The use of modeling in the classroom at the initial level. Report "the use of modeling in technology lessons as a means of developing graphic literacy among junior schoolchildren" methodological development on technology on the topic

Modeling - visual and practical teaching method. The model is a generalized image of the essential properties of the modeled object.

The modeling method developed by D.B. Elkonin, L.A. Wenger, N.A. Vetlugina, N.N. Poddyakov is that the child's thinking is developed with the help of special schemes, models that reproduce the hidden properties and connections of an object in a visual and accessible form.

The modeling method is based on the principle of substitution: a child replaces a real object with another object, its image, or some conventional sign. At the same time, the main purpose of the models is taken into account - to facilitate the child's cognition, to open access to hidden, not directly perceived properties, qualities of things, their connections. These hidden properties and connections are very essential for the cognized object. As a result, the child's knowledge rises to more high level generalizations, approaching concepts.

Teachers primary grades MAOU SOSH №11 Borovichi successfully apply the modeling method in their teaching activities.

So, in reading lessons, to include each child in an active cognitive process and the formation of special reading skills (the ability to navigate in books, understand the features literary work), we use the modeling method - the introduction of a system of "substitutes" (symbols) of genres, themes, heroes, as well as drawing up schematic plans and cover models.

When drawing up a cover model, genres are indicated by figures:

Poem

Reading topics are replaced with color:

about the Motherland - red, about children - yellow, about nature - green, about animals - brown, about adventure, magic, fantasy - blue or purple.

For example, we will compose a cover model for the story "Volchishko" by E. Charushin. Replace the author's surname with a red rectangle, the title with a blue rectangle, and designate the genre and topic with a brown circle. The finished cover model will look like this:

Theme and genre (story about animals)

Heading

We use the modeling method in reading lessons when drawing up a schematic plan, in which a printed letter surrounded by a circle serves as a “substitute” for the characters. For example, a hare, a bear.

Model schematic plan for Russian folk tale "Kolobok" looks like this:

According to the presented plan, it is easy to understand what events took place in the fairy tale and in what sequence.

Modeling in math lessons is used in the very early stages of children's learning. So, we offer the following assignments to students of the kindergarten:

We actively use the modeling method as the main method of problem analysis, which helps students see the problem as a whole and not only understand it, but also find the correct solution for themselves.

When solving word problems, actions must go through 3 stages:

1. Purposefully practiced in operations with volumetric objects or their substitutes;
2. It is spoken, first loudly, then to itself;
3. Transition to mental action.

We use the following graphic schemes.

Problem number 1

The children planted 6 lime trees and 4 birches near the school. How many trees have the children planted near the school?

Problem number 2

Our house has 9 floors, It is 4 floors more than the neighboring one. How many floors are there in the neighboring house?

Tasks for choosing a model for a given problem (or vice versa) help the student understand the structure of the problem. As a rule, if students cope with this task, then they do not have problems in solving word problems.

For example, we suggest choosing a model for problem no. 3 “Several birds were sitting on a branch. After 5 birds flew away, there were 9 of them left. How many birds were sitting on the branch? "

The peculiarity of modeling in the lessons of familiarization with the surrounding world and natural history is that visibility is not a simple demonstration of natural objects, but stimulates independent practical activity of students. The students themselves, under the guidance of the teacher, create various models: they draw a plan of the area, build the simplest graphs and diagrams, draw diagrams of all kinds of connections. The main purpose of the model in the lesson is to gain an idea of \u200b\u200bthe nature and characteristics of the object under study based on the results of its research. Modeling is the process of creating by students, under the guidance of a teacher, an image of the object being studied, which fixes its most essential features.

In the first grade, when studying the world around us, in working with students, we use traffic light models made of paper, model toys vehicle, globe. In the classroom, students make models of the Sun, Earth from plasticine, models-applications of rainbows, clouds, models reflecting the richness and diversity of the nature of our planet (schemes). In the subsequent classes, much attention is paid to modeling the simplest food connections between organisms, the characteristics of the interaction between man and nature. This is drawing up, for example, diagrams of food chains, ecosystems of natural communities, the cycle of water and substances in nature, the change of day and night, etc.

As an example, we offer the following tasks:

Task 1. Choose and designate with the appropriate letter the words that "contain" water - B (air - OT, soil - P, light - C): rain, sun, meadow, steam, rubber ball, ravine, lake, flower pot, soup, bonfire, moon.)

Task 2.

Which of the figures below would you designate water, air, light, soil? Draw with these figures a picture depicting all these phenomena, paint them with paints.

Based on the work done, we came to the conclusion that the use of the modeling method in primary school has many advantages. Among which are ease of perception, accessibility, it is interesting and understandable for children. The use of modeling helps both in acquainting children with new material and in diagnosing the knowledge gained.

Thus, modeling in teaching acts as a way of cognition in identifying and fixing in a visual form those universal relations that reflect the scientific and theoretical essence of the objects under study; it is a sign-symbolic activity, which consists in obtaining new information in the process of operating with sign-symbolic means.

The theory of the gradual formation of mental actions is based on the fact that the learning process is the process of mastering the system of mental actions. This process is quite lengthy and consists of several stages, starting from the stage of material or materialized action, moving on to the stages of speech action, internal mental action. The stage of materialized action involves the construction and use of models for the assimilation of knowledge and skills. At the same time, the main purpose of the models is taken into account - to make it easier for the younger student to learn, to open access to hidden, not directly perceived properties, qualities of things, their connections. These hidden properties and connections are very essential for the cognized object. As a result, the knowledge of the younger student rises to a higher level of generalization, approaches the concepts.

So, modeling is a special and specific task in mathematics, since no concept can be built without modeling. But at the same time, modeling as an ability of primary schoolchildren can be formed only with special organized training... When designing a lesson, the teacher should take into account the fact that there are different children in the class and should be taught in different ways, based on the learning style preferred by the student. This is the understanding of the formation of action modeling in primary school.

Svetlana Khrabrova

"Stop alasy kimdigini bilim blimini

technicians shyarmashyly mektebi»KMM

KSU "School technical creativity

of education department of akimat of Kostanay city "

PROJECT

Making a flying model« ARROW»

(circle« Initial technical modeling» )

Leader: Khrabrova Svetlana Pavlovna

Kostanay 2017

1. Introduction

2. Purpose, objectives, relevance.

3. Preparatory stage

4. Practical stage.

5. Test model

Society today is in need

in creatively active and technically literate

young people. Renewed interest

youth to modern technique.

N. A. Nazarbayev

One of the tasks of the modern Kazakh school is to develop technical creativity of students. Occupation technical modeling - one of the forms of distribution among children of different ages technical education, instilling their interest in technical specialties.

Under technical modeling is understood as one of the types technical activitieswhich is to reproduce objects surrounding reality on an enlarged or reduced scale by copying objects in accordance with diagrams, drawings. Catching up technical modeling, children get to know different technologies processing of materials (paper, wood, foam, plastic, as well as technology use of ready-made forms in modeling.

Currently, children have a need for classes technical creativity... Despite the abundance in the trading network technical toys, with great interest the guys do it yourself make car models, aircraft, helicopters, ships, robots and other techniques... And these are not just toys made by guys... Competitions can be organized with technical models of various levels, take part in competitions, prepare a presentation, speech. And also such model is a good gift, made by hand.

Catching up making modelslinks with the following school subjects can be identified:

Maths (geometric shapes and geometric bodies) and etc. ,

-technology(skills in working with various tools,

History (knowledge of development history techniques,

OBZH (study safe work techniques, rules of conduct for

art (arts and crafts and art and design activities).

Lessons technical modeling realizes scientific and technical orientation, contribute to the formation of children's interest in technique, instilling special knowledge, skills and abilities, development of design skills and technical thinking.

My model

purpose the project:

Making a flying model of an aircraft from cardboard« Arrow» .

Tasks the project:

Introduction to technical creativity and independent work;

Receiving initial knowledge, skills, skills in making aircraft models;

Inclusion in the micro-research on the history of aviation;

Fostering persistence in achieving goals, self-confidence.

Relevance:

in the process model making« Arrow» happens:

Acquisition of the necessary in the future for the design and modeling skills,

Familiarity with the design aircraft,

Acquisition of sports and competitive skills,

Preparing to work on more complex ones models.

Materials and tools:

Cardboard, carbon paper, clamps, ruler, pencil, pusher, scissors, glue, felt-tip pens, stickers, wood block, elastic band, jigsaw, vice.

Working process:

1. Preparatory stage.

Let's recall the device of modern aircraft... An airplane is a complex machine, consisting of a large number of separate, well-coordinated parts. These details are grouped into five main parts. aircraft: fuselage, wing, tail unit, aircraft engine (engine, chassis.

2. Practical stage.

Making a flying model« Arrow»

The first step is making a model drawing... Any car model, robot, the aircraft is made according to the drawing... And the copying paper helps us to make a drawing.

1. Cardboard, 2. Copy paper, 3. we fix the drawing with clamps

Copy the drawing. We make a drawing with a ruler.

We receive the drawing model airplane on cardboard

The second step is to push the fold lines in the drawing using a ruler and a metal pusher to make the paper fold easier.

The third step is to cut model.

Fourth step - glue the received parts:

Fuselage aircraft,

Fifth stage - registration model

Sixth stage - making a catapult.

From a block of wood using a vise and a jigsaw we make a catapult... We put an elastic band on it.

3. Test model

You can hold mini-competitions that will reveal the flying qualities model, eliminate imperfections.

4.conclusions: at the end of the work guys

Know the safety rules when working with materials and tools;

Requirements for the organization of the workplace; elementary properties of paper and cardboard, names of the main parts manufactured model.

Know how to work with a drawing;

Do practical work yourself (including according to the drawing);

Use it competently in speech technical terminology, technical concepts and information;

Compare technical objects on various grounds, make generalizations.

I like to build model airplane and watch, how is she flies! Even without a motor, it just glides in the air flow, but it looks really great!

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Modeling as a means of cognitive development of preschool children: models, types of models, organization conditions 2.3. Modeling as a means of children's cognitive development: models, types of models, organization conditions. Modeling is visual and practical.

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Introduction
Chapter I. Theoretical and methodological basis of modeling in the system primary education

1.1 The meaning of the concepts "model" and "modeling"
1.2 The Role and Location of Modeling in the Next Generation Primary School Standard
1.3 Using simulation in teaching mathematics
Chapter I Conclusions

Conclusion
Literature

Glossary on categorical apparatus

Personal Glossary
INconducting

The relevance of research.The Federal State Educational Standard (hereinafter - FSES) of the new generation does not imply serious changes in mathematical preparation for primary schoolchildren. It maintains the tradition of elementary math education, but sets different emphasis and priorities. The main thing in goal-setting, in the selection and structuring of content, in the context of its implementation, is the importance of the initial course in mathematics in continuing education in general, also in mathematics, and, of course, the ability to use knowledge and skills in solving various practical and cognitive problems.

Contradictions. Despite the fact that attention is paid to the initial course in mathematics in the Federal State Educational Standard, there are still problems in teaching how to solve various problems when studying the course of mathematics in elementary school.

Problemteaching a younger student to solve various problems at different stages of development mathematics education was and is one of the most pressing problems. A variety of studies are devoted to its solution, in the role of a subject in which different sides of learning to solve various problems played. This is a sample of their content and a system, this is the function of tasks in the very process of teaching mathematics, and their role in the formation of educational activity and mathematical concepts in schoolchildren, as well as in the development of logical thinking of schoolchildren. Modeling is of particular importance in teaching and, first of all, in solving problems, in the conditions of education, which is focused on the development of thinking in younger students. studies have shown that it favors the formation of generalized knowledge. This moment also determines the ways of organizing the activities of schoolchildren, which are aimed at developing thinking in the course of analyzing the problem and searching for a solution plan using modeling, the formation of skills and methods of action necessary to implement this. In this work, modeling is considered not only as a way of forming general skill solve problems, but also as one of the goals in teaching mathematics.

Considering modeling as a particular, specific type of general method of activity with mathematical concepts and relationships, it is supposed to build the formation of constructive skills in the student in the process of modeling the studied mathematical concepts and relationships. Also, the representation of the studied concept or relationship in a visual model (layout or design) makes it possible for children to form an adequate idea of \u200b\u200bsomething abstract at a visual level, which is most consistent with their capabilities and needs.

Research topic: modeling in math lessons in elementary school.

The purposework is a theoretical substantiation of the effectiveness of the use of modeling in the learning process in primary school.

An objectohm researchis the process of teaching students to model the content of various tasks.

Thingohm researchmodeling the content of various tasks in the study of the course of mathematics in elementary school.

Hypothesis:Teaching younger students to solve various problems will be effective if:

· Students will acquire the skills to translate the specific content of tasks on an abstract basis;

· Toys, objects will be used in modeling instead of real objects;

· When drawing up diagrams, students will be given the opportunity to build models on a project basis;

· A gradual transition from subject models to ideal models has been made.

Research objectives:

1. To study the psychological and pedagogical literature on the research problem.

2. To study the role of modeling in the Federal State Educational Standard of the new generation.

3. Analyze the effectiveness of using modeling in teaching mathematics.

Methodologicallyohresearch basisthe most important studies of the methodology of teaching mathematics in the elementary grades by various authors (Leontiev A.I., Istomina N.B., Mentsis Ya.Ya. and others) appeared. As well as works that reveal the levels of modeling in mathematics (Beloshistaya A.V., Shikova R.N., etc.).

The theoretical basis of the research were the works of foreign and domestic scientists, instructional and reference materials, regulatory documents, articles of pedagogical magazines and newspapers.

Method research:analysis and generalization of psychological and pedagogical literature;

Work structure.

Course work consists of this introduction, two chapters, bibliography, glossary and appendices.

The first chapter "Theoretical and methodological basis of modeling in the primary education system" examines the theoretical and practical aspects of modeling, its place in education, as well as the levels of modeling the content of various tasks in primary school.

In the conclusion, the results of the study are summarized and the key points of this course work are described.

The work is presented on 74 sheets.

ChapterI. Theoretical and methodological basis for modeling in the primary education system

1.1 FROMthought of the concepts "mdress» and« modeling»

From these definitions of the model, two characteristics follow:

1) model - the deputy of the object of study;

2) the model and the object under study are in certain correspondence relations (and in this sense, the model reflects the object). However, both characteristics are interrelated, because the replacement of one object by another can occur only due to their correspondence in some respect. [№8, p.91]

V.A. Shtoff distinguishes models:

a) material, reproducing the geometric and physical properties of the original (children's toys, visual teaching aids, models, etc.);

b) ideal, transmitting information about the properties and states of an object, process, phenomena, reflecting their relationship with the outside world. Ideal models can be figurative and symbolic (drawings, diagrams, graphs, etc.) [№10, p.23]

modeling

The growing interest of the cognitive methodology to the topic of modeling was due to the importance that the modeling method received in modern science, and especially in such its sections as chemistry, physics, biology, cybernetics, as well as many technical sciences.

The word "model" comes from the Latin word "modelium", means: measure, method, etc. Beloshistaya A.V. Reception of graphic modeling in teaching problem solving // primary school, 2009, 8, p.15 Its initial value was associated with building art, and in almost all European languages \u200b\u200bit was used to denote an image or thing that is similar in some respect to another thing. " According to the opinions of many writers (Vedenov A.A., Kochergin A.N., Shtoff V.A.), the model was first used as an isomorphic theory (two theories are called isomorphic if they have structural unity in relation to each other) ...

Modeling is a method of studying objects of knowledge on their models; construction and study of models of really existing objects and phenomena (organic and inorganic systems, technical devices, various processes - physical, chemical, biological, social) and constructed objects to determine or improve their characteristics, rationalize the methods of their construction, management, etc. ... Modeling can be:

Ё objective (study of the basic geometric, dynamic, functional characteristics of an object on a model);

Ё physical (reproduction of physical processes);

Ё objectively - mathematical (the study of a physical process through the experimental study of any events of a different physical entity, but described by the same mathematical relations as the modeled process);

Ё sign (computational modeling, abstract - mathematical) Mathematics and design in the 1st grade. Book for the teacher. Murmansk. MO IPKRO. - 2011.-p. 72.

Before moving on to the issues of applying modeling, consider the main functions of models.

The main functions of the models.

Modeling as a tool for experimental research.

Considering material models as a means of research activity makes it necessary to find out how the experiments in which the models are used differ from those where they are not applied. The transformation of experiment into one of the main figures of practice, which took place in parallel with the development of science, was the result from the minutes when the widespread use of natural science became possible in production, which in turn was the product of the first industrial revolution, which opened the era of automatic production. The specificity of the experiment as a form of practical activity is that the experiment expresses the active participation of a person in reality. Methodological solution to the problem of correction of deficit school-significant functions in primary education (based on the material of mathematical education) / "Childhood in the era of society transformation." Materials of the international scientific and practical conference. T. 2. Murmansk: MGPI. - 2007 .-- p. 53 - 55. In the persuasiveness of this, in Marxist epistemology there is a sharp difference between experiment and scientific knowledge. Although every experiment includes observation as a mandatory phase of the study. Nevertheless, in addition to observation, an experiment also contains such an important factor for revolutionary practice as an active intrusion into the course of the process being studied. “Experiment means the type of activity undertaken for the purpose of scientific knowledge, the discovery of objective regularities and consisting in the impact on the studied object (process) through special tools and devices ”How to design universal educational actions in primary school. From action to thought: a guide for teachers / A.G. Asmolov, G.V. Burmenskaya, I.A. Volodarskaya and others; ed. A.G. Asmolova. - 3rd ed. - M .: Education, 2011. Series "Standards of the second generation".

There is a peculiar form of experiment, which is characterized by the use of existing material models as separate means of experimental research. This form is called a model experiment. Unlike the next experiment, where the means of experiment, in one way or another, interact with the subject of research, there is no interaction here, because they are experimenting not with the subject itself, but with its substitute. In this case, the substitute object and the experimental setup are combined, merged into a whole in the operating model. Consequently, the ambiguous role that the model plays in the experiment is manifested: it is both an object of research and an experimental tool. For a model experiment, according to the opinions of a number of authors, the following basic procedures are characteristic:

1. transition from a natural object to a model - building a model (modeling in the real sense of the word);

2. empirical study of the model;

3. the transition from a model to a natural object, which consists in transferring the results obtained during the study to a given object Shikova R.N. The use of modeling in the process of teaching mathematics // Elementary school, 2008, 12..

The model enters the experiment, not only replacing the object of study, it can also replace the conditions in which a certain object of an ordinary experiment is studied. A simple experiment assumes the existence of a theoretical moment only at the initial moment of the study - the hypothesis, its assessment, etc., and also at the final stage - the discussion and interpretation of the data obtained, their generalization. In a model experiment, it is also necessary to substantiate the position of similarity between the model and a natural object and the ability to extrapolate the obtained data to this object. V.A. Shtoff in his book "Modeling and Philosophy" says that the theoretical basis of the model experiment, mainly in the field of material modeling, is the concept of similarity About the possibility of building a system for the development of mathematical thinking of preschoolers / In the collection "Actual problems of teaching and development of preschool children ". Murmansk: MGPI. - 2009 .-- p. 7-16. It provides modeling rules for cases where the model and nature have a common (or approximately the same) physical nature. However, at the moment, the practice of modeling has gone beyond the relatively limited range of mechanical phenomena. The emerging mathematical models, which differ in their material nature from the modeled object, made it possible to overcome the modest possibilities of physical modeling. In mathematical modeling, the model-reality relationship is a generalization of the similarity theory that takes into account the qualitative heterogeneity of the model and the object, their belonging to various forms of matter movement. This generalization takes the form of a more abstract theory of system isomorphism.

Modeling and the problem of truth.

An interesting question is what role modeling itself plays in the course of proving the truth and searching for true knowledge. What should be understood by the truth of the model? If truth in general is “the ratio of our knowledge to reality,” then the truth of a model means that the model corresponds to an object, and the falsity of a model means the absence of such a relationship. This indication is mandatory, but not sufficient. Further clarifications are required, based on taking into account the conditions on the basis of which a model of one type or another reproduces the phenomenon under study. For example, the requirements for the equality of the model and the object in mathematical modeling based on physical analogies, assuming, when the physical processes in the model and the object are different, the identity of the mathematical form in which their universal laws are expressed, are more general, more abstract. Consequently, when constructing certain forms, they are always deliberately distracted from certain countries, properties and even relations, due to which, it is deliberately allowed not to preserve the unity between the model and the original for a number of parameters. Thus, Rutherford's planetary model of the atom turned out to be correct in the framework of studying the electronic structure of the atom, and the model of J.J. Thompson turned out to be incorrect, since its structure did not coincide with the electronic circuit. Visual geometry in the 1st grade. Tutorial. Murmansk: MGPI. - 2008 .-- 56p. ... Truth is a property of knowledge, and the objects of the material world are not true, not false, they simply are. The model implements two types of knowledge:

1. cognition of the model itself (its structure, processes, functions) as a system created for the purpose of reproducing an object;

2. theoretical information through which the model was built.

Keeping in mind precisely the theoretical concepts and methods that underlie the construction of the model, it is possible to determine the questions of how correctly and fully the established model reflects the subject. In this case, an idea arises about the comparability of any object created by a person with similar authentic objects and about the truth of this object. However, this makes sense only if such objects are created with a special purpose to depict, copy, convey these features of a natural object. Therefore, we can talk about the truth inherent in material models:

Ё due to their connection with certain knowledge;

Ё due to the presence (or absence) of isomorphism of its structure with the structure of the modeled process or phenomenon;

Ё due to the relationship of the model to the modeled object, it makes it part of cognitive process and allows the identification of certain cognitive problems.

"And in this position the material model is epistemologically secondary, acts as an element of epistemological reflection" Modeling as the basis for the formation of the ability to solve problems. Guidelines for primary school teachers. Murmansk: IPK. - 2011 .-- 64 p. ...

The model can be analyzed not only as a tool for checking whether, in fact, there are such connections, relationships, structures, patterns that are formulated in a given concept and are implemented in the model. The successful operation of the model is a practical proof of the truth of the theory, i.e. it is part of an exploratory proof of the truth of a given theory.

The process of creating and applying a model is called modeling.

In all disciplines, models act as a powerful means of knowledge.

For instance:

1. People have long been interested in how our Universe works. This interest is not only cognitive, however, and extremely practical, because people wanted to learn to predict periodic phenomena associated with the structure of the Universe, such as: the eclipse of the sun and moon, the onset of the seasons.

For the sake of solving these problems, scientists built their ideas about the Universe in the form of a diagram of a picture of the world, in which the objects of the Earth, the sun and stars, planets, the earth and the moon were depicted as points moving along some curves - the trajectories of their movement. Such are, for example, the schemes constructed by Ptolemy, in which the main space was occupied by our Planet, or the Copernican scheme, in which the Sun occupied the main place.

Using these schemes, scientists deduced the tasks of predicting special astronomical phenomena. These diagrams or pictures of the world are the essence of the model of the Universe, and the method of studying the Universe, determining the laws and solving problems associated with these models, is a way of modeling.

2. People have long been interested in how they themselves are arranged, how the human body works. However, it is very difficult to study these questions on a living human body. Since such a study before the appearance of special devices was associated with the death of this organism. Here scientists began to study the structure of the human body on animals similar to its body. The study of the body of animals, their functioning has helped to determine many of the most important laws of the functioning of the human body.

In these studies, animal organisms acted as a model of the human body, and at the same time the method is modeling Borodulko M.A., Stoilova L.G. Learning to solve problems and modeling // Elementary school. - 2008. - No. 8. - S. 26-32. ...

In mathematics, the modeling method is widely used in solving problems.

A mathematical model can be used to characterize a specific representation (often approximate) of a certain problem, situation, which makes it possible to use the formal logical apparatus of mathematics in the process of its analysis. In mathematical modeling, we are dealing with a theoretical copy, which, in a mathematical model, expresses the basic laws, properties of the studied subject.

In the process of mathematical modeling, three stages are distinguished:

1. Formalization - translation of the problem (situation) into the language of the mathematical system (construction of a mathematical model of the problem).

2. Solution of a problem within the framework of a mathematical system (they say: a solution within a model).

3. Translation of the result of the exact definition of the problem into the language in which the initial goal was formulated (interpretation of the solution).

Most often, an accurate imitation is a somewhat simplified table (description) of the original, which means it has an undoubted level of error. model mathematics learning task

One and the same model can define various processes, objects, therefore products within the model study of the action itself can often be transferred to another action. This is one of the main values \u200b\u200bof mathematical modeling.

Mathematics not only created various internal models of algebra, geometry, functions of a complex variable, differential equations, etc., but also helped natural science to build mathematical models of mechanics, electrodynamics, thermodynamics, chemical kinetics, microworld, space-time and gravitation, message transmission capabilities , management, logical conclusion Arginskaya I.I. Maths. 1 class. A teacher's guide to a stable textbook. - M .: Federal Scientific and Methodological Center named after L.V. Zankova, 2011.

By creating models, mathematician often outstripped the needs of natural science and technology.

The implementation of the global mathematical method of cognition is the main task and task of modern mathematics. It includes, first of all, the creation of new, unknown mathematical models, for example, in biology, for the knowledge of the life and function of the brain, the microworld, new, fantastic technologies and technology, as well as the knowledge of economic and social phenomena also using mathematical models using various mathematical methods. ...

Now that the main theoretical aspects of models and modeling have been analyzed, we can proceed to consider specific examples of the widespread use of modeling as a means of cognition in education.

1.2 Roleand the scene of the simulation in cnew generation standard for primary school

A distinctive feature of the new standard is its activity-oriented nature, which makes the development of the student's personality the main task. The education system abandons the traditional understanding of learning outcomes in the form of knowledge, skills and abilities; the standard's wording lists the obvious activities that the student is required to learn by the end of primary education. Requirements for learning outcomes are formulated in the form of personal, subject and real results.

An integral part of the core of the new standard is common learning activities (ULE). UUD is understood as "general educational skills", "general methods of activity", "over-subject actions", etc. A special program is provided for UUD - the program for creating universal educational actions (UUD). An individual approach in the formation and development of mathematical abilities of a younger student // Primary school: plus - minus. - 2011. - №7. - from. 3 - 15..

All types of UUD are considered in the context of the content of certain academic subjects.

In a broad sense, the term "universal educational actions" means the ability to learn, that is, the ability of a person to self-development and self-improvement through deliberate and active appropriation of new social experience. In a narrower (strictly psychological) sense, this term can be expressed as a set of methods of action of a student (as well as related skills of educational work) that provide independent study new knowledge, the formation of skills, including the organization of this process.

The general nature of educational activities is manifested in the fact that they:

They are of a supra-subject, metasubject nature; provide a community of general cultural, personal and cognitive development and self-development of the individual;

Provide communication between all stages of the educational process;

They lie at the heart of the organization and regulation of any student's activity, regardless of its specially-subject content.

Universal educational actions provide the stages of comprehension of educational content and formation psychological abilities student.

The teacher must create the conditions in which UUD are formed most effectively, not "in spite of, but thanks to" the teaching method of the subject.

This allows the student to self-develop and improve himself.

Universal Learning Activities (ULE) are divided into 4 groups:

regulatory,

personal,

communicative

and cognitive (see table 1) Zaitsev V.V. Mathematics for younger students. Methodological guide for teachers and parents. -M .: "Vlados", 2009, p. 89.

Table 1. Universal Learning Activities (ULE)

The application of modeling in the practical activity of a teacher contains two aspects.

Firstly, modeling is the content that should be studied by students as a result of learning, the method of cognition that they must master, and secondly, modeling is that educational action and a means without which real learning is impossible. LM Fridman in the "Federal State Educational Standard of Primary General Education", put at the forefront the development of universal educational actions that provide schoolchildren with the ability to learn, the ability to self-development and self-improvement. One of the most important cognitive universal actions is the ability to solve problems or tasks. Due to the complex systemic nature of the universal method for solving problems, this universal educational action can be considered as a model for the system of cognitive actions.

The solution of various problems acts both as a goal and as a means of education. The art of defining and solving especially word problems is one of the main signs of the level of development of students, it opens up ways for them to master new knowledge. When teaching problem solving, you need to use a general problem solving approach. At the heart of the emergence of the general ability to solve problems is the method of modeling, which is the main feature of the development of symbolic and symbolic universal educational actions. For successful learning in primary school, the following universal educational activities should be created: - coding / substitution (use of signs and symbols as conditional substitutes for material objects and objects); - decoding / reading information; - the ability to use explicit models (diagrams, drawings, plans), reflecting the spatial distribution of objects or relations between objects or their parts to solve problems; - the ability to create schemes, models, etc. Leontyev A.I. On the development of the child's arithmetic thinking. On Sat. "School 2100" issue 4 Priority areas of development educational program - M .: "Balass", 2010, p.109.

So, modeling is included in educational activity as one of the actions that should be developed by the end of primary school.

Models and modeling in teaching primary schoolchildren

Younger school age is the beginning of the formation of educational activities in children. At the same time, modeling is an action that is carried out beyond the limits of primary school age into further types of human activity and reaches a new level of its development. With the help of modeling it is possible to reduce the study of the complex to the simple, the unfamiliar to the familiar, that is, to make the object available for careful study. In order to "equip" students with modeling as a method of cognition, it is necessary that the students themselves build models, themselves study any objects, phenomena with the help of modeling. [No. 7]

Despite the fact that modeling is used in the educational and cognitive process of a modern elementary school (textbooks by I.I. Arginskaya, E.I. Aleksandrova, T.E. Demidova, N.B. Istomina, G.G. Mikulina, L.G. Peterson and others), the problem of teaching modeling was not adequately reflected in the teaching aids for elementary school. In the system of D.B. Elkonin - V.V. Davydov, modeling is singled out as an educational action that is part of educational activity, which should be formed by the end of primary school. [No. 6, p..29-33]

The concept of "model" and "modeling" is interpreted ambiguously by a number of authors. Let's consider the definitions of the concepts "model" and "modeling".

In the Great Soviet Encyclopedia “Model - image (including conventional or mental - image, description, diagram, drawing, graph, plan, map, etc.) or prototype (sample) of any object or system of objects (“ original "Of this model), used under certain conditions as their" substitute "or" representative ". [No. 2, p. 399.]

Shtoff V.A. believes that “a model (from Lat. modulus - measure) is a substitute for the original, providing the study of some of its properties. It is created for the purpose of obtaining and (or) storing information (in the form of a mental image, description by symbolic means or a material system), reflecting the properties, characteristics and connections of the original, essential for solving the problem ”[No. 10]

According to P.V. Trusov, “a model is such a material or mentally imagined object that, in the process of cognition (study), replaces the original object, retaining some of its typical features important for this research” [No. 3, p.18]

A. B. Vorontsov believes that "the model acts as an instrument of joint activity of students and teachers. It reflects general relations and connections within the studied object". [№4]

V.V.Davydov, A.U. Vardanyan believe that the model creates a language of communication, which, by objectifying the content of the object of research, makes it possible to reveal its essence.

Having analyzed the above definitions, we conclude that in the definitions of V.A. Shtoff, P.V. Trusova and the Great Soviet Encyclopedia, a model is an image, and for A.B. Vorontsov's model is a "tool"; goals in explicit and implicit form are highlighted in P.V. Trusova and V.A. Shtoff, but in the encyclopedia and in A. B. Vorontsov the goal is not defined; V.A. Shtoff, P.V. Trusova and in the Great Soviet Encyclopedia, the model is presented in the form of a mental image.

Two of its characteristics follow from these definitions of the model: 1) the model is a substitute for the object of study; 2) the model and the object under study are in certain correspondence relations (and in this sense, the model reflects the object). However, both characteristics are interrelated, because the replacement of one object with another can occur only due to their correspondence in some respect. [№8, p.91]

Analysis of psychological and pedagogical literature showed that there are several classifications. We will consider separately each classification of V.A. Shtoff and L.M. Friedman, then we will compare them.

Shtoff V.A. classifies models on various grounds. In the practice of primary education, it is of interest to classify models according to the form of presentation.

VA Shtoff distinguishes models: a) material, reproducing the geometric and physical properties of the original (children's toys, visual teaching aids, models, etc.); b) ideal, transmitting information about the properties and states of an object, process, phenomena, reflecting their relationship with the outside world. Ideal models can be figurative and symbolic (drawings, diagrams, graphs, etc.) [№10, p.23]

V.A. Shtoff and L.M. Friedman's classification of the model is initially divided into two groups: material and non-material. In turn, L.M. Friedman subdivides material models into: figurative, sign and mental. V.A. Shtoff's mental models are separated into a separate group (intangible), and figurative-iconic and significant V.A. Shtoff refers to material (material) models.

V.A. Shtoff classifies models according to the form of presentation, and L.M. Friedman - by the nature of the means from which they are built.

L.M. Friedman, material models are built from any material materials or living beings. Their feature is that they exist in reality, objectively. In turn, material ones are divided into static (motionless) and dynamic (acting, moving).

Fig. 1.3. Static model Fig.1.4. Figurative model

Ideal models are divided into three types: figurative (iconic), sign (sign-symbolic) and mental (imaginary, mental).

Figurative models include various kinds of drawings, maps, diagrams that convey in a figurative form the structure or other features of the objects being modeled.

Sign-symbolic models represent a record of some peculiarities, patterns of the original with the help of signs of an artificial language (for example, mathematical). These include all sorts of mathematical equations, chemical formulas.

Fig 1.5. Sign-symbolic models

Mental models are mental (imaginary) ideas about any phenomena, processes, objects. Such a model is an idea of \u200b\u200bthe properties of the modeled object. [No. 9]

According to P.V. Trusov, V.V.Davydov and N.G. Salmina modeling - this is activity, and for V.V. Davydov, A.U. Vardanyan - this is a method of cognition.

P.V. Trusov refers to the process of modeling the construction and use of the model. [No. 3, p.18]

And V.V.Davydov, A.U. Vardanyan call modeling by the method of cognizing the qualities of an object of interest to us through models. These are actions with models that allow us to explore individual qualities of interest to us, properties of an object or prototype. [No. 5]

VV Davydov, NG Salmina, LM Fridman and others consider modeling as a sign-symbolic activity, which consists in obtaining new information in the process of operating with symbolic means.

The modeling method developed by D.B. Elkonin, L.A. Wenger, N.A. Vetlugina, N.N. Podyakov, is that the child's thinking is developed with the help of different schemes, models that reproduce the hidden properties and connections of an object in a visual and accessible form for him.

The model of the studied mathematical concept or relationship plays the role of a universal means of studying the properties of mathematical objects. With this approach to the formation of the initial mathematical representations not only the specificity of mathematics (the science that studies the quantitative and spatial characteristics of real objects and processes) is taken into account, but children are also taught general ways of working with mathematical models of reality and ways of constructing these models.

As a general technique for studying reality, modeling allows you to effectively form such techniques mental activity as a classification, comparison, analysis and synthesis, generalization, abstraction, inductive and deductive ways of reasoning, which in turn stimulates in the future the intensive development of verbal-logical thinking. (No. 1, p. 43-47)

So modeling and modeling are not the same thing. There are different models: mental, figurative, sign, etc. Modeling is both a method of cognition and sign-symbolic activity.

The use of models and modeling is one of the requirements for the results of mastering the basic educational program of primary general education. Therefore, the acquaintance of schoolchildren with modeling methods is relevant for the modern school, especially in the context of the constantly increasing volume of educational information, the emergence of new carriers (electronic textbooks, computer encyclopedias) and means of access to it. Students need to comprehend the process of cognition itself, determine the place in this process of such a cognitive technique as modeling.

1.3 ANDusemodeling in teaching mathematics

Simulations are used to interpret actions on objects to make the use of those objects more accessible. By modeling a task is meant replacing actions with ordinary objects with actions with their models - reduced samples, dummies, mock-ups, as well as with their graphic images: drawings, drawings, diagrams. The importance of graphical modeling in the formation of the ability to analyze and solve problems is explained by the fact that the models clearly display each element of the relationship, which allows them to:

- remain simple in any transformation of this relationship;

-Allows you to see the structural components in the text in a "pure" form, without distraction to particular specific characteristics (numerical values \u200b\u200bof quantities, bright images, etc.);

- possess the properties of objective visualization, concretize abstract relations that cannot be seen, for example, by making a short note of the problem;

- provide a search for a solution plan, which allows you to constantly correlate physical (or graphic) and mathematical actions.

The process of purposeful training in graphic modeling should be carried out gradually, reflecting the transition from the concrete to the abstract in the form of a drawing, conventional drawing, drawing, diagram (schematized drawing). Models of this type act as forms of displaying the structure of the problem, where each subsequent form is built in a more generalized and abstracted form, a mathematical model is a description of a real process in mathematical language.

The use of simplified drawings, objects of conventional drawings, graphic drawings often causes difficulty in the process of finding solutions to problems; students cannot choose the required arithmetic operation, because recalculation is enough to answer the question. Models of this kind can be used only with small numerical data (otherwise the drawing will take up a lot of space in the notebook and will require an unjustified investment of time in the lesson). It is impossible to use these models even if the numerical data is replaced by letters, geometric shapes, etc. sometimes the drawings do not allow the student to distract from the insignificant signs and see the essential, common, that unites the data. However, these types of graphic models cannot be completely excluded, since they help children to make the transition from reality (objective situation) to a schematized drawing, which is very important in the formation of the ability to translate a problem from a natural language into a mathematical symbolic language.

In the initial course of mathematics, the creation of symbolic actions during training and the creation of models can be carried out in different ways.

Materialization of the structure of the text of the problem by presenting all the components of the text with the help of symbolic means in accordance with the sequence of presentation of information. Completion of building a model with this method will be a symbolic image of the problem question. The created model makes it possible to highlight the relationship between the components of the problem, on the basis of which the actions leading to the answer to the question are found. With this version of modeling, various sign-symbolic means are used (segments, iconic signs, etc.). Each given task is represented as separate specific symbols. The classification of simple problems is based on the relationship between objects and their values. Therefore, four types of relations are distinguished for the attribute: whole or part, difference, multiplicity, equality. Students become familiar with the names of the components of the actions of addition, subtraction, multiplication, division, but the working terms when describing these actions are not they, but the names of the components of relations. It is the relationships that connect the quantities with each other that determine the mathematical structure of the problem. These relationships are represented by different types of models: arrow diagrams, drawings, generalizing formulas. Diagrams and schematic drawings, i.e. Spatial-graphic models, representing a visible quantity, allow real transformations, the results of which can not only be assumed, but also observed. These models reflect the essential relationships and connections of the object, identified by means of appropriate transformations. It is the abstract material that is associated with mastering the general mode of action in solving problems. Letter models or generalizing formulas fix the results of actually or mentally performed actions with objects. The appearance of letter symbols is often associated with the end of educational work on solving problems, although it can serve as a means of fixing actions in the process of work at any of the stages or a means of “grasping” the foundations of an objective action.

Materialization of the structure of the text of the problem with the aim of considering the conditions and the question, highlighting the relationship, which is the basis of the general method of solving it, is carried out in two directions. First, the model is built after or in the process of manipulating the object material. Then, on the contrary, according to the given model, you need to perform the appropriate actions. Thus, coding and decoding of information is carried out in two directions:

I. Coding of text elements and their relationships in a graphic language, which includes the following stages:

1) the subject level of work for each type of relationship;

2) the use of schemes to fix the relations proposed by the text;

3) depicting each type of relationship using a drawing;

4) sign modeling of relations using formulas.

II. Decoding information:

1) drawing up and solving problems according to arrow diagrams, schematic drawings, formulas for all studied types of relations;

2) replacement of some forms of auxiliary models with others;

3) the use of rational types of models.

Replacing some forms of models with others using the example of the relationship of the whole and equal parts with literal data:

A task. The tourists were on the road for 5 days. Every day they passed T km. How many kilometers in total did they go in 5 days? (2nd grade)

Structural models are one of the types of representative (auxiliary) models of simple problems. Known values \u200b\u200bare indicated by squares and unknowns by circles. The main term of the ratio, which is the result of the action, is separated from the other terms by an arrow, and these latter are connected by the sign of action: in the ratios of parts and the whole - addition, in the ratio of difference comparison - division, in the ratio - the dependence between the values \u200b\u200bof different quantities - multiplication.

Consider the structural model of the problem:

A task. One vessel contains 7 liters of water, and the other contains 3 liters. How many liters of water are there in the first vessel than in the second?

Materialization of the scheme for analyzing the text of the problem, starting with the symbolic representation of the question and all the data (known and unknown) necessary to answer it. In such a model, the sequence of actions to solve the problem is recorded. With this variant of modeling, graphs are the most convenient. The representation of the sequence of operations of the solution in the form of a graph follows from the general schemes of analysis, which reflect the basic relations between the data of tasks.

Since this type of model represents the end result of working with the text of the problem, their construction requires the ability to carry out a complete analysis of the text, to select all components (known, unknown objects, quantities, relations between them, basic and intermediate questions). Such modeling assumes another scheme for analyzing the text of the problem, including a certain sequence of reasoning, for example:

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