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, this topic was chosen for research in the course work.

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 content and sources educational problems ny situations in the lesson of mathematics.

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 learning and the development of students' cognitive abilities.

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 Foundations of Problem-Based 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 the psychological mechanisms of the 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 educational material and the dominant role of intuitive thinking in the process of assimilation of 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 the basis for the development of 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 the natural sciences and humanities.

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, the 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 formation of the theory of problem learning were the works of domestic psychologists who developed the position that mental development characterized not only by the volume and quality of acquired knowledge, but also by the structure of thought processes, the system logical operations and mental actions (S.L. Rubinstein, 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 spreading, problem-based learning penetrated from the general education school to the secondary and higher vocational schools.

1.2 Signs of problem learning

The development of creative cognitive activity of students is largely facilitated by problem-based learning. 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 does not contain anything new in comparison with modern teaching practice. 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 skills developed with an unknown fact or phenomenon, he discovers 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 the lessons of literature presents the students with an artistic detail of the work, 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 terms. 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 the questions that he will answer, but, having created a problematic situation, he interested the audience in a common problem: what kind of mystery lies in this hidden life that 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 of the 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 of 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 cognitive independence of students, the stability of learning motives and mental (including creative) abilities in the course of mastering scientific concepts and methods of activity determined by the 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 the optimal combination of their independent activities 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 psychological foundations 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 a problem - a hidden or obvious contradiction inherent in the phenomena of 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 student's cognitive need and creating internal conditions for the 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 educational and life situations that arise when students perform practical tasks.

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 in nature and are given in the history of science to the formulation of a 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 of the student in independently mastering 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, connection with life serves as the most important means of creating problem situations and (directly or indirectly) a criterion for assessing the correctness of solving educational problems.

The fourth feature of problem-based learning is the teacher's systematic use of the most effective combination of various types and types of students' independent work. 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 of an individual approach. In problem-based learning, individualization is due to the presence of educational 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, there is no dynamism in traditional education; 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 of 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 generates different levels of both the intellectual difficulties of the trainees and their cognitive activity: the cognitive independence of the trainee can be either very high or almost completely absent. In this regard, attempts to single out the types and levels of problem-based learning are quite understandable. The types of problem-based learning are most correctly distinguished according to the existing types of 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 - search practical solution, that is, a method of applying 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 laboratory, practical classes, in a subject circle, in an elective course, in 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 the 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. In order to create a problem situation, the teacher most often only changes the order of the reported facts, demonstrations, experiments, showing visual aids and, as additional content elements, uses interesting facts from the history of the development of the concept under study or facts that tell about the practical application of 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 the didactic principles of 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 he has chosen 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 methodological system problems and problematic tasks, adapts it to a specific situation of the educational process, presents it to students, thereby managing their educational 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 creatively master 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 students learn all the educational material only through independent solution problems and the discovery of 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 the problem learning it tension is especially great and pronounced. The intensity of the internal tension of the 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 a 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.

A feature of the subject of the cognitive process, its 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: enters the necessary information, manages the value organization, determines the degree of freedom of choice, directs them to find adequate ways 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 the 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) designs the pedagogical management of the solution of the educational topic on the part of students, for which he develops a methodology for managing educational activities, composes instructional assignments;

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 students' independent work are included in the study of a new scientific question, a 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 drawn on different stages 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, learning activities are carried out in the form of educational 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 particular 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 recent years, the problem of formation creative qualities The individual was at the center of the vital demands 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 learning 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, it is of great importance past experience, transferring existing knowledge to new conditions, ways of understanding the unknown from the perspective of the already known, processing already familiar information in order to apply it for a practical solution, assessing the situation and one's capabilities. 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 necessary when the task is set of special training of 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 an object and a subject, characterized by such a mental state of the subject (student) in 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 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 the sides of the new trapezoid; they know one base, and find the length of the second, which is middle line, cannot (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 - to find examples of the use of a truncated pyramid in the surrounding life 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 the required amount building materials, that is, indicates the practical significance of 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 the 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 an educational and experimental area, in a workshop, laboratory or classroom, as well as in the lessons of 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 comparison reveals the special properties of new facts, their inexplicable features.

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 the material of the subject does not provide 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 a general pattern, a general mode of activity, or general conditions 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 various types assignments.

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 one of the important rules about triangles was violated in this task."

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 students do not understand the meaning of the problem, further work useless over her. 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 modern lesson Based on the principle of problematicness, they 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.

structural elements 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 the problems of teaching individual subjects. This is especially true for the problems of pedagogy of mathematics.

It is in the lessons of mathematics that a favorable atmosphere develops for the introduction of elements of problem-based learning, since problematic way it is advisable to study such material 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 of the main task, selection, reproduction of known theoretical positions that can be used in the indicated direction of solving the problem, comparative assessment of the direction of the solution and the choice of one of them, development of a plan for solving the problem in the chosen direction and its implementation as a whole, detailed implementation of the plan for solving the problem and substantiation of correctness all steps of the emerging solution of the problem).

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

6. Application of new knowledge by solving specially selected learning tasks 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 of 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 the 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 is quite difficult to logically connect everything, therefore, from the moment this concept appeared 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.

Problem posing does not always lead to a problem situation. Problems are not interesting for a student if they are not related to his life, if they are of a general nature. A problematic situation does not arise even when the student has too low a level of 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 many options as possible to solve 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 a traditional school, and becomes the one who wakes up, develops, observes the mental operations of students, corrects mistakes, and 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 the help of skillfully 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 an effective way of actively acquiring knowledge, 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.

Skillful combination of group and individual form classes provides a comprehensive development of activity and independence in the learning of all students, provides an opportunity 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 characteristics 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.	Instructions: refer 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 consolidation: the teacher gives more complex tasks to consolidate a new topic.	Reflection - determination of the degree of assimilation.
Stage number 6	Summing up the lesson

Problem learning

The concept of problem-based learning has become widespread, however, there are several approaches to its interpretation.

Problem-based learning is a set of such actions as organizing problem situations, formulating problems, providing students with the necessary assistance in solving problems, checking these solutions, and, finally, managing the process of systematizing and consolidating acquired knowledge (V. Okon, 1975).

Problem-based learning is a type of developmental learning, the content of which is represented by a system of problematic tasks of various levels of complexity, in the process of solving which students acquire new knowledge and methods of action, and through this, creative abilities are formed: productive thinking, imagination, cognitive motivation, intellectual emotions.

Problem-based learning is such an organization of training sessions that involves the creation of problem situations under the guidance of a teacher and the active independent activity of students to resolve them, as a result of which there is a creative mastery of professional knowledge, skills and abilities and the development of mental abilities (G. K. Selevko, 1998).

Problem-based learning is a method of active interaction of the subject with the problem-represented content of learning, organized by the teacher, during which he is attached to the objective contradictions of scientific knowledge and ways to solve them. Learns to think, creatively acquire knowledge.

History of occurrence

Thinking is necessary for a person, first of all, in order to more deeply reflect the continuously changing conditions of life and activity. By virtue of their constant variability, these conditions inevitably turn out to be new, and everything new is necessarily unknown at first. Thus, in the process of searching for and discovering an essentially new person, he deals with the unknown. This determines the main task and at the same time the main difficulty of any thinking. How is it possible to know the unknown if we don't know anything about it yet? Already the philosophers of ancient Greece were seriously aware of this initial and universal difficulty of mental activity. They expressed it in the form of the following paradox of thought: if I (already) know thatOI'm looking for, what else should I look for; What if I (yet) don't know whatOI'm looking, how can I search? Such a paradox partly correctly expresses the most important contradiction of all thinking - the contradiction between the initial and final stages of the thought process. As one of the main mental realities in the study of creative processes of thinking was discoveredproblem situation, which, as psychologists note, is the initial moment of thinking, the source of creative thinking]. It is the problem situation that helps to evoke a certain cognitive need in students, to give the necessary direction to their thoughts, and thereby create internal conditions for the assimilation of new material.

Problem-based learning is based on the theoretical principles of the American philosopher, psychologist and educator J. Dewey, who founded an experimental school in Chicago in 1894, in which the curriculum was replaced by a game and labor activity]. Classes in reading, counting, writing were carried out only in connection with the needs - instincts that arose spontaneously in children, as they matured physiologically. Problem-based learning technology became widespread in the 20-30s in the Soviet and foreign school. The emergence of a didactic system of problem-based learning in Soviet pedagogy is associated with the research of L.V. Zankova (organization of content and construction of the learning process), M.A. Danilova (construction of the learning process), M.N. Skatkina, I.Ya. Lerner (content and teaching methods), N.A. Menchinskaya and E.N. Kabanova-Meller (building a system of methods of cognitive activity), T.V. Kudryavtsev and A.M. Matyushkin (construction of the learning process), V.V. Davydov and D. Bruner (organization of content) and M.I. Makhmutov (construction of the learning process).

Having put forward the idea of ​​a new didactic system, L.V. Zankov presented it as a combination of new didactic principles, built taking into account the laws of correlation between education and development of (younger) schoolchildren, experimentally proved the advantage of the new scheme of the educational process over the traditional one. The new didactic system was further developed in the studies of V. V. Davydov, who substantiated the need to have a new structure of the content of educational material, built on the basis of a combination of modern formal logic with dialectical logic. Having experimentally proved the possibility of forming theoretical thinking in younger schoolchildren, V. V. Davydov formulated a number of principles for constructing educational subjects and revealed the dialectical connection between the content and teaching methods.

Problem learning- this is the modern level of development of didactics and advanced pedagogical practice. It arose as a result of the achievements 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 name itself is connected not so much with the etymology of the word as with the essence of the concept. Training is called problematic because the organization of the educational process is based on the principle of problematicity, and the systematic solution of educational problems is a characteristic feature of this type of training. Since the whole system of methods is aimed at the comprehensive development of the student, his cognitive needs, and the formation of an intellectually active personality, problem-based learning is truly developing learning. Based on a generalization of practice and analysis of the results of theoretical studies, the following definition of the concept of "problem learning" can be given:Problem learning- this is a type of developmental education, which combines independent systematic search activity of students with the assimilation of 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 the worldview of students, their cognitive independence, stable motives for learning and mental (including creative) abilities in the course of mastering scientific concepts and methods of activity, determined by a system of problem situations.

The problem situation primarily characterizes a certain psychological state of the student that occurs in the process of performing such a task, which requires the discovery (assimilation) of new knowledge about the subject, methods or conditions for performing the task. The main element of the problem situation is the unknown, the new, something that should be open to correct execution tasks to perform the desired action.

Problem-based learning is the leading element modern system developmental education, including the content of training courses, different types of education and ways of organizing the educational process at school.

Problem-based learning is characterized by a system of not any methods, namely, methods built taking into account goal-setting and the principle of problematicity. "Problem situation" and "learning problem" are the basic concepts of problem-based learning, which is seen not as a mechanical addition of teaching and learning activities, but as a dialectical interaction and interconnection of these two activities, each of which has its own functional structure. A significant shortcoming in modern practice and theory of problem-based learning is considered to be a limited understanding of the problem statement.

The impact on the emotional-sensory sphere of students creates conditions conducive to active mental activity. In the traditional type of education, the activation of educational activity was largely achieved precisely by increasing the interest of students, arousing their desire, etc. Without underestimating the importance of such motivation, it must be emphasized that it is the problem that is the root cause of active thinking, its immediate stimulus that determines the highest level mental activity. Emotionality and how to create it are an integral element of problem-based learning, but by no means its equivalent.

Features of the technique

Problem-based learning was based on the ideas of an American psychologist, philosopher and teacher (1859-1952), who in 1894 founded an experimental school in which the basis of learning was not the curriculum, but games and work. Methods, techniques, new teaching principles used in this school were not theoretically substantiated and formulated in the form of a concept, but became widespread in the 20-30s of the twentieth century. In they were also used and even considered as revolutionary, but in 1932 they were declared a scheme and banned. The following took an active part in the development of the fundamental provisions of the concept of problem-based learning:, and others. The scheme of problem-based learning is presented as a sequence of procedures, including: setting a learning-problem task by the teacher, creating a problem situation for students; awareness, acceptance and resolution of the problem that has arisen, in the process of which they master generalized ways of acquiring new knowledge; application of these methods for solving specific systems of problems. The theory proclaims the thesis about the need to stimulate the student's creative activity and assist him in the process of research activity and determines the ways of implementation through the formation and presentation of educational material in a special way. The basis of the theory is the idea of ​​using the creative activity of students by setting problem-formulated tasks and activating, due to this, their cognitive interest and, ultimately, all cognitive activity.

Basic psychological conditions for the successful application of problem-based learning

Problem situations should meet the goals of forming a knowledge system.

Be accessible to and relevant to students cognitive abilities.

Must cause their own cognitive activity and activity.

Tasks should be such that the student could not complete them based on existing knowledge, but sufficient for independent analysis of the problem and finding the unknown.

Human life constantly poses acute and urgent tasks and problems. The emergence of such problems, difficulties, means that in the reality around us there is still a lot of unknown, hidden. Therefore, we need an ever deeper knowledge of the world, the discovery in it of more and more new processes, properties and relationships between people and things. Therefore, no matter what new trends, born by the demands of the time, penetrate the school, no matter how programs and textbooks change, the formation of a culture of intellectual activity of students has always been and remains one of the main general educational and educational tasks. The success of the intellectual development of the student is achieved mainly in the classroom, when the teacher is left alone with his pupils. And the degree of students' interest in learning, the level of knowledge, readiness for constant self-education, i.e. their intellectual development, which convincingly proves modern psychology and pedagogy.

Most scientists admit that the development of schoolchildren's creative abilities and intellectual skills is impossible without problem-based learning. N. A. Menchinskaya, P. Ya. Galperin, N. F. Talyzina, T. V. Kudryavtsev, Yu. K. Babansky, I. Ya. Lerner, M. I. Makhmutov, A. M. Matyushkin, I. S. Yakimanskaya, etc.

Theoretical provisions and examples of the essence of problem-based learning and its structure should be associated with such an important category of didactics as teaching methods. The method is a means of implementing the theory of learning in everyday practice, the main tool in the technology of the learning process. In the history of philosophy, "method" is a means scientific research(F. Engels), the mode of activity (J. Mill), the rules of how to act (I. Kant) and the form of movement of content (G.-W. F. Hegel).

The didactic system includes the following principles for organizing educational material and building the process of problem-based learning:

1) to organize the main part of the educational material from the general to the particular, from the principle to the application in the order of the logical deployment of the initial concepts into the system of concepts of this science;

2) start learning with updating by creating a problem situation by introducing new information;

3) to introduce new concepts and principles both through the activity of students in solving educational problems, and through explaining their essence;

4) to achieve the assimilation of concepts and methods of mental activity by applying the corresponding sign systems(words, formulas, statements, diagrams) and images through the analysis of information, the solution of educational problems and the classification of specific objects;

5) to form in students a system of techniques and methods of mental activity for various types of problem situations;

6) provide the student with current information about the results of his own actions, necessary for assessment and self-assessment;

7) provide the student with the necessary sources of information and manage the course of its analysis, systematization and generalization (extraction of new knowledge and methods of activity from it). The nature of the presentation of educational material by the teacher depends on the internal conditions, which are the level of problematic learning and the level of effectiveness of teaching.

Problem situation - the main link of problem-based learning

A problem situation is the central link in problem-based learning, with the help of which a thought, a cognitive need are awakened, thinking is activated, conditions are created for the formation of correct generalizations. The creation of problem situations that determine the initial moment of thinking is a necessary condition for organizing the learning process that contributes to the development of genuine productive thinking in children, their creative abilities.

“In order to create a problematic situation in learning,” notes A.M. Matyushkin, - you need to put the child in front of the need to complete such a task, in which the knowledge to be learned will take the place of the unknown. Let's bring the simplest example(from the experiments of A.M. Matyushkin). Younger students who do not yet know that the sum of the interior angles of a triangle is 180?, but who already know how to build angles of a given size on the drawing, are given tasks to build triangles with angles of strictly defined sizes. First, the teacher selects such values ​​so that they add up to 180?, and in this case, the students successfully complete the tasks. However, then the teacher specifically suggests such angles, the sum of which is greater or less than 180?. Now - unexpectedly for schoolchildren - all their attempts to build given triangles end in failure. So, in the course of their activities, a problematic situation naturally arises, which means that they have come across an obvious, but so far incomprehensible obstacle that hinders their further actions. This obvious problematic situation for students contains a pronounced contradiction between the desire and the inability to continue the previous actions. Thus, it constitutes the necessary initial conditions for thinking: it naturally induces to resolve the contradiction that has arisen, i.e. first of all, to comprehend the reasons for the failures that have begun in the implementation of certain activities. The strongest motivation for thinking is formed precisely in a problem situation. As a result, a person has a desire (motive) to find out, find out, understand the real causes of the difficulties that he unexpectedly encountered. The very fact of encountering a difficulty, the impossibility of completing the proposed task with the help of existing knowledge and methods of action, creates a need for new knowledge. This need is the main condition for the emergence of a problem situation, one of its main components. However, when faced with a difficulty, students may not have a cognitive need if the task, which should reveal the difficulty in children, is given without taking into account their capabilities (intellectual capabilities and the level of knowledge they have achieved). Therefore, as another component of the problem situation, the student's capabilities in the analysis of the conditions of the assigned task and the assimilation (discovery) of new knowledge are singled out. The degree of difficulty of the task should be such that with the help of available knowledge and methods of action, students could not complete it, but this knowledge would be sufficient for independent analysis (understanding) of the content and conditions for completing the task. Only such a task contributes to the creation of a problem situation.

It is problem situations that make it possible to create such a logic of explaining new material that reflects the logic of the relevant science, didactically refracted in relation to the level of thinking of students of a certain age. The correct logic of explaining new material, reflecting the logic of science, contributes to the fact that one situation passes into another in a natural way, based on the interconnection and interdependence of things and phenomena. The process of thinking begins with the analysis of the problem situation. “As a result of its analysis, a task arises, formulated,problemin the proper sense of the word. The emergence of the problem - in contrast to the problem situation - means that now it was possible at least preliminary and approximately to separate the given (known) and the desired (unknown). This division appears in the verbal formulation of the problem. These provisions help to determine the ways of organizing problem-based learning in the school. The problem situation should be created taking into account real, significant for students contradictions. Only in this case it is a powerful source of motivation for the cognitive activity of schoolchildren, activates their thinking, directs them to search for the unknown. This provision is of fundamental importance for the practice of problem-based learning.

Classifications of problem situations, ways and means of their creation

Experience shows that there are already more than 20 classifications of problem situations.

• The first class includes those in which the goal (the subject of the action) is the assimilated unknown. In accordance with this, A. M. Matyushkin characterizes this class of problem situations as theoretical.

Example . Lesson " The world". Most rodents feed on solid plant food, which they gnaw off and grind with their teeth. The teeth must wear out, “wear out”, but they are always the same size. How can one explain that a beaver, who sharpens tree trunks all his life, does not lose his teeth and do not become blunt throughout his life? (Answer: Rodent teeth grow throughout life.)

The second class includes such situations in which the assimilated unknown constitutes the mode of action. Problem situations of this kind are widely represented in the assimilation of many subjects that involve the formation of rather complex ways for students to perform certain actions (language, mathematical operations, many practical skills and motor skills). This also includes situations that arise in the process of learning general and specific ways of solving problems in various academic subjects.

Example. Russian language lesson. The word "flycatcher" is written on the board. It is necessary to highlight the root in the word. There are different opinions. On the basis of word-formation analysis, children come to a new way of isolating the root (in compound words).

The third class includes such problem situations in which new conditions of action are unknown. Situations of this kind were most often considered in the study of the formation of skills, that is, at various stages of training a learned action. Especially often situations of this kind are encountered in the teaching of professional skills, when it is necessary to provide not only the main ways of performing professional actions, but also all the conditions in which they will have to be performed.

Example. Lesson "World around". Experience "Measuring the temperature of water." The thermometer reading in water differs from the temperature reading after removing the thermometer from the water. (While the water thermometer is out of the water, it gives an indication of the air temperature.).

This typology allows you to create a system of sequential problem situations. All types of problem situations have different didactic purposes. Thus, situations of the first class (theoretical) are used in the assimilation of new knowledge. Problem situations of the second class are used if the way to perform the action is unknown. The functional basis in this classification is very important, as it helps to identify the features and types of problem situations depending on the specifics of the subject. Fundamentally new in this classification is the allocation as the basis of the level of development achieved by students and the intellectual capabilities of the child. This allows you to take into account the age and individual capabilities of students and thereby contribute to their development. Accounting for intellectual capabilities allows you to analyze the conditions for the emergence and solution of problem situations.

A discrepancy, sometimes reaching a contradiction, arises:

1. between old, already learned knowledge and new facts that are discovered in the course of solving these problems.

Example. Math lesson. The boy wrote down mathematical expressions for tasks: 1) add 5 to 2 and multiply by 3; 2) add 5 times 3 to 2. He got the following entries: 2+5*3=21

2+5*3=17

Find the mistake in the notes.

Correct option: (2+5)*3=21

2+5*3=17

2) between knowledge of the same nature, but of a lower and higher level.

Example. Russian language lesson. The teacher says: “There is an oak by the road. What is the last word? (Oak) What sounds in order do we hear when we say this word? [e][y] [p] Look at how this word is spelled. Compare with the sound composition of the word. The following is an introduction to spelling.

3) between scientific knowledge and pre-scientific, everyday, practical knowledge.Example. Lesson "World around". Theme of the lesson: "Plan and map." Students are invited to draw an apple, a life-size pencil in a notebook. Then the teacher gives the task to depict the house in full size. Since this is not possible, students, under the guidance of a teacher, come to the conclusion that it is necessary to use a scale.

A problematic situation arises when a teacher deliberately confronts students' life ideas with facts that students do not have enough knowledge and life experience to explain.

It is possible to deliberately collide the life ideas of students with scientific facts with the help of not only experience, but also a story about an interesting fact, experience. As a rule, this is connected with an excursion into the history of science.

As a result, not only the assimilation of new knowledge occurs, but also the formation of a cognitive need, without which successful learning and the development of students' thinking are impossible.

It is also possible to intentionally collide the life ideas of students with scientific facts using various visual means, with the help of practical tasks, during the performance of which students will certainly make mistakes. This allows you to cause surprise, sharpen the contradiction in the minds of students and mobilize them to solve the problem.

Methodical methods for creating problem situations:

- the teacher brings students to the contradiction and invites them to find a way to solve it;

- expresses different points of view on the same issue;

- invites the class to consider the phenomenon from different positions (for example, commander, lawyer, financier, teacher);

- encourages students to make comparisons, generalizations, conclusions from the situation, compare facts;

- raises specific questions (for generalization, substantiation, concretization, logic of reasoning);

- defines problematic theoretical and practical tasks (for example: research);

Sets problematic tasks (for example: with insufficient or redundant initial data, with uncertainty in the formulation of the question, with conflicting data, with obviously made mistakes, with a limited solution time, to overcome "psychological inertia", etc.). For the implementation of problematic technology, it is necessary: ​​- selection of the most relevant, essential tasks;

- determination of the features of problem-based learning in various types of educational work;

- building an optimal system of problem-based learning, creating educational and methodological manuals and manuals;

- the personal approach and skill of the teacher, capable of arousing the interest of students in the case.

The task of the teacher is not to form infallible thinking, but to teach students to follow the path of independent finds and discoveries.

At the same time, both the teacher and the students become relatively equal participants in joint educational activities.

So, the use of problem situations in the educational process helps the teacher to fulfill one of the important tasks set by the school reform - to form students' independent, active, creative thinking. The development of such abilities can be carried out only in the creative independent activity of students, specially organized by the teacher in the learning process. Therefore, the teacher must be aware of the conditions in which schoolchildren should be placed in order to stimulate genuine productive thinking. One of these conditions is the creation of problem situations that constitute the necessary regularity of creative thinking, its initial moment. However, the effective development of creative thinking is provided only by a system problematic situations. In addition, the inclusion of schoolchildren in independent search activities under the guidance of a teacher helps them master the elementary methods of science and methods of independent work. The resolution of the system of problem situations teaches schoolchildren to mental stress, without which it is impossible to prepare for life, for work for the benefit of society.

Natural science grade 4 (problem learning)

Subject: Leather

Target:

acquaintance with the meaning of the skin and its structure;

challenge already existing knowledge on the issue under study;

activation of students, motivation for further work.

Equipment: task cards.

DURING THE CLASSES

1. Psychological attitude.

(Students are divided into groups)

Hold hands. Remember, you are one. Respect the opinion of your comrades, know how to listen and not interrupt each other. Remember the “open mic” rule.

2. Challenge of knowledge.

A)What is this?(Work in groups). The children are given task cards.

1 group -It does not get wet in heavy rain, does not absorb moisture, but freely passes water.

2 group -It constantly dies and is constantly reborn. We always fit.

3 group-This is our only clothing given by nature. She does not wrinkle, does not fade. You can wear it for at least 100 years.

4 group -Make a pattern: spine, ribs, skin, skull.

B)What do you think of when you hear the word "skin"?What are your associations? (The teacher writes the answers of the children on the board)

3. Observation and reflection.

A) Examine the skin on your hand, on your fingertips, on the palm of your hand. Tell about your observations (students name, and the teacher makes a diagram-drawing on the board).

B) Work on the textbook.

Look at the picture and read the text.

What else do you know about skin? What have we not said about the skin?

Conclusion:the skin protects us from bumps, scratches, bumps.

C) Drawing up a table “Skin Specialties” (work in a notebook).

Meaning

How does it work?

Protects

From bumps, scratches, bumps

(Reading in commands the text “What else the skin can do” with stops for discussion and filling in the table)

1 card - 1 stop. How do sweat glands work?

Meaning

How does it work?

Cools

Saves from internal overheating

2nd card - 2nd stop. If you collect all the water in a day, can you drink tea 3 times?

Meaning

How does it work?

Removes bitter-salty substances from sweat. Removes unnecessary body substances: salts, lactic acid, nitrogen compounds

3 card - 3 stop. Why is 1 liter of blood stored in the skin?

Meaning

How does it work?

Blood Keeper

During long work

Wound on the body - loss of a large amount of blood

4 card - 4 stop. Why would our bones be fragile and soft without the normal functioning of the skin?

Meaning

How does it work?

Produces vitamin D. The sun produces vitamin D, which helps to absorb calcium. Hence the strong bones.

5 card. What can you now say about the meaning of the skin?

4. Reflection.

Match the “new” information with the “old” information. Look at our "sun". Maybe add something new, change?

5. Game "Detectives".

Since 1905, fingerprints have been used in the investigation of crimes. Find your friend's prints (students receive papers and paints).

6. Homework.

Textbook. Find additional material about the skin. Record new words in a dictionary.

APPLICATION

1 card

Leather- an amazing invention of nature. She has several specialties. You already know about one of them: it is to protect against mechanical, chemical and other influences. Do you want to know about the rest?

As a result of the work of our internal organs, a large amount of heat is released. This heat could boil about 7 buckets of water! But it's not safe for us to boil! So you need to cool down. They are working on thissweat glands,which are hidden in the deep layer of the skin.

Question:How do sweat glands work?

2 card

They constantly wet the surface of the skin with sweat. Sweat constantly evaporates and at the same time carries away heat. If you're healthy, you don't even notice it. But remember what happened with a cold. You have a fever, i.e. a high temperature. After some time, the skin became moist, in some places (on the forehead, on the upper lip) quite noticeable droplets of water appeared. Following this, the temperature dropped rapidly. Grandmothers and mothers rejoice in such cases: “I sweat, so I’m on the mend!”. Imagine, even when the temperature is normal 36.6, the skin releases almost half a liter of water during the day.

So we figured out the second specialty: the skin saves from overheating.

Question:If you collect all the water in a day, can you drink tea 3 times?

3 card

No you can not. Various substances unnecessary for our body are dissolved in this water: all kinds of salts, lactic acid, various nitrogen compounds. That's whysweatbitter-salty taste. The skin helps the body get rid of these bitter-salty substances. Here is the third specialty of the skin.

There is also a fourth specialty. You know that there are many blood vessels in the deep layer of the skin. They are very thin, sometimes thinner than a hair. But there are many. So many that they can store a whole liter of blood.

Question:Why is 1 liter of blood stored in the skin?

4 card

About stock. When you're watching TV or reading, you certainly don't need this liter of blood. But if you go on a long hike or dig a garden, this blood will have to work. And it is already quite necessary when a person has a wound on his body, and a large amount of blood has been lost. So, the fourth specialty is the storage of blood. And you know that without the normal functioning of the skin, our bones would be fragile.

Question:Why would our bones be fragile and soft without the normal functioning of the skin?

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Required for bone strengthcalcium,and in order for the bone tissue to be able to assimilate, you needvitamin D. So here it isvitamin Dproduces leather. And, only if you visit the sun. Especially a lot of vitamin is formed from the morning rays of the sun. Here is such a fifth specialty of the skin.

Problem-based learning is a type of learning characterized by the creative "discovery" of knowledge by students. The place of problem-based learning is a lesson in learning new material on any subject content. Usage success problem method depends on the interested position of the teacher and the high internal motivation of students.

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Problem learning technology.

“Children learn better and are a thousand times more successful when they are given the opportunity to independently explore the basics of the material being studied.”

Peter Kline

The technology of problem-based learning is not new: it became widespread in the 1920s and 1930s in Soviet and foreign schools. Problem-based learning is based on the theoretical assumptions of the American philosopher, psychologist and educator J. Dewey (1859 - 1952), who founded an experimental school in Chicago in 1894, in which the curriculum was replaced by play and work activities. Classes in reading, counting, writing were carried out only in connection with the needs - instincts that arose spontaneously in children, as they developed physiologically. Dewey identified four instincts for learning: social, construction, artistic expression, and research.

To satisfy these instincts, the child was provided with the following sources of knowledge: the word, works of art, technical devices. Children were involved in the game and practical activities - work.

Deep research in the field of problem-based learning began in the 60s. The idea and principles of problem-based learning in line with the study of the psychology of thinking were developed by Soviet psychologists S.L. Rubinshtein, D.N. Bogoyavlensky, N.A. Menchinskaya, A.M. Danilov, M. N. Skatkin. T. V. Kudryavtsev, D. V. Vilkeev, Yu. K. Babansky, M. I. Makhmutov, and I. Ya. Research in this area is now being carried out by other representatives of pedagogical science.

Problem-based learning was a response to the challenge that the learning process itself, the changing conditions of life and human activity, and the person himself with his desire for self-improvement made to pedagogical science. In the pedagogical literature there are a number of attempts to define this phenomenon.

By problem-based learning, V. Okon understands “a set of such actions as organizing problem situations, formulating problems, providing students with the necessary assistance in solving problems, checking these solutions, and, finally, managing the process of systematizing and consolidating acquired knowledge.” Okon V. Fundamentals of problem-based learning. - M.: Enlightenment, 1986.

D. V. Vilkeev, by problem-based learning, means such a nature of learning when it is given some features of scientific knowledge.

I. Ya. Lerner sees the essence of problem-based learning 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 definitely system that corresponds to the educational goals of the school.” Lerner I.Ya. Issues of problem-based learning at the All-Union Pedagogical Readings.//Soviet Pedagogy, 1986.-No. 7.

T. V. Kudryavtsev sees the essence of the process of problem-based learning in the presentation of didactic problems to students, in their solution and in the mastery of generalized knowledge and principles of problem tasks by students. Such an understanding is also found in the works of Yu. K. Babansky.

Based on a generalization of practice and analysis of the results of theoretical studies, M. I. Makhmutov gives the following definition of the concept of “problem learning”: “Problem learning is a type of developmental learning that combines systematic independent search activity of students with their assimilation of ready-made conclusions of science, and the system of methods 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 cognitive independence of students, 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. Makhmutov M.I. Problem learning. Basic questions of theory.-M.: Pedagogy, 1995.

Today, problem-based learning is understood as such a form of organizing training sessions, which involves the creation of problem situations under the guidance of a teacher and the active independent activity of students to solve them, as a result of which knowledge, skills and abilities are mastered and mental abilities are developed.

In problem-based learning, the teacher's activity lies in the fact that, giving an explanation of the content of the most complex concepts, if necessary, he systematically creates problem situations, informs students of facts and organizes their educational and cognitive activities. Based on the analysis of facts, students independently draw conclusions and generalizations, formulate (with the help of a teacher) definitions of concepts, rules, or independently apply known knowledge in a new situation. With problem-based learning, the teacher systematically organizes independent work of students to acquire new knowledge, skills, repeat the fixed and develop skills. Students themselves acquire new knowledge, they develop the skills of mental operations and actions, develop attention, creative imagination, conjecture, develop the ability to discover new knowledge and find new ways of acting by putting forward hypotheses and substantiating them.

Stages of problem-based learning technology:

1. Statement of the educational problem; organization of a problem situation. The result of this stage is the difficulty of students and the formulation of a problematic question, which will be the goal of the lesson.

2. Finding a solution to the problem:

Through dialogue;

Putting forward hypotheses.

3. Testing hypotheses, starting with a false one.

4. Formulation of the rule, method; comparing it with a scientific model in a textbook.

5. Training in the formulation of educational questions (problems).

6. Carrying out control and verification work with the inclusion of tasks of a problematic nature:

Ask a problematic question;

Put forward a hypothesis;

Prove it.

The most optimal is the following structure of the problem lesson:

Problematic situation.

Problem formulation.

Putting forward hypotheses.

Proof or refutation of hypotheses.

Checking the correctness of decisions (reflection-introspection).

Playing new material (decision expression).

Consider each stage of the problematic lesson.

I. Problem situation.

Conditions for creating a problem situation.

1. The teacher needs to know:

Search methods of teaching.

Knowledge of the factual material (deeply and firmly).

The technology of raising questions that “reveal” contradictions before
students.

- Operating words, terms familiar to students.

2. Consider age features students, their level of development,
intellectual capabilities (in the first and second grades, it is necessary to teach children to answer and formulate problematic questions themselves), to be able to find different approaches to the classification of objects, words, to have different points of view on the same plot, phenomenon, to highlight the main thing. And third-graders and fourth-graders will already be able to independently organize their activities for the assimilation of knowledge, find means for solving a specific educational problem.

3. The problem should be difficult enough, but feasible, based on previous knowledge, skills and abilities.

According to the emotional response, the reactions of students, E.L. Melnikova identified 2 types of problem situations:

With surprise (different opinions about doing the same
tasks).

With difficulty (practical task for new material, which
guys can't handle it.

Ways to create a problem situation (according to Makhmutov M.I.).

When students encounter life phenomena, facts,
requiring a theoretical explanation (a problematic situation arises when a teacher deliberately confronts students' life ideas with facts that they do not have enough experience and knowledge to explain).

When organizing the practical work of students.

When encouraging students to compare, compare, contrast.

For research assignments.

Techniques for creating a problem situation.

1 . Unintentional - student error.

2. Intentional - the problematic question "Is it possible ..."; false conclusion - the teacher says: “I think that ..., what do you think?”;analogies (For example, form a new word from the words “fisherman” and “catch”, use the sample: he flies himself - an airplane); use of conflicting information (For example, “Choose the correct answer:Noun...a) Denotes an object or its attribute. B) Answers the question "Who?" or "What?" c) Denotes an object or natural phenomena, answers the questions "Who?" or "What?")

Questions to understand the contradiction:

What surprised you? What interesting things have you noticed? What facts poured?

How much different opinions in class? What did you first think?

What did you assume? What really happened?

Were you able to complete this task? What is the difficulty?

What did you want to do? What knowledge was applied? Mission completed?

II) Formulation of the learning problem:

The problem can be expressed as:

The theme of the lesson (" Spelling prefixes and prepositions»).

The question, the answer to which will be new knowledge (How to divide an amount by a number?

The best option for posing the problem is if it is voiced by the students themselves. But if they cannot recognize the contradiction and formulate the problem, then the teacher can use two types of dialogue:

inciting (encourages awareness of the contradiction and formulation of the problem (“Are you surprised? Why? What interesting things have you noticed? What questions arise?»).

Leading (Questions and tasks feasible for the student, which, step by step, lead him to the realization of the problem (“Remember", "Compare", "Analyze").

III) When hypothesizing

The teacher "guides" students with the help of leading judgments:

Let's assume...

In what order will you solve the problem ...

Express your point of view

What are the guesses?

If the students did not put forward their hypotheses, then the teacher offers his own (among them there may be consciously erroneous ones).

IV) When proving or refuting hypotheses.

Receptions:

Observation and analysis.

Comparison, highlighting common features.

Selection by exclusion("That doesn't fit because...").

Combination of observation and experience.

To put forward hypotheses, their evidence and refutation, students should develop such practical skills as:

the ability to set a goal;

find and formulate contradictions;

to put forward and substantiate hypotheses;

argue, argue, compare your opinion with the statements of others;

draw up a plan for solving or completing a task;

check and evaluate your actions.

V) Checking the correctness of decisions.

tricks

1. Comparison with the wording of the rule in the textbook, a ready-made plan of action.

2. Formulation of the conclusion using tables, diagrams, algorithms and memos.

3. Implementation of practical tasks on this topic.

VI) Reproduction of knowledge.

This step is not strictly required, but highly desirable, because:

deepens understanding of new material;

contributes to the formation of visual-figurative thinking;

develops active speech, creative abilities.

This is the creativity of students, which is ensured by the performance of productive tasks of three types:

to formulate (topics, questions on the topic);

reference signal (symbol, scheme, reference words);

(For example, C b G - separates, C b C - denotes softness.)

artistic image: metaphor, riddle, poem.

(For example, We are no longer kids, we know how to write JI-SHI.)

These tasks can be performed both during the lesson and at home, if desired.

At the stages: putting forward hypotheses, proving or refuting them, expressing a solution, students can work independently, in pairs, microgroups.

The success of a problematic lesson depends on:

Awareness of the learning task by students.

A clear statement of the problem.

Children's knowledge of supporting material.

Children's ability to express their point of view, draw conclusions

Thus:

Problem-based learning is a type of learning characterized by the creative "discovery" of knowledge by students.

Place of problem-based learning: this is a lesson in learning new material on
any subject matter.

The purpose of problem-based learning:

development of intelligence and creative abilities of students;

formation of solid knowledge;

increasing motivation through emotional coloring lesson;

upbringing of an active personality.

The success of using the problematic method largely depends on the interested position of the teacher and the high internal motivation of students. In the process of using problem-based learning, both the assimilation of the material and the development of mental activity occur.

The main result of using the technology of problem-based learning is that the graduate of the school is guided by modern values, gains experience in creative activity, that he is ready for interpersonal and intercultural cooperation.

The course "Pedagogical Theory for the Modern Teacher"

COURSE PLAN

newspaper number	Educational material
	Lecture No. 1. Didactics as a universal tool for pedagogical creativity
	Lecture No. 2. Content biological education in modern conditions and its composition
	Lecture #3. Teaching methods, their specificity. Test No. 1(Deadline - November 15, 2004)
	Lecture No. 4. Problem-based learning in biology lessons
	Lecture No. 5. Project activity. Test No. 2(deadline - until December 15, 2004)
	Lecture No. 6. Structure and types of lessons
	Lecture No. 7. Intellectual and moral development in biology lessons
	Lecture No. 8. Methodological aspects of science in biology lessons
The final work is the development of the lesson. The final work, accompanied by certificates from the educational institution (acts of implementation), must be sent to Pedagogical University no later than February 28, 2005

Lecture No. 4. Problem-based learning in biology lessons

The concept of a problem and a problem situation.
Learning to search, formulate and solve problems.
The system of tasks in biology lessons.

In this lecture, we will talk about a topic without understanding which it is impossible to build a full-fledged modern education. I mean authentic, conscious, not spontaneous problem-based learning. Much is written about its necessity, much less often it is used, not only because it has not become part of the pedagogical consciousness of the teacher, but also because it has not become an instrument of his activity. These words, it would seem, sound rather strange today against the backdrop of an ever more widely developing project activity, teacher competitions of various scales and ranks, a system of olympiads, and, nevertheless, the need for problem-based learning has not been fixed in the mass teacher's mind.

All methods generally recognized today, including the problem-based learning methods discussed above, can be fully implemented only if the teacher knows the basic didactic patterns of the learning process, the ability to apply this knowledge in real teaching practice. Only then is it possible to achieve the main goals of any education: the development of the intellectual potential of students, their abilities for creative thinking, the formation of a value attitude to the very process of cognition and the content being cognized.

So what is problem-based learning? According to I.Ya. Lerner, this is such training in which students are systematically involved in the process of solving problems and problem tasks built on the content of the program material. Two conclusions follow from this definition:

- problem-based learning involves an independent complete or partial solution of problems that are feasible for students;

To solve these problems, students need to create a situation that encourages them to solve problems.

Therefore, in addition to defining the concept of "problem", it is necessary to define the concept of "problem situation". The fact is that the same question or task, depending on the situation, may or may not be a problem for the student. On the other hand, for one student a particular issue is a problem, but for another it is not. This is determined by the totality of his knowledge and skills, his readiness to solve this problem, the feasibility of the problem, the degree of fame of the answer, etc.

"The problem situation characterizes the attitude of the student to the obstacle that has arisen in the practical or intellectual sphere of activity." In fact, a problematic situation always arises against the background of perceived difficulties and an incentive to solve the problem. Without these conditions, there is no problem situation. It is necessary to realize the existence of a contradiction and want to overcome it.

Ways to solve problems in purposefully created problem situations and teach problem learning methods .

There are three such methods: problem statement, heuristic And research. Their application in educational practice it is effective, first of all, when the teacher sets the task: on the basis of existing knowledge and skills, to form qualitatively new ways of activity - the ability of schoolchildren to independently formulate and solve discovered or posed problems, the ability to propose hypotheses and ways to test them, plan experiments.

Each of the methods is specific both in the activity of the teacher and in the activity of the student. These methods are applied depending on the subject and content of the material being studied, the preparedness of students and the specific goals of this lesson.

Until now, one can hear that the use of problem-based learning methods is uneconomical. At the initial stage of training, this is probably the case. However, it should be understood that the correct, thoughtful and systematic application of these methods has a powerful learning effect and saves a lot of time in subsequent training.

Is it economical to teach only by illustrative or reproductive methods that reduce the intellectual activity of students to a minimum? Isn't it important to develop students' thinking so that they independently and quickly navigate the educational material, evaluate its significance, complexity, and the scope of applicability of the acquired knowledge in relation to other knowledge? And then, isn't it important that the use of problem-based learning methods allows you to develop the creative abilities of each student at his individual level?

Ignoring problem-based learning leads to the fact that some children are looking for ways to use their abilities in a completely different social field than active professional and public life. Among the criminals who studied poorly at school, there are many truly creative people.

What is the reason why problem-based learning has not become so widespread in programs, textbooks, and in real mass practice? The answer to this question is not as simple as it seems. One of the reasons is that, unfortunately, so far, despite all the abundance of didactic and methodological literature, didactics and methodology are not united in the teacher's mind in their interconnection and interaction.

To this day there are conceptual and terminological differences between didacticists and methodologists, although they often use similar verbal terms. Examples of these discrepancies were given in the third lecture. So, for example, a method in didactics is a way of organizing interaction between a teacher and a student in the learning process, reflecting the activity of students in mastering educational material. The method in the methodology is interpreted as a form and method of teaching, reflecting the activities of the teacher, adequate to the content of the educational material and the goals of the teacher.

Speaking about the translation of didactic categories into methodological ones, I mean the importance of the teacher's assessment of his own activity through the prism of the interconnectedness of the relationship teacher - student - subject. In these relations, each element performs its function, determined by the content of the material studied in the lesson, the organization of activities for its assimilation and the method of assimilation of this material.

The second, and most important, reason is that school textbooks for the most part, they do not direct the cognitive activity of students. They differ in content, the volume of terms and concepts proposed for assimilation, but most of the available textbooks are focused on reproductive activity. Teachers, following the logic of the presentation of the textbook, require students to present the paragraph and the ability to answer questions to it. This is clearly not enough to achieve the goals of education declared in various documents, including the educational programs of schools.

Textbooks and additional teaching aids can and should offer students material that encourages the reader to think, to look for answers to the questions posed. That is why problematic material is capable of performing all educational functions and, on the contrary, a text rich in facts, but dry text, can only push the student away from the subject. I will give an example illustrating the stated idea. This is a fragment of one of the textbooks for the 6th grade, showing how you can build a problematic presentation of the material.

Research by L. Spallanzani

In this paragraph, you will get acquainted with one of the most brilliant scientists and his research. Follow the thought of the Italian scientist Lazzaro Spallanzani and his main opponent, the monk Needham. After working with this paragraph, you will be able to:

1. Formulate a problem that interested Spallanzani.
2. State the course of his research in your own words.
3. Formulate the hypothesis put forward and tested by Spallanzani.
4. Assess the significance of Spallanzani's experiments for the development of science.

Let's look at one of the examples of scientific research and prove that all the signs of science given earlier are in this research.

In the XVIII century. biologists, doctors, philosophers were interested in the question: Can living beings be born on their own, without outside participation, “out of nothing”, or does each organism have parents? This question, the answer to which any modern high school student knows, is not as simple as it seems. We know that all living beings are born from their parents - a mouse from mice, a birch tree grows from a birch seed, and an elephant and a turtle also have their own father and mother. But who was the parent of the very first organism that appeared on Earth? Throughout the history of science, two main answers to this question have been proposed. First - all living organisms appeared from inanimate bodies, thanks to the many chemical transformations of substances that were part of the Earth. Second answer: everything and the Earth itself, and its population, i.e. plants and animals, bacteria and people - was created by a creator invisible to us.

One of the scientists who took the liberty of solving such a significant problem for science was Lazzaro Spallanzani, an Italian, professor at several universities in Italy, an inquisitive and courageous person who doubted both the teachings of Aristotle and the divine origin of life. In his time, many believed in the spontaneous generation of life (birth without parents). One of the "scientific treatises" wrote: "To dispute that beetles and wasps are born from cow dung is the same as arguing against reason, common sense and real experience. Even animals as complex as mice do not have to have fathers and mothers. If anyone is in doubt, let him go to Egypt and there make sure that the fields are positively teeming with mice, born from the dirty mud of the Nile River, which is a great disaster for the population.

Spallanzani did not believe in such "scientific truths". He decided to prove that any living beings, even bacteria, should be born only from the same living beings. The living is only from the living.

First, Spallanzani studied the data of modern science and selected those that were in doubt. After all, if there are doubts, then they must be checked and convinced either of one's own or of someone else's rightness. He doubted the validity of the birth of mice from mud, the emergence of a swarm of bees from the horns of a calf, the emergence of microbes from lamb gravy, and many other similar facts. He studied the evidence cited by the authors of scientific papers, and began to doubt the purity, and therefore the reliability of their experiments. Then Spallanzani began experiments with microscopic animals. Here is the course of his reasoning.

“All the studies I have read about or listened to talks about are observational. In most cases, experimental studies have not been conducted. Consequently, I must confirm my idea of ​​the impossibility of spontaneous generation in experiment. What kind of experience is required? All authors say that the smallest creatures can be born anywhere - in broths, decoctions, gravies. But none of them tried to check it. Although no, there was a letter to the Royal Society of a certain Needham - a priest from England. He boiled the mutton gravy, poured it into bottles, and sealed it tightly with corks so that no creature could enter it. To be sure, he heated the gravy again in hot water. A few days later he opened the bottles, and what? He saw under a microscope that the gravy was teeming with germs.”

Spallanzani decides that Needham did not boil the vessels long enough and sealed them poorly. After all, microbes are so small, they can penetrate the gap between the cork and the bottle. In addition, they can probably tolerate high temperatures for a while. “Consequently,” the scientist decides, “I must boil my vessels with decoctions and broths for a long time, for example, an hour.” But how to prevent microbes from entering the vessels? Spallanzani figured out how to do it. He began to solder glass vessels on fire in order to completely exclude microbes from entering the flasks. Then he began to boil his flasks. Some for a few minutes, others for hours. In addition, he prepared another group of flasks with the same decoctions, but not sealed, but closed with stoppers. He boiled them for an hour and set them apart.

Several days have passed. Spallanzani, one by one, began to open his sealed vessels. In the liquid, which he boiled for an hour or more, he did not find anything even with the help of his most powerful microscopes. Then he examined the liquids from the sealed but short-boiled bottles. There was a certain number of "insignificant little animals", as they were then called. Finally, he turned to a group of corked bottles set aside. The broth taken from there was teeming with germs. This experience allowed Spallanzani not only to refute the evidence of not too conscientious scientists, but also to announce to students who listened to his brilliant lectures that life originates only from the living, that everyone should have parents. Thus, Spallanzani rejected the theory of spontaneous generation of the living from the non-living. But one question still remained open. Try to remember which one. Now let's return to the signs of science and find out if they coincide with the results of Spallanzani's research.

1. Spallanzani certainly knew a lot about microbes and experiments with them. We may well be convinced that he had a vast knowledge of contemporary biology.

In sealed flasks, the transparency of the broth with bacteria depends on the boiling time.

2. The knowledge gained by Spallanzani gave rise to a whole series of new studies that continue to this day. And the French culinary specialist F. Apper, having read the works of Spallanzani, invented canned food, which interested Emperor Napoleon (why?).

3. All subsequent experiments confirmed the correctness of the Italian scientist. (IN workbook read about the experiments of R. Koch and complete the task.)

Not everyone becomes a scientist in life. But no matter what a person does - building houses, raising animals, working on a machine tool, driving a car or cleaning the streets, he must do his job well. And for this it is necessary to know how to do this business better, more precisely, more economically and act in the same way as scientists do in their work:

observe;

select the necessary information and identify patterns associated with observed events, phenomena, facts;

ask questions to yourself and nature, i.e. formulate problems;

make assumptions that can be tested - hypotheses;

test the hypotheses put forward, i.e. set up experiments;

explain the results obtained and cross-check them;

ask new questions.

Review questions

1. Tell us about Spallanzani's research.
2. What facts did the scientist have before the start of the research?
3. What facts were established by him in the course of research?
4. What problem did Spallanzani formulate?
5. Which of the hypotheses did Spallanzani test:

a) if microbes are born in lamb gravy, then boiling will kill them;
b) if microbes get into the gravy from the air, then sealed vessels will stop them from accessing it;
c) if you boil the gravy and stop air from entering the vessels, then microbes will not appear there;
d) hypotheses b And V;
e) all hypotheses?

6. Why were the results of Spallanzani's experiments more accurate than those of other scientists?
7. Some scientists who repeated Spallanzani's experiments did not confirm his results. List possible reasons for their failure.
8. Why did experiments related to the problem of spontaneous generation continue after Spallanzani? Prepare short reports about the experiments of F. Redi and L. Pasteur.

This fragment illustrates almost all the ideas expressed in connection with problem-based learning implemented in educational texts. Firstly, 6th grade students are offered a fascinatingly written text to work with. Secondly, it contains both the formulation of the problem, and its discussion, and ways to solve it. However, each time the reader, together with the author, follows the thought of the scientist and can agree with it, object, reflect, etc. The entire text is based, on the one hand, on factual materials and refers to the knowledge available to the student, and on the other hand, it forms new, methodological, knowledge about how to obtain information, about research methods. Questions to the paragraph suggest different types activities - from reproductive to creative.

My own teaching experience, the experience of working as a deputy director and director of a school, a teacher in advanced training courses, as well as numerous visits to classes show that it is important for a teacher not only to understand what and how he does it, but why he does it and where it will lead. Let me explain this idea with a concrete example.

Lesson on the first topic of genetics - “Laws of Mendel. Monohybrid cross. How can you build a lesson? Tell the story of G. Mendel, describe the logic of his experiments, show the progress of monohybrid crossing on the table and board and analyze the results, then give the students a task for monohybrid crossing and ask them to do their homework.

Did the lesson take place and were the goals achieved? To a certain extent, the lesson took place and the goals were achieved. The students listened to the teacher, outlined his story and solved one or more problems. At home, they practice solving problems for monohybrid crossing.

The classical lesson of presenting and consolidating knowledge was methodically constructed. But whether the students understood the ideas of genetics, whether they were able to connect the previous material with the newly studied material, whether they saw the problems of the topic, whether they themselves were able to come to some conclusions from the lesson - it is not clear if the description of this lesson is reduced to the above. Now another description of the same lesson on the same topic.

One of the earliest texts on genetics can be read in the Bible.

Jacob served his kinsman Laban for a long time in order to get his daughter Rachel as a wife. Laban was a liar, and Jacob decided to leave him, asking only speckled and mottled goats and brown sheep as a reward. And from now on, he said, every non-speckled and non-motley goat, and non-brown sheep will be considered stolen from Jacob. Laban agreed and drove off all the speckled animals for a distance of three days' journey. Thus, Jacob did not have any spotted animals. What did he do?

“... and Jacob took fresh rods of poplar, almond and sycamore, and Jacob cut white stripes on them (removing the bark to whiteness, which is on the rods), and put the rods with cuttings in front of the cattle in the watering troughs, where the cattle came to drink and where when he came to drink, he conceived before the bars, and he conceived cattle before the bars; and multicolored cattle were born, and with speckles, and with spots - and Jacob separated the lambs, and set the cattle facing the motley and all the black cattle of Laban; and he kept his flocks apart, and did not put them together with Laban's cattle; every time when strong cattle conceived, Jacob laid twigs in troughs before the eyes of the cattle, so that they conceived before the twigs, and when weak cattle conceived, then he did not lay (and the weak cattle went to Laban, and the strong ones to Jacob); and this man became very, very rich, and he had a multitude of flocks and herds, and female slaves and slaves, and camels and donkeys. (Gen. 31:37-43).

Already in this text, at least two problems are hidden, which the teacher, after a short commentary and clarification of the text, asks the students to formulate and, in case of difficulty, helps them.

1. How much does the environment influence the inheritance of traits?

2. How are traits inherited?

The solution of these problems becomes the immediate prospect of studying the topic. Further, the task is somewhat clarified and the objectives of the lesson are formulated:

- to identify patterns of inheritance of parental traits;
- assess the complexity of the problem that arose before G. Mendel;
- learn the terms necessary to solve genetic problems and explain genetic patterns;
– learn to solve some types of genetic problems;
- evaluate the role of G. Mendel in the development of biology and suggest the directions in which his ideas developed.

Then the teacher organizes the study of new material, revealing the logic of G. Mendel's research, from which the hypotheses formulated by him, the conditions and technique of the experiment, the results obtained are revealed and, together with the students, analyzes them. On the basis of a joint partial solution of only one of the problems posed at the beginning of the lesson, namely: “How are traits inherited?”, The law of splitting is formulated and further ways to find answers to the questions posed about the influence of the environment on inheritance, about the different nature of inheritance, about the functions of the gene are determined etc.

The lesson constructed in this way does not have a momentary completion, it leaves ground for reflection and motivates to search for answers to the questions posed. Perhaps the solution of the genetic problem in this lesson is not its most important result. More important is the realization of the wealth of biological ideas that were revealed at the first presentation of the topic.

What is methodical and what is didactic in this lesson? What is the relationship between methodology and didactics?

The didact first thinks about which components of the educational content will dominate in this lesson. In this case, it is knowledge. Consequently, he must organize their assimilation in accordance with the patterns of knowledge assimilation. Having solved the issue of dominance, the ratio of the components of the content of education in the lesson, he must choose teaching methods to achieve his goal and then methodically build a lesson so that at any given moment the teaching methods are adequate to both the content and the activities of students. This is both a didactic and a methodological task.

The didactic student should think about the inclusion of an emotional component in the fabric of the lesson, and the methodologist should find a place for the appropriate educational material and ways to present it. That is why a teacher is both a didactic and a methodologist rolled into one. He must select the content, structure it, choose the appropriate teaching methods, anticipating the learning outcomes, and decide on the methods and methods of presenting the material, and therefore on organizing the assimilation of the selected content.

Thus, problem-based learning and its methods are aimed at the formation of active cognitive independence of the student. The creative abilities of students developing at the same time are fully manifested when they perform independent research, participate in other creative work.

The application of problem-based learning methods is impossible without a system of tasks constructed in a certain way, through which problem situations are created. In the previous lecture, we already spoke about the typology of questions and tasks that require students to partially or completely independently search. Here I should also mention some requirements for the system of assignments, for which I will allow myself to refer to the work of the teachers of the 354th school in Moscow on the organization of the Dalton Hours and partially quote it:

1. Assignments should cover a sufficient amount of educational material.
2. The system of tasks provides for the assimilation of educational material at different levels: (conceptual, reproductive, creative).
3. The didactic system of tasks provides for the possibility of repeating educational material at different levels.
4. Assignments should be interesting for the student.
5. Assignments should be designed for the possibility of their independent implementation by students.
6. Tasks involve various forms of work with them.
7. Assignments involve cooperation with other participants in the process.
8. The tasks provide for the possibility of control and self-control.
9. The same problem can be presented in different contexts.”

In conclusion, I would like to say that only creative activity teachers are able to inspire students to be creative. There is nothing more interesting in professional activity than creating something new - designing a lesson, writing a tutorial, putting on a play, etc. After all, our mass profession is in fact individual and marked by the stamp of originality. So is it worth it to be afraid to embark on the path of creation? “Create! Make it up! Try it!

Questions and tasks for independent work

1. What is the difference between a problem presentation and a heuristic conversation?
2. Present any textbook passage you choose using problem-based learning logic.
3. Create a typology of questions to be taught to students when planning and setting up an experiment.
4. Create a system of tasks for any topic of the course.

Literature

Lerner I.Ya. Problem learning. – M.: Knowledge, 1974.

window V. Fundamentals of problem-based learning. - M .: Education, 1968.

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 verification);

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. new information students receive 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 the 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

he carries out actions for setting and solving the problem 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
			Conducts general organization, control and 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 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.

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 problem method cannot be turned into a universal method of teaching. 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.

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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?