is necessary to regularly complete tasks in without fail learn to control your thinking.

In many ways, the formation of such arbitrary, controlled thinking is facilitated by the instructions of the teacher in the lesson, encouraging children to think.

Teachers know that the thinking of children of the same age is quite different. Some children are easier to solve problems of a practical nature, when it is necessary to use the methods of visual-effective thinking, for example, tasks related to the design and manufacture of products in labor lessons. Others are more easily given tasks related to the need to imagine and represent any events or any states of objects or phenomena. For example, when writing summaries, preparing a story from a picture, etc. A third of the children reason more easily, build conditional judgments and inferences, which allows them to solve mathematical problems more successfully than other children, derive general rules and use them in specific cases.

There are such children for whom it is difficult to think practically and operate with images, and to reason, and those for whom it is easy to do all this (Teplov BM: 1961, p. 80).

The presence of such diversity in the development different types thinking in different children greatly complicates and complicates the work of the teacher. Therefore, it is expedient for him to more clearly represent the main levels of development of the types of thinking in younger students.

The presence of one or another type of thinking in a child can be judged by how he decides the appropriate this species task thinking. So, if when solving easy problems - on the practical transformation of objects, or on operating with their images, or on reasoning - the child does not understand their condition well, gets confused and lost when looking for their solution, then in this case it is considered that he has the first level of development in the appropriate form of thinking (Zak A.Z.: 1984, p. 42).

If a child successfully solves easy problems designed to apply one or another type of thinking, but finds it difficult to solve more complex problems, in particular because he cannot imagine the whole solution as a whole, since the ability to plan is not sufficiently developed, then this case, it is considered that he has the second level of development in the corresponding type of thinking.

And finally, if a child successfully solves both easy and difficult problems within the framework of the corresponding type of thinking and can even help other children in solving easy problems, explaining the reasons for their mistakes, and can also come up with easy problems himself, then in this case it is considered that it is the third level of development of the corresponding type of thinking.

Based on these levels in the development of thinking, the teacher will be able to more specifically characterize the thinking of each student.

For the mental development of a younger student, you need to use three types of thinking. At the same time, with the help of each of them, certain qualities of the mind are better formed in the child. So solving problems with the help of visual-effective thinking allows students to develop the skills to control their actions, the implementation of purposeful, rather than random and chaotic attempts to solve problems.

Such a feature of this type of thinking is a consequence of the fact that it solves problems in which objects can be picked up in order to change their states and properties, as well as arrange them in space.

Since, when working with objects, it is easier for the child to observe his actions to change them, then in this case it is easier to control actions, stop practical attempts if their result does not meet the requirements of the task, or, on the contrary, force himself to finish the attempt to the end, to obtain a certain result. , rather than abandoning its execution without knowing the result.

With the help of visual-effective thinking, it is more convenient to develop in children such an important quality of the mind as the ability to act purposefully, consciously manage and control their actions when solving problems.

The peculiarity of visual-figurative thinking lies in the fact that when solving problems with its help, the child does not have the opportunity to actually change images and ideas, but only by imagination.

This allows you to develop different plans to achieve the goal, mentally coordinate these plans to find the best one. Since when solving problems with the help of visual-figurative thinking, the child has to operate only with images of objects (i.e., operate with objects only mentally), in this case it is more difficult to control their actions, control them and be aware than in the case when it is possible to operate on the objects themselves.

Therefore, the main goal of the development of visual-figurative thinking in children is to use it to form the ability to consider different paths, different plans, different variants achievement of the goal, different ways of solving problems.

This follows from the fact that by operating with objects in the mental board, by imagining possible options for their changes, you can find the right solution faster than by performing each option that is possible. Moreover, there are not always conditions for multiple changes in a real situation.

The peculiarity of verbal-logical thinking, in comparison with visual-effective and visual-figurative thinking, is that this is abstract thinking, during which the child does not act with things and their images, but with concepts about them, formalized in words or signs. At the same time, the child acts according to certain rules, being distracted from the visual features of things and their images.

Therefore, the main goal of work on the development of verbal-logical thinking in children is to use it to form the ability to reason, draw conclusions from those judgments that are offered in the number of initial ones, the ability to limit oneself to the content of these judgments and not involve other considerations related to external features of those things or images that are reflected and denoted in the original judgments.

So, there are three types of thinking: visual-effective, visual-figurative, verbal-logical. The levels of thinking in children of the same age are quite different. Therefore, the task of teachers and psychologists is a differentiated approach to the development of thinking in younger students.

1.3. The development of visual-effective and visual-figurative thinking in the study of geometric material in the lessons of experienced teachers.

One of the psychological features of children of primary school age is the predominance of visual-figurative thinking, and it is at the first stages of teaching mathematics that great opportunities for the further development of this type of thinking, as well as visual-effective thinking, are provided by work with geometric material, design. Knowing this, primary school teachers include geometric tasks in their lessons, as well as tasks related to design, or conduct integrated lessons in mathematics and labor training.

This paragraph reflects the experience of teachers in using assignments that contribute to the development of visual-effective and visual-figurative thinking of younger students.

For example, teacher T.A. Skranzhevskaya uses the game "Postman" in her classes.

The game involves three students - the postman. Each of them needs to deliver a letter to three houses.

Each house depicts one of the geometric shapes. The postman's bag contains letters - 10 geometric shapes cut out of cardboard. on a signal from the teacher, the postman looks for the letter and carries it to the appropriate house. The winner is the one who quickly delivers all the letters to the houses - decomposes geometric shapes.

Teacher of Moscow School No. 870 Popkova S.S. offers such tasks for the development of the considered types of thinking.

1. What geometric shapes are used in the drawing?

2. What are the geometric shapes that make up this house?

3. Lay out triangles from sticks. How many sticks did it take?

Many tasks for the development of visual-effective and visual-figurative thinking are used by Krapivina E.A. I will cite some of them.

1. What figure will you get if you connect its ends, consisting of three segments? Draw this shape.

2. Cut the square into four equal triangles.

Fold four triangles into one triangle. What is he?

3. Cut the square into four shapes and fold them into a rectangle.

4. Draw a segment in each figure to make a square.

Let us consider and analyze the experience of the primary school teacher of Borisov secondary school No. 2 Belous I.V., who pays great attention to the development of thinking of younger students, in particular visual-effective and visual-figurative, conducting integrated lessons of mathematics and labor training.

Belous I.V., taking into account the development of students' thinking, in the integrated lessons she tried to include elements of the game, elements of entertainment, she uses a lot of visual material in the lessons.

So, for example, when studying geometric material, children in an entertaining way got acquainted with some basic geometric concepts, learned to navigate in the simplest geometric situations and detect geometric shapes in the environment.

After studying each geometric figure, the children performed creative work, designed from paper, wire, etc.

Children got acquainted with a point and a line, a segment and a ray. When constructing two rays emanating from one point, a new geometric figure was obtained for children. They themselves determined its name. This is how the concept of angle is introduced, which, in the course of practical work with wire, plasticine, counting sticks, and colored paper, improves and becomes a skill. After that, the children began to build various angles with a protractor and a ruler and learned to measure them.

Here Irina Vasilievna organized work in pairs, groups, according to individual cards. The knowledge gained by students on the topic "Angles" was connected with practical application. Having formed the concept of a segment, a ray, an angle, she led the children to get acquainted with polygons.

In grade 2, introducing children to concepts such as circumference, diameter, arc, shows how to use a compass. As a result, children acquire the practical skill of working with compasses.

In grade 3, when students were introduced to the concepts of a parallelogram, trapezoid, cylinder, cone, ball, prism, pyramid, the children modeled and constructed these figures from scans, got acquainted with the game "Tangram", "Guessing".

Here are fragments of several lessons - travel to the city of Geometry.

Lesson 1 (fragment).

Topic: What is the city made of?

Target: introduce the basic concepts: point, line (straight line, curve), segment, polyline, closed polyline.

1. A fairy tale about how the line was born.

Once upon a time there was a red Dot in the city of Geometry (the dot is put on the blackboard by the teacher, and by the children on paper). Point One was bored and decided to go on a journey to find friends. The red dot just went beyond the mark, and the dot also goes towards it, only green. The green Dot approaches the red one and asks where she is going.

I'm going to look for friends. Stand next to me, we will travel together (children put a green dot next to the red one). After a while they meet a blue dot. Friends are walking along the road - points and every day they become longer and more and, finally, there are so many of them that they lined up in one row, shoulder to shoulder, and a line turned out (students draw a line). When the dots go straight, the line is straight, when uneven, crooked - the line is curved (students draw both lines).

One day Pencil decided to take a walk in a straight line. Goes, tired, and when the line is not visible.

How long do I have to go? Will I make it to the end? he asks Direct.

And she answered him.

Oh you, I have no end.

Then I will turn the other way.

And there will be no end to the other side. The line has no end at all. I can even sing a song

Without end and edge, the line is straight!

At least a hundred years follow me,

You won't find the end of the road.

Upset Pencil.

What should I do? I don't want to walk endlessly!

Well, then mark two points on me, - the straight line advised.

So Pencil did. - There are two ends. Now I can walk from one end to the other. But then I thought about it.

And what did this happen?

My cut! - said Direct (students practice drawing different segments).

a) How many segments are in this broken line?

Lesson 2 (fragment).

Topic: Roads in the city of Geometry.

Target: introduce the intersection of lines, with parallel lines.

1. Fold a sheet of paper. Expand it. What line did you get? Bend the sheet to the other side. Expand. You have received another direct.

Do these two lines have a common point? mark her. We see that the lines intersect at a point.

Take another sheet of paper and fold it in half. What do you see?

Such lines are called parallel.

2. Find parallel lines in the class.

3. Try to lay out a figure with parallel sides from sticks.

4. Using seven sticks, lay out two squares.

5. In a figure consisting of four squares, remove two sticks so that two squares remain.

Having studied the experience of Belousov I.V. and other teachers, we were convinced that it is very important, starting from the elementary grades, to use various geometric objects when presenting mathematics. It is even better to conduct integrated lessons of mathematics and labor training using geometric material. An important means of developing visual-effective and visual-figurative thinking is practical activity with geometric bodies.

Chapter II . Methodological and mathematical foundations of the formation

visual-effective and visual-figurative

thinking of younger students.

2.1. Geometric figures on the plane

In recent years, there has been a tendency to include a significant amount of geometric material in the initial course of mathematics. But in order to be able to introduce students to various geometric shapes, to teach them how to depict them correctly, he needs appropriate mathematical training. The teacher should be familiar with the leading ideas of the geometry course, know the basic properties of geometric shapes, and be able to construct them.

When depicting a flat figure, there are no geometric problems. The drawing serves either as an exact copy of the original, or represents a similar figure to it. Considering the image of a circle in the drawing, we get the same visual impression as if we were considering the original circle.

Therefore, the study of geometry begins with planimetry.

Planimetry is a branch of geometry in which figures on a plane are studied.

A geometric figure is defined as any set of points.

Segment, line, circle - geometric shapes.

If all points of a geometric figure belong to the same plane, it is called flat.

For example, a segment, a rectangle are flat figures.

There are figures that are not flat. This is, for example, a cube, a ball, a pyramid.

Since the concept of a geometric figure is defined through the concept of a set, we can say that one figure is included in another, we can consider the union, intersection and difference of figures.

For example, the union of two rays AB and MK is the straight line KB, and their intersection is the segment AM.

There are convex and non-convex figures. A figure is called convex if, together with any two of its points, it also contains a segment connecting them.

Figure F 1 is convex, and figure F 2 is non-convex.

Convex figures are a plane, a line, a ray, a segment, a point. it is easy to verify that a convex figure is a circle.

If we continue the segment XY to the intersection with the circle, we get the chord AB. Since the chord is contained in the circle, the segment XY is also contained in the circle, and, therefore, the circle is a convex figure.

The main properties of the simplest figures on the plane are expressed in the following axioms:

1. Whatever the line, there are points belonging to this line and not belonging to it.

Through any two points you can draw a line, and only one.

This axiom expresses the main property of the belonging of points and lines in the plane.

2. Of the three points on a line, one and only one lies between the other two.

This axiom expresses the main property of the location of points on a line.

3. Each segment has a certain length greater than zero. The length of a segment is equal to the sum of the lengths of the parts into which it is divided by any of its points.

Obviously, axiom 3 expresses the main property of the measurement of segments.

This sentence expresses the main property of the location of points relative to a straight line on a plane.

5. Each angle has a certain degree measure, greater than zero. The expanded angle is 180 o. The degree measure of an angle is equal to the sum of the degree measures of the angles into which it is divided by any ray passing between its sides.

This axiom expresses the basic property of measuring angles.

6. On any half-line from its starting point, a segment of a given length can be drawn, and only one.

7. From any half-line in a given half-plane, you can set aside an angle with a given degree measure less than 180 O, and only one.

These axioms reflect the basic properties of laying off angles and segments.

The main properties of the simplest figures include the existence of a triangle equal to the given one.

8. Whatever the triangle, there is an equal triangle at a given location with respect to a given half-line.

The main properties of parallel lines are expressed by the following axiom.

9. Through a point that does not lie on a given line, at most one straight line parallel to the given line can be drawn on the plane.

Consider some geometric shapes that are studied in elementary school.

An angle is a geometric figure that consists of a point and two rays emanating from this point. The rays are called the sides of the angle, and their common beginning is its vertex.

An angle is called straight if its sides lie on the same straight line.

An angle that is half a straight angle is called a right angle. An angle less than a right angle is called an acute angle. An angle greater than a right angle but less than a straight angle is called an obtuse angle.

In addition to the concept of an angle given above, the concept of a plane angle is considered in geometry.

A flat corner is a part of a plane bounded by two different rays emanating from the same point.

There are two flat angles formed by two rays with a common origin. They are called extras. The figure shows two flat corners with sides OA and OB, one of them is shaded.

Corners are adjacent and vertical.

Two angles are called adjacent if they have one side in common and the other sides of these angles are complementary half-lines.

The sum of adjacent angles is 180 degrees.

Two angles are called vertical if the sides of one angle are the complementary half-lines of the sides of the other.

The AOD and SOV angles, as well as the AOS and DOV angles, are vertical.

Vertical angles are equal.

Parallel and perpendicular lines.

Two lines in a plane are called parallel if they do not intersect.

If the line a is parallel to the line b, then write a II c.

Two lines are called perpendicular if they intersect at a right angle.

If line a is perpendicular to line b, then write a.

Triangles.

A triangle is a geometric figure that consists of three points that do not lie on the same straight line, and three pairs of segments connecting them.

Any triangle divides the plane into two parts: internal and external.

In any triangle, the following elements are distinguished: sides, angles, heights, bisectors, medians, midlines.

The altitude of a triangle dropped from a given vertex is the perpendicular drawn from that vertex to the line containing the opposite side.

The bisector of a triangle is the segment of the bisector of the angle of a triangle that connects a vertex to a point on the opposite side.

The median of a triangle drawn from a given vertex is the segment that connects this vertex to the midpoint of the opposite side.

The midline of a triangle is the line segment that connects the midpoints of its two sides.

Quadrangles.

A quadrangle is a figure that consists of four points and four segments connecting them in series, and no three of these points should lie on the same straight line, and the segments connecting them should not intersect. These points are called the vertices of the triangle, and the connecting segments are called its sides.

Sides of a quadrilateral that originate from the same vertex are called opposite sides.

In the quadrilateral ABCD, the vertices A and B are adjacent, and the vertices A and C are opposite; sides AB and BC are adjacent, BC and AD are opposite; the segments AC and BD are the diagonals of this quadrilateral.

There are convex and non-convex quadrilaterals. Thus, the quadrilateral ABCD is convex, while the quadrilateral KRMT is non-convex.

Among convex quadrilaterals, parallelograms and trapezoids are distinguished.

A parallelogram is a quadrilateral whose opposite sides are parallel.

A trapezoid is a quadrilateral in which only two opposite sides are parallel. These parallel sides are called the bases of the trapezium. The other two sides are called lateral. The segment connecting the midpoints of the sides is called the midline of the trapezium.

BC and AD are the bases of the trapezium; AB and SD - sides; KM - the middle line of the trapezoid.

Of the many parallelograms, rectangles and rhombuses are distinguished.

A rectangle is a parallelogram with all right angles.

A rhombus is a parallelogram in which all sides are equal.

From the set of rectangles, squares are selected.

A square is a rectangle in which all sides are equal.

Circle.

A circle is a figure that consists of all points of the plane equidistant from a given point, which is called the center.

The distance from the points to its center is called the radius. A line segment connecting two points on a circle is called a chord. The chord passing through the center is called the diameter. OA is the radius, SD is the chord, AB is the diameter.

A central angle in a circle is a flat angle with a vertex at its center. The part of a circle located inside a flat angle is called an arc of a circle corresponding to this central angle.

According to new textbooks in new programs M.I. Moro, M.A. Bantova, G.V. Beltyukova, S.I. Volkova, S.V. Stepanova in the 4th grade is given construction tasks, such that there were no earlier in the mathematics program in elementary school. These are tasks such as:

Construct a perpendicular to the line;

Divide the segment in half;

Construct a triangle on three sides;

Construct a regular triangle, an isosceles triangle;

Construct a hexagon;

Construct a square using the properties of the diagonals of a square;

Construct a rectangle using the rectangle's diagonals property.

Consider the construction of geometric figures on the plane.

The section of geometry that studies geometric constructions is called constructive geometry. The basic concept of constructive geometry is the concept of "construct a figure". The main proposals are formed in the form of axioms and are reduced to the following.

1. Each given figure is constructed.

2. If two (or more) figures are constructed, then the union of these figures is also constructed.

3. If two figures are constructed, then it is possible to determine whether their intersection will be an empty set or not.

4. If the intersection of two constructed figures is not empty, then it is constructed.

5. If two figures are constructed, then it is possible to determine whether their difference will be an empty set or not.

6. If the difference of the two constructed figures is not an empty set, then it is constructed.

7. You can draw a point belonging to the drawn figure.

8. You can build a point that does not belong to the constructed figure.

To construct geometric figures that have some of the specified properties, various drawing tools are used. The simplest of them are: a one-sided ruler (hereinafter simply a ruler), a two-sided ruler, a square, compasses, etc.

Various drawing tools allow you to perform various constructions. The properties of drawing tools used for geometric constructions are also expressed in the form of axioms.

Since the construction of geometric figures with the help of a compass and a ruler is considered in the school geometry course, we will also dwell on the basic constructions performed by these particular drawings with tools.

So, with the help of a ruler, you can perform the following geometric constructions.

1. construct a segment connecting two constructed points;

2. construct a straight line passing through two constructed points;

3. construct a ray that starts from the constructed point and passes through the constructed point.

The compass allows you to perform the following geometric constructions:

1. construct a circle if its center and a segment equal to the radius of the circle are constructed;

2. construct any of the two additional circle arcs, if the center of the circle and the ends of these arcs are constructed.

Elementary tasks for construction.

Construction tasks are perhaps the most ancient mathematical problems, they help to better understand the properties of geometric shapes, contribute to the development of graphic skills.

The construction problem is considered solved if the method of constructing the figure is specified and it is proved that as a result of the specified constructions, a figure with the required properties is actually obtained.

Consider some elementary construction tasks.

1. Construct a segment SD on a given straight line, equal to a given segment AB.

The possibility of only construction follows from the axiom of postponing a segment. With the help of a compass and a ruler, it is carried out as follows. Let a line a and a segment AB be given. We mark the point C on the straight line and build a circle with the straight line a centered at the point C and denote D. We get the segment SD equal to AB.

2. Through a given point, draw a line perpendicular to the given line.

Let points O and a line a be given. Two cases are possible:

1. The point O lies on the line a;

2. The point O does not lie on the line a.

In the first case from we denote a point C not lying on the line a. From point C as from the center we write off a circle of arbitrary radius. Let A and B be the points of its intersection. From points A and B we describe a circle of one radius. Let the point O be the point of their intersection, different from C. Then the half-line CO is the bisector of the developed angle, as well as the perpendicular to the line a.

In the second case, from the point O as from the center we draw a circle intersecting the straight line a, and then from points A and B with the same radius we draw two more circles. Let O be the point of their intersection lying in a half-plane different from the one in which the point O lies. The line OO/ is the perpendicular to the given line a. Let's prove it.

Denote by C the point of intersection of the lines AB and OO/. Triangles AOB and AO/B have three equal sides. Therefore, the angle OAC equal to the angle O/AC are equal in two sides and the angle between them. Hence from the angles ACO and ACO/ are equal. And since the angles are adjacent, they are right angles. Thus, OS is a perpendicular to the line a.

3. Through a given point, draw a line parallel to the given one.

Let a line a and a point A outside this line be given. Let us take some point B on the line a and connect it with point A. Draw a line C through point A, forming the same angle with AB as AB forms with the given line a, but on the opposite side from AB. The constructed line will be parallel to the line a., which follows from the equality of the cross-lying angles formed at the intersection of the lines a and with the secant AB.

4. Construct a tangent to the circle passing through a given point on it.

Given: 1) circle X (O, h)

2) point A x

Construct: tangent AB.

Construction.

2. circle X (A, h), where h is an arbitrary radius (axiom 1 of the compass)

3. points M and N of intersection of the circle x 1, and the straight line AO, that is, (M, N) = x 1 AO (axiom 4 is general)

4. circle x (M, r 2), where r 2 is an arbitrary radius, such that r 2 r 1 (axiom 1 of the compass)

5. circle x (Nr 2) (axiom 1 of the compass)

6. Points B and C of the intersection of the circles x 2 and x 3, that is, (B, C) = x 2 x 3 (general axiom 4).

7. BC is the desired tangent (axiom 2 of the ruler).

Proof: By construction, we have: МВ = МС = NВ = NC = r 2 . So the figure MBNC is a rhombus. tangent point A is the intersection point of the diagonals: A = MNBC, BAM = 90 degrees.

Having considered the material of this paragraph, we remembered the basic concepts of planimetry: segment, ray, angle, triangle, quadrilateral, circle. Considered the main properties of these concepts. And they also found out that the construction of geometric shapes with given properties using a compass and a ruler is carried out according to certain rules. First of all, you need to know what constructions can be done with a ruler that does not have divisions and with a compass. These structures are called basic. In addition, one must be able to solve elementary construction problems, i.e. be able to build: a segment equal to a given one: a straight line perpendicular to a given straight line and passing through a given point; a line parallel to a given point and passing through a given point and tangent to the circle.

Already in elementary school, children begin to get acquainted with elementary geometric concepts, geometric material occupies a significant place in traditional and alternative programs. This is due to the following reasons:

1. It allows you to actively use the visual-effective and visual-figurative level of thinking, which are the closest to children of primary school age, and based on which, children go to the verbal-figurative and verbal-logical levels.

Geometry, like any other subject, cannot do without visualization. As far back as the beginning of the 20th century, the well-known Russian methodist-mathematician Belyustin V.K. noted that "no abstract consciousness is possible if it is not preceded by the enrichment of consciousness with the necessary ideas." The formation of abstract thinking in schoolchildren from the first school steps requires preliminary replenishment of their consciousness with specific ideas. At the same time, the successful and skillful use of visualization encourages children to become cognitively independent and increases their interest in the subject, which is the most important condition for success. In close connection with the visibility of training is its practicality. It is from life that concrete material is drawn for the formation of visual geometric representations. In this case, education becomes visual, consistent with the life of the child, and is distinguished by practicality (N/Sh: 2000, No. 4, p. 104).

2. An increase in the volume of geometric material makes it possible to more effectively prepare students for the study of a systematic course in geometry, which causes great difficulties for schoolchildren in general and secondary schools.

The study of elements of geometry in elementary grades solves the following problems:

Development of planar and spatial imagination in schoolchildren;

Clarification on the enrichment of geometric representations of students acquired at preschool age, as well as in addition to schooling;

Enriching the geometric representations of schoolchildren, the formation of some basic geometric concepts;

Preparation for the study of a systematic course of geometry in the middle school.

"In modern studies of teachers and methodologists, the idea of ​​\u200b\u200band three levels of knowledge through which the mental development of a student passes in one way or another is gaining increasing recognition. Erdniev B.P. and Erdniev P.M. state them as follows:

1st level - knowledge-acquaintance;

2nd level - logical level of knowledge;

Level 3 is the creative level of knowledge.

Geometric material in elementary grades is studied at the first level, that is, at the level of knowledge-acquaintance (for example, the names of objects: a ball, a cube, a straight line, an angle). At this level, no rules and definitions are learned by heart. if he distinguishes visually or by touch a cube from a ball, an oval from a circle - this is also knowledge that enriches the world of ideas and words. (N/S: 1996, No. 3, p. 44).

At present, teachers themselves compose, select mathematical problems from a sufficiently diverse literature published in sufficient quantity, aimed at the development of thinking, including such types of thinking as visual-effective and visual-figurative, include them in extracurricular work.

These are, for example, the construction of geometric shapes from sticks, the recognition of figures obtained by bending a sheet of paper, the division of whole figures into parts and the composition of whole figures from parts.

I will give examples of mathematical tasks for the development of visual-effective and visual-figurative thinking.

1. Make up from sticks:

2. Continue

3. Find the parts into which the rectangle shown on the left is divided and mark them with a cross.

4. Connect the images and the names of the corresponding figures with arrows.

Rectangle.

Triangle.

Circle.

Curve line.

5. Put the number of the figure in front of its name.

Rectangle.

Triangle.

6. Construct from geometric shapes:

The course of mathematics is initially integrated. This contributed to the creation of an integrated course "Mathematics and Design.

Since one of the tasks of labor training lessons is the development of all types of thinking in children of primary school age, including visual-effective and visual-figurative, this created continuity with the current mathematics course in the primary grades, which ensures the mathematical literacy of students.

the most common type of work in labor lessons is applications from geometric shapes. When making an application, children improve their marking skills, solve the problems of sensory development of students, develop thinking, because by dividing complex figures into simple ones and, conversely, composing more complex ones from simple figures, schoolchildren consolidate and deepen their knowledge of geometric shapes, learn to distinguish them in shape, size, color, spatial arrangement. Such classes provide an opportunity for the development of creative design thinking.

The specificity of the goals and content of the integrated course "Mathematics and Design" determines the originality of the methods of its study, the forms and methods of conducting classes, where the independent design and practical activities of children come to the fore, implemented in the form of practical work and tasks, arranged in order of increasing difficulty level and their gradual enrichment with new elements and new activities. The stage-by-stage formation of skills for independent implementation of practical work includes both the performance of tasks according to the model and tasks of a creative nature.

It should be noted that, depending on the type of lesson (lesson of studying new mathematical material or lesson of consolidation and repetition), the center of gravity in its organization in the first case is focused on the study of mathematical material, and in the second - on the design and practical activities of children, during which active use and consolidation of previously acquired mathematical knowledge and skills in new conditions.

Due to the fact that the study of geometric material in this program is carried out mainly by the method of practical actions with objects and figures, much attention should be paid to:

Organization and implementation of practical work on modeling geometric shapes;

Discussion of possible ways to perform one or another design and practical task, during which the properties of both the simulated figures themselves and the relationships between them can be revealed;

Formation of skills to transform an object according to given conditions, functional properties and parameters of the object, recognize and highlight the studied geometric shapes;

Formation of elementary skills of construction and measurement.

Currently, there are many parallel and alternative programs for the course of mathematics in elementary grades. Let's take a look and compare them.

Chapter III . Experimental development work

visual-effective and visual-figurative thinking

junior schoolchildren in integrated lessons

mathematics and labor education.

3.1. Diagnostics of the level of development of visual-effective and visual-figurative thinking of younger schoolchildren in the process of conducting integrated lessons in mathematics and labor training in the 2nd grade (1-4).

Diagnostics as a specific type of pedagogical activity. is an indispensable condition for the effectiveness of the educational process. It is a real art to find in a student what is hidden from others. With the help of diagnostic techniques, the teacher can more confidently approach correctional work, correct the identified gaps and shortcomings, playing the role of feedback, as an important component of the learning process (Gavrilycheva G. F. In the beginning there was childhood // Primary school. -1999, - No. 1).

Mastering the technology of pedagogical diagnostics allows the teacher to competently implement the principle of age and individual approach to children. This principle was put forward back in the 40s by the psychologist S. L. Rubinstein. The scientist believed that "studying children, educating and teaching them, in order to educate and educate, studying them - this is the path of the only full-fledged pedagogical work and the most fruitful way of understanding the psychology of children. (Davletishina A. A. Studying the individual characteristics of a younger student // Primary school. -1993, - No. 5)

The work on the graduation project presented me with one, but very important question: "How does visual-effective and visual-figurative thinking develop in integrated lessons of mathematics and labor training?"

Prior to the introduction of the system of integrated lessons, a diagnosis of the level of development of thinking of younger schoolchildren was carried out on the basis of Borisov secondary school No. 1 in the 2nd grade (1 - 4). The methods are taken from the book by Nemov R.S. "Psychology" 3 volume.

Method 1. "Rubik's Cube"

This technique is designed to diagnose the level of development of visual-effective thinking.

Using the well-known Rubik's cube, the child is given practical tasks of varying degrees of complexity to work with him and offered to solve them in conditions of time pressure.

The methodology includes nine tasks, followed by the number of points in brackets that the child receives by solving this task in 1 minute. The total time for the experiment is 9 minutes. Moving from solving one problem to another, each time it is necessary to change the colors of the collected faces of the Rubik's cube.

Task 1. On any face of the cube, collect a column or row of three squares of the same color. (0.3 points).

Task 2. On any face of the cube, collect two columns or two rows of squares of the same color. (0.5 points)

Task 3. Completely assemble one face of the cube from squares of the same color, that is, a complete one-color square, including 9 small squares. (0.7 points)

Task 4. Collect completely one face of a certain color and to it one more row or one column of three small squares on the other face of the cube. (0.9 points)

Task 5. Collect completely one side of the cube and in addition to it two more columns or two rows of the same color on some other side of the cube. (1.1 points)

Task 6. Completely collect two faces of the cube of the same color. (1.3 points)

Task 7. Collect completely two sides of the cube of the same color and, in addition, one column or one row of the same color on the third side of the cube. (1.5 points)

Task 8. . Completely collect two faces of the cube and to them two more rows or two columns of the same color of the third face of the cube. (1.7 points)

Task 9. Completely collect all three faces of the cube of the same color. (2.0 points)

The results of the study are presented in the following table:

No. p \ p	F. I. student	Exercise									Overall result (point)	The level of development of visual-effective thinking
		1	2	3	4	5	6	7	8	9
1	Kushnerev Alexander	+	+	+	+	+	+	+	-	-	6,3	high
2	Danilina Daria	+	+	+	+	+	-	-	-	-	3,5	average
3	Kirpichev	+	+	+	+	+	-	-	-	-	3,5	average
4	Miroshnikov Valery	+	+	+	+	-	-	-	-	-	2,4	average
5	Eremenko Marina	+	+	+	-	-	-	-	-	-	1,5	average
6	Suleimanov Renat	+	+	+	+	+	+	+	+	-	8	high
7	Tikhonov Denis	+	+	+	+	+	-	-	-	-	3,5	average
8	Cherkashin Sergey	+	+	-	-	-	-	-	-	-	0,8	short
9	Tenizbaev Nikita	+	+	+	+	+	+	+	+	-	8	high
10	Pitimko Artem	+	+	-	-	-	-	-	-	-	0,8	short

The evaluation of the results of work with this technique was carried out in the following way:

10 points - very high level,

4.8 - 8.0 points - high level,

1.5 - 3.5 points - average level,

0.8 points - low level.

The table shows that most of the children (5 people) have an average level of visual-effective thinking, 3 people have a high level of development and 2 people have a low level.

Methodology 2 . "The Raven Matrix"

This technique is designed to assess the visual-figurative thinking of a younger student. Here, visual-figurative thinking is understood as one that is associated with operating with various images and visual representations when solving problems.

The specific tasks used to check the level of development of visual-figurative thinking in this technique are taken from the well-known Raven test. they are a specially selected selection of 10 gradually becoming more complex Raven matrices. (see Appendix No. 1).

The child is offered a series of ten progressively more difficult tasks of the same type: to search for patterns in the arrangement of ten parts on the matrix and to select one of the eight data below the drawings as the missing insert to this matrix, corresponding to its drawing. Having studied the structure of a large matrix, the child must indicate the details that best fit this matrix, i.e., corresponds to its pattern or the logic of arranging its details vertically and horizontally.

The child is given 10 minutes to complete all ten tasks. After this time, the experiment is terminated and the number of correctly solved matrices is determined, as well as the total amount of points scored by the child for solving them. Each correctly solved matrix is ​​worth 1 point.

Below is an example of a matrix:

The results of the children's implementation of the methodology are presented in the following table:

No. p \ p	F. I. student	Exercise										Correctly solved problems (points)
		1	2	3	4	5	6	7	8	9	10
1	Kushnerev Alexander	+	+	-	-	+	+	-	+	+	-	6
2	Danilina Daria	+	-	-	-	+	+	+	+	-	-	5
3	Kirpichev	-	+	+	+	-	-	+	+	+	-	6
4	Miroshnikov Valery	+	-	+	-	+	+	-	+	-	+	6
5	Eremenko Marina	-	-	+	+	-	+	+	+	-	-	5
6	Suleimanov Renat	+	+	+	+	+	-	+	+	+	-	8
7	Tikhonov Denis	+	+	+	-	+	+	+	-	-	+	7
8	Cherkashin Sergey	+	-	-	-	+	-	-	+	-	-	3
9	Tenizbaev Nikita	+	+	+	-	+	+	+	-	+	+	8
10	Pitimko Artem	-	+	-	-	-	+	+	-	-	-	3

Conclusions about the level of development:

10 points - very high;

8 - 9 points - high;

4 - 7 points - average;

2 - 3 points - low;

0 - 1 point - very low.

As can be seen from the table, 2 children have a high level of development of visual-figurative thinking, 6 children have an average level of development, and 2 children have a low level of development.

Method 3. "Labyrinth (A. L. Wenger).

The purpose of this technique is to determine the level of development of visual-figurative thinking of children of primary school age.

The child needs to find a way to a certain house among other, incorrect, paths and dead ends of the labyrinth. In this he is helped by figuratively given instructions - by which objects (trees, bushes, flowers, mushrooms) he will pass. the child must navigate the maze itself and the scheme. reflecting the sequence of stages of the path. At the same time, it is advisable to use the "Labyrinth" technique as exercises for the development of visual-figurative and visual-effective thinking (see Appendix No. 2).

Result evaluation:

The number of points received by a child is set on a rating scale (see Appendix No. 2).

After carrying out the method, the following results were obtained:

2 children have a high level of development of visual-figurative thinking;

6 children - average level of development;

2 children - low level of development.

Thus, during the preliminary experiment, a group of students (10 people) showed the following results:

60% of children have an average level of development of visual-effective and visual-figurative thinking;

20% - high level of development and

20% - low level of development.

The diagnostic results can be presented in the form of a diagram:

3.2. Features of the use of integrated lessons in mathematics and labor training in the development of visual-effective and visual-figurative thinking of younger students.

On the basis of a preliminary experiment, we determined that visual-effective and visual-figurative thinking is not sufficiently developed in children. for a higher level of development of these types of thinking, integrated lessons in mathematics and labor training were held. the lessons were conducted according to the program "Mathematics and Design", the authors of which are S. I. Volkova and O. L. Pchelkina. (see Appendix No. 3).

Here are fragments of lessons that contributed to the development of visual-effective and visual-figurative thinking.

Topic: Acquaintance with the triangle. Construction of triangles. Types of triangles.

This lesson is aimed at developing the ability to analyze, creative imagination, visual-effective and visual-figurative thinking; to teach as a result of practical exercises to build a triangle.

Fragment 1.

Connect point 1 to point 2, point 2 to point, point 3 to point 1.

What it is? Circulus asked.

Yes, it's a broken line! Dot exclaimed.

And how many segments does it have, guys?

And the corners?

Well, this is the triangle.

After the children got acquainted with the types of triangle (acute-angled, rectangular, obtuse-angled), the following tasks were given:

1) Circle the top of the right angle of the triangle with a red pencil, an obtuse angle in blue, and an acute angle in green. Fill in the right triangle.

2) Fill in the acute triangles.

3) Find and mark right angles. Count and write down how many right triangles are shown in the drawing.

Topic: Acquaintance with the quadrilateral. Types of quadrilaterals. Construction of quadrilaterals.

This lesson is aimed at developing all kinds of thinking, spatial imagination.

I will give examples of tasks for the development of visual-effective and visual-figurative thinking.

Fragment 2.

I. Repetition.

a) repetition about angles.

Take a sheet of paper. Bend it randomly. expand. got a straight line. Now fold the sheet in a different way. Look at the corners you got without a ruler and pencil. Name them.

Bend from wire:

After getting acquainted with the quadrilateral and its types, the following tasks were proposed:

How many squares?

2) Count the rectangles.

4) Find 9 squares.

Fragment 3.

For practical work, the following task was proposed:

Copy this quadrilateral, cut it out, draw diagonals. Cut the quadrilateral into two triangles along the diagonal that is longer and lay out from the resulting triangles such shapes as shown below.

Topic: Repetition of knowledge about the square. Acquaintance with the game "Tangram", construction from its parts.

This lesson is aimed at activating cognitive activity through solving logical problems, developing visual-figurative and visual-effective thinking, attention, imagination, stimulating active creative work.

Fragment 4.

II. Verbal counting.

Let's start the lesson with a small excursion to the "geometric forest".

Children, we are in an unusual forest. In order not to get lost in it, one must name the geometric figures that "hid" in this forest. Name the geometric shapes you see here.

The task is to repeat the concept of a rectangle.

Find matching pairs so that when they are added, you get three rectangles.

In this lesson, the game "Tangram" was used - a mathematical constructor. it contributes to the development of the types of thinking we are considering, creative initiative, ingenuity (see Appendix No. 4).

To compose planar figures according to the image, it is necessary not only to know the names of geometric figures, their properties and distinguishing features, but also the ability to imagine, imagine what will happen as a result of combining several figures, visually dismember the sample, represented by a contour or silhouette, into its constituent parts.

Teaching children the game "Tangram" was carried out in four stages.

Stage 1. Familiarizing children with the game: telling the name, examining individual parts, clarifying their names, the ratio of parts by size, learning how to connect them together.

Stage 2. Compilation of plot figures based on an elementary image of an object.

Compilation of subject figures according to an elementary image consists in a mechanical selection, copying the method of arranging the parts of the game. It is necessary to carefully consider the sample, name the components, their location and connection.

Stage 3. Compilation of plot figures based on a partial elementary image.

Children are offered samples on which the location of one or two components is indicated, they must arrange the rest on their own.

Stage 4. Drawing up plot figures according to a contour, or silhouette, pattern.

This lesson was an introduction to the game "Tangram"

Fragment 5.

This is an ancient Chinese game. In general, it is a square divided into 7 parts. (diagram showing)

From these parts you must construct an image of a candle. (diagram showing)

Topic: Circle, circumference, their elements; compass, its use, construction of a circle with a compass. "Magic circle", drawing up various figures from the "magic circle".

This lesson served to develop the ability to analyze, compare, logical thinking, visual-effective and visual-figurative thinking, imagination.

Examples of tasks for the development of visual-effective and visual-figurative thinking.

Fragment 6.

(after explaining and showing the teacher how to draw a circle with a compass, the children do the same work).

Guys, you have cardboard on your tables. Draw a circle with a radius of 4 cm on the cardboard.

Then, on red sheets, students draw a circle, cut out circles, use a pencil and a ruler to divide the circles into 4 equal parts.

One part is separated from the circle (blank for a mushroom cap).

They make a leg for the mushroom, glue all the parts.

Compilation of subject pictures from geometric shapes.

In the "Land of Round Figures", the inhabitants have come up with their own games that use circles divided into various shapes. One of these games is called "Magic Circle". Help. of this game, you can lay out various little men from the geometric shapes that make up the circle. And these little men are necessary in order to collect the mushrooms you made today in the lesson. You have circles on the tables, divided by lines into figures. Take scissors and cut the circle along the marked lines.

Then the students lay out the little men.

3.3. Processing and analysis of experimental materials.

After conducting integrated lessons in mathematics and labor training, we conducted an ascertaining study.

The same group of students participated, the tasks of a preliminary experiment were used to determine by what percentage the level of development of thinking of a younger student increased after conducting integrated lessons in mathematics and labor training. After the entire experiment, a diagram is drawn from which you can see by how many percent the level of development of visual-effective and visual-figurative thinking of children of primary school age has increased. The corresponding conclusion is made.

Method 1. "Rubik's Cube"

After carrying out this technique, the following results were obtained:

No. p \ p

F. I. student

Exercise

Overall result (point)

The level of development of visual-effective thinking

1

2

3

4

5

6

7

8

9

1

Kushnerev Alexander

+

+

+

+

+

+

+

+

-

8

high

2

Danilina Daria

+

+

+

+

+

+

+

-

-

6,3

high

3

Kirpichev

+

+

+

+

+

-

-

-

-

3,5

average

4

Miroshnikov Valery

+

+

+

+

+

+

-

-

-

4,8

high

5

Eremenko Marina

+

+

+

+

+

-

-

-

-

3,5

average

6

Suleimanov Renat

+

+

+

+

+

+

+

+

+

10

very tall

7

Tikhonov Denis

+

+

+

+

+

+

+

-

-

6,3

high

8

Cherkashin Sergey

+

+

+

-

-

-

-

-

-

1,5

average

9

Tenizbaev Nikita

+

+

+

+

+

+

+

+

+

10

very tall

10

Pitimko Artem

+

+

+

-

-

-

-

-

-

1,5

average

The table shows that 2 children have a very high level of development of visual-effective thinking, 4 children have a high level of development, 4 children have an average level of development.

Method 2. "Raven Matrix"

The results of this technique are as follows (see Appendix No. 1):

2 people have a very high level of development of visual-figurative thinking, 4 people have a high level of development, 3 people have an average level of development and 1 person has a low level.

Method 3. "Labyrinth"

After carrying out the methodology, the following results were obtained (see Appendix 2):

1 child - a very high level of development;

5 children - a high level of development;

3 children - the average level of development;

1 child - low level of development;

Compiling the results of diagnostic work with the results of the methods, we found that 60% of the subjects have a high and very high level of development, 30% - an average level and 10% - a low level.

The dynamics of the development of visual-effective and visual-figurative thinking of students is shown in the diagram:

So, we see that the results have become much higher, the level of development of visual-effective and visual-figurative thinking of the younger student has increased significantly, this indicates that the integrated lessons of mathematics and labor training we conducted have significantly improved the development of these types of thinking in second graders, which was the basis for proving the correctness of our hypothesis.

Conclusion.

The development of visual-effective and visual-figurative thinking in the course of integrated lessons of mathematics and labor training, as shown by our study, is a very important and urgent problem.

Exploring this problem, we have selected methods for diagnosing visual-effective and visual-figurative thinking in relation to primary school age.

To improve geometric knowledge and develop the types of thinking under consideration, we developed and conducted integrated lessons in mathematics and labor training, in which children needed not only mathematical knowledge, but also labor skills.

Integration in elementary school, as a rule, has a quantitative character - "a little about everything". This means that children receive more and more new ideas about concepts, systematically supplementing and expanding the range of existing knowledge (moving in knowledge in a spiral). In elementary school, it is advisable to build integration on the unification of fairly close areas of knowledge.

In our lessons, we tried to combine two subjects that are diverse in terms of the way they are mastered: mathematics, the study of which is theoretical in nature, and labor training, the formation of skills and abilities in which is of a practical nature.

In the practical part of the work, we studied the level of development of visual-effective and visual-figurative thinking before conducting integrated lessons in mathematics and labor training. The results of the primary study showed that the level of development of these types of thinking is weak.

After the integrated lessons, a control study was conducted using the same diagnostics. Comparing the results obtained with those previously identified, we found that these lessons were effective for the development of the considered types of thinking.

Thus, we can conclude that the integrated lessons of mathematics and labor training contribute to the development of visual-effective and visual-figurative thinking.

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