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Examples of graphic models in everyday life. Lesson Abstract "Graphic Information Models

4.8 Graphic information models.

The graphic information model is a good way to represent objects and processes in the form of graphic images. These include: drawings, graphs, charts, shaped models, diagrams (cards, graphs, block diagrams).

Graphic (geometric) information models transmit external signs of the object - dimensions, shape, color, location. In graphical information models, conditional are used for visual display objects. graphic images (shaped elements). Often graphic models are complemented by numbers, symbols and texts (iconic elements). In this case, they are called mixed models.

The figurative models are visual images of objects recorded on any carrier of information (paper, photo and film and dr.). These include drawings, photos.

Scheme- This is the presentation of some object in the general, main features with conventions. Scheme - This is a graphical display of the composition and structure of a complex system. With the help of circuits can be presented and appearance object, and its structure. The scheme as the information model does not pretend to complete the provision of information about the object. With the help of special techniques and graphic designations, one or more features of the object under consideration are more relocated.

In the computer science, the construction of flowcharts occupies a special place. Flowchart Vividly reflect the algorithm, i.e. Sequence of actions when solving the problem. They are built under programming - the creation of new programs.

Map Describes a specific locality that is an object of modeling for it. This is a reduced generalized image of the earth's surface on a plane in a particular symbol system. .

The card is created with certain goals for determining:

locations of settlements;
terrain relief;
the location of motorways;
measurements of distances between real objects on the ground
etc.

Now they got a big distribution of geo-information models (for example, http://maps.google.ru/ - satellite shooting of the map of the area).

Drawing - accurate geometric copy of the real object. Drawing- Conditional graphic image of an object with an accurate ratio of its size obtained by projection. The drawing contains images, dimensional numbers, text. Images give views of the geometric form of the object, the number is the magnitude of the object and its parts, the inscriptions - about the title, scale in which images are made. The drawings are created by designers, designers, they must be very accurate, because They include all the necessary dimensions of the real object. There are a lot of different computer media for creating design drawings: autocadus, adem, compass, 3D MAs - for three-dimensional modeling, etc.

Graphs and charts are information models that are visual form represent numerical and statistical data.

Schedule- A line that gives a visual idea of \u200b\u200bthe character of the dependence of one value (for example, paths) from another (for example, time). Schedule - mapping and visualization of various processes (natural, economic, public and technical). The schedule allows you to track the dynamics of data change.

Diagram- a graphic image that gives a visual idea of \u200b\u200bthe ratio of any values \u200b\u200bor several values \u200b\u200bof one value, about changing their values. More details are the types of diagrams and methods for their construction will be considered when studying spreadsheets.

Private place among graphic models Count graphs.

4.9 graphs
Graphs are wonderful mathematical objects, with their help you can solve a lot of different, externally similar to each other tasks. In mathematics there is a whole section - theory of graphswhich studies graphs, their properties and application. Programs are built in computer science. In this paragraph, only the most basic concepts, graph properties and some ways to solve problems are considered.

If the objects of some system are depicted by points (circles, ovals, rectangles ...), and the relationship between them - lines (arcs, arrows ...), then we will obtain the information model of the system in question in the form of a graph. Graphit is a set of vertices and connecting their ribs. The vertices of the graph can be indicated by letters, numbers, words ...

If the edge of the graph is characterized by some for more information (pronounced numbers), called it weighted, and numbers - weighsröber. The weight of the Ryber can match, for example, the distance between the objects (cities).

If the edges of the graph indicate the direction (represented by arrows), then the graph is called oriented (Orgraf). Movement in an oriented graph is possible only in one direction (by arrows). Communication between objects - vertices in this case is considered asymmetric. A non-oriented graph of communication between objects - vertices is symmetrical.

The same, but differently drawn graphs, called isomorphic. The same vertices are connected in isomorphic graphs.

Degreethe vertices of the graph are called the number of edges coming from it. A vertex having an even degree called even vertex, A vertex having an odd degree is called an odd vertex.In the drawing of the vertex A, B, D - even. Their degree is 2. The vertices with, e - odd. Their degree is 3.

One of the main theorems of the theory of graphs is associated with the concept of the top of the vertex - the number of odd vertices theorem.

Theorem : Any graph contains an even number of odd vertices.

To illustrate, consider the task.

In the city of small 5 phones. Is it possible to connect them with wires so that each phone is connected exactly with 3 others?

Decision: Suppose it is possible to connect phones. Then imagine the graph in which the peaks indicate the phones, and the ribs are wires, connecting them. We calculate how much the wires will turn out. Exactly 3 wires are connected to each telephone, i.e. The degree of each vertex of our graph - 3. To find the number of wires, it is necessary to sum up the degrees of all vertices of the graph and the resulting result is divided by 2 (because each wire has two ends and when the degrees are summarized, each wire is taken 2 times). (3 * 5) / 2 \u003d 15/2 \u003d 7.5

But this number is not a whole, that is, the number of wires will be different. It means our assumption that you can connect every phone exactly with five others, turned out to be incorrect.

Answer. Connect phones is thus impossible.
There is another important concept relating to the graphs - the concept of connected. Count is called svyaznoye, if any two tops can be connected way, those. Continuous sequence of ribs. There are a number of tasks whose solution is based on the concept of connectivity of the graph. The graph appears below has three components of the connectivity (consists of three separate parts).

A vertex that does not have a Röbebe called isolated The vertex is a separate component of connectivity. The vertex having only one edge is called terminal or hanging.

The path to the vertices and the edges of the graph, in which any edge of the graph enters no more than once, called chain (1) . Chain, initial and final vertices of which coincide, called cycle (2). Wood (hierarchy) - This is a graph in which there are no cycles (3), i.e. in it, it is impossible to go from some vertices to several different edges and return to the same vertex. A distinctive feature of the tree is that there is a single way between any two peaks.

(1)
(2)
(3)

Any hierarchical system can be represented by wood. The tree highlights one main vertex called its root. Each vertex of the tree (except the root) has only one ancestor, designated by it the object is in one class1 of the highest level. Any vertex of the tree can generate several descendants - vertices corresponding to the lower level classes. This principle of communication is called "one-to-many". The vertices that do not have generated vertices are called leaves.

For example, related links between family members are conveniently represented using a graph called a genealogical or pedigree tree.

Count with a cycle called network.If the heroes of some literary work are presenting the vertices of the graph, and the existing communication between them is a picture with Rybrachi, then we will get a graph called semantic network.

4.10 Using graphs when solving tasks
Example 1. In order to write down all three-digit numbers consisting of numbers 1 and 2, you can use the graph (wood)

The tree can not be built if you do not need to write all possible options, and you just need to specify their number. In this case, it is necessary to argue like this: in the discharge of hundreds can be any of the numbers 1 and 2, in the discharge of dozens - the same two options, in the discharge of units - the same two options. Consequently, the number of different options: 2 2 2 \u003d 8.

In general, if you know the number of possible options for choosing at each step of constructing a graph, then all these numbers need to calculate the total number of options multiply.

Example 2. Consider a somewhat modified classical task of crossing.

On the banks of the river there is a peasant (k) with a boat, and next to him - a dog (c), fox (l) and goose (D). The peasant should cross himself and transport the dog, foxes and goose to the other side. However, the boat except the peasant is placed either only a dog or only fox, or only goose. Leave the dog with a fox or fox with Guses without supervision. - The dog is dangerous for fox, and Fox is for a goose. How should the peasant organize the crossing?

D. to make this task to make a graph, whose vertices will be the initial placement of characters on the river bank, as well as all sorts of intermediate states achieved from the previous ones per step of crossing. Each vertex-state of the crossing is denoted by oval and connect Ribs with states formed from her. Invalid under the condition of the state problem are highlighted by a dotted line; They are excluded from further consideration. The initial and final state of the crossing is highlighted by a bold line.

The graph shows that there are two solutions to this task. We give a corresponding transfer plan to one of them:

the peasant transports the fox;
the peasant returns;
the peasant transports the dog;
the peasant returns with the fox;
the peasant is transporting a goose;
the peasant returns;
the peasant transports the fox.

Example 3. Consider the following game: First, 5 matches lie in the pile; Two players remove matches in turn, and for 1st course you can remove 1 or 2 matches; Wins the one who leaves a match in a bunch. Find out who wins with the right game - the first (I)or the second (Ii)player.

Player I can remove one match (in this case they will remain 4) or 2 (in this case, there will remain 3).

If player I.left 4 matches, player II.can leave 3 or 2 matches as its move. If after the course of the first player there are 3 matches, the second player can win, taking two matches and leaving one.

If after the player II.3 or 2 matches left, then player I.each of these situations has a chance to win.

Thus, with the correct strategy of the game, the first player will always win. To do this, he must take one match.

In fig. 2.8 shows the graph called tree game;all reflected on it possible options, Including erroneous (losing) moves of players.

Control questions.

What information models refer to graphic?
Give examples of graphic information models with whom you have:

a) when studying other items; b) B. everyday life.

What is a graph? What is the peaks and edges of the graph? Specify on your own graph-example.
Which graph is called oriented?Weighted?
What graphs are called isomorphic?
What is the degree of vertices? Specify the degrees of the vertices in your graph.
Formulatetheorem about the readiness of the number of odd vertices.
What graph call connected? Picture graph with two connected components.
What vertex is called isolated? Hanging? Specify on your own example - the column.
What is the path? Chain? Cycle?Give examples of chains and cycles available in your graph.
What is a tree? What systems can trees serve as models? Give an example of such a system.
Make a semantic network in the Russian folk fairy tale "Kolobok".

| §1.3 Graphic information models

Lesson 4.
§1.3 Graphic information models

Keywords:

Scheme
map
drawing
schedule
diagram
graph
net
wood

1.3.1. Mature of graphic information models

In graphical information models, conditional graphic images (shaped elements) are used for visual display of objects, often complemented by numbers, symbols and texts (iconic elements). Examples of graphic models can serve all sorts of schemes, cards, drawings, graphics and charts.

The scheme is a representation of a certain object in common, main features using conventional designations.. With the help of circuits, the appearance of the object can also be presented, and its structure. The scheme as the information model does not pretend to complete the provision of information about the object. With the help of special techniques and graphic designations, one or more features of the object under consideration are more relocated. Examples of schemes are shown in Fig. 1.5.

Fig. 1.5. Examples of schemes used in the lessons of physics, biology, history

A reduced generalized image of the earth's surface on a plane in a particular symbol system gives us a geographical map.

Drawing is a conditional graphic image of an object with an accurate ratio of its size obtained by projection. The drawing contains images, dimensional numbers, text. Images give views of the geometric form of the object, the number is the magnitude of the object and its parts, the inscriptions - about the title, scale in which images are made.

The graph is a graphic image that gives a visual idea of \u200b\u200bthe character of the dependence of one value (for example, paths) from another (for example, time). The schedule allows you to track the dynamics of data change.

The diagram is a graphic image that gives a visual idea of \u200b\u200bthe ratio of any values \u200b\u200bor several values \u200b\u200bof one value, about changing their values. More details are the types of diagrams and methods for their construction will be considered when studying spreadsheets.

1.3.2. Graphs

If some objects depict the vertices, and the links between them are lines, then we will receive the information model in the form of a graph. The vertices of the graph may be depicted with circles, ovals, dots, rectangles, etc. Unired (without an arrow) line connecting the vertices of the graph is called a rib. The direction directed (with an arrow) is called arc; In this case, the vertex, from which the arc comes, is called the initial, and the top where the arc is included - the ultimate.

The graph is called non-orientedIf its vertices are connected by ribs (Fig. 1.6, a). The vertices of the oriented graph are connected by arcs (Fig. 1.6, b). The path is the sequence of Röbebe (arcs), which can be moved from one vertex to another.

Count is called suspendedIf its vertices or ribs are characterized by some additional information - the weights of the vertices or the roiber. In fig. 1.6, in using a weighted ne-oriented graph, roads are depicted between five settlements A, B, C, D, E; Weight Ryubers - the length of the roads in kilometers.

The path to the vertices and edges of the graph, in which any edge of the graph enters no more than once, is called a chain. The chain, the initial and final vertices of which coincide, is called a cycle.

Fig. 1.6. Graphs

Count with a cycle is called a network. If the heroes of some literary work present the vertices of the graph, and the bonds existing between them are Rybrami, then we will receive a graph called the semantic network.

Counts like information models Find widespread use in many areas of our life. For example, you can carry out existing or newly designed houses, facilities, quarters of the vertices, and connecting their roads, engineering networks, power lines, etc. - edge of the graph. According to such graphs, you can plan optimal transport routes, the shortest bypass pathways, the location of outlets and other objects.

Tree is a graph in which there are no cycles, i.e. in it, it is impossible to go from some vertices to several different edges and return to the same vertex. A distinctive feature of the tree is that there is a single way between any two peaks.

Any hierarchical system can be represented by wood. The tree highlights one main vertex called its root. Each vertex of the tree (except the root) has only one ancestor, marked by the ancestor, the object is included in one class1 * of the highest level. Any vertex of the tree can generate several descendants - vertices corresponding to the lower level classes. This principle of communication is called "one-to-many". The vertices that do not have generated vertices are called leaves.

Related links between family members are conveniently depicting using a graphcalled the genealogical or pedigree tree.

The resource "Live pedigree" (145555) is a tool for forming and analyzing genealogical trees containing examples of pedigree. With it, you can explore the genealogical trees of many famous families and build a genealogical tree of your family (http://sc.edu.ru/).

Class - Many objects possessing common features.

1.3.3. Using graphs when solving tasks

Counts are convenient to use when solving some classes of tasks.

Example 1.. Figure 1.7 shows the road scheme connecting trading points A, B, C, D, E. On each road can only be moved in the direction indicated by the arrow. How many different paths are there from point a to point e?

Fig. 1.7. Scheme of roads represented by oriented graph

You can only get from the vertices of C and D. If we know the number of ways from the vertex and to the vertex with and from the vertex and in the top D, then, after laying them, we obtain the desired number of ways from A in E. Indeed, in order To get from the vertex and at the top e, we are simply all the ways from the top and to the vertex with adding the arc of the CE, and the paths from the top and to the vertex D add the Arc de. The number of paths will not change. So, the number of paths from the vertex and at the top of E is equal to the sum of the paths of the A B C and from A in P.

It can be said that our task broke into two more simple tasks. I will decide each of them individually.

At the vertex C can be reached directly from the vertex A and from the vertex. V. In turn, there is a single path from the vertex A into the vertex. Thus, from the vertex and to the top of the C can be reached in two ways: 1 (directly from a) + 1 (via c) \u003d 2.

Try to prove that the path is from the top and at the top of the only one.

As for the vertex D, it is the final vertex for three arcs: BD, AD and CD. Consequently, it is possible to get from the vertices A, B and C:

So, there are four ways from the vertex and at the top of D.

Now execute the calculation of ways from A in E:

2 (through C) + 4 (via d) \u003d 6.

The solution to the problem will be much easier if you move from the top A (beginning of the route) to the top of E and to lift the weights of the vertices - the number of paths from A to the current vertex (Fig. 1.8). At the same time, the weight of the vertices can be taken for 1. Indeed, there is a single way to get out of and in a - remain in place.

Fig. 1.8. Scheme of roads represented by a suspended graph

Example 2. In order to record all three-digit numbers consisting of numbers 1 and 2, it is possible to use the graph (wood) in Fig. 1.9.

Fig. 1.9. Tree to solve the task of writing three-digit numbers

In general, if you know the number of possible options for choosing at each step of constructing a graph, then to calculate the total number of options, you need to multiply all these numbers. (Remember the multiplication rule from the combinatorics!)

Example 3.. Consider a somewhat modified classical task of crossing.

On the banks of the river there is a peasant (K) with a boat, and next to him - a dog (c), fox (l) and goose (d). The peasant should cross himself and transport the dog, foxes and goose to the other side. However, the boat except the peasant is placed either only a dog or only fox, or only goose. Leave the dog with a fox or fox with Guses without supervision the peasant can not - the dog is a danger to fox, and Fox - for a goose. How should the peasant organize the crossing?

To solve this problem, we will make a graph whose vertices will be the initial and resulting placement of characters on the banks of the river, as well as all sorts of intermediate states achieved from the previous over one step of the crossing. Each vertex-state of the crossing is denoted by oval and connect Ribra with states formed from it (Fig. 1.10).

Invalid under the condition of the state problem are highlighted by a dotted line; They are excluded from further consideration. The initial and final state of the crossing is highlighted by a bold line.

The graph shows that there are two solutions to this task. We give a corresponding transfer plan to one of them:

1) the peasant transports the fox;
2) the peasant returns;
3) the peasant transports the dog;
4) the peasant returns with the fox;
5) the peasant is transporting a goose;
6) the peasant returns;
7) The peasant is transporting a fox.

Example 4. Consider the following game: first in the pile lie 5 matches; Two players remove matches in turn, and for 1st course you can remove 1 or 2 matches; Wins the one who leaves 1 match in a bunch. We find out who wins with the right game - the first (I) or the second (ii) player.

Player I can remove one match (in this case they will remain 4) or 2 (in this case, there will remain 3).

If the player I left 4 matches, the player II can leave 3 or 2 matches as its move. If after the course of the first game. ka will remain 3 matches, the second player can win, taking two matches and leaving one.

If after player II left 3 or 2 matches, the player I in each of these situations has a chance to win.

Thus, with the correct strategy of the game, the first player will always win. To do this, he must take one match.

In fig. 1.11 is a graph called the game tree; It reflects all possible options, including erroneous (losing) strokes of players.

Fig. 1.11. Tree game

THE MOST IMPORTANT THING

In graphical information models, conditional graphic images (shaped elements) are used for visual display of objects, often complemented by numbers, symbols and texts (iconic elements). Examples of graphic models are all sorts of schemes, cards, drawings, graphs and charts, graphs.

The graph consists of vertices connected by lines - ribs or arcs. Count is called weightedIf its tops or ribs (arcs) are characterized by some additional information - the weights of the vertices (Ryuber, Arc).

The graph of the hierarchical system is called tree. A distinctive feature of the tree is that there is a single way between any two peaks.

Questions and tasks

1. Familiarize yourself with the presentation materials for the paragraph contained in electronic application To the textbook. What can you say about the form of information presentation in the presentation and in the textbook? What slides do you could add a presentation?

2. What information models refer to graphic?

3. Give examples of graphic information models with whom you have:

a) when studying other items;
b) in everyday life.

4. What is a graph? What is the peaks and edges of the graph in fig. 1.6, in? Give examples of chains and cycles available in this graph. Determine which two points are most removed from each other (two items are considered the most remote, if the length of the shortest path between them is greater than the length of the shortest path between any other two points). Specify the length of the shortest path between these items.

5. Give an example of a system, the model of which can be represented in the form of a graph. Picture the appropriate graph.

6. The dirt road passes consistently through settlements A, B, C and D. At the same time, the length of the dirt road between A and B is equal to 40 km, between B and C - 25 km, and between C and D - 10 km. There is no road between a and d. Between A and C built a new asphalt highway with a length of 30 km. Evaluate the minimum possible time of the cyclist movement from point A to point B if its speed on the dirt road is 20 km / h, on the highway - 30 km / h.

7. The figure shows the scheme of roads connecting trading points A, B, B, G, D, B, K. On each road can only be moved in the direction indicated by the arrow. How many different paths are there from point a to point to?

8. Working in a group, make a semantic network on one of the Russian folk fairy tales: "Kolobok", "Ryaba", "Rack".

9. What is a tree? What systems can trees serve as models? Give an example of such a system.

10. How many three-digit numbers can be recorded using numbers 2, 4, 6 and 8, provided that there should be no identical numbers in the number of numbers?

11. How many three-digit numbers exist, all the numbers are different?

12. To compile chains, beads are used marked with letters A, B, C, D, E. In the first place in the chain costs one of the beads A, C, E. On the second - any vowel, if the first letter is vowel, and any consonant, If the first consonant. In third place is one of the beads with, D, E, not standing in the chain in the first place. How many chains can be created according to this rule?

13. Two players play the next game. Before them is a bunch of 6 stones. Players take stones in turn. In one run, you can take 1, 2 or 3 stones. Loses the one who takes the last stone. Who wins with an error-free game of both players - a player who makes the first move, or a player doing the second course? What should be the first prime player? Justify the answer.

Information model- The object model presented in the form of information describing the parameters and variables of the object substantial for this review, the inputs and objects of the object, and allowing the information to model the possible states of the object to simulate the possible states of the object.

Information models can not touch or see, it does not have a material embodiment, because they are built only on information. The information model is a set of information that characterizes the essential properties and states of the object, process, phenomena, as well as the relationship with the outside world.

The information model is a formal model of a limited set of facts, concepts or instructions designed to meet specific requirement.

To build an information model, it is necessary to pass a number of stages presented in Scheme 3. The process conducted from the "object of cognition" facility "formal design" is called "Formalization", and the inverse process - "Interpretation" - most often used in the knowledge of peace and training .

The basis of information modeling is three postulates:

everything consists of elements;

elements have properties;

elements are interconnected by relationships.

The object to which these postulates apply can be represented by the information model.

Stages of building an information model.

F object of knowledge and

On learning subjects

P Personal performance

M formed thought e

And "Live" word p

L recorded word n

And scientific text

S formal designs e

Classification of information models:

- Fashion of description:

With the help of formal languages \u200b\u200b(language of mathematics, tables, programming languages, expansion of a natural human language, etc.);

Graphic (block diagrams, charts, graphs, etc.).

- Creating a goal:

Classification (tree, family tree, directory tree in computer);

Dynamic (as a rule, based on the solution of differential equations and serve to solve management and forecasting tasks).

- By the nature of the simulated object:

Deterministic (defined), for which the laws are known to be changed or developing an object;

Probable (processing of statistical uncertainty and some species of fuzzy information).

Historical origin and methodological significance of the concepts of the model and analogy.

The word "model" occurred from the Latin word "modulus", means "measure", "sample". Its initial importance was associated with construction art, and in almost all European languages, it was used to designate an image or a prerequisite, or things similar to that with another thing.

Modeling in scientific research began to be applied in deep antiquity and gradually excited all new areas of scientific knowledge: technical design, construction and architecture, astronomy, physics, chemistry, biology and, finally, social sciences. Big successes and recognition in almost all branches of modern science brought the method of modeling the twentieth century. However, the modeling methodology has developed in separate sciences for a long time independently of each other. There was no uniform system of concepts, single terminology. Only gradually began to be aware of the role of modeling as a universal method of scientific knowledge.

The term "model" is widely used in various spheres of human activity and has many semantic values. In this section, we will consider only such models that are tools for obtaining knowledge.

In this way, model- Simplified view of a real object, process or phenomenon. The model is such a material or mentally represented object, which in the process of study replaces the original object so that its direct study gives new knowledge about the original object.

Under modelingit is understood as the process of building, studying and applying models. It is closely related to such categories as abstraction, analogy, hypothesis, etc. The simulation process necessarily includes the construction of abstractions, and conclusions by analogy, and the design of scientific hypotheses. Modeling- Building models for research and study of objects, processes, phenomena.

Models of objects must reflect something really existing. Therefore, often under the models of objects understand the abstract generalization of actually existing objects. For example, object models can be copies of architectural structures, solar system, the structure of the parliamentary power in the country, etc. The model can describe the phenomena of alive and inanimate nature, and not one, but a whole class of phenomena with common properties. In models of objects or phenomena, the properties of the original are reflected - its characteristics, parameters.

You can also create processes models, i.e. Model actions on material objects: the course, consistent change of states, the development stages of one object or their system. Examples of this are well known: these are models of economic or environmental processes, the development of the universe or society, etc.

Methodological basis modeling.

The modeling theory is based on a systematic approach. The system approach is that the researcher is trying to study the behavior of the system as a whole, and not concentrate its attention on its separate parts. This approach is based on the recognition that even if each element or subsystem has optimal structural or functional characteristics, the resulting behavior of the system as a whole can be only suboptimal due to the interaction between its individual parts.

The increasing complexity of organizational systems and the need to overcome this complexity led to the fact that the systemic approach becomes an increasingly necessary research method.

A certain set of elements of the system under consideration may be presented as its subsystem. It is believed that subsystems include some independently functioning parts of the system. Therefore, to simplify the study procedure, it is initially necessary to competently allocate the subsystems of a complex system, that is, to determine its structure. The structure of the system is a time-resistant set of relationships between its components (subsystems). And with a systematic approach, an important step is to determine the structure of the study described by the system.

The system is an integer composed of parts. The system is a plurality of elements in relations and connections with each other and forming certain integrity and unity.

Computer model.

Computer model- Model implemented by means of a software environment.

Having a deal with a computer with a tool, you need to remember that it works with information. Therefore, it should be processed from what information and in what form can perceive and process a computer. Modern computer is able to work with sound, video, animation, text, schemes, tables, etc. But to use the entire variety of information, both technical (hardware) and software (SoftWare) provision. Both are computer simulation tools. There are now a wide range of programs that allow you to create various types of computer iconic models: text processors, editors of formulas, spreadsheets, control systems in databases, professional design systems, as well as various programming environments.

Modern computers represent ample opportunities for modeling various phenomena and processes. In the educational process, the computer should not simply replace the blackboard, a poster, a cinema and diaperoctor, a natural experiment. Such a replacement is appropriate only when the use of computers will give a significant additional effect compared to the use of other learning tools.

computer simulation (km) is a promising method of activating the educational process. It is becoming increasingly more and more important in modern scientific knowledge, and, in addition, it is currently becoming a popular didactic agent. Consider this direction in more detail.

The subject of km is the study of processes and phenomena using a computer, which at the same time acts as an experimental installation. When using KM to solve problems, stages of setting the problem, develop a model, computer (computational) experiment, analyzing modeling results. If the simulation results do not correspond to the target, then the need to return to the previous steps.

Mathematical models.

Mathematical modeling allows with the help of mathematical symbols and dependencies to make a description of the process of what is happening.

Mathematical model- This is a combination of mathematical objects and relations between them, adequately displays the properties and behavior of the object under study. The model is considered adequate if the studied properties with acceptable accuracy reflect. Accuracy is assessed by the coincidence of predicted during the computing experiment on the model of the output parameter values \u200b\u200bwith their true values.

The mathematical model covers a class of undefined (abstract, symbolic) mathematical objects such as numbers or vectors, and relationships between these objects.

A mathematical relationship is a hypothetical rule that connects two or more symbolic objects. Many relationships can be described using mathematical operations that bind one or more objects with another object or multiple objects (the result of the operation).

The mathematical model will reproduce the appropriately selected parties to the physical situation if you can set a compliance rule that connects specific physical objects and relationships with certain mathematical objects and relationships. Instructive and / or interesting may also be the construction of mathematical models for which there is no analogues in the physical world. The most well-known mathematical models are systems of integers and real numbers and Euclidean geometry; The defining properties of these models are more or less direct abstraction of physical processes (account, ordering, comparison, measurement).

Objects and operations of more general mathematical models are often associated with sets of valid numbers, which can be correlated with the results of physical measurements.

As mathematical objects, there are numbers, variables, sets, vectors, matrices, and the like.

Classification of mathematical models based on the characteristics of the applied mathematical apparatus.

What examples of information models can be brought to educational institutions? How can teachers use them in their work? Let's try to find answers together to questions.

What is the model

What are iconic information models? Examples of them are used in their work all teachers who own modern information technology. IN general The model is different methods Representations of the analyzed reality.

Varieties

You can give examples of information models of the material and ideal species.

Washing options are based on an objective example, they exist independently of man, his consciousness. Currently, they are divided into physical and analog options, which are based on the phenomena associated with the subject being studied.

The ideal models are associated with human thinking, his perception, imagination. Among them can be noted intuitive, which are not suitable for any variant classification.

When applying examples of a figurative information model, you can mention one of these models. Consider more of their classification.

Text ideal models

Verbal models apply teachers of the humanitarian cycle. They help to describe with successive proposals a specific area, phenomenon, object, event. What will the lesson information model look like? Example Take from the course of literature. When studying the novel L. N. Tolstoy "War and Peace", the teacher describes the image of Natasha Rostova. For this, he uses the text model. Guys, listening to the teacher, create on the basis of his perception of the image of this heroine, their image of the heroine of Tolstoy.

If the history teacher asks for his pupils: "Give examples of the shared information model of events that occurred during the Kulikov battle, based on viewed fragments," the guys create their own image of that battle. They transmit it in the form of suggestions related to the story.

You can cite examples of information models of verbal species and from the course of physics. When studying the topic "Pressure of solid bodies" in the seventh grade, the teacher tells children how difficult it is to move around the loose snow without skis. Then, schoolchildren are invited to explain the cause of this phenomenon, to identify the parameters on which the studied physical value depends. The image that arises into the consciousness of the guys after the story of the teacher, helps them to answer the question.

As examples of such a model, a textbook, road rules can be noted.

Mathematical models

They are considered a wide class of iconic models. Mathematical models are based on the use of relations, comparisons, other methods used in this science. The resulting examples of information models based on mathematical methods can be mentioned by the solution of square equations, the preparation of proportions. All sections of geometry involving the conclusion and proof of the theorems are also associated with the construction of a mathematical model. Does not do without them and such a school subject as an economy.

Information models

They are considered a class of iconic models that describe any information processes: appearance, transmission, change, application of information in different systems. Examples of tabular information models at school can be founded in the course of grade 10. When studying economic geography, a tabular model helps to visually see the main characteristics of the country, use the material to compile a full story.

In addition, examples of tabular information models can be found in any school course. In chemistry, this is the solubility table of the compounds, as well as the periodic system of Mendeleev. In physics, without tables, the teacher is difficult to explain the main terms studied in the topic "Electricity". In history with their help, knowledge systematization is carried out, the guys enter in one column important historical dates, and in the other - describe the events that corresponded to them.

Interconnection of models

There is a conditional face between informational, mathematical, verbal models. All 3 examples of information models are found in school disciplines. So, for mathematics, physics, computer science, mathematical and informational options are considered the most sought-after. But without a verbal model, the guys will not be able to explain the phenomena, algorithms, equations and inequalities.

Simulation features

Before considering examples of graphic information models, find out the features of modeling. The model is an object created artificially. This is necessary to simplify the presentation of this object or phenomenon. The model fully reflects all the features of the most source process. If task is given: "Give an example of an information model", it is necessary to understand the essence of the process.

We are talking about building a model that is intended to study information phenomena, processes. In computer science, as such an item, you can consider programming. Using a specific mathematical programming language, you can submit text material in graphical form.

Modeling involves the construction of the model that is designed to study and study the source object, phenomena, process. The created copy is only endowed with the qualities and properties that are characteristic of the original item, but allows some deviations from the ideal.

Activity approach

Full models can be obtained by using a system approach. This is especially true in educational institutions. The transformations that touched the schools in recent years have made it possible to establish a logical connection between individual disciplines.

Such an activity option contributes to the formation of a harmoniously developed personality that understands the unity of the living world, the relationship of individual processes and phenomena.

If teachers ask: "Give an example of an information model", it can safely choose any academic subject. There is no such discipline in which tables, graphs, diagrams, presentations would not be used.

Features of modern school

New standards that were introduced into Russian schools suggest a consideration of one phenomenon from different points of view. For example, from the course of physics, the guys learn that the electrons are necessary for the flow in metals. electric current. They receive information about the charge of this negative particle, determining their number of different metals. At the lessons of chemistry, schoolchildren talk about the probability of electron location in the energy levels.

When studying the topic "Redox reactions", schoolchildren appear information about what is happening with these negative particles in chemical interaction. Despite the fact that information is provided from different positions, we are talking about one object - electrons. A similar systematic approach allows the formation of a complete picture of the structure of the substance, its transformations in the consciousness of schoolchildren.

In the above example, the object being studied is considered as a complete system, an integral part of the whole (substance). Depending on the educational discipline Use certain characteristics, additions. In the case of a systematic approach, the first place is not causal explanations of the existence of an object, but the need to include other component parts from it.

Of particular importance is the formation of universal models acquires with experimental activities. Using a personal computer, you can calculate the parameters that will be associated with the analyzed object.

Such modeling is important for scientific knowledge of natural phenomena. In the school course of informatics, such actions are called the computing experiment, which is based on three important concepts: models, algorithm, program.

School use personal computer Perhaps in three main options:

conducting direct calculations using PC;
creating a database, transformation into a program or a specific algorithm;
maintaining between computer and schoolboy interface.

Signs of models

Among the most common signs that can be classified by all models, we will highlight: the purpose of application, the scope of knowledge, a temporary factor, a representation option.

Depending on which purpose is set in front of the model, you allocate experienced, educational, game, imitation, scientific and technical options for models. For example, at the initial stage of school education, the most applicable and significant game technologies that allow the guys to feel themselves as a teacher, a doctor, a policeman. Game models in children seven-eight years are well formed, because in pre-school educational institutions, they are used as a mandatory element in the formation of the personal qualities of the child.

Varieties of models

Depending on the field of knowledge for which the model is drawn up, currently allocate economic, biological, sociological, chemical species. For example, it is important for the natural science cycle to form a model that would allow to explain the phenomena that occur in a living and inanimate nature. In sociology, the emphasis on the processes occurring in society.

According to the temporary factor, static and dynamic variants of models are distinguished. The static variant characterizes the parameters and structure of the object, allows you to describe the selected phenomenon (object) at a particular period of time, helps to receive reliable and timely information about it.

Any model has a specific form, view, version option, description. The school suggests a consideration of more material and intangible models, depending on the specifics of the academic discipline.

Material models involve a real embodiment, they fully repeat the inner or external structure of the object itself. For example, in geography as such a reduced model, the globe layout (globe) stands on which all seas and oceans, continents and islands are applied. These models are directly related to the research approach to learning modern schoolchildren. They are needed in teaching chemistry, physics, biology, astronomy, geography.

Intangible modeling involves the use of theoretical method of knowledge.

Conclusion

Any information model is a set of information about the phenomenon, object, process. With it, it is possible to characterize any process that occurs in a living and inanimate nature. A variety of graphs, cards, tables, charts that are actively used by teachers on all levels of learning, give their positive result.

Intuitive (mental) modeling contributes to the creation of the first impression on the process occurring in chemistry or biology. Due to the combination of all options for information models, the younger generation of our country has an adequate assessment of the unity of the living and non-living world. School graduates can independently build any models, use them to explore, analyze, evaluate events and phenomena.