The use of modeling in the lessons at the initial level. Project "Manufacture of the flying model "Strela" (circle "Initial technical modeling")

Svetlana Khrabrova

"stay alas kіmdіgіnі bіlіm blimіnі

technicians shyarmashyly mektebi» KMM

KSU "School technical creativity

Department of Education of the Akimat of the city of Kostanay "

PROJECT

Making a flying model« ARROW»

(circle« Initial technical modeling» )

Supervisor: Khrabrova Svetlana Pavlovna

Kostanay 2017

1. Introduction

2. Purpose, tasks, relevance.

3. Preparatory stage

4. Practical stage.

5. Test models

Society today is in need

in creative and technically literate

young people. Need to revive interest

youth to modern technique.

N. A. Nazarbaev

One of the tasks of the modern Kazakh school is the development technical creativity of students. Class technical modeling- one of the forms of distribution among children of different ages technical education instilling in them an interest in technical specialties.

Under technical modeling refers to one of the types technical activities, which consists in the reproduction of objects environmental reality on an enlarged or reduced scale by copying objects in accordance with diagrams, drawings. Pursuing technical modeling children get to know different technologies processing materials (paper, wood, foam, plastic, as well as technology use of ready-made forms in modeling.

Currently, children are in need of lessons technical creativity. Despite the abundance in the trading network technical toys, with great interest, guys with their own hands make car models, airplanes, helicopters, ships, robots and other technology. And it's not just toys made by guys. Competitions can be organized technical models of various levels, take part in competitions, prepare a presentation, speech. And also such model is a good gift made by hand.

Pursuing model makingconnections can be made with the following school subjects:

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

-technology(skills in working with various tools,

History (knowledge of the history of development technology,

OBZH (study safe work techniques, rules of conduct for

art (decorative-applied and art-design activity).

Lessons technical modeling implement scientific and technical orientation help children develop an interest in technique, instilling special knowledge, skills, development of design abilities and technical thinking.

My models

Target project:

Making a flying model aircraft from cardboard« Arrow» .

Tasks project:

Introduction to technical creativity and independent work;

Receipt initial knowledge, skills in aircraft model making;

Inclusion in a micro-study on the history of aviation;

Education of perseverance in achieving the goal, self-confidence.

Relevance:

during model making« Arrow» going on:

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

Getting to know the design aircraft,

Acquisition of sports and competitive skills,

Preparing to work on more complex models.

Materials and tools:

Cardboard, carbon paper, clips, ruler, pencil, punch, scissors, glue, felt-tip pens, stickers, wood block, rubber band, jigsaw, vise.

Working process:

1. Preparatory stage.

Recall the device of modern aircraft. An airplane is a complex machine, consisting of a large number of individual, well-coordinated parts. These details are grouped into five main parts. aircraft: fuselage, wing, tail, aircraft engine (engine, landing gear.

2. Practical stage.

Making a flying model« Arrow»

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

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

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

We get a drawing airplane models on cardboard

The second step is to push the fold lines on the drawing with a ruler and a metal punch to make the paper fold more easily.

The third step is to cut model.

Fourth step - glue the received parts:

Fuselage aircraft,

Fifth stage - design models

Sixth stage - making a catapult.

From a block of wood with a vice and a jigsaw we make a catapult. We put a rubber band on it.

3. Test models

You can hold mini-competitions that will reveal flying qualities models, eliminate defects.

4.findings: after 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.

Able to work with a drawing;

Do practical work on your own (including according to the drawing);

Properly used in speech technical terminology, technical concepts and information;

Compare technical objects on various grounds, make generalizations.

I like to build airplane model and watch, how is she flies! Let it be without a motor, it just glides in the air currents, but it looks really cool!

Related publications:

Pre-school and primary education in the modern world For a modern teacher today, it is important not only to master the forms, means, methods of training and education, to study the existing experience.

Innovative project "School radio as part of the model of internal communications of an open school" Introduction “Vocational guidance for high school students is necessary, it should return to schools. Introduce our students to professions that.

Wellness circle. Dance club "Michieene" Health-improving circle Dance circle "Michiieene" Musically-rhythmic movements are a type of activity based.

The proposed model of a flying saucer can be used as a decoration for entertainment for Cosmonautics Day, a sports festival dedicated to.

Logistics support for preschoolers A big role in the effectiveness of the quality of the educational process in senior group allocated to logistics.

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

The project "Teaching children of senior preschool age to safe behavior in everyday life through the simulation of dangerous situations" Creative project Topic: "Education of older children preschool age safe behavior in everyday life through modeling dangerous situations.

Project for the development, testing and translation of the model of the adaptation club "Gymnasium for crumbs" for young children Project type: creative Project duration: long-term Project participants: children entering preschool, educators,

Technological map of short-term educational practice. Technical design "Robot" Technological map of short-term educational practice Technical design "Robot" for children 5 years old Children will learn how to do.

Image Library:

Modeling in the classroom primary school Slide 1. Primary school age is the beginning of the formation of educational activities in children. At the same time, modeling is an action that goes beyond the limits of primary school age into further types of human activity and reaches a new level of its development. Why do younger students need to master the modeling method? (slide No. 2) Modeling in education is necessary for a number of reasons: 1) to make it possible for students to fully and firmly master the methods of cognition and methods of learning activity; 2) for the formation of full-fledged mental actions in schoolchildren; 3) to form a scientific-theoretical style of thinking; 4) for the development of reflective activity of students. People face different models in their life. In childhood, these are all kinds of toys (cars, dolls, constructors). And in subsequent years - educational models at school, clothing models, drawings, diagrams, etc. Slide 3. A model is a diagram of some object or phenomenon. It is used as a substitute for clarifying or clarifying any signs. Modeling is a method of cognition of the surrounding world, consisting in the creation and study of models. 1 Classification of models  Taking into account the time factor  By area of knowledge  By area of use  By presentation area  By implementation method tabular tables verbal description in natural languages in a mental or spoken form (protocol) Examples are on the information sheets. Slide 5. Graphic schemes Maps Graphics Drawings Drawings Graphs Mathematical special formulas Notes Chemical formulas Signs There are four stages of modeling:  Identification of the essential features of the object Consistent acquaintance with new concepts, disclosure of the topic  Building a model.  Study of the model. conscious orientation of students in the scheme, possession of evidence using schemes, addition of the scheme, correction of errors in the scheme, various types of work with schemes, independent completion of tasks on the topic. 2  Transferring the information obtained on the models to the object under study. "Reading" the wording of the rule from a brief diagram, the child develops memory, imagination, speech, thinking. The peculiarity of modeling in comparison with visibility is that the object is not studied directly, but by studying this object. Slide 6. You can use the study plan. What? Where? How? How? it is necessary to check Slide 7. When studying and consolidating new material, the main work is carried out to create schemes with varying degrees of independence of students, the teacher builds a scheme - students observe; the teacher starts the simulation - the students continue and complete the work; Students create their own diagram. when repeating what was previously learned, when checking and consolidating knowledge (they used ready-made schemes and reproduced them). To diversify work with a finished scheme or to create it, various techniques are used, for example: Slide 8. give examples of objects that correspond to this scheme; "decode the schema"; find an error in the arrangement of schematic cards; come up with a symbol denoting one of the elements of the model; arrange the chart cards correctly; 3 Slide 9. choose the model corresponding to this object from several presented schemes; complement the simulated series; draw up a diagram in the course of the teacher's story (creative work). To analyze one's own activity in the lesson (at the stage of reflection), the POPS formula model is used. The value of this method lies in the fact that it allows students to briefly and comprehensively express their own position and present their opinion in a clear and concise form on the topic studied. This technique was created by law professor David McCoydMason from South Africa. It was translated into Russian by Arkady Gutnikov, vice-president of the association “For civic education”, First Vice-Rector of the St. Petersburg Institute of Law. Slide 10. In this case, students are invited to write sentences reflecting the following four points of POPS - formulas: P - position, O - explanation (or justification), P - example, C - consequence Scheme "POPS -formulas": The first of the sentences (position ) should begin with the words: "I believe that ...". The second sentence (explanation, justification of one's position) begins with the words: "Because ...". The third sentence (focused on the ability to prove the correctness of one's position in practice) begins with the words: "I can prove this with an example ...". And, finally, the fourth sentence (consequence, judgment, conclusions) begins with the words: 4 "Based on this, I conclude that ...". Slide 11. Practical part Let's consider modeling in the Russian language lessons. Now we will model, i.e. convert the spelling into a model or scheme, highlighting its essential features. Slide 12. The most significant part of the spellings of the Russian language, according to scientists, are spellings of weak positions, which include  unstressed vowels in different parts words, consonants, paired by voiced deafness, standing at the end of words and before other consonants, unpronounceable consonants at the root of the word.  For an unstressed vowel at the root, for a paired consonant at the root, for an unpronounceable consonant at the root, the minimum “spelling field” is  this is the root of the word. An unstressed vowel at the root of a word. The identification features of this spelling are  “dangerous sounds”, giving the greatest number of mismatches. Double consonant in a word. Identification features - deaf paired consonants at the end of the root. An unpronounceable consonant in a word. Identification features - 5  unpronounceable consonants at the end of the root. All essential features will be expressed by symbols that will become elements of the modeled spelling scheme. Schematic elements can be used in a color image. Because we work according to different teaching materials, the symbols will be different, but the meaning is the same. Slide 13. 1). Let's try together to model the rule "Unstressed vowels at the root of the word" using the modeling steps. Read the rule. Unstressed vowels in the root of a word To check an unstressed vowel in the root, it is necessary to change the form of the word or choose a related word so that the vowel being tested is stressed. Stages of modeling  Identification of the essential features of the object  Building a model  Studying the model  Transferring the information obtained on the models to the object under study 1) Give examples of objects that correspond to this model. 2) At the stage of reflection, we use the POPS formula. 6 I believe that unstressed vowels should be checked with stress, because in a weak position we hear a different sound. For example: in the word water we hear unstressed a, and if I put the vowel under the stress of water, then o will be heard clearly. Based on this, I conclude that the unstressed vowel at the root of the word must be checked with stress. Slide 14. Drawing up a model of the rule “Unpronounceable consonants in the root of the word” Unpronounceable consonants in the root of the word Consonants D, T, L, V are written but not pronounced. To check the unpronounceable consonant at the root of a word, you need to change the word or choose a related word so that the consonant is heard clearly. Stages of modeling  Identification of the essential features of the object  Building a model  Studying the model  Transferring the information obtained on the models to the object under study Give examples of objects that correspond to this model. 2). Let's work on the research plan. Slide 15. Independent work. Drawing up a model of the rule “Paired consonants at the root of the word” Paired consonants by voicedness - deafness at the root of the word L M N R Y. Stages of modeling  Identification of the essential features of the object  Building a model  Studying the model  Transferring the information obtained on the models to the object under study [l], [m], [n], [r], [th "] 8 1 ) Give examples of objects that correspond to this model. 2) Arrange the cards of the scheme correctly. Summarizing. The ability to think in symbols does not come by itself. We all, to one degree or another, use color, graphic signs, and drawings in teaching from the first grade With the age of children, this ability of this kind of perception of educational information will develop in the process of purposeful learning.It is especially useful in difficult situations when children are in they return to a genetically earlier level of thinking - visual and effective, which helps them, in case of difficulty, to solve the task set outside of practical actions with objects. Therefore, in the lessons it is necessary to apply the activity method of discovering something new. A very important condition in working with diagrams is that they must certainly be connected to the work in the lesson, and not hang like posters. Only then will they help the teacher to teach better and the children to learn more easily. Slide 16. Thus, support schemes include visual memory in the memorization process, develop figurative thinking, allow you to diversify work in the lesson, develop spelling vigilance, activate students' cognitive activity, increase the "density" of the lesson, make it possible to apply unusual forms of control. Conclusion: When students build various models of objects or phenomena being studied, Slide 17.9 this method acts as a learning tool and a way to generalize educational material, helps children "learn actively", forms general educational universal learning activities. And this means that the child can apply them in another type of activity, which corresponds to the competence of “teach learning”. Do you think it is necessary to use simulation in elementary school lessons? Fill in the POPS chart of the reflection formula on the topic "Modeling in the lessons in elementary school" on your worksheets. Read out. References 1. Venger L. A. Perception and learning. M. , 1969.-340 p. 2. Lvov M.R. Fundamentals of teaching spelling in elementary school / M.R. Lvov. – M.: Prometheus, 1988. – 90 p. 3. Textbook Grade 2 Authors: S.V. Ivanov, A.O. Evdokimova, M.I. Kuznetsova word root. 6. Ermolaeva A.A. Modeling in the classroom in elementary school 7. Prokhorova L.N. Development of spelling vigilance based on modeling // Elementary school. - 2007. No. 3. - P. 43 - 45 8. Gaysina R.S. Modeling - we know the world // Elementary school. 2006. - No. 9. - P.67 - 71 10 11

Send your good work in the knowledge base is simple. Use the form below

Students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

Posted on http://www.allbest.ru/

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

1.1 The meaning of the concepts "model" and "simulation"
1.2 The role and place of modeling in the new generation standard for elementary school
1.3 Using simulation in teaching mathematics
Chapter I Conclusions

Conclusion
Literature

Glossary on the categorical apparatus

Glossary of personalities
ATconducting

The relevance of research. The Federal State Educational Standard (hereinafter referred to as the Federal State Educational Standard) of the new generation does not imply serious changes in the mathematical preparation for younger students. It maintains the tradition of primary mathematics education, but places different emphasis and defines other priorities. The main thing in goal-setting, in the selection and structuring of content, in the conditions of its implementation is the importance of the initial course of mathematics in continuing education in general, as well as mathematics, and, of course, the ability to use knowledge and skills in solving various practical and cognitive problems.

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

Problem teaching 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 which the role of the subject was played by different aspects of learning to solve various problems. This is a selection of their content and a system, these are the functions of tasks in the very process of teaching mathematics, and their role in the formation of schoolchildren's educational activities and mathematical concepts, as well as in the development of schoolchildren's logical thinking. Of particular importance in teaching and, above all, in solving problems, in the conditions of education, which is focused on the development of thinking in younger students, modeling acquires, because. 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, forming the skills and methods of action necessary to implement this. In this paper, modeling is considered not only as a way to form a general ability to solve problems, but also as one of the goals in teaching mathematics.

Considering modeling as a particular, specific kind general way activities with mathematical concepts and relations, it is supposed to build the formation of constructive skills in the student in the process of modeling the studied mathematical concepts and relations. Also, the presentation of the concept or relationship being studied in a visual model (layout or design) makes it possible for children to form an adequate idea of something abstract at a visual level, which is most consistent with their capabilities and needs.

Research topic: modeling in mathematics lessons in elementary school.

aim The work is a theoretical substantiation of the effectiveness of the use of modeling in the learning process in elementary school.

An objectohmresearch is the process of teaching students to model the content of various tasks.

Thingohmresearch performs the modeling of 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;

· when modeling toys, objects instead of real objects will be used;

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

· gradual transition from subject models to ideal models is carried out.

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 simulation in teaching mathematics.

methodologicalohresearch basis were the most important studies of the methodology of teaching mathematics in primary school by different authors (Leontiev A.I., Istomina N.B., Mentsis Ya.Ya., etc.). As well as works that reveal the levels of modeling in mathematics (Beloshistaya A.V., Shikova R.N., etc.).

The theoretical basis of the study served as the works of foreign and domestic scientists, instructive and reference materials, normative documents, articles of pedagogical magazines and newspapers.

Methodresearch: analysis and generalization of psychological and pedagogical literature;

Work structure.

The course work consists of this introduction, two chapters, a list of references, a glossary and applications.

The first chapter "Theoretical and methodological basis of modeling in the primary education system" discusses 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 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 of modeling in the primary education system

1.1 Withthe idea of the concepts "mdress» and« modeling»

Two characteristics of the model follow from these definitions:

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 displays 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 singles out models:

a) real, reproducing the geometric and physical properties of the original (children's toys, visual study guides, layouts, etc.);

b) ideal, conveying information about the properties and states of an object, process, phenomenon, 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 methodology of cognition in the topic of modeling was due to the importance that the modeling method received in modern science, and especially in its sections such as chemistry, physics, biology, cybernetics, as well as many technical sciences.

The word "model" comes from the Latin word "modelium", which means: measure, method, etc. Beloshistaya A.V. Reception of graphic modeling in teaching problem solving // elementary school, 2009, 8, p. other thing." According to the opinions of many writers (A. A. Vedenov, A. N. Kochergin, V. A. Shtoff), the model was first used as an isomorphic theory (two theories are called isomorphic if they have structural unity with respect to each other) .

Modeling -- 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 subject (study of basic geometric, dynamic, functional characteristics object on the model);

E physical (reproduction of physical processes);

Ё subject - mathematical (study of a physical process by experimental study of any events of a different physical nature, but described by the same mathematical relationships as the simulated process);

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

Before proceeding to the issues of applying modeling, let's consider the main functions of models.

The main functions of the models.

Modeling as a means of experimental research.

The consideration of material models as a means of research activity raises the need to find out how those experiments in which models are used differ from those where they are not used. The transformation of the experiment into one of the main figures of practice, which took place in parallel with the development of science, was the result of the minutes when the wide use of natural science became possible in production, which in turn was a 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. Methodical solution of the problem of correction of deficient school-significant functions in primary education (on the material of mathematical education) / "Childhood in the era of transformation of society." Materials of the international scientific-practical conference. T. 2. Murmansk: MGPI. - 2007. - p. 53 - 55. In the credibility of this, in Marxist epistemology there is a sharp difference between experiment and scientific knowledge. Although every experiment also includes observation as an obligatory phase of the study. Nevertheless, in addition to observation, the experiment also contains such an important factor for revolutionary practice as active intervention in the course of the process being studied. “An experiment is a kind of activity undertaken for the purpose of scientific knowledge, the discovery of objective patterns and consisting in influencing the object (process) under study through special tools and devices” How to design universal educational activities in elementary 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.: Enlightenment, 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 the experiment, 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. At the same time, the substitute object and the experimental setup are combined, merging into a whole in the operating model. Consequently, the ambiguous role that the model performs in the experiment is manifested: it is both an object of study and an experimental tool. For a model experiment, according to the opinions of a number of authors, the following main procedures are typical:

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

2. empirical study of the model;

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

The model enters the experiment, not only replacing the object of study, it can also replace the conditions under which some object of the usual experiment is studied. A simple experiment assumes the existence of a theoretical moment only at the initial moment of the study - putting forward a hypothesis, evaluating it, etc., as well as at the final stage - 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 the natural object and the possibility of extrapolating the obtained data to this object. V.A. Shtoff in his book "Modeling and Philosophy" says that the theoretical basis of a model experiment, mainly in the field of material modeling, is the concept of similarity. ". Murmansk: MGPI. - 2009. - p. 7-16. . It gives 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 object being modeled, made it possible to overcome the modest possibilities of physical modeling. In mathematical modeling, the relation model-reality is such a generalization of the theory of similarity, which takes into account the qualitative heterogeneity of the model and the object, their belonging to different forms of matter movement. Such a generalization takes the form of a more abstract theory of system isomorphism.

Modeling and the Problem of Truth.

An interesting question is what role does modeling itself play in the course of proving the truth and searching for true knowledge. What should be understood by the truth of the model? If the truth in general is “the ratio of our knowledge of reality”, then the truth of the model means the correspondence of the model to the object, and the falsity of the model means the absence of such a ratio. 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 a model and an object in mathematical modeling based on physical analogies, which assume that, with a difference in physical processes in the model and the object, the identity of the mathematical form in which their universal laws are expressed is more general, more abstract. Consequently, when building certain forms, they are always consciously abstracted from certain countries, properties, and even relations, due to which, it is deliberately allowed not to maintain unity between the model and the original in a number of parameters. So Rutherford's planetary model of the atom turned out to be correct in the framework of studying the electronic structure of the atom, and J. J. Thompson's model turned out to be wrong, because. its structure did not coincide with the electronic circuit Visual geometry in grade 1. Tutorial. Murmansk: MGPI. - 2008. - 56s. . Truth is a property of knowledge, and the objects of the material world are not true, not false, they simply exist. The model implements two types of knowledge:

1. knowledge of the model itself (its structure, processes, functions) as a system created to reproduce some object;

2. theoretical information through which the model was built.

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

E due to their connection with certain knowledge;

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

E, due to the relationship of the model to the object being modeled, it makes it part of the cognitive process and allows you to determine 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. Methodical recommendations for teachers primary school. 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 this 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. this is part of the research evidence for the truth of this theory.

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

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

For example:

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 foresee periodic phenomena associated with the structure of the universe, such as: an eclipse of the sun and moon, the onset of the seasons.

In order to solve 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, the planets, the earth and the moon, were depicted as points moving along some kind of curves - the trajectories of their movement. Such, for example, are the schemes built by Ptolemy, in which our Planet occupied the main space, or the scheme of Copernicus, in which the Sun occupied the main place.

With the help of these schemes, scientists derived the problem of predicting special astronomical phenomena. These schemes 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 method 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 in a living human body. Since such a study before the advent of special devices was associated with the death of this organism. Here scientists began to study the device of the human body on animals similar to its body. The study of the organism of animals, their functioning helped to determine many of the most important patterns 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. Teaching problem solving and modeling // Primary School. - 2008. - No. 8. - S. 26-32. .

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

A mathematical model can 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 main regularities, properties of the subject under study.

There are three stages in the process of mathematical modeling:

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

2. Solving the problem within the framework of a mathematical system (they say: the solution is within the 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 exact imitation is a somewhat simplified table (description) of the original, which means that it has an undeniable level of error. model math learning task

The same model can define different processes, objects, so the products within the model study of the action itself can often be transferred to another action. This is one of the main values of mathematical modeling.

Mathematics not only created a variety of 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, the microworld, space-time and gravitation, and the possibilities of transmitting messages. , control, inference Arginskaya I.I. Mathematics. 1 class. A teacher's guide to a stable textbook. - M.: Federal scientific and methodological center. L.V. Zankova, 2011.

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

The implementation of the global mathematical way 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 understanding the life and function of the brain, the microcosm, new, fantastic technologies and techniques, 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 standardfor elementary school

A distinctive feature of the new standard is its active nature, which puts the main task of developing the student's personality. The education system is abandoning the traditional understanding of learning outcomes in the form of knowledge, skills and abilities; the wording of the standard 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 inseparable part of the core of the new standard is the common learning activities (CLE). UUD is understood as “general educational skills”, “general methods of activity”, “above-subject actions”, etc. A special program is provided for UUD - a program for creating universal educational activities (UUD) Individual approach in the formation and development of the mathematical abilities of a younger student // Primary school: plus - minus. - 2011. - No. 7. - with. 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 learning activities" means the ability to learn, that is, the ability of a person to self-development and self-improvement through the deliberate and active appropriation of new social experience. In a narrower (actually psychological) sense, this term can be described as a set of student action methods (as well as related learning skills) that ensure independent study of 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 have a supra-subject, meta-subject character; provide commonality of general cultural, personal and cognitive development and self-development of the individual;

Provide communication of all stages of the educational process;

They underlie the organization and regulation of any activity of the student, regardless of its specially-subject content.

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

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

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

Universal learning activities (UUD) 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 (UCA)

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 training, that method of cognition that they must master, and Secondly, modeling is the educational action and means without which real learning is impossible. L.M. Fridman in the “Federal State Educational Standard of Primary General Education”, put the development of universal educational activities at the forefront, providing schoolchildren with the ability to learn, the ability for self-development and self-improvement. One of the most important cognitive universal action- the ability to solve problems or problems. Due to the complex systemic nature of the universal method of problem solving, this universal educational action can be considered as a model for a 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 text 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 an approach that involves the emergence of a general ability to solve problems. At the basis of the emergence of a general ability to solve problems, there is a modeling method, which is the main sign of the development of sign-symbolic universal learning activities. For successful education 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) that reflect the spatial distribution of objects or relationships between objects or their parts to solve problems; -- the ability to create schemes, models, etc. Leontiev A.I. To the question of the development of the child's arithmetic thinking. On Sat. "School 2100" issue 4 Priority directions for the development of the educational program - M.: "Balass", 2010, p.109.

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

Models and modeling in teaching younger students

Primary school age is the beginning of the formation of educational activities in children. At the same time, modeling is an action that goes beyond the limits of primary school age into further human activities 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 "arm" students with modeling as a way of cognition, it is necessary that students themselves build models, study any objects, phenomena themselves with the help of modeling. [#7]

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

The concept of "model" and "modeling" is interpreted by a number of authors ambiguously. Consider the definitions of the concept of "model" and "modeling".

In the Great Soviet Encyclopedia “Model is an image (including a conditional or mental image, description, diagram, drawing, graph, plan, map, etc.) or a prototype (sample) of an object or system of objects (“original ” of this model), used under certain conditions as their “deputy” or “representative”. [No. 2, p. 399.]

Shtoff V.A. considers, “a model (from Latin modulus - measure) is a substitute for the original, which provides the study of some of its properties. It is created in order to obtain and (or) store information (in the form of a mental image, description by sign means or a material system), reflecting the properties, characteristics and connections of the original, essential for solving the task” [№10]

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

A. B. Vorontsov believes that “the model acts as a ‘tool’ for the joint activity of students and teachers. It reflects the general relations and connections within the object under study.” [№4]

VV Davydov, AU Vardanyan believe that the model creates a language of communication, which, objectifying the content of the object of study, allows to reveal its essence.

After analyzing the above definitions, we conclude: in the definitions of V.A. Shtoff, P.V. Trusova and the Great Soviet Encyclopedia, the model is an image, while A.B. The Vorontsov model is a "tool"; goals in explicit and implicit form are identified by P.V. Trusova and V.A. Shtoff, but in the encyclopedia and in A. B. Vorontsov, the goal is not defined; at 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 displays 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]

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

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

V.A. Shtoff distinguishes models: a) real, reproducing the geometric and physical properties of the original (children's toys, visual teaching aids, layouts, etc.); b) ideal, conveying information about the properties and states of an object, process, phenomenon, 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 models is initially divided into two groups: tangible and intangible. In turn, L.M. Friedman subdivides real models into: figurative, sign and mental. V.A. Shtoff mental models are singled out in a separate group (non-material), and figurative-iconic and sign V.A. Shtoff refers to real (material) models.

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

At L.M. Friedman, material models are built from any material materials or living beings. Their feature is that they exist really, objectively. In turn, the material ones are divided into static (fixed) and dynamic (active, mobile).

Rice. 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 different kind drawings, maps, diagrams that convey in a figurative form the structure or other features of the simulated objects.

Sign-symbolic models are a record of some features, patterns of the original using the signs of some artificial language (for example, mathematical). These include various kinds 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 a representation of the properties of the modeled object. [#9]

According to the definition of 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.

PV Trusov refers to the process of modeling the construction and use of the model. [#3, p.18]

And V.V. Davydov, A.U. Vardanyan call modeling a method of knowing the qualities of an object that are of interest to us through models. These are actions with models that allow us to explore individual qualities that are of interest to us, properties of an object or prototype. [#5]

V.V. Davydov, N.G. Salmina, L.M. Fridman and others consider modeling as a sign-symbolic activity, which consists in obtaining new information in the process of operating with sign-symbolic means.

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

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

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

So models and simulations are not the same thing. There are different models: mental, figurative, symbolic, etc. Modeling is both a method of cognition and a 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 a modern school, especially in the context of an ever-increasing amount of educational information, the emergence of new media (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

Modeling is used to interpret actions on objects to make the use of those objects more accessible. Task modeling is understood as the replacement of actions with ordinary objects for actions with their models - reduced samples, dummies, layouts, as well as with their graphic images: drawings, drawings, diagrams. The importance of graphic modeling in the formation of the ability to analyze and solve problems is explained by the fact that models clearly display each element of the relationship, which allows them to:

-remain simple under any transformations of this relation;

- allow you to see the structural components in the text in a "pure" form, without being distracted by particular specific characteristics (numerical values of quantities, bright images, etc.);

-have the properties of subject visibility, concretize abstract relationships, which cannot be seen, for example, by making a brief record of the task;

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

The process of targeted training in graphic modeling should be carried out gradually, reflecting the transition from the concrete to the abstract in the form of a drawing, a conditional drawing, a drawing, a diagram (schematic drawing). Models of this type act as a form 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 some real process in a mathematical language.

The use of simplified drawings, objects of conditional drawings, graphic drawings often causes difficulty in the process of finding solutions to problems; students cannot choose the necessary arithmetic operation, because it is enough to recalculate to answer the question. Models of this type can only be used with small numerical data (otherwise, the drawing will take up a lot of space in the notebook and require unjustified time in the lesson). It is also impossible to use these models if numerical data is replaced by letters, geometric shapes, etc.; sometimes the drawings do not allow the student to distract from the non-essential features 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 when developing the ability to translate a task from a natural language into a mathematical language of symbols.

In the initial course of mathematics, the creation of sign-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 task by representing all the components of the text with the help of sign-symbolic means in accordance with the sequence of presentation of information. The completion of building a model with this method will be a symbolic image of the issue of the problem. The created model makes it possible to identify the relationship between the components of the task, on the basis of which actions are found that lead to the answer to the question. At this option modeling uses various sign-symbolic means (segments, iconic signs, etc.). Each given task is represented as separate specific symbols. The basis of the classification simple tasks relation between objects and their magnitudes. Therefore, four types of relations are distinguished for the sign: whole or part, difference, multiplicity, equality. Students get acquainted with the names of the components of the actions of addition, subtraction, multiplication, division, but the working terms in describing these actions are not they, but the names of the relationship components. It is the relations 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-graphical models, representing a visible value, 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, highlighted through the appropriate transformations. It is the abstract material that is associated with the development of the general mode of action in solving problems. Literal models or generalizing formulas record the results of real or mentally performed actions with objects. The appearance of alphabetic 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 grounds for an objective action.

The materialization of the structure of the text of the task in order to consider the conditions and the issue, to highlight the relationship, which is the basis of the general way of solving it, is carried out in two directions. First, the model is built after or during manipulations with the subject material. Then, on the contrary, according to the given model, you need to perform the appropriate actions. Thus, encoding and decoding information is carried out in two directions:

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

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

2) the use of schemes for fixing the relationships proposed by the text;

3) the image of each type of relationship using a drawing;

4) sign modeling of relations using formulas.

II. Information decoding:

1) compiling and solving problems on turnout diagrams, schematic drawings, formulas for all studied types of relationships;

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

3) the use of rational types of models.

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

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

One type of representative (auxiliary) models of simple tasks are structural models. Known values quantities are indicated by squares, and unknowns by circles. The main member of the ratio, which is the result of the action, is separated from the other members by an arrow, and these latter are connected by the sign of the action: in the ratio of parts and the whole - addition, in the ratio of difference comparison - division, in the ratio - dependence between the values of different quantities - multiplication.

Consider the structural model of the problem:

Task. In one vessel there are 7 liters of water, and in the other - 3 liters. How many liters of water are in the first vessel than in the second?

Materialization of the text analysis scheme of the problem, starting with a 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 fixed. With this modeling option, graphs are the most convenient. The representation of the sequence of solution operations in the form of a graph follows from the general analysis schemes, which reflect the main relationships between the given problems.

Since models of this type represent the final 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, relationships between them, basic and intermediate questions). Such modeling assumes a different scheme for analyzing the text of the problem, including a certain sequence of reasoning, for example:

...