Experts prove the superiority of technical education over the humanities, prove that Russia is in dire need of highly qualified engineers and technical specialists, and this trend will continue not only in 2014, but also in subsequent years. According to recruiters, if the country expects economic growth in the coming years (and there are prerequisites for this), then it is very likely that the Russian educational base will not be able to handle many industries (high technology, industry). "At the moment, there is an acute shortage of specialists in the field of engineering and technical specialties, in the field of IT: programmers, software developers. Engineers of almost all specializations remain in demand. At the same time, the market is oversaturated with lawyers, economists, journalists, psychologists," - He speaks CEO recruitment agency unique specialists Ekaterina Krupin. Analysts, making long-term forecasts until 2020, are sure that the demand for technical specialties will grow rapidly every year. The urgency of the problem. Therefore, the quality of preparation for the exam in physics is relevant. Mastering the methods for solving physical problems is decisive. A variety of physical tasks are graphic tasks. 1) The solution and analysis of graphic problems allow you to understand and remember the basic laws and formulas in physics. 2) In CIMs for conducting the exam in physics included tasks with graphic content.

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PURPOSE OF THE PROJECT WORK:

The study of types of graphic tasks, varieties, features and methods of solution .

WORK OBJECTIVES:

1. Study of literature on graphic tasks; 2. Study USE materials(prevalence and level of complexity of graphic tasks); 3. The study of general and special graphic problems from different branches of physics, the degree of complexity. 4. Study of solution methods; 5. Conducting a sociological survey among students and teachers of the school.

Physical task

In the methodological and educational literature, educational physical tasks are understood as expediently selected exercises, the main purpose of which is to study physical phenomena, form concepts, develop the physical thinking of students and instill in them the ability to apply their knowledge in practice.

Teaching students to solve physical problems is one of the most difficult pedagogical problems. I consider this issue to be very important. My project aims to solve two problems:

1. Help in teaching schoolchildren the ability to solve graphic problems;

2. Involve students in this type of work.

The solution and analysis of the problem allow us to understand and remember the basic laws and formulas of physics, create an idea of ​​their characteristic features and limits of application. Tasks develop skills in using the general laws of the material world to solve specific issues of practical and cognitive importance. The ability to solve problems is the best criterion for assessing the depth of study of the program material and its assimilation.

In studies to identify the degree of assimilation by students of individual operations included in the ability to solve problems, it was found that 30-50% of students various classes indicate their lack of such skills.

The inability to solve problems is one of the main reasons for the decline in success in the study of physics. Studies have shown that the inability to independently solve problems is the main reason for irregular homework. Only a small part of students masters the ability to solve problems, considers it as one of the most important conditions for improving the quality of knowledge in physics.

This state in the practice of teaching can be explained by the lack of clear requirements for the formation of this skill, the lack of internal incentives and cognitive interest among students.

Solving problems in the process of teaching physics has many-sided functions:

• Mastering theoretical knowledge.
• Mastering the concepts of physical phenomena and quantities.
• mental development, creative thinking and special abilities students.
• Introduces students to the achievements of science and technology.
• It brings up diligence, perseverance, will, character, purposefulness.
• It is a means of monitoring the knowledge, skills and abilities of students.

Graphic task.

Graphical tasks are such tasks in the process of solving which graphs, diagrams, tables, drawings and diagrams are used.

For example:

1. Construct a graph of the path of uniform motion if v = 2 m/s or uniformly accelerated at v 0 =5 m/s and a = 3 m/s 2.

2. What phenomena characterizes each part of the graph ...

3. Which body is moving faster

4. In what area did the body move faster

5. Determine the distance traveled from the speed graph.

6. On what part of the movement the body rested. The speed increased and decreased.

Solving graphical problems helps to understand the functional relationship between physical quantities, instilling skills in working with graphs, and developing the ability to work with scales.

According to the role of graphs in solving problems, they can be divided into two types: - tasks, the answer to the question of which can be found as a result of constructing a graph; - tasks, the answer to the question of which can be found by analyzing the graph.

Graphic tasks can be combined with experimental ones.

For example:

Using a beaker filled with water, determine the weight of a piece of wood...

Preparation for solving graphic problems.

To solve graphic problems, the student must know various types of functional dependencies, which means the intersection of graphs with axes, graphs among themselves. You need to understand how the dependencies differ, for example, x \u003d x 0 + vt and x \u003d v 0 t + at 2 / 2 or x \u003d x m sinω 0 t and x \u003d - x m sinω 0 t; x =x m sin(ω 0 t+ α) and x =x m cos (ω 0 t+ α), etc.

The preparation plan should contain the following sections:

· a) Repeat the graphs of functions (linear, quadratic, power) · b) Find out what role graphs play in physics, what information they carry. · c) Systematize physical problems according to the importance of graphs in them. d) Study methods and techniques for analyzing physical graphs e) Develop an algorithm for solving graphic problems in various areas of physics f) Find out general pattern in solving graphic problems. To master the methods of solving problems, it is necessary to solve a large number of different types of problems, observing the principle - "From simple to complex". Starting with simple ones, master the methods of solving, compare, generalize different problems both on the basis of graphs and on the basis of tables, diagrams, diagrams. Attention should be paid to the designation of quantities along the coordinate axes (units physical quantities, the presence of longitudinal or multiple prefixes), scale, type of functional dependence (linear, quadratic, logarithmic, trigonometric, etc.), on the slope angles of the graphs, the points of intersection of graphs with coordinate axes or graphs with each other. Particular attention should be paid to tasks with embedded "mistakes", as well as to tasks with photographs of measuring instrument scales. In this case, it is necessary to correctly determine the division value of measuring instruments and accurately read the values ​​of the measured quantities. In geometrical optics problems, it is especially important to carefully and accurately build rays and determine their intersections with the axes and with each other.

How to solve graphics problems

Mastering the general algorithm for solving physical problems

1. Implementation of the analysis of the conditions of the problem with the allocation of the tasks of the system, phenomena and processes described in the problem, with the definition of the conditions for their flow

2. Implementation of coding the condition of the problem and the solution process at various levels:

a) a brief statement of the condition of the problem;

b) execution of drawings, electrical circuits;

c) execution of drawings, graphs, vector diagrams;

d) writing an equation (system of equations) or building a logical conclusion

3. Selection of the appropriate method and methods for solving a specific problem

4. Application of a general algorithm for solving problems of various types

The solution of the problem begins with reading the condition. You need to make sure that all the terms and concepts in the condition are clear to the students. Incomprehensible terms found out after the initial reading. At the same time, it is necessary to single out which phenomenon, process or property of bodies is described in the problem. Then the task is read again, but with the selection of data and the desired values. And only after that, a brief record of the condition of the problem is carried out.

Planning

The action of orientation makes it possible to carry out a secondary analysis of the perceived condition of the problem, as a result of which physical theories, laws, and equations are singled out that explain a specific problem. Then, methods for solving problems of one class are singled out and the optimal method for solving this problem is found. The result of the students' activity is a solution plan, which includes a chain of logical actions. The correctness of the actions to draw up a plan for solving the problem is controlled.

Solution Process

First, it is necessary to clarify the content of already known actions. The action of orientation at this stage involves once again highlighting the method of solving the problem and clarifying the type of problem being solved by the method of setting the condition. The next step is planning. A method for solving the problem is planned, that apparatus (logical, mathematical, experimental) with the help of which it is possible to carry out its further solution.

Solution Analysis

The last step in the process of solving the problem is to check the result. It is carried out again by the same actions, but the content of the actions changes. The act of orientation is to ascertain the essence of what needs to be tested. For example, the results of the solution can be the values ​​of the coefficients, physical constant characteristics of mechanisms and machines, phenomena and processes.

The result obtained in the course of solving the problem must be plausible and consistent with common sense.

The prevalence of graphics tasks in CMMs in USE assignments

The study of the USE materials for a number of years (2004 - 2013) showed that in the USE assignments in various sections of physics, graphic tasks in various sections of physics are common. In tasks A: in mechanics - 2-3 in molecular physics - 1 in thermodynamics - 3 in electrodynamics - 3-4 in optics - 1-2 in quantum physics - 1 in atomic and nuclear physics - 1 In tasks B: in mechanics - 1 in molecular physics - 1 in thermodynamics - 1 in electrodynamics - 1 in optics - 1 in quantum physics - 1 in atomic and nuclear physics - 1 In tasks C: in mechanics - in molecular physics - in thermodynamics - 1 in electrodynamics - 1 in optics - 1 in quantum physics - in atomic and nuclear physics - 1

Our research

A. Analysis of errors in solving graphic problems

An analysis of the solution of graphic problems showed that the following common errors occur:

Errors in reading charts;

Errors in operations with vector quantities;

Errors in the analysis of graphs of isoprocesses;

Errors on graphic dependency electrical quantities;

Errors in construction using the laws of geometric optics;

Errors in graphic assignments for quantum laws and the photoelectric effect;

Errors in the application of the laws of atomic physics.

B. Opinion poll

In order to find out how school students are aware of graphic tasks, we conducted a sociological survey.

We asked the students and teachers of our school the following questions: profiles:

1. 1. What is a graphic task?

a) tasks with pictures;

b) tasks containing schemes, diagrams;

c) I don't know.

1. 2. What are graphics tasks for?

b) to develop the ability to build graphics;

c) I don't know.

3. Can you solve graphics problems?

a) yes; b) no; c) not sure ;

4. Do you want to learn how to solve graphic problems?

A) yes ; b) no; c) find it difficult to answer.

50 people were interviewed. As a result of the survey, the following data were obtained:

CONCLUSIONS:

1. As a result of work on the project "Graphic Tasks", we studied the features of graphic tasks.
2. We studied the features of the methodology for solving graphic problems.
3. An analysis of typical errors was carried out.
4. Conducted a sociological survey.

Reflection of activity:

1. It was interesting for us to work on the problem of graphic tasks.
2. We have learned to research activities, compare and compare research results.
3. We have found that mastering the methods of solving graphic problems is necessary for understanding physical phenomena.
4. We have found that mastery of methods for solving graphic problems is necessary for successful delivery USE.

All constructions in the process of graphical reckoning are performed using a laying tool:

navigation protractor,

parallel line,

caliper,

drawing compass with a pencil.

The lines are applied with a simple pencil and removed with a soft rubber band.

Take the coordinates of a given point from the map. Most accurately, this task can be performed using a measuring compass. To remove the latitude, one leg of the compass is placed in given point, and the other is brought to the nearest parallel so that the arc described by the compass touches it.

Without changing the angle of the legs of the compass, bring it to the vertical frame of the card and put one leg on the parallel to which the distance was measured.
The other leg is placed on the inner half of the vertical frame towards the given point and the latitude reading is taken with an accuracy of 0.1 of the smallest division of the frame. The longitude of a given point is determined in the same way, only the distance is measured to the nearest meridian, and the longitude reading is taken along the upper or lower frame of the map.

Draw a point at the given coordinates. The work is usually performed using a parallel ruler and a measuring compass. The ruler is applied to the nearest parallel and one half of it is moved to a given latitude. Then, using a compass solution, take the distance from the nearest meridian to a given longitude along the upper or lower frame of the map. One leg of the compass is placed at the cut of the ruler on the same meridian, and with the other leg a weak prick is also made at the cut of the ruler in the direction of the given longitude. The injection site will be the set point

Measure the distance between two points on the map or set aside known distance from a given point. If the distance between the points is small and can be measured with a single compass solution, then the legs of the compass are placed at one and the other points, without changing its solution, and placed against the side frame of the map at about the same latitude as the measured distance.

A large distance when measuring is divided into parts. Each part of the distance is measured in miles in the latitude of the area. You can also use a compass solution to take from the side frame of the map a "round" number of miles (10.20, etc.) and count how many times to put this number along the entire measured line.
At the same time, miles are taken from the side frame of the map approximately opposite the middle of the measured line. The remaining distance is measured in the usual way. If it is necessary to set aside a small distance from a given point, then it is removed with a compass from the side frame of the map and set aside on the laid line.
The distance is taken from the frame approximately at the latitude of a given point, taking into account its direction. If the distance to be set aside is large, then they are taken from the frame of the map approximately against the middle of the specified distance of 10, 20 miles, etc. and set aside the required number of times. From the last point measure the rest of the distance.

Measure the direction of a true course or bearing line plotted on a chart. A parallel ruler is applied to the line on the map and a protractor is attached to the cut of the ruler.
The protractor is moved along the ruler until its central stroke coincides with any meridian. The division on the protractor, through which the same meridian passes, corresponds to the direction of the course or bearing.
Since two readings are marked on the protractor, when measuring the direction of the laid line, one should take into account the quarter of the horizon in which the given direction lies.

Plot a true course or bearing line from a given point. When performing this task, a protractor and a parallel ruler are used. The protractor is placed on the map so that its central stroke coincides with some meridian.

Then the protractor is turned in one direction or the other until the stroke of the arc corresponding to the reading of the given course or bearing coincides with the same meridian. A parallel ruler is applied to the lower cut of the protractor ruler, and, having removed the protractor, move it apart, leading to a given point.

A line is drawn along the cut of the ruler in the desired direction. Move a point from one map to another. The direction and distance to a given point from a beacon or other landmark marked on both maps are taken from the map.
On another map, having plotted the desired direction from this landmark and plotting the distance along it, a given point is obtained. This task is combined

Graphic puzzles

1. Connect the four points with three lines without taking your hands off and return to the starting point.

. .

1. Connect nine dots with four lines without taking your hands off.

. . .

. . .

. . .

1. Show how to cut a rectangle with rows 4 and 9 units into two equal parts so that when they are added, they get a square.

1. A cube, colored on all sides, was sawn as shown in fig.

a) How many cubes

Not dyed at all?

b) How many cubes of colored

Will there be one edge?

c) How many cubes will have

Are two faces painted?

d) How many cubes are colored

Will there be three edges?

e) How many cubes are colored

Will there be four edges?

Situational, design

And technological challenges

A task. Balls of three sizes under the influence of their own weight roll down the inclined tray in a continuous stream. How to continuously sort balls into groups depending on size?

Solution. It is necessary to develop the design of the calibrating device.

The balls, leaving the tray, roll further along the wedge-shaped caliber. In the place where the width of the slot coincides with the diameter of the ball, it falls into the corresponding receiver.

A task. The heroes of one fantastic story take on a flight, instead of thousands of necessary spare parts, a synthesizer-machine that can do everything. When landing on another planet, the ship is damaged. You need 10 identical parts to repair. It turns out that the synthesizer does everything in one instance. How to find a way out of this situation?

Solution. It is necessary to order the synthesizer to produce itself. The second synth gives them another one, and so on.

Answers to graphic puzzles.

1. . .

2. . . .

. . .

. . .

1

1 Branch of the Federal State Budgetary educational institution higher vocational education"Ural State University means of communication"

Training of specialists technical profile includes a mandatory stage of graphic preparation. Graphic training of technical specialists takes place in the process of performing various types of graphic work, including when solving problems. Graphic tasks can be divided into different types, according to the content of the task conditions and according to the actions that are performed by the trainees in the process of solving the problem. Development of a typology of tasks, principles of their classification, subdivision of tasks into different types for their effective use in the learning process, development of task characteristics based on the classification of graphic tasks. In order to develop the motivation for graphic training of students, it is necessary to involve creative tasks in the educational process, which involve the inclusion of elements of creative search in the learning process. Systematization of the creative interactive task developed by us for the development of vitagen-oriented graphic tasks, classification of the types of task and the product of its implementation into groups in accordance with certain characteristics: by the content of the task, by actions on graphic objects, by coverage educational material, according to the method of solving and designing the results of the solution, according to the role of the task in the formation of graphic knowledge. Comprehensive systematization of graphics tasks different levels mastering the material allows you to comprehensively develop the graphic abilities of students, thereby improving the quality of training of technical specialists.

levels of assimilation of graphic knowledge

the plot of a vitality-oriented task

performed when solving graphic tasks

actions and operations

classification of graphic tasks

task and solving systems of a graphic problem

creative interactive tasks for the development of vitagen-oriented tasks

graphic task of classical content

1. Bukharova G.D. Theoretical foundations of teaching students the ability to solve physical problems: Proc. allowance. - Ekaterinburg: URGPPU, 1995. - 137 p.

2. Novoselov S.A., Turkina L.V. Creative tasks in descriptive geometry as a means of forming a generalized orienting basis for teaching engineering graphic activity. Obrazovanie i nauka. News of the Ural branch Russian Academy education. - 2011. - No. 2 (81). – pp. 31-42

3. Ryabinov D.I., Zasov V.D. Problems in descriptive geometry. - M .: State. Publishing House of Technical and Theoretical Literature, 1955. - 96 p.

4. Tulkibaeva N.N., Fridman L.M., Drapkin M.A., Valovich E.S., Bukharova G.D. Solving problems in physics. Psychological and methodological aspect / Under the editorship of Tulkibaeva N.N., Drapkina M.A. Chelyabinsk: From ChGPI "Fakel", 1995.-120p.

5. Turkina L.V. Collection of tasks on descriptive geometry of vitality-oriented content / - Nizhny Tagil; Yekaterinburg: UrGUPS, 2007. - 58 p.

6. Turkina L.V. Creative graphic task - the structure of content and solutions // Contemporary Issues science and education. - 2014. - No. 2; URL: http://www..03.2014).

One of the main components of the training of technical specialists is practical educational activities, including activities to solve educational problems. Solving problems of various types makes it possible to form skills and abilities, solve problems of an educational nature, develop readiness for the development of creative search in the process professional activity future professionals.

A variety of types of tasks that are offered for students to solve expands the horizons of students, teaches practical application knowledge and motivate their independent learning activities. In order to apply the whole range of educational tasks in a particular discipline, it is necessary to have an idea of ​​all their diversity, classify them according to one or another feature and purposefully use them to form the personality traits of future specialists that are in demand in professional activities.

One of the main components of the training of technical specialists is graphic training, which includes a practical component in the form of solving graphic problems. Solving graphic problems is the foundation for the formation of drawing skills, knowledge of projection theory, rules for the design of graphic images. The purpose of the graphic task is to create a graphic image of a given object, built in accordance with the rules of the Unified Design Documentation System, or to transform or supplement a given graphic image of an object. Bukharova as a complex didactic system, where components (task and decision systems) are presented in unity, interconnection, interdependence and interaction, each of which, in turn, consists of elements that are in the same dynamic dependence.

The task system, as is known, includes the subject, conditions and requirements of the task, the solving system includes a set of interrelated methods, methods and means of solving the problem.

The task system of a graphic task is determined by its content, which can be classified according to the sections of graphic disciplines used (for example, descriptive geometry). To systematize the types and types of graphic tasks, it is necessary to develop the foundations, principles and build a system for dividing them into groups. To do this, we propose the concept of typology (classification) of graphic tasks developed by us. The classification of tasks developed by us is similar to the classification of tasks in physics, but it has its own characteristics characteristic of teaching graphic disciplines, which are characterized not only by mastering a specific area of ​​knowledge, but also by developing a skill for their application in the development of graphic documentation.

The task condition as an incoming element of the task system determines the student's further actions and allows classifying graphic tasks by types of graphic actions on objects.

According to the types of objects on which graphic actions are performed, they can be as follows:

• problems with flat objects (point, line, plane);
• tasks with spatial objects (surfaces, geometric bodies);
• problems with mixed objects (point, line, plane, surface, geometric body).

According to the coverage of the educational material of descriptive geometry, tasks can be classified into homogeneous (one section) and mixed (several sections) polygenic.

• tasks with a text condition;
• tasks with a graphical condition;
• tasks with mixed content.

According to the sufficiency of information, tasks are classified into:

• tasks defined;
• search tasks.

The problem solving process determines solver system and allows you to classify graphic tasks according to the following parameters and features of the process of performing actions on task objects:

By types of graphical operations on objects, tasks can be as follows:

• tasks to determine the position of an object in space relative to projection planes and change its position;
• tasks to determine the relative position of objects;
• metric tasks (determination of the natural size of objects: sizes linear quantities, forms)

According to the actions aimed at the subject, the tasks can be:

• execution tasks;
• transformation tasks;
• design tasks;
• proof tasks;
• matching tasks;
• research objectives.

According to the method of solving graphic problems can be:

• tasks to be solved graphically;
• problems solved by analytical (computational) method;
• tasks that are solved in a logical way with a graphic design of the solution.

According to the use of means of solving graphic problems are divided into:

• tasks solved by manual means;
• tasks solved using information technologies.

According to the number of solutions, the problem can be:

• problems with one solution;
• problems with multiple solutions;
• problems with no solutions.

According to the role of tasks in the formation of graphic knowledge, they can be classified into tasks that form:

• graphic concepts (concepts) and terms;
• skills and abilities to apply the projection method;
• skills and abilities to apply methods for converting a drawing;
• skills and abilities to apply methods for determining the location of an object;
• skills and abilities to apply methods for determining the common parts of two or more objects (crossing lines);
• skills and abilities to apply methods for determining the size of an object;
• skills and abilities to apply methods for determining the shape of an object;
• skills and abilities of application of methods for determining the development of an object.

For example:

Task No. 1. Construct point B on the diagram, which belongs to the horizontal projection plane, is 40 mm away from the frontal projection plane, and 20 mm further from the profile projection plane than from the frontal one.

The task is homogeneous, its content belongs to the section "Point and Line" of the discipline "Descriptive Geometry". The task requires a graphical action on a flat object, the condition of the task is presented in text form, the task has a sufficient amount of information and does not apply to search ones. This is a classic example of the task of determining the position of an object in space relative to projection planes and depicting it in a drawing (diagram). Task - the execution of certain actions specified by the condition of the task; This problem can only be solved graphically. It can be solved both with the help of manual means and with the help of a CAD computer program, the problem has one solution. This task forms graphic concepts and terms (the name and position of the projection plane, the concept of "point", the coordinates of the point), the skills and abilities of using the projection method - projecting a point.

The solution to the problem is shown in Figure 1.

Task number 2. Construct a development of the surface B, containing the projections of the points A and C, and intersecting with the surface K - a cylinder of the front-projecting direction, the axis of which intersects the axis of the surface B.

Task No. 2 is polygenic, as it combines the following sections: "Point in the projection system", "Intersection of surfaces", "Deployment of curved surfaces". This is a problem with mixed objects (points, surfaces), the condition of the problem also has a mixed (complex) content, consisting of a text and a graphic part. The condition of the problem is not completely defined, since the cylinder that intersects the given surface B does not have a diameter and its position is not defined in the drawing. This is a task for determining the relative position of objects and determining the surface development, that is, an execution task that can be solved graphically, both manually and using information technology. The task has many solutions and forms graphical concepts - a point, surfaces of revolution (cone, cylinder), skills in applying methods for determining the common parts of objects (cutting planes method) and skills in constructing a sweep of surfaces of revolution.

The solution to problem No. 2 is shown in Figure 3.

The process of solving the graphic problem, given above, illustrates the peculiarity of teaching graphic disciplines, which consists in the fact that geometric objects in projections and graphic constructions are difficult for mastering by junior students, yesterday's schoolchildren who have a minimum level of graphic training due to the fact that the drawing course has been translated in alternative courses. To motivate graphic cognition, reduce the abstractness of educational material, some teachers proposed tasks with materialized objects and tasks for developing tasks of vitality-oriented content.

The classification of creative vitality-oriented tasks is similar to the classification of graphic tasks of classical content, but has a number of differences determined by the fact that the task system of a creative task is a task for developing the task itself. This information determines the direction of further learning activities student, the content of the graphic module, within which a graphic task can be developed, but not limiting the scope of knowledge of the subject and the creative imagination of the student.

• tasks are homogeneous (one topic);
• mixed tasks (several sections).

According to the requirements for the content of the task can be:

• tasks that specify the requirements for the content of the task;
• tasks of free choice of the content of the task (task on the above topic).

According to the requirements for the selection of material objects, the content of the task can be:

• tasks with obligatory use of objects of vital experience;
• tasks with the obligatory use of objects of professional activity;
• tasks with the obligatory use of interdisciplinary knowledge;
• tasks without special requirements for task objects.

According to the method of searching for means of solving the problem defined in the task for developing the problem, problems can be classified into:

• free search tasks;
• tasks using methods of activating thinking;
• tasks solved by analogy with the standard task: replacing an abstract object with a materialized object.

For example, a task for developing a task can be formulated as follows:

Develop a task in descriptive geometry, applying the knowledge of the topic "Projection of a point, a straight line" in a real life situation, having previously studied the theoretical positions and considered the tasks of the classical content. When compiling the problem, use the material analogues of geometric objects (point, line).

The task is homogeneous, not putting forward any requirements to the content of the task being developed, or to the nature of the objects used in the task, or to the method of searching for material analogues of geometric objects.

Task execution example:

The miner descended into the mine on an elevator to a depth of 10 m, walked along the tunnel directed along the X axis to the right for 25 m, turned 90 ° to the left and walked along the tunnel directed along the Y axis for another 15 m. Construct a diagram of a point that determines the location of the miner. The point of intersection of the earth's surface with the elevator shaft is taken as the origin of the coordinate axes. Take the elevator axis as the Z axis.

Figure 4 shows the horizontal projection of the point A-A1 and the frontal projection of the point A-A2, which characterizes the location of the object, which is located below the ground level, which we took as the horizontal projection plane.

The content of the developed task determines the actions to solve the problem and allows classifying creative vitagenically oriented tasks, as well as tasks of classical content, by types of geometric operations on objects, by the scope of the educational material of the graphic discipline, by the type and content of the task conditions, by actions aimed at the subject of the formulated problem, according to the sufficiency of information contained in the developed condition of the problem, according to the method of searching for means of solution.

The main difference between a vitagenic-oriented creative task and classical graphic tasks in descriptive geometry is the presence of a storyline based on a technical problem solved by means of descriptive geometry. Vitagen-oriented task, first of all, is a story about any sphere of human activity, in which methods and methods of graphic disciplines are applied. The creative search of students in the development of vitality-oriented tasks is not limited to: technical problems life, plot development using the knowledge of other disciplines, the use of professional knowledge.

According to the storyline of the task conditions, they can be considered as:

• tasks using everyday situations for the plot of the task;
• tasks using the production technical situation for the plot of the task;
• tasks using a historical plot;
• tasks using knowledge from other areas to develop the plot of the task (geography, biology, chemistry, physics);
• tasks using literary plots;
• tasks with the use of folklore stories.

The solution of the formulated task is an integral part of the tasks for the development of the task; the solvability of the developed task is a criterion for the correctness of the solution of the task. The solution process also makes it possible to classify the developed problems according to some features. For example, according to the use of means for solving a problem, there can be:

• solved by graphic manual means;
• solved with the use of information technology;
• solvable analytically (calculations);
• solved by combined means.

Vitagen-oriented tasks compiled as a result of the solution can be classified in the same way as classical graphic tasks according to the number of solutions and the role of tasks in the formation of graphic knowledge (the classification method is given above).

For example, a student has developed the following problem:

The nail is driven into the wall to a depth of 100 mm at a height of 500 mm. Construct a diagram of a straight line segment represented as a nail if its length is 200 mm.

The wall is the V plane, the floor is the H plane. Take the W plane arbitrarily. Specify visibility.

Fig.5. The solution of the problem

The given task refers to tasks with flat objects, homogeneous in terms of determining the position of the object relative to the projection planes, the task of execution, the task has an incomplete amount of information for the image of the object, since the location of the nail relative to the profile plane of the projection (x coordinate) is not indicated and, therefore, has a set solutions. The solution to this problem can only be graphical and performed both manually and using information technology. The task forms the concept of a projecting line and the position of geometric objects in the 1st and 2nd quadrants. The information presented in the task is part of the student's life experience, which demonstrates in practice the front-projecting straight line and helps to master the topics of projection of flat objects. A complete description of the task from the point of view of the classification of graphic tasks allows you to effectively use it in the educational process.

After analyzing various types of graphic tasks and determining the basis for their systematization and classification, we can conclude the following:

Teaching graphic disciplines requires the mandatory introduction of a practical component educational process, which forms the skills of graphic activity. Practical graphic activity in the learning process consists in solving graphic tasks covering various sections of graphic disciplines, tasks of various levels of complexity, designed to master various graphic concepts, actions and operations that form knowledge of various levels. To achieve this, it is necessary to use the entire range of graphic tasks: from simple ones that form the reproductive level of knowledge, to creative tasks with elements of scientific search, suggesting a productive level of assimilation of graphic knowledge. Systematization of tasks in graphic disciplines makes it possible to effectively and correctly use various types of tasks at different stages of the educational process, coordinate the graphic activities of students of various levels of training and create conditions for their motivational and creative activity and sustainable interest in graphic disciplines, thereby enhancing their independent graphic activity. and improve the quality of graphic preparation.

Reviewers:

Novoselov S.A., Doctor of Pedagogy, Professor, Director of the Institute of Pedagogy and Childhood Psychology, Ural State Pedagogical University, Yekaterinburg city;

Kuprina N.G., Doctor of Pediatric Sciences, Professor, Head of the Department of Aesthetic Education, Ural State Pedagogical University, Yekaterinburg.

Bibliographic link

Turkina L.V. CLASSIFICATION OF GRAPHIC TASKS // Modern problems of science and education. - 2015. - No. 1-1 .;
URL: http://science-education.ru/ru/article/view?id=19360 (date of access: 07/12/2019). We bring to your attention the journals published by the publishing house "Academy of Natural History"

Solving graphic problems in physics

In graphical tasks, the object of study is the graphs of the dependence of physical quantities. Graphs can be given in the condition of the problem or they must be built in the process of solving the problem. To successfully solve graphic problems, you need to be able to "read" them, to see the nature of the relationship between quantities. Let's consider the solution of some graphic problems.

Task #1 (Assignment from version of the exam)

The figure shows a graph of the dependence of the projection of the body's velocity on time.

The projection of the acceleration of the body in the time interval from 12 to 16 s is represented by a graph

To successfully and quickly solve such a task, you need to know the acceleration formula a= . Select the specified area on the chart. In 4 s, the speed changed from -10 m/s to 0 m/s. Hence, a \u003d (0m / s - (-10 m / s)) / 4 s \u003d 2.5 m / s 2.

and 0 means the correct answer is #4.

Task #2 (Assignment from the exam option)

The graph shows the dependence of the speed of the body on time. What is the path traveled by the body up to the point in time t= 4 s?

1) 7 m; 2) 6 m; 3) 5 m; 4) 4 m.

There is no need to “search” for a path in 4 seconds of movement according to the kinematics formulas. This is time-consuming. Let's find the path as the area of ​​the resulting trapezoid. The upper base of the trapezoid is a time interval of 4 s, the lower one is 2 s. The height of the trapezoid is 2 m/s. Next, find the area: S = = 6 m.

Some problems in thermodynamics are solved similarly.

Task #3

The operating cycle of the heat engine is shown in the figure.

Given: ν \u003d 1 mol, P 2 \u003d 6P 1, T 4 \u003d 2T 1, T 1 \u003d 300K

BUT? (for the whole cycle)

First, find the work done in each process.

A 1-2 =0, A 3-4 =0,

A 2-3 \u003d P 2 (V 2 -V 1),

A 4-1 \u003d P 1 (V 1 -V 2). The work done for the entire cycle is:

A \u003d A 2-3 + A 4-1 \u003d P 2 (V 2 -V 1) + P 1 (V 1 -V 2) \u003d

P 2 (V 2 -V 1) - P 1 (V 2 -V 1) \u003d (V 2 -V 1) (P 2 - P 1) \u003d

\u003d (V 2 -V 1) 5 P 1.

Let's write the equation

Mendeleev-Clapeyron.

state (parameters at point 1: P 1 ,V 1 ,T 1):

P 1 V 1 =νRT 1 ;

2 state (point 4): P 1 V 2 =νRT 4; Solving the system of equations, we get:

(V 2 -V 1)P 1 \u003d νRT 4 - νRT 1.

(V 2 -V 1)P 1 \u003d νR (T 4 -T 1) \u003d νRT 1.

(V 2 -V 1) \u003d νRT 1 / P 1.

A \u003d (V 2 -V 1) 5P 1 \u003d (νRT 1 / P 1) ∙ 5P 1 \u003d 5 νRT 1.

Let's find work as the area of ​​a figure (rectangle): A = (P 2 - P 1) (V 2 - V 1) = 5 P 1 νRT 1 / P 1, because P 1 V 1 \u003d νRT 1; P 1 V 2 \u003d νRT 4, whence (V 2 -V 1) \u003d νRT 1 / P 1.

Task #4

Compare the motion graphs of bodies and determine which one has the highest speed.

You can calculate the speed of movement of all bodies and then compare them. But there is a faster way to complete this task. The greater the angle of inclination of the graph to the time axis, the greater the speed of the body. This is consistent with the speed formula : v= , because the ratio of the coordinate change (x – x 0) to the time interval t shows the tangent of the slope of the motion graph to the time axis. The answer is obvious: the highest speed corresponds to graph 2.