Graphic tasks. Modern problems of science and education

Often, a graphical representation of a physical process makes it more visual and thereby facilitates understanding of the phenomenon under consideration. Sometimes making it possible to significantly simplify calculations, graphs are widely used in practice to solve various problems. The ability to build and read them is mandatory for many specialists today.

We consider the following tasks to be graphical tasks:

for construction, where drawings and drawings are very helpful;
schemes solved using vectors, graphs, diagrams, diagrams and nomograms.

1) The ball is thrown vertically upward from the ground with an initial speed v O. Plot a graph of the speed of the ball versus time, assuming that the impacts on the ground are perfectly elastic. Neglect air resistance. [solution ]

2) A passenger who was late for the train noticed that the penultimate car passed him by t 1 = 10 s, and the last one - for t 2 = 8 s. Assuming the train's motion to be uniformly accelerated, determine the delay time. [solution ]

3) In a room high H a light spring with stiffness is attached to the ceiling at one end k, having a length in the undeformed state l o (l o< H ). A block of height is placed on the floor under the spring x with base area S, made of material with a density ρ . Construct a graph of the pressure of the block on the floor versus the height of the block. [solution ]

4) The bug crawls along the axis Ox. Determine the average speed of its movement in the area between the points with coordinates x 1 = 1.0 m And x 2 = 5.0 m, if it is known that the product of the insect’s speed and its coordinate remains constant all the time, equal to c = 500 cm 2 /s. [solution ]

5) To a block of mass 10 kg a force is applied to a horizontal surface. Considering that the friction coefficient is equal to 0,7 , define:

friction force for the case if F = 50 N and directed horizontally.
friction force for the case if F = 80 N and directed horizontally.
draw a graph of the acceleration of the block versus the horizontally applied force.
What is the minimum force required to pull the rope to move the block evenly? [solution ]

6) There are two pipes connected to the mixer. Each pipe has a tap that can be used to regulate the flow of water through the pipe, changing it from zero to the maximum value J o = 1 l/s. Water flows in pipes at temperatures t 1 = 10°C And t 2 = 50°C. Plot a graph of the maximum flow of water flowing out of the mixer versus the temperature of that water. Neglect heat losses. [solution ]

7) Late in the evening a young man tall h walks along the edge of a horizontal straight sidewalk at a constant speed v. On distance l There is a lamppost from the edge of the sidewalk. The burning lantern is fixed at a height H from the surface of the earth. Construct a graph of the speed of movement of the shadow of a person’s head depending on the coordinate x. [solution ]

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

navigation protractor,

parallel ruler,

measuring compass,

drawing compass with pencil.

The lines are drawn with a simple pencil and removed with a soft eraser.

Take the coordinates of a given point from the map. This task can be most accurately performed using a measuring compass. To measure latitude, one leg of the compass is placed at a 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 map and place 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.

Place a point at the given coordinates. The work is usually carried out using a parallel ruler and a measuring compass. The ruler is applied to the nearest parallel and one half of it is moved to the specified 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 injection is made also at the cut of the ruler in the direction of the given longitude. The injection site will be the given point

Measure the distance between two points on a map or plot a known distance from a given point. If the distance between the points is small and can be measured with one compass solution, then the legs of the compass are placed at one and the other point, without changing its solution, and placed on the side frame of the map at approximately the same latitude in which the measured distance lies.

When measuring a large distance, it 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 to take a “round” number of miles (10,20, etc.) from the side frame of the map and count how many times to place this number along the entire line being measured.
In this case, miles are taken from the side frame of the map approximately opposite the middle of the measured line. The remainder of the distance is measured in the usual way. If you need to set aside a small distance from a given point, then remove it with a compass from the side frame of the map and set it off 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 being set aside is large, then they take it from the map frame approximately opposite the middle of the given distance 10, 20 miles, etc. and postpone the required number of times. The remainder of the distance is measured from the last point.

Measure the direction of the true course or bearing line drawn on the map. A parallel ruler is applied to the line on the map and a protractor is placed on the edge 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 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.

Draw a line of true course or bearing from a given point. To perform this task, use a protractor and a parallel ruler. The protractor is placed on the map so that its central stroke coincides with any 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 edge of the protractor ruler, and, having removed the protractor, they move it apart, bringing it 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 any lighthouse or other landmark marked on both maps is taken from the map.
On another map, by plotting the desired direction from this landmark and plotting the distance along it, the given point is obtained. This task is a combination

Problems of this type include those in which all or part of the data is specified in the form of graphical dependencies between them. In solving such problems, the following stages can be distinguished:

Stage 2 - find out from the given graph what quantities the relationship is between; find out which physical quantity is independent, i.e. an argument; what quantity is dependent, i.e., a function; determine by the type of graph what kind of dependence it is; find out what is required - define a function or an argument; if possible, write down the equation that describes the given graph;

Stage 3 - mark the given value on the abscissa (or ordinate) axis and restore the perpendicular to the intersection with the graph. Lower the perpendicular from the intersection point to the ordinate (or abscissa) axis and determine the value of the desired quantity;

Stage 4 - evaluate the result obtained;

Stage 5 - write down the answer.

Reading the coordinate graph means that from the graph you should determine: the initial coordinate and speed of movement; write down the coordinate equation; determine the time and place of meeting of the bodies; determine at what point in time the body has a given coordinate; determine the coordinate that the body has at a specified moment in time.

Problems of the fourth type - experimental . These are problems in which to find an unknown quantity it is necessary to measure part of the data experimentally. The following operating procedure is suggested:

Stage 2 - determine what phenomenon, law underlies the experience;

Stage 3 - think over the experimental design; determine a list of instruments and auxiliary items or equipment for conducting the experiment; think over the sequence of the experiment; if necessary, develop a table for recording the results of the experiment;

Stage 4 - perform the experiment and write the results in the table;

Stage 5 - make the necessary calculations, if required according to the conditions of the problem;

Stage 6 - think about the results obtained and write down the answer.

Particular algorithms for solving problems in kinematics and dynamics have the following form.

Algorithm for solving problems in kinematics:

Stage 2 - write down the numerical values of the given quantities; express all quantities in SI units;

Stage 3 - make a schematic drawing (trajectory of movement, vectors of velocity, acceleration, displacement, etc.);

Stage 4 - choose a coordinate system (you should choose a system so that the equations are simple);

Stage 5 - compile basic equations for a given movement that reflect the mathematical relationship between the physical quantities shown in the diagram; the number of equations must be equal to the number of unknown quantities;

Stage 6 - solve the compiled system of equations in general form, in letter notation, i.e. get the calculation formula;

Stage 7 - select a system of units of measurement (“SI”), substitute the names of units in the calculation formula instead of letters, perform actions with the names and check whether the result results in a unit of measurement of the desired quantity;

Stage 8 - express all given quantities in the selected system of units; substitute into the calculation formulas and calculate the values of the required quantities;

Stage 9 - analyze the solution and formulate an answer.

Comparing the sequence of solving problems in dynamics and kinematics makes it possible to see that some points are common to both algorithms, this helps to remember them better and apply them more successfully when solving problems.

Algorithm for solving dynamics problems:

Stage 2 - write down the condition of the problem, expressing all quantities in SI units;

Stage 3 - make a drawing indicating all the forces acting on the body, acceleration vectors and coordinate systems;

Stage 4 - write down the equation of Newton’s second law in vector form;

Stage 5 - write down the basic equation of dynamics (the equation of Newton’s second law) in projections on the coordinate axes, taking into account the direction of the coordinate axes and vectors;

Stage 6 - find all the quantities included in these equations; substitute into equations;

Stage 7 - solve the problem in general form, i.e. solve an equation or system of equations for an unknown quantity;

Stage 8 - check the dimension;

Stage 9 - obtain a numerical result and correlate it with real values.

Algorithm for solving problems on thermal phenomena:

Stage 1 - carefully read the problem statement, find out how many bodies are involved in heat exchange and what physical processes occur (for example, heating or cooling, melting or crystallization, vaporization or condensation);

Stage 2 - briefly write down the conditions of the problem, supplementing with the necessary tabular values; express all quantities in the SI system;

Stage 3 - write down the heat balance equation taking into account the sign of the amount of heat (if the body receives energy, then put the “+” sign, if the body gives it away, put the “-” sign);

Stage 4 - write down the necessary formulas for calculating the amount of heat;

Stage 5 - write down the resulting equation in general form relative to the required quantities;

Stage 6 - check the dimension of the resulting value;

Stage 7 - calculate the values of the required quantities.

CALCULATION AND GRAPHIC WORKS

Job No. 1

INTRODUCTION. BASIC CONCEPTS OF MECHANICS

Key points:

Mechanical movement is a change in the position of a body relative to other bodies or a change in the position of body parts over time.

A material point is a body whose dimensions can be neglected in this problem.

Physical quantities can be vector and scalar.

A vector is a quantity characterized by a numerical value and direction (force, speed, acceleration, etc.).

A scalar is a quantity characterized only by a numerical value (mass, volume, time, etc.).

Trajectory is a line along which a body moves.

The distance traveled is the length of the trajectory of a moving body, designation - l, SI unit: 1 m, scalar (has a magnitude, but no direction), does not uniquely determine the final position of the body.

Displacement is a vector connecting the initial and subsequent positions of the body, designation - S, unit of measurement in SI: 1 m, vector (has a module and direction), uniquely determines the final position of the body.

Speed is a vector physical quantity equal to the ratio of the movement of a body to the period of time during which this movement occurred.

Mechanical motion can be translational, rotational and oscillatory.

Progressive movement is a movement in which any straight line rigidly connected to the body moves while remaining parallel to itself. Examples of translational motion are the movement of a piston in an engine cylinder, the movement of ferris wheel cabs, etc. During translational motion, all points of a rigid body describe the same trajectories and at each moment of time have the same velocities and accelerations.

Rotational the motion of an absolutely rigid body is a motion in which all points of the body move in planes perpendicular to a fixed straight line, called axis of rotation, and describe circles whose centers lie on this axis (rotors of turbines, generators and engines).

Oscillatory motion is a movement that repeats itself periodically in space over time.

Reference system is a combination of a body of reference, a coordinate system and a method of measuring time.

Reference body- any body chosen arbitrarily and conventionally considered motionless, in relation to which the location and movement of other bodies is studied.

Coordinate system consists of directions identified in space - coordinate axes intersecting at one point, called the origin and the selected unit segment (scale). A coordinate system is needed to quantitatively describe movement.

In the Cartesian coordinate system, the position of point A at a given time relative to this system is determined by three coordinates x, y and z, or radius vector.

Trajectory of movement of a material point is the line described by this point in space. Depending on the shape of the trajectory, the movement can be straightforward And curvilinear.

Movement is called uniform if the speed of a material point does not change over time.

Actions with vectors:

Speed– a vector quantity showing the direction and speed of movement of a body in space.

Every mechanical movement has absolute and relative nature.

The absolute meaning of mechanical motion is that if two bodies approach or move away from each other, then they will approach or move away in any frame of reference.

The relativity of mechanical motion is that:

1) it makes no sense to talk about motion without indicating the body of reference;

2) in different reference systems the same movement can look different.

Law of addition of speeds: The speed of a body relative to a fixed frame of reference is equal to the vector sum of the speed of the same body relative to a moving frame of reference and the speed of the moving system relative to a stationary one.

Control questions

1. Definition of mechanical motion (examples).

2. Types of mechanical movement (examples).

3. The concept of a material point (examples).

4. Conditions under which the body can be considered a material point.

5. Forward movement (examples).

6. What does the frame of reference include?

7. What is uniform motion (examples)?

8. What is called speed?

9. Law of addition of velocities.

Complete the tasks:

1. The snail crawled straight for 1 m, then made a turn, describing a quarter circle with a radius of 1 m, and crawled further perpendicular to the original direction of movement for another 1 m. Make a drawing, calculate the distance traveled and the displacement module, do not forget to show the snail’s movement vector in the drawing.

2. A moving car made a U-turn, describing half a circle. Make a drawing showing the path and movement of the car in a third of the turning time. How many times is the distance traveled during the specified period of time greater than the modulus of the vector of the corresponding displacement?

3. Can a water skier move faster than a boat? Can a boat move faster than a skier?

1 Branch of the Federal State Budgetary Educational Institution of Higher Professional Education "Ural State Transport University"

The training of technical specialists includes a mandatory stage of graphic preparation. Graphic training of technical specialists occurs in the process of performing graphic work of various types, including solving problems. Graphic tasks can be divided into various types, according to the content of the task conditions and according to the actions that are performed by students in the process of solving the problem. Development of a typology of tasks, principles of their classification, division of tasks into various types for their effective use in the learning process, development of task characteristics based on the classification of graphic tasks. To develop 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 we developed for the development of vitality-oriented graphic tasks, classification of the types of task and the product of its implementation into groups in accordance with certain criteria: according to the content of the task, according to actions on graphic objects, according to the coverage of educational material, according to the method of solution and presentation of the results solutions on the role of the task in the formation of graphic knowledge. A comprehensive systematization of graphic tasks at various levels of mastery of the material allows for the comprehensive development of the graphic abilities of students, thereby improving the quality of training of technical specialists.

levels of mastering graphic knowledge

plot of a vitality-oriented task

performed when solving graphic problems

actions and operations

classification of graphics tasks

problem-solving and graphical problem-solving systems

creative interactive tasks for developing vitality-oriented tasks

graphic task of classical content

1. Bukharova G.D. Theoretical foundations of teaching students the ability to solve physical problems: textbook. 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 indicative basis for teaching engineering graphic activity // Education and Science. News of the Ural Branch of the Russian Academy of Education. – 2011. – No. 2 (81). – pp. 31-42

3. Ryabinov D.I., Zasov V.D. Tasks on 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 / Edited by Tulkibaeva N.N., Drapkina M.A. Chelyabinsk: Publishing house of ChGPI “Fakel”, 1995.-120 p.

5. Turkina L.V. Collection of problems on descriptive geometry with vitagen-oriented content / – Nizhny Tagil; Ekaterinburg: UrGUPS, 2007. – 58 p.

6. Turkina L.V. Creative graphic task – structure of content and solution // Modern problems of 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 develop skills and abilities, solve problems of an educational nature, and develop readiness for the development of creative search in the process of professional activity of future specialists.

The variety of types of problems that are offered to students to solve broadens the students’ horizons, teaches them the practical application of knowledge and motivates their independent learning activities. In order for the entire range of educational tasks in a particular discipline to be applied, it is necessary to have an idea of all their diversity, classify them according to certain criteria and purposefully use them to develop 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 developing drawing skills, knowledge of projection theory, and rules for designing graphic images. The purpose of a graphical task is to create a graphical image of a given object, built in accordance with the rules of the Unified System of Design Documentation, or to transform or supplement a given graphical image of an object. The structure of the graphical task is essentially similar to the structure of the physics problem, which was defined by G.D. Bukharova as a complex didactic system, where components (task and solution 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 problem system, as is known, includes the subject, conditions and requirements of the problem; 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 fundamentals, principles and build a system for dividing them into groups. To do this, we offer the concept of typology (classification) of graphic tasks that we have developed. The classification of problems we have developed is similar to the classification of problems in physics, but 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 skills in their application in the development of graphic documentation.

The condition of the task, as an incoming element of the task system, determines the student’s further actions and makes it possible to classify graphic tasks according to the types of graphic actions on objects.

The types of objects on which graphic actions are performed can be as follows:

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

Based on the scope of educational material in descriptive geometry, tasks can be classified into homogeneous (one section) and mixed (several sections) polygenic.

tasks with text conditions;
tasks with graphical conditions;
tasks with mixed content.

Based on the sufficiency of information, tasks are classified into:

tasks defined;
search tasks.

The process of solving a problem determines the solving system and allows you to classify graphical tasks according to the following parameters and characteristics of the process of performing actions on task objects:

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

tasks of determining the position of an object in space relative to projection planes and changing its position;
tasks to determine the relative position of objects;
metric tasks (determining the natural size of objects: dimensions of linear quantities, shapes)

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

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

According to the method of solving graphic problems, they can be:

problems solved graphically;
problems solved by analytical (computational) method;
problems solved in a logical way with a graphical design of the solution.

Based on the use of solution tools, graphical problems are divided into:

tasks solved manually;
problems solved using information technology.

Depending on the number of solutions, the problem can be:

problems that have one solution;
problems with multiple solutions;
problems that have no solutions.

Based on the role of tasks in the formation of graphic knowledge, they can be classified into formative tasks:

graphic concepts (concepts) and terms;
skills and abilities to apply the projection method;
skills and abilities to apply drawing transformation methods;
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 (intersection 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 to apply 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 farther from the frontal projection plane, and 20 mm further from the profile projection plane than from the frontal one.

The problem is homogeneous, its content relates to the “Point and Line” section of the “Descriptive Geometry” discipline. The task requires performing graphical actions on a flat object, the condition of the task is presented in text form, the task has a sufficient amount of information and is not a search task. This is a classic example of a task of determining the position of an object in space relative to projection planes and depicting it in a drawing (diagram). Task - execution of certain actions specified by the condition of the task; This problem can be solved exclusively graphically. It can be solved either manually or using a CAD computer program; the problem has one solution. This task forms graphic concepts and terms (name and position of the projection plane, the concept of “point”, coordinates of a point), skills and abilities in using the projection method - point projection.

The solution to the problem is presented in Figure 1.

Task No. 2. Construct a development of surface B, containing projections of points A and C, and intersecting with surface K - a cylinder of the front-projecting direction, the axis of which intersects the axis of surface B.

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

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

The process of solving a graphic problem given above illustrates a feature of teaching graphic disciplines, which is that geometric objects in projections and graphic constructions are difficult to master for junior students, yesterday's schoolchildren who have a minimum level of graphic training due to the fact that the drawing course has been transferred in variative courses. To motivate graphic cognition and reduce the abstractness of educational material, some teachers proposed tasks with materialized objects and tasks to develop tasks with 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 to develop the task itself. This is information that determines the direction of the student’s further educational actions, the content of the graphic module, within the framework of which a graphic task can be developed, but does not limit the scope of application of the knowledge of the subject and the creative imagination of the student.

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

According to the content requirements, tasks 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 the obligatory use of objects of vitagenic experience;
tasks with mandatory use of objects of professional activity;
tasks with mandatory use of interdisciplinary knowledge;
tasks without special requirements for task objects.

According to the method of searching for means of solving a problem defined in the task development task, 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 development task can be formulated as follows:

Develop a task on descriptive geometry, applying knowledge of the topic “Projecting a point, a line” in a real life situation, having previously studied theoretical principles and considered problems of classical content. When composing a task, use material analogues of geometric objects (point, straight line).

The task is homogeneous, making no demands on the content of the problem being developed, on the nature of the objects used in the task, or on the method of searching for material analogues of geometric objects.

Example of completing a task:

The miner went down into the mine by 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 the point that determines the location of the miner. Take the point of intersection of the earth's surface with the elevator shaft as the origin of the coordinate axes. Take the elevator axis as the Z axis.

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

The content of the developed problem determines the actions to solve the problem and makes it possible to classify creative vitality-oriented problems as well as problems of classical content by types of geometric operations on objects, by the scope of educational material of the graphic discipline, by the type and content of the problem conditions, by actions aimed at the subject of the compiled task, by the sufficiency of information contained in the developed condition of the problem, by the method of searching for means of solution.

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

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

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

Solving a constructed problem is an integral part of completing task development tasks; the solvability of the developed problem is a criterion for the correctness of the solution to the task. The solution process also allows you to classify the developed problems according to certain criteria. For example, the use of problem solving tools can be:

solved by graphical manual means;
solved using information technology;
solvable analytically (by calculations);
solved by combined means.

The vitagen-oriented problems compiled as a result of the solution can be classified in the same way as classical graphic problems by the number of solutions and by the role of the problems in the formation of graphic knowledge (the classification method is given above).

For example, a student 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 in the form of a nail, if its length is 200 mm.

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

Fig.5. The solution of the problem

The given task relates to problems with flat objects, homogeneous in determining the position of the object relative to the projection planes, an execution task, the task has an incomplete amount of information for the image of the object, since the location of the nail relative to the profile projection plane (x coordinate) is not indicated and, therefore, has a set decisions. The solution to this problem can only be graphical and done either manually or using information technology. The task forms the concept of a projecting straight line and the position of geometric objects in the 1st and 2nd quarters. The information presented in the problem is part of the student's life experience, which demonstrates the frontal projection line in practice and helps to master the topics of projection of plane objects. A complete description of the task in terms of classification of graphical tasks allows for its effective use in the educational process.

Having analyzed various types of graphic tasks and determined the basics of their systematization and classification, we can conclude the following:

Teaching graphic disciplines requires the mandatory introduction of a practical component of the educational process, which develops graphic skills. Practical graphic activity in the learning process consists of solving graphic problems 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, forming a reproductive level of knowledge, to creative tasks with elements of scientific research, 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 intensifying their independent graphic activity and improve the quality of graphic preparation.

Reviewers:

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

Kuprina N.G., Doctor of Pedagogical 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 (access date: 07/12/2019). We bring to your attention magazines published by the publishing house "Academy of Natural Sciences"