The place and importance of computer modeling in the school computer science course. Thesis: The use of educational and creative tasks in teaching computer modeling to develop the creative abilities of students Application of computer modeling
Master student
Mordovian State Pedagogical Institute named after M.E. Evsevieva
Department of Informatics and Computer Engineering
Safonov V.I., Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Informatics and Computer Engineering
Annotation:
The article shows the importance of modeling in school course in Informatics. Demonstrated modeling and classification models shown software and interactive environment for the realization of computer simulation.
Keywords:
modeling; computer science; formalization; model; mathematical model; math modeling.
modeling; computer science; formalization; model; mathematical model; mathematical modeling.
UDC 004
The study of modeling is a significant aspect of the preparation of schoolchildren. It is necessary to consider modeling as a way of developing a student's thinking, and in addition, as a tool for solving various problems. Modeling is an important method of scientific knowledge. In various subjects, in addition to computer science, modeling is studied, for example, in mathematics, physics, biology, chemistry, etc. However, directly in the lessons of informatics, the steps of building a model, checking a model, creating models in a variety of computer programs are considered.
Almost all topics of the school computer science course are related to modeling, including algorithms and programming. The authors of computer science textbooks believe that the most important task in teaching modeling is the formation of the ability to analyze and build models. However, these skills are also needed in other sections of informatics, for example, "Information Processes". Thus, modeling is present in many sections of the computer science course, being fundamental in the study of the school computer science course.
In the course of informatics, not only mathematical models are studied, but also informational ones, which include figures, tables, programs, algorithms, which gives informatics an interdisciplinary nature.
A model is a simplified resemblance to a real object or process. The key concept in modeling is the goal. The goal of modeling is the purpose of the future model. The target defines the properties of the original object to be reproduced in the model. Both material objects and processes can be modeled. An information model is a description of an object to be modeled. On the basis of presentation, the models are divided into tabular, graphical, object-information and mathematical.
Formalization is the replacement of a real object or process with its formal description, i.e. its information model. The content line of the modeling theme fulfills the most important task: the development of students' systems thinking.
Spreadsheets are the most common and convenient tool environment for solving mathematical modeling problems. A mathematical model is a description of the state of behavior of any real system (process, object) in the language of mathematics, i.e. using formulas, equations and other mathematical relationships. The implementation of a mathematical model is the use of a specific method for calculating the values of the output parameters from the values of the input parameters. Spreadsheet technology is one method of implementing a mathematical model. There are also methods for the implementation of a mathematical model, which include the compilation of programs in programming languages, the use of mathematical packages (MathCad, Mathematics, 1C: Mathematical Designer, etc.), the use of specialized software systems for modeling. The mathematical models created by such means are called computer mathematical models.
Interconnected teaching of computer science, mathematics and physics makes it possible to acquaint students with the use of applied mathematical packages as a tool for solving typical problems. Therefore, the section "Modeling and formalization" reveals the metasubject role of informatics.
Modeling is one of the difficult sections in the school computer science course. The content-structural component "Modeling and formalization" is an important component of the discipline, which is constantly being improved, as a result of which the study of the methodology of its study has not yet been completed. At the moment, there are a large number of methods of teaching computer modeling, which are actively used in computer science lessons at school.
Software and resource support of the topic "Information Modeling" at the level of basic general and secondary general education is represented by software and Internet resources, in particular, the resources of a single collection of digital educational resources.
One of the available modeling tools is the office application Microsoft Excel, since almost all schools have an MS Office package. Microsoft Excel is a spreadsheet program that allows you to analyze large amounts of data. This program uses more than 600 mathematical, financial, statistical and other specialized functions, with which you can link various tables to each other, choose arbitrary data presentation formats, and create hierarchical structures.
Mathcad is an engineering and mathematical computing application, the industry standard for conducting, distributing, and storing calculations. Mathcad is a universal system, i.e. can be used in any field of science and technology - wherever mathematical methods are applied.
KOMPAS is a computer-aided design system. Using the KOMPAS system, you can create 3-dimensional associative models of parts and individual units that contain original or standardized structural elements.
Blender is a free 3D modeling software. The trick in this program is that during the creation of a 3D scene, the utility window can be divided into parts, each of which will be an independent window with a specific view of the 3D scene, a timeline ruler, and object settings. The number of such parts is limited only by the screen resolution. The application also has tools for spline modeling, and B-splines and Bezier curves are also used to generate 3D objects.
Computer simulation has a number of advantages only when the computing and graphic capabilities of the computer are fully utilized, which will make it possible to realize the variety of capabilities of the corresponding software.
An example of a graphical solution to an equation in the interactive environment "1C: Mathematical Designer":
How many solutions does the equation log1 / 16x = (1/16) x have? At first glance, the graphs of the left and right sides have only one solution lying on the straight line y = x (Fig. 1). However, using the Zoom and Shift Sheet tools, you can zoom in and discover the unexpected intertwining of two graphs that leads to three, not one, roots!
Rice. 1. Solving the graphical equation
Intuition in this case deceives: if we draw these graphs of the equation by hand, we will see that the equation has one root - at the intersection of both graphs with a straight line y = x(i.e. the root of the equation (1/16) x = x). But it is easy to notice and check by substitution that the numbers x= 1/2 and x= 1/4 are also roots. Where do they come from?
If you build graphs in the "Mathematical constructor", then the program will find three points of their intersection (Fig. 2), although in the vicinity of these points at the "normal" scale the graphs "stick together". Using the tool Change scale you can enlarge the image and see how the graphs are "intertwined".
Rice. 2. Solving the graphical equation
Thus, building simple graphical models, such as solving simple math problems, is appropriate already in a basic computer science course. Self-development of graphic models requires programming knowledge, and this refers to material of increased difficulty, which is studied in a specialized computer science course or as part of an elective course.
Bibliography:
1. Korolev, A. L. Computer modeling / A. L. Korolev. Korolyov. - M: BINOM. Knowledge laboratory, 2010 - 230 p.
2. Safonov, V.I. Computer modeling: textbook. allowance / V.I.Safonov. - Mordov. State Ped. in – t. - Saransk, 2009 .-- 92 p.
3. Tarasevich, Yu.Yu. Mathematical and computer modeling. Introductory course: textbook. manual / Yu.Yu. Tarasevich. - M.: LIBROKOM, 2013 .-- 152 p.
Reviews:
11/25/2017, 14:51 Feofanov Alexander Nikolaevich
Review: The article is poorly structured, it is not clear who the reader is. Let them show the difference between 1 and 2 picture. What should be I imagine, and what is - this is a repetition of Fig. 1.After revision, publication in the journal is possible. Doctor of Technical Sciences, prof. Feofanov A.N.
19.12.2017, 20:53 Feofanov Alexander Nikolaevich
Review: Have you made any corrections to the material? (there is nothing on the link) - who is the reader (teacher or student). Who is the article for? - the difference in fig. 1 and 2 - must be different scales. But this has not been done! The scale in the figures remains the same. In 1 figure, the intersection points were not visible, in 2 they were set. But this is not the result of computer simulations. - there are repetitions in the article. Doctor of Technical Sciences, prof. Feofanov A.N.
12/19/2017 09:21 PM Reply to the author's review Natalya Sergeevna Rezaeva:
The reader is mostly a student, but also partly a teacher. It is with the help of the program that you can enlarge this graph and see these intersections, all this increases and decreases in the program, and it makes no sense to increase it in the pictures.
20.12.2017, 7:31 Feofanov Alexander Nikolaevich
Review: It is better and clearer to show an example with triangles or circles (intersections, common points, etc.) And the article does not reveal the functionality of the automated scaling of the "1C: Mathematical Designer" program. Feofanov A.N.
22.01.2018, 16:16 Bovtruk Natalia Sergeevna
Review: the article has a very good title, and the article just does a little analysis of the programs. It is necessary to analyze the essence of the programs in your case more.
480 RUB | UAH 150 | $ 7.5 ", MOUSEOFF, FGCOLOR," #FFFFCC ", BGCOLOR," # 393939 ");" onMouseOut = "return nd ();"> Dissertation - 480 rubles, delivery 10 minutes, around the clock, seven days a week
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Rozova Natalia Borisovna. Application of computer modeling in the learning process: 13.00.01, 13.00.02 Rozova, Natalia Borisovna Application of computer modeling in the learning process (On the example of studying molecular physics in a secondary school): Dis. ... Cand. ped. Sciences: 13.00.01, 13.00.02 Vologda, 2002 163 p. RSL OD, 61: 03-13 / 523-2
Introduction
Chapter 1. Models and modeling in science and teaching 14
1.1 Models and modeling in modern science 14
1.2 Application of models in the process of teaching students 26
1.3 Computer simulation in teaching 33
Chapter 2. Psychological and pedagogical foundations of computer learning 50
2.1 Psychological and pedagogical aspects of computer learning 50
2.2 Features of educational activities and their management based on computer learning 58
Chapter 3. Methods of organizing and conducting physics lessons in the 10th grade of a secondary school when studying the topic "Molecular Physics" using computer modeling 74
3.1 Analysis of the state of computer modeling in the section "Molecular Physics" 74
3.2 Characteristics of the experimental program for computer simulation of the dynamics of many-particle systems and the possibility of its use in the educational process 83
3.3 Methods of organizing and conducting physics lessons in grade 10 when studying the section "Molecular Physics" on the basis of the experimental program 92
4.1 Tasks of the experiment and the organization of its conduct 128
4.2 Analysis of the results of the pedagogical experiment 140
Conclusion 147
Introduction to work
One of the most important directions in the development of society is education. Education “works” for the future, it determines the personal qualities of each person, his knowledge, skills, behavior, culture, worldview, thereby creating the economic, moral and spiritual potential of society. Information technologies are one of the main tools in education, therefore, the development of a strategy for their development and use in education is one of the key problems. Consequently, the use of computer technology is gaining national importance. Many experts believe that at present the computer will allow for a qualitative breakthrough in the education system, since the teacher has got his hands on a powerful teaching tool. Usually there are two main directions of computerization. The first aims at achieving universal computer literacy, the second is to use the computer as a means of increasing the effectiveness of learning.
In the training system, there are two types of activities: teaching and learning. N.F. Talyzina and T.V. Gabay proposed to consider the role of the computer in learning from the point of view of the function that it performs.
If a computer performs the function of controlling educational activities, then it can be considered as a teaching tool that replaces the teacher, since the computer simulates educational activities, asks questions and reacts to the answers and questions of the student as a teacher.
If a computer is used only as a means of educational activity, then its interaction with students is carried out as a "computer user". In this case, the computer is not a learning tool, although it can communicate new knowledge. Therefore, when they talk about computer learning, they mean the use of a computer as a means of managing learning activities.
Despite the fact that there is still no unified classification of training programs, many authors distinguish among them the following five types: training, mentoring, problem learning, imitation and modeling, game. Computer models have the highest rank among the above. According to V.V. Laptev, “a computer model is a software environment for a computational experiment that combines, on the basis of a mathematical model of a phenomenon or process, the means of interactive interaction with the object of the experiment and the development of a means of displaying information ... Computer models are the main object for computational physics, the distinctive method of which is a computational experiment is just like the distinctive method of experimental physics is a natural experiment. " Academician V.G. Razumovsky notes that "with the introduction of computers into the educational process, the possibilities of many methods of scientific cognition increase, especially the modeling method, which can sharply increase the intensity of training, since the very essence of phenomena is highlighted during modeling and their generality becomes clear."
The current state of computer training is characterized by a large set of training programs that differ significantly in quality. The fact is that at the initial stage of the computerization of schools, teachers who used computer learning created their own training programs, and since they were not professional programmers, the programs they created were ineffective. Therefore, along with programs that provide problem learning, computer modeling, and so on, there are a large number of primitive training programs that do not affect the effectiveness of training. Thus, the teacher's task is not to develop training programs, but to use ready-made high-quality programs that meet modern methodological, psychological and pedagogical requirements.
One of the main criteria for the didactic significance of modeling programs is the possibility of conducting research that was previously impracticable in a school physics classroom. The content of physical school education contains a number of sections, in which a natural experiment only qualitatively describes the phenomenon or process being studied. The use of computer models would also make it possible to carry out a quantitative analysis of these objects.
One of these areas of school physics is molecular physics, the state of computer learning in which we will analyze. Studying it, students encounter a qualitatively new form of motion of matter - thermal motion, in which, in addition to the laws of mechanics, the laws of statistics also operate. Natural experiments (Brownian motion, diffusion, interaction of molecules, evaporation, surface and capillary phenomena, wetting) confirm the hypothesis of the molecular structure of matter, but do not allow observing the mechanism of the ongoing physical processes. Mechanical models: Stern's experiment, Galton's board, an installation for demonstrating gas laws make it possible to illustrate Maxwell's law of distribution of gas molecules over velocities and to obtain experimentally the relationships between pressure, volume and temperature necessary to derive gas laws.
The use of modern electronic and electronic computing technology makes it possible to significantly supplement the design and conduct of the experiment. Unfortunately, the number of works on this topic is very small.
The paper describes the use of a computer to demonstrate the dependence of the speed of molecules of various gases on temperature, the calculation of changes in the internal energy of a body during evaporation, melting and crystallization, as well as the use of a computer in the processing of laboratory work. Here is a description of the lesson on determining the efficiency of an ideal heat engine based on the Carnot cycle.
The technique of setting up an experiment with the use of electronic and electronic computing technology is described by V.V. Laptev. The scheme of the experiment looks like this: measured values - sensors - analog-to-digital converter-microcalculator MK-V4 or a Yamaha computer. According to this principle, a universal electromechanical installation was designed for studying the physics of gas laws in a school course.
In the book by AS Kondrat'ev and VV Laptev "Physics and Computer", programs have been developed that analyze in the form of graphs the formula of the Maxwellian distribution of molecules by velocities, use the Boltzmann distribution to calculate the ascent height and study the Carnot cycle.
I.V. Grebenev presents a program that simulates heat transfer by colliding particles of two bodies.
In the article "Modeling the laboratory work of a physical workshop" V.T. Petrosyan and others contain a program for modeling the Brownian motion of particles, the number of which is set by experiment.
The most complete and successful development of the section of molecular physics is the educational computer course "Open Physics" LLP NTs PHYSICS. The models presented in it cover the entire course of molecular physics and thermodynamics. Computer animation, graphs, and numerical results are presented for each experiment. Good quality programs, user-friendly, allow you to observe the dynamics of the process when changing the input macroparameters.
At the same time, in our opinion, this computer course is most suitable for consolidating the material covered, illustrating physical laws, and students' independent work. But the application of the proposed experiments as computer demonstrations is difficult, since they do not have methodological support, it is impossible to control the time of the ongoing process.
It should be noted that to date “no established view has been developed on a specific indication: where and when to use a computer in the learning process, no practical experience has been gained in assessing the impact of a computer on the effectiveness of training, there are no established regulatory requirements for the type, type and parameters of hardware educational software ".
Questions about the methodological support of pedagogical software were posed by I.V. Grebenev. “The most important criterion for the effectiveness of computer learning should probably be considered the possibility of students gaining new, important knowledge of the subject in a dialogue with a computer, by means of such a level or with such a nature of cognitive activity that are impossible with machineless learning, provided, of course, that their pedagogical effect and pays for the time spent by the teacher and the student ”.
This means that in order for the use of a computer to bring real benefits, it is necessary to determine where the existing methodology is imperfect, and to show what properties of a computer and how can increase the effectiveness of training.
Analysis of the state of computer modeling indicates that:
1) computer modeling is represented by a small number of programs in general and in particular those that simulate physical processes based on the provisions of the molecular kinetic theory (MKT);
2) in programs that simulate on the basis of MCT, there are no quantitative results, but there is only a qualitative illustration of any physical process;
3) in all programs the connection between the microparameters of the particle system and its macroparameters (pressure, volume and temperature) is not presented;
4) there is no developed methodology for conducting lessons using computer simulation programs for a number of physical processes of MCT.
This determines the relevance of the study.
The object of the research is the learning process in a secondary general education school.
The subject of the research is the process of using computer modeling in teaching physics in secondary schools.
The purpose of the research is to study the pedagogical possibilities of computer modeling and to develop methodological support for the use of computer modeling programs based on the material of the school physics course.
Based on the purpose of the study, the following tasks were set in the work:
1) conduct a holistic analysis of the possibilities of using computer modeling in the learning process;
2) determine the psychological and pedagogical requirements for educational computer models;
3) analyze domestic and foreign computer programs that simulate physical phenomena and give a real learning effect;
4) develop a computer simulation program based on the physical content of secondary general education (section "Molecular Physics");
5) check the application of the experimental computer simulation program and evaluate its didactic-methodical result.
Research hypothesis.
The quality of knowledge, skills and information culture of students can increase if, in the process of teaching physics, computer simulation programs are used, the methodological support of which is as follows:
Adequately to the theoretical foundations of computer modeling in the learning process, the tasks, place, time, form of using educational computer models are determined;
The variability of forms and methods of management of students' activities is carried out;
Schoolchildren are trained to switch from real objects to models and back.
The methodological basis of the research consists of: systemic and activity-based approaches to the study of pedagogical phenomena; philosophical, cybernetic, psychological theories of computer modeling (A.A. Samarsky, V.G. Razumovsky, N.V. Razumovskaya, B.A.Glinsky, B.V.Biryukov, V.A. other); psychological and pedagogical foundations of computerization of education (V.V. Rubtsov, E.I. Mash-bits) and the concept of developing education (L.S.Vygotsky, D.B. Elkonin, V.V. P.Ya. Halperin).
Research methods:
Scientific and methodological analysis of philosophical, psychological, pedagogical and methodological literature on the problem under study;
Analysis of the experience of teachers, analysis of their own experience in teaching physics in high school and physics methods at a university;
Analysis of modeling computer programs on molecular physics by domestic and foreign authors in order to determine the content of the program;
Modeling physical phenomena in molecular physics;
Computer experiments based on selected simulation programs;
Questioning, conversation, observation, pedagogical experiment;
Methods of mathematical statistics.
Base of research: schools No. 3, 11, 17 of Vologda, Vologda State Natural and Mathematical Lyceum, Physics and Mathematics Faculty of Vologda State Pedagogical University.
The research was carried out in three stages and had the following logic.
At the first stage (1993-1995), the problem, goal, objectives and hypothesis of the study were determined. The philosophical, pedagogical and psychological literature was analyzed in order to identify the theoretical foundations for the development and use of computer models in the learning process.
At the second stage (1995 - 1997), experimental work was carried out within the framework of the problem under study, methodological developments were proposed for the use of computer modeling programs in physics lessons.
At the third stage (1997 - 2000), the analysis and generalization of experimental work was carried out.
The reliability and validity of the results obtained is guaranteed by: theoretical and methodological approaches to the study of the problem of computer modeling in teaching; a combination of qualitative and quantitative analysis of the results, including the use of methods of mathematical statistics; methods adequate to the purpose and subject of the research; scientifically based requirements for the development of a computer simulation program.
The latter requires some explanation. We have developed a program for modeling the dynamics of systems of many particles, the calculation of the motion of which is based on the Verlet algorithm used by H. Gould and J. Tobochnik. This algorithm is simple and gives accurate results even at short time intervals, which is very important when studying statistical patterns. The original interface of the program allows not only to see the dynamics of the process and change the parameters of the system, recording the results, but also makes it possible to change the time of the experiment, stop the experiment, save this frame and start the subsequent work on the model from it.
The system under study consists of particles whose velocities are set randomly and which interact with each other according to the laws of Newtonian mechanics, and the forces of interaction between molecules are displayed by the Lennard-Johnson curve, that is, the program contains a model of a real gas. But by changing the initial parameters, you can bring the model to an ideal gas.
The computer simulation program presented by us allows us to obtain numerical results in relative units, confirming the following physical laws and processes:
a) the dependence of the interaction force and potential energy of particles (molecules) on the distance between them;
b) Maxwell's velocity distribution;
c) the basic equation of molecular kinetic theory;
d) Boyle-Mariotte and Charles laws;
e) Joule and Joule-Thomson experiments.
The above experiments can confirm the validity of the statistical physics method, since the results of the numerical experiment correspond to the results obtained on the basis of the laws of statistics.
The pedagogical experiment confirmed the effectiveness of the lesson methodology using computer simulation programs.
Scientific novelty and theoretical significance of the research:
1. A comprehensive description of computer modeling used in the learning process (philosophical, cybernetic, pedagogical) has been carried out.
2. The psychological and pedagogical requirements for computer training models have been substantiated.
3. The method of computer simulation of the dynamics of many particles was applied, which made it possible for the first time in the school course of molecular physics to create a computer model of an ideal gas, which makes it possible to demonstrate the relationship between the microparameters of the system (velocity, momentum, kinetic, potential and total energy of moving particles) with macroparameters (pressure, volume, temperature).
4. On the basis of computer simulation programs in the physics methodology, the following numerical experiments have been carried out: the basic equation of the molecular kinetic theory has been obtained; the relationship between temperature and the kinetic energy of the translational motion of particles (molecules) is shown; Joule and Joule-Thomson experiments are simulated for ideal and real gases.
The practical significance of the study lies in the fact that the selected content and the developed computer simulation programs can be used in secondary schools to conduct a numerical experiment on a number of issues in molecular physics. A methodology for conducting lessons in molecular physics using simulation computer programs has been developed and tested in an experiment. The materials and results of the research can also be applied in the process of teaching students of pedagogical universities and improving the qualifications of teachers of physics and informatics.
Approbation of the main materials and results "obtained in the course of the study, was carried out
At the international electronic scientific and technical conference (Vologda, 1999);
At the interuniversity scientific-practical conference "Social aspects of youth adaptation to changing living conditions" (Vologda, 2000);
At the second regional scientific and methodological conference "Modern technologies in higher and secondary vocational education" (Pskov, 2000);
At the sixth All-Russian scientific-practical conference "The problem of educational physical experiment" (Glazov, 2001);
When teaching physics in secondary schools in the city of Vologda, in the classroom on the methods of teaching physics with students of VSPU, at seminars of graduate students of VSPU and teachers of the Department of General Physics and Astronomy.
The following are submitted for defense:
1. Theoretical approaches to the application of computer modeling in the learning process and its methodological support.
3. Methods of organizing and conducting physics lessons in the 10th grade of a secondary general education school when studying the topic "Molecular Physics" on the basis of a computer simulation program.
The structure of the thesis.
The structure of the thesis is determined by the logic and sequence of solving the tasks. The dissertation consists of an introduction, four chapters, a conclusion, and a bibliography.
Models and Simulation in Modern Science
Currently, models and modeling, as one of the methods of cognition of the surrounding world, are widely used in science, technology and teaching.
The term "model" comes from the Latin word modulus, which means measure, pattern, norm. A person's holistic view of the world in most cases is reflected in his consciousness in the form of a certain physical model.
In modern philosophy, the following definitions of the concepts of model and modeling are given.
“A model (French modele) in the logic and methodology of science is an analogue (scheme, structure, sign system) of a certain fragment of natural or social reality, a product of human culture, conceptual and theoretical education, etc., of the original model. This analogue serves to store and expand knowledge (information) about the original, its properties and structures, to transform or control it. From an epistemological point of view, a model is a “representative”, “deputy” of the original in cognition and practice. The results of processing and research of the model under certain conditions, clarified in logic and methodology, and specific for various areas and types of models, are transferred to the original. “Modeling is a method of studying objects of knowledge on their models; construction and study of models, real-life objects and phenomena (organic and inorganic systems, engineering devices, various processes - physical, chemical, biological, social) and constructed objects to determine or improve their characteristics, rationalize the methods of their construction, control them, etc. NS." ... Subject and sign modeling are distinguished depending on the type of models. In subject modeling, research is carried out on a model that reproduces certain geometric, physical or functional characteristics of the original. For example, in analog modeling, mechanical, acoustic, hydrodynamic and other phenomena are studied using energy models, since the functioning of the model and the original is described by the same differential equations.
"In sign modeling, models are schemes, drawings, formulas proposed in a certain alphabet (natural or artificial language), etc." ... Modeling is one of the important methods of cognition, therefore it belongs to the epistemological category. The results obtained during the study of models can be transferred to the original if the model reflects the properties of the original.
This classification is based on the method of reproducing the properties of the original in the model. All models are divided into two classes: material and ideal. Material models include models that exist objectively and created by man to reproduce the structure and essence of the process or phenomenon under study.
For spatially similar models, a prerequisite is geometric similarity to their original, because they reflect the spatial properties and relationships of the object. This group includes various layouts, models of technical devices, crystal lattices, etc.
In physically similar models, the similarity of its physical nature with the original and the identity of the laws of motion are necessary. Such models differ from the nature displayed by them only by a change in the spatial or time scale. This group includes operating models of various technical devices, for example, electric motors and generators, ships, aircraft, etc.
Mathematically similar models of the functioning of the objects of research should be described by the same mathematical equations and, as a rule, do not have physical and geometric similarities with the original. Mathematical models include analog, structural, digital, cybernetic models.
Psychological and pedagogical aspects of computer learning
In recent years, domestic and foreign psychologists have paid attention to the role of individual characteristics of students in the learning process. The search for ways to preserve and further develop the individuality of the child, his potential, abilities led to the development of concepts of individualization of learning. Assistance by means of individualization in the implementation of curricula by each student, prevention of student failure; the formation of general educational skills and abilities based on the zone of proximal development of each student; improving learning motivation and developing cognitive interests; the formation of personal qualities: independence, hard work, creativity - the essence of the individualization of training. The main advantage is that individualization allows you to fully adapt the content, methods and pace of the child's learning activity to his characteristics, monitor his actions at each stage of solving the problem, make timely adjustments to the activities of the student and teacher, adapt them to the constantly changing, but controlled situations on the part of the student and teacher. All this allows the student to work economically, control the expenditure of his forces, and achieve higher results.
The technology of individualization of training covers all links of the educational process - goals, content, methods and means. The characteristics of individualized learning are humanistic in their philosophical basis; development factors: bio-, socio- and psychogenic; the principle of management is the "tutor" system, the approach to the child is humane and personal, organizational forms are academic, individual and group; the predominant method is programmed, self-developing, creative. One of the options for individualizing learning is the development of adaptive learning ideas. It takes into account both age and individual characteristics of students. Adaptation can be based on information collected from the learning experience of each student or programmed in advance. An adaptive system, programmed in advance, usually implements training according to a branched program, where, depending on the nature of the error made, it is indicated which auxiliary actions are issued. Adaptive training systems, as a rule, take into account: a) the correctness of the answer, b) the reasons that caused difficulties in completing educational tasks.
The development of technology, the development of various kinds of technical devices make it possible to combine the possibilities of the technology of individualization of teaching with the use of modern computer technology.
Computer training based on flexible and operational adaptation to the individual characteristics of each student is able to prevent the occurrence of psychological discomfort, a decrease in self-esteem, a decrease in educational motivation, as it is able to take into account the student's individuality as much as possible.
L.V. Shenshev describes three options for adaptive learning. The first option is the concept of maximum adaptability of the English cyberneticist G. Pask. The second is the theory of partial adaptability of the American psychologist N. Crowder. The third is the concept of minimal adaptability by B. Skinner. Authors of adaptive learning theories are similar in assessing the reasons for the low effectiveness of traditional learning and in choosing to eliminate these reasons. The concepts of adaptive learning impose certain requirements on the educational process:
1. Prompt adaptation to the individual characteristics of students, taking into account the pace of learning, diagnosing the causes of difficulties, timely adjusting the educational material.
2. Continuous and purposeful management of the affective-motivational sphere of the student, stabilization of his condition. 3. Maintaining continuous dialogue, stimulating student activity.
4. Automation of training.
The fulfillment of the listed requirements can be more easily attributed to computer learning, since the teacher is not able to simultaneously adapt to different students, while the machine is impartial, patient and tireless.
The above concepts of adaptive learning quickly came into mainstream practice, giving rise to a fashionable hobby for teaching devices and programs for computers. Amateur and primitive in their pedagogical capabilities, they ignored the main idea of taking into account individual characteristics and stabilizing the positive emotional mood of students. In connection with this state of affairs, the effectiveness of computer training is called into question. The current case for using computers mirrors the findings of the developers of adaptive learning. This is both the importance of taking into account the dynamics of assimilation, and the automation of teaching, which allows the teacher not to be distracted by organizational tasks.
Analysis of the state of computer modeling in the section "Molecular Physics"
In the first and second chapters, we examined the issues of using computer modeling in teaching from the standpoint of epistemology, pedagogy and psychology, and also determined their place and functions. The use of computer models in teaching physics makes it possible to show the importance of modeling as a method of cognizing the surrounding world, contributes to the formation of abstract thinking, the development of cognitive interest, and the mastery of elements of information culture. At the same time, in order to fully realize such advantages as the possibility of individual learning, management of educational activities, visibility, imitation properties of computer models, it is necessary to identify that branch of physics, the use of computer modeling in which will give a real teaching effect, and to determine methodological techniques for including it in the lesson. ...
The difficulty of studying the course "Molecular Physics and Thermodynamics" in basic secondary school is that here students are faced with a qualitatively new form of motion of matter - thermal motion, in which, in addition to the laws of mechanics, the laws of statistics also operate. In addition, natural experiments (Brownian motion, diffusion, interaction of molecules, evaporation, surface and capillary phenomena, wetting) only confirm the hypothesis of the molecular structure of matter, but do not allow observing the mechanism of the ongoing physical processes. Mechanical models: Stern's experiment, Galton board, apparatus for demonstrating gas laws allow us to illustrate Maxwell's law of molecular velocity distribution and to obtain experimentally the relationships between pressure, volume and temperature necessary to derive gas laws. Increasing the effectiveness of the lesson can give the expansion and improvement of the demonstration or laboratory experiment using a computer (we pointed out the importance of computer models in the study of physics in). Such software tools for conducting a demonstration experiment in the school course of molecular physics and thermodynamics are available, albeit in small numbers. We have reviewed a number of works in, and here we present an analysis of all computer programs known to us used in the study of molecular physics and thermodynamics.
The use of modern electronic and electronic computing technology can significantly improve the design and conduct of the experiment. The article describes the use of a computer to demonstrate the dependence of the speed of nitrogen, hydrogen, argon and air molecules on temperature, the calculation of changes in the internal energy of a body during melting and crystallization, during evaporation and for a gaseous state, as well as the use of a computer in processing the results of laboratory work.
In the same book, a description of a lesson is given on determining the efficiency of an ideal heat engine based on the Carnot cycle. A computer acted as a model of the Carnot cycle, which programmatically implements adiabats and isotherms on the monitor screen, graphically representing the Carnot cycle.
The technique of setting up an experiment with the use of electronic and computer technology is described by V.V. Laptev. He used the versatility of the electrical signal, which not only contains the necessary information, but can also be processed by electronic computers. Therefore, it is necessary to convert all non-electrical quantities participating in the experiment into electrical ones using primary converters - sensors, at the output of which an electrical analog signal appears, usually in the form of an electrical voltage. V.V. Laptev Several sensors for measuring illumination, temperature and time have been developed and manufactured with employees. The sensor signals can be recorded with pointer or digital measuring devices. In order to use digital electronic computing equipment in processing the results of the experiment, it is necessary to convert the analog signal into digital using an analog-to-digital converter, using the appropriate microcircuits for this. Thus, the scheme of the experiment looks like this: measured values - sensors - analog-to-digital converter - MK-64 microcalculator or Yamaha computer. This principle was used to construct a universal electromechanical demonstration installation for studying the physics of gas laws in a school course. The values of pressure, volume and temperature measured in the experiment are in turn recorded on a demo digital indicator and fed to the data bus of the computer, which displays graphs of all possible dependencies between pressure, volume and temperature on the display screen. After plotting the graphs, the numerical values of these quantities are entered into the computer RAM and can be displayed on the display screen in the form of an experiment data table and used for quantitative calculations. Thus, students have the opportunity to observe the quantitative and qualitative characteristics of gas processes simultaneously.
Thesis on the topic:
"The use of educational and creative tasks in teaching computer modeling for the development of students' creative abilities"
Introduction
Chapter I. Theoretical foundations of the development of creative abilities of schoolchildren in the process of teaching computer modeling
Chapter II. Experimental work on the study of the role of educational and creative tasks in teaching computer modeling in the development of students' creative abilities
Conclusion
Bibliography
Application
Introduction
The present time is characterized by the massive introduction of information technologies in all spheres of human life and activities, a change in the role and place of personal computers in modern society. A person who skillfully and effectively owns technology and information has a different, new style of thinking, differently approaches the assessment of the problem that has arisen, to the organization of his activities. The growing role of computer technology presents the user with new opportunities that can affect his education, worldview and creativity.
Our time is a time of change, we have entered the knowledge society. The goals and values of education have changed. If earlier the goal was subject knowledge, now the main value of education is personal development. At the present stage of development, society needs people with good creative potential, who are able to make non-standard decisions, who are able to think creatively.
Unfortunately, the modern mass school still retains a non-creative approach to the assimilation of knowledge. Monotonous, stereotyped repetition of the same actions kills interest in learning. Children are deprived of the joy of discovery and may gradually lose the ability to be creative. One of the main problems of modern education is the low creative initiative of students. The overwhelming majority of schoolchildren show a complete inability to solve problems that do not have standard solution algorithms. The task of the modern school is the development and application of special techniques aimed at the development of creative abilities.
The analysis and systematization of various aspects of the formation and development of creative abilities are devoted to the works of D.B. Bogoyavlenskaya, L.S. Vygotsky, V.N. Druzhinin, N.S. Leites, A.N. Luka, I. Ya. Ponomareva, S.L. Rubinstein, B.M. Teplova, V.D. Shadrikov and others.
The success of a student's intellectual development is achieved mainly in the classroom, where the degree of students' interest in learning, the level of knowledge, and readiness for constant self-education depend on the teacher's ability to organize systematic cognitive activity. their intellectual development.
Many scientists - A.I. Bochkin, V.A. Dalinger, G.G. Vorobiev, V.G. Kinelev, K.K. Colin et al. There are several reasons for this. First, informatics is a fundamental and complex science that covers all spheres of human activity. Secondly, informatics, in a narrow sense, is the science of how computers and telecommunication systems are used in human activity, which, in turn, can play the role of an effective means of developing students' creative abilities.
Our research work is aimed at studying the influence of educational and creative tasks in teaching computer modeling in computer science lessons on the development of the creative abilities of schoolchildren.
The work of V.K. Beloshapki, S.A. Beshenkova, I. V. Galygina, A.G. Hein, A.V. Goryacheva, T.B. Zakharova, I.I. Zubko, A.A. Kuznetsova, B. C. Ledneva, A. S. Lesnevsky, V.P. Linkova, N.V. Makarova, N.V. Matveeva, E.A. Rakitina, Yu.F. Titova, E.K. Henner, A.P. Shestakova, M.I. Shutikova and other authors.
Formation of an idea of the subject area in the mind of the student, associated with the organization of his information activities to analyze the subject area and the formation or use of a system of concepts to describe the subject area. Therefore, we can say that learning is "building in the head" of the student information models of the studied subject area. Therefore, modeling is of particular importance in pedagogy, as a method of cognition of the world around us, information processes occurring in nature and society, and the study of information-logical modeling in the school course of computer science as a learning tool, a learning tool and an object of study is gaining more and more importance. This requires studying the problem of information and information-logical modeling in the learning process.
One of the ways to develop the creative abilities of students is the idea of using educational and creative problems and solving them with the help of a computer. When solving such problems, an act of creativity occurs, a new path is found, or something new is created. This is where special qualities of the mind are required, such as observation, the ability to compare and analyze, to find connections and dependencies, all that together constitute creative abilities.
Solving educational and creative tasks with professionally oriented content is not only a means of realizing intersubject connections, but also a methodological approach that allows you to demonstrate the importance of information technology, both in the modern world and in future specific professional activities. And since such problems are solved with the help of a computer, there is an increasing interest in the study of information technology not only as a tool that allows one to carry out the necessary calculations, but also as a means of modeling real production and other processes.
Object of study: development of creative abilities of students.
Subject of study: development of creative abilities of students in the process of teaching computer modeling.
Purpose of the study: to explore the possibilities of developing the creative abilities of students in teaching computer modeling using educational and creative tasks in the school computer science course.
To achieve the goal of the study, it is planned to solve the following tasks :
Reveal the essence of the creative abilities of schoolchildren;
Determine the place and meaning, goals and objectives of teaching computer modeling;
Study the list of basic knowledge and concepts of computer modeling, reveal their essence;
Expand the role of using educational and creative tasks in teaching modeling in the development of creative abilities;
Experimentally check the effectiveness of the application of creative tasks of computer modeling for the development of students' creative abilities;
Analyze and draw conclusions on theoretical research and experimental verification of the effectiveness of the development of students' creative abilities when using creative tasks of computer modeling.
As research hypotheses it was suggested that one of the most important factors in the development of students' creative abilities is the use of educational and creative tasks.
To solve the set tasks and test the hypothesis, a set of complementary research methods :
computer simulation creativity
Theoretical: analysis of psychological and pedagogical, scientific and methodological, educational literature, materials of periodicals and regulatory documents;
Diagnostic (student testing);
Experiment.
The structure of our research work:
The work consists of an introduction, 2 chapters, a conclusion, a list of used literature and an appendix.
The introduction substantiates the relevance of the topic of this work.
The first chapter examines the theoretical foundations of the development of the creative abilities of schoolchildren in the process of teaching computer modeling.
The second chapter describes the experimental work on the study of the role of educational and creative tasks in teaching computer modeling in the development of students' creative abilities, methodological developments are given.
In the conclusion, the theoretical and practical significance of the results obtained is disclosed.
Chapter I. Theoretical foundations of the development of creative abilities of schoolchildren in the process of teaching computer modeling
1.1 Creativity and creativity
The problem of creativity has become so urgent these days that it is rightfully considered the "problem of the century." Creativity is far from a new subject of research. It has always interested thinkers of all eras and evoked the desire to create a "theory of creativity."
Creation is interpreted as a socio-historical phenomenon that arises and develops in the process of interaction between a subject and an object on the basis of social practice. From the standpoint of philosophy, creativity is the activity of people that transforms the natural and social world in accordance with the goals and needs of a person on the basis of the objective laws of activity.
Creativity is understood as an activity aimed at creating essentially new things; as a process included in the formulation and solution of problems, non-standard tasks; as a form of cognition of reality, etc. ...
The types of creativity are very different in nature - they are artistic, scientific, technical, pedagogical creativity. Following L.S. Vygotsky, who defined the “creativity of social relations,” that is, "creative ability for quick and skillful social orientation", we can distinguish communicative and adaptive creativity.
Creativity is thinking in its highest form, which goes beyond the known, as well as activity that generates something qualitatively new. The latter includes the formulation or selection of a problem, the search for conditions and a way to solve it, and as a result - the creation of a new one.
Creativity can take place in any area of human activity: scientific, production-technical, artistic, political and others.
Creativity is a phenomenon related primarily to specific subjects and associated with the characteristics of the human psyche, the laws of higher nervous activity, mental labor.
Psychologically, creativity is a set of those components of the subject's activity, which for this subject are carriers of qualitatively new ideas.
Applied to the learning process creativity should be defined as a form of human activity aimed at creating values that are qualitatively new for him and have social significance, i.e. important for the formation of personality as a social subject.
Under creative activity we understand such human activity, as a result of which something new is created - whether it is an object of the external world or a construction of thinking leading to new knowledge about the world, or a feeling that reflects a new attitude towards reality.
This is a form of human or collective activity - the creation of a qualitatively new one that has never existed before. A stimulus to creative activity is a problematic situation that cannot be resolved using traditional methods. The original product of activity is obtained as a result of the formulation of a non-standard hypothesis, the discretion of non-traditional interconnections of the elements of a problem situation, and so on.
The prerequisites for creative activity are flexibility of thinking, criticality, the ability to converge concepts, the integrity of perception, and others.
Creative activity is a tool for the development of creative abilities since performing creative tasks in particular and carrying out creative activity in general, the subject uses his abilities to solve a problem and, therefore, develops them in the course of solving.
The makings of creativity are inherent in any person. You need to be able to reveal and develop them.
Creativity ranges from large and flamboyant talent to modest and subtle, but the essence of the creative process is the same for everyone. The difference lies in the specific material of creativity, the scale of achievements and their social significance.
Investigating the nature of creativity, scientists have proposed to call the ability corresponding to creative activity, creativity.
Creativity ( from lat. creatio - creation) - the general ability to be creative, characterizes the personality as a whole, manifests itself in various spheres of activity, is considered as a relatively independent factor of giftedness.
Creativity is an integrative ability that incorporates systems of interconnected abilities - elements. For example, creative abilities are imagination, associativity, fantasy, daydreaming.
The impetus for highlighting creativity was the data on the lack of connection between traditional tests of intelligence and the success of solving problem situations.
It was recognized that the latter (creativity) depends on the ability to use the information given in tasks in different ways at a fast pace. This ability was called creativity and began to be studied independently of intelligence - as an ability that reflects the property of an individual to create new concepts and form new skills. Creativity is associated with the creative achievements of an individual.
From an activity point of view, creativity can manifest itself in different ways: both at the level of an integral personality (scientific, artistic, pedagogical creativity), and individual components of cognitive activity - in the course of solving creative problems, participating in projects, etc. But you can always find a manifestation of the ability to establish at first glance unexpected connections and relationships, when a creative person independently builds a system of relations with the subject and social environment. And this is what should be considered the most important in the creative process, without denying, nevertheless, the significance of the final result. Thus, in the pedagogical terms, the main thing in creativity is that the student in the course of cognitive creative activity realizes his significance as a "transformer of the world", a discoverer of a new one, realizing himself as a person. And where the teacher managed to achieve this, we can talk about the formation of a reflexive attitude towards creativity, which also implies the presence of one's own point of view, a certain courage and independence in decision-making.
Creativity is a fusion of many qualities. And the question of the components of human creativity is still open, although at the moment there are several hypotheses regarding this problem.
The well-known Russian researcher of the problem of creativity A.N. Onion, based on the biographies of prominent scientists, inventors, artists and musicians, distinguishes the following Creative skills :
1. Ability to see the problem where others do not see it.
2. The ability to curtail mental operations, replacing several concepts with one and using symbols that are more and more information-capacious.
3. Ability to apply the skills acquired in solving one problem to solving another.
4. The ability to perceive reality as a whole, without splitting it into parts.
5. Ability to easily associate distant concepts.
6. The ability of memory to give out the right information at the right moment.
7. Flexibility of thinking.
8. Ability to choose one of the alternatives for solving a problem before checking it.
9. Ability to incorporate newly perceived information into existing knowledge systems.
10. The ability to see things as they are, to distinguish the observed from what is introduced by the interpretation.
11. Ease of generating ideas.
12. Creative imagination.
13. Ability to refine details, to improve the original concept.
Candidates of psychological sciences V.T. Kudryavtsev and V.S. Sinelnikov, based on a wide historical and cultural material (history of philosophy, social sciences, art, individual spheres of practice) identified the following universal creativity developed in the course of human history:
1. Realism of imagination - figurative grasping of some essential, general tendency or pattern of development of an integral object, before a person has a clear concept of it and can enter it into a system of strict logical categories.
2. Ability to see the whole before the parts.
3. The over-situational-transformative nature of creative solutions - the ability, when solving a problem, not just to choose from the alternatives imposed from the outside, but to independently create an alternative.
4. Experimentation - the ability to consciously and purposefully create conditions in which objects most vividly reveal their essence hidden in ordinary situations, as well as the ability to trace and analyze the features of the "behavior" of objects in these conditions.
Scientists and educators involved in the development of programs and methods of creative education based on TRIZ (theory for solving inventive problems) and ARIZ (algorithm for solving inventive problems) believe that one of the components of creativity a person is made up of the following abilities:
1. Ability to take risks.
2. Divergent thinking.
3. Flexibility in thinking and acting.
4. The speed of thinking.
5. Ability to express original ideas and invent new ones.
6. Rich imagination.
7. Perception of the ambiguity of things and phenomena.
8. High aesthetic values.
9. Developed intuition.
Many psychologists associate the ability for creative activity, first of all, with the peculiarities of thinking. In particular, the well-known American psychologist J. Guilford, who studied the problems of human intelligence, established that the so-called divergent thinking... People with this type of thinking, when solving a problem, do not concentrate all their efforts on finding the only correct solution, but begin to look for solutions in all possible directions in order to consider as many options as possible. Such people tend to form new combinations of elements that most people know and use only in a certain way, or to form connections between two elements that at first glance have nothing in common. A divergent way of thinking is at the heart of creative thinking.
Divergent thinking characterizes :
· rapidity- ability to express the maximum the number of ideas, ways to solve a particular problem, and here their quantity is important, not quality;
· flexibility- the ability to nominate varied ideas, for example, related to the use of objects, methods, etc. (in the most common test for checking the flexibility of thinking, it is proposed to come up with different ways to use an object of everyday use);
· originality- the ability to generate new non-standard ideas, distant associations, find unusual answers that differ from the generally accepted ones;
· accuracy- ability improve product of creativity, adding details, strive for completeness.
However, the success of creative achievements provides a special combination of two types of thinking - divergent and convergent. Only with a high level of ability to "act in the mind", a rich imagination based on personal experience and knowledge, high emotionality, is it possible to display a high level of creativity.
Creative thinking - plastic and original thinking, in which the subject assumes many decisions. In cases where an ordinary person can find only one or two, it is not difficult for creative thinking to move from one aspect of the problem to another, not limited to one single point of view, it generates unexpected, non-trivial, unusual solutions. Both intuition and logic are inherent in the mechanism of creative thinking.
In the process of studying abilities, the important role of imagination in the disclosure and expansion of creative possibilities was revealed.
Imagination is the process of transforming representations that reflect reality, and the creation of new representations on this basis.
The most important value of imagination is that it allows you to imagine the result of labor before it begins, thereby orienting a person in the process of activity.
Imagination and creativity are closely related to each other. The connection between them, however, is in no way such that one can proceed from imagination as a self-sufficient function and derive creativity from it as a product of its functioning. The leading is the inverse relationship; imagination is formed in the process of creative activity. The specialization of various types of imagination is not so much a prerequisite as the result of the development of various types of creative activity. Therefore, there are as many specific types of imagination as there are specific, unique types of human activity - constructive, technical, scientific, artistic, pictorial, musical, etc. All these types of imagination, which are formed and manifested in various types of creative activity, constitute a kind of the highest level - creative imagination .
The creative imagination arising in labor presupposes the independent creation of images that are realized in the original and valuable products of activity 926, p.65].
In any kind of activity, creative imagination is determined not so much by what a person can conceive, regardless of the real requirements of reality, but by how he knows how to transform reality, burdened with random, insignificant details.
Thus, having analyzed the above approaches to disclosing the concepts of "creativity", "creativity" and the definition of the constituents of creative abilities, we can conclude that, despite the difference in their definition, researchers unanimously single out creative thinking and creative imagination as essential components of creative abilities.
1.2 Teaching computer modeling in the school computer science course
In our research work, we assume that the most effective in terms of developing the creative abilities of students is the material related to information modeling. Before testing this hypothesis, let us consider the place and significance of computer modeling, the goals and objectives of teaching computer modeling and the concepts formed in teaching modeling.
1.2.1 The place and importance of computer modeling in the school computer science course
In the obligatory minimum of the content of education in informatics there is a line "Modeling and formalization", which, along with the line of information and information processes, is the theoretical basis of the basic course of informatics.
The topic of modeling should not be assumed to be purely theoretical and independent of all other topics. Most of the sections of the basic course are directly related to modeling, including topics related to the technological line of the course. Text and graphic editors, DBMS, spreadsheet processors, computer presentations should be considered as tools for working with information models. Algorithmization and programming are also directly related to modeling. Consequently, the modeling line is cross-cutting for many sections of the basic course.
According to Beshenkov S.A. and other topics "Information and information processes" and "Formalization and modeling" are key topics in the course of computer science. These topics combine such traditional course topics as "Algorithms and Executors", "Information Technologies", etc. into a single whole.
The creators of the author's courses "Informatics in games and tasks" and "Informatics-plus" believe that the main task of the school computer science course is the formation and development of the ability to analyze and build information-logical models.
Boyarshinov M.G. considers it expedient to introduce a computer modeling course within the framework of the subject of informatics, the purpose of which will be to familiarize students with the methods of solving problems in physics, chemistry, mathematics, economics, ecology, medicine, sociology, humanitarian disciplines, design and technological problems using modern computer technology.
A.A. Kuznetsov, S.A. Beshenkov, E.A. Rakitina believe that the main components of the informatics course, which give it a systemic character, are "Information Processes", "Information Models", "Information Foundations of Management". The solution to the problem always begins with modeling: building or choosing a number of models: the model of the content of the problem (formalization of conditions), the model of the object chosen as a working one for solving this specific problem, the model (method) of the solution and the model of the process of solving the problem.
Thus, the study of information processes, like any phenomenon of the external world in general, is based on the modeling methodology. The specificity of informatics is that it uses not only mathematical models, but also models of all kinds of forms and types (text, table, figure, algorithm, program) - information models. The concept of the information model gives the computer science course that wide range of intersubject connections, the formation of which is one of the main tasks of this course in basic school. The very activity of building an information model - information modeling is a generalized type of activity that characterizes information science.
One of the effective methods of cognizing the surrounding reality is the modeling method, which is a powerful analytical tool that has absorbed the entire arsenal of the latest information technologies.
The generalizing nature of the concept of "information modeling" is due to the fact that when working with information, we always either deal with ready-made information models (we act as their observer), or we develop information models.
Information modeling is not only an object of study in computer science, but also the most important way of cognitive, educational and practical activity. It can also be viewed as a method of scientific research and as an independent activity.
I. I. Zubko information modeling defines as "a new general scientific method of cognizing objects of the surrounding reality (real and ideal), focused on the use of a computer." Modeling is seen as a way of knowing, on the one hand, and as content that must be assimilated by students, on the other. The author believes that the most effective teaching of information modeling is possible if the project method is implemented in practice, which integrates research, independent and creative work in a variety of ways.
Galygina I.V. believes that training in information modeling is advisable to be carried out on the basis of the following approaches:
model, in accordance with which modeling is considered as an instrument of cognition, an object of study and a means of teaching;
object, implying the selection and analysis of different types of objects: the object of study, the information model as a new object, objects of the modeling language used to build the model.
Information modeling in pedagogy can be considered in three aspects, as:
a cognitive tool, since the acquisition of new knowledge about a real object corresponding to an information model, objects of the modeling language used to describe this model occurs in the process of building and researching the model;
a learning tool, since the learning process in most cases is associated with the operation of information models of the studied object, such as a verbal description, a graphic image,
formula representation of regularities, etc .;
the object of study, since the information model can be considered as an independent information object, with its inherent features, properties, characteristics.
The main difference between these aspects from the point of view of the student is that in the first case, in the process of cognitive activity, the student himself builds a model of the studied object based on his own experience, knowledge, and associations. In the second case, the student is provided with a model of the studied object, developed by the teacher, the author of the textbook or the creator of a scientific theory. In the latter case, the set of models is the object under study.
Inclusion in the content line "Modeling and formalization" of the basic course of informatics of the module "Information Modeling" will create a solid foundation for:
conscious use of information models in educational activities;
acquaintance of students with the methodology of scientific research activities;
subsequent in-depth study of information modeling in specialized courses in computer science.
Titova Yu.F. believes that the most important educational function is the development of the creative potential of students. The experience of creative activity is formed through the solution of problematic tasks of different directions and, in particular, through research activities. Modeling is one of the most important research tools. The author has developed a methodology for teaching modeling in a basic computer science course, combining theoretical material, which is based on a formalized approach to the development and research of models, and a set of research tasks that integrates knowledge from various educational areas. The author believes that the use of this technique will ensure the development of a wide range of intellectual skills in students, such as abstraction and concretization, generalization, classification, analysis, and comprehension of the results of their actions.
1.2.2 Goals and objectives of teaching modeling and formalization
Goals and objectives of teaching informatics in basic school are formulated as follows:
Acquisition of computer literacy and initial competence in the use of information and communication technologies, the simplest computer models in solving educational and practical problems in school and outside it; obtaining the necessary training to use the methods of informatics and information technology means in the study of the academic disciplines of the basic school and educational programs of the subsequent stage of training, as well as for the development of professional activities in demand in the labor market: mastering the skills of working with various types of information using a computer and other means of information technologies, the ability to apply these skills: to search, select, critically evaluate, organize, present and transmit information, plan and organize their own information activities and their results;
Gaining experience in the implementation of individual and collective projects related to various academic disciplines, including publishing school magazines, creating school pages on the Internet, virtual local history museums, etc. using information and communication technologies; use of information available on the Internet and on various media;
Mastering the system of knowledge related to the informational picture of the world, including: basic concepts necessary for the formation of specific ideas about information processes, systems and technologies; ideas about the generality and patterns of information processes in various social and technological systems, about the mechanisms of perception and processing of information by humans, technological and social systems, about a modern information civilization;
Acquaintance with the use of information and communication technologies as methods of cognition of nature and society, observation and registration of natural and social phenomena, presentation of their results in the form of information objects;
Development of cognitive interests, intellectual creative abilities in information activities;
Fostering the necessary norms of behavior and activity in accordance with the requirements of the information society as a natural stage in the development of civilization.
There is no doubt that computer modeling plays an important role in achieving the goals and objectives of teaching computer science.
The state educational standard provides for the study of issues related to information modeling, both in the basic course of the basic school and in the senior classes. The approximate program of the computer science course recommends studying the topic "Formalization and Modeling" in the 8th grade at the level of examples of modeling objects and processes. First of all, it is supposed to use graphical and tabular models. In the senior grades, a general (theoretical) introduction to the topic and the study of various types of computer modeling at the level of mathematical ("calculation"), graphic, simulation models associated with social, biological and technical systems and processes is provided. Elective courses for high school students are an effective form of advanced study of computer modeling.
Basic concepts, which should be assimilated by students after studying the section "Formalization and Programming":
Object, model, modeling; formalization; information model; information technology for solving problems; computer experiment.
At the end of the section, students should know :
· About the existence of many models for the same object;
· Stages of information technology for solving problems using a computer.
students should be able to :
· Give examples of modeling and formalization;
· Give examples of a formalized description of objects and processes;
· Give examples of systems and their models.
· Build and explore the simplest information models on a computer.
V a sample program in computer science and information technology, compiled on the basis of the federal component of the state standard of basic general education for the content line " Formalization and modeling "is given 8 hours. It is supposed to study the following issues:
Formalization of the description of real objects and processes, examples of modeling objects and processes, including computer modeling. Computer controlled models.
Types of information models. Blueprints. 2D and 3D graphics.
Diagrams, plans, maps.
Table as a modeling tool.
- Cybernetic model of control: control, feedback.
Practical work:
1. Setting up and conducting an experiment in a virtual computer laboratory.
2. Building a genealogical tree of the family.
3. Creation of a diagram and drawing in the computer-aided design system.
4. Construction and research of a computer model that analyzes the results of measurements and observations using a programming system.
5. Construction and research of a computer model that analyzes the results of measurements and observations using dynamic tables.
6. Construction and research of a geoinformation model in spreadsheets or a specialized geoinformation system.
Based on this, the following division of the "Formalization and Modeling" line into topics is possible:
· An object. Classification of objects. Object models. 2h
· Classification of models. The main stages of modeling. 2h
· Formal and informal statement of the problem.
· Basic principles of formalization. 2h
· The concept of information technology for solving problems.
· Building an information model. 2h
Educational tasks solved in the course of studying information modeling.
The solution of the tasks listed below makes it possible to have a significant impact on the general development and formation of the students' worldview, to integrate knowledge on different disciplines, to work with computer programs at a more professional level.
General development and formation of students' worldview.
When teaching information modeling, a developmental function must be performed, students continue their acquaintance with another method of cognizing the surrounding reality - the method of computer modeling. In the course of working with computer models, new knowledge, skills, and abilities are acquired. Some previously obtained information is concretized and systematized, viewed from a different angle.
Mastering modeling as a method of cognition.
The main emphasis should be placed on the development of a general methodological approach to the construction of computer models and work with them. Necessary:
1.demonstrate that modeling in any area of expertise has similarities; it is often possible to obtain very similar models for different processes;
2. to highlight the advantages and disadvantages of a computer experiment in comparison with a full-scale experiment;
3. to show that both the abstract model and the computer represent the ability to cognize the world around, and sometimes control it in the interests of a person.
Development of practical skills in computer modeling.
Using the example of a number of models from various fields of science and practice, it is necessary to trace all the stages of computer modeling from the study of the simulated subject area and the formulation of the problem to the interpretation of the results obtained in the course of a computer experiment, to show the importance and necessity of each link. When solving specific problems, it is necessary to highlight and emphasize the corresponding stages of working with the model. The solution to this problem involves the gradual formation of practical modeling skills, for which educational tasks with a gradually increasing level of complexity and computer laboratory work are used.
Promotion of vocational guidance and the development of the creative potential of students.
Students of the senior stage of school are faced with the problem of choosing a future profession. Conducting a course in computer modeling is able to identify those of them who have the ability and inclination to research activities. Students' ability to conduct research should be developed in various ways, throughout the course, to maintain interest in performing computer experiments with various models, to offer tasks of increased complexity to complete. Thus, the development of the creative potential of students and career guidance is one of the objectives of the course.
Overcoming subject dissociation, knowledge integration.
Within the framework of the training course, it is advisable to consider models from various fields of science, which makes the course partially integrated. In order to understand the essence of the phenomenon under study, to correctly interpret the results obtained, it is necessary not only to master the techniques of modeling, but also to navigate the area of knowledge where the model research is carried out. The implementation of interdisciplinary connections in such a course is not only declared, as is sometimes the case in other disciplines, but is often the basis for mastering the educational material.
Development and professionalization of computer skills.
Students are given the task of not only realizing the proposed model on a computer, but also most clearly, in an accessible form, to display the results obtained. Construction of graphs, diagrams, dynamic objects can help here, animation elements are also useful. The program must have an adequate interface, conduct a dialogue with the user. All this presupposes additional requirements for knowledge and skills in the field of algorithms and programming, introduces them to a more complete study of the possibilities of modern paradigms and programming systems.
1.2.3 Formation of basic concepts in teaching computer modeling
At the present stage of human development, it is impossible to find such an area of knowledge in which models would not be used to one degree or another. The sciences, in which the appeal to model research has become systematic, no longer rely only on the intuition of the researcher, but develop special theories that reveal the laws of the relationship between the original and the model.
The history of modeling goes back thousands of years. The person appreciated early and often used the method of analogies in practice. Simulation has come a long way - from intuitive analogy to a strictly scientific method.
Before starting teaching modeling, it is necessary to focus the attention of students on the relevance of what is being studied: a person has long been using modeling to study objects, processes, phenomena in various fields. The results of these studies serve to determine and improve the characteristics of real objects and processes; to understand the essence of phenomena and develop the ability to adapt or manage them; for the construction of new objects or the modernization of old ones. Modeling helps a person to make informed and well-considered decisions, to anticipate the consequences of their activities. Thanks to computers, not only the scope of modeling is significantly expanded, but also a comprehensive analysis of the results obtained is provided.
Throughout the Formalization and Modeling section, students become familiar with the basics. Students should understand what a model is and what types of models are. This is necessary so that, while conducting research, students would be able to choose and effectively use the software environment and appropriate tools suitable for each model.
The study of the section proceeds in a spiral: it begins with the concept of "object".
An object is a certain part of the world around us, which can be considered as a whole.
Object properties - a set of characteristics of an object, by which it can be distinguished from other objects.
After the systematization of the concepts associated with the object, there is a smooth transition to the concepts of model, modeling, classification of models.
The terms "model", "modeling" are inextricably linked, so it is advisable to discuss them at the same time.
The word "model" comes from the Latin word modelium, which means measure, image, method, etc. Its original meaning was associated with the art of building, and in almost all European languages it was used to denote an image, or prototype, or thing, similar in some respect to another thing.
In the explanatory dictionary "Informatics" a model is understood as "a real physical object or process, a theoretical construction, an information image representing any properties of the object, process or phenomenon under study."
In the philosophical literature, one can find definitions that are close in meaning, which are generalized as follows: "A model is used in the development of a theory of an object in the case when its direct following is not possible due to the limitations of the current level of knowledge and practice. Data on an object of direct interest to the researcher is obtained by studying another object, which is combined with the first commonality of characteristics that determine the qualitative and quantitative specifics of both objects. "
In a similar definition, V.A. Shtoff, such model features:
· It is a mentally imagined or materially realizable system;
· It reproduces or displays the object of research;
· It is able to replace objects;
· Its study gives new information about the object.
A.I. Uemov highlights generalized model features :
1. A model cannot exist in isolation, because it is always associated with the original, that is, that material or ideal system that it replaces in the process of cognition.
2. The model should not only be similar to the original, but also different from it, and the model reflects those properties and relationships of the original that are essential for the person who uses it.
3. The model has a specific purpose.
Thus, model- it is a simplified (in one sense or another) image of the original, inextricably linked with it, reflecting the essential properties, connections and relationships of the original; a system, the study of which serves as a tool, a means for obtaining new and (or) confirming existing information about another system.
The concept of a model refers to fundamental general scientific concepts, and modeling is a method of cognizing reality used by various sciences.
Modeling - building models for studying objects, processes, phenomena.
Simulation object- a broad concept that includes objects of animate or inanimate nature, processes and phenomena of reality. The model itself can be either a physical or an ideal object. The former are called full-scale models, the latter are called information models. For example, a building model is a full-scale model of a building, and a drawing of the same building is its information model presented in graphic form (graphic model).
Classification of information models can be based on different principles. If we classify them according to the dominant technology in the modeling process, then we can distinguish mathematical models, graphic models, simulation models, tabular models, statistical models, etc. (biological) systems and processes, models of processes of optimal economic planning, models of educational activities, models of knowledge, etc. Classification issues are important for science, because they allow you to form a systematic view of the problem, but their importance should not be overestimated. Different approaches to classifying models can be equally useful. In addition, a specific model can by no means always be attributed to one class, even if we limit ourselves to the list above.
Material (full-scale) and information models.
According to the method of presentation, models are divided into material and informational (see. Scheme 2).
Material models can otherwise be called objective or physical. They reproduce the geometric properties of the original and have a real embodiment.
Examples of material models:
1. Children's toys (dolls - a model of a child, soft animal toys - a model of live animals, cars - a model of real cars, etc.).
2. Globe - a model of the planet Earth.
3. School aids (human skeleton - a model of a real skeleton, a model of an oxygen atom, etc.)
4. Physical and chemical experiments.
Information models cannot be touched or seen, they have no material embodiment, because they are built only on information.
Information model - a set of information that characterizes the properties and states of an object, process, phenomenon, as well as the relationship with the outside world.
Information models include verbal and sign models.
Verbal model is an informational model in mental or spoken form.
Examples of verbal patterns:
1. Model of human behavior when crossing the street. A person analyzes the situation on the road (traffic signals, the presence and speed of cars and develops a model of his movement)
2. The idea of the inventor - the model of the invention.
3. A musical theme that flashed through the composer's head - a model of a future piece of music.
Sign model - an information model expressed by special signs, i.e. by means of any formal language.
Examples of iconic models:
1. Drawing of kitchen furniture - a model of furniture for the kitchen.
2. Scheme of the Moscow metro - a model of the Moscow metro.
3. The graph of changes in the euro exchange rate is a model of growth (depreciation) of the euro exchange rate.
Verbal and sign models are usually interconnected. A mental image (for example, a path to a certain address) can be clothed in a symbolic form, for example, in a diagram. Conversely, the sign model helps to form the correct mental image in the mind.
According to the method of implementation, informational sign models are divided into computer and non-computer ones.
Information models are used in theoretical studies of modeling objects. Nowadays, the main tool for information modeling is computer technology and information technology.
A computer model is a model implemented by means of a software environment.
Computer modelling includes the progress of the realism of the information model on a computer and the study with the help of this model of the object of modeling - a computational experiment.
It is convenient to implement graphic, tabular and mathematical modeling by means of a computer. For this, there are now a variety of software tools: programming systems (SP), electronic tables (ET), mathematical packages (MP), database management systems (DBMS), graphic editors (GR), etc.
Formalization.
The subject area of computer science includes tools and methods of computer modeling. A computer model can only be created on the basis of a well-formalized information model. What is formalization?
Formalization of information about a certain object is its reflection in a certain form. You can also say this: formalization is the reduction of content to form. Formulas describing physical processes are the formalization of these processes. The radio circuit of an electronic device is a formalization of the functioning of this device. The notes written on a sheet of music are the formalization of music, etc.
A formalized information model is a certain set of signs (symbols) that exist separately from the modeling object and can be transmitted and processed. Implementation of an information model on a computer comes down to its formalization into data formats that a computer can "handle" with.
But we can talk about the other side of formalization as applied to a computer. A program in a certain programming language is a formalized representation of the data processing process. This does not contradict the above definition of a formalized information model as a set of signs, since a machine program has a sign representation. A computer program is a model of human activity in information processing, reduced to a sequence of elementary operations that a computer processor can perform. Therefore, computer programming is the formalization of the information processing process. And the computer acts as the formal executor of the program.
Information Modeling Stages
In the process of modeling, 4 stages are distinguished (see. Scheme 3):
1. Statement of the problem.
2. Development of the model.
3. Computer experiment.
4. Analysis of the simulation results.
 |
Formulation of the problem
Description of the task
The task (or problem) is formulated in ordinary language and the description should be clear. The main thing at this stage is to define the object of modeling and understand what the result should be.
Formulation of the simulation goal
Modeling goals can be:
Knowledge of the surrounding world;
Creation of objects with specified properties (this goal corresponds to the formulation of the problem "how to do to ...");
Determination of the consequences of impact on the object and making the right decision (this goal corresponds to the statement of the problem "what will happen if ...");
Determination of the effectiveness of object (process) management.
Object analysis
At this stage, based on the general formulation of the problem, the modeled object and its main properties are clearly identified. Since in most cases the original object is a whole set of smaller components that are in some interconnection, the analysis of the object will imply the decomposition (dismemberment) of the object in order to identify the components and the nature of the connections between them.
2. Model development
Information model
At this stage, the properties, states and other characteristics of elementary objects are revealed, an idea of the elementary objects that make up the original object is formed, i.e. information model.
Iconic model
The information model, as a rule, is presented in one or another symbolic form, which can be either computer or non-computer.
Computer model
There are a large number of software systems that allow research (modeling) of information models. Each environment has its own tools and allows you to work with certain types of information objects, which causes the problem of choosing the most convenient and effective environment for solving the problem.
3. Computer experiment
Simulation plan
The modeling plan should reflect the sequence of work with the model. Test development and model testing should be the first items in this plan.
Testing- the process of checking the correctness of the model.
Test- a set of initial data for which the result is known in advance.
If the test values do not match, it is necessary to look for and eliminate the cause.
Modeling technology
Simulation technology- a set of purposeful actions of the user over the computer model.
4. Analysis of simulation results
The ultimate goal of modeling is decision making, which should be developed on the basis of a comprehensive analysis of the results obtained. This stage is decisive - either the research continues (return to 2 or 3 stages), or ends.
Testing and experimenting results are the basis for developing a solution. If the results do not correspond to the goals of the task, then mistakes were made in the previous stages. This may be an oversimplified construction of an information model, or an unsuccessful choice of a method or environment for modeling, or a violation of technological techniques when building a model. If such errors are found, then the model needs to be edited, i.e. return to one of the previous stages. The process continues until the simulation results meet the objectives of the simulation.
When solving a specific problem, some of the stages can be excluded or improved, some added.
1.3 Development of creative abilities of students when using educational and creative tasks of computer modeling
The list of goals, the achievement of which is ensured by teaching computer science at the stage of basic general education, indicates the development of creative abilities by means of ICT. If we look at the goals of teaching computer science and information technology at the stage of secondary (complete) education, we will see that here, in addition to ICT tools, it is assumed the development of creative abilities through the development and use of computer science methods. In our opinion, it is modeling and formalization that are to the greatest extent those methods of informatics, the development and use of which, in combination with their implementation by means of ICT, will lead to an increase in the level of development of creative abilities.
Modeling is a creative process, therefore, teaching this topic has ample opportunities to develop the creative abilities of students. Let's consider some aspects of teaching modeling in a school computer science course.
According to M.P. Lapchik and others. The topic "The main stages of computer modeling" should be studied in specialized courses focused on modeling. The same authors point out that when studying the line "Modeling and formalization" in the basic course, students should be able to "carry out in simple cases a system analysis of an object (formalization) in order to build its information model" and "conduct a computational experiment on the simplest mathematical model." These skills are an integral part of a holistic modeling process. Therefore, we believe that the study of this topic is mandatory in the basic course.
Let's carry out a comparative analysis of the main stages of computer modeling (author - N.V. Makarova), and the structure of the creative process (author - Ya.A. Ponomarev):
| Simulation steps | Stages of the creative process |
1. Statement of the problem: description of the task; the purpose of the simulation; analysis of the object. |
1. Awareness of the problem: the emergence of a problem situation; making sense and understanding of available data; statement of the problem (question). |
| 2. Development of the model. | 2. Resolution of the problem: hypothesis development; solution development, experiment. |
| 3. Computer experiment. | |
| 4. Analysis of the simulation results (if the results do not meet the goals, then mistakes were made at the previous stages). | 3. Verification of the solution (as a result of the implementation of this stage, the hypothesis put forward may not be justified, then it is replaced by another). |
Comparison of the stages allows us to conclude that the modeling process fits easily, is consistent with the creative process. Therefore, teaching students to model, and in particular to its stage-by-stage planning, leads to the formation of knowledge and planning of creative activities.
Since all the stages of modeling are determined by the task and the goals of modeling, for each specific class of models the scheme may undergo some changes. So, in relation to mathematical models, the problem statement is divided into the following stages:
1. highlighting the assumptions on which the mathematical model will be based;
3. record of mathematical relationships connecting the results with the initial data (this relationship is a mathematical model).
Here is an example of two students completing an assignment to develop a mathematical model of the mass of a schoolchild's portfolio:
| Solution 1: | Solution 2: |
1. Highlighting assumptions: the mass of the diary is equal to the mass of the notebook; the number of notebooks and the number of textbooks is equal to the number of subjects on a given day; the briefcase contains only notebooks, a diary, textbooks and a pencil case. m4 (kg) is the weight of the canister; n (pcs) - the number of subjects; 3. Mathematical model М = m1 + m2 n + m3 (n + 1) + m4, where m1> 0, m2> 0, m3> 0, m4> 0, n> 1. |
1. Highlighting assumptions: all textbooks have the same mass; all notebooks have the same mass; the briefcase may contain notebooks, a diary, textbooks, a pencil case and "something else" (a toy, a sandwich, etc.). 2. Determination of the initial data and the result: m1 (kg) - empty portfolio weight; m2 (kg) - the mass of one textbook; m3 (kg) - the mass of one notebook; m4 (kg) is the mass of the diary; m5 (kg) - the mass of the canister; m6 (kg) is the mass of "something else"; n1 (pcs) - the number of textbooks; n2 (pcs) - the number of notebooks; M (kg) is the mass of the student's portfolio. 3. Mathematical model: М = m1 + m2 n1 + m3 n2 + m4 + m5 ++ m6, where m1> 0, m2> 0, m3> 0, m4> 0, m5> 0, m6> 0, n1> 0, n2> 0. |
This example clearly confirms that tasks of this type allow you to clearly trace the phased creation of a model and are a vivid example of the creative activity of students. By making different assumptions, each student gets his own distinct model.
After reviewing and analyzing the task apparatus of computer science textbooks recommended for secondary school students, for the presence of modeling tasks related to educational and creative ones, we can conclude that practically all textbooks contain tasks for the formalization and application of mathematical methods, as well as tasks of other types, the solution of which is reduced to the use of a mathematical apparatus. However, the authors of textbooks practically do not offer tasks for the development of such components of the creative abilities of an individual as the ability to see problems and contradictions, critical thinking and the ability to make value judgments, the ability to find the necessary information and transfer, apply it in the conditions of the problem, the ability to formulate and reformulate tasks, communication and creativity, etc.
By the frequency of its use, the term "task" is one of the most widespread in science and educational practice. Some authors consider the concept of "task" as undefined and in the broadest sense means something that requires execution, a solution. In the aspect of using teaching aids, it acts as a means of purposeful formation of knowledge, skills, and abilities. Unfortunately, in textbooks, tasks are still used mainly to form the ability to apply knowledge (in the sense of memorizing facts and their reproduction). In our study, we will consider educational and creative tasks that involve a different solution scheme, using non-traditional methods and means. This is already a new stage in the use of tasks, when they serve as the development of personality and education of students.
Most of the tasks of information modeling relate to educational and creative tasks (UTT), the definition, justification of the content and role, as well as the classification of which were proposed by V.I. Andreev. Let us dwell in more detail on the concept of educational and creative tasks and their classification.
"Educational and creative task- this is a form of organizing the content of educational material, with the help of which the teacher manages to create a creative situation for students, directly or indirectly set the goal of the conditions and requirements of educational and creative activity, in the process of which students actively master knowledge, skills, skills, develop the creative abilities of the individual. "
In our opinion, when teaching modeling, it is possible to use educational and creative tasks for the development of various components of creative abilities.
The classification of educational and creative tasks proposed by V.I. Andreev is quite extensive.
Classification of educational and creative tasks in connection with their use for the development of the creative abilities of the individual:
| Examples of modeling tasks | Developable components of creativity | |
| 1. Problems with incorrectly presented information | The already mentioned problem of the student's portfolio, in which there is practically no initial information, but only the goal of the activity. Develop a relational model for a travel agency. |
Ability to find the information you need and apply it in the context of the task |
| 2. Tasks for forecasting | Mathematical modeling: what will the population of Russia be by 2050? Verbal or graphic modeling: develop a model for a 21st century school. |
Ability to generate ideas, hypothesize |
| 3. Tasks for optimization | What are the dimensions of the length and width of the rectangular section of area S, the least amount of picket fence will be consumed? | Flexibility, rationalism of thinking |
| 4. Tasks for peer review | Tasks for assessing the adequacy of the model: a mathematical model of the dependence of the growth of the amoeba population on fertility is expressed by the following formula: H (I + 1) = H (I) * 2. Does this model reflect a real process? What additional factors should be considered? | Critical thinking, the ability to make value judgments |
| 5. Tasks for detecting contradictions and formulating the problem | The city's cinema, with a capacity of 100 seats, hosts 5 screenings per day. The film "Turkish Gambit" will be shown during the week. Explore the situation from different points of view by forming tasks for solving problems such as "what will happen if ..." and "how to do to ...". Formulate conclusions and make recommendations. | Ability to see problems and contradictions |
| 6. Tasks for the development of algorithmic and heuristic prescriptions | Develop an algorithm for creating a chessboard model in a graphic editor. Develop an algorithm for converting unstructured information about an object into a table of the form "object-property" or "object-object". Create a descriptive model of behavior when meeting a person of the opposite sex. |
The ability to generalize and curtail mental operations, the ability to reflect on thinking |
| 7. Tasks for the correct formulation of the problem | A mathematical model is given in the form of a diagram. Build a table for which such a diagram can be created (the table should be meaningful). Think of a problem, as a result of the solution of which a logical model of the form (А В) → С can be obtained. |
Ability to formulate and reformulate objectives |
| 8. Logical tasks | Tasks for the creation of logical models. Tasks for the development of structural (hierarchical, network, relational) models. |
Intellectual and logical abilities |
| 9. Design tasks | Computer design, modeling of an object according to a technical drawing or a drawing with missing lines on it, finalizing the shape of the object's details, etc. | Design ability |
Of course, the limited number of hours devoted to studying the "Modeling and Formalization" line in the basic computer science course is an obstacle to fully using the system of educational and creative tasks in teaching. However, these tasks can be classified under various informatics topics. It can be seen from the conditions of the problems that for their solution and for the implementation of information models, it is sufficient to possess the skills of working in universal software environments: a graphic and text editor, computer presentations, spreadsheets and a DBMS. The capabilities of these software tools are such that with skillful selection of tasks, creating an atmosphere of creativity in the classroom, the use of these programs helps to develop students' imagination, fantasy, intuition, initiative, i.e. those personal qualities that are classified as creative. Therefore, some of the tasks can be applied when teaching information technology in a basic computer science course. It is also possible to use them in specialized courses focused on modeling or information technology.
The educational and creative tasks recommended by us are applied at the stage of setting and formalizing the task and in developing a symbolic information model, information technologies are only a means of implementing and researching the created model. So, for example, tasks with incorrectly presented information (tasks with missing initial information, tasks with redundant information, tasks with conflicting initial information, tasks in which there is practically no initial information, but only the goal of the activity) can be used when teaching work in any software environment. The need to develop an algorithmic prescription can be contained in the condition of the problem, or it can arise in the process of its solution or software implementation. Management tasks and communicative-creative tasks can be applied in project activities and group work. Thus, we consider it possible to jointly teach information technology and information modeling for a deeper, conscious and meaningful study of both lines, and most importantly, to increase the level of development of students' creative abilities.
Thus, teaching the development of models as an integral step-by-step process and the widespread use of educational and creative tasks allows us to point out the pedagogical possibilities of teaching information modeling as a creative process.
Chapter II. Experimental work on the study of the role of educational and creative tasks in teaching computer modeling in the development of students' creative abilities
A special role in pedagogical research is played by experiment - specially organized testing of one method or another, work acceptance to identify its pedagogical effectiveness.
An experiment (from Lat. Experimentum - trial, experience) is a method of cognition, with the help of which a pedagogical phenomenon is investigated in natural conditions or artificially created, controlled and controlled conditions, and a way to solve a scientific problem is sought. Thus, an experiment is a method of pedagogical research in which there is an active influence on pedagogical phenomena by creating new conditions corresponding to the goal of the research. The experiment should be the answer to some question. It should aim to test the hypothesis. There is no experiment without hypotheses, just as there is no experiment without convincing theoretical and statistical evidence that meets modern requirements.
There are various classifications of types of experiments.
In our case, we will use a comparative experiment - when in one group work (training) is carried out using a new methodology, and in the other - according to a generally accepted one or another than in the experimental group, and at the same time the task is to identify the greatest effectiveness of various methods. Such an experiment is always carried out on the basis of a comparison of two similar parallel groups, classes - experimental and control.
2.1 Description of experimental work
The pedagogical experiment was carried out at the state educational institution of the city of Moscow, the educational center No. 1456. The participants in the experiment are students in one of the 9 grades. The research was conducted during the 3rd quarter of the 2008-2009 academic year.
Part of the students (10 people) who attended the elective make up the experimental group; from the remaining students, 10 were randomly selected to form a control group.
The compared groups of students are equal in terms of initial data and in terms of the conditions of the pedagogical process when conducting a formative experiment.
We need to find out how the use of educational and creative tasks in teaching computer modeling affects the development of students' creative abilities.
For this purpose, a comparative pedagogical experiment is carried out, where one group (experimental) attends optional classes, which are conducted in accordance with the methodology developed by us, and the other (control) does not study using this methodology.
As a working hypothesis, it was suggested that teaching computer modeling according to our developed methodology, where educational and creative tasks are used, will contribute to an increase in the level of development of students' creative abilities (namely, such components of creative abilities as originality and uniqueness).
The experimental work consisted of three stages.
Stage 1 - ascertaining. Its purpose was to identify the level of development of students' creative abilities.
Stage 2 - Formative. Purpose: to increase the level of development of the creative abilities of schoolchildren through the use of educational and creative tasks when teaching graphic modeling in optional classes.
Stage 3 - control. The purpose of this stage is to identify the level of development of the creative abilities of schoolchildren (retesting).
So, Stage 1 - ascertaining - identifying the level of development of students' creative abilities.
Initially, the level of development of students' creative abilities was analyzed. At this stage, we carried out entrance testing: the test "Diagnostics of non-verbal creativity" (see the appendix). The diagnostic capabilities of the adapted version of the methodology of this test make it possible to assess two components of creative abilities such as originality and uniqueness.
See table 3 for the test results.
Stage 2 - Formative. The purpose of the stage: to increase the level of development of the creative abilities of schoolchildren by teaching computer modeling in optional classes.
At this stage, when conducting optional classes, we used the block of the optional course developed by us, corresponding to the following thematic planning (see Table 1). As a software environment for the development of creative abilities through training in computer modeling, we have chosen the graphic editor Paint.
Table 1.
Thematic plan of the block "Graphic modeling"
| Lesson number | Lesson topic | Number of hours | Type of educational activity |
| 1 | Model and modeling concepts. Model classifications. Graphic models | 1 | Lecture with conversation elements |
| 2 | Simulation steps | 1 | Lecture with conversation elements |
| 3-5 | Laboratory work No. 1 "Modeling geometric shapes" | 3 (1+2) | Laboratory workshop |
| 6-9 | Design is a kind of modeling. Laboratory work No. 2 "Computer design" |
4 (2+2) | Lecture with elements of conversation. Laboratory workshop |
| 10-13 | Laboratory work No. 3 "Modeling of volumetric structures" | 4 (2+2) | Laboratory workshop |
| 14 | Summarizing. Exhibition of works by students | 1 | |
| Total: | 14 |
While developing a course on teaching computer modeling, we tried to select tasks for laboratory work in such a way that they contribute to the development of the creative abilities of students.
The main part of the block is made up laboratory works ... Laboratory work is the main form of work in a computer class. Laboratory work provides students with the opportunity to independently engage in research activities, which allows them to consolidate the knowledge gained and helps to lay the foundation for further independent work.
The laboratory work consists of two parts: the first part includes samples of educational and creative tasks in which all stages of modeling are traced; the second part contains tasks for self-fulfillment. Such a structure of laboratory work is justified: the first part allows you to form skills at the reproductive level, the second provides an opportunity to consolidate the acquired skills, contributes to the manifestation and development of creative abilities.
Laboratory works are given to students in printed form. The content of the fragments of laboratory work, highlighted in gray, is the result of the joint work of the teacher and the students, namely, the process of discussing the task (see & 2).
All the students who attended the elective had the skills to work in the environment of the graphic editor Paint, since they attended the elective in computer science in grade 8. Under other circumstances, the classes we have developed can be conducted after studying the topic "Technology of processing graphic information" in the computer science course, for example, in grade 10 or 11.
The last, final stage of the experimental work is control stage. The purpose of this stage is to identify the level of development of the creative abilities of schoolchildren.
This stage includes re-testing the participants in the experimental and control groups using the test "Diagnosis of non-verbal creativity" (see Appendix), to check the effectiveness of the training, as well as comparison with the results of the ascertaining stage.
See Table 4 for the test results.
2.2 Methodological developments for teaching graphic modeling in the course of computer science
As with any other modeling, starting graphic modeling, you should select its object, determine the goals of modeling, form an information model in accordance with the task and select a modeling tool.
In the environment of a graphical editor, which is a convenient tool for building graphical models, graphical objects are created - pictures. Any drawing, on the one hand, is a model of some original (real or mental object), and on the other hand, it is an object of a graphic editor.
In a graphical editor environment, it is very important to be able to create a generalized information model of a graphical object (see Table 2).
table 2
Information model of a graphical object
To build computer graphic models, the following tasks should be solved:
· Modeling of geometric operations, providing accurate construction in a graphical editor;
Modeling of graphic objects with specified properties, in particular, shape and size
The list of requirements for the knowledge and skills of students required to study graphic modeling:
1. Students should know:
· Ways of representation of images in computer memory; concepts of pixel, raster, color coding, video memory;
What are the areas of application of computer graphics;
· Appointment of graphic editors;
· The purpose of the main components of the environment of the graphic editor Paint: working area, tool menu, graphic primitives, palette, eraser, etc.
2. Students should be able to:
· Build images using the graphic editor Paint;
· Save drawings to disk and load from disk.
Examples of laboratory work:
Laboratory work No. 1 "Modeling geometric shapes"
Task 1. "Regular triangle"
Stage 1. Formulation of the problem
DESCRIPTION OF THE PROBLEM
Construct an equilateral triangle with a given side.
PURPOSE OF SIMULATION
FORMALIZATION OF THE PROBLEM
Stage 2. Model development
Construct a triangle using the algorithm (see Fig. 1) and prove that the resulting triangle is indeed correct. This algorithm was proposed by Euclid in the IV century. BC.
Fig. 1. Algorithm for constructing an equilateral triangle with a given side
EXPERIMENTAL plan
1. Testing the model built according to a given algorithm by aligning it with the original segment.
2. Building and testing the model using our own algorithm with the same initial data.
3. Research and analysis of two construction algorithms in order to determine the best one.
CONDUCTING RESEARCH
1. Prove the correctness of the above and own algorithms for the model.
2. Combine the constructions made according to different algorithms.
Stage 4. Analysis of the results
If the figures did not match when aligning, then change the construction algorithm or increase the accuracy of the algorithm by working on an enlarged scale (under a magnifying glass). If matched, then choose the most convenient algorithm.
Problem 2. "Regular hexagon"
Stage 1. Formulation of the problem
DESCRIPTION OF THE PROBLEM
Construct a regular hexagon with a given side.
PURPOSE OF SIMULATION (space for student answers)
_____________________________________________________________
FORMALIZATION OF THE PROBLEM (the table is filled in by students)
| Clarifying question | Answer |
Stage 2. Model development
Construct a hexagon using the algorithm (see Fig. 2) and prove that the resulting hexagon is indeed correct.
Fig. 2. Algorithm for constructing an equilateral hexagon with a given side
Stage 3. Computer experiment
EXPERIMENTAL Plan (space for student answers)
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
DOING A RESEARCH (student response space)
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
Stage 4. Analysis of results (space for students' answers)
_____________________________________________________________
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1. Construct an isosceles triangle for a given base a and height h.
2. Construct a right-angled triangle along the hypotenuse and leg.
3. Construct an isosceles triangle along the side and apex angle.
4. Construct a triangle on three sides.
5. Construct a regular octagon with a given side.
6. Construct a triangle along two sides and an angle between them.
7. Construct a parallelogram along the given sides and the angle between them.
8. Construct a triangle along the side opposite to it by the angle and height, drawn from the vertex of this angle.
9. Construct a triangle along two sides and a height lowered to one of them.
10. Construct an isosceles triangle along the base and radius of the circumscribed circle.
Laboratory work No. 2 "Computer design"
Task. "Parquet modeling"
Stage 1. Formulation of the problem
DESCRIPTION OF THE PROBLEM
In St. Petersburg and its environs there are magnificent palaces-museums, which contain works of art by the great Russian and European masters. In addition to wonderful works of painting, sculpture, furniture, unique samples of parquet have been preserved here. The sketches of these parquet floors were created by great architects. And their ideas were realized by the parquet flooring craftsmen.
Parquet is made up of parts of different shapes and types of wood. Parquet details can vary in color and wood pattern. From these parts, parquet flooring workers assemble blocks compatible with each other on a special table. Real parquet is assembled from these blocks on the floor in the room.
One of the parquet varieties is made up of regular geometric shapes (triangles, squares, hexagons or more complex shapes). In various combinations, parquet details can give unique patterns. Imagine yourself as a parquet designer completing an order.
The task is of the "How to do to ..." type.
PURPOSE OF SIMULATION
Develop a parquet sketch.
INTERMEDIATE OBJECTIVES
Develop a set of standard parquet parts - parquet menu (see Fig. 1).
Fig. 1. Parquet menu
Design a standard parquet block from parts.
FORMALIZATION OF THE PROBLEM
| Clarifying question | Answer |
| What is being modeled? | Geometric Object - Polygon |
| The polygon is regular. The number of sides of the polygon - 3, 4, 6 | |
| What is asked? | Line segment equal to the side of the polygon |
| What do you need to get? | Parquet details, parquet block, geometric parquet |
| Ruler, compasses | |
| There is no compass. The compass replaces the inscribed square |
Stage 2. Model development
INFORMATION MODEL
COMPUTER MODEL
To model a set of compatible parts, parquet blocks and parquet as a whole, you can use the Paint editor environment.
MODEL 1. Modeling geometrical objects with specified properties to create a standard set of parquet parts with compatible dimensions.
Create a complete set of details required for modeling (see Fig. 2) yourself (using algorithms known to you), using the capabilities of rotations and reflections of fragments.
Fig. 2. Parquet menu objects
Perform construction of a square inclined by 30 0 (60 0) according to the algorithm (see Fig. 3).
Fig. 3. Algorithm for constructing a square inclined by 30 0 (60 0)
Color the finished figures, imitating the texture of various types of wood.
Save the created menu in the "Parquet Menu" file and protect it from writing.
MODEL 2. Parquet block modeling.
The number of parts in a parquet block depends on the number of sides of the polygon.
Blocks can be assembled from parts of one, two or three types (see Fig. 4).
Fig. 4. Parquet block models
MODEL 3. Parquet layout from the created blocks.
Parquet is assembled from ready-made blocks on the floor. The resulting voids in the corners and at the walls are sealed with parts from the standard set.
A computer sketch of a parquet is formed according to the same principle on the working area of a graphic editor (see Fig. 5).
Fig. 5. Parquet samples
Stage 3. Computer experiment
EXPERIMENTAL plan
1. Testing a standard set of parts - checking compatibility.
2. Development of a parquet block.
3. Testing blocks - checking their compatibility.
4. Modeling of sketches of parquet.
CONDUCTING RESEARCH
1. Develop several options for the parquet block and parquet sketches.
2. Offer them a choice to the customer.
Stage 4. Analysis of the results
If the type of parquet does not correspond to the customer's intention, then return to one of the previous steps: create another block from the same set of parts or develop a different set of parts.
If the type of parquet suits the customer, then a decision is made on the development of drawings on a real scale and the selection of materials.
Self-study assignments:
1. Imagine that you are the head of a fabric factory. Design fabrics with geometric patterns.
2. Imagine that you are a stained glass master. Design a set of glasses for composing stained glass windows and create a stained glass window.
3. Imagine that the director of a toy factory has come to you. He asks you to design a set of mosaic pieces and demonstrate what patterns can be folded from these pieces.
4. Create a menu for a tea or coffee service (top view) and "set" a festive table for six people according to the rules of etiquette.
5. Imagine that you are the artist of a ceramic tile factory. Design a set of ceramic tiles and use it to create objects of the underwater world to simulate the composition "Underwater" for the bathroom.
6. Imagine that you are an artist in a workshop specializing in the production of carpets. Design a carpet pattern.
7. Imagine that you are the chief specialist of a carpet factory. Design carpet patterns for the kids' room.
8. One of the latest trends in interior design is finishing the ceiling with tiles specially designed for this purpose. Design a set of ceiling tiles to decorate the theater foyer.
9. How the city is transformed when sidewalks, squares, squares are paved with paving stones (paving slabs). Try your hand at being a paving stone factory painter. Design multiple options for sidewalk tiles.
10. Linoleum is a very practical coating that does not require special care. But, speaking of practicality, we must not forget about beauty. Design a few samples of linoleum that mimics a marble finish.
Laboratory work No. 3 "Modeling of volumetric structures"
Task. "Creating a set of building bricks"
Stage 1. Formulation of the problem
DESCRIPTION OF THE PROBLEM
Create a set of bricks with the specified parameters a, b, c (see Fig. 1).
Fig. 1. Brick menu
The task is of the "How to do to ..." type.
PURPOSE OF SIMULATION
Construction of an object with specified properties.
FORMALIZATION OF THE PROBLEM
| Clarifying question | Answer |
| What is being modeled? | Brick |
| What properties does it possess? | The brick has the shape of a rectangular parallelepiped |
| What is asked? | Sections equal to the length, width and height of the brick |
| What do you need to get? | Set of bricks |
| How many positions can a brick take? | 6 |
| In what environment can you build? | On paper or in a graphics editor |
| What tools are needed for plotting on paper? | Ruler |
| What tools are needed to build in a graphical editor environment? | Line tool |
| What features of the graphics editor can I use? | The ability to rotate fragments of the picture at certain angles and their reflections |
| How many brick positions is it enough to build? | 3 |
Stage 2. Model development
Build a brick in three positions according to the algorithm. Using the Fill tool, paint the edges with paint of the same tone, but different shades (see Fig. 2).
Fig. 2. Brick building algorithm
Using the ability to rotate the fragments of the drawing at certain angles and their reflections, get all six positions of the brick.
General task:
Build the model from the picture:
Self-study assignments:
· Build a volumetric model from bricks.
To draw precise horizontal, vertical and 45 0 lines, as well as circles and squares, use the key
· To construct parallel lines, copy and paste an existing line is used.
· To build figures with given dimensions, it is advisable to place the original segments of a given length in the upper part of the sheet as references and use their copies.
· When constructing regular polygons, take into account their property to fit into a circle, which can be used as an additional construction.
· When solving graphic problems, it is often necessary to use additional constructions. For additional constructions, an auxiliary color is selected, which is removed at the end of the work by filling with white (background color).
2.3 Research results and their analysis
As a result of the first, ascertaining, stage, we carried out entrance testing: the test "Diagnostics of non-verbal creativity". We have evaluated and analyzed such two components of creativity as originality and uniqueness (see Table 3).
Table 3.
| Originality index | Uniqueness index | |||
| Pupils | X1 | X2 | X1 | X2 |
| 1 | 0,88 | 0,74 | 1 | 2 |
| 2 | 0,58 | 0,59 | 1 | 0 |
| 3 | 0,45 | 0,69 | 0 | 1 |
| 4 | 0,63 | 0,67 | 1 | 1 |
| 5 | 0,91 | 0,87 | 2 | 2 |
| 6 | 0,88 | 0,69 | 1 | 1 |
| 7 | 0,88 | 0,81 | 1 | 2 |
| 8 | 0,67 | 0,71 | 2 | 1 |
| 9 | 0,63 | 0,71 | 1 | 0 |
| 10 | 0,63 | 0,49 | 1 | 0 |
|
meaning |
0,71 | 0,70 | 1,18 | 1,09 |
| Note. | ||||
After analyzing the results obtained and comparing them with the maximum possible (for the originality index - 1, for the uniqueness index - 3), we can conclude that the components of students' creative abilities are not sufficiently developed, and the results of the control and experimental groups differ insignificantly.
At the second stage, optional classes were held for the experimental group, where educational and creative tasks were used to develop the creative abilities of students in laboratory work.
As a result, at the final, control, stage of experimental work to check the effectiveness of the training, we again revealed the level of development of the creative abilities of schoolchildren with the help test "Diagnostics of non-verbal creativity". Received the following results: (see table 4).
Table 4.
Research data on the level of development of creative abilities of schoolchildren (mean value)
| Originality index | Uniqueness index | |||
| Pupils | X1 | X2 | X1 | X2 |
| 1 | 0,88 | 0,80 | 1 | 2 |
| 2 | 0,88 | 0,67 | 2 | 1 |
| 3 | 0,60 | 0,71 | 1 | 0 |
| 4 | 1,00 | 0,87 | 3 | 2 |
| 5 | 0,73 | 0,73 | 1 | 1 |
| 6 | 1,00 | 0,87 | 3 | 2 |
| 7 | 0,89 | 0,89 | 1 | 2 |
| 8 | 0,91 | 0,59 | 2 | 0 |
| 9 | 0,77 | 0,77 | 2 | 1 |
| 10 | 0,77 | 0,73 | 2 | 1 |
|
meaning |
0,84 | 0,76 | 1,80 | 1, 20 |
Percentage ratio,% |
18 | 9 | 52 | 10 |
| Note. X1 - experimental group; X2 - control group | ||||
The results of the conducted pedagogical experiment are presented in the form of diagrams (see Fig. 1, Fig. 2).
Fig. 1. Dynamics of the components of creativity (experimental group)
Fig. 2. Dynamics of creativity components (control group)
So, in comparison with the control group, in the experimental group, the level of originality and uniqueness at the control stage of our experiment increased significantly. This allows us to conclude that the developed didactic and methodological materials, the selected educational and creative tasks quite fully ensure the organization and conduct of classes for the study of graphic modeling, contribute to the effective development of the creative abilities of students.
The hypothesis we formulated was confirmed: the use of educational and creative tasks in teaching computer modeling contributes to an increase in the level of development of students' creative abilities.
Conclusion
Creative abilities are individual characteristics, qualities of a person that determine the success of his performance of creative activities of various kinds.
A retrospective analysis of the problem of the development of creative abilities in the learning process made it possible to gain a deeper understanding of the trends of its development at the present stage. Numerous studies devoted to the study of creativity indicate that these issues have always worried the best minds of mankind (I. Kant, N.A. Berdyaev, P.L. Lavrov, BC Soloviev, E.V. Ilyenkov, L.S. Vygotsky, S. L. Rubinstein, Ya.A. Ponomarev, A. N. Luk, N. S. Leites, B. M. Teplov, and others), but we don’t have a common understanding of what “creativity” is discovered.
An analysis of the philosophical, scientific, pedagogical and psychological literature shows that a significant amount of research has been devoted to the problem of personality development, its creative potential, the development and use of non-traditional pedagogical technologies that contribute to this development.
However, in the literature known to us, the issues related to the development of students' creative abilities in teaching computer modeling using educational and creative tasks have not been sufficiently investigated. In educational practice, teachers quite often use elements of various technologies of developmental education. But the chaos and unsystematic nature of their implementation, inadaptation to the conditions of education in the framework of information technologies do not give the desired effectiveness.
Creativity is especially important in the learning process because Creativity makes learning fun, making it fun and imaginative. Teaching computer science is no exception. With the appropriate choice of teaching aids, the teacher can help develop students' creativity.
It is important to note that creativity does not develop in spontaneous conditions, but requires a specially organized process of teaching and upbringing: revising the content of curricula, developing a procedural mechanism for implementing this content, creating pedagogical conditions for self-expression in creative activity.
This is what we tried to do in our work. We examined educational and creative tasks as a means of forming the creative abilities of students. When solving such problems, an act of creativity occurs, a new path is found, or something new is created. This is where special qualities of the mind are required, such as observation, the ability to compare and analyze, to find connections and dependencies, all that together constitute creative abilities.
In the practical part for teaching graphic modeling, we have developed a block of an optional course and set out guidelines for its use.
The developed block of classes was implemented by us in the course of optional classes for students of one of the 9 classes (GOU TSO No. 1456).
To find out how the use of educational and creative tasks in teaching graphic modeling affects the development of students' creative abilities, a comparative pedagogical experiment was carried out.
The results of our research give grounds to assert that the developed didactic and methodological materials sufficiently fully ensure the organization and conduct of classes in the study of graphic modeling, contribute to the effective development of the creative abilities of students.
The lack of knowledge of this topic opens up great opportunities for its research, the creation of teaching methods and the development of creative tasks for computer modeling. We hope that the didactic and methodological materials developed by us will find their application in the modern school.
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Application
DIAGNOSTICS OF NON-VERBAL CREATIVITY
(E. Torrens method, adapted by A.N. Voronin, 1994)
Carrying out conditions:
The test can be performed individually or as a group. To create favorable conditions for testing, the leader needs to minimize the motivation for achievement and orient the tested to the free manifestation of their hidden abilities. At the same time, it is better to avoid open discussion of the subject orientation of the methodology, i.e. there is no need to report that it is creativity (especially creative thinking) that is being tested. The test can be presented as a technique for "originality", the ability to express oneself in a figurative style, etc. Testing time is not limited as much as possible, approximately 1 - 2 minutes for each picture. At the same time, it is necessary to cheer the test takers if they hesitate for a long time or hesitate.
The proposed version of the test is a set of pictures with a certain set of elements (lines), using which the subjects need to draw the picture to some meaningful image. In this version of the test, 6 pictures are used that do not duplicate each other in their original elements and give the most reliable results.
The test uses the following indicators of creativity:
1. Originality(Op), revealing the degree of dissimilarity of the image created by the subject to the images of other subjects (statistical rarity of the response). It should be remembered that there are no two identical images, respectively, we should talk about the statistical rarity of the type (or class) of drawings. The atlas attached below shows the various types of drawings and their conventional names, proposed by the author of the adaptation of this test, reflecting the general essential characteristic of the image. It should be noted that the conventional names of the figures, as a rule, do not coincide with the names of the figures given by the subjects themselves. Since the test is used to diagnose non-verbal creativity, the names of the pictures suggested by the subjects are excluded from the subsequent analysis and are used only as an aid to understanding the essence of the picture.
2. Uniqueness ( Un), defined as the sum of completed tasks that have no analogues in the sample (atlas of figures).
Test instructions
Here is a form with incomplete pictures. You need to finish them, be sure to include the proposed elements in context and try not to go beyond the bounding box of the picture. You can finish drawing anything and how you want, while the form can be rotated. After completing the drawing, you must give it a name, which should be signed in the line below the drawing.
Processing test results
For the interpretation of test results, an atlas of typical drawings is presented below. For each series of figures, the Оr index was calculated for the sample. To assess the test results of the subjects, the following algorithm of actions is proposed.
It is necessary to compare the finished pictures with those in the atlas, paying attention to the use of similar details and semantic connections; when finding a similar type, assign the originality specified in the atlas to this drawing. If there is no such type of drawings in the atlas, then the originality of this completed picture is considered 1.00, i.e. she is unique. The originality index is calculated as the arithmetic average of the originality of all pictures, the uniqueness index - as the sum of all unique pictures. Using percentile the scale built for these two indices based on the results of the control sample, it is possible to determine the indicator of a given person's non-verbal creativity as his place relative to this sample:
| 1 | 0% | 20% | 40% | 60% | 80% | 100% |
| 2 | 0,95 | 0,76 | 0.67 | 0,58 | 0,48 | 0,00 |
| 3 | 4 | 2 | 1 | 1 | 0 | 0 |
Note:
1 - the percentage of people whose results exceed the specified level of creativity;
2 - the value of the originality index;
3 - value of the uniqueness index.
Interpretation example : let the first picture you analyze be similar to picture 1.5 of the atlas. Its originality is 0.74. The second picture is similar to picture 2.1. Its originality is 0.00. The third drawing is not like anything, but the elements originally proposed for drawing are not included in the drawing. This situation is interpreted as a departure from the task and the originality of the given drawing is evaluated as 0. The fourth drawing is missing. The fifth figure is recognized as unique (it has no analogues in the atlas). Its originality is 1.00. The sixth picture turned out to be similar to picture 6.3 and its originality is 0.67. Thus, originality index for this protocol:
2,41/5 = 0,48
Uniqueness index(number of unique pictures) of this protocol - 1 ... The results of the protocol discussed above show that the subject is on the border between 60 and 80% of the people whose results are shown in the atlas. This means that about 70% of the subjects in this sample have higher non-verbal creativity than him. At the same time, the uniqueness index, showing how truly new a person can create, is secondary in this analysis due to the insufficient differentiating power of this index, therefore, the total originality index serves as the determining factor here.
INCENTIVE REGISTRATION FORM
Surname, initials _________________________________
Age _______ Group ____________ Date _______________
Draw pictures and give them names!
You can finish drawing anything and how you want.
Signs must be legible in the line below the picture.
Atlas of Typical Drawings
Picture №4
Applying Simulation to Teaching Computer Science
R. P. Romanski
Technical University, Sofia, Bulgaria
Introduction
For the development of computer technology and the improvement of the architectural organization of computer systems (CS), continuous training and self-improvement of computer specialists and students is necessary. In carrying out this training, it is necessary to combine the forms of traditional education with the possibilities of self-study, distance learning, practical project development and implementation of research experiments. An essential role in teaching in the field of computer science is played by the use of modern methods of studying the architectural organization and analyzing the system performance of the CS. In this sense, the application of modeling methods in the process of studying the basic structures of various CS and organizing computer processes allows one to develop a suitable mathematical description of the object under study and create software for performing computer experiments [Romanski, 2001, Arons, 2000]. Analysis of the experimental results of modeling [Bruyul, 2002] makes it possible to assess the main characteristics of the system and the performance of the studied CS.
The use of modeling in the process of studying the COP allows you to explore the features of the architecture and the organization of computation and control. This can be done on the basis of a model experiment, the organization of which involves designing a computer model as a sequence of three components (conceptual model, mathematical model, software model) and implementing this model in a suitable operating environment. This paper considers the possibility of using different methods for studying CS in the process of their study, and in particular the application of modeling principles to study ongoing processes, as well as analysis of the system performance of CS. The main goal is to define a generalized computer modeling procedure as a sequence of interrelated stages and to represent the main stages of the model research methodology. For this, in the next part, the general formalization of computer information processing and the features of computer calculations as an object of study are presented. The application of the principles of modeling in the process of studying CS is associated with the methodological organization of training in the traditional, distance, or distributed sense.
Computer systems as an object of study and research methods
One of the main objectives of specialized training courses in the field of computer systems and performance research is to train future and current computer designers, computer equipment developers and CS consumers in the correct use of the technological capabilities of modeling and measuring the characteristics of systems. These capabilities are used both in the process of evaluating the effectiveness of new computer projects, and for comparative analysis of existing systems. In the learning process, the task is to clarify the sequence of research stages and the possibility of processing experimental results to obtain adequate estimates of performance indices. This task can be clarified depending on the specific area of computer training and the peculiarities of the principles of the considered computer information processing.
Rice. 1. Information support of computer processing.
In general, computer processing is concerned with the implementation of certain functions for transforming input data into final solutions. This defines two levels of functional transformation of information (Fig. 1):
mathematical transformation of information - real data processing in the form of mathematical objects and is represented by a generalized function f: D®R, which depicts the elements of the data set D in the elements of the set of results R;
computer implementation of processing - represents a specific implementation f *: X®Y of the mathematical function f, depending on the computer and software equipment, based on a suitable physical representation of real information objects.
As a result, it is possible to write a generalized functional model of computer processing r = f (d) ºj 2 (f * [1 (d)]), where functions j 1 and j 2 are auxiliary for encoding and decoding information.
Considering the CS as an object of study, it should be borne in mind that computer processing consists of processes, each of which can be represented in the form of a structure I =, where: t is the initial moment of the process; A - defining attributes; T - process trace. The last component of the formal description determines the time sequence of events e j for addressing this process to the elements of the system resource S = (S 1, S 2,…, S n). The sequence of time stages and the load of the system resource make it possible to determine the profile of the computation process (Fig. 2).
Rice. 2. An approximate profile of a computer process.
The support of different processes in the organization of computer processing forms the system load of the computer environment. For each moment (t = 1,2, ...) it can be represented by the vector V (t) = Vt =, whose elements express the free (vj = 0) or busy (vj = 1) device S j єS (j = 1 , 2, ..., n).
When studying the CS, it is necessary to determine a set of basic system parameters that reflect the essence of computer processing, and also to develop a methodology for studying the behavior of a system resource and ongoing processes. As the main system parameters (performance indices), one can study, for example, the workload of each element of the system resource, the total system load of the CS, the response time when solving a complex of tasks in multiprogram mode, the degree of stability (durability) of equipment, the cost of computer processing, the efficiency of parallel planning. or pseudo-parallel processes, etc.
A typical course of study in the field of analysis and research of performance of the COP should discuss the main theoretical and practical problems in the following directions:
the possibility of researching the performance of computer equipment and the efficiency of computer processes;
application of effective research methods (measurement, modeling);
technological features of measuring system parameters (benchmark, monitoring);
technological features and organization of modeling (analytical, simulation, etc.);
methods of analysis of experimental results.
All this is associated with the application of this research method and the selection of the appropriate instrumentation. In this sense, Fig. 3 shows an approximate classification of methods for studying CS and processes. Three main groups can be identified:
Software blends - represent mathematical relationships for evaluating processor performance based on the application factors of individual operating classes. They allow you to estimate the processor load by statistical analysis after the execution of typical programs.
Counting methods - allow you to obtain reliable information about the course of computer processes based on the direct registration of certain values of the available parameters of the COP. To do this, it is necessary to use or develop a suitable counting tool (monitor) and organize the execution of the counting experiment. It should be noted that modern operating systems have their own system monitors that can be used at the software or firmware level.
Modeling methods are used when there is no real object of the experiment. The study of the structure or ongoing processes in the CC is carried out on the basis of a computer model. It reflects the most important aspects of the behavior of structural and system parameters, depending on the goal. To develop a model, it is necessary to choose the most suitable modeling method that allows you to obtain maximum adequacy and reliability.
Rice. 3. Classification of methods for studying the COP and processes.
The traditional learning process involves conducting a basic course of lectures in conjunction with a set of classroom exercises and / or laboratory practice. In the field of computer science, when studying the organization of the CS and the principles of managing computer processes (at low and high levels), as well as when analyzing system performance, it is often necessary to develop computer models while performing laboratory tasks in the classroom or when independently implementing projects. To successfully complete these practical works and to obtain the necessary practical skills, it is necessary to determine the sequence of stages and present the technological features of model development. This will allow trainees to acquire the necessary knowledge about the development of adequate and reliable computer models for research, assessment and comparative analysis of the system performance of different computer architectures. As a result of this, a generalized procedure for carrying out modeling is proposed, as well as a methodological scheme for a model study of CS and processes.
The procedure of computer modeling in the study of CC and processes
The main task of computer modeling in the study of CS and processes is to obtain information about performance indices. Planning a model experiment in the learning process is carried out on the basis of the following stages:
collection of empirical data for specific values of basic system parameters;
structuring and processing of empirical information and the development of a functional diagram of the model;
determination of a priori information and definitional areas of operating parameters for the development of a suitable mathematical model of the original object;
implementation of model experiments, accumulation of model information and its subsequent analysis.
A generalized formalized procedure for a model study for organizing a model experiment is shown in Fig. 4.
Rice. 4. Model research procedure.
The initial goal is determined by the need to study a real object (system or process). The main stages of the procedure are as follows:
Determination of the basic concept of building a model by decomposing an object into subsystems and introducing an acceptable degree of idealization for some aspects of the behavior of system processes.
Mathematical formalization of the structure and relationship in the investigated object on the basis of a suitable formal system.
Mathematical description of the functioning of a real system and the development of a suitable functional model depending on the purpose of the simulation.
Implementation of a mathematical model using the most suitable modeling method.
Description of the created mathematical model by means of a suitable software environment (specialized or universal).
Carrying out experiments on the basis of the created model and subsequent processing and interpretation of the model information to estimate the parameters of the research object.
The main methods of computer modeling are as follows:
Analytical methods - use mathematical tools to describe the components of a real system and ongoing processes. Based on the chosen mathematical approach, the mathematical model is usually built as a system of equations that allows easy programming, but implementation requires high accuracy of formulations and accepted working hypotheses, as well as significant verification.
Simulation (imitation) methods - the behavior of a real object is imitated by a software simulator, which in its work uses a real workload (emulation), or a software model of the workload (simulation). Such models allow the study of complex systems and obtaining reliable results, but they are performed in time and this determines the main disadvantage of the method - a significant consumption of computer time.
Empirical methods are quantitative techniques for registering, accumulating and analyzing information on the functioning of a real object, on the basis of which a statistical model can be built for its study. Usually linear or non-linear equations are used to represent the relationship of selected parameters (for example, from a set of primary factors) and to calculate statistical characteristics.
The main task of computer modeling is to create an adequate model, with the help of which it is possible to accurately represent the structure of the system under study and the ongoing processes. The development of a computer model includes three sequential levels - a conceptual model (the conceptual concept of structuring a model), a mathematical model (image of a conceptual model by means of a mathematical formal system) and a software model (software implementation of a mathematical model with a suitable language environment). At each level of computer simulation, it is necessary to check the adequacy of the model to ensure the reliability of the final model and the accuracy of the results of model experiments. The specificity of the individual stages of the modeling procedure determines the applied approaches and means of assessing the adequacy. These features have found a place in the developed methodology of computer modeling, which is presented below.
Model research methodology
In the process of computer modeling, regardless of the method used, it is possible to determine a generalized mathodological scheme of a model study (Fig. 5). The proposed formalized methodological sequence includes several main phases, presented below. Basically, it represents an iterative procedure for obtaining the necessary reliability of the developed computer model based on the formulation of the initial model hypothesis and its subsequent modification. This approach is successful in the study of complex systems, as well as in the absence of sufficient a priori information for the object under study.
Stage "Formulation"
At the first stage of model development, it is necessary to accurately and clearly define the object of modeling, the conditions and hypotheses of the study, as well as the criteria for assessing the model efficiency. This will allow you to develop a conceptual model and define it in abstract terms and concepts. Typically, an abstract description defines the initial principles of model building (basic approximations, definitional ranges of variables, performance criteria and types of expected results). At this stage, the following sub-steps can be identified:
Definition and analysis of the task. Includes a clearly defined essence of the research task and the planning of necessary activities. Based on the analysis of the problem, the scope of the expected actions and the need for decomposition of the problem are determined.
Clarification of the type of initial information. This information allows you to get the correct output results of modeling and therefore it is necessary to provide the necessary level of confidence in the estimates.
Introduction of assumptions and hypotheses. This is necessary if there is not enough information to implement the model. Assumptions replace missing or complete data. Hypotheses refer to the type of possible outcomes or to the environment for the implementation of the investigated processes. During the modeling process, these hypotheses and assumptions can be accepted, discarded, or modified.
Determination of the main content of the model. On the basis of the applied modeling method, the peculiarity of the real object, the assigned task and the means of its solution are reported. The results of this sub-step include the formulation of the basic concept of the model, a formalized description of real processes and the selection of an appropriate approximation.
Determination of model parameters and selection of performance criteria. At this sub-stage, primary and secondary factors, input actions and expected responses of the model are determined, which is especially important for achieving the required accuracy of the mathematical description. Refinement of efficiency criteria is associated with the definition of functional dependencies for assessing the system's response when changing model parameters.
An abstract description of the model. The phase of the general formulation of the conceptual model completes the construction of the abstract model in a suitable environment of abstract terms - for example, in the form of a structural diagram, as a flow diagram (Data Flow Diagram), in the form of a graphical diagram (State Transition Network), etc. This abstract representation makes it easy to build a mathematical model.
Rice. 5. Methodological scheme of the model research.
Stage "Design"
The design of a computer model is associated with the development of a mathematical model and its programmatic description.
A mathematical model is a representation of the structure of the object under study and the ongoing processes in a suitable mathematical form Y = Ф (X, S, A, T), where: X is a set of external influences; S - set of system parameters; A - reflects functional behavior (algorithms of functioning); T is the running time. Thus, the behavior (reaction) of the object Y simulates a set of functional influences F, representing analytical dependences (deterministic or probabilistic). In this sense, a mathematical model is a description of an abstract model by means of a chosen mathematical system, evaluating the accepted hypotheses and approximations, initial conditions and defined research parameters. When developing a mathematical model, it is possible to apply well-known mathematical formulas, dependencies or mathematical laws (for example, probability distributions), as well as combine and supplement them. The most common theoretical mathematical systems for the purpose of modeling provide an opportunity to present a mathematical model in a graphical form - Petri nets, Markov chains, queuing systems, etc. adequacy, and then you can approve or reject it.
A software model is the implementation of a mathematical description in a software language - for this, suitable technical and technological means are selected. In the process of software implementation, a logical structural and functional diagram of the model is developed on the basis of a mathematical model. To build this circuit, you can use traditional block diagrams, or graphical tools that are represented by a specialized simulation environment, such as in GPSS (General Purpose Simulation System). The software implementation of the model is a software development task and in this sense is subject to the principles of programming technology.
Stage "Refinement"
The actions of this stage are intended to fully validate the designed model and confirm its adequacy. An assessment of the current adequacy at the previous stages is essential for their effectiveness. In this sense, the process of model refinement should be considered as a set of distributed actions at all previous stages of computer modeling. In general terms, the refinement stage can be thought of as an iterative procedure (Fig. 6), allowing sequential modification of the initial version of the developed model.
Rice. 6. An iterative procedure to refine the model.
The main purpose of checking the model reliability is to determine the level of accuracy of the match when presenting the processes of a real object and the mechanism for registering model results. In general terms, a computer model represents a collection of individual components and in this sense it is especially important to correctly plan the adequacy checks.
Stage "Execution"
This is the stage of implementation of the created model (solution by a numerical method or execution in time). The most important goal is to obtain the maximum information for the minimum waste of computer time. There are two substages:
Planning a model experiment - determining the value of the controlled factors and the rules for registering the observed factors during the execution of the model. The choice of a specific experimental design depends on the stated research goal while optimizing the execution time. To obtain an effective design, statistical methods are usually used (full design, univariate design, randomized design, etc.), which make it possible to remove the joint influence of the observed factors and estimate the acceptable experimental error.
Implementation of the experiment - preparation of input data, computer implementation of the experimental design and storage of experimental results. The experiment can be implemented as follows: control modeling (to check the performance and sensitivity of the model and estimate the model time); working modeling (actual implementation of the developed experimental plan).
Stage "Analysis and interpretation of model results"
When implementing the plan of a model experiment, information (simulation results) is accumulated, which must be analyzed to obtain an assessment and conclusions about the behavior of the object under study. This determines two aspects - the choice of methods for analyzing experimental information and the use of suitable methods for interpreting the obtained estimates. The latter is especially important for the formation of correct conclusions of the study. In the sense of the first aspect, statistical methods are usually used - descriptive analyzes (calculation of boundary values of parameters, mathematical expectation, variance and root-mean-square error; determination of the stratification for the selected factor; calculation of a histogram, etc.); correlation analysis (determination of the level of factor relationship); regression analysis (study of the causal relationship in a group of factors); analysis of variance (to establish the relative influence of certain factors based on experimental results).
The results of the analysis of model data can be presented in numerical or tabular form, using graphical dependencies, diagrams, histograms, etc. To choose the appropriate graphic means, the analysis method used is essential, as well as the experimenter's subjective skills for formatting the experiment results.
Conclusion
The main goal of organizing each model experiment is to implement effective modeling. It is associated with machine time - a significant amount of processing in the model increases the cost of modeling and decreases efficiency. Rapid model validation and convergence are essential to the effectiveness of the study. For each real system, it is often necessary to create many different models, differing in the method of decomposition and level of detailing, modeling method, software implementation tools, etc. In the process of choosing the best option, only the assessment of accuracy and adequacy is insufficient. Of the many converging models, you need to choose the most effective option that spends the minimum time on implementation.
The language of software implementation, as well as the completeness of the formal system of the abstract representation of the conceptual model, the simplicity of the description terms, the development of an optimal plan, etc., are essential for achieving sufficient efficiency of the model. The use of universal software systems differs in the absence of specific language operators and therefore they are suitable primarily for analytical modeling. For the implementation of simulation models, it is advantageous to use specialized language environments.
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Teaching computer modeling in the school computer science course
In our research work, we assume that the most effective in terms of developing the creative abilities of students is the material related to information modeling. Before testing this hypothesis, let us consider the place and significance of computer modeling, the goals and objectives of teaching computer modeling and the concepts formed in teaching modeling.
The place and importance of computer modeling in the school computer science course
In the obligatory minimum of the content of education in informatics there is a line "Modeling and formalization", which, along with the line of information and information processes, is the theoretical basis of the basic course of informatics.
The topic of modeling should not be assumed to be purely theoretical and independent of all other topics. Most of the sections of the basic course are directly related to modeling, including topics related to the technological line of the course. Text and graphic editors, DBMS, spreadsheet processors, computer presentations should be considered as tools for working with information models. Algorithmization and programming are also directly related to modeling. Consequently, the modeling line is cross-cutting for many sections of the basic course.
According to Beshenkov S.A. and other topics "Information and information processes" and "Formalization and modeling" are key topics in the course of computer science. These topics combine such traditional course topics as "Algorithms and Executors", "Information Technologies", etc. into a single whole.
The creators of the author's courses "Informatics in games and tasks" and "Informatics-plus" believe that the main task of the school computer science course is the formation and development of the ability to analyze and build information-logical models.
Boyarshinov M.G. considers it expedient to introduce a computer modeling course within the framework of the subject of informatics, the purpose of which will be to familiarize students with the methods of solving problems in physics, chemistry, mathematics, economics, ecology, medicine, sociology, humanitarian disciplines, design and technological problems using modern computer technology.
A.A. Kuznetsov, S.A. Beshenkov, E.A. Rakitina believe that the main components of the informatics course, which give it a systemic character, are "Information Processes", "Information Models", "Information Foundations of Management". The solution to the problem always begins with modeling: building or choosing a number of models: the model of the content of the problem (formalization of conditions), the model of the object chosen as a working one for solving this specific problem, the model (method) of the solution and the model of the process of solving the problem.
Thus, the study of information processes, like any phenomenon of the external world in general, is based on the modeling methodology. The specificity of informatics is that it uses not only mathematical models, but also models of all kinds of forms and types (text, table, figure, algorithm, program) - information models. The concept of the information model gives the computer science course that wide range of intersubject connections, the formation of which is one of the main tasks of this course in basic school. The very activity of building an information model - information modeling is a generalized type of activity that characterizes information science.
One of the effective methods of cognizing the surrounding reality is the modeling method, which is a powerful analytical tool that has absorbed the entire arsenal of the latest information technologies.
The generalizing nature of the concept of "information modeling" is due to the fact that when working with information, we always either deal with ready-made information models (we act as their observer), or we develop information models.
Information modeling is not only an object of study in computer science, but also the most important way of cognitive, educational and practical activity. It can also be viewed as a method of scientific research and as an independent activity.
I. I. Zubko information modeling defines as "a new general scientific method of cognizing objects of the surrounding reality (real and ideal), focused on the use of a computer." Modeling is seen as a way of knowing, on the one hand, and as content that must be assimilated by students, on the other. The author believes that the most effective teaching of information modeling is possible if the project method is implemented in practice, which integrates research, independent and creative work in a variety of ways.
Galygina I.V. believes that training in information modeling is advisable to be carried out on the basis of the following approaches:
model, in accordance with which modeling is considered as an instrument of cognition, an object of study and a means of teaching;
object, implying the selection and analysis of different types of objects: the object of study, the information model as a new object, objects of the modeling language used to build the model.
Information modeling in pedagogy can be considered in three aspects, as:
a cognitive tool, since the acquisition of new knowledge about a real object corresponding to an information model, objects of the modeling language used to describe this model occurs in the process of building and researching the model;
a learning tool, since the learning process in most cases is associated with the operation of information models of the studied object, such as a verbal description, a graphic image,
formula representation of regularities, etc .;
the object of study, since the information model can be considered as an independent information object, with its inherent features, properties, characteristics.
The main difference between these aspects from the point of view of the student is that in the first case, in the process of cognitive activity, the student himself builds a model of the studied object based on his own experience, knowledge, and associations. In the second case, the student is provided with a model of the studied object, developed by the teacher, the author of the textbook or the creator of a scientific theory. In the latter case, the set of models is the object under study.
Inclusion in the content line "Modeling and formalization" of the basic course of informatics of the module "Information Modeling" will create a solid foundation for:
conscious use of information models in educational activities;
acquaintance of students with the methodology of scientific research activities;
subsequent in-depth study of information modeling in specialized courses in computer science.
Titova Yu.F. believes that the most important educational function is the development of the creative potential of students. The experience of creative activity is formed through the solution of problematic tasks of different directions and, in particular, through research activities. Modeling is one of the most important research tools. The author has developed a methodology for teaching modeling in a basic computer science course, combining theoretical material, which is based on a formalized approach to the development and research of models, and a set of research tasks that integrates knowledge from various educational areas. The author believes that the use of this technique will ensure the development of a wide range of intellectual skills in students, such as abstraction and concretization, generalization, classification, analysis, and comprehension of the results of their actions.
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