The concept of problem-based learning Kudryavtsev Lerner Matyushkin Makhmutov. Problem-Based Learning Theory and I Lerner mn

Introduction

The whole life of a person constantly poses complex and urgent tasks and problems for him. The emergence of such problems, difficulties, surprises means that in the reality around us there is still a lot of unknown, hidden. Consequently, an ever deeper knowledge of the world is needed, the discovery in it of more and more new processes, properties, relationships between people and things. Therefore, no matter what new trends, born, born by the requirements of the times, penetrate the school, no matter how programs and textbooks change, the formation of a culture of problematic activity of students has always been and remains one of the main general educational and educational tasks. Problem-based learning is the most important aspect of preparing the younger generation.

The success of problem-based learning of a student is achieved mainly in the classroom, when the teacher is left alone with his pupils. And from his ability to “fill the vessel and light the torch”, from his ability to organize systematic cognitive activity, the degree of students' interest in learning, the level of knowledge, readiness for constant self-education, that is, their development, which convincingly proves modern psychology and pedagogy, depends.

Most scientists recognize that the development of the creative abilities of schoolchildren is impossible without problem-based learning.

Creativity is realized through problem-solving activities.

The psychological basis of the concept of problem-based learning is the theory of thinking as a productive process, put forward by S.L. Rubinstein. Thinking plays a leading role in problem-based human learning.

The idea of ​​problem-based learning is not new. The greatest educators of the past have always looked for ways to transform the learning process into a joyful process of learning, developing the mental strength and abilities of students.

In the 20th century, the ideas of problem-based learning were intensively developed and spread in educational practice. A significant contribution to the disclosure of problem-based learning was made by N.A. Menchinskaya, P.Ya. Galperin, N.F. Talyzina, T.V. Kudryavtsev, Yu.K. Babansky, I.Ya. Lerener, M.I. Makhmutov, A.M. Matyushkin, I.S. Yakimanskaya and others.

Although this problem is considered in detail in the Psychological-pedagogical and methodological literature, it has not received due attention in the practice of the school. Therefore, for research into term paper this topic has been chosen.

The purpose of the course work- to reveal the theoretical provisions, features of the content and methods of problem-based learning in the pedagogical process.

The course work identified the following tasks :

1. To study and analyze the psychological, pedagogical and methodological literature on the research topic.

2. Highlight the signs of problem learning.

3. Describe the methods of problem-based learning technology that can be used in learning activities in mathematics lessons.

4. Study the structure of problem-based learning.

5. Consider the content and sources of educational problem situations in a mathematics lesson.

Object of study is a problem-based learning process.

Subject of study- methods, forms, content of problem-based learning in educational activities.

Coursework hypothesis: the use of problematic tasks and questions has an impact on the effectiveness of training and development cognitive abilities students.

In this course work at the theoretical level, the following research methods: at the theoretical level - analysis, comparison, analysis of literature, analysis of the conceptual and theoretical system, at the empirical level - the study and generalization of mass and individual pedagogical experience.

Chapter 1. Theoretical basis problem learning

1.1 History of the development of problem-based learning

Problem-based learning is not a completely new pedagogical phenomenon. Elements of problem-based learning can be seen in the heuristic conversations of Socrates, in the development of lessons for Emil by J.J. Rousseau. K.D. was especially close to this problem. Ushinsky. For example, he wrote: the best way We consider the transfer of mechanical combinations to rational ones for all ages, and especially for children, the method used by Socrates and named after him Socrates. Socrates did not impose his thoughts on his listeners, but, knowing what contradictions of a series of thoughts and facts lie next to each other in their heads dimly lit by consciousness, he called these contradictory series into the bright circle of consciousness with questions and, thus, forced them to collide, or destroy each other. , or to try on in the third of their connecting and clarifying thought.

Problem-based learning arose as a result of the achievement of advanced practice and theory of education and upbringing, in combination with the traditional type of education, is an effective means of general and intellectual development of students.

The history of problem-based learning proper begins with the introduction of the so-called research method, many of whose rules in bourgeois pedagogy were developed by John Dewey. Deep research in the field of problem-based learning began in the 60s.

However, in the history of pedagogy, the posing of questions to the interlocutor that causes difficulty in finding an answer to them is known from the conversations of Socrates, the Pythagorean school, and sophists. The ideas of enhancing learning by including students in research activities are reflected in the works of J.-J. Russo, I. Pestalozzi, F.A. Disterweg, K.D. Ushinsky, representatives of the new education and others.

The development of methods for activating the mental activity of students led in the second half of the 19th - early 20th centuries. to the introduction of heuristic (G.E. Armstrong), experimental-eristic (A.L. Gerd), laboratory-heuristic (F.A. Winterhalter), method of laboratory lessons (K.P. Yagodsky) and others into the teaching of individual subjects methods that B.E. Raikov, due to the general nature of their essence, replaced the term "research method".

in American pedagogy in the early 20th century. There are two main concepts of problem education. J. Dewey intended to replace all types and forms of education with independent learning by schoolchildren through problem solving.

In the 20th century, the ideas of problem-based learning were intensively developed and spread in educational practice. In foreign pedagogy, the concept of problem-based learning developed under the influence of the ideas of J. Dewey. In How We Think (1909), the American philosopher, psychologist, teacher rejects traditional dogmatic teaching and opposes it to the active independent practical activity of students in solving problems. Thinking, says J. Dewey, is a solution to problems.

In the second edition of this book (1933), J. Dewey substantiates psychological mechanisms ability to solve problems. He argues that students' ability to solve problems is based on their natural intelligence. The individual's thought moves to a state where everything in the task is clear, passing through certain stages:

1. all possible decisions or assumptions are taken into account;

2. the individual is aware of the difficulty and formulates a problem to be solved;

3. Assumptions are used as hypotheses to guide observations and collection of facts;

4. Argumentation and putting in order of the discovered facts is carried out;

5. a practical or imaginary verification of the correctness of the hypotheses is carried out.

A significant role in the development of the theory of problem learning was played by the concept of the American psychologist J. Bruner. It is based on the ideas of structuring the educational material and the dominant role of intuitive thinking in the process of mastering new knowledge. J. Bruner pays special attention to the following issues:

− the importance of the knowledge structure in the organization of training;

- the willingness of the student to learn as a learning factor;

− intuitive thinking as a basis for development mental activity;

− motivation for learning in modern society.

The key problem for the scientist is the problem of the structure of knowledge, which, in his opinion, includes all the necessary elements of the knowledge system and determines the direction of the student's development.

The essence of the second concept is the mechanical transfer of the findings of psychology to the learning process. V. Burton believed that learning is the acquisition of new reactions or the change of old ones and reduced the learning process to simple and complex reactions without taking into account the influence of the environment and upbringing conditions on the development of the student's thinking.

Biggest impact on development modern concept problem-based learning was provided by the work of J. Bruner ("Learning Process", 1960) . It is based on the ideas of instructing educational material and the dominant role of intuitive thinking in the process of mastering new knowledge as the basis of heuristic thinking.

In the domestic pedagogical literature, the ideas of problem-based learning have been updated since the second half of the 1950s. XX century.

The most prominent didactics M.A. Danilov and V.P. Esipov formulate the rules for activating the learning process, which reflect the principles of organizing problem-based learning:

- to lead students to generalization, and not to give them ready-made definitions, concepts;

− episodically introduce students to the methods of science;

- to develop the independence of their thoughts with the help of creative tasks.

From the beginning of the 60s. In the literature, the idea of ​​the need to strengthen the role of the research method in teaching natural sciences and the humanities is persistently developing.

Eminent scientists again raise the question of the principles of organizing problem-based learning. The task arises of a wider application of the elements of the research method, or rather, research principle. The task is to gradually lead students to master the method of science, to awaken and develop their independent thought. You can formally communicate knowledge to a student, and he will learn it, and you can teach creatively, communicate knowledge in its development and movement.

It was the idea of ​​communicating knowledge in its movement and development that became the most important principle of the problematic presentation of educational material and a sign of one of the ways to organize problem-based learning. Since the second half of the 60s. the idea of ​​problem-based learning begins to be comprehensively and deeply developed. Of great importance for the development of the theory of problem-based learning were the works of domestic psychologists, who developed the position that mental development is characterized not only by the volume and quality of acquired knowledge, but also by the structure of thought processes, a system of logical operations and mental actions (S.L. Rubinshtein, N. A. Menchinskaya, T.V. Kudryavtsev). The position on the role of a problem situation in thinking and learning (A.M. Matyushkin) was of significant importance in the development of the theory of problem-based learning. A special contribution to the development of the theory of problem-based learning was made by M.I. Makhmutov, A.M. Matyushkin, A.V. Brushlinsky, T.V. Kudryavtsev, I.Ya. Lerner, I.A. Ilnitskaya and others.

Of great importance for the development of the theory of problem-based learning were the works of psychologists who concluded that mental development is characterized not only by the volume and quality of acquired knowledge, but also by the structure of thought processes, the system of logical operations and mental actions that the student owns (S.A. Rubinshtein , N.A. Menchinskaya, T.V. Kudryavtsev), and revealing the role of the problem situation in thinking and learning (A.M. Matyushkin) .

The experience of using individual elements in the school was studied by M.I. Makhmutov, I.Ya. Lerner and others. The starting points for the development of the theory of problem-based learning were the provisions of the theory of activity (S.A. Rubinshtein, L.S. Vygodsky, A.N. Leontiev). Problematic learning was considered as one of the patterns of mental activity of students. Methods for creating problematic situations in various academic subjects have been developed and criteria for assessing the complexity of problematic cognitive tasks have been found. Gradually spread, problem-based learning infiltrated from secondary school to secondary and higher vocational schools.

1.2 Signs of problem learning

Creative cognitive activity problem-based learning contributes greatly to students. Sometimes problem-based learning is opposed to the forms of teaching methods that have developed in theory and practice, which is deeply erroneous. The problematic nature of learning in a certain sense is inherent in any scientifically based method and in any form of organization of the educational process. It does not follow from this that problem-based learning is not fraught with anything new in comparison with modern practice learning. It is aimed at such an organization and methodology of the educational process, in which students creatively seek answers to their questions and use the most advanced methods of self-acquisition of knowledge.

The task of the school is the formation of a harmoniously developed personality. In modern pedagogy, questions of the general development of children in the learning process are investigated. The most important indicator of a comprehensively and harmoniously developed personality is the presence of a high level of mental abilities.

What is the essence of problem-based learning? It is best to turn to the most ancient example - to the way Socrates taught his students about 2.5 thousand years ago. In one of the dialogues ("Theag"), Plato describes how the young man Theag came to Socrates to find out how and from whom to learn to be wise. And Socrates, instead of answering the young man's question, begins to ask him about what he considers wisdom, what he really wants.

Socrates himself asks questions to the student, formulating them in such a way that the student has something to think about, at the same time he has enough knowledge to answer the question or find the answer in the course of reasoning. A long series of interconnected questions, each of which is subordinate to the main, first one, asked by the student, makes the student, finding answers to these questions, finally reject the wrong opinion and affirm the true one. This kind of conversation was called Socratic or heuristic, developing.

In the conditions of modern education, when students do not themselves come to teachers with questions, but go to school to study in accordance with the curriculum. Shaping the problem and the questions they need to figure out is the job of the teacher. Therefore, problem-based learning, for the most part, is an artificial phenomenon in school, coming not from a student looking for an answer to a question that interests him, but from a teacher who is concerned about how to interest students in educational work, which has only an external obligation related to their today's life, but not an internal motivating factor.

Overcoming this situation, the teacher himself artificially creates a problem situation, that is, it causes such a state of the student when, as a result of comparing his knowledge or developed skills with unknown fact or a phenomenon reveals a discrepancy between past knowledge and a new fact, moreover, contradictions in existing knowledge. For example, children know that a body whose density is greater than the density of water does not sink in water. But here the teacher carefully puts the steel needle on the water, and it remains on the surface. Why didn't the steel needle sink in water? After all, this contradicts the law of Archimedes! Thus, a state of surprise is created, puzzled by the fact that the fact contradicts the previously acquired correct knowledge: “This cannot be, but it is.” This makes it necessary to formulate the problem as a whole: under what conditions does the law of Archimedes not be realized? Or is it not the law, but something else?

Having formulated a problematic issue, narrowing the problem to a scale that is comparable with the knowledge of students, the teacher considers the interaction of the water surface with the surface of the body placed on it, communicates new knowledge about the structure of the surface layer of water and its properties, or involves students in activities to identify new knowledge.

The essence of problem-based learning lies in the search activity of students, which begins with the formulation of questions laid down in the curriculum, then consistently put forward in textbooks, in the presentation and explanation of knowledge by the teacher, in a variety of independent work of students.

The essence of this method is that it ensures that students are turned off to solve their problem. And in order for the educational problem to become exciting for them, it is necessary to create a problem situation - a certain mental state or intellectual difficulty that occurs when it is impossible to explain the phenomenon, fact, process of interest with the help of known knowledge or perform the necessary action in a known way.

So teacher E.A. Ilyin at literature lessons presents students artistic detail works, stimulating them to see the work being studied through it. For example, having read to the students how “... rushing into the upper room, Davydov, who nevertheless managed to shoot twice into the darkness, fell under a machine-gun burst. Losing consciousness, he fell on his back, painfully throwing his head back, clutching in his left hand a rough chip, chipped from the door lintel by a bullet. The teacher asks: “Well, tell me, why did Sholokhov need this chip in the picture, where everything is so big, fast, creepy?” Or another example: Raskolnikov killed an old woman - a pawnbroker and her sister Lizaveta. The teacher asks the students a question: “In general, how many did he kill? Is his crime limited to these two murders? .

It is impossible to imagine a high school student not interested in these problems, who accepted the artistic presentation of such details by the great masters of the artistic word.

The same can be said about the lessons of natural and mathematical disciplines. For example, when studying halogens (possibly in general when studying the properties chemical elements), introducing students to the structure of the atom of fluorine, chlorine, bromine, iodine, which differ so much both in the mass of the nucleus, and in the number of electrons and in physical properties, you can show them the common thing that unites all these halogens. What is the reason for this common? It will be interesting to find out this for everyone who received the first information and the second, which seems to contradict the first (about difference and similarity).

Thus, at the heart of the problem situation is surprise, puzzlement that a new fact contradicts the existing correct knowledge, or rather cannot be explained with their help.

Thinking always begins with a problem or a question, surprise or bewilderment, with a contradiction. This problematic situation determines the involvement of the individual in the thought process.

Problem situations can be created in various ways:

Showing the inconsistency of the new fact with known knowledge,

Comparing opposite opinions about one fact,

Showing the "impossibility" of using theoretical knowledge in certain non-standard situations,

Encouraging to predict the further development of the events of the finished work or their deployment in other conditions,

Giving the task to compare seemingly incomparable facts and the like. There is a large amount of literature on the varieties of ways to create and ways to solve problems.

The problem situation ends with the formulation of the problem in general view. The general problem is concretized in the problem question. An unsuccessfully formulated question can nullify all previous efforts of the teacher, kill the interest that has arisen in the area of ​​the unknown under discussion. This, in particular, happens if the question is too complicated, and the students understand the complete futility of finding a way out of the problem situation, and also if the question is too easy.

Correctly formulated questions concretize, narrow the area of ​​the unknown, what exactly should be clarified to solve problems. Thus, the teacher “should achieve that the student:

Really felt a certain theoretical or practical difficulty,

Formulated a problem or clarified one formulated by the teacher,

Wanted to solve this problem

I was able to do it."

For example, you can observe how he created a problem situation and what problem questions K.A. formulated. Timiryazev in the popular lecture “Seed”: “We begin our review of the vital functions of plants from the time when the activity of the seed is discovered, which has lain all winter under the protection of the snow cover or in the spring thrown into the soil by the hand of the farmer. Hardly any phenomenon in the life of a plant attracted so much attention as its first manifestation: it caused scientists, thinkers, poets to think, it was even dressed in some kind of veil of poetic mystery ... Indeed, there is something tempting, inciting thought in this sudden awakening of activity ... There is something mysterious in this hidden, hidden life, which suddenly breaks out.

As you can see, K.A. Timiryazev has not yet raised questions that he will answer, but, having created a problematic situation, he interested the audience common problem: what kind of mystery lies in this hidden life, which suddenly breaks out? Only after that he will formulate two specific questions: “Without in any way encroaching on the poetic ideas with which the imagination likes to surround this phenomenon, let us try to apply to it a rigorous analysis of science, we will try to decompose this complex phenomenon into its simplest components, we will try to explain how the dormant seed differs from active and what is the impulse, the impetus that causes this activity.

Having created a problem situation, having formulated a problem and problematic issues, the teacher reveals the path of scientific research that led to its solution, or shows how it can be solved using modern methods. Moreover, in one case, he sets out everything himself, posing the question, ensuring that the students follow through his reasoning and evidence, and in the other, he attracts students to solve part or all of the problem.

P.F. Kapterev united ideas about all these different, but having much in common, options for the work of a teacher in a lesson with a single name - the genetic form pedagogical method. V. Okon calls the first option the classical problematic method, and, in addition, characterizes the method of chances, the situational method, the bank of ideas, microteaching. AND I. Lerner and M.N. Skatkin define these options as problem presentation, partial search and research methods. Any of them can be used in the teacher's work both in the classroom and in educational work outside of school hours: moral, aesthetic and other problems are of the same nature as problems in physics and literature, history or biology. To interest in them, creating problem situations, to organize students to solve them by applying one method or another - this is the task of the class teacher, as well as the one that he, as a teacher, solves in his lessons.

Does this mean that explanatory-productive methods should not be used at all? Of course not. The accumulation of knowledge about facts, the acquisition of information of an information nature, and the like are most effectively provided by the use of reproductive methods, the use of which is not associated with the expenditure of such a significant amount of time as when using problem-based learning methods. A lot of knowledge in language, history, geography and other subjects is acquired in a reproductive way, like many skills in the lessons of these and other disciplines. On the other hand, when studying material that is too difficult for students, the explanatory-illustrative method turns out to be more productive than problematic methods.

Thus, developmental education, that is, leading to general and special development, can only be considered such training in which the teacher, relying on knowledge of the patterns of development of thinking, with special pedagogical means, conducts targeted pedagogical work to develop the mental abilities of his students in the process of studying the basics Sciences. Such training is problematic.

By problem-based learning, V. Okon understands “a set of such actions as organizing problem situations, formulating problems, providing students with the necessary assistance to students in solving problems, checking these solutions, and, finally, managing the process of systematizing and consolidating acquired knowledge” .

D.V. Vilkeev under problem learning means such a nature of learning when it is given some features scientific knowledge.

The essence of problem-based learning I.Ya. Lerner sees it in the fact that “a student, under the guidance of a teacher, takes part in solving new cognitive and practical problems for him in a certain system that corresponds to the educational goals of the school” .

T.V. Kudryavtsev sees the essence of the process of problem-based learning in putting forward didactic problems for students, in solving them and mastering generalized knowledge and principles of problem tasks by students. Such an understanding is also found in the works of Yu.K. Babansky.

Based on the generalization of practice and analysis of the results of theoretical studies, M.I. Makhmutov gives the following definition of the concept of “problem-based learning”: Problem-based learning is a type of developmental learning that combines the systematic independent search activity of students with the assimilation or ready-made conclusions of science, and the system of methods is built taking into account goal-setting and the principle of problematicity; the process of interaction between teaching and learning is focused on the formation of students' cognitive independence, the stability of learning motives and mental (including creative) abilities in the course of mastering scientific concepts and methods of activity, determined by a system of problem situations.

Problem-based learning, training in which the teacher systematically creates problem situations and organizes the activities of students to solve educational problems, provides an optimal combination of them. independent activity with the assimilation of ready-made conclusions of science.

Problem-based learning contributes to the development of the intellect of students, its emotional sphere and the formation of a worldview on this basis. This is the main difference between problem-based learning and traditional explanatory-illustrative learning. Problem-based learning involves not only the assimilation of the results of scientific knowledge, but also the very path of knowledge, ways of creative activity. It is based on the personal-activity principle of organizing the learning process, the priority of the search educational and cognitive activity of students.

The well-known Polish scientist V. Okon writes in his book Fundamentals of Problem-Based Learning that the more students strive to get on the path followed by the researcher in the course of their work, the better the results are achieved.

Domestic psychologists T.V. Kudryavtsev, A.I. Matyushkin, Z.I. Kalmykova and others developed the psychological foundations of the so-called problem-based learning in its various modifications. Its essence is as follows. The students are given a problem, a cognitive task, and the students, with the direct participation of the teacher or independently, explore ways and means of solving it. They build a hypothesis, outline and discuss ways to test its truth, argue, conduct experiments, observations, analyze their results, argue, prove.

Problem-based learning is based on the analytical and synthetic activity of students, implemented in reasoning, reflection. This is a heuristic, exploratory type of learning with great developmental potential. The distinctive characteristics of problem-based learning are given in the table (see Appendix 1).

The didactic foundations of problem-based learning are determined by the content and essence of its concepts. According to M.I. Makhmutov, the main concepts of the theory of problem-based learning should be "learning problem", "problem situation", "hypothesis", as well as "problem teaching", "problem teaching", "problematic content", "mental search", "problem question" , "problem presentation" .

Problem-based learning involves such an organization and methodology of the educational process, in which students would be as much as possible able to search for and prepare answers to their questions.

A problem is a question that, on the one hand, follows from the knowledge that students have, relies on them, and on the other hand, indicates their incompleteness and the need for further search to create a comprehensive understanding of the object of study. A question without relying on the life experience of the student and the knowledge he has accumulated about the phenomenon under study cannot become a problem for the student. A problematic issue should always be associated with overcoming certain contradictions, which are the basis for creating a problematic situation and posing a problem.

The problem, framed as a question or task, limits the task of the sought, in need of discovery, and thereby suggests the direction of the search. For example, a teacher poses such problematic questions to students: “As you know, L.N. Tolstoy was a spokesman for the mood of the patriarchal peasantry, he did not understand the revolution and moved away from the revolution, he gave distorted images of the revolutionaries. However, V.I. Lenin, who perfectly knew the work of the great writer, called L.N. Tolstoy as a mirror of the Russian revolution. On what basis did he do it?

The problematic approach to teaching should and can be reflected in curricula, in the presentation of knowledge by the teacher, in the independent work of students, and so on. At the same time, it must be borne in mind that not every question and not every independent search of students should be attributed to problem-based learning. Problem-based learning can only be where a particular problem arises in the very process of studying vital issues, is fraught with a certain novelty in its disclosure, and allows various interpretations and solutions.

The main concepts of problem-based learning include: "problem situation", "problem task", "problem", "problem", "problematization".

The assimilation of the realization of the learning goal is the problem inherent in any life of a “capable” object and excess, which can be in a hidden and expressed form, that is, be internal and external.

The way to create problematicity is a problematic situation, which fixes the moment when the excess of the object, the content of the problematicity is assigned.

The means of creating a problem situation can be a problem task formalized in text data.

The mechanism that reveals the problematic is the problematization of the object and the subject, that is, the process of revealing internal and external contradictions inherent in the object, problems.

The unit of the process is the problem - a hidden or obvious contradiction inherent in the phenomena of the material and ideal world.

Problematicness is the main condition for the development of an object (the world and the subject), a person can be considered as a dialectical category, side by side with others, or as the main feature of these categories in development, or as the main principle of their action, activity, or as the need to act.

A problem situation is a way of revealing an objectively existing problem, expressed explicitly or implicitly, which manifests itself as a mental state of intellectual difficulty in the interaction of the subject and object.

A problem task - a means of creating a problem situation - has a shell, materialized in its formulation (oral or written), focused on the needs and capabilities of the object.

Problematization is a mechanism that underlies the discovery of the problematic nature of an object by a subject materialized in a given problematic task.

Problem - contradiction - a unit of content and process of movement in the material and ideal space, generating the process of development of the world and man and generated by a developed person. This process is not interrupted. The role of the teacher is to make the student feel the difficulty of a practical or theoretical nature, to understand the problem posed by the teacher, or to formulate it himself, to want to solve the problem, to solve it.

The problem solving process depends on the nature of the problem and the complexity of its solution. The nature of the problem is determined by the degree of its complexity. In addition to simple problems, there are those that, before starting the solution, must be divided into private ones, and only the solution of the latter makes it possible to solve the main problem.

The difficulty of solving the problem is twofold. One is that in order to make a decision, it is necessary to activate some part of the previous experience, precisely that without which the decision is not possible. Another is the need to simultaneously find new elements (links) unknown to the student that allow solving the problem.

It is important that the educational problem is the form of implementation of the principle of problematicity in learning.

There is a didactic classification of educational problems, which is based on the following variables:

1. area and place of origin;

2. role in the learning process;

3. social and political significance;

4. ways of organizing the decision process.

The psychological classification of educational problems is based on indicators such as:

1. the nature of the unknown and posed difficulty;

2. solution method;

3. the nature of the content and the ratio of the unknown and the known in the problem.

The problem situation is the initial moment of thinking, causing the cognitive need of the student and creating internal conditions for active assimilation of new knowledge and methods of activity.

The classification of ways to create problem situations is based on the nature of the contradiction that arises in the process of learning:

1. the collision of students with phenomena and facts that require a theoretical explanation.

2. the use of training and life situations arising from the implementation of practical tasks by students.

3. setting educational problem tasks to explain the phenomenon and find ways to practical application.

4. encouraging students to analyze the facts and phenomena of reality, confronting them with contradictions between everyday representatives and scientific concepts about these facts.

5. putting forward hypotheses, formulation of conclusions and their experimental verification.

6. encouraging students to compare, compare and contrast the facts of phenomena, rules, actions, as a result of which there is a cognitive difficulty.

7. encouragement of students to a preliminary generalization of new facts.

8. familiarization of students with facts that seem to be inexplicable and are given in the history of science for staging scientific problem.

9. organization of interdisciplinary connections.

There are three types of problem-based learning according to the type of creative activity being implemented: scientific creativity; practical creativity; artistic creativity.

Scientific creativity is based on the formulation and solution of theoretical educational problems. Practical creativity is based on the formulation and solution of practical educational problems. Artistic creativity is an artistic reflection of reality based on creative imagination, including literary compositions, drawing, writing a piece of music, work, and others.

Thus, it is possible to identify the signs of problem-based learning. The first and most important feature is the specific intellectual activity student on independent assimilation of new concepts by solving educational problems, which ensures consciousness, depth, strength of knowledge and the formation of logical-theoretical and intuitive thinking. The second feature is that problem-based learning is the most effective means of forming a worldview, since the features of critical, creative, dialectical thinking are formed in the process of problem-based learning. Independent problem solving by students is at the same time the main condition for the transformation of knowledge into beliefs, since only a dialectical approach to the analysis of all processes and phenomena of reality forms a system of strong and deep convictions. The third feature follows from the regular relationship between theoretical and practical problems and is determined by the didactic principle of the connection between learning and life. The connection with practice and the use of students' life experience in problem-based learning act not as a simple illustration of theoretical conclusions, rules (although this is not excluded), but mainly as a source of new knowledge and as a sphere for applying learned methods of solving problems in practical activities. For this reason, the connection with life serves the most important means creation of problem situations and (direct or indirect) criterion for assessing the correctness of solving educational problems.

The fourth feature of problem-based learning is the systematic use by the teacher of the most effective combination of various types and types of independent work students. This feature lies in the fact that the teacher organizes the performance of independent work, requiring both the actualization of previously acquired knowledge and the assimilation of new knowledge. ways of activity.

The fifth feature is determined by the didactic principle individual approach. In problem-based learning, individualization is due to the presence of learning problems of varying complexity, which are perceived differently by each student. Individual perception of the problem causes differences in its formulation, putting forward various hypotheses and finding certain ways to prove them.

The sixth feature is the dynamism of problem-based learning (the mobile interconnection of its elements). This feature is due to the dynamism of the problem itself, which is always based on the contradiction inherent in any phenomenon, fact of reality. The dynamism of problem-based learning lies in the fact that one situation passes into another in a natural way based on the law of interconnection and interdependence of all things and phenomena of the surrounding world. As the researchers point out, traditional education there is no dynamism, instead of problematicness, “categorical” prevails there.

The seventh feature is the high emotional activity of the trainees, due, firstly, to the fact that the problem situation itself is the source of its excitation, and, secondly, to the fact that the active mental activity of the trainee is inextricably linked with the sensory-emotional sphere. mental activity. Independent mental activity of a search nature, associated with the individual "acceptance" of an educational problem, causes a personal experience of the student, his emotional activity.

The eighth feature of problem-based learning is that it provides a new ratio of induction and deduction and a new ratio of reproductive and productive assimilation of knowledge.

The first three features of problem-based learning have a social orientation (provide the strength of knowledge, the depth of beliefs, the ability to creatively apply knowledge in life). The remaining features are of a specially didactic nature and generally characterize problem-based learning.

There is no doubt that problem-based learning cannot be effective in different settings. Practice shows that the process of problem-based learning gives rise to various levels of both the intellectual difficulties of the trainees and their cognitive activity: the cognitive independence of the student can be either very high or almost completely absent. In this regard, attempts to identify types and levels of problem-based learning are quite understandable. Types of problem-based learning are most correctly distinguished by existing species creativity. In accordance with the distinguished basis, he classifies three types of problem-based learning:

Scientific creativity - theoretical research, that is, the search for the discovery by students of a new rule, law, evidence; this type of problem-based learning is based on the formulation and solution of theoretical educational problems;

Practical creativity - the search for a practical solution, that is, a way to apply known knowledge in a new situation, design, invention; this type of problem-based learning is based on the formulation and solution of practical learning problems;

Artistic creativity is an artistic representation of reality based on creative imagination, including drawing, playing, playing music, and the like.

All types of problem-based learning are characterized by the presence of reproductive, productive and creative activities of students, the presence of a search and problem solving. However, the first type of problem-based learning is most often used in theoretical classes, where an individual, group or frontal problem solving is organized. The second - in the laboratory, practical exercises, on a subject circle, on an elective course, on production. The third type is in classroom and extracurricular activities. The last two types of problem-based learning are characterized by the solution, mainly, of individual or group learning problems.

Each type of problem-based learning has a complex structure, which, depending on many factors, gives different learning outcomes. An effective learning process is one that:

Increasing the amount of knowledge, skills and abilities of students;

Deepening and strengthening of knowledge, a new level of learning;

A new level of cognitive needs of teaching;

A new level of formation of cognitive independence and creative abilities.

All of the listed types of problem-based learning can occur with varying degrees of cognitive activity of students. Determining this degree is important for managing the process of forming the cognitive independence of students. The above types of problem-based learning can have different levels. Conventionally, there are four levels of problem-based learning:

The level of ordinary dependent activity is the students' perception of the teacher's explanations, the assimilation of a model of mental action in a problem situation, the performance of independent work, exercises of a reproducing nature.

The level of semi-independent activity is characterized by the application of acquired knowledge in a new situation and the participation of students in a joint search with the teacher for a way to solve the educational problem posed.

The level of independent activity provides for the performance of independent work of the reproductive-search type, when the student independently works according to the text of the textbook, applies the acquired knowledge in a new situation, constructs a solution to a problem of an average level of complexity, and proves hypotheses by logical analysis with little help from a teacher.

The level of creative activity characterizes the performance of independent work that requires creative imagination, logical analysis, discovery of a new way of solving, independent proof. At this level, independent conclusions and generalizations, inventions are made; there is also artistic creativity.

The levels of problem-based learning reflect not only the different levels of assimilation of new knowledge and ways of mental activity by students, but also different levels of thinking. Each level of problem-based learning can have different organization options, depending on various factors of a psychological and pedagogical nature. The transfer of students from the first to a higher level is the result of problem-based learning and at the same time the process of managing their educational and cognitive activities.

1.3 Methods and types of problem-based learning

Methods of problem learning. We can talk about six didactic ways of organizing the process of problem-based learning, which are three types of presentation of educational material by the teacher and three types of organization of independent learning activities of students. Consider them.

1. Method of monologue presentation

The teacher reports the facts in a certain sequence, gives them the necessary explanation, demonstrates experiments in order to confirm them. The use of visual aids and technical teaching aids is accompanied by an explanatory text. The teacher reveals only those connections between phenomena and concepts that are required to understand this material, introducing them in the order of information. The alternation of facts is built in a logical sequence, however, in the course of presenting the attention of students to the analysis of cause-and-effect relationships, it is not specified. The facts "for" and "against" are not given, the correct final conclusions are immediately reported.

If problem situations are created, then only in order to attract the attention of students, to interest them. After its creation, the answer to the question “why is this and not otherwise?” is not required from the students, but the actual material is immediately reported. When using the monologue teaching method, the material is slightly rebuilt. The teacher most often only changes the order of reported facts, demonstrations, experiments, showing visual aids in order to create a problem situation and uses them as additional elements of content. Interesting Facts from the history of the development of the concept under study or facts that tell about the practical application of the acquired knowledge in science and technology. The role of the student when using this method is rather passive, the level of cognitive independence necessary for working with this method is low.

With such an organization of the process of assimilation of new knowledge, the teacher complies with all the basic requirements for the lesson, implements didactic principles clarity, accessibility of presentation, observes a strict sequence in the order of information, maintains students' steady attention to the topic being studied, however, the teaching method chosen by him turns the student into a passive listener, does not activate his cognitive activity. The information-reporting method of teaching used in this case allows achieving only one goal - to replenish the stock of students' knowledge with additional facts.

2. Reasoning teaching method

If the teacher aims to show an example of the study of the formulation and solution of a holistic problem, then he uses the reasoning method. At the same time, the material is divided into parts, the teacher for each stage provides a system of rhetorical questions of a problematic nature in order to attract students to a mental analysis of problem situations, exposes objective contradictions of the content, but he himself allows the use of sentences of a narrative and interrogative type, informational questions (that is, such questions, the answers to which need to reproduce already known knowledge, give information about known knowledge) are not posed, the narration is in the form of a lecture.

The method of restructuring the material for work by this method differs, first of all, in that a system of rhetorical questions is introduced into the content as an additional structural element. The order of the reported facts is chosen in such a way that the objective contradictions of the content are presented especially emphasized, convex, arouse the cognitive interest of students and the desire to resolve them.

In the presentation of the teacher, it is no longer the categorical nature of the information that prevails, but the elements of reasoning, the search for a way out of the difficulties that arise due to the peculiarities of the construction of the material. The teacher, as suggested by M.I. Makhmutov, "demonstrates the very path of scientific cognition, forcing students to follow the dialectical movement of thought towards the truth", he not only creates problem situations, but poses and solves problems, shows how various hypotheses were put forward and collided.

Having chosen the reasoning method of teaching, the teacher, in the process of organizing the assimilation process, uses the explanatory method of teaching, the essence of which is that it "includes the teacher's communication of the facts of this science, their description and explanation, that is, it reveals the essence of new concepts with the help of words, visualization and practical actions".

3. Dialogical method of presentation

If the teacher sets himself the task of involving students in direct participation in the implementation of a method for solving a problem in order to activate them, increase their cognitive interest, draw attention to what is already known in the new material, he, using the same content construction, supplements its structure with information questions, answers to given by students.

The use of the dialogical method of teaching provides a higher level of cognitive activity of students in the process of learning, since they are already directly involved in solving the problem under the cruel control of the teacher.

4. Heuristic method of presentation

The heuristic method is used where the teacher aims to teach students the individual elements of problem solving, to organize a partial search for new knowledge and ways of action. Using the heuristic method, the teacher applies the same construction of educational material as in the dialogical method, but somewhat supplements its structure by setting cognitive tasks and assignments for students at each individual stage of solving an educational problem. Thus, the form of implementation of this method is a combination of heuristic conversation with the solution of problematic tasks and assignments.

The essence of the heuristic method is that the discovery of a new law, rule, and the like is not done by the teacher with the participation of students, but by the students themselves under the guidance and with the help of the teacher.

5. Research method

The concept of the research method was most fully revealed by I.Ya. Lerner, who referred to the research method a method that organizes the process of assimilation by “solving problems and problematic tasks. Its essence is that the teacher constructs a methodological system of problems and problematic tasks, adapts it to a specific situation of the educational process, presents it to students, thereby managing their learning activities, and students, solving problems, provide a shift in the structure and level of mental activity, gradually mastering the procedure of creativity, and at the same time they creatively assimilate the methods of cognition.

When conducting a lesson using the research method, the same construction of the material is again used, and the elements of the structure of the heuristic method and the order of questions, instructions, tasks are taken. If in the process of implementing the heuristic method these questions, instructions and tasks are of a proactive nature, that is, they are posed before solving the sub-problem that makes up the content of this stage, or in the process of solving it and performs a guiding function in the solution process, then in the case of using the research method, questions are posed in at the end of the stage, after the majority of students have solved the sub-problem.

6. Method of programmed tasks

The method of programmed tasks is the setting by the teacher of a system of programmed tasks. The level of effectiveness of the exercise is determined by the presence of problem situations and the possibility of independent formulation and solution of problems. The application of programmed tasks is as follows: each task consists of individual frame elements; one frame contains part of the studied material, formulated in the form of questions and answers, or in the form of a presentation of new tasks, or in the form of exercises.

Types of problem learning. Problem-based learning cannot be equally effective in all conditions. Practice shows that the process of problem-based learning generates different levels of both intellectual difficulties for students and their cognitive activity and independence when acquiring new knowledge than when applying previous knowledge in a new situation.

The types of problem-based learning are most correctly distinguished by the corresponding types of creativity. On this basis, three types of problem-based learning can be distinguished. The first type (“scientific” creativity) is theoretical research, that is, the search and discovery for students of a new rule, law, theorem, and so on. This type of problem-based learning is based on the formulation and solution of theoretical learning problems.

The second type (practical creativity) is the search for a practical solution, that is, the search for a way to apply known knowledge in a new situation, design, invention. This type of problem-based learning is based on the formulation and solution of practical learning problems.

The third type (artistic creativity) is an artistic reflection of reality based on creative imagination, including literary compositions, drawing, writing a piece of music, playing, and so on. All types of problem-based learning are characterized by the presence of a reproductive, productive and creative activity of the student, the presence of a search and a solution to the problem. They can be carried out in various forms of organization. pedagogical process. However, the first type is most often found in the classroom, where there is an individual, group and frontal problem solving. The second - in laboratory, practical classes. The third type is in the classroom and in extracurricular activities.

It is quite clear that each type of problem-based learning, as an internally differentiated activity, has a complex structure, which, depending on many factors, gives different learning outcomes. Each of the listed types of problem-based learning can proceed with a different degree of cognitive activity of the student. Determining this degree is important for managing the process of forming the cognitive independence of schoolchildren.

Each species corresponds to one of essential conditions problem-based learning - the presence of a certain level of cognitive independence of the student.

So, having studied the psychological and pedagogical literature on problem-based learning, it was found that it is called problematic not because all educational material students learn only by solving problems on their own and "discovering" new concepts. Here there are explanations of the teacher, and the reproductive activity of the teacher, and the setting of tasks, and the implementation of exercises by students. But the organization of the educational process is based on the principle of problems, and the systematic solution of educational problems is a characteristic feature of this type of education.

Chapter 2. Features of the content and methodology of problem-based learning in the real pedagogical process

2.1 Structure of problem-based learning

Problem - based learning has technological characteristics in the organization of the learning process . Its peculiarity lies in the fact that the educational activity managed by the teacher should reflect the search activity of students and a reflective attitude to their own activities. Therefore, problem-based learning is consistent with the structure of research cognitive activity and performs the function of managing the creative learning process. The definition of the process of problem-based learning through its specificity is based primarily on the characteristics of its functional units and the relationships between them.

If we consider the goal of learning as the desire of the system to achieve a result, then in the course of problem-based learning this tension is especially great and pronounced. Intensity internal stress system - the educational process - is the higher, the more actively the subject of activity - the student - behaves and the deeper he is involved in solving the problem, searches for and evaluates the real goal as a task set for him to solve. There is also Feedback: the more active the cognitive process, the more intense the feeling of its results by the students becomes.

The main thing is that in the conditions of problem-based learning, the goal acquires the character of a goal-task and a goal-image. Both types of goals: the goal as a task and the goal in the form of an image are presented in problem-based learning. The first goal is obvious, and the goal-image takes place when problem-based learning is not an episodic phenomenon in the learning system, but a systematic pedagogical management of the educational process, and, secondly, when the student realizes the necessary result of his actions. The result model, in most cases the goal is an image, represents the social aspect of motivation and is present in the course of problem-based learning. The mechanism that stimulates the role of the goal lies in the psychological nature of motivation, as well as in the ways of stimulating learning activity from the standpoint of predicting the result. In both respects, the goal regulates the behavior of students and therefore can act as a system-forming factor in the learning process. At the same time, the goal is the main parameter of problem-based learning.

Feature of the subject cognitive process, his relationship to the object of knowledge in the course of problem-based learning is the maximization of development goals. This is the main normative characteristic of problem-based learning. Thus, motivation is set, which should have a cognitive function and at the same time perform a developing function that has a fundamental impact on the self-determination of the subject of knowledge.

The didactic basis of problem-based learning is the problem situation. The problem situation has a cognitive function, its design will be created by the teacher in order to stimulate the activity of students. For the teacher, the construction of the problem is a condition for the organization of problem-based learning. The teacher develops tasks and tasks that allow students to engage in an active cognitive process, creates problem situations.

The didactic characteristic of problem-based learning is based on the application of problem situations in the educational and pedagogical process. The teacher creates problem situations of a given type and thereby provides the necessary assistance to students in the analysis of educational material and in organizing a mental search for its solution, regulates the solution process: introduces necessary information, directs the value organization, determines the degree of freedom of choice, directs to the search for adequate methods of action, contributes to the semantic understanding of information.

Problem-based learning consists of problem-based teaching and problem-based learning. Problem teaching is based on the design of educational activities, a system of cognitive situations, as well as the psychological and pedagogical management of their resolution by students. Problem learning can be considered as a complete structure of educational activities for the assimilation of knowledge and methods of action, which presents an analysis of the task-situation from the standpoint of the information composition, goals and conditions for solving, ending with the formulation of the problem, the formulation of a hypothesis and its justification, “making a decision and work program actions, performance activities and analysis of the results.

The educational situation becomes problematic if its characteristics are perceived and evaluated by the subject in terms of his goals and values. The problem situation is understood as a gap in activity, a mismatch between the goals and capabilities of the subject, as a task, which is a model of the problem situation. But any learning task is similar to a problem situation, and only those that involve learning actions to complete the information basis of actions. Learning tasks aimed exclusively at performing activities and achieving learning goals related to the consolidation of knowledge, as well as the development of a solution algorithm, do not constitute a problem situation for students, but play the role of exercises when the solution of the problem is built according to known rules. This is all the more obvious if we consider the educational task as a didactic unit of the educational text, identical to the information unit. Yu.N. Kulyutkin considers: an objectively arising mismatch (contradiction) between the goal that meets some actual practical need and the means to achieve it; the emergence of a proper cognitive attitude to the situation; the appearance of an orienting reaction in the subject, the emergence of a need to understand the situation, the formation of the position of the subject.

Thus, the subjective position of a person facing a problematic situation consists of two conditions, which undoubtedly play a fundamental role in making a decision:

1) subjective understanding of goals, attitude to the object of study;

2) visions of uncertainty that exists in an explicit or latent form, in a situation of an existing gap between what is known and what is unknown. Only under these conditions are actions aimed at eliminating the contradiction and solving the problem possible. Therefore, the problem situation must be objectified by the subject.

According to this logic, any problem situation is considered from the position of the subject. This applies to both the teacher and the student. The psychological nature of the perception of a problem situation is equivalent for them. The difference lies in the content side and in the degree of uncertainty. For the student, the problem situation has a learning function. The level of uncertainty included in it, which makes up the didactic meaning, which is deliberately laid down by the teacher, is limited and to a certain extent defined, designed for the student's capabilities, therefore its assessment by the student is visible and predictable. For the student, the problem situation is perceived as naturally arising in the learning process.

The subjective assessment of the problem situation is fully personified, as it depends on its subjective understanding of professionally oriented goals. At the same time, it should be taken into account that the subject content of the situation itself is completely different: the students are tied to the study of the subject object, and the teacher is aimed at teaching and developing students through the information reconstruction of knowledge about this subject object. The student is focused on receiving and systematizing information about an object, phenomenon or event organized by the teacher, and the teacher directs his actions to transform information in order to manage educational activities.

The ultimate goal of the teacher is the formation of personality. The means is educational activity, the content is information about a person, about nature, matter, and the noosphere. Its structure and composition determine educational activity, in the process of which a system of student behavior is formed, his cognitive actions, activity, motivation develop, goals and values ​​are formed. The problem situation is a didactic condition for the nomination and formulation of an educational problem and is the result of a certain stage. professional activity teacher for structuring educational material. Pedagogical modeling of an educational problem in the learning process is associated with a number of preliminary actions:

1) pedagogical development of a specific task of training and education;

2) analysis of the content of educational material;

3) analysis of the readiness of students and determination of the level of operational knowledge, skills and abilities, as well as their psychological readiness;

4) establishing a correspondence between the level of complexity of the educational problem and the readiness of students to solve it.

After this prepared stage of work, the teacher performs the following actions:

1) formulates the problem in the form of a question or assignment;

2) design pedagogical solution management learning topic on the part of students, for which he develops a methodology for managing educational activities, draws up instructive tasks;

3) creates a methodological apparatus for correcting errors, inaccuracies that may be made by students, - composes a system of individual additional tasks and questions to identify incorrectly performed actions of students, determines methods of methodological prompting and pedagogical assistance;

4) organizes self-control of students over the performance of work through a series of control questions and tasks;

5) checks the performance of work by students, organizes discussion and discussion on the results of work, introduces pedagogical correction of errors into the educational process;

6) the results of independent work of students include in the study of new scientific question, new problem .

During the discussion of the results of the students' work, it is necessary to pay attention to the methodology for correcting the mistakes made. The teacher corrects the course of the decision through a series of additional questions or tasks arising from the discussed results, which are conditionally accepted as reliable. Through reasoning and consistent construction, deriving on the basis of the results obtained, it is required to bring students to a clearly absurd position, showing the erroneousness of the result obtained, its inconsistency from the standpoint of scientific theories and practice, and thereby convince students of the incorrectness of the results obtained, force them to return to the analysis of the chosen path of research and intermediate conclusions made at different stages of the work. In this way, under the guidance of a teacher, inaccurate actions performed by students or incorrectly formulated conclusions are corrected in order to correct the mistakes made and orient them towards the correct solution strategy.

This completes one cycle of problem-based learning, which entails the next, associated with a new problem. At the same time, it is very important that the subsequent educational problem flow organically from the solution of the first one. The consistent solution of these problems should be interconnected. A system of tasks is formed that determines the sequential course of solving these problems. In general, the logic of the cognitive process is subordinated to the achievement of educational goals. A clear structure of the task composition of the pedagogical management of activities is required, which is formed on the basis of the subordination of specific educational problems, and a general strategy for their solution is needed. To ensure conscious participation and cognitive activity, students must see these logical connections, understand them, be aware of the logic of the cognitive process and evaluate the prospect of solving the main problem.

A problematic situation arises whenever a person faces the need to obtain new informational or procedural knowledge, which is born in the process of restructuring the acquired information or principles of action.

In the process of problem-based learning, educational activities are carried out in the form of educational and research activities, therefore, for a teacher organizing problem-based learning, knowledge of the patterns of mental activity and the ability to build the structure of educational material in such a way that it is adequate to the research style of thinking acquires special importance. Due to its didactic design, problem-based learning has the best opportunities for stimulating and developing students' creative thinking.

The question of creativity is far from new in pedagogy. He attracted the attention of scientists from different eras of world culture. IN last years the problem of the formation of the creative qualities of the individual turned out to be at the center of the vital requirements of society.

Of interest is the didactic regulation of heuristic educational activity, which provides for an independent research search for students. This refers to the pedagogical design of the cognitive process of students, which unfolds in the logic of debatable knowledge and is associated with overcoming their own cognitive difficulties caused by breaks in information links in the logic of the text or in the task, with a creative approach to finding ways and means of solving, making a decision and taking responsibility for it. Ways to solve such a problem, as a rule, are not formalized, unknown to students, they need to be created, and thereby carry out the creative process. To manage this creative process, it is necessary to carry out methodical work in two directions: to develop non-rigid algorithmic prescriptions for learning to solve creative problems and to create ways to manage heuristic educational activities that regulate the activities of students and provide the necessary conditions for the development and implementation of active educational cognitive activity that has educational and research functions.

Any solution to a problematic task involves the restructuring of information in the conditions of educational and research activities.

The repeated application of once found methods for solving a problem will no longer be creativity, since a solution algorithm is used. A lot of original problems involve a lot of algorithms. Thinking will work with the choice of algorithms as with independent task; their application is connected with the analysis of the problem situation, with the formulation of a question that reveals the relationship between the known and the unknown, and with the search for the required solution.

There is a sequential alternation of elements of creativity (when a method for solving a problem is found for the first time) and the use of a solution algorithm (when solving the problem again), then again creativity (the conditions of the problem will be known problem algorithms) and again the algorithm of the algorithm. There is an ascent from concrete cognition to abstract cognition of the first, second and next orders, a spiral process in which intuition is interconnected with algorithmization.

The cognitive process in educational and research activities is always based on a combination of creative solutions using an algorithm. When the task is re-constructed, it becomes the subject of study and assimilation, and with repeated repetition it can play the role of a methodological apparatus for solving and at the same time constitute the subject of study as a guide to action.

Modern research conducted in the field of pedagogy convinces of the need and possibility of using problem-based learning methods in order to ensure the overall development of students, the formation of a theoretical style of thinking based on the concrete. Through the students' knowledge of special structures of the content of the educational material, reflecting the determinism of the studied phenomena, events, facts, one can show their interrelation and interdependence.

As you know, in the learning process there is an interconnected activity of the teacher and students. Pedagogical management of educational activities can be different. It is important that, along with reproductive cognitive activity, creative ways of cognition take place. In the course of such training, students are involved in the process of solving cognitive problems, as a result of which they learn the experience of creative activity and acquire independence, criticality and flexibility of thinking.

Thus, at the heart of the problematic didactic situation lies the task aimed at transforming the object of cognition, at finding solutions, which implies some limitations in the choice of solutions. A problem or a problematic situation is such, first of all, insofar as it contains unknowns, as it were, uncertainties that are to be filled - x's, in the place of which knowledge must be put.

The main stages of cognitive activity in solving a problem situation are: understanding the problem, solving the problem, checking the solution.

The first stage - awareness of the problem in the learning environment - depends on how the problem situation is didactically constructed. If the task is formulated, then the awareness of its problematic nature on the part of students is associated with the ability to see the gap between the known and the unknown, with the analysis of information, the allocation of contradictions in it. Understanding the problem is also associated with the choice of means of solution, which is accompanied by the reconstruction of what is already known, with the definition of the relationships indicated in the problem and the missing links, with interpretation in accordance with general theoretical provisions. As a result of this activity, a question is formulated that fixes the ratio of the reported information with previously known provisions. The question, as it were, reveals, reveals the main thing, the subject of study, and thereby outlines the sequence of decision acts, determines the direction in which the answer should be sought. The posing of the question ends the first stage.

The second stage - the planning of performing actions, the conceptual model - involves the development of a hypothesis and the adoption of a decision. This is the central stage. A hypothesis is a result projected by the subject, a choice of solutions leading to the elimination of identified contradictions; hypothetical thinking - forecasting, heuristic search procedures. The hypothesis allows you to make a mental transition from what is obvious to what should be found. At this stage, as well as at the previous one, past experience, the transfer of existing knowledge to new conditions, ways of comprehending the unknown from the position of the already known, processing already familiar information in order to apply it for a practical solution, assessing the situation and one's capabilities are of great importance. Some researchers single out the formulation of a hypothesis as an independent stage, then the development of the process of solving a problem is considered as a separate stage, and the hypothesis plays the role of an idea as a way of interpreting the problem.

The third stage is the verification of the produced solution. This is the final step in solving the problem. It includes an assessment of the hypothesis, the correctness of the actions performed, is an approbation of a hypothetical solution, an analysis and assessment of the reliability of the results obtained, their compliance with the main theoretical provisions of science, as well as practice. If the verification confirms the correctness of the chosen solution strategy, then the solution of the problem is completed. In the event that a discrepancy between the results obtained and the main criteria of reliability is found, then the cognitive process continues: adjustments are made, a new hypothesis is built - a solution strategy is built again, the problem is solved and control is carried out. This is the second round of the spiral development of the process of cognition. There may be a third and a fourth turns, and so on.

In a cognitive act built according to this scheme, creativity is manifested, especially at the stage of constructing a hypothesis - at the stage of constructing a draft solution, an action plan, when creating a theoretical, conceptual basis for actions to find a solution. It is here that individuality, the ability to solve a mental problem, is revealed. The construction of a hypothesis is an important stage in inventive activity, and therefore, in the organization of problem-based learning, the purpose of which is to design didactic conditions similar to a task that requires a creative solution.

The educational process in the course of problem-based learning involves the analysis of the goal, the allocation of the main, essential, the analysis of the initial data of the task, the clarification of the relationship between the elements, conditions and requirements of the task.

Many scientists are of the opinion that new knowledge can only be obtained by a leap of thought, that the discovery is made with the help of intuition. However, there is another point of view, according to which the achievement of new knowledge is carried out through a thought process that combines logical and heuristic methods of thinking. In the service of this point of view, heuristic programs represented by a set of formalized heuristic rules, as well as methods for solving mental problems (G.S. Altshuller, D. Poya, V.N. Sokolov, O.K. Tikhomirov, L.M. Fridman) .

In the course of solving a problematic task, the main data are identified - the conditions of the problem - and variables are introduced, then the results are projected, a hypothetical solution is built, heuristic methods are searched, and the solution strategy is determined. The results obtained are analyzed, errors and inaccuracies are corrected, and the working goal is re-formulated. Such is the psychological structure of the problem situation.

Any solution to a problem is associated with a change in the problem situation and redesign of the problem data depending on the requirements of the problem. The transformation leads to the establishment of a relationship between the known and the unknown. Hence the possibility of constructing a hypothesis based on a new problem situation constructed by the subject himself. In the course of this process, there is an understanding of the links indicated in the condition of the problem, the actualization of the necessary theoretical and factual knowledge, as well as methods for solving the problem, the construction of proposals and the use of available means to find the answer. The purpose of problem-based learning is to build such a structure of educational material that corresponds to the logic of productive thinking, which is most clearly manifested in solving original problems.

Since problem-based learning is used in the structure of other methods, it cannot be considered either as a special teaching method, or as some kind of new system learning. It would be more correct to consider it as a special approach to the organization of learning, manifested primarily in the nature of the organization of the cognitive activity of students.

Undoubtedly, not every material can serve as a basis for creating a problem situation. The non-problematic elements of the educational material include all specific information containing numerical and quantitative data, facts, dates, and the like that cannot be “opened”.

Problem-based learning can be used to master generalized knowledge - concepts, rules, laws, cause-and-effect and other logical dependencies. It is needed when the task is set special education students in the techniques and methods of mental activity necessary for obtaining knowledge and solving search problems.

A.M. Matyushkin characterizes the problem situation as "a special kind of mental interaction between the object and the subject, characterized by such mental state subject (student) in solving problems that require the discovery (discovery or assimilation) of new knowledge or methods of activity previously unknown to the subject. In other words, a problem situation is a situation in which the subject wants to solve some difficult tasks for himself, but he does not have enough data and he must look for them himself.

Problem situations can be classified in several ways:

By area of ​​scientific knowledge or academic discipline(physics, mathematics, etc.);

By focusing on finding the missing new (new knowledge, methods of action, identifying the possibility of applying known knowledge and methods in new conditions);

By the level of problem (very sharp contradictions, medium severity, weakly or implicitly expressed contradictions);

According to the type and nature of the content side of the contradictions (for example, between worldly ideas and scientific knowledge, an unexpected fact and the inability to explain it, etc.).

Didactically and methodically based ways of creating problem situations can be found only if the teacher knows the general patterns of their occurrence. In the literature on problem-based learning, there are attempts to formulate these patterns in the form of types of problem situations.

Studies have shown that it is possible to single out the most characteristic types of problem situations for pedagogical practice, common to all subjects.

1. It should be considered the most general and widespread: a problem situation arises if the student does not know how to solve the problem, they cannot answer the problematic question, give an explanation for a new fact in an educational or life situation, that is, if students realize the insufficiency of the previous knowledge to explain a new fact.

A teacher at a geometry lesson in the 7th grade on the topic "Trapezoid" offered the students a task: in the trapezoid ABCD (BC||AD) the middle line MN was drawn. Base |BC| equals 8 cm. |AO|=14cm, |AB|-5cm. |CB|=9cm. Calculate the perimeter of the trapezoid MBCN.

Solving the problem, the guys easily find sides new trapezoid; they know one base, but they cannot find the length of the second, which is the midline (there is not enough knowledge about the trapezoid). There is a contradiction between the need to solve the problem and the insufficiency of previous knowledge.

2. Problem situations arise when students encounter the need to use previously acquired knowledge in new ones. practical conditions. As a rule, teachers organize these conditions not only so that students can apply their knowledge in practice, but also face the fact of their insufficiency. Awareness of this fact by students arouses cognitive interest and stimulates the search for new knowledge.

For example, a teacher on the eve of a lesson on the topic "The volume of a truncated pyramid" gives students homework- find in surrounding life examples of the use of a truncated pyramid and try to determine its volume. He explains that for the construction of, for example, a railway embankment, it is necessary to calculate its volume in advance in order to determine required amount building materials, that is, points to practical significance homework.

The next day, the lesson begins with a conversation. Students name mounds of sand, rubble, cardboard boxes, towers, machine parts, and so on as examples of a truncated pyramid. They talk about their attempts to find solutions, but they cannot calculate the volume of the truncated pyramid. A problematic situation arises and the need to find solutions to a problem that has (for students) practical significance.

Thus, the process of the formation of new knowledge began in the course of fulfilling the task of the teacher at home, in a life situation that revealed the main problem, revealed the contradictions between the emerging cognitive need and the need to satisfy it with previously acquired knowledge. Here we see an element of perspective learning; homework is designed to prepare for the assimilation of new knowledge; the repetition of what has been passed takes place not in the form of re-reading the pages of the textbook indicated by the teacher or rewriting the exercises, but in the form of independent work, the content of which is the solution of the problem of a practical or theoretical problem.

A problematic situation easily arises if there is a contradiction between the theoretically possible way of solving the problem and the practical impracticability of the chosen method.

A problematic situation arises when there is a contradiction between the practically achieved result of completing an educational task and the students' lack of knowledge for its theoretical justification.

The ability to manage the learning process lies in the fact that the problem situation in its psychological structure has not a subject-content, but also a motivational, personal side (the interests of the student, his desires, needs, opportunities, and so on).

What didactic goals are pursued by the creation of problem situations in educational process? The following didactic goals can be indicated:

1) draw the student's attention to the issue, task, educational material, arouse his cognitive interest and other motives for activity;

2) put him in front of such a cognitive difficulty, the continuation of which activated mental activity;

3) help him determine the main problem in the cognitive task, question, task and outline a plan for finding ways out of the difficulty that has arisen; to encourage the student to active search activity;

4) help him determine the boundaries of the previously learned tasks that are being updated and indicate the direction of the search for the most rational way out of the situation of difficulty.

Ways to create problem situations. You can specify several basic ways to create problem situations.

1. Encouraging students to a theoretical explanation of phenomena, facts, external inconsistencies between them. This causes the search activity of students and leads to the active assimilation of new knowledge.

2. The use of educational and life situations that arise when students perform practical tasks at school, at home or at work, in the course of observing nature, and so on. Problem situations in this case arise when trying to independently achieve the practical goal set for them. Usually, students, as a result of analyzing the situation, formulate the problem themselves.

At the geometry lesson in the 6th grade on the topic “The length of the broken line”, the students were offered work in 2 versions: the first is to draw a broken line, consisting of two links; the second is to draw a broken line consisting of 3 links. By measuring, compare the length of the polyline with the distance between its ends. The students completed this task easily. The teacher writes some of the results obtained in 2 columns on the board:

The result is different for everyone, but the teacher asks the children to carefully consider the numbers and make an assumption about the relationship between the length of the broken line and the distance between its ends. The student formulates an assumption: “The length of the broken line is greater than the distance between its ends” and proceeds to solve it in general terms.

3. Statement of educational problem tasks to explain the phenomenon or search for ways of its practical application. An example would be any research students in the educational and experimental area, in the workshop, laboratory or classroom, as well as in the lessons in the humanities.

4. Encouragement of the student to analyze the facts and phenomena of reality, which generates contradictions between worldly ideas and scientific concepts about these facts.

5. Making assumptions (hypotheses), formulating conclusions and their experimental verification.

6. Encouraging students to compare, compare facts, phenomena, rules, actions, as a result of which a problem situation arises.

7. Encouraging students to a preliminary generalization of new facts. Students are given the task to consider some facts, phenomena contained in new material for them, compare them with known ones and make an independent generalization. In this case, how does the comparison reveal special properties new facts, their inexplicable signs.

8. Familiarization of students with facts that seem to be inexplicable and have led in the history of science to the formulation of a scientific problem. Usually, these facts and phenomena, as it were, contradict the ideas and concepts that have developed among students, which is explained by the incompleteness and insufficiency of their previous knowledge.

9. Organization of intersubject communications. often material subject does not provide for the creation of a problem situation (when developing skills, repeating what has been passed, etc.). In this case, one should use the facts and data of the sciences (school subjects) that are related to the materials being studied.

10. Variation of the task, reformulation of the question.

Rules for creating problem situations.

1. In order to create a problematic situation, students should be given a practical or theoretical task, the implementation of which requires the discovery of new knowledge and the acquisition of new skills; here we can talk about general pattern, general mode of activity or general conditions for the implementation of activities. The task must correspond to the intellectual capabilities of the student. The degree of difficulty of the problem task depends on the level of novelty of the teaching material and on the degree of its generalization.

2. The problematic task is given before the explanation of the material to be learned.

3. Problem tasks can be:

assimilation;

The wording of the question;

practical buildings.

A problem task can lead to a problem situation only if the above rules are taken into account.

5. The same problem situation can be caused by different types of tasks.

6. The teacher directs a very difficult problematic situation by indicating to the student the reasons for not fulfilling the practical task given to him or the impossibility of explaining certain facts to him. For example; "You couldn't build a triangle with 3 known angles, because in this task one of the important rules touching triangles".

The student's readiness for problematic teaching is determined, first of all, by his ability to see the problem put forward by the teacher (or that arose during the lesson), formulate it, find solutions and solve it with effective methods.

Does the student always get out of the cognitive difficulty that has been created? As practice shows, there can be 4 ways out of a problem situation:

1) The teacher himself poses and solves the problem;

2) The teacher himself poses and solves the problem, involving students in formulating the problem, making assumptions, proving the hypothesis and checking the solution;

3) Students independently pose and solve the problem, but with the participation and (partial or complete) help of the teacher;

4) Students independently pose a problem and solve it without the help of a teacher (but, as a rule, under his guidance).

On the basis of a linguistic definition: a problem is a task to be solved, researched. What is the nature of the problem that arises in the learning process? Many teachers identify the concept of "problem" with the concept of "question" and "task", the problem in teaching is confused with the problem in its commonly used meaning.

A learning problem is not the same as a task. Both in life and at school there are many problems, the solution of which requires only mechanical activity, which not only does not contribute to the development of independent thinking, but also hinders this development.

Educational problem - a form of implementation of the principle of problematic learning. An educational problem is a subjective phenomenon and exists in the student's mind in an ideal form, in thought, just like any judgment, until it becomes logically complete. The task is an objective phenomenon, for the student it exists from the very beginning in a material form, and the task turns into a subjective phenomenon only after its perception and awareness.

The main elements of the learning problem are "known" and "unknown" (you need to find a "connection", "relationship" between the known and the unknown). The conditions of the task necessarily contain such elements as "given" and "requirements".

An educational problem is a form of manifestation of the logical-psychological contradiction of the process of assimilation, which determines the direction of mental search, arouses interest in the study (explanation) of the essence of the unknown and leads to the assimilation of a new concept or a new mode of action.

The main functions of the learning problem:

1) Determination of the direction of mental search, that is, the student's activity to find a way to solve the problem.

2) Formation of cognitive abilities, interest, motives for the student's activity in assimilating new knowledge.

There are several requirements for this problem. If at least one of them is not fulfilled, the problem situation will not be created.

1. The problem should be understandable to students. If the meaning of the problem has not reached the students, further work on it is useless. Therefore, the problem must be formulated in terms known to the student so that all, or at least most of the students, understand the essence of the problem posed and the means for solving it.

2. The second requirement is the feasibility of the proposed problem. If the problem put forward by the majority of students cannot be solved, the teacher will have to spend too much time or solve it himself; neither will give the desired effect.

3. The formulation of the problem should interest students. Of course, the main thing in creating interest is the mathematical side of things, but it is very important to choose the proper wording. Entertaining form often contributes to the success of problem solving.

4. The naturalness of the problem statement plays a significant role. If students are specifically warned that a problematic task will be solved, this may not arouse their interest at the thought that a transition to a more difficult one is ahead.

The teacher's knowledge of the basic requirements for the curriculum is one of the most important conditions for the successful formulation of the problem and the organization of independent cognitive activity of students.

The formulation of the educational problem is carried out in several stages:

a) analysis of the problem situation;

b) awareness of the essence of the difficulty - vision of the problem;

c) verbal formulation of the problem.

The learning problem is not a problem for the teacher. The teacher poses a problematic question or problematic task to the students. Such a statement leads to the emergence of a problem situation - the student's acceptance of the problem formulated and posed by the teacher.

The process of setting an educational problem should be carried out taking into account the basic logical and didactic rules:

1) separation (limitation) of the known from the unknown,

2) localization (limitation) of the unknown.

The organization of problem-based learning involves the use of such techniques and teaching methods that would lead to the emergence of interrelated problem situations and predetermine the use of appropriate teaching methods by schoolchildren.

However, the emergence of problem situations and search activity of students is not possible in every situation. It is, as a rule, possible in such types of educational and cognitive activity of students as: solving ready-made non-standard tasks; drawing up tasks and solving them; logical text analysis; student research; composition; rationalization and invention; construction and others.

Therefore, the creation by the teacher of a chain of problem situations in various types of creative educational activities of students and the management of their mental (search) activities for the assimilation of new knowledge by independently (or collectively) solving educational problems is the essence of problem-based learning.

Based on the idea of ​​developing the cognitive independence of students, all varieties of the modern lesson, based on the principle of problematicity, are divided into problematic and non-problematic.

From the point of view of internal specificity (logical and psychological), a lesson should be considered problematic if the teacher deliberately creates problem situations and organizes the search activity of students to independently formulate educational problems and solve them (the highest level of problematicity) or he himself poses problems and solves them, showing students the logic of the movement of thought in a search situation (the lowest level of problem).

The didactic (external) indicator of a problematic lesson is its complexity, synthetic character. The essence of a synthetic lesson is that the repetition of what has been passed, as a rule, merges with the introduction of new material, there is a continuous repetition of knowledge, skills and abilities in new connections and combinations, which is typical for a problem lesson.

The structural elements of a modern lesson are:

1) actualization of the previous knowledge of students (which means not only the reproduction of previously acquired knowledge, but also their application often in a new situation, stimulating the cognitive activity of students, teacher control);

2) the assimilation of new knowledge and methods of action (in a more specific sense than the concept of "learning new material");

3) the formation of skills and abilities (including both special repetition and consolidation).

This structure reflects both the main stages of teaching and the stages of organizing a modern lesson. But in relation to the mental activity of students, being an expression of the goals of education, it acts as an external indicator of learning, that is, it does not reflect the process of productive cognitive activity of students and cannot ensure the management of this activity. Since an indicator of the problematic nature of a lesson is the presence of stages of search activity in its structure, it is natural that they represent the inner part of the structure of a problematic lesson:

1) the emergence of a problem situation and the formulation of the problem;

2) making assumptions and substantiating the hypothesis;

3) proof of the hypothesis;

4) checking the correctness of the solution to the problem.

Thus, the structure of a problem lesson, unlike the structure of a non-problem one, has elements of the logic of the cognitive process (the logic of productive mental activity), and not just the external logic of the learning process. The structure of the problem lesson, which is a combination of external and internal elements of the learning process, creates opportunities for managing the student's independent educational and cognitive activity.

Within the framework of problem-based learning in pedagogy, not only general pedagogical problems are studied, but also problems of learning individual items. This is especially true for the problems of pedagogy of mathematics.

It is in mathematics lessons that a favorable atmosphere develops for the introduction of elements of problem-based learning, since it is advisable to study such material in a problematic way that contains cause-and-effect relationships and dependencies, which is aimed at the formation of concepts, laws and theories.

An approximate scheme for organizing a mathematics lesson in the form of problem-based learning.

1. Creation of an educational problem situation (real or formalized) in order to arouse students' interest in this educational problem and motivate the expediency of its consideration.

2. Statement of a cognitive task (or tasks) arising from a given problem situation, its clear formulation.

3. The study of various conditions that characterize the task, discussing the possibilities of modeling its condition or replacing the existing model with a simpler and more descriptive one.

4. The process of solving the task (discussing the task in general and in detail, identifying the essential and insignificant in its conditions, orientation in possible difficulties in solving it, calculating the subtask and the sequence of its solution, the relationship of this task with the available knowledge and experience. Development of possible directions for solutions main task, selection, reproduction of known theoretical positions that can be used in indicated direction problem solving, a comparative assessment of the direction of the solution and the choice of one of them, the development of a plan for solving the problem in the chosen direction and its implementation as a whole, a detailed implementation of the plan for solving the problem and justifying the correctness of all steps of the emerging solution to the problem).

5. Study of the obtained solution of the problem, discussion of its results, identification of new knowledge.

6. Application of new knowledge through the solution of specially selected learning objectives for its assimilation.

7. Discussion of possible extensions and generalizations of the results of solving the problem within the framework of the initial problem situation.

8. The study of the obtained solution of the problem and the search for other more economical or more elegant ways to solve it.

9. Summing up the results of the work done, identifying the essential in the content, methods of solution, results, discussion of possible prospects for the application of new knowledge and experience.

This schematic plan for organizing a problem lesson in mathematics (like any other) is dynamic (depending on the specific characteristics of a particular educational problem). It is carried out in whole or in part, individual points of the plan can be combined together, and the like.

2.3 Application of technology in mathematics lessons

Currently, much attention is paid to the so-called technologization educational systems, which is associated with scientific and technological progress, informatization and technologization of society, as well as the features of the education system. Pedagogy in modern world, says I.P. Vile, is going through a turbulent period of rethinking approaches, abandoning some established traditions and stereotypes. As a result, the concept of “technology” is actively included in pedagogical and speech practice, which, translated from Greek, literally means “the doctrine of mastery” and mainly refers to the production sector, where technology is “a set of methods for processing, manufacturing, measuring the state, properties, form of raw material, material or semi-finished product, carried out in the process of production.

The term "technology" arose with the advent of means of production, the power of which exceeded the productivity of one artisan. Initially, technology meant the process of manufacturing products by technical means - machines, a group of machines, and so on. Thus, technology is an algorithmic sequence of operations for obtaining a product based on the use of technical or any other means under human control.

Where is technology hiding in education? In tasks, results or in the process itself? Obviously, technology primarily and most of all refers to the procedural part - methods, forms, means.

The main questions to which, therefore, it must answer are how to teach and educate, how to develop? How to lead students, how to create the most favorable conditions for their cognitive activity, how to get a product of a given quantity and quality. In fact, there is a search for an answer to the most important question - how to act so that the results coincide with the requirements set, so I would like to “define” it and present it visually, and this is the main difficulty. In the learning process, the mind, skill, ideas, methods and forms, means and results, and much more are fused in a special way. And if the latter are more or less developed in pedagogical science, then mastery in the traditional view is an intangible subject, as a result of which ideas, ideal concepts and real relationships, at least somehow connected with mastery, are brought together. All definitions revolve around the process, its organization, mastery pedagogical technology, but there are a lot of parts and it’s quite difficult to connect everything logically, therefore, from the moment of appearance this concept in the pedagogical dictionary in the 70s - 80s. about 300 definitions of pedagogical technology have been developed.

The application of problem-based learning as a technology in mathematics lessons includes the use of so-called technological components, which are as follows.

Problematic study of the material. Goals:

Activation of students' thinking.

Formation of interest in the studied material.

One of the common methods of activating the activity of students is to pose problems during a lecture.

The problematic method, or perplexing, boils down to the following: the teacher poses a problem to the student. This can be done with the help of questions (there may be one question, a system of questions, a question may concern any detail of the subject under study, around which all the material is built, and the like). If the students cannot give an answer, they wait for the teacher's explanation.

The problem can be posed with the help of graphs, drawings, drawings, photographs, and the like.

Students' work on a problem is as valuable, and often more valuable, than the solution itself. Students remember the very reaction to the problem. Work on a problem is successful when a problem situation arises, that is, such a mental state of a student experiencing intellectual difficulty that directs his mental activity to solve the problem. In a problem situation, the student either does not have enough knowledge, or he does not know the methods of action to solve this problem.

Statement of the problem does not always lead to a problem situation. Problems are not interesting for the student if they are not related to his life, if they are of a general nature. There is no problem situation even when the student has too low level knowledge to solve this problem or, conversely, he quickly finds a solution and he is not interested in the further course of reasoning.

There are various options for posing and solving problems in mathematics lessons:

1. The teacher solves the problem

The teacher poses a problem or problems, and solves them himself, presenting the lecture material. With this form of conducting a lesson, students are outwardly passive, but inside each of them the processes of understanding, acceptance and memorization can proceed intensively.

This approach is used more often than others. The lecturer's own answer to the question posed is most acceptable in large classrooms where feedback is difficult. It is desirable to use it where the audience is elderly or conservatively tuned to the lecture.

This approach can be used in teaching students speech creativity. The teacher sets the task to compose a fairy tale (story, story, etc.) and composes it at the moment of the lesson. Students on the example of the teacher learn speech creation. The teacher sets the task to compose a fairy tale (story, story, and so on) and composes it at the moment of the lesson. Students learn from the example of the teacher in this process.

2. Lecture-conversation

The teacher poses problems for students and offers to solve them together. Asking new questions, clarifying and supplementing the answers (but not criticizing unsuccessful ones), the teacher structures, systematizes statements and leads to general conclusions on individual sections of the lecture. He is, as it were, the leader of the conversation, and the classical idea of ​​a lecturer disappears here.

Conducting a problematic lecture-conversation requires the teacher to have deep knowledge of the topic under discussion. He must be able to pose questions clearly and understandably, quickly navigate in the statements of students, develop them and direct additional clarifying questions to solve the problem.

The time of the speech of the teacher depends on the situation, he should avoid going away from the topic of the lecture. This form can be used in youth or small audiences, with a positive attitude of students towards the teacher.

This approach can be used in teaching speech creation. Having set the task, the teacher activates the students with stimulating questions.

3. Small groups (alternatives)

The teacher sets out the problem and gives several students the opportunity to speak, fixes attention on two or three most common approaches to the problem. Students are invited to break into small groups of "adherents" of a particular opinion.

After a short group work, the leaders defend their point of view. The teacher makes an analysis of the speeches, develops them and sets forth the lecture material further.

This method can be used in a classroom in which students want to express their opinion; at school, in universities, at the FPC.

If the audience came to a one-time lecture and want to get information from the lecturer, then the described method will not always be appropriate.

4. Small groups (your solution to the problem)

The next version of the lecture is with the use of small groups: small groups of five to seven people are formed. In these groups, discussion leaders are selected.

The teacher distributes a pre-printed sheet to each group, which describes the problems. After a short discussion, each group presents their solution in writing. If the solutions to the problem are incomplete or incorrect, then the teacher tries to dwell on them in detail in his lecture.

This approach is used to study the opinions of students on the issues under discussion, it is better to use it in educational lectures at schools, technical schools, universities, FPC.

5. Brainstorming

By majority vote, students choose nine representatives of the group. They are located at the first tables. These are the participants of the assault. The teacher introduces the students to the problem. Group representatives are given cards on which they write their opinion within five minutes. Then the cards are passed to each other, and everyone gets acquainted with the opinions of others. After that, within three minutes, the participants of the "brainstorming" fill out new cards. It is better to put a surname in the corner of the card so that the teacher can compare the change in opinions.

The teacher announces the most common opinions on this issue, gives and proves the correct answer, draws attention to the ability of students to critically analyze their own judgments. Next, the teacher presents the material of the topic.

This method can be used in educational lectures: in schools, technical schools, universities, at the FPC.

6. Generators-critics

The teacher poses a problem that does not require a long discussion or calculations. Two groups are formed. The first group of students are generators. They give as much as possible more solutions to the problem, which can be the most fantastic. All this is done without prior preparation. Nobody criticizes each other. All decisions are made. The work is done quickly. (Groups of no more than seven people.)

The second group (critics) receives these proposals and chooses the most suitable ones. The teacher directs the work of students in such a way that they can derive one or another rule or pattern, solve some problem, resorting to their experience and knowledge.

The described techniques are used in lectures and seminars. It is possible to propose for discussion educational problems, the solution of which, in principle, is already known to science, in practice, but unknown to students. You can try to consider scientific problems. Students are interested in solving moral problems.

These techniques can be used at the end of the lecture to enhance the independent work of students. Goals:

Technology is carried out in classes in which it is necessary to develop interest in the subject.

It contributes to the development of students' literacy.

Develops communication skills.

1. Half of the class is assigned sentries (controllers, customs officers, etc.). Each is given a sample password. It can be single words, sentences, or multiple sentences. On the leaflets there are words, sentences on the rules that the students went through according to the program.

You can pass the checkpoint only by correctly writing the password under dictation.

All sentries are placed in the classroom in such a way as not to interfere with each other. All participants in the dramatization have sheets where they enter passwords.

2. At the next stage, each student approaches the point he has chosen. The sentry reads the password to him.

3. The student writes this password on his sheet without looking at the sentry sheet.

4. The sentry takes the student's sheet and first checks with red paste.

5. Then he takes the green paste and checks this password against his standard.

6. If the answer is correct, then the sentry hands over his standard to the student, leaves the post and goes to another point, which he himself tries to pass. In his place is the student who just wrote. If the answer is wrong, then the sentry remains at his post, and the student goes to another point and tries to pass it in the same way. The dramatization can last as long as it is necessary for the assimilation of the material.

So, it is necessary to distinguish between the conceptual varieties of "pedagogical technology": for example, it was noted that the concept of "pedagogical technology" in science and practice is not unambiguously defined, there is also the phenomenon of using pedagogical technology as synonyms for the concepts of pedagogical technology (private-subject and local levels) and teaching methods . But, considering the difference between technology and methodology, Professor A. Kushnir distinguished that “technology is distinguished by its reproducibility of results, the absence of many “ifs”: if the teacher is talented, the children are talented, the school is rich” . The technique arises as a result of the generalization of experience or the invention of a new way of teaching. Technology, in contrast, is designed based on specific conditions and focusing on a given result. The technologist relies on well-known, tried and substantiated facts. He deals with exactly predictable material, the technology has a guaranteed result, all its parts are obligatory, arranged in a logical sequence, therefore, easy restructuring, interchangeability of principles or methods of work indicates a lack of manufacturability.

The mixing of technologies and methods leads to the fact that sometimes methods are part of technologies, or vice versa, technologies are part of teaching methods.

There is also the use of so-called terms - labels in the names of some technologies (a collective method of learning, the method of V.F. Shatalov, the Paltyshev system), and it is not always possible to avoid these errors.

The skill of the teacher is manifested most of all in the organization of problem situations. With problem-based learning, the teacher remains the leader of the educational process, but leaves the not always grateful role of a person communicating knowledge in traditional school, and becomes the one who wakes up, develops, observes the mental operations of students, corrects mistakes, clarifies doubts.

Observing the work of teams, he sees something that he often did not notice when working with everyone - after all, an individual student can be observed at moments of calm work, at moments of creative search, discussions.

The implementation of problem-based learning raises a very important question, which is a problem in itself: “what kind of training do teachers need to receive in order to successfully cope with this kind of learning?” .

The teacher must master both explanatory and research methods of teaching. Acting as a facilitator of problem-based learning, the teacher is called upon to act more as a leader and partner than as a source of ready-made knowledge and directives for students. In the process of preparation, the teacher should gain experience that will allow him to:

1. Subtly feel the problematic situation faced by students and be able to set real learning tasks for the class in a form understandable to children?

2. Act as a coordinator and partner. In the course of exploring various aspects of the problem, help individual students and groups, avoiding directive methods.

3. Try to captivate students with the problem and the process of its in-depth study, stimulate creative thinking with well-posed questions.

4. Show tolerance for students' mistakes, made or in attempts to find their own solution, offering their help or referring to the right sources of information only in those cases when the student begins to feel hopeless in their search.

Putting the teacher in the background does not mean that he loses his importance to some extent. This is only formally the second plan, although coming from the student, despite the fact that the teacher appears on the stage less often than the student, in fact he is the main character. Everything that happens or does not happen to the student depends on him. However, his role as the main actor, as well as the director of the school scene, he performs properly only when he knows how to evoke strength and creativity in students and use them in a well-organized educational process.

Problem-based learning is useful when:

2) Pupils are prepared for the problematic study of the topic.

3) Students solve problems for the development of independent thinking, the formation of research skills, a creative approach to business.

1. Precise definition the volume and content of the educational material intended for study in the lesson.

2. Systematization of educational material in accordance with the logic of the subject, its structure, as well as in accordance with the principles of didactics.

3. The division of educational material into easily digestible and closely related parts.

4. Assimilation of parts, accompanied by control and correction of the results of assimilation.

5. Accounting for the individual pace of assimilation of educational material by schoolchildren and the pace of the group's work.

Types of educational work of schoolchildren in conditions of problem learning.

Problem-based learning allows you to effectively combine both individual and group work of students in the classroom. In traditional teaching group work of students is used extremely rarely. Meanwhile, group - collective work of students is also effective way active acquisition of knowledge by them, not to mention its educational value.

How to combine group and individual work of students in problem-based learning? In the approximate scheme of the problem lesson, the main place is naturally occupied by the solution of the problem.

At this stage, work with students can take the form of:

1) frontal work with the whole class,

2) group work,

3) individual work.

The choice of this or that type of work is influenced by the nature of the work, the available teaching aids (sets of teaching aids and other materials), as well as the time available to the teacher.

Group work involves dividing the class into groups of both approximately the same (in terms of level) development, and sometimes different students. The number of groups can vary.

Some principles of organizing group work can be pointed out.

1. It is most expedient to create study groups of 4-6 people.

2. The composition of student groups should not change frequently, it is better if it is constant, but differentiated. This contributes to the manifestation of the activity of all members of the group and the acceleration of the work of "weak" students.

3. One of the students is appointed as the leader of the group. At the same time, different students lead the work of the group in different lessons.

4. Study groups focus on work at about the same pace, which makes it possible to conduct a business discussion of the material being studied.

The collective work of students on the solution of some educational problem in no way excludes the individual work of each of them, since group work essentially combines the individual work of each of the members of the group.

A skillful combination of group and individual forms of classes ensures the comprehensive development of activity and independence in teaching all students, makes it possible to discuss the topic under study, evaluate the results of their observations, and express hypotheses.

So, problem-based learning is based on the principle of problematicity, implemented through various types of learning problems and through a combination of reproductive, productive and creative activities of the student.

Should all learning be problem-based? Not all, if by problem-based learning we mean only the solution of educational problems and only the independent assimilation of all educational material. All learning should be developmental, in which independent assimilation of knowledge by solving educational problems, through discoveries is combined with the reproductive assimilation of knowledge presented by the teacher or student. The student cannot and should not repeat the entire historical path of the development of human knowledge. But he must repeat the principles of this development and the generalized modes of action in order to assimilate them and develop in himself methods of creative activity.

Problem-based learning means to understand it as a type of learning that provides, in combination with the traditional and the new that has been introduced into pedagogy by many researchers and practitioners, the development of the entire set of feelings and reason, the student’s thinking and his memory, the development of a holistic, intellectually active personality.

The problematic type of education does not solve all educational and upbringing tasks, therefore it cannot replace the entire education system, including different types, methods, organization of the educational process. But also the system of education cannot be truly developing without problem-based learning.

Are problem-based learning accessible to all students? Almost everyone. However, the level of problematicness and the degree of cognitive independence will vary greatly depending on age and individual features students, on the degree of their training in problem-based learning methods, and so on.

Conclusion

Having considered in the course work the main aspects of the implementation of problem-based learning as a pedagogical technology in mathematics lessons, we can draw the following conclusions:

1. Problem-based learning is learning in which the teacher poses a problem to the students and organizes the process of solving it.

2. Yu.K. Babansky, P.L. Galperin, N.A. Menchinsky, A.M. Matyushkina, M.I. Makhmutova and other authors.

3. Problem-based learning is one of the most effective means of activating the thinking of students.

4. Problem situation and learning problem are the basic concepts of problem learning.

5. There are principles of the main ways to create problem situations, as well as rules for creating problem situations.

6. A learning problem is a form of implementing the principle of problematicness in learning.

7. In the problem put forward, there are requirements that must be taken into account by the teacher when organizing training within the framework of the pedagogical technology under consideration.

8. The learning problem is not a problem for the teacher.

9. There are three types of problem solving, depending on whether the solver has certain experience in relation to the class of problematic tasks.

10. The solution of an educational problem is the result of an active thought process.

11. The first lessons of any topic are problematic.

12. There is a structure for organizing problem-based learning in high school.

13. Problem-based learning combines the individual and collective forms of work of students.

14. There are the following methods of problem-based learning: the method of monologue presentation, reasoning, dialogic, heuristic, research, the method of program tasks.

15. There are the following types of problem-based learning: theoretical research, search for a practical solution, artistic representation of reality, and others.

16. Problem-based learning is available to almost all students.

The continuation of the work is the further study of the effectiveness of the forms and methods of influence of this technology on the formation of the mental processes of students, the development of their creative abilities.

Literature

1. Babansky Yu.K. Methods of teaching in a modern general education school.-M. Enlightenment, 1985.

2. Babansky Yu.K. Problem-based learning as a means of improving the effectiveness of schoolchildren's learning. - Rostov-on-Don, 1970.

3. Vilkeev D.V. Cognitive activity of students with the problematic nature of teaching the basics of science at school. - Kazan, 1967.

4. Galperin P.Ya. Teaching methods and mental development of the child. - M.: Publishing House of Moscow State University, 1985.

5. Krutetsky V.A. Psychology of training and education of schoolchildren. - M.: Enlightenment, 1986.

6. Kudryavtsev T.V. Research and experience in problem-based learning. In the book: "On problem-based learning": Issue. 2.- M.: Higher school, 1969.

7. Kudryavtsev T.V. Problem-based learning: origins, essence, perspectives. - M.: 3nanie, 1991.

8. Lerner I.Ya. Issues of problem-based learning at the All-Union Pedagogical Readings.// Soviet Pedagogy.-1968.-No. 7.

9. Lerner I.Ya. System of teaching methods. - M.: Knowledge, 1976.

10. Lyudmilov D.S., Dyshinsky E.A., Lurie A.M. Some questions of problematic teaching of mathematics: A guide for teachers. - Perm, 1975.

11. Matyushkin A.M. Problem situations in thinking and learning. - M .: Pedagogy, 1972.

12. Makhmutov M.I. Organization of problem-based learning at school. A book for teachers. - M .: Education, 1977.

13. Makhmutov M.I. Problem learning. Basic questions of theory. - M .: Pedagogy, 1975.

14. Mochalova N.M. Methods of problem-based learning and the limits of their application. - Kazan, 1978.

15. Okon V. Fundamentals of problem-based learning.- M.: Enlightenment, 1968.

16. The search for rational ways of teaching mathematics (from the experience of Tatar teachers). - M. Education, 1968.

17. The development of students in the learning process: Ed. L.V. Zankova.-M., 1963.

Annex 1

The difference between problem-based learning and traditional learning

Comparison indicators	Traditional learning	Problem learning
goals	Acquisition of knowledge by students by their own work.	Gaining knowledge with the help of a teacher.
Stages of the lesson: stage number 1	Organization of student attention
Stage #2	Actualization of previously studied material: the teacher asks leading questions in order to repeat previously studied material.	Instruction: reference to previous experience (for example, the teacher reminds that power function students have already studied, is there a repetition of properties, plotting graphs, the situation where it is used?
Stage #3	Learning new material: the teacher himself explains the topic, gives examples, and then demands from the students.	Discussion of the topic in the group: the class is divided into groups, first there is a discussion of the topic in the group, and then with the whole class.
Stage #4	Reinforcement: the teacher provides students with certain numbers on a given topic, and students consolidate their knowledge in practice.	The gap is the moment when students must realize that there are gaps in their knowledge that they themselves must fill.
Stage number 5	Secondary reinforcement: the teacher is already for reinforcement new topic gives more difficult tasks.	Reflection - determination of the degree of assimilation.
Stage number 6	Summing up the lesson

Conceptual foundations: I. Problem-based learning is a type of learning in which the teacher, systematically creating problem situations and organizing students' activities to solve educational problems, ensures the optimal combination of their independent search activities with the assimilation of ready-made scientific conclusions.

III. General functions: 1. Assimilation by students of the system of knowledge and methods of mental and practical activity. 2. Development of cognitive independence and creative abilities of students. 3. Formation of dialectical materialistic thinking of children.

Special functions: 1. Cultivating the skills of creative assimilation of knowledge and the ability to solve educational problems. 2. Formation of skills for the creative application of knowledge and the ability to solve educational problems.

Special functions: 3. Formation and accumulation of experience in creative activity (mastery of methods scientific research, practical problem solving). 4. Formation of motives for teaching, social, moral and cognitive needs.

IV. Features: 1. Independent solution of educational problems (consciousness, depth, strength of knowledge, development of logical and theoretical thinking). 2. The transformation of knowledge into beliefs (development of critical, creative, dialectical thinking).

3. Practice as a source of new knowledge and as a sphere for the implementation of learned methods of activity. 4. A combination of various types of independent work. 5. Dynamism - one problem situation goes into another.

6. Individualization - the presence of educational problems of varying complexity; individual perception of the problem. 7. High emotional activity of children - individual acceptance of the problem, the relationship of active mental activity with the sensory-emotional sphere of mental activity.

Types: 1. Scientific creativity - the search and discovery by students of a new rule, law, evidence; the basis is the formulation and solution of theoretical educational problems.

Types: 2. Practical creativity - the search for a way to apply known knowledge in a new situation, design, invention; the basis is the formulation and solution of practical educational problems.

Types: 3. Artistic creativity - an artistic reflection of reality based on creative imagination (drawing, playing, playing music, etc.).

Levels: 1. The level of normal activity - the students' perception of the teacher's explanations, the assimilation of a model of mental action in a problem situation, the performance of independent work, exercises of a reproducing nature.

Levels: 2. The level of semi-independent activity - the application of acquired knowledge in a new situation, the participation of children in a joint search with the teacher for a way to solve the educational problem posed.

Levels: 3. The level of independent activity - the performance of independent work of a reproductive and search nature, when the student independently applies the acquired knowledge in a new situation, constructs a solution to a problem of an average level of complexity.

Levels: 4. The level of creative activity - the performance of independent work that requires creative imagination, logical analysis, discovery of a new way of solving, independent proof.

Elements of problem-based learning: 1. A problematic question is a question that causes intellectual difficulties for students, since the answer to it is not contained in the previous knowledge of students, not in the information presented.

Elements of problem-based learning: 2. A problematic task is a form of organizing educational material with given conditions and unknown data, which involves active mental activity of students: analysis of facts, identification of the causes of the origin of objects, analysis of cause-and-effect relationships.

Elements of problem-based learning: 3. Problem-based task - an assignment or instruction to students on their independent search and cognitive activity aimed at obtaining the desired result (search, writing, invention, etc.).

Elements of problem-based learning: 4. Problem situation - a state of mental difficulty of students caused by the insufficiency of previously acquired knowledge and methods of activity to solve a cognitive task, task or educational problem.

Types of problem situations: 1. Collision with the need to use previously acquired knowledge in new practical conditions. 2. The contradiction between the theoretically possible way of solving the problem and its practical impracticability or inexpediency.

Types of problem situations: 3. The contradiction between the practically achieved result of the assignment and the lack of knowledge for its theoretical justification. 4. Students' ignorance of the solution method, inability to answer a problematic question, awareness of insufficient previous knowledge to explain a new fact.

The activity of the teacher 1. Creates a problem situation 2. Organizes reflections on the problem and its formulation. 3. Organizes the search for a hypothesis. Students' activities 1. Recognize the contradiction in the phenomenon under study. 2. Formulate the problem. 3. Put forward hypotheses. 4. Organizes hypothesis testing. 4. Test hypotheses in experiment, problem solving, analysis. 5. Organize summarization 5. Analyze results and application. tata, draw conclusions, apply knowledge.

Problem-based learning is based on the acquisition of new knowledge by students by solving theoretical and practical problems, tasks in problem situations that are created for this.
The well-known Polish scientist V. Okon writes in his book Fundamentals of Problem-Based Learning that the more students strive to get on the path followed by the researcher in the course of their work, the better the results achieved. Domestic psychologists T.V. Kudryavtsev, A.M. Matyushkin, Z.I. Kalmykova and others developed the psychological foundations of the so-called problem-based learning in its various modifications. Its essence is as follows. The students are given a problem, a cognitive task, and the students (with the direct participation of the teacher or on their own) explore ways and means of solving it. They build a hypothesis, outline and discuss ways to test its truth, argue, conduct experiments, observations, analyze their results, argue, prove. This includes, for example, tasks for the independent “discovery” of rules, laws, formulas, theorems (independent derivation of the law of physics, spelling rules, mathematical formula, discovery of a method for proving a geometric theorem, etc.).
Problem-based learning includes several stages:
1) awareness of the general problem situation;
2) its analysis, formulation of a specific problem;
3) problem solving (promotion, substantiation of hypotheses, their consistent testing);
4) checking the correctness of the solution to the problem.
This process unfolds by analogy with the three phases of the mental act that occurs in a problem situation and
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includes awareness of the problem, its solution and the final conclusion. “Thinking,” notes A.V. Brushlinsky, “originates in a problem situation, which means that in the course of his activity a person begins to experience some incomprehensible difficulties that prevent successful progress ... Thus, the problem situation that has arisen turns into a conscious human task".
Therefore, problem-based learning is based on the analytical-synthetic activity of students, implemented in reasoning, reflection. This is a heuristic, exploratory type of learning with great developmental potential.
Distinctive characteristics of problem-based learning are shown in Table 10.

Table 10 Characteristics of informal and problem-based learning (according to V. Okon)
Informative learning Problem based learning
1. The material is given in finished form, the teacher pays attention primarily to the program
2. Gaps, barriers and difficulties arise in the oral presentation of the material or through the textbook, caused by the temporary exclusion of the student from the didactic process.
3. The pace of information transfer is focused on stronger, average or weak students
4. The control of school achievements is only partly related to the learning process; it is not an organic part of it
5. There is no way to provide all students with 100% results; the greatest difficulty is the application of information in practice 1. Students receive new information in the course of solving theoretical and practical problems
2. In the course of solving the problem, the student overcomes all difficulties, his activity and independence reach a high level here
3. The rate of communication depends on the student or group of students
4. Increased activity of students contributes to the development of positive motives and reduces the need for formal verification of results
5. Teaching outcomes are relatively high and sustainable. Students can more easily apply what they have learned to new situations and at the same time develop their skills and creativity.

The main concepts of problem-based learning include: “problem situation”, “problem task”, “problem”, “problem-ness” (“levels of problematicity”, “principles of problematicity” and DR-)> “problematization”.
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The condition for the realization of the learning goal is the problematic inherent in any "viable" object and subject, which can exist in a hidden and expressed form, i.e. be internal and external.
A way to create problematicity is a problematic situation that fixes the moment when the subject assigns an object containing problematicity.
The means of creating a problem situation can be a problem task formalized in textual data.
The mechanism that reveals the problematic is the problematization of the object and the subject, that is, the process of revealing internal and external contradictions inherent in the object, problems.
The unit of the process is a problem - a hidden or obvious contradiction inherent in things, phenomena of the material and ideal world.
Problematicness - the main condition for the development of an object (the world) and a subject (a person) - can be considered as a dialectical category, side by side with others, or as the main feature of these categories in development, or as the main principle of their action, activity, or as the need to act.
A problem situation is a way of revealing an objectively existing problem, expressed explicitly or implicitly, which manifests itself as a mental state of intellectual difficulty in the interaction of the subject and object.
A problem task - a means of creating a problem situation - has a shell materialized in its formulation (oral or written), focused on the needs and capabilities of the subject.
Problematization is the mechanism that underlies the discovery of the problematic nature of an object by the subject, materialized in this problematic task.
A problem - a contradiction - is a unit of the content and process of movement in the material and ideal space, which generates the process of development of the world and man and is generated by a developed person. This process is continuous.
According to V. Okon, "the essence of the process of learning by solving problems comes down in each case to creating a situation that forces the student to independently seek a solution" . According to V. Okon, the role of the teacher is to make the Student feel the difficulty of a practical or theoretical nature, to understand the problem posed by the teacher, or to formulate it himself, to want to solve the problem, to solve it.
What is the problem solving process? According to V. Okon, it depends on the nature of the problem and the complexity of its solution. “The nature of the problem is determined by the degree of its complexity. In addition to simple problems, there are those that, before starting to solve
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it is necessary to divide into particular ones, and only the solution of the latter makes it possible to solve the main problem. The difficulty of solving the problem is twofold. One is that in order to make a decision, it is necessary to update some part of the previous experience, precisely that without which the decision is impossible. Another is the need to simultaneously find new elements (links) unknown to the student that allow solving the problem.
The didactic foundations of problem-based learning are determined by the content and essence of its concepts. According to M. I. Makhmutov, the main concepts of the theory of problem-based learning should be “educational problem”, “problem situation”, “hypothesis”, as well as “problem teaching”, “problem teaching”, “problematic content”, “mental search”, “problem question”, “problem statement”.
The educational problem is a subjective phenomenon and exists in the mind of the student in an ideal form, in thought. The task is an objective phenomenon, for the student it exists from the very beginning in a material form (in sounds or signs), and the task turns into a subjective phenomenon only after its perception and awareness. It is also important that the educational problem is the form of implementation of the principle of problem-ness in education.
M. I. Makhmutov offers a didactic classification of educational problems, which is based on the following variables: 1) area and place of origin; 2) role in the learning process; 3) social and political significance; 4) ways of organizing the decision process. The psychological classification of educational problems is based on such indicators as: 1) the nature of the unknown and caused difficulty; 2) solution method; 3) the nature of the content and the relationship between the known and the unknown in the problem.
Defining the problem situation, M. I. Makhmutov notes that it is the initial moment of thinking, causing the cognitive need of the student and creating internal conditions for the active assimilation of new knowledge and methods of activity. At the same time, two types of problem situations can be distinguished that arise in the formulation of both theoretical and practical problems.
The classification of ways to create problem situations is based on the nature of the contradiction that arises in the process of learning: “1. Collision of students with phenomena and facts that require theoretical explanation. 2. The use of educational and life situations that arise when students perform practical tasks. 3. Statement of educational problem tasks to explain the phenomenon or search for ways of its practical application. 4. Encouraging students to analyze facts and phenomena
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reality, confronting them with contradictions between worldly ideas and scientific concepts about these facts. 5. Putting forward hypotheses, formulating conclusions and their experimental verification. 6. Encouragement of students to compare, compare and contrast facts, phenomena, rules, actions, as a result of which there is a cognitive difficulty. 7. Encouraging students to a preliminary generalization of new facts. 8. Familiarization of students with facts that seem to be inexplicable and have led in the history of science to the formulation of a scientific problem. 9. Organization of intersubject communications ".
M.I. Makhmutov distinguishes three types of problem-based learning according to the type of creative activity being implemented: 1) scientific creativity; 2) practical creativity; 3) artistic creativity. What underlies each type of learning and creativity? Scientific creativity is based on the formulation and solution of theoretical educational problems. Practical creativity is based on the formulation and solution of practical educational problems. Artistic creativity is "an artistic representation of reality based on creative imagination, including literary compositions, drawing, writing a piece of music, playing, etc." .
The main thing in problem-based learning is the creation of a problem situation. Of course, not every question to which the student does not know the answer creates a genuine problem situation. Questions like: “What is the number of inhabitants in Moscow?”, “When was the Battle of Poltava?” or “Which city is the capital of Turkey?”, “What was Gogol’s name?” - are not problems from a psychological and didactic point of view, since the answer can be obtained from a reference book, an encyclopedia without any participation of the thought process. Not a problem and such a task that does not present difficulties for the student (for example, calculate the area of ​​a triangle, if he knows how to do it).
A learning task can cause mental activity under certain conditions. Psychologists see the source of student activity, in particular, in the contradictions between their experience (knowledge, skills) and the problems that arise in solving cognitive learning problems. This contradiction causes active mental activity. For example, a student must solve a particular cognitive problem, but: a) its conditions do not suggest a way to solve it, and b) the student’s past experience does not contain any ready-made solution scheme that could be applied in this case. The student is faced with the need to create a new solution scheme that is not available in his experience, a new system of methods of action.
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A problem situation arises in a person if he has a cognitive need and intellectual capabilities to solve a problem in the presence of difficulty, a contradiction between the old and the new, the known and the unknown, the given and the desired, conditions and requirements. Problem situations are differentiated by A. M. Matyushkin according to the criteria: 1) the structure of actions that must be performed when solving a problem (for example, finding a method of action); 2) the level of development of these actions in the person solving the problem; 3) intellectual abilities of the student.
A. M. Matyushkin characterizes a problem situation as a special type of mental interaction between an object and a subject (student), characterized by such a mental state of the subject when solving problems that requires the discovery (discovery or assimilation) of new knowledge or methods of activity previously unknown to the subject. In other words, a problem situation is a situation in which the subject wants to solve problems that are difficult for him, but he does not have enough data, and he must look for them himself.
In the book “Problem situations in thinking and learning”, A. M. Matyushkin presents the following six rules for their creation.
1. In order to create a problematic situation, students should be given a practical or theoretical task, the implementation of which will require the discovery of new knowledge and the acquisition of new skills; here we can talk about a general pattern, a general mode of activity, or general conditions for the implementation of an activity.
2. The task must correspond to the intellectual capabilities of the student. The degree of difficulty of the problem task depends on the level of novelty of the teaching material and on the degree of its generalization.
3. The problematic task is given before the explanation of the material to be learned.
4. Problem tasks can be: a) assimilation, b) wording of the question, c) practical tasks. However, problem tasks and problem situations should not be confused with each other. A problem task can lead to a problem situation only if the above rules are taken into account.
5. The same problem situation can be caused by different types of tasks.
6. The teacher directs a very difficult problematic situation by indicating to the student the reasons for not fulfilling the practical task given to him or the impossibility of explaining certain facts to him.
Problem-based learning can be of different levels of difficulty for the student, depending on what and how many actions
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actions for the formulation and solution of the problem he carries out himself. V. A. Krutetsky proposed a scheme of levels of problematic learning in comparison with the traditional one based on the separation of the actions of the teacher and the student (Table 11).

Table 11 Scheme of levels of problematic learning (according to V.A. Krutetsky)
Level Number of links kept by the teacher Number of links given to the student What the teacher does9 What the student does9
0 (traditional) 3 Assesses the problem, formulates it, solves the problem Remembers the solution to the problem
I 2 1 State the problem, formulate it Solve the problem
II 1 2 Sets a problem Formulates a problem, solves a problem
III 3 Conducts general organization, control and skillful leadership Recognizes
problem, formulates it, solves the problem

The scheme of levels of problem-heuristic learning proceeds from how many and what links are transferred by the teacher to the student. In the traditional form of teaching, the teacher himself formulates and solves the problem (deduces a formula, proves a theorem, etc.). The student must understand and remember someone else's thought, remember the formulation, the principle of decision, the course of reasoning.
There are four levels of difficulty in learning:
1. The teacher himself sets the problem (task) and solves it himself with active listening and discussion by students.
2. The teacher poses a problem, the students independently or under his guidance find a solution. The teacher directs the student to independent search for solutions (partial search method). Here there is a detachment from the sample, opens up space for reflection.
3. The student poses a problem, the teacher helps to solve it. The student develops the ability to independently formulate the problem.
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4. The student himself poses the problem and solves it himself. The teacher does not even point out the problem: the student must see it on his own, and having seen it, formulate and explore the possibilities and ways to solve it.
As a result, the ability to independently see the problem, independently analyze the problem situation, and independently find the correct answer is brought up.
The third and fourth levels are the research method.
If the teacher feels that students are having difficulty completing a particular task, then he can introduce additional information, thereby reducing the degree of problematicness and transfer students to a lower level of problem-heuristic learning.
In problem-based learning, the teacher is like an experienced conductor organizing this exploratory search. In one case, the teacher himself, with the help of the students, can conduct this search. Having posed a problem, he reveals the way to solve it, argues with the students, makes assumptions, discusses them with the students, refutes objections, proves the truth. In other words, the teacher demonstrates to students the path of scientific thinking, makes students follow the dialectical movement of thought towards the truth, makes them, as it were, accomplices in scientific search.
In another case, the role of the teacher may be minimal - he provides students with the opportunity to independently seek ways to solve problems. But even here the teacher does not take a passive position, but, if necessary, imperceptibly directs the students' thoughts in order to avoid fruitless attempts, unnecessary loss of time. That is why the teaching method associated with the independent search and discoveries of certain truths by schoolchildren is called the problem-heuristic, or research, method.
Thus, under the conditions of problem-based learning, the development of activity in the mental activity of students can be characterized as a transition from actions stimulated by the teacher's tasks to independent formulation of questions; from actions related to the choice of already known ways and methods, to independent searches for solving problems, and further - to developing the ability to independently see problems and explore them.
The research method cultivated in problem-based learning is such an organization of educational work in which students become familiar with scientific methods acquiring knowledge and, mastering the elements of scientific methods available to them, master the ability to independently obtain new knowledge, plan a search and discover a new dependence or pattern for themselves.
In the learning process, it is important to gradually transfer students to a higher level of problem-heuristics.
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academic training. Of course (and this is important to emphasize), the ability to see, formulate and solve a problem does not develop spontaneously, as a spontaneous development of initially laid down tendencies. This is the result of learning. The teacher teaches independent formulation and problem solving, independent thinking develops with the decisive and leading role of the teacher. It is wrong to assume, as D. Dewey did, that the inborn and uncorrupted state of childhood, distinguished by love for experimental research, is very close to scientific thinking.
Among the modern developments of forms of problem-based learning, the experience of its implementation in the methodology and practice of teaching deserves attention. foreign languages. One of the latest original "versions" of such a didactic construction is the development of E. V. Kovalevskaya. In her study, devoted to teaching speaking in a foreign language, the task was to form ways to create problem situations at the communicative level. During the experiment, it was found that problem situations for teaching speaking should be based on the inclusion of obstacles to achieving the goal and varying the number of unknown components (place, time, participants in communication), which determines the degree of complexity of the problem situation and the variability of solutions. For example: “You need to be at the institute on time, but you can’t leave because you are waiting for an important phone call...” This situation is problematic because it contains an obstacle to achieving the goal, as well as unknown components (time and communication participants).
Thus, in the course of the experiment, the expediency of introducing stepwise problem situations was proved, which contribute to the stimulation of speech due to a series of successively emerging obstacles to achieving the goal. The development of creative activity of students was ensured by involving them in the process of setting and solving problems, individualization of learning based on the choice of problems in accordance with the cognitive and communicative needs and capabilities of each student.
E. V. Kovalevskaya developed “step-by-step” situations in which the goal of the simulated action is complicated not by one, but by a chain of obstacles built in a certain logical sequence. For example: “You need to be at the institute on time, but: 1. You can’t leave because you are waiting for an important phone call ... 2. You ask your neighbor to take you to work, but he refuses because ... 3. You you are traveling by bus, but you don’t have time to get a ticket, the controller enters ... 4. The bus leaves, you stop a taxi, but a person appears who is late for the plane ... 5. You stop the car, but on the way the driver
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breaks the rules traffic... 6. You arrive at the institute, but you do not have a wallet (money) to pay for the fare ... 7. You manage to pay the fare, but you are late for the lecture ... etc.” Based on the stepwise situations presented orally in a foreign language, the teacher maintains communication, offering more and more new problems to solve.
Further, E.V. Kovalevskaya considers one of the central issues of problem-based learning - the issue of "appropriation" of objective problem situations, provided they correspond to the cognitive and communicative needs and abilities of students and if they are accepted by the teacher.
The appropriation process can be optimized based on the formation of students' skills to resolve problem situations and the skills of teachers to manage this process. The search skills of students and teachers were based on the stages of solving the problem. Students' skills to resolve problem situations include: 1) the ability to see problems and put them on their own; 2) the ability to create a solution hypothesis, evaluate it, moving on to a new one in case the original one is unproductive; 3) the ability to direct and change the course of the decision in accordance with their interests; 4) the ability to evaluate one's own decision and the decisions of interlocutors. The skills of teachers to manage the process of resolving problem situations are as follows: 1) the ability to anticipate possible problems on the way to achieving the goal in a problem situation; 2) the ability to instantly reformulate a problem situation, facilitating or complicating it on the basis of regulating the number of unknown components; 3) the ability to choose problem situations in accordance with the train of thought of those who solve the problem; 4) the ability to impartially assess the options for students' decisions, even if the points of view of students and teachers do not coincide.
By analogy with the levels of problematicity for a student, E. V. Kovalevskaya builds levels of problematicity for a teacher: at the first level, the teacher acquires methodological knowledge in the process of reasoning presentation of the main provisions and concepts of problem-based learning in relation to a foreign language; at the second level, the teacher uses problem situations from the textbook in his work; at the third level, independently thinks through possible problem situations during preparation for the lesson, and also creates them in the lesson; at the fourth level, he becomes the author of a new textbook, methodology, and scientific research. In the process of creativity, the teacher becomes the author of his script (textbook), the director of his own performance (lesson), the creator of a new theater ( scientific direction). The foregoing made it possible to show the multilevel nature of the problematic idea, its development in space and time.
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In conclusion, it is necessary to dwell on the place and role of problem-based learning in the system of a holistic educational process.
According to I.Ya. Lerner, problem-based learning should be carried out only when studying part of the educational material, which allows creative processing of information obtained both in problem-based and non-problem learning.
What are the functions of problem-based learning? There are three of them: 1) the development of creative potentials and the formation of structures of creative activity; 2) creative assimilation of knowledge and methods of activity; 3) creative mastery of the methods of modern science.
At the same time, as I.Ya. Lerner notes, only a few students can see problem situations. In order for the majority of students to see and solve problems, a system of problem situations, problems and problem tasks is needed, included in the fabric of the content of education and the learning process. The following characteristics should be indicators of the system of problematic tasks: 1) coverage different traits creative activity; 2) the presence of various degrees of complexity. As for the content of the educational material on which the system of problems should be built, it is subject to the main content principle of the system of problem tasks, based on the identification of “cross-cutting” or “aspect” problems in various fields of science.
According to M. I. Makhmutov, problem-based learning cannot replace all learning, but without the principle of problematic learning, learning cannot be developing. “The problematic type of education,” the author writes, “does not solve all educational and upbringing tasks, therefore it cannot replace the entire education system, which includes different types, methods and forms of organizing the educational process. But also the general system of education cannot be truly developing without problem-based learning, the basis of which is a system of problem situations.
Of course, the problematic method cannot be turned into a universal teaching method. As V. A. Krutetsky noted, “... for some students who do not yet possess the skills of independent thinking, it is somewhat difficult (although other students can be very successful in it: in our experiments, for example, the most capable ones “discovered” for themselves almost entire course of geometry). Yes, and it requires more time than the traditional information-reporting presentation. But the latter circumstance should not be exaggerated. The loss of time at the first stages of the introduction of the problematic method is compensated later, when the student's independent thinking develops sufficiently.
The benefits of problem-based learning are clear. First of all, these are great opportunities for developing attention, observing
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activity, activation of thinking, activation of cognitive activity of students; it develops independence, responsibility, criticality and self-criticism, initiative, non-standard thinking, caution and determination, etc. In addition, which is very important, problem-based learning ensures the strength of the acquired knowledge, because they are obtained in independent activity.
Problem-based learning has a number of advantages compared to traditional learning, since: 1) it teaches you to think logically, scientifically, dialectically, creatively; 2) makes the educational material more evidence-based, thereby contributing to the transformation of knowledge into beliefs; 3) as a rule, more emotionally evokes deep intellectual feelings, including a sense of joyful satisfaction, a sense of confidence in one’s abilities and strengths, therefore, it captivates schoolchildren, forms a serious interest of students in scientific knowledge; 4) it has been established that independently “discovered” truths, patterns are not so easily forgotten, and in case of forgetting, independently acquired knowledge can be restored faster.
Problem-based learning is associated with research and therefore involves a solution of a problem extended in time. The student finds himself in a situation similar to that in which there is an agent who solves a creative task or problem. He constantly thinks about it and does not get out of this state until he solves it. It is due to this incompleteness that solid knowledge, skills and abilities are formed.
The disadvantages of problem-based learning include the fact that it always causes difficulty for the student in the learning process, so it takes much more time to comprehend and find solutions than with traditional learning. In addition, as with programmed learning, the development of problem-based learning technology requires a lot of effort from the teacher. pedagogical excellence and a lot of time. Apparently, it is precisely these circumstances that do not allow the widespread use of problem-based learning. At the same time, problem-based learning meets the requirements of modernity: to teach by researching, to research by teaching. This is the only way to form creative personality, i.e., to realize the main task of pedagogical work.
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Questions
1. What are the main trends, varieties and features of modern areas of education?
2. What is the essence of the problem of the relationship between training and development, as well as approaches to its solution?
3. Can training ensure the full development of the personality, what is the essence of the provisions of the concept of L.S. Vygotsky?
4. What are the main provisions of the concept of developmental education by L.V. Zankov (lines and principles of development, distinctive features developmental learning)?
5. What is the peculiarity of building a teaching methodology in primary school according to L.V. Zankov (the structure of the lesson and textbooks, the logic of building a course of study)?
6. What are the features of the formation of educational activities according to the methodology of L. B. Elkonin-V. V. Davydov?
7. What are the scientific background and forms of programmed learning?
8. What is the essence of the algorithmization of learning and the theory of the gradual formation of mental actions by P. Ya. Galperin?
9. What goals and provisions underlie the concept of programming the educational process by N.F. Talyzina?
10. What is the peculiarity of the development of programmed manuals and training programs?
11. What are the essence and didactic characteristics of the organization of problem-based learning?
12. What is the peculiarity and meaning of creating problem situations in learning?
13. What is the characteristic of the levels of problem-based learning and its role in the educational process?

Problem learning is based on the acquisition by students of new knowledge by solving theoretical and practical problems, tasks in the problem situations created for this.

The well-known Polish scientist V. Okon writes in his book Fundamentals of Problem-Based Learning that the more students strive to get on the path followed by the researcher in the course of their work, the better the results achieved. Domestic psychologists T.V. Kudryavtsev, A.M. Matyushkin, Z.I. Kalmykova and others developed the psychological foundations of the so-called problematic education in its various modifications. Its essence is as follows. The students are given a problem, a cognitive task, and the students (with the direct participation of the teacher or on their own) explore ways and means of solving it. They build a hypothesis, outline and discuss ways to test its truth, argue, conduct experiments, observations, analyze their results, argue, prove. This includes, for example, tasks for the independent “discovery” of rules, laws, formulas, theorems (independent derivation of the law of physics, spelling rules, mathematical formula, discovery of a method for proving a geometric theorem, etc.).

Problem-based learning includes several stages:

1) awareness of the general problem situation;

2) its analysis, formulation of a specific problem;

3) problem solving (promotion, substantiation of hypotheses, their consistent testing);

4) checking the correctness of the solution to the problem.

This process unfolds by analogy with the three phases of the mental act that occurs in a problem situation and

includes awareness of the problem, its solution and the final conclusion. “Thinking,” notes A.V. Brushlinsky, “originates in a problem situation, which means that in the course of his activity a person begins to experience some incomprehensible difficulties that prevent successful progress ... Thus, the problem situation that has arisen turns into a conscious human task".

Therefore, problem-based learning is based on the analytical-synthetic activity of students, implemented in reasoning, reflection. This is a heuristic, exploratory type of learning with great developmental potential.

Distinctive characteristics of problem-based learning are shown in Table 10.

Table 10 Characteristics of informal and problem-based learning (according to V. Okon)

Informative learning

Problem learning

1. The material is given in finished form, the teacher pays attention primarily to the program 2. Gaps, barriers and difficulties arise in the oral presentation of the material or through the textbook, caused by the temporary exclusion of the student from the didactic process. 3. The pace of information transfer is focused on stronger, average or weak students 4. The control of school achievements is only partly related to the learning process; it is not an organic part of it 5. There is no way to provide all students with 100% results; the greatest difficulty is the application of information in practice

1. Students receive new information in the course of solving theoretical and practical problems 2. In the course of solving the problem, the student overcomes all difficulties, his activity and independence reach a high level here 3. The rate of communication depends on the student or group of students 4. Increased activity of students contributes to the development of positive motives and reduces the need for formal verification of results 5. Teaching outcomes are relatively high and sustainable. Students can more easily apply what they have learned to new situations and at the same time develop their skills and creativity.

The main concepts of problem-based learning include: “problem situation”, “problem task”, “problem”, “problem-ness” (“levels of problematicity”, “principles of problematicity” and DR-)> “problematization”.

Condition realization of the learning goal is problematic, inherent in any "viable" object and subject, which can exist in a hidden and expressed form, i.e. be internal and external.

way problematic is problematic situation fixing the moment of appropriation by the subject of the object containing the problem.

means creating a problem situation may be problem task, formalized in text data.

mechanism, revealing the problem is problem-ization object and subject, i.e. the process of revealing internal and external contradictions inherent in the object, problems.

unit process is problem - hidden or obvious contradiction inherent in things, phenomena of the material and ideal world.

Problematic - The main thing condition development of the object (the world) and the subject (man) - can be considered as a dialectical category, side by side with others, or as the main feature of these categories in development, or as the main principle of their action, activity, or as the need to act.

Problem situation- way revealing an objectively existing problem, expressed explicitly or implicitly, which manifests itself as a mental state of intellectual difficulty in the interaction of subject and object.

problem task- means creating a problem situation - has a shell, materialized in its formulation (oral or written), focused on the needs and capabilities of the subject.

Problematization is a mechanism underlying the discovery of the problematic nature of the object by the subject, materialized in this problematic task.

Problem- contradiction - a unit of the content and process of movement in the material and ideal space, generating the process of development of the world and man and generated by a developed person. This process is continuous.

According to V. Okon, "the essence of the process of learning by solving problems comes down in each case to creating a situation that forces the student to independently seek a solution" . According to V. Okon, the role of the teacher is to make the Student feel the difficulty of a practical or theoretical nature, to understand the problem posed by the teacher, or to formulate it himself, to want to solve the problem, to solve it.

What is the problem solving process? According to V. Okon, it depends on the nature of the problem and the complexity of its solution. “The nature of the problem is determined by the degree of its complexity. In addition to simple problems, there are those that, before starting to solve

it is necessary to divide into particular ones, and only the solution of the latter makes it possible to solve the main problem. The difficulty of solving the problem is twofold. One is that in order to make a decision, it is necessary to update some part of the previous experience, precisely that without which the decision is impossible. Another is the need to simultaneously find new elements (links) unknown to the student that allow solving the problem.

The didactic foundations of problem-based learning are determined by the content and essence of its concepts. According to M. I. Makhmutov, the main concepts of the theory of problem-based learning should be “educational problem”, “problem situation”, “hypothesis”, as well as “problem teaching”, “problem teaching”, “problematic content”, “mental search”, “problem question”, “problem statement”.

Learning problem- a subjective phenomenon and exists in the mind of the student in an ideal form, in thought. Task - an objective phenomenon, for the student it exists from the very beginning in a material form (in sounds or signs), and the task turns into a subjective phenomenon only after its perception and awareness. It is also important that the educational problem is the form of implementation of the principle of problem-ness in education.

M. I. Makhmutov offers a didactic classification of educational problems, which is based on the following variables: 1) area and place of origin; 2) role in the learning process; 3) social and political significance; 4) ways of organizing the decision process. The psychological classification of educational problems is based on such indicators as: 1) the nature of the unknown and caused difficulty; 2) solution method; 3) the nature of the content and the relationship between the known and the unknown in the problem.

Defining the problem situation, M. I. Makhmutov notes that it is the initial moment of thinking, causing the cognitive need of the student and creating internal conditions for the active assimilation of new knowledge and methods of activity. At the same time, two types of problem situations can be distinguished that arise in the formulation of both theoretical and practical problems.

The classification of ways to create problem situations is based on the nature of the contradiction that arises in the process of learning: “1. Collision of students with phenomena and facts that require theoretical explanation. 2. The use of educational and life situations that arise when students perform practical tasks. 3. Statement of educational problem tasks to explain the phenomenon or search for ways of its practical application. 4. Encouraging students to analyze facts and phenomena

reality, confronting them with contradictions between worldly ideas and scientific concepts about these facts. 5. Putting forward hypotheses, formulating conclusions and their experimental verification. 6. Encouragement of students to compare, compare and contrast facts, phenomena, rules, actions, as a result of which there is a cognitive difficulty. 7. Encouraging students to a preliminary generalization of new facts. 8. Familiarization of students with facts that seem to be inexplicable and have led in the history of science to the formulation of a scientific problem. 9. Organization of intersubject communications ".

M.I. Makhmutov distinguishes three types of problem-based learning according to the type of creative activity being implemented: 1) scientific creativity; 2) practical creativity; 3) artistic creativity. What underlies each type of learning and creativity? Scientific creativity is based on the formulation and solution of theoretical educational problems. Practical creativity is based on the formulation and solution of practical educational problems. Artistic creativity is "an artistic representation of reality based on creative imagination, including literary compositions, drawing, writing a piece of music, playing, etc." .

The main thing in problem-based learning is the creation problematic situation. Of course, not every question to which the student does not know the answer creates a genuine problem situation. Questions like: “What is the number of inhabitants in Moscow?”, “When was the Battle of Poltava?” or “Which city is the capital of Turkey?”, “What was Gogol’s name?” - are not problems from a psychological and didactic point of view, since the answer can be obtained from a reference book, an encyclopedia without any participation of the thought process. Not a problem and such a task that does not present difficulties for the student (for example, calculate the area of ​​a triangle, if he knows how to do it).

A learning task can cause mental activity under certain conditions. Psychologists see the source of student activity, in particular, in the contradictions between their experience (knowledge, skills) and the problems that arise in solving cognitive learning problems. This contradiction causes active mental activity. For example, a student must solve a particular cognitive problem, but: a) its conditions do not suggest a way to solve it, and b) the student’s past experience does not contain any ready-made solution scheme that could be applied in this case. The student is faced with the need to create a new solution scheme that is not available in his experience, a new system of methods of action.

A problem situation arises in a person if he has a cognitive need and intellectual capabilities to solve a problem in the presence of difficulty, a contradiction between the old and the new, the known and the unknown, the given and the desired, conditions and requirements. Problem situations are differentiated by A. M. Matyushkin according to the criteria: 1) the structure of actions that must be performed when solving a problem (for example, finding a method of action); 2) the level of development of these actions in the person solving the problem; 3) intellectual abilities of the student.

A. M. Matyushkin characterizes a problem situation as a special type of mental interaction between an object and a subject (student), characterized by such a mental state of the subject when solving problems that requires the discovery (discovery or assimilation) of new knowledge or methods of activity previously unknown to the subject. In other words, a problem situation is a situation in which the subject wants to solve problems that are difficult for him, but he does not have enough data, and he must look for them himself.

In the book “Problem situations in thinking and learning”, A. M. Matyushkin presents the following six rules for their creation.

1. In order to create a problematic situation, students should be given a practical or theoretical task, the implementation of which will require the discovery of new knowledge and the acquisition of new skills; here we can talk about a general pattern, a general mode of activity, or general conditions for the implementation of an activity.

2. The task must correspond to the intellectual capabilities of the student. The degree of difficulty of the problem task depends on the level of novelty of the teaching material and on the degree of its generalization.

3. The problematic task is given before the explanation of the material to be learned.

4. Problem tasks can be: a) assimilation, b) wording of the question, c) practical tasks. However, problem tasks and problem situations should not be confused with each other. A problem task can lead to a problem situation only if the above rules are taken into account.

5. The same problem situation can be caused by different types of tasks.

6. The teacher directs a very difficult problematic situation by indicating to the student the reasons for not fulfilling the practical task given to him or the impossibility of explaining certain facts to him.

Problem-based learning can be difficulty level for the student, depending on what and how many actions

actions for the formulation and solution of the problem he carries out himself. V. A. Krutetsky proposed a scheme of levels of problematic learning in comparison with the traditional one based on the separation of the actions of the teacher and the student (Table 11).

Table 11 Scheme of levels of problematic learning (according to V.A. Krutetsky)

	Number of links kept by the teacher	The number of links transmitted to the student	What does a teacher do 9	What does student 9 do
0 (traditional)			Sets a problem, formulates it, solves a problem	Remembers the solution to a problem
			Sets a problem, formulates it	Solves the problem
			Poses a problem	Formulates a problem, solves a problem
			Carries out general organization, control and skillful leadership	Realizes problem, formulates it, solves the problem

The scheme of levels of problem-heuristic learning proceeds from how many and what links are transferred by the teacher to the student. In the traditional form of teaching, the teacher himself formulates and solves the problem (deduces a formula, proves a theorem, etc.). The student must understand and remember someone else's thought, remember the formulation, the principle of decision, the course of reasoning.

There are four levels of difficulty in learning:

1. The teacher himself sets the problem (task) and solves it himself with active listening and discussion by students.

2. The teacher poses a problem, the students independently or under his guidance find a solution. The teacher directs the student to independent search for solutions (partial search method). Here there is a detachment from the sample, opens up space for reflection.

3. The student poses a problem, the teacher helps to solve it. The student develops the ability to independently formulate the problem.

4. The student himself poses the problem and solves it himself. The teacher does not even point out the problem: the student must see it on his own, and having seen it, formulate and explore the possibilities and ways to solve it.

As a result, the ability to independently see the problem, independently analyze the problem situation, and independently find the correct answer is brought up.

The third and fourth levels are the research method.

If the teacher feels that students are having difficulty completing a particular task, then he can introduce additional information, thereby reducing the degree of problematicness and transfer students to a lower level of problem-heuristic learning.

In problem-based learning, the teacher is like an experienced conductor organizing this exploratory search. In one case, the teacher himself, with the help of the students, can conduct this search. Having posed a problem, he reveals the way to solve it, argues with the students, makes assumptions, discusses them with the students, refutes objections, proves the truth. In other words, the teacher demonstrates to students the path of scientific thinking, makes students follow the dialectical movement of thought towards the truth, makes them, as it were, accomplices in scientific search.

In another case, the role of the teacher may be minimal - he provides students with the opportunity to independently seek ways to solve problems. But even here the teacher does not take a passive position, but, if necessary, imperceptibly directs the students' thoughts in order to avoid fruitless attempts, unnecessary loss of time. That is why the teaching method associated with the independent search and discoveries of certain truths by schoolchildren is called problem-heuristic, or research, method.

Thus, under the conditions of problem-based learning, the development of activity in the mental activity of students can be characterized as a transition from actions stimulated by the teacher's tasks to independent formulation of questions; from actions related to the choice of already known ways and methods, to independent searches for solving problems, and further - to developing the ability to independently see problems and explore them.

The research method cultivated in problem-based learning is such an organization of educational work in which students get acquainted with scientific methods of obtaining knowledge and, mastering the elements of scientific methods available to them, master the ability to independently obtain new knowledge, plan a search and discover a new dependence or pattern for themselves.

In the learning process, it is important to gradually transfer students to a higher level of problem-heuristics.

academic training. Of course (and this is important to emphasize), the ability to see, formulate and solve a problem does not develop spontaneously, as a spontaneous development of initially laid down tendencies. This is the result of learning. The teacher teaches independent formulation and problem solving, independent thinking develops with the decisive and leading role of the teacher. It is wrong to assume, as D. Dewey did, that the inborn and uncorrupted state of childhood, distinguished by love for experimental research, is very close to scientific thinking.

Among the modern developments of forms of problem-based learning, the experience of its implementation in the methodology and practice of teaching foreign languages ​​deserves attention. One of the latest original "versions" of such a didactic construction is the development of E. V. Kovalevskaya. In her study, devoted to teaching speaking in a foreign language, the task was to form ways to create problem situations at the communicative level. During the experiment, it was found that problem situations for teaching speaking should be based on the inclusion of obstacles to achieving the goal and varying the number of unknown components (place, time, participants in communication), which determines the degree of complexity of the problem situation and the variability of solutions. For example: “You need to be at the institute on time, but you can’t leave because you are waiting for an important phone call...” This situation is problematic because it contains an obstacle to achieving the goal, as well as unknown components (time and communication participants).

Thus, during the experiment, the expediency of introducing stepwise problem situations, which contribute to the stimulation of speech through a series of successively occurring obstacles to achieving the goal. The development of creative activity of students was ensured by involving them in the process of setting and solving problems, individualization of learning based on the choice of problems in accordance with the cognitive and communicative needs and capabilities of each student.

E. V. Kovalevskaya developed “step-by-step” situations in which the goal of the simulated action is complicated not by one, but by a chain of obstacles built in a certain logical sequence. For example: “You need to be at the institute on time, but: 1. You can’t leave because you are waiting for an important phone call ... 2. You ask your neighbor to take you to work, but he refuses because ... 3. You you are traveling by bus, but you don’t have time to get a ticket, the controller enters ... 4. The bus leaves, you stop a taxi, but a person appears who is late for the plane ... 5. You stop the car, but on the way the driver

breaks the rules of the road... 6. You arrive at the institute, but you do not have a wallet (money) to pay for the fare... 7. You manage to pay the fare, but you are late for the lecture... etc.” . Based on the stepwise situations presented orally in a foreign language, the teacher maintains communication, offering more and more new problems to solve.

Further, E.V. Kovalevskaya considers one of the central issues of problem-based learning - the issue of "appropriation" of objective problem situations, provided they correspond to the cognitive and communicative needs and abilities of students and if they are accepted by the teacher.

The appropriation process can be optimized based on the formation of students' skills to resolve problem situations and the skills of teachers to manage this process. The search skills of students and teachers were based on the stages of solving the problem. Students' skills to resolve problem situations include: 1) the ability to see problems and put them on their own; 2) the ability to create a solution hypothesis, evaluate it, moving on to a new one in case the original one is unproductive; 3) the ability to direct and change the course of the decision in accordance with their interests; 4) the ability to evaluate one's own decision and the decisions of interlocutors. The skills of teachers to manage the process of resolving problem situations are as follows: 1) the ability to anticipate possible problems on the way to achieving the goal in a problem situation; 2) the ability to instantly reformulate a problem situation, facilitating or complicating it on the basis of regulating the number of unknown components; 3) the ability to choose problem situations in accordance with the train of thought of those who solve the problem; 4) the ability to impartially assess the options for students' decisions, even if the points of view of students and teachers do not coincide.

By analogy with the levels of problematicness for a student, E.V. Kovalevskaya builds levels of problematicity for a teacher: first level, the teacher acquires methodological knowledge in the process of reasoning presentation of the main provisions and concepts of problem-based learning in relation to a foreign language; on second level, the teacher uses problem situations from the textbook in his work; on third level independently thinks through possible problem situations during preparation for the lesson, and also creates them in the lesson; on fourth level becomes the author of a new textbook, methodology, scientific research. In the process of creativity, the teacher becomes the author of his script (textbook), the director of his own performance (lesson), the creator of a new theater (scientific direction). The foregoing made it possible to show the multilevel nature of the problematic idea, its development in space and time.

In conclusion, it is necessary to dwell on the place and role of problem-based learning in the system of a holistic educational process.

According to I.Ya. Lerner, problem-based learning should be carried out only when studying part of the educational material, which allows creative processing of information obtained both in problem-based and non-problem learning.

What are the functions of problem-based learning? There are three of them: 1) the development of creative potentials and the formation of structures of creative activity; 2) creative assimilation of knowledge and methods of activity; 3) creative mastery of the methods of modern science.

At the same time, as I.Ya. Lerner notes, only a few students can see problem situations. In order for the majority of students to see and solve problems, a system of problem situations, problems and problem tasks is needed, included in the fabric of the content of education and the learning process. Indicators of the system of problematic tasks should be the following characteristics: 1) coverage of various features of creative activity; 2) the presence of various degrees of complexity. As for the content of the educational material on which the system of problems should be built, it is subject to the main content principle of the system of problem tasks, based on the identification of “cross-cutting” or “aspect” problems in various fields of science.

According to M. I. Makhmutov, problem-based learning cannot replace all learning, but without the principle of problematic learning, learning cannot be developing. “The problematic type of education,” the author writes, “does not solve all educational and upbringing tasks, therefore it cannot replace the entire education system, which includes different types, methods and forms of organizing the educational process. But also the general system of education cannot be truly developing without problem-based learning, the basis of which is a system of problem situations.

Of course, the problematic method cannot be turned into a universal teaching method. As V. A. Krutetsky noted, “... for some students who do not yet possess the skills of independent thinking, it is somewhat difficult (although other students can be very successful in it: in our experiments, for example, the most capable ones “discovered” for themselves almost entire course of geometry). Yes, and it requires more time than the traditional information-reporting presentation. But the latter circumstance should not be exaggerated. The loss of time at the first stages of the introduction of the problematic method is compensated later, when the student's independent thinking develops sufficiently.

The benefits of problem-based learning are clear. First of all, these are great opportunities for developing attention, observing

activity, activation of thinking, activation of cognitive activity of students; it develops independence, responsibility, criticality and self-criticism, initiative, non-standard thinking, caution and determination, etc. In addition, which is very important, problem-based learning ensures the strength of the acquired knowledge, because they are obtained in independent activity.

Problem-based learning has a number of advantages compared to traditional learning, since: 1) it teaches you to think logically, scientifically, dialectically, creatively; 2) makes the educational material more evidence-based, thereby contributing to the transformation of knowledge into beliefs; 3) as a rule, it evokes deep intellectual feelings more emotionally, including a feeling of joyful satisfaction, a sense of confidence in one’s abilities and strengths, therefore it captivates schoolchildren, forms a serious interest of students in scientific knowledge; 4) it has been established that independently “discovered” truths, patterns are not so easily forgotten, and in case of forgetting, independently acquired knowledge can be restored faster.

Problem-based learning is associated with research and therefore involves a solution of a problem extended in time. The student finds himself in a situation similar to that in which there is an agent who solves a creative task or problem. He constantly thinks about it and does not get out of this state until he solves it. It is due to this incompleteness that solid knowledge, skills and abilities are formed.

The disadvantages of problem-based learning include the fact that it always causes difficulty for the student in the learning process, so it takes much more time to comprehend and find solutions than with traditional learning. In addition, as with programmed learning, the development of problem-based learning technology requires a teacher of great pedagogical skill and a lot of time. Apparently, it is precisely these circumstances that do not allow the widespread use of problem-based learning. At the same time, problem-based learning meets the requirements of modernity: to teach by researching, to research by teaching. This is the only way to form a creative personality, that is, to realize the main task of pedagogical work.

Literature

1. Antsiferova L. I. The principle of connection between consciousness and activity and the methodology of psychology // Methodological and theoretical problems of psychology. - M., 1969.

2. Arginskaya I. I., Dmitrieva N. Ya., Polyakova A. V., Romanovskaya 3.fleetothers We train according to the system of L.V. Zankov. - M., 1991.

3. Bruner J. Psychology of knowledge. - M., 1977.

4. Brushlinsky A.V. Psychology of thinking and problem learning. - M., 1983.

5. Age-related opportunities for learning / Ed. D. B. Elkonin, V. V. Davydova. - M., 1966.

6. Questions of algorithmization and programming of learning / Ed. L. N. Landy. - M., 1973. - Issue. 2.

7. Vygotsky L.S. Questions of theory and history of psychology // Sobr. cit.: In 6 volumes - M., 1982.-T. 2.

8. Vygotsky L.S. Child psychology // Sobr. cit.: In 6 vols. - M., 1984. - T. 4.

9. Vygotsky L.S. Problems of general psychology // Sobr. cit.: In 6 volumes - M., 1982.-T. 2.

10. Vygotsky L.S. Problems of the development of the psyche // Sobr. cit.: In 6 volumes - M., 1983.-T. 3.

11. Galperin P. Ya. To the study of the intellectual development of the child // Questions of psychology. - 1969. - No. 1.

12. Galperin P. Ya. The main results of the study on the problem of "Formation of mental actions and concepts." - M., 1965.

13. Galperin P. Ya. Development of research on the formation of mental actions // Practical Science in the USSR: In 2 volumes - M., 1959. - V. 1.

14. Davydov V.V. Principles of teaching in the school of the future. - M., 1974.

15. Davydov V.V. Problems of developing education. - M., 1986.

16. Davydov V. V., Zinchenko V. P. To the 90th anniversary of the birth of L. S. Vygotsky // Soviet Pedagogy. - 1986. - No. 11. - S. 111 - 114.

17. Order. The development of theoretical thinking in younger students. - M., 1984.

18. Zankov L.V. Didactics and life. - M., 1968.

19. Zankov L.V. Selected pedagogical works. - M., 1990.

20. Zankov L.V. Education and development. - M., 1975.

21. Zimnyaya I. A. Pedagogical psychology: Textbook for universities. - M., 1999.

22. Ilyenkov E. V. Dialectical Logic: Essays on History and Theory. - M., 1974.

23. Ilyina T. A. Theory and practice of programmed learning // Soviet Pedagogy. - 1964. - No. 7. - S. 61 -66.

24. Kovalevskaya E.V. Problem-based learning: Approach, method, type, system (on the basis of teaching foreign languages): In 2 books. - M., 2000.

25. Krutetsky V. A. Fundamentals of educational psychology. - M., 1972.

26. Landa L. N. Algorithmization in teaching. - M., 1966.

27. Leontiev A.N. Selected psychological works: In 2 volumes - M., 1983.-T. 2.

28. Lerner I. Ya. Problem learning. - M., 1974.

29. Matyushkin A. M. Problem situations in thinking and learning. - M., 1972.

30. Makhmutov M. I, Problem-Based Learning: Basic Issues of Theory. - M., 1975.

31. window V. Introduction to general didactics: Per. from Polish. - M., 1990.

32. window V. Fundamentals of problem-based learning: Per. from Polish. - M., 1968.

33. Piaget J. Selected psychological works. - M., 1969.

34. The development of younger students in the process of learning: Experimental and pedagogical research / Ed. M. V. Zvereva. - M., 1983.

35. The development of students in the learning process / Ed. L. V. Zankova. - M., 1963.

36. Rubinstein S. L. Fundamentals of General Psychology: In 2 vols. - M, 1989. - Vol. 1.

37. Talyzina N. F. Pedagogical psychology. - M., 1998.

38. Talyzina N. F. Theoretical problems of programmed learning. - M., 1969.

39. Chuprikova N. I. Mental development and learning: Psychological foundations of developmental learning. - M., 1996.

40. Shiyanov E.N., Kotova I.B. Development of personality in learning. - M., 1999.

41. Elkonin D.B. Psychological issues of the formation of educational activity in primary school age // Reader on age and pedagogical psychology / Ed. I.I.Ilyasova, V.Ya.Lyau-dis. - M., 1989.

42. Elkonin D.B. Psychology of teaching younger students. - M., 1974.

1. What are the main trends, varieties and features of modern areas of education?

2. What is the essence of the problem of the relationship between training and development, as well as approaches to its solution?

3. Can training ensure the full development of the personality, what is the essence of the provisions of the concept of L.S. Vygotsky?

4. What are the main provisions of the concept of developmental education by L.V. Zankov (lines and principles of development, distinctive features of developmental education)?

5. What is the peculiarity of building teaching methods in primary school according to L.V. Zankov (the structure of the lesson and textbooks, the logic of building a course of study)?

6. What are the features of the formation of educational activities according to the methodology of L. B. Elkonin-V. V. Davydov?

7. What are the scientific background and forms of programmed learning?

8. What is the essence of the algorithmization of learning and the theory of the gradual formation of mental actions by P. Ya. Galperin?

9. What goals and provisions underlie the concept of programming the educational process by N.F. Talyzina?

10. What is the peculiarity of the development of programmed manuals and training programs?

11. What are the essence and didactic characteristics of the organization of problem-based learning?

12. What is the peculiarity and meaning of creating problem situations in learning?

13. What is the characteristic of the levels of problem-based learning and its role in the educational process?

A country:

Citizenship = USSR, Russia

Scientific area: Place of work:

Institute of Theory and History of Pedagogy of the Russian Academy of Education

Academic degree:

doctor of pedagogical sciences

Academic title: Known as:

outstanding teacher

Lerner Isaak Yakovlevich(April 4 - March 1) - Soviet teacher.

Biography

AND I. Lerner lost his parents due to pogroms in civil war. In 1939 he graduated from the history department of Moscow State University. Since 1937, he taught at various universities of the RSFSR, was an assistant professor, head of the department. Member of the Great Patriotic War. He was repressed under Article 58.10 in 1950 and spent five years in the Ivdel general regime camp. He was accused of making two statements in a conversation with a friend - about the undemocratic nature of the elections and about the need to establish a minimum wage for collective farmers for a workday. Since 1959 he has been working at the APN of the USSR. Doctor of Pedagogical Sciences, Professor. Corresponding member of the APN of the USSR since December 20, 1990, full member of the Russian Academy of Education since June 15, 1992. He was a member of the Department of Philosophy of Education and Theoretical Pedagogy. Honored Scientist of the RSFSR (1987). From 1985 to 1991, he led the development of the theory of construction of a modern school textbook. Son Georgy Isaakovich Lerner is the successor of the educational traditions of his father, Ph.D., head. Biology Laboratory of the Moscow Institute of Open Education. I.Ya. died. Lerner was buried in 1996 at the Vostryakovsky cemetery.

Contribution to the development of pedagogy

AND I. Lerner is one of the developers of problem-based learning. He revealed the didactic foundations and developed a system of teaching methods. He revealed the connection between teaching methods, organizational forms, means and methods of teaching. Substantiated the composition and structure of the content of education, adequate to social experience. Developed a holistic concept of the educational process as a system.

Classification of teaching methods

1. Information receptive method. The activities of the teacher. Presentation of information (by a teacher or a substitute means). Organization of student actions with the object of study. Student activity. Perception of knowledge. Awareness of knowledge. Memorization (mostly arbitrary).
2. reproductive method. The activities of the teacher. Drawing up and presenting a task for the reproduction of knowledge and methods of mental and practical activity. Management and control over implementation. Student activity. Knowledge update. Reproduction of knowledge and methods of action based on samples shown by others (teacher, book, TCO). Arbitrary and involuntary memorization (depending on the nature of the task)
3. Problem presentation method. The activities of the teacher. Statement of the problem and disclosure of an evidence-based way to solve it. Student activities. Perception of knowledge. Awareness of knowledge and problems. Attention to consistency and control over the degree of persuasiveness of the solution to the problem. Mental forecasting of the next steps of the decision logic. Memory (largely involuntary)
4. heuristic method. The activities of the teacher. Statement of problems. Compilation and presentation of assignments for the implementation of individual stages, the solution of cognitive and practical problematic tasks. Planning the steps of the solution. Management of students' activities (adjustment and creation of problem situations). Student activities. Perception of a task that is part of a task. Understanding the conditions of the problem. Updating knowledge about ways to solve similar problems. Independent solution of a part of the problem. Self-control in the process of solving and checking its results. The predominance of involuntary memorization of the material associated with the task. Reproduction of the course of the solution and its independent.
5. research method. The activities of the teacher. Compilation and presentation of problematic tasks for finding solutions. Control over the course of the decision. Student activities. Perception of the problem or self-discretion of the problem. Understanding the conditions of the problem. Planning stages of research (solution). Planning research methods at each stage. Self-control in the process of research and its completion. Predominance of involuntary memorization. Reproduction of the course of the study, motivation of its results.

Proceedings

• Lerner I.Ya. The content and methods of teaching history in the V - VI classes of the evening (shift) school. - M., 1963;
• Lerner I.Ya. Problem learning. - M., 1974.
• Lerner I.Ya. The learning process and its patterns. - M., 1980.
• Lerner I.Ya. Didactic foundations of teaching methods. –M., 1981.
• Lerner I.Ya. The human factor and the functions of the content of education // Soviet Pedagogy. - 1987. - No. 11
• Lerner I.Ya. Theory of the modern learning process, its significance for practice // Soviet Pedagogy.- 1989.- No. 11
• Lerner I.Ya. Pedagogical notes from behind bars // Soviet Pedagogy.- 1990.- No. 12
• Lerner I.Ya. Painful points of the learning process // Soviet Pedagogy.- 1991.- No. 5.
• Lerner I.Ya. Developing education from didactic positions // Pedagogy.- 1996.- No. 2
• Didactics high school/ Ed. M. N. Skatkina, I. Ya. Lerner. - M., 1975.
• Theoretical foundations of the learning process in the Soviet school / Ed. V. V. Kraevsky, I. Ya. Lerner. - M., 1989.

Notes

Links

• International scientific-practical conference "Classical didactics and modern education", dedicated to the 90th anniversary of the birth of I.Ya.Lerner. Moscow, April 9-10, 2007
• Video by I.Ya.Lerner about creative thinking
• Video by I.Ya.Lerner about school reforms

Categories:

• Personalities in alphabetical order
• Scientists alphabetically
• April 4
• Born in 1917
• Deceased March 1
• Deceased in 1996
• Deceased in Moscow
• USSR teachers
• Repressed in the USSR

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