Message “Methods of productive learning.” Reproductive and problem-search methods of teaching

"Methods of productive learning."

Teaching methods are ways of joint activities of the teacher and students, aimed at achieving their educational goals

(A.V. Khutorskoy).

A method is a way, a way to achieve a goal. The success of the entire educational process largely depends on the choice of methods used. This causes special attention to teaching methods.

A method is part of the type of activity of a student or teacher, a unit of action performed. The choice of teaching methods is determined by: the semantic goals of education, the characteristics of the training course, the purpose of a particular lesson, the capabilities of students, the availability of time and means of teaching, the preferences of the teacher and the characteristics of the didactic system he uses.

An integral part of the method isreception . Certain techniques may be included in different methods (for example, the technique of formulating a question to find out the reasons - in methods of research, explanation, reflection, etc.).

Classification of teaching methods

The role and place of methods in teaching is determined by their types and functions. Therefore, the key didactic problem is the classification of teaching methods. However, there is no uniform classification of teaching methods. But consideration of different approaches to dividing them into groups allows us to systematize the methods as a didactic toolkit.

First, let's compare the reproductive and productive options for educational activities.

There are two options (directions) of educational activity - reproductive (reproducing) and productive (creative).

Reproductive variant includes perception of facts and phenomena and their subsequent comprehension . Both of these stages lead to understanding, assimilation and mastery.

Slide 6

Scheme of the reproductive teaching method

Purely reproductive training with its main pedagogical slogan “Do as I do!”, like most reproductive methods, is practically dying out.

Productive option , in contrast to reproductive,contains a number of new elements (proposing and testing hypotheses, evaluating options, etc.) and consists of three main stages - indicative, executive and control-systematizing

Productive learning

Teaching methods according to the “nature of cognitive activity”

    Reproductive methods

    EXPLANATORY-ILLUSTRATIVE METHOD

It is characterized by the fact that the teacher presents knowledge in a processed, “ready-made” form, and the students perceive and reproduce it. The stages of activity of the teacher and students in this didactic process look like this:

TECHNIQUES APPROPRIATE EXPLANATORY-ILLUSTRATIVE TRAINING METHOD

    the teacher’s intonation highlighting of logically important points of presentation;

    repeated, briefer presentation of ready-made knowledge to students;

    a detailed summary by the teacher of each individual completed stage of presentation;

    accompanying the teacher’s generalized conclusions with specific examples;

    demonstration to students of natural objects, diagrams, graphs in order to illustrate individual conclusions;

    presenting the finished plan to students during the presentation;

    presenting students with reformulated questions and task texts that make it easier to understand their meaning;

    instructing students (on drawing up tables, diagrams, working with textbook text, etc.);

    a hint containing ready-made information.

The “explanatory-illustrative” method assumes that the teacher communicates ready-made information through various means. But this method does not allow one to develop practical skills and abilities. Only another method of this group - “reproductive” - allows us to take the next step. It provides an opportunity to develop skills and abilities through exercise. By acting according to the proposed model, students acquire skills and abilities to use knowledge.

2) REPRODUCTIVE TRAINING METHOD

Characterized by less productivity, reproductive thinking nevertheless plays an important role in both cognitive and practical human activity. On the basis of this type of thinking, problems of a structure familiar to the subject are solved. Under the influence of the perception and analysis of the conditions of the problem, its data, the desired, functional connections between them, previously formed systems of connections are updated, providing a correct, logically sound solution to such a problem.

Reproductive thinking is of great importance in the educational activities of schoolchildren. It ensures understanding of new material when it is presented by a teacher or in a textbook, application of knowledge in practice, if this does not require significant transformation, etc. The possibilities of reproductive thinking are primarily determined by a person’s initial minimum knowledge

TECHNIQUES APPROPRIATE REPRODUCTIVE TRAINING METHOD

    assigning students to individually pronounce known rules and definitions if necessary, using them in the process of solving problems;

    task students to pronounce “to themselves” the rules used,

    task to compile brief explanations of the progress of the task;

    task for students to reproduce by heart (rules, laws, etc.);

    assignment for students to fill out diagrams and tables following the teacher;

    organizing students’ assimilation of standard methods of action using a choice situation;

    assigning students to describe an object using a model;

    tasking students to give their own examples that obviously confirm a rule, property, etc.;

    guiding questions to students, encouraging them to update their knowledge and methods of action.

I turn to productive teaching methods.

Under productivity of educational activities is understood as a pedagogical process that promotes the development of the individual in a team and the development of the team itself through productive and orientational activities in a real life situation and taking place as part of a group of students with the support of a teacher.

Experts (Amonashvili Sh.A., Ksenzova G.Yu., Lipkina A.N., etc.) argue that the product of educational activity is an internal new formation of the psyche and activity in motivational, holistic and semantic terms. Further human activity, in particular, the success of educational and professional activities and communication, largely depends on its structured organization, systematicity, depth, strength, systematicity. The main product of educational activity in the proper sense of the word is the formation of theoretical thinking and consciousness in the student.

Now let's move on to productive methods

II . Productive learning methods

1) Cognitive methods, or methods of educational knowledge of the surrounding world. These are, first of all, research methods in various sciences - methods of comparison, analysis, synthesis, classification. The purpose of use is to understand the object

Empathy method: a person’s “getting used to” the state of another object. The method of semantic “vision” involves answering the questions: what is the reason for this object, what is its origin, how it works. The method of figurative “vision” involves describing what the object under study looks like. The method of heuristic questions involves searching for information in the process of answering questions (who, what, why, where, with what, how, when). The method of heuristic observation involves personal perception of different objects. The method of facts is the search for facts, distinguishing them from non-facts; finding the differences between what we see and what we think. Research method. Method of constructing concepts Method of constructing rules. Hypothesis method. Forecasting method. The error method involves identifying the causes of errors

2) Creative methods provide students with the opportunity to create personal educational products, allowing students to create their own educational products. In this case, cognition occurs “in the course” of creative activity itself. The invention method is implemented by replacing the qualities of one object with the qualities of another. The figurative painting method suggests perceiving and understanding the object being studied holistically. The hyperbolization method involves increasing or decreasing the object of knowledge or part of it. The agglutination method offers to combine qualities that are incompatible in reality. Brainstorming method. The morphological box method involves finding new and original ideas by putting together various combinations of known ones.

3) Organizational activities methods,those. methods of teachers, students, education managers. Methods of teachers and students - educational goal setting, planning, review method, self-control, reflection, etc. Administrative methods are associated with the creation and development of the educational process both on the scale of the curriculum and the entire school. Methods of student goal setting involve students choosing goals from a set proposed by the teacher. Methods of student planning involve students planning their educational activities. The rule-making method involves students developing norms for individual and collective activity. The self-organized learning method involves working with real objects and making models. Peer learning method. The review method involves students reviewing a friend's educational product.

Let's look at it in more detailcreative (productive, creative) methods.
The following terms are used as synonyms for the concept of “productive thinking”: creative thinking, independent, heuristic, creative. Or our children can develop elements of creative thinking, we cannot stop at their development. It has already been proven that if children are developed, they move to a higher level of thinking.

Synonyms for reproductive thinking are the following terms: verbal-logical, rational.

Of course, it’s easier for us to work this way. There is no need to prepare creative assignments personally for the most capable students and offer them regular assignments that are given to the whole class. The method of individualization puts children in unequal conditions and divides them into capable and incapable. Creative tasks should be given to the whole class. When they are completed, only success is assessed. The teacher must see individuality in each child. The American scientist Rosenthal argued that in a situation where a teacher expects outstanding success in children, they actually achieve these successes, even if they were previously considered not very capable.

In order to develop creative thinking, teachers should encourage students to independently check their work results. Set tasks for him - not to check his results with the students’ answers, with the textbook, with the dictionary, with the teacher’s model, but to independently check the task; who guessed how to check the problem, what rule will you use when checking the exercise?


Teacher questions play an important role in the development of creative thinking. For example: By what means was the author able to describe the beauty of nature with such expressiveness? In reading lessons, it is necessary to give students as often as possible the opportunity to talk about what they felt and experienced while reading, to talk about their own mood; be able to evaluate the actions of the heroes of the work, the author’s attitude to the events described.

To develop creative thinking, you can use a wide variety of methods in Russian language and reading lessons. For example: choose words that are similar or opposite in meaning; continue the story; make a memo; come up with a fairy tale, words, phrases; make sentences with words, from given words, according to a picture, according to a diagram, with a phrase; distribute the offer; compose a story based on questions, on the content of the text, on pictures, based on your own impressions; draw a verbal picture for the story; title the story, parts of the story; poems, etc.

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

Following G.K. Selevko,the main goal of the teacher in the lesson - This activation of student thinking . Problem-based learning is one of the most effective means of activating student thinking. The essence of activity achieved through problem-based learning is that the student must analyze factual material and operate with it in such a way as to obtain new information from it. In other words, it is an expansion, deepening of knowledge using previously acquired knowledge or a new application of previous knowledge. Neither a teacher nor a book can give a new application of previous knowledge; it is sought and found by the student, placed in the appropriate situation. This is the search method of teaching as an antipode to the method of perceiving the teacher’s ready-made conclusions.

Taskbased on the initial level of knowledge, but directed through the zone of proximal development towards its promising solution . Thus, the cognitive task reflects the main contradiction of teaching - between the new promising needs of schoolchildren and the already achieved (initial) level of their knowledge.

The greatest effect in problem-based learning is provided by tasks that involve the discovery of cause-and-effect relationships, patterns, and general features of solving a whole class of problems that are new to students, based on relationships between certain components of the specific situations being studied that are not yet known to the subject.

The choice of task-problem also depends on whether students have an initial minimum of knowledge (including their operator side) or the ability, in a relatively short time before posing the problem, to familiarize students with the information necessary for an independent solution. At the same time, we must remember that this knowledge should serve as a support for searching for a solution, and not “guide” or suggest this path, otherwise the task will cease to be problematic.

Both the analysis of the problem situation and the identification of its connections and relationships are expressed in the form of tasks. Therefore, the structural unit of problem-based learning isproblematic situation .

Whether a problem situation arises in a particular student’s learning environment, whether he or she will turn to the most effective method of productive thinking to solve it - “analysis through synthesis” or to mechanical manipulation of data - depends not only on objective factors, but also on subjective factors , and above all - from the mental development of schoolchildren. Since schoolchildren of the same age have very significant differences in the level of mental development they have achieved, the full implementation of the problem-solving principle cannot be achieved without individualizing education.

A person tries to solve a problem that is new to him using methods known to him and becomes convinced that familiar methods do not provide him with success. Awareness of this leads to the emergence
(problem situation(, i.e., it activates productive thinking, ensuring the discovery of new knowledge, the formation of new systems of connections, which will later provide it with the solution of similar problems.

Classification of creative methods by increasing degree of complexity .

    Methods of problem presentation

When presenting a problem, the teacher does not communicate ready-made knowledge, but organizes students to search for it: concepts, patterns, theories are learned in the course of search, observation, analysis of facts, mental activity, the result of which is knowledge. The process of learning, educational activity is likened to scientific research and is reflected in the concepts: problem, problem situation, hypothesis, means of solution, experiment, search results.

The essenceProblem presentation lies in the fact that the teacher poses a problem to the students and solves it himself, but at the same time he shows the course of his thoughts and reasoning. Otherwise, this method can be calledstory-reasoning. When using this method, students control the teacher’s train of thought and follow the logic of his reasoning.
Using this method allows students to learn the method and logic of solving problems of this type, but without the ability to apply them independently. Therefore, this method is used, as a rule, when studying complex educational issues. The teacher can use any means: words (logical reasoning), book text, tables, films, magnetic recordings, etc.
With this method, students not only perceive, understand and remember ready-made information, but also follow the logic of evidence, the movement of the teacher’s thoughts, controlling its persuasiveness.

TECHNIQUES APPROPRIATE METHOD OF PROBLEM PRESENTATION

    presentation to students of deliberately violated logic of presentation, proof and analysis by the teacher of the results obtained;

    disclosure by the teacher of the causes and nature of failures encountered on the way to solving problems;

    teacher discussion of the possible consequences of incorrect assumptions;

    dividing the material presented by the teacher into developing semantic points;

    fixing students' attention on the sequence of contradictions that arise during problem solving;

    an intriguing description by the teacher of the object being presented followed by posing a question;

    the teacher’s attitude towards students’ mental solution of the logical task put forward during the presentation;

    rhetorical questions from the teacher during the presentation;

    presenting students with a conflict example.

    Partial search method.

Partial search (or heuristic) method. In this method, the method of finding a solution to a problem is determined by the teacher, but the students themselves find solutions to individual issues.
Domestic pedagogical science paid attention to the use of such a teaching method back in the 20s, it was then that progressive scientists and practitioners tried to introduce a method of independently acquiring knowledge in extracurricular activities. However, the social conditions of that time were not conducive to the development of such methods, since ideology reduced the learning process only to the transfer of certain information in ready-made form.
The partial search method involves such complex tasks as developing the skills to see problems and pose questions, build your own evidence, draw conclusions from the facts presented, make assumptions and make plans for testing them. As one of the options for the partial search method, they also consider the way of fragmenting a large problem into a set of smaller subtasks, as well as constructing a heuristic conversation consisting of a series of interrelated questions, each of which is a step towards solving a general problem and requires not only the activation of existing knowledge , but also searching for new ones.

TECHNIQUES APPROPRIATE PARTIALLY SEARCH METHOD OF TEACHING

    inclusion of students in the argumentation of the hypothesis put forward by the teacher;

    tasking students to search for hidden key links in the reasoning proposed by the teacher;

    assigning students to solve several subproblems separated from the difficult initial one, after which students return to the original problem;

    guiding questions to students, helping them choose the right ways to solve a problem, while simultaneously pointing out different approaches to it;

    a task for students to find errors in reasoning, requiring original thought;

    organization of specific observations of the student, prompting the formulation of the problem;

    task for students to generalize the facts presented by the teacher in a special sequence;

    showing the method of action with partial disclosure of its internal connections with the student;

    task for students to put forward the next step of reasoning in the logic given by the teacher;

    demonstration of an object, phenomenon, encouraging the isolation of the essence;

    highlighting a part of a diagram or a record in color, orienting students to put forward a problem.

    Research method

Research method. This is a way of organizing the creative activity of students to solve problems that are new to them. When completing them, students must independently master the elements of scientific knowledge (recognize the problem, put forward a hypothesis, build a plan for testing it, draw conclusions, etc.). The main feature of this method, unlike the previous two, is to teach schoolchildren to see problems and be able to set tasks independently.
Tasks performed using the research method must include all elements of an independent research process (statement of the problem, justification, assumption, search for appropriate sources of necessary information, process of solving the problem).
When using this method, traditional teaching tools such as words, visuals, and practical work are used.

The center of gravity in teaching when applying the research method is transferred to the facts of reality and their analysis. At the same time, the word, which reigns supreme in traditional teaching, is relegated to the background.

TECHNIQUES ADEQUATE RESEARCH METHOD OF TEACHING

    assigning students to independently compose non-standard problems;

    assignment to students with an unformulated question;

    job with redundant data;

    asking students to make independent generalizations based on their own practical observations;

    tasking students with an essential description of an object without using instructions;

    task for students to determine the degree of reliability of the results obtained;

    task for students to calculate the mechanism of the phenomenon;

    a task for students “for instant guessing”, “for consideration”.

Let's summarize, once again compare the reproductive method (explanatory-illustrative) and the productive method (problematic, creative, creative)

    Active and intensive learning methods

In the 60s, didactics began to look for ways to activate students in the learning process. The cognitive activity of the student is expressed in a stable interest in knowledge, in independent various educational activities, etc. In the traditional learning process, the student plays a “passive” role: listens, remembers, and reproduces what the teacher gives. This forms knowledge at the level of familiarity and does little to develop the student.
One of the ways to activate a student is through new systems, technologies and teaching methods. The latter are called “active” (AMO). These are teaching methods in which the student’s activity is productive, creative, and exploratory in nature. These include didactic games, analysis of specific situations, solving problem problems, learning using an algorithm, etc.
The term Intensive Training Methods (IMT) refers to the delivery of training in short periods of time over long, one-time sessions and using active methods. Activating and intensifying learning also means relying on emotions and the subconscious. With the help of psychological training techniques, the perception, processing, memorization and application of information is activated. This is most often used in intensive foreign language courses, in teaching business, marketing, practical psychology, and pedagogy.

We will study these methods later. I'll tell you about them briefly.

1)Method (brainstorming, brainstorming, brainstorming ) is an operational method of solving a problem based on stimulating creative activity, in which participants in the discussion are asked to express as many possible solutions as possible, including the most fantastic ones. Then, from the total number of ideas expressed, the most successful ones are selected that can be used in practice.

2) Brain attack

Scientific research method -brain attack - can be used as a teaching method. Characteristics of the method. The leader explains to the participants the task (problem) that needs to be solved. Participants express ideas for solving a problem within a certain time (10-30 minutes). The ideas are then analyzed by experts. If necessary, the session can be repeated, clarifying the tasks. Rules of brainstorming: any ideas are expressed, even the most absurd, criticism of ideas at the time of attack is prohibited, but only their development, participants are recommended to sit at a round table or in other positions that facilitate interaction, all ideas are written down by the leader (his assistant) and provided with them review for participants.
At school, the method can be used when repeating a section (topic), when studying new material in a problematic way, and in other cases. The leader is the teacher, ideas are written on the board, overhead projector film. Results: students’ mental activity is activated, heuristic abilities develop.

3) Didactic game aims at training, development and education. The essence of the educational game is modeling and imitation. The game reproduces and simulates the reality and operations of the participants in a simplified form, simulating real actions.
Advantages of the game: the material being studied becomes personally significant for the student, an attitude towards the material is formed; the game stimulates creative thinking; creates increased motivation to learn; forms communicative qualities. Limitations in the use of the game: requires a lot of teacher development costs; Often the excitement of the game to win overshadows cognitive goals for the student. In addition to simulation games, there are conditional competitive games (KVN, etc.). Unfortunately, while attending the lessons of our teachers, we saw practically no didactic games.

4) Project method

Project method - This a method aimed at developing cooperation and business communication skills in a team, involving a combination of individual independent work with group classes, discussion of debatable issues, the presence of a research methodology within oneself, and the creation by students of the final product (result) of their own creative activity.

projects- This techniques, actions of students in their specific sequence to achieve a given task - solving a certain , meaningful for students and framed in the form of a certain final . Main MP consists of providing students with the opportunity to independently acquire knowledge in the process of solving practical problems or problems that require the integration of knowledge from various subject areas. If we talk about the project method as a pedagogical technology, then this technology involves a combination of research, search, and problem-based methods that are creative in nature.

As part of schoolingproject method can be defined aseducational technology aimed at acquiring new knowledge by students in close connection with real life practice, developing in them specific skills and abilities through the systematic organization of problem-oriented educational search.

5) Trainings

The purpose of the training is to develop specific skills on a particular topic (the knowledge is already available).

6) Methods of collective creativity

Cooperative activities – the process of organizing collective cognitive activity, during which the division of functions between students occurs, their positive interdependence of students is achieved, requiring individual responsibility of each.

Traditional pedagogy does not make enough use of productive methods.

In student-centered learning, the main factors in choosing methods are the task of organizing students’ productive activities and their acquisition of personal meaning.

The first and most important principle that can be offered to a creative teacher is this: “Whatever you want to say, ask!”

During the lesson, it is important to create a learning environment where the student would ask questions about his achievements, difficulties and successes, and build a trajectory of his own development together with the teacher.

The nomenclature and classification of teaching methods is characterized by great diversity depending on what basis is chosen for their development. From the very essence of the methods it follows that they must answer the question “how?” and show how the teacher acts and how the student acts.

Methods are divided according to dominant means into verbal, visual and practical. They are also classified depending on the main didactic tasks: methods of acquiring new knowledge; methods of developing skills, abilities and application of knowledge in practice; methods of testing and assessing knowledge, skills and abilities.

This classification is supplemented by methods of consolidating the material being studied and methods of independent work by students. In addition, the variety of teaching methods is divided into three main groups:

^ organization and implementation of educational and cognitive activities ;

^ stimulation and motivation of educational and cognitive activities awn;

^ control and self-control for the effectiveness of educational and cognitive activities.

There is a classification that combines teaching methods with corresponding teaching methods: information-generalizing and performing, explanatory and reproductive, instructive-practical and productive-practical, explanatory-motivating and partially searching, motivating and searching.

The most optimal classification of teaching methods proposed by I.Ya. Lerner and M.N. Skatkinsh, in which the nature of educational and cognitive activity (or method of assimilation) of students in their assimilation of the material being studied is taken as a basis. This classification includes five methods:

> explanatory and illustrative (lecture, story, work with literature, etc.);

* reproductive method;

^ problematic presentation;

^- partial search (heuristic) method;

> research method.

These methods are divided into two groups:

^ reproductive(1 and 2 methods), in which the student assimilates ready-made knowledge and reproduces (reproduces) methods of activity already known to him; ^ productive ( 4 and 5 methods), characterized in that the student acquires (subjectively) new knowledge as a result of creative activity. Problem presentation occupies an intermediate position, since it equally involves both the assimilation of ready-made information and elements of creative activity. However, teachers usually, with certain reservations, classify problematic presentation as productive methods. Taking this into account, let's consider both groups of methods.

a) Reproductive teaching methods

Explanatory and illustrative method.

It consists in the fact that the teacher communicates ready-made information through various means, and the students perceive, realize and record this information in memory. The teacher communicates information using the spoken word (story, lecture, explanation), the printed word (textbook, additional aids), visual aids (pictures, diagrams, films and filmstrips, natural objects in the classroom and during excursions), practical demonstration of methods of activity (showing a method for solving a problem, proving a theorem, methods for drawing up a plan, annotations, etc.). Students listen, watch, manipulate problems and knowledge, read, observe, relate new information to previously learned information, and remember.



Explanatory and illustrative method- one of the most economical ways of transmitting the generalized and systematized experience of humanity. The effectiveness of this method has been proven by many years of practice, and it has won a strong place at all levels of education. This method incorporates as means and forms of implementation such traditional methods as oral presentation, work with a book, laboratory work, observations on biological and geographical sites, etc. But when using all these various means, the activities of the students remain the same - perception, comprehension, memorization. Without this method it is impossible to ensure any of their targeted actions. Such an action is always based on some minimum of his knowledge about the goals, order and object of the action.

Reproductive method. To acquire skills and abilities through a knowledge system, the activities of students are organized to repeatedly reproduce the knowledge communicated to them and the methods of activity shown. The teacher gives tasks, and the students complete them -

solve similar problems, draw up plans, reproduce chemical and physical experiments, etc. How difficult the task is and the student’s abilities determine how long, how many times and at what intervals he should repeat the work.

Reproduction and repetition of a method of activity according to a model are the main feature of the reproductive method. The teacher uses the spoken and printed word, visual different types, and the students complete the tasks, having a ready-made sample.

Both described methods enrich students with knowledge, skills and abilities, form their basic mental operations (analysis, synthesis, abstraction, etc.), but do not guarantee the development of creative abilities, do not allow their systematic and purposeful formation. This goal is achieved through productive methods. -

b) Productive teaching methods

The most important requirement for educational institutions and an indispensable condition for scientific, technical and social progress is the formation of the qualities of a creative personality. An analysis of the main types of creative activity shows that with its systematic implementation, a person develops such qualities as “quickness of orientation in changing conditions, the ability to see a problem and not be afraid of its novelty, originality and productivity of thinking, ingenuity, intuition, etc., etc. i.e. such qualities, the demand for which is very high in the present and will undoubtedly increase in the future.

The condition for the functioning of productive methods is the presence of a problem. We use the word “problem” in at least three senses. An everyday problem is an everyday difficulty, overcoming which is important for a person, but which cannot be solved on the spot with the help of the opportunities that a person currently has. A scientific problem is a current scientific problem. And finally, the educational problem is | As a rule, a problem has already been resolved by science, but for the student it appears as new, unknown. An educational problem is a search task for which the learner needs new knowledge, and in the process of solving which this knowledge must be acquired.

In solving an educational problem, four main stages (stages) can be distinguished:

> creating a problematic situation;

^ analysis of the problem situation, formulation of the problem and its presentation in the form of one or more problematic tasks;

^ solving problematic problems (problems) by putting forward hypotheses and consistently testing them; * checking the solution to the problem.

Problem situation is a mental state of intellectual difficulty caused, on the one hand, by an acute desire to solve a problem, and on the other, by the inability to do this with the help of an existing stock of knowledge or with the help of familiar methods of action, and creating a need to acquire new knowledge or search for new methods of action. To create a problem situation, a number of conditions (requirements) must be met: the presence of a problem; optimal problem difficulty; the significance for students of the result of solving the problem; the presence of cognitive needs and cognitive activity among students.

Analysis of the problem situation- an important stage in the student’s independent cognitive activity. At this stage, what is given and what is unknown, the relationship between them, the nature of the unknown and its relationship to the given known is determined. All this allows us to formulate the problem and present it in the form of a chain of problematic tasks of one task). A problematic task differs from a problem by its clear definition and limitation of what is given and what should be determined.

Correct formulation and transformation of the problem into a chain of clear and specific problematic tasks is a very significant contribution to solving the problem. Next, you need to consistently work with each problematic task separately. Assumptions and conjectures are put forward about a possible solution to the problem problem. From a large number of guesses and assumptions, as a rule, several hypotheses are put forward, i.e. educated guesses are sufficient. Then problematic problems are solved by sequential testing of the hypotheses put forward.

Checking the correctness of solutions to a problem involves comparing the goal, the conditions of the problem and the result obtained. Great importance has an analysis of the entire path of the problematic search. It is necessary, as it were, to go back and look again to see if there are other clearer and clearer formulations of the problem, more rational ways of solving it. It is especially important to analyze errors and understand the essence and reasons for incorrect assumptions and hypotheses. All this allows you not only to check the correctness of the solution to a specific problem, but also to gain valuable meaningful experience and knowledge, which is the main acquisition of the student.

The role of the teacher and students at the four considered stages (stages) of solving an educational problem can be different: if all four stages are performed by the teacher, then this is a problematic presentation. If all four stages are performed by the student, then this is a research method. If some stages are carried out by the teacher, and some by the students, then a partial search method takes place.

Learning using productive methods is usually called problem-based learning .

Reproductive and problem-search methods of teaching are identified primarily on the basis of assessing the degree of creative activity of schoolchildren in learning new concepts, phenomena and laws.
Reproductive methods. The reproductive nature of thinking involves the active perception and memorization of educational information communicated by a teacher or other source. The use of these methods is impossible without the use of verbal, visual and practical teaching methods and techniques, which are, as it were, the material basis of these methods.
When constructing a story reproductively, the teacher formulates facts, evidence, definitions of concepts in a ready-made form, and focuses on the main thing that needs to be learned especially firmly.
A lecture is structured in a similar way, in which certain scientific information is presented to the listeners, corresponding notes are made on the board, recorded by the listeners in the form of short notes.
A reproductively organized conversation is conducted in such a way that the teacher during it relies on facts already known to the students, on previously acquired knowledge and does not set the task of discussing any hypotheses or assumptions.
Visualization in the reproductive method of teaching is also used for the purpose of more active and lasting memorization of information. An example of such clarity, for example, is the supporting notes used in the experience of teacher V.F. Shatalov. They consistently display especially bright numbers, words and sketches that activate the memorization of the material.
Practical tasks of a reproductive nature are distinguished by the fact that during their course, students apply previously or just acquired knowledge according to a model. At the same time, during practical work, students do not independently increase their knowledge. Reproductive exercises are especially effective in facilitating the development of practical skills, since the transformation of a skill into a skill requires repeated actions according to a model.
Reproductive methods are used especially effectively in cases where the content of educational material is primarily informative, represents a description of methods of practical action, is very complex or fundamentally new so that students can carry out an independent search for knowledge.
Programmed training is most often carried out on the basis of reproductive methods.
In general, reproductive teaching methods do not allow adequate development of schoolchildren’s thinking, and especially independence and flexibility of thinking; to develop students' search skills. When used excessively, these methods contribute to the formalization of the process of acquiring knowledge, and sometimes simply to cramming. Reproductive methods alone cannot successfully develop such personality qualities as a creative approach to work and independence. All this requires the use, along with them, of teaching methods that ensure the active search activity of schoolchildren.
Problem-search methods of teaching. Problem-search methods are used during problem-based learning. When using problem-search methods of teaching, the teacher uses the following techniques: creates a problem situation (poses questions, proposes a task, an experimental task), organizes a collective discussion of possible approaches to resolving a problem situation, confirms the correctness of the conclusions, puts forward a ready-made problem task. Students, based on previous experience and knowledge, make assumptions about ways to resolve a problem situation, generalize previously acquired knowledge, identify the causes of phenomena, explain their origin, and choose the most rational option for resolving a problem situation.
Problem-based learning methods are also used in practice using verbal, visual and practical teaching methods. In this regard, it is customary to talk about methods of problematic presentation of educational material, about problematic and heuristic conversations, about the use of visual methods of problem-search type, about carrying out problem-search practical work or even research-type work.
The presentation of educational material by the method of a problem story and a problem-based lecture assumes that the teacher, in the course of presentation, reflects, proves, generalizes, analyzes facts and leads the thinking of listeners, making it more active and creative.
One of the methods of problem-based learning is heuristic and problem-search conversation. During the course, the teacher poses a series of consistent and interrelated questions to the students, answering which they must make some assumptions and then try to independently prove their validity, thereby making some independent progress in mastering new knowledge. If during a heuristic conversation such assumptions usually concern only one of the main elements of a new topic, then during a problem-search conversation students resolve a whole series of problem situations. Therefore, the differences between these conversations are conditional and relate only to the measures of application of problem situations.
Visual aids in problem-search methods of teaching are no longer used for the purpose of activating memorization, but for setting experimental tasks that create problematic situations in the classroom. In addition, recently, visual aids have been increasingly produced, in which a certain educational situation is depicted in the form of a series of drawings and diagrams, requiring independent reflection by students in order to express some generalizations, identify dominant causes, etc.
Problem-search exercises are used when students can independently, on the instructions of the teacher, perform certain types of actions that lead them to mastering new knowledge. Such exercises, for example, are widely presented in a physics textbook for the VIII grade, where in the process of solving practical problems, schoolchildren do not apply, but rather acquire, new elements of knowledge, which are then comprehended and applied in practice when performing training exercises. Problem-search exercises can be used not only when approaching the assimilation of a new topic, but also when consolidating it on a new basis, that is, when performing exercises that deepen knowledge.
A valuable type of problematic practical work is research laboratory work, during which students, for example, independently determine the laws of floating of bodies, the laws of oscillation of a mathematical pendulum, etc. Such laboratory work is carried out before studying the theory and confronts students with the need to make some educational discoveries. Experimental work at the school site is of a similar nature, when students solve available research problems.
Problem-search methods are used primarily for the purpose of developing skills in creative educational and cognitive activity; they contribute to a more meaningful and independent acquisition of knowledge. These methods are used especially effectively in cases where the content of educational material is aimed at the formation of concepts, laws and theories in the relevant field of science, and not at the communication of factual information, the development of laboratory and experimental skills and work skills; when the content of the educational material is not fundamentally new, but logically continues what has been previously studied, on the basis of which students can take independent steps in the search for new knowledge; when the content is available for schoolchildren to independently search for, i.e., problem situations are in the zone of proximal development of schoolchildren’s cognitive abilities; when the content reveals cause-and-effect and other connections between phenomena, leads to generalizations, etc. Search methods are used in cases where teachers have prepared students for activities to resolve problem situations.
Compared to reproductive methods, search learning has a number of weaknesses that do not allow it to be the only type of learning in school. The weaknesses of search methods, compared to reproductive ones, include the significantly greater time spent on studying educational material; their insufficient effectiveness in solving problems of developing practical skills, especially of a labor nature, where demonstration and imitation are of great importance; their weak effectiveness when mastering fundamentally new sections of educational material, where the principle of apperception (reliance on previous experience) cannot be applied, when studying complex topics where a teacher’s explanation is extremely necessary, and independent search is inaccessible to most schoolchildren.
In general, the above leads to the need to combine search methods with their other types described above. Practice shows that such a combination is necessary in many cases, since the content of the same topic contains elements of material containing problem situations, while others do not allow this to be done due to complexity, lack of basis for students to make independent decisions, or, conversely , because of their elementary nature, simplicity, and their purely informative nature. Therefore, the teacher intersperses elements of students’ search activity into the explanation or, conversely, introduces direct information about issues that are inaccessible to students’ own discovery into the process of independent search for knowledge. But this does not mean that only a combination of problematic and reproductive methods is always necessary. There are such teaching tasks, such content of the material, such specificity of schoolchildren’s preparedness, in which reproductive or search methods of teaching themselves, so to speak, in their pure form, can and should be applied.

The reproductive method of teaching is a method in which the application of what has been previously learned is carried out based on a pattern or rule. When using this method, students’ activities have the character of an algorithm.

The reproductive method of teaching is used mainly for the successful formation of skills in school-age children, promotes the accurate reproduction of acquired knowledge, their use according to the established model or in altered, but sufficiently identifiable situations. The teacher, using a system of tasks, competently organizes the educational activities of schoolchildren to repeatedly reproduce the knowledge given to them or the specified methods of school activities demonstrated. Even the name of this method outlines only the activity of the student, but from the full description of the method it is clear that it allows for the organizational activity of the teacher that encourages action. A qualified teacher practices the printed and spoken word, subject teaching aids, and his students use these same means to correctly complete tasks, as if having a model that the teacher told them or demonstrated. The reproductive method emerges during the oral reproduction of knowledge communicated to students, during a reproductive conversation, and during the solution of complex physical problems. This method is also used when organizing work of a laboratory and practical nature, the execution of which requires the presence of fairly accurate and detailed instructions.

In order to increase the effectiveness of the reproductive method, teachers and methodologists are developing a special structure of reproductive teaching methods, it includes exercises and tasks (called “didactic materials”), programmed materials that can establish feedback and complete self-control. However, it is necessary to remember the long-known truth that the number of repetitions is not always directly proportional to the quality of the acquired knowledge. Given the general importance of reproduction, the use of a large volume of assignments, tasks, and exercises of the same type reduces students’ interest in the material being learned. Therefore, it is necessary to strictly measure measures for the use of the reproductive method of education, while keeping records of the individual capabilities of schoolchildren. During teaching in schools, the reproductive method is usually used in smooth combination with explanatory and illustrative ones. Over the course of one standard lesson, an experienced teacher is able to explain new material to students using the explanatory and illustrative method, consolidate what has been newly learned by organizing its reproduction, and can also continue to explain new information again. Such an approximate change in teaching methods contributes to a change in the type and form of students’ activities, makes the school lesson more dynamic, and in this way increases the students’ interest in the subject being studied.

To acquire skills, abilities and knowledge through a system of special tasks, the activities of the students being trained are organized to reproduce the knowledge of their activities given to them more than once. The teacher must know what the reproductive method of teaching is - he presents tasks, and the student, in turn, carries them out - solves problems, actively makes plans, and so on. How difficult the task is and the mental abilities of the student directly determine how long, how many times and at what time intervals he must repeat this work. Scientists have found that the assimilation of new words during careful study of a foreign language requires that these words occur approximately 20 times over a certain period of time. In a word, we can say that reproduction and repetition of the method of activity according to a model are the main features of the reproductive method of teaching. This teaching method enriches schoolchildren with knowledge, skills and abilities, forms their main mental operations, such as comparison and generalization, analysis and synthesis, but cannot guarantee the development of creative abilities.

Reproductive education of schoolchildren usually includes a full perception of facts and phenomena, the process of understanding them (establishing the necessary connections, highlighting the main and main point, and so on), which accordingly leads to its understanding. The main feature of reproductive education is to correctly convey some obvious knowledge to students. The student must memorize new educational material, overload his memory, while other mental processes, such as alternative and independent thinking, in turn must be blocked. The reproductive nature of thinking characterizes the active acceptance and memorization of new information presented by teachers and other sources. The use of this method is not possible without the use of verbal, practical and visual methods and teaching techniques, which are the material basis of such methods. The following main features are distinguished in reproductive technologies. The main and significant advantage of this method is its economy. Due to this, it is possible to transfer a considerable amount of knowledge in a minimum period of time with very little personal effort. With repeated repetition, the strength of the acquired knowledge can be strong.

During the reproductive construction of the story, the teacher in a ready-made form presents facts, important definitions of certain concepts, smoothly focuses the attention of schoolchildren on the main things that should be learned first, and most importantly, so that the assimilation takes place in a lasting way. With reproductive methods, the clarity of school education is used for the purpose of more active and accurate memorization of the information received. Special reproductive exercises most effectively promote the development of practical skills and computer skills, since the transformation of skills into skills also requires repeated actions according to the established pattern. Reproductive methods are used to a particular extent in cases where the content of school educational material is informative in nature, is an accurate and detailed description of the methods of all practical actions on computers, and is the most difficult for schoolchildren to carry out independent search and processing of knowledge. Programmed learning most often occurs on the basis of the reproductive method. The method of reproductive direction in a computer science lesson is used when working using simulator programs, for example, such as a keyboard simulator, training and control programs, for example, the principle of computer operation, monitoring knowledge of practical and theoretical material, performing all kinds of introductory and training tasks, exercises with further commenting.

Introductory exercises are used when first getting acquainted with software tools and are usually performed under the strict guidance of your teacher. Tasks with commenting are used to develop in students the ability to correctly work with operations that are difficult to master normally. Thus, commenting will be useful during activities on formatting, as well as copying the taken text. Commenting leads the student to a clear understanding of each of his actions, allows teachers to make significant amendments to various student actions, and competently eliminate incorrect actions and interpretations. Training tasks are aimed at repeated repetition of necessary actions and operations in order to develop skills and abilities. Such exercises combine into one system of presented tasks, which involve a gradual increase in the degree of complexity, as well as creative independence in the activities of students.

In order to increase the effectiveness of the reproductive method, methodologists and didactics, together with psychologists, are developing such systems of tasks, exercises, and programmed materials that provide proper self-control, in other words, feedback. Great attention is paid to improving the methods of instructing all students. In addition to oral explanations and demonstrations of work methods, it is for these purposes that written instructions and detailed diagrams and designs are used, showing film clips and others, in labor lessons - such simulators that will provide full opportunity to quickly master the necessary skills and abilities. In general, the reproductive method of teaching does not provide the opportunity to adequately develop the mental thinking of schoolchildren, and this is especially true with regard to independence and flexibility of thinking, and the development of research skills in students. With the intensive use of these methods, there are often cases when this leads to the formalization of the educational process of acquiring new knowledge, and sometimes simply to ordinary cramming.

Therefore, along with the teaching method discussed above, it is also necessary to use teaching methods that organize the active search activity of students.

Explanatory and illustrative method. It can also be called information-receptive, which reflects the activities of the teacher (teacher) and student (student) with this method. It consists in the fact that the teacher communicates ready-made information through various means, and the students perceive, realize and record this information in memory. The teacher conveys information using the spoken word (story, lecture, explanation), the printed word (textbook, additional manuals), visual aids (pictures, diagrams, films and filmstrips, natural objects in the classroom and during excursions), practical demonstration of methods of activity ( showing a method for solving a problem, proof of a theorem, methods of drawing up a plan, annotations, etc.). Students listen, watch, manipulate objects and knowledge, read, observe, relate new information to previously learned information, and remember.

The explanatory and illustrative method is one of the most economical ways to convey the generalized and systematized experience of mankind. The effectiveness of this method has been tested by many years of practice, and it has won a strong place in schools of all levels, at all levels of education. This method incorporates, as means and forms of implementation, such traditional methods as oral presentation, work with a book, laboratory work, observations on biological and geographical sites, etc. But when using all these various means, the activities of the students remain the same same – perception, comprehension, memorization. Without this method it is impossible to ensure any of their targeted actions. Such an action is always based on some minimum of his knowledge about the goals, order and object of the action.

Reproductive method. To acquire skills and abilities through a system of tasks, students’ activities are organized to repeatedly reproduce the knowledge communicated to them and the methods of activity shown. The teacher gives tasks, and the student carries them out - solves similar problems, draws up plans, reproduces chemical and physical experiments, etc. How difficult the task is, and the abilities of the student determine how long, how many times and at what intervals he should repeat work. Learning to read and write clearly takes several years; learning to read takes much less time. It has been established that learning new words when learning a foreign language requires that these words be encountered about 20 times over a certain period of time. In a word, reproduction and repetition of a method of activity according to a model are the main feature of the reproductive method. The teacher uses the spoken and printed word, visual aids of various types, and the students complete tasks with a ready-made sample.

Both described methods enrich students with knowledge, skills and abilities, form their basic mental operations (analysis, synthesis, abstraction, etc.), but do not guarantee the development of creative abilities, do not allow their systematic and purposeful formation. This goal is achieved through productive methods.

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