The concept of "heuristic competence" has been clarified, by which we mean a meaningful generalization of theoretical and empirical knowledge in the field of conscious, structured creative activity to create new mathematical models and identify mathematical patterns, presented in the form of concepts, principles, semantic provisions; "heuristic competence" as the ability to put into practice one's heuristic competence. The structure of heuristic competence has been identified and substantiated: a motivational component, which includes: motivation for creative activity, the desire for self-improvement and self-realization in mathematical activity, the need to achieve a goal; a cognitive component that contains knowledge of the theoretical foundations of heuristic activity, developed creative and logical thinking; activity component, which is determined by the possession of methods of action in non-standard mathematical situations, heuristic methods for solving non-standard mathematical problems, self-organization skills, as well as flexibility of thinking, reflection and strong-willed qualities. The stages of development of heuristic competence are singled out and described: motivational-diagnostic stage, cognitive stage, algorithmic stage, search and creative stage.

heuristic competence for mathematicians

competence

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Mathematicians, while studying at a university and later, sometimes have to deviate from the stereotype of knowledge gained during the study of disciplines and industrial practices; solve creative problems; realize your competence.

Analyzing the specifics of the activities of mathematicians, we have clarified the concepts of "heuristic competence" and "heuristic competence":

Under heuristic competence - a meaningful generalization of theoretical and empirical knowledge in the field of conscious, structured creative activity to create new mathematical models and identify mathematical patterns, presented in the form of concepts, principles, semantic provisions;

We interpret heuristic competence as the ability to put into practice one's heuristic competence.

Defining the components of heuristic competence, we, relying on the works of E.F. Zeera, select:

A motivational component that characterizes the purposeful and conscious nature of actions, the enthusiasm for heuristic activities in the field of solving mathematical problems. This component includes: motivation for creative activity, the desire for self-improvement and self-realization in mathematical activity, the need to achieve a goal.

The cognitive component is a set of knowledge necessary for the student in the process of performing creative tasks to create new mathematical models and identify mathematical patterns. This component contains: knowledge of the theoretical foundations of heuristic activity, developed creative and logical thinking;

The activity component characterizes the integration of knowledge and skills, the motivational and personal components necessary for successful heuristic activity in the field of mathematics. This component is determined by the possession of methods of action in non-standard mathematical situations, heuristic methods for solving non-standard mathematical problems, self-organization skills (planning heuristic activities in solving mathematical problems, the ability to bring things to a close), as well as flexibility of thinking, reflection and volitional qualities (persistence and self-control) [ 4].

The formation of the components of heuristic competence takes place as a purposeful step-by-step process in the study of the humanities, through the implementation of pedagogical assistance to this process. The basis for the formation of heuristic competence in our study was a specially developed course "Heuristics for mathematicians". The content of the course is built on the following stages:

The motivational-diagnostic stage, the main purpose of which was the development of heuristic activity motivation, included topics related to the disclosure of the essence of creative activity for specialists in the field of mathematics and computer science; the history of the formation of heuristics as a science; the current state of heuristics as a science and practice. For example:

The history of the emergence and development of heuristics;

Information society and the place of creativity in it;

Heuristics in inventive activity;

Mathematical Science and Heuristics;

Creativity as an exact science, etc.

No less important tasks of the motivational-diagnostic stage were the diagnostics and self-diagnosis of students' heuristic abilities; the formation of adequate ideas about their abilities and capabilities.

Therefore, along with those listed above, the following topics were considered:

Heuristic competence as metocompetence;

The structure of heuristic competence for a specialist in mathematics;

Self-assessment of the formation of heuristic competence;

The use of heuristic abilities in collective creative activity, etc.

At this stage, when students did not yet master the heuristic search technology, the tasks were related to diagnostics, self-diagnosis and the development of those abilities and personality traits that are necessary for heuristic activity.

For example, students were given the opportunity to solve the following tasks, which assessed the level of their critical analysis:

1. Mr. Brown lives west of Mr. Smith. Mr Burton lives west of Mr Brown. Who lives further west?

2. Susan and Stella love pizza and Sookie and Sally love pasta. Susan and Sally love lasagna. Who loves pizza and lasagna?

Much attention in the course of solving problems was paid to the development of reflection, which was achieved through a joint analysis of solving problems with the gradual transfer of control functions to the students themselves.

The development of intuition was achieved by removing psychological barriers and thinking stereotypes of students of mathematical specialties (priority of logical thinking). For example, the following tasks were proposed:

Two tourists are walking along the road. One of them takes steps 10% shorter and at the same time 10% more often than the other. Which tourist is going faster? Without solving the problem, give an intuitive answer, and then justify it with a solution.

How to cut a piece from a piece of matter 8 m long with a 5 m tire without using measuring instruments? What unambiguous solution hypothesis can be put forward immediately?

At the same time, an atmosphere of emancipation, lack of criticism, psychological comfort, corporatism was created.

The cognitive stage is associated with the development by students of the theoretical foundations of heuristic activity. Topics covered at this stage were:

Heuristic activity and its components;

Elementary heuristic activity

Systematic application of elements of heuristic activity;

Learning task as a subject of heuristic activity, etc.

Much attention in the first two stages was given to the creation of a "team" to solve creative problems. It was this quality that became a priority for students when performing collective creative tasks at subsequent stages. For this, tasks of the type were used:

Choose the student who will come up with the most fantastic situations, while the others should come up with the most possible solutions. For example:

- “if each person from birth acquires the ability to read the thoughts of another, how will life on Earth change?”;

- “if the force of gravity on Earth suddenly disappeared, i.e. all objects and beings have completely lost their weight, then ... ";

- "If all people suddenly lost the power of speech, then ...".

The material of the algorithmic stage has a more practical orientation. It included topics related to heuristic activity technology:

Associative methods for solving problems: the method of the catalog, focal objects, garlands of randomness and associations, the method of control questions;

Brainstorming method and its modifications: oral brainstorming, written brainstorming, individual brainstorming; reverse brainstorming.

Synectic processes and methods of their use: morphological analysis and synthesis; algorithm for solving inventive problems, generalized heuristic algorithm, etc.

At this stage, students got acquainted with the technological methods of heuristic activity. In this regard, the tasks were selected in such a way as to consolidate the acquired knowledge. Typically they were:

By the nature of the activity - reproductive;

According to the degree of complexity of the activity - focused on the direct use of funds;

According to the degree of independence - they had a low, less often an average level.

For example, on the topic “Elementary heuristic activity. Reduction. Drawing up a plan for solving problems ”, students were asked to update their knowledge in this area, answering the questions: What are the stages of elementary heuristic activity and their purpose? What heuristic functions do keywords perform in the task? What is planning? What are the three types of strategies for solving problems and what are they based on?

And then solve problems like:

- “The old problem “The Peasant and the Devil”. A peasant walks along the road and complains about his poor life. Approaching the bridge, he meets the devil, who is going to help him in this way: as soon as the peasant crosses the bridge, his money will begin to double. For this, each time the peasant must give the devil 24 kopecks. The peasant was tempted. He fulfilled the contract, but after three transitions he was left completely without money. How much money did the peasant have at first? Use an end to end strategy."

At the same time, most of the tasks were of a mathematical orientation. For example, on the topic “Heuristic properties of generalization. Heuristic comparison functions. Symmetry and inversion. Superposition and specialization” students solved the following tasks:

Using a ruler without divisions with parallel edges, draw the bisector of your chosen angle. Use the symmetry property of the angle bisector;

Of the four identical-looking rings, one differs somewhat in weight from the others. Find it by no more than two weighings on a pan balance. Use the idea of splitting the task into two (two rings each) and explore the cause-and-effect relationship between them.

Synergetic systems as open, complex probabilistic systems;

Laws of development of synergetic systems and ways of managing them;

The use of heuristic methods in the process of mathematical modeling of various systems;

Laws of development of technical systems;

The use of heuristic methods in modeling economic systems, etc.

The tasks of the search and creative stage had a higher level of independence, by the nature of the activity they were mainly search and creative, aimed at coordinating learned actions and searching for new actions.

At this stage, much attention was paid to the professional orientation of tasks, their connection with real production, with special disciplines. For example:

At the engine building plant, after assembly, the engines go for a run-in. To do this, the motor shaft is connected to an electric drive, which gives a constant, relatively small number of revolutions. The pistons of the engine are set in motion relative to the inner surface of the cylinders and are gradually lapped; bumps, protrusions, roughness are smoothed out, and the pistons fit better to the cylinder walls. The process is essentially extremely simple: one rough surface is rubbed against another rough surface until the roughness is smoothed out.

Run-in must be carried out until the pistons rub against the cylinders. But how to catch it? We tried to follow the process by adding a phosphor to the oil and observing the quenching of luminescence under the action of metal particles entering the oil, but this turned out to be too cumbersome. An even more cumbersome way to periodically stop the engine to disassemble and inspect lapping surfaces.

Capital of 1 billion rubles. can be placed in a bank at 50% per annum or invested in production, and the investment efficiency is expected to be 100%, and the costs are given by a quadratic dependence. Profits are subject to certain taxes. Optimize the value of the tax to obtain the most efficient production (compare with the placement of capital in a bank).

Problem solving is the basis for the implementation of projects, which, depending on the stage, have their own specifics.

Information type projects aimed at collecting information on a particular topic were used. Preference is given to material related to the chosen specialty:

Heuristics and mathematics;

Creativity in the works of mathematicians (the names of great mathematicians are given a choice);

Heuristics and new information technologies (at the initial stage, the topic is specified, for example, when creating the first computers, when developing software, etc.);

The creative and role-playing projects that were carried out, which were short in time and were carried out on the basis of brainstorming, aroused great interest among students. As a rule, they took from 2 to 4 hours. These projects did not have a detailed structure. Only the problem and the forms of presenting the results were outlined. In the first case, the results were presented on paper or electronic media. In the second case - a presentation in the form of a team defense of the project.

Examples of projects include:

Specialty website model;

Non-embodied ideas of science fiction writers;

Optimization of self-management in the university;

Student holiday, etc.

A high level of development of heuristic competence also implies a high level of integration of all its components (cognitive, motivational, activity), so the above combination of projects will contribute to this process.

Reviewers:

Lezhneva N.V., Doctor of Pedagogical Sciences, Professor, Troitsk branch of FGBOU VPO "ChelGU", Troitsk;

Starchenko A.S., Doctor of Pedagogy, Director of the Troitsk Natural Science Lyceum No. 13, Troitsk.

Bibliographic link

Osipenko S.A. PEDAGOGICAL ASSISTANCE TO THE DEVELOPMENT OF HEURISTIC COMPETENCE IN MATHEMATICS // Modern problems of science and education. - 2015. - No. 4.;
URL: http://science-education.ru/ru/article/view?id=20720 (date of access: 01.02.2020). We bring to your attention the journals published by the publishing house "Academy of Natural History"

Heuristics and maieutics of Socrates.

There are enough examples in the history of scientific knowledge when theoretical concepts with the development of science are filled with more precise content, sometimes absorbing the original term, and in some cases even significantly changing it. This happened with the concept of "heuristics".

Word " heuristic" comes from the Greek Heurisko- I find, I find, I discover, what denoted in ancient Greece the teaching method used by Socrates (“Socratic conversation”). The structure of such a conversation consisted of a system of questions leading the student to the correct solution of the problem posed to him.

Heuristics is considered to be maieutics (translated from Greek - obstetrics, midwifery) - one of the methods of establishing the truth in a conversation or dispute. Its essence lay in the fact that Socrates, with the help of skillfully posed questions and the answers received, consistently led the interlocutor to true knowledge. Maieutics, according to Socrates, was always implemented in combination with other techniques:

irony, when the interlocutor is caught in contradictory statements, that is, in ignorance of the object of the conversation;

by induction, requiring a transition to general concepts from ordinary representations and single examples;

definition, meaning a gradual entry to the correct definition of the concept on the basis of the original definitions.

A dispute or conversation using the maieutics method should take place according to the following scheme: the interlocutor is required to define (define) the issue under discussion, and if his answer turns out to be superficial, that is, does not affect the essence, then the interlocutor is offered new examples to clarify the original definition. The result is a more precise definition, which is then tested with new examples, and so on until the true thought is “born”.

Thus, the essence of Socratic heuristics as a question-answer form of learning is the system of questions of the teacher-mentor. The developmental effect of training largely depends on his skill, knowledge of alternative ways to achieve the goal.

Archimedes method .

Simultaneously with the Socratic understanding of heuristics, many ancient scientists used various methods to find a solution to the problem. These methods, in the modern sense. were heuristic. So, Archimedes (287 - 212 BC) in the essay "The Doctrine of the Methods of Mechanics" sets out the theory of finding solutions to new problems: with the help of mechanical representations (in modern terminology - physical models), hypotheses of the solution are found, which are further studied and tested with the help of mathematics. The art of solving difficult problems for which there are no simple and easily chosen ways, gets its name from the famous exclamation of jubilation "Eureka!" (“Found!”) at the moment when the scientist realized how to determine the volume of the crown (irregularly shaped body).

Heuristic Dad.

An interesting source related to heuristics is the Mathematical Compilation by the Greek mathematician Pope (c. 300 AD). In his VII volume, he discusses the branch of science, which in Greek can be interpreted as heuristics.

The starting point of his analysis is that it is required to prove that the problem has already been solved. Conclusions were drawn from this task, other conclusions were drawn from these conclusions, and so on. until they come to such a conclusion that can be used as the beginning of a synthesis, because in the analysis they consider that what is required to be done according to the conditions of the problem has already been completed (what is sought is already found; what is required to be proved is proven). Determine from which antecedent the inference of interest can be obtained, then re-determine which inference can be obtained from that antecedent, and so on, moving from one inference to the antecedent that caused it, until one arrives at the conclusion that was obtained before or taken as true. This approach is called analogy or by solving problems to the end, or by regressive reasoning.

In synthesis, changing the order of this process, one starts from the last conclusion of the analysis, from what is already known or accepted as true. Taking what is known as a starting point, one draws the conclusion that preceded it in the analysis, and continues to draw conclusions in this way until, going back along the path traversed in the analysis, one arrives at what needs to be proved. This approach is called synthesis or constructive decision, or progressive reasoning.

There are two types of analysis. One type of analysis is the solution of "proof problems". He sets himself the goal of establishing true theorems. Another type of analysis is the analysis of the solution of "problems for finding". This type of analysis aims to find the unknown.

Obviously, Pope's techniques are by no means limited to mathematical problems. These methods of intellectual activity are universal and do not depend on the subject of research. An interesting non-mathematical interpretation of the methods of analysis and synthesis described by Pappus was given by D. Poya.

Let's consider a specific example. Primitive man needs to cross a fairly deep stream. He can't do it normally. So crossing becomes a problem where "stream crossing" is an unknown X this problem. A person may remember that he once crossed another stream on a fallen tree. He will start looking around to find such a fallen tree that becomes the new unknown. at . Let's assume that he failed to find such a tree. However, there are other trees along the stream. Naturally, he would like one of them to fall. Can he make the tree fall across the stream? This is a wonderful idea! But a new unknown arises z : how to cut down a tree across a stream?

Heuristics in the works of Descartes.

Rene Descartes (1596 - 1650) made a significant push in the direction of scientific thought towards the study of heuristic activity. He was engaged in research in many natural areas of science. In mathematics, his scientific interests were in the development of new methods. So, R. Descartes combined the methods of algebra and geometry, as a result of which analytical geometry appeared. It technically revolutionized the methodology of mathematics, since the use of equations made it possible to prove various properties of geometric curves much more simply than by purely geometric methods.

Continuing research in the field of methodology, R. Descartes sought to develop a universal method for solving problems. Here is a scheme that he suggested could be applied to all sorts of problems:

– a problem of any kind is reduced to a mathematical problem;

- a mathematical problem of any kind is reduced to an algebraic problem;

- any problem is reduced to solving a single equation.

Over time, Descartes himself admitted that there are cases where his scheme does not work, although it is suitable for a huge number of them. Problems relating to the intellectual activity of a person when solving problems are set in the "Rules for the Guidance of the Mind". In them, Descartes suggested considering:

- what should be the process of mental work in solving problems;

– analysis of the solution of correctly and incorrectly posed problems.

Heuristic ideas of Leibniz.

The German philosopher Gottfried Leibniz (1646 - 1716), like Descartes, was engaged in extensive scientific activity in the field of mathematics, physics, biology, history and logic. He considered scientific activity as a religious mission entrusted to scientists. His philosophy of science was aimed at encouraging man to discover and invent. Numerous and original fragments describing the organization of the creative process are scattered in his writings. These are actually various heuristic rules and techniques that help find ways to solve new problems. Leibniz argued that nothing is more important than the ability to find the source of an invention, which is even more interesting than the invention itself.

One of his scientific goals, he considered the creation of the logic of invention, based on the property of the mind not only to evaluate the obvious, but also to discover the hidden. To do this, he used combinatorics. Logic, according to Leibniz, should teach other sciences the method of discovering and proving all the consequences that follow from given premises.

Its main principles are:

each concept can be reduced to a fixed set of simple, further indecomposable concepts;

complex concepts are deduced from simple ones only with the help of operations of logical multiplication and intersection of the volumes of concepts in the logic of classes;

a set of simple concepts must satisfy the consistency criterion;

any statement can be equivalently translated into another form;

Every true affirmative sentence is analytic.

The formation of Leibniz's methodological views was influenced by Descartes' thoughts about the possibility of constructing a universal logical-mathematical method for solving scientific problems. Leibniz and Descartes hoped that they would be able to expand logic into a universal science of thought applicable to all areas of the human mind - to build a kind of universal calculus of thought.

According to Leibniz's plans, which were somewhat more specific than Descartes' plans, three main elements are necessary to build a universal logic. The first element is a universal scientific language, partially or wholly symbolic, and applicable to all truths deduced by reasoning. The second element is an exhaustive set of logical forms of thinking that allow any deductive conclusion to be drawn from initial principles. The third element is a set of basic concepts through which all other concepts are defined, a kind of alphabet of thinking that allows you to match a symbol with each simple idea. By combining symbols and performing various operations on them, it is possible to express and transform more complex concepts.

Introduction

Any productive human activity, in essence, is creativity. But, depending on the volume and depth of knowledge, accumulated experience, intuition, the level of creativity is different. Inventive skill is largely determined by the ability to see the trends in the development of technology. A new technical solution to a problem, as a rule, is based on the developer's extensive research, engineering, production experience and is unthinkable without a thorough study of technical and patent literature, continuous comparative analysis with known analogues.

Mankind has accumulated a huge amount of knowledge, which formed the basis of the theory, methodology and practice of creative activity. However, information about many existing methods, techniques, strategies and tactics of creativity is scattered and not systematized. Therefore, until now, the most common method of creative activity is the so-called trial and error method, which consists in a “blind” enumeration of options for solving problems. The effectiveness of the trial and error method depends on the depth of knowledge, intuition, perseverance of the creator and a number of other factors. In the second half of the 20th century, the “third culture” turned into a positive reality - a design culture that spread in all spheres of human activity (technical, artistic, political, social design). All this caused the need to systematize knowledge about the theory, methodology and practice of creativity.

The purpose of this work is to give a detailed description of heuristic approaches in creativity.

The object of research is the meaning and application of the above categories in the field of innovation and TRIZ.

In accordance with the purpose, object and subject, the following research tasks were set:

Describe heuristic approaches and give examples of their practical use;

Reveal the meaning and scope of heuristic methods in TRIZ;

Point out typical errors that arise as a result of studying creativity using heuristic techniques.

The essence of heuristics, its origin and history of development

The term "heuristics" comes from the Greek heuresko - I seek, I open. Several meanings of this term are currently in use. The heuristic can be understood as:

1) scientific and applied discipline that studies creative activity;

2) methods for solving problematic problems under conditions of uncertainty, which are usually opposed to formal methods of solving, based, for example, on exact mathematical algorithms.

3) teaching method;

4) one of the ways to create computer programs.

Some sources indicate that the concept of "heuristics" first appeared in the writings of the Greek mathematician Pappus of Alexandria, who lived in the second half of the 3rd century AD, in others, the priority of the first mention is given to the works of Aristotle.

For the first time the doctrine of heuristic methods was developed and put into practice by Socrates. Similar procedures - in the form of disputes - were widespread in medieval universities. The construction of disputes was carried out in accordance with the developed standards, which were creatively rethought in the 20th century.

In the XVIII century. Georg Leibniz (1646 - 1716) and Rene Descartes (1596 - 1650) independently developed R. Lull's idea and proposed universal languages for classifying all sciences. These ideas formed the basis of theoretical developments in the field of artificial intelligence.

Starting from about the 30s of the last century, publications of various authors began to appear, offering their methods for solving creative problems in the field of engineering design, and later for solving a number of humanitarian and social problems.

From the end of the 40s, G.S. Altshuller created and began to develop such a powerful approach to solving engineering and inventive problems as TRIZ. In the 60s of the last century, the so-called. heuristic programming.

In his studies of the nature of scientific discovery, Imre Lakatos (1922 - 1974) introduced the concepts of positive and negative heuristics.

Within the scientific school, some rules prescribe which paths to follow in the course of further reasoning. These rules form the positive heuristic. Other rules tell you which paths to avoid. This is a negative heuristic.

EXAMPLE. The "positive heuristic" of a research program can also be formulated as a "metaphysical principle". For example, the Newtonian program can be stated in the following formula: "The planets are rotating tops of approximately spherical shape, attracted to each other."

No one has ever exactly followed this principle: planets have not only gravitational properties, they have, for example, electromagnetic characteristics that affect movement.

Therefore, a positive heuristic is, generally speaking, more flexible than a negative one.

Moreover, it happens from time to time that when a research program enters a regressive phase, a small revolution or creative push in its positive heuristics can move it back into a progressive shift.

Therefore, it is better to separate the "hard core" from the more flexible metaphysical principles expressing positive heuristics.

1. The current stage of development of heuristics: concept, main tasks

At present, one can speak of heuristics as a science that studies the patterns of constructing new actions in a new situation.

In ancient Greece, this word meant the teaching method used by Socrates. Socrates shared maieutics - a special technique for establishing the truth in a conversation or dispute. The essence lies in the fact that Socrates, with the help of artificially posed questions and received answers, consistently led the interlocutor to a true conclusion. inference- this is a complex intellectual action, i.e. an action that can only be performed in the mind, based on internal reasoning.

Modern stage of development heuristics began in the 2nd half of the 20th century and is associated with the emergence of cybernetics and the need to develop heuristic search systems for scientific and inventive activities.

The main tasks of heuristics are cognition, selection, description and modeling of situations in which heuristic activity is manifested.

Currently, heuristics have come to mean:

1. special methods for solving creative problems

2. organization of productive creative thinking processes

3. way of writing computer programs (HEURISTIC PROGRAMMING)

4. the science that studies heuristic activity, a special branch of the science of thinking

5. special methods of teaching or collective problem solving

6. special methods of creative problem solving, called. Modern heuristics

The main tasks of heuristics as a science

1. knowledge of the patterns of productive processes based on the psychological characteristics of their course

2. identification and description of real situations in which the heuristic activity of a person is manifested

3. studying the principles of organizing models for heuristic activities

4. function of the level of knowledge of objects, which allows describing their structure and predicting the dynamics of their development

5. design of technical means that implement the laws of heuristic activity

2. Heuristic activity and its components

The main components of any activity:

· Motives that motivate a person to act

· Goals as results of activities

· The means by which the activity is carried out.

In the process of his intellectual activity, a person realized the need to find the best way to achieve the goal. For this, the possibilities of science were used, which did not always help, since it was necessary to solve problems that were not amenable to algorithmization. Experience, intuition and imagination came to the rescue.

Essential for heuristic activity is intuitive activity, the results of which precede their systematic substantiation by logical means.

The nature of intuition is based on the repetition of inferences, like thoughts of actions that become habits of thought.

Another type of heuristic activity is imagination. Imagination is not the attraction of a few outstanding people. In psychology, imagination is classified by degree:

· Intentions (voluntary and involuntary)

· Activities ( reproducing and creative)

· Generalizations of images (scientific, inventive, artistic)

The product of the imagination is the ideal as the image of what is due, and the dream as the image of what is desired. The success of the imagination depends on the depth of knowledge of the patterns of development of the object of interest, on the ability to identify the direction of further development.

3. Heuristic Decision Theory

Intellectual activity consists of decisions, which are the problem of choosing between several modes of behavior based on a comparative assessment according to a certain criterion of optimality.

TPR groups all decisions made by a person into 3 groups: deductive, abductive and inductive.

deduction is called a method of inference meaning the derivation of a statement from one or more others.

Induction - this is a way of inference, meaning the possibility of moving from single facts to a generalization.

Abductive solutions are considered in the class of rigorous and heuristic solutions. The abductive solution is rather vague and is the process of identifying the most likely initial statements from some final statement based on inverse transformations. The abductive decision is based on the extensive use of past experience.

Inductive solutions are typical heuristic solutions that are characterized by great uncertainty and represent the process of finding the most probable mechanisms of action in solving a problem based on a comparison of the initial information with a given goal.

4. The main factors of successful heuristic activity

The main heuristic questions are: optimization of educational and cognitive activity. A necessary condition for solving this problem is a systematic approach. Thanks to systematization, we get the opportunity to carry out the transfer of modes of action, i.e. perform the learned way of action in the changed conditions. One of the most important varieties of systemic handling of heuristic information is forecasting of various types and directions. A forecast should be understood as scientifically based judgments about the possible states of a certain object in future or alternative ways of occurrence and change of these states.

The main factors contributing to successful heuristic activity:

· Understand the ways and methods of productive educational and cognitive activity

· To systematize educational information into interdisciplinary complexes and operate it in a heuristic search, when performing any actions.

· Adapt to changing learning activities and anticipate their outcome

Selection by database: Abstract. Frontier control to section 3. Marmazova.docx, 4-6 sections of checkers.docx.
Pedagogical heuristics
CHAPTERI.

Heuristics in the system of modern knowledge.

Formation and development of heuristics.
Topic number 1.

Introduction to the discipline
"Eureka!" - this exclamation of the ancient scientist and inventor Archimedes is familiar to everyone since childhood. This word is not just a statement of the fact of the find. In our minds, it is associated with the expression of a higher sense of satisfaction, joy and delight from the found solution to a problem that no one has been able to solve before. More than two millennia have passed, the word appeared in our vocabulary "Heuristic" . At present, the concept corresponding to it is widely used. In our minds, it is always associated with creative activity. The common links linking together heuristics and creativity are ideas about non-triviality, originality, novelty, uniqueness.

Heuristic methods can be widely applied in the practice of a modern leader of any rank, including in the activities of a modern manager. Holding meetings, business games using heuristic methods (“brainstorming”, empathy, inversion, synectics, etc.) usually gives a lot of ideas, fundamentally new approaches to solving various types of management problems in commercial activities. Heuristic methods are now widely used in business and management, as they stimulate the development of intuitive thinking, imagination and creativity.

A creative, productive process in any field of activity is a multifaceted, complex process containing many components, even the circle of which is currently difficult to outline completely. It is associated with a high tension of all the spiritual forces of a person, requires intense activity and imagination, concentration of attention, volitional tension, mobilization of all knowledge and experience to solve the problem.

Creation - this is a purposeful theoretical and practical activity of people, which leads to the creation of new, previously unknown hypotheses, theories, methods, new equipment and technologies, works of art and literature.

Heuristic activity - one of the components of creativity, and heuristics - the oldest scientific field. It considers the fundamental issues of organizing mental activity in non-standard situations, that is, when a person faces a task (problem), the solution of which he had not previously encountered. It is difficult to form strong skills of heuristic activity in a future specialist without knowledge of its fundamental principles and classical methods. The use of heuristic systems and methods in scientific, technical, inventive, and any other creative work has now become a common approach to solving many emerging problems. Acquaintance with heuristic methods is the basis for effective practical activity of a specialist, including in the field of management. If a future manager is preparing for such a professional activity in which he must often form his decisions in changing (dynamic) and non-standard situations, then he needs knowledge of heuristic methods. Acquaintance with heuristic methods will allow you to fully realize yourself.

The Oxford English Dictionary defines heuristics as follows: Heuristic - the art of finding the truth, in particular, is used to characterize a system in which a person is taught to independently find an explanation for phenomena. Somewhat simplified, heuristics can be viewed from two sides. On the one hand, this is the art of finding the truth, which must have generally accepted scientific foundations and principles of its development. On the other hand, on the basis of the known patterns of heuristic activity, it is possible to build a system that would most optimally use the potential of thinking in activity and purposefully develop it qualitatively. The two considered sides put forward the need to develop heuristics that would harmoniously unite them: the areas of theoretical and practical heuristics, the area of organizing activities based on it.

The formation and development of heuristics occurred simultaneously with the development of science. Scientists and philosophers of ancient Greece thought about the questions: how can we look for what we do not know, and if we know what we are looking for, then why should we look for it? In the course of such reasoning, it was noticed that in order to find solutions to emerging scientific and practical problems, a person uses largely the same mental and organizational actions. The further development of science and the emergence of cybernetics marked the beginning of the modern stage of heuristics (50s), which is characterized by an intensive study of all aspects of productive thinking.

As a result, at the intersection of many scientific disciplines that study human intellectual behavior, synthesizing their achievements, heuristics in its modern sense arose as a science that studies the patterns of organization of human intellectual behavior when solving emerging new problems.

The fundamental ideas and patterns of heuristics, proven classical methods and heuristic search systems are studied with the aim of their subsequent purposeful application in the training of specialists in various fields of human activity, including management. All this should serve as the basis for the development of their creative potential. Outside of such conditions, creative inclinations are formed on the basis of the transition of the number of solved problems into the quality of skills for solving them, which naturally is not the optimal way to acquire them.

It was found that heuristics really provides an independent movement towards knowledge, as well as the acquisition of solid, operational knowledge and skills, but at the same time it requires too much work and time to obtain these results.

At the present stage of formation of heuristics there is an intensive development of the conceptual and terminological apparatus. Synthesizing the achievements of various scientific fields, in the intersection of which it develops, heuristics simultaneously transfers them into terminology, although such a trend, of course, is of a general scientific nature. It is important to understand that a person is born not with knowledge, but with the ability to master and extract it. The specificity of heuristic activity is such that it is not uniquely defined, so heuristics wins the most when it is approached critically.

Heuristics originated and developed for a long time in the depths of philosophy. Scientists of antiquity conducted various studies in the fields of mathematics, physics, mechanics and other branches of knowledge, at the same time trying to answer the questions: how to conduct research so that they lead to the discovery of new patterns? How to properly solve emerging problems? How to organize your mental activity so that it proceeds purposefully? Such questions did not receive an unequivocal answer, but gradually their study acquired a deeper, more objective and practical character. These qualitative thought processes have been called heuristic.

In addition to philosophy, other scientific disciplines began to study these processes, the task of which was to study the intellectual behavior of a person, his thinking and the processes of its flow. Thus, at the intersection of a number of scientific disciplines, modern heuristics arose, which synthesized the knowledge of these areas in its specific object of study.
Topic number 2.

Formation and development of heuristics. history of its evolution.
Heuristics and maieutics of Socrates.
There are enough examples in the history of scientific knowledge when theoretical concepts with the development of science are filled with more precise content, sometimes absorbing the original term, and in some cases even significantly changing it. This happened with the concept of "heuristics".

Word " heuristic" comes from the Greek Heurisko- I find, I find, I discover, which meant in ancient Greece the teaching method used by Socrates (“Socratic conversation”). The structure of such a conversation consisted of a system of questions leading the student to the correct solution of the problem posed to him.

Heuristics is considered to be maieutics(translated from Greek - obstetrics, midwifery) - one of the methods of establishing the truth in a conversation or dispute. Its essence lay in the fact that Socrates, with the help of skillfully posed questions and the answers received, consistently led the interlocutor to true knowledge. Maieutics, according to Socrates, was always implemented in combination with other techniques:

by induction, requiring a transition to general concepts from ordinary representations and single examples;

definition, meaning a gradual entry to the correct definition of the concept on the basis of the original definitions.

In the modern sense, this method is used in teaching and consists in the fact that the trainee, through a series of questions, is led to a solution to the problem to be considered. This method is applicable in all cases when one wants to excite in the trainee the ability to combine known data. This method is applicable when thought tension and deduction are required. With the correct and systematic formulation of questions, the method can develop ingenuity and ingenuity. With the inept formulation of questions, on the contrary, he develops in the trainee the desire for answers at random.
Archimedes method .
Simultaneously with the Socratic understanding of heuristics, many ancient scientists used various methods to find a solution to the problem. These methods, in the modern sense. were heuristic. So, Archimedes (287 - 212 BC) in the essay "The Doctrine of the Methods of Mechanics" sets out the theory of finding solutions to new problems: with the help of mechanical representations (in modern terminology - physical models), hypotheses of the solution are found, which are further studied and tested with the help of mathematics. The art of solving difficult problems for which there are no simple and easily chosen ways, gets its name from the famous exclamation of jubilation "Eureka!" (“Found!”) at the moment when the scientist realized how to determine the volume of the crown (irregularly shaped body).
Heuristic Dad.
An interesting source related to heuristics is the Mathematical Compilation by the Greek mathematician Pope (c. 300 AD). In his VII volume, he discusses the branch of science, which in Greek can be interpreted as heuristics.

The starting point of his analysis is that it is required to prove that the problem has already been solved. Conclusions were drawn from this task, other conclusions were drawn from these conclusions, and so on. until they come to such a conclusion that can be used as the beginning of a synthesis, because in the analysis they consider that what is required to be done according to the conditions of the problem has already been completed (what is sought is already found; what is required to be proved is proven). Determine from which antecedent the inference of interest can be obtained, then re-determine which inference can be obtained from that antecedent, and so on, moving from one inference to the antecedent that caused it, until one arrives at the conclusion that was obtained before or taken as true. This approach is called analogy or solving problems to the end, or regressive reasoning.

Such a train of thought, in the terminology of the Pope, should be called analysis. Indeed, this primitive man may become the inventor of the bridge and the axe, if he succeeds in completing his analysis. What will be the synthesis in this case? Turning these ideas into action. The final stage of the synthesis will be a tree crossing through the stream. The same elements constitute analysis and synthesis. In analysis, the human mind is exercised, and the muscles in synthesis. Analysis is thought, synthesis is action. There is another difference - the opposite of order. Summarizing, we can say that analysis is invention, synthesis is execution, analysis is drawing up a plan, and synthesis is its implementation.
Heuristics in the works of Descartes.
Rene Descartes (1596 - 1650) made a significant push in the direction of scientific thought towards the study of heuristic activity. He was engaged in research in many natural areas of science. In mathematics, his scientific interests were in the development of new methods. So, R. Descartes combined the methods of algebra and geometry, as a result of which analytical geometry appeared. It technically revolutionized the methodology of mathematics, since the use of equations made it possible to prove various properties of geometric curves much more simply than by purely geometric methods.

Continuing research in the field of methodology, R. Descartes sought to develop a universal method for solving problems. Here is a scheme that he suggested could be applied to all sorts of problems:

– a problem of any kind is reduced to a mathematical problem;

- a mathematical problem of any kind is reduced to an algebraic problem;

- any problem is reduced to solving a single equation.

- what should be the process of mental work in solving problems;

– analysis of the solution of correctly and incorrectly posed problems.

Descartes saw his main goal in finding a way to establish the truth in any area. He dedicated the main work of his life, Discourses on Method, to this. Descartes' project is considered great, it had a greater impact on science than thousands of other small projects, even those that could be realized.
Heuristic ideas of Leibniz.
The German philosopher Gottfried Leibniz (1646 - 1716), like Descartes, was engaged in extensive scientific activity in the field of mathematics, physics, biology, history and logic. He considered scientific activity as a religious mission entrusted to scientists. His philosophy of science was aimed at encouraging man to discover and invent. Numerous and original fragments describing the organization of the creative process are scattered in his writings. These are actually various heuristic rules and techniques that help find ways to solve new problems. Leibniz argued that nothing is more important than the ability to find the source of an invention, which is even more interesting than the invention itself.

Its main principles are:

complex concepts are deduced from simple ones only with the help of operations of logical multiplication and intersection of the volumes of concepts in the logic of classes;

a set of simple concepts must satisfy the consistency criterion;

any statement can be equivalently translated into another form;

Every true affirmative sentence is analytic.

The formation of Leibniz's methodological views was influenced by Descartes' thoughts about the possibility of constructing a universal logical-mathematical method for solving scientific problems. Leibniz and Descartes hoped that they would be able to expand logic into a universal science of thinking applicable to all areas of the human mind - to build a kind of universal calculus of thinking.

Neither Descartes nor Leibniz succeeded in developing a consistent symbolic calculus of logic. They created only fragments that were very far from their task: to reduce any reasoning to calculation. Leibniz dreamed of creating a situation in which one of the disputants could always say to the other: “You say one thing, I say another; Well, let's figure out which of us is right.
Topic number 3.
Benchmarking in heuristicsXIXcentury
Works by Saint-Simon and Bolzano
The French scientist A. Saint-Simon (1760-1825) paid much attention to the study of comparison as an important cognitive tool. He argued that "the whole work of the human mind, in the end, comes down to comparisons: to say, for example, that a thing is good or bad is to say that it is better or worse than the other with which it is compared." He put forward the idea of creating a special science of comparing ideas, pointing out mathematics as a model for it, which is "the science of the most accurate and deepest comparisons." It should be noted that the comparative method in the XIX century. It has been widely used in the sciences that have accumulated a large amount of empirical material.

Of considerable interest in determining the essence of heuristics are the ideas of the Czech logician, mathematician and philosopher Bernardo Bolzano (1781-1848), set forth in the "Science", his main logical and philosophical work. It deals with the problems of classical logic, theory of knowledge, theory of science, psychology of thinking, heuristics and pedagogy. Such a fundamental approach to the study of intellectual activity made it possible to consider the following questions: what is cognition and knowledge? What is truth? What are the means and ways of knowing the truth? What are the forms and rules of any cognitive activity?

In his presentation of the heuristic activity B. Bolzano takes a step forward in comparison with Descartes and Leibniz, critically developing the ideas of his predecessors. Thus, Bolzano showed that reference to any kind of evidence cannot serve as evidence in scientific research. All delusions, according to Bolzano, stem from the fact that we incorrectly estimate the probabilities of heuristic conclusions and often use these conclusions as proven ones.
Boole Algebra.
Irish professor of mathematics George Boole (1815-1864) made outstanding progress in the critical revision of logic. He proposed and developed a generalization of algebraic reasoning in the form of an algebra of operators. His position was that algebra does not have to deal with numbers alone and that the laws of algebra should coincide with the laws of arithmetic for real and complex numbers. Boole's main idea is that the existing laws of thought can be represented in a symbolic form, which makes it possible to give a more precise meaning to ordinary logical reasoning and to simplify their application.
Heuristics in the works of Poincaré.
The French mathematician Henri Poincaré (1854-1912) paid much attention to questions of the methodology of science and heuristics itself. He believed that the laws of science do not refer to the real world, but are arbitrary agreements that should serve the most convenient and useful (in accordance with Mach's "principle of economy of thought") description of the relevant phenomena.

Considering the mechanism of mathematical creativity, Poincare emphasized that it does not differ significantly from any creative activity, therefore, by studying it, we have the right to count on penetration into the very essence of the human mind. For this, first of all, the scientist believed, it is necessary to know the psychological mechanism of creativity, therefore, observations on the work of a mathematician, in his opinion, are especially instructive for a psychologist.

Poincaré believed that a solution or a proof can evoke in us a sense of elegance when there is a harmony of individual parts, their symmetry, their happy balance - everything that brings order, that tells these parts the whole at the same time as the details.

The scientific method of Poincaré is observation and experiment, but since time is limited, the scientist must make certain choices in order to establish patterns. The principles of choice for many researchers are not devoid of analogy. A rule is preliminarily established that covers systematically repeated facts. Further, such facts are of no interest, since they no longer teach anything new. Exceptions are now of interest, and above all the sharpest ones, because they are not only the most conspicuous, but also the most instructive. Thus, if any rule is established, we must first investigate those cases in which the rule is most likely to be wrong.

Having carried out research on the similarity of facts to the rule and their differences, it is necessary to focus on those analogies that are often found in apparent differences. A new result is worthy of high appraisal if it links together known elements, which until then were scattered and seemed alien to each other. He brings order suddenly to where there has been chaos so far. Scientific progress is driven by unexpected convergences between different parts of science.

Poincaré attached great importance to sudden insight. He was struck by the nature of insight, which undoubtedly testifies to a long preliminary unconscious work. This work is fruitful only if it is preceded and followed by a period of conscious work. In any case, the role of this unconscious work in the process of mathematical creativity is great and undeniable. Random facts Poincaré considered random for the ignoramus, but not for the scientist. Randomness in his interpretation is a measure of our ignorance, therefore random phenomena will be those whose laws are unknown to us.

In his extensive methodological works, Poincaré paid great attention to both mathematical creativity and the teaching of mathematics. The questions of scientific creativity developed by him are related to the problems of heuristics, outlined on the basis of his own experience.
Engelmeyer's heuristic.
In the first half of the 20th century, work began to appear on the problems of heuristic activity in certain specific areas. So, in 1910. PC. Engelmeyer published the theory of creativity" - a study on scientific and technical creativity, in which he also developed more general issues of creating a whole science of creativity - neurology, emphasizing the unity of the heuristic and logical principles of this science.

Technical creativity of P.K. Engelmeyer considered it as a phenomenon characteristic of any developing organism. He divided the single organic process of creativity into three qualitatively different acts.

The first act is intent. Only this act is related to psychology. Its result is the emergence of an idea, that is, a hypothesis of a future invention. The act begins with an intuitive feeling of an idea and ends with its clarification. A concrete way of solution comes to the inventor in the process of thinking suddenly, like an instantaneous flash in the understanding of the goal.

The second act is the plan. This act is based on logic, since its result is a logical scheme of the future construction.

The third act is action. This act is related to the real, since at this stage the inventor gives way to the artisan.

At the same time - the first decade of the XX century. - there are works of teachers-mathematicians who associated successful teaching of mathematics with heuristics. Thus, the French teacher Lezan presented his system in the form of advice to the teacher. These tips are based on keeping the trainee's mind open and supporting imitation of self-discovery. A similar concept was supported by S.I. Shorokh-Trotsky. Much attention was paid to heuristic methods of teaching by N.A. Izvolsky, who saw the main task of teaching in the development of creative abilities based on these methods.

Based on the analysis of the processes of formation and development of heuristics, the following conclusions can be drawn:

It turned out that to solve such problems, it is possible to apply fairly general guidelines, rules, and recommendations that do not concern only a narrow subject area. They do not guarantee the achievement of the goal, but they significantly increase the likelihood of success with their goal-oriented sequence compared to unorganized search.

The attempts made to formalize such systems on the basis of the identification of logic and thinking did not reach the goal. This was an unpromising path for the development of heuristics, on which, however, new scientific directions were born.

During the development of heuristics, almost all existing methods of traditional heuristic activity have arisen and studied.

In fact, a view was formed on heuristics as a science, which is based on areas that study the intellectual behavior of a person.

Topic number 4.
The current stage of development of heuristics
Significance of Poya's work.
The modern stage of development of heuristics begins in the second half of the 20th century. It is associated with the emergence of cybernetics and the need to develop search heuristic systems for scientific and inventive activities. By this time, D. Poya's fundamental research on heuristics appeared, summing up its development at the previous stage and outlining its prospects. He wrote: “Descartes pondered over a universal method suitable for solving any problems; Leibniz formulated the idea of the perfect method most clearly. However, the search for a universal, perfect method gave no more effect than the search for the philosopher's stone, which turns base metals into gold. However, such unattainable ideals do not remain useless - while no one has reached the North Star, but many, looking at it, have found the right path. Polya's work was the first to consider the need for early purposeful training in heuristic activity skills. He expressed the main idea of his works in the following words: “The process of solving a problem is a search for a way out of a difficulty or a way around an obstacle - this is a process of achieving a goal that initially does not seem immediately available. Problem solving is a specific feature of intelligence, and intelligence is a special gift of a person; Therefore, problem solving can be considered as one of the most characteristic manifestations of human activity.

Gradually, the efforts of scientists shifted from trying to find a universal method to a consistent study of the patterns of heuristic human activity. "Heuristics aims to establish the general patterns of those processes that take place in solving all kinds of problems, regardless of their content."
Modern definitions of heuristics.
The study of the heuristic intellectual activity of a person and the practical application of the identified patterns of its course in various scientific activities caused the contextual definition of heuristics. The understanding of heuristics in various scientific fields of knowledge has been transformed under the influence of the specifics of its application in these areas. There was a quantitative accumulation of information.

Under heuristics began to understand:

Organization of the process of productive creative thinking (heuristic activity). In this sense, heuristics is understood as a set of mechanisms inherent in a person, with the help of which procedures are generated aimed at solving creative problems (for example, mechanisms for establishing situational relationships in a problem situation, cutting off unpromising branches in a tree of options, forming rebuttals using counterexamples, etc. ). These mechanisms, which together determine the metatheory of solving creative problems, are universal in nature and do not depend on the specific problem being solved. A way of writing computer programs (heuristic programming). If in conventional programming a programmer recodes a ready-made mathematical solution method into a form understandable by a computer, then in the case of heuristic programming, he tries to formalize the intuitively understandable method of solving a problem that, in his opinion, a person uses when solving such problems. Like heuristic methods, heuristic programs do not ensure the absolute achievement of the goal and the optimality of the result.

The science that studies heuristic activity; special branch of the science of thinking. Its main object is creative activity; the most important problems-tasks related to decision-making models (in conditions of non-standard problem situations), the search for a new structuring of descriptions of the external world for the subject or society (based on classifications such as the periodic system of elements by D.I. Mendeleev or plant taxonomy by K. Linnaeus). Heuristics as a science develops at the intersection of psychology, the theory of artificial intelligence, structural linguistics, and information theory.

A special teaching method (“Socratic conversations”) or a method of collective problem solving. Heuristic learning, dating back historically to Socrates, consists of asking learners a series of leading questions and examples. A collective method for solving difficult problems, called "brainstorming", is based on the fact that team members ask the author ideas for solutions, leading questions, examples, counterexamples.

Such definitions confirm the opinion of many researchers that heuristics will survive its period of formation. The emphasis of research began to shift from obtaining a result to organizing intellectual activity to obtain it. There is an increasing scientific interest in the methods of organizing the receipt of results, which made it possible to apply the found method to other emerging problems in various areas of human professional activity, including the field of management.
Topic number 5.
The subject and tasks of heuristics.
The considered definitions of heuristics show that heuristic activity is a complex, multifaceted and multifaceted type of human intellectual activity, which to a greater extent occurs hidden and cannot be objectively studied and described within the framework of one science.

Therefore, heuristics synthesizes the results of various sciences and, on this basis, establishes the patterns of organization of heuristic activities. Such sciences are, first of all, the psychology of thinking, the physiology of higher nervous activity, philosophy, cybernetics, logic, pedagogy, and some others. In general, any scientific field that studies human intelligence necessarily concerns certain aspects of the organization of creative processes, which include heuristic activity. All this justifies the need to build a special science - heuristics, which, based on the scientific achievements of other disciplines and using its methods of generalization and research, would study the specific quality of human intelligence - heuristic activity. Heuristics should also investigate the regularities of such activity in technical cybernetics.

All this allows us to give the following definition heuristics: by heuristics as a science we will understand the science that studies the patterns of constructing new actions in a new situation.

A new situation is a problem that has not been solved by anyone or a technical device that has not been invented, the need for which has been identified. The situation will also be new when a specialist encounters a non-standard problem of his level, the proof of which he must independently find. Getting into a new situation, a person is looking for ways out of it, that is, solutions that are unknown to him and which he has not yet met in his practice. This may be a fundamentally new method or a new sequence of well-known actions. Thus, heuristics focuses on the study of the patterns of constructing new actions that are similar in many ways, regardless of the subject area of application. If the situation is not new, then the person's actions are algorithmic in nature, that is, he simply remembers their sequence, which will certainly lead to the goal. In these actions there are no elements of productive thinking, in contrast to the new situation, when the result must be objective or subjective - when the result is new for the person who received it.

Heuristics as a science originates in the psychology of thinking. As the main subject of research, she considers the organization of productive intellectual activity, based on mental acts, with the help of which the heuristic search process takes place.

As is known, thinking committed and develops in the following forms:

abstraction, generalization, concretization;

induction, deduction, analogy;

finding connections and relationships;

formation of concepts, their classification and systematization.

However, as the main subject of study heuristics considers the main operations based on these mental acts, from which it starts as given. main subject her research is the study of ways to search and form information with their help to find solutions. The person solving the problem forms hypotheses based on the information model of the problem task, starting with the most general and oriented one. At the first stages of the decision, he lacks information to draw a categorical and confident conclusion. Its subsequent accumulation makes it possible to anticipate the path of the solution more and more reasonably. The second feature in the subject of heuristics research is that different types and forms of thinking do not occur separately, but in interconnection, therefore, the main thing in solving a problem is a combination of various heuristic and logical operations, their systematic application. At the same time, complex search operations act not as a result of the usual mechanical combination of elementary operations, but as a result of complex intellectual activity, in which heuristic, algorithmic, algorithmic (logical) components of thinking are interconnected, and often subjectively.

The main tasks of heuristics as sciences are:

knowledge

patterns of productive processes

identification and description of real situations, in which heuristic human activity or its elements are manifested;

study of the principles of organization of conditions (models), for heuristic activity;

modeling situations in which a person manifests heuristic activity, with the aim of studying its course and learning its organization;

creation of targeted heuristic systems(general and particular) on the basis of the known objective patterns of heuristic activity;

design of technical devices, realizing the laws of heuristic activity.

Topic number 6.

Heuristics in the system of other sciences.
Heuristics and psychology of thinking
The formation and development of heuristics as a science that arose at the intersection of several scientific disciplines makes it necessary to consider its fundamental connections with them.

One of the main areas of traditional scientific research on heuristic human activity is psychology of thinking , in which heuristics stood out in one of its sections. It conducts work on the study of the nature of human mental operations in solving various problems, regardless of their specific content and subject area. The main task of the psychological analysis of thinking in this case is to clarify the heuristics used by a person, their systematization and the development of recommendations for the active management of the process of their assimilation and application. Studies are carried out on specially selected material, convenient for analysis, and are, as a rule, of a short-term nature. Heuristics in these studies are understood as guesses, special methods and techniques based on generalized experience in solving intellectual problems. The combination of these techniques and methods develops the ability to find approaches to problems, the methods for solving which are unknown to man.

Thinking - a complex cognitive mental process of interaction between a knowing person and a cognitive object. It is the leading form of human orientation in reality. Almost always, thinking is, in fact, a creative process with elements of a heuristic search of a certain level, since it occurs in situations in which new information and ways of processing it are needed to make a decision. In the process of thinking, a person can set himself tasks and formulate answers, put forward hypotheses, build evidence, create scientific theories and inventions. In any complex mental activity, there is heuristic activity as an element of creative thinking. Thinking is able to combine, compare and contrast information about phenomena and objects that are not directly related to each other. Revealing natural essential connections, thinking is able to foresee the ways of further development of the material world - forecasting, and thus outperform it. These abilities are based on the most important characteristics of thinking - generalizations and mediation reflections of the surrounding reality.

One of the theories claiming to describe thinking is based on the classical association theory . In it, thinking is understood as a connection between stimuli and reactions or elements of behavior and is interpreted as laws governing the sequence of elements of behavior (“ideas”). An "idea" in classical association theory is a copy, a trace of stimuli. The theory is based on the following law of succession: if two objects A and B often occur together, then the presentation of A will recall the object B, that is, the connection is based on the principle of superficial external causation (as, for example, the connection of a telephone number with the name of the owner).

The list of operations in association theory is as follows:

the role of frequency of repetition, novelty;

recalling past experiences;

trial and error with occasional success;

learning based on repetition of a successful trial;

actions in accordance with conditioned reactions and habits.

However, the thought process differs from free association primarily in that thinking is directed association. The factor that directs association and turns it into thinking is the goal. An essential property of associative links is that they represent the basis of such an ordered storage of information in the human brain, which provides a quick search for the necessary information by referring to the necessary material by association.
Heuristics and logic.
There is an approach to describing thinking based on identification of the functions of thinking and logic . Currently logics (Greek - word, thought, speech, mind) as science is a synthesis of scientific achievements about the laws and forms of thinking. Traditional and mathematical logics study the laws of obtaining knowledge from previously established truths, without recourse in each case to experience. This happens on the basis of the laws of inferential knowledge.

Traditional logic can be called the arithmetic of logic. She studies the following general laws:

identity law

law of contradiction: two opposite thoughts about the same subject, taken at the same time and in the same relation, cannot be true at the same time;

law of the excluded middle: of two contradictory statements at the same time and in the same respect, one is necessarily true;

law of sufficient reason: every true thought must be justified by other thoughts, the truth of which has been proven.

Traditional logic considers how to build reasoning correctly in form, so that, subject to the correct application of formal-logical laws, to come to a true conclusion from true premises. Mathematical logic is the algebra of formal logic. She studies the action of basically the same laws, but by mathematical methods, which allows her results to be applied, for example, in cybernetics. Based on the laws and rules of logic, certain combinations of judgments make it possible to obtain “new” correct judgments, but their novelty is only in the obvious expansion of existing knowledge. Logic, studying the structure of a separate thought and various combinations of thoughts into complex forms, abstracts not only from the specific content, but also from the processes of emergence, formation, creative development of thoughts, which excludes the possibility of describing thinking in terms of traditional logic.

Logics has great educational value:

- constant striving for true knowledge;

- special attention to the difference between a simple statement, belief, exact judgment;

- finding and studying the difference between insufficiently clear concepts, vague generalizations and precise formulations;

- the development of formal criteria to detect errors, ambiguities, illegal generalizations, hasty conclusions;

– understanding the importance of evidence; the requirement of persuasiveness and rigor of each individual step of thinking.

These virtues of traditional logic refute the claim that it is not related to real behavior. Real behavior will not achieve a reasonable goal if it is determined by factors analogous to errors in traditional logic.
Heuristics and cybernetics. Heuristics and intelligence.
With the development of information theory and cybernetics, many researchers began to describe thinking as a process of processing information by a person. Cybernetics (Greek - the art of management) - the science of managing, receiving, transmitting and converting information in systems of any nature (cybernetic systems): technical, biological, economic, etc. This approach does not define thinking, it points to one of its main properties, which is its cognitive side of actively extracting information from the external environment and processing it. Regarding this approach, Academician A.K. Kolmogorov spoke as follows: “I belong to those cybernetics who do not see any fundamental limitations in the cybernetic approach to the problem of life, and I believe that it is possible to analyze life in its entirety, including human consciousness with all its complexity, using the methods of cybernetics.”

When considering thinking, the concept " intelligence "(lat. - knowledge, understanding, reason). Intelligence is a system of mental abilities as a level of development of thinking. Sometimes they say that thinking is intelligence in action. The intellect includes a system of all cognitive functions of a person: from sensation and perception to thinking and imagination.

The main qualities that characterize intelligence and are studied in various disciplines include:

- the ability to understand and learn from experience; acquire and retain knowledge; mental capacity;

- the ability to measure quickly and correctly respond to a new situation; the ability to reason when choosing an action strategy;

- a measure of success in using the listed abilities in the performance of a specific activity.

The formation and development of intellect occurs on the basis of labor as a purposeful activity in the surrounding world. Here the most essential quality of the human intellect is also manifested, which allows you to reflect the laws of the surrounding world and, on this basis, transform it. This is also related to the generalization of the understanding of intelligence as the cognitive activity of any complex systems capable of learning, purposeful processing of information and self-regulation. At the same time, heuristic activity must be considered as an intellectual (thinking) activity in a new non-standard situation. All this is explained by the approach to research that cybernetics implements.