Algorithmic learning is based on the development of appropriate models of thought processes, consistent mental actions that provide the solution of learning problems.

The basic concepts of this type of training are "algorithm" and "algorithmization". What is their essence?

An algorithm is a complete and precise prescription for the execution in a certain sequence of operations (actions) aimed at achieving a goal or solving a problem from a certain, given class of problems. This concept entered the theory and practice of education in the late 50s of the XX century. in connection with the development of programmed learning and the use of learning machines. The term "algorithmization" means: 1) a section of computer science that studies methods and techniques for constructing algorithms, as well as their properties; 2) the stage of solving the problem, which consists in constructing a solution algorithm based on the condition of the problem and the requirements for the final results. In its last meaning, this term is used when considering the essence of the designated problem. Algorithmization of learning consists in the development and implementation of algorithms for students or algorithms for teaching persons (or machines). An important theoretical and methodological basis for this type of learning, as well as for programmed learning, is the cybernetic approach. The main goal of algorithmic learning is to increase the efficiency of managing the learning process. The teacher's activity in algorithmization of students' activities, that is, dividing it into separate interconnected elements (actions, steps), consists of the following operations: highlighting the conditions necessary for the implementation of learning actions; highlighting the learning activities themselves; determination of methods of communication between teaching and learning activities (V.A. Slastenin and others).

Algorithms for students are divided into two groups: a) algorithms related to the subject being studied and allowing to successfully solve problems specific to this subject; b) algorithms of learning (assimilation), which prescribe the actions necessary for the assimilation of both the intended algorithms and the subject material.

Pedagogical evaluation of algorithmic learning. This type of education is valuable primarily because it equips students with the means to control their thinking and practical actions, that is, it forms in the student the necessary personality traits as a subject of their own learning activities. This type of training creates the necessary prerequisites for preparing students for creative activity, since in the process of algorithmization, students master the methods of activity, including mental activity. Algorithmization increases the weight of independent work of students and contributes, as already noted, to the improvement of the management of the educational process. At the same time, this type of training strictly formalizes the student's actions and deprives them of creative search. This is a significant drawback of algorithmic learning.

4. Personal-activity approach as the basis for organizing the educational process
Personal-activity approach - methodological concept of domestic psychology, considering psychology as a science of the generation and functioning of the psyche in the process of activity-based interaction of individuals with the environment.

The main postulate of this concept: the psyche is formed and manifested in activity. All other principles of psychology are based on this postulate: development, historicism, activity, objectivity, internalization-exteriorization, the unity of the structure of external and internal activity, a systematic analysis of the psyche, the dependence of mental reflection on the place of the object in the structure of activity.

Based on this concept, a theory of leading activity in mental development individual, the theory of the structural organization of activity: activity - action - operation, shift of motive to the goal, shift of the conditions of activity to the goal, means and conditions of activity, psychology and psychophysiology of regulation of activity; conceptual and psychological concepts of the meaning and meaning of actions, the hierarchy of personality motives are formed. The concept of the activity approach is widely and fruitfully used in all applied branches of domestic psychology (medical, pedagogical, engineering, legal, etc.).

By definition, the term "approach to learning" is ambiguous. These are: a) an ideological category that reflects the social attitudes of the subjects of education as carriers of social consciousness; b) global and system organization and self-organization of the educational process, including all its components and, above all, the subjects of pedagogical interaction themselves: a teacher (teacher) and a student (student). The approach as a category is broader than the concept of "learning strategy" - it includes it, defining the methods, forms, techniques of learning.

The foundations of the personality-activity approach were laid in psychology by the works of L.S. Vygotsky, A.N. Leontiev, S.L. Rubinstein, B.G. Ananiev, where the personality was considered as a subject of activity, which itself, being formed in activity and in communication with other people, determines the nature of this activity and communication. Personal approach, according to K.K. Platonov, this is the principle of personal conditioning of all mental phenomena person, his activities, his individual psychological characteristics.

The personal-activity approach in its personal component assumes that the student himself is at the center of learning - his motives, goals, his unique psychological make-up, i.e. the student, the student as a person. Based on the interests of the student, the level of his knowledge and skills, the teacher (teacher) determines the educational goal of the lesson and forms, directs and corrects the entire educational process in order to develop the student's personality. Accordingly, the goal of each lesson, lesson in the implementation of the personal-activity approach is formed from the position of each individual student and the entire group as a whole. For example, the goal of the lesson can be set as follows: "Today each of you will learn how to solve a certain class of problems." This formulation means that the student must reflect on the current, initial, current level of knowledge and then evaluate their successes, their personal growth.

5. Sign-complex training. Competence-based approach in modern education.
Sufficiently widespread in professional (higher and secondary) education is currently receiving sign-contextual, or contextual learning. In this direction of learning, educational information is presented in the form of educational texts (“signs”), and the tasks constructed on the basis of the information contained in them set the context for the future. professional activity. According to A.A. Verbitsky, the subject and social content of future professional activity is modeled in educational process by all didactic means, forms, methods, among which one of the main places is occupied by a business game. A business game is a form of active activity learning. It involves the definition of goals (actually playing and pedagogical: didactic and educational), the content of the game and the presence of game and simulation models (A.A. Verbitsky, N.V. Borisova). The simulation model, which reflects a didactically processed (generalization, simplification, problematization) fragment of professional reality, is the subject basis of students' quasi-professional activities.

Teaching technology (pedagogical technology) is a new (since the 50s of the XX century) direction in pedagogical science, which is engaged in the design of optimal learning systems, the design of educational processes.

Pedagogical technology is based on the idea of ​​complete controllability of the educational process, design and reproducibility of the training cycle. Traditional learning is characterized by the uncertainty of setting goals, poor controllability of learning activities, the impossibility of repeating learning operations, weak feedback, and subjectivity in assessing the achievement of goals. Specific features of learning technology:

Development of diagnostically set learning goals;

Orientation of all educational procedures to the guaranteed achievement of educational goals;

Operational feedback, assessment of current and final results;

Reproducibility of training procedures.

Setting diagnostic learning goals. To achieve a given (desired) level of learning, it is necessary to set goals diagnostically, that is, to determine them through the results expressed in the actions of students, which (actions) the teacher can measure and evaluate. In traditional teaching, the goals are set vaguely, “non-instrumentally”: “to study the theorem”, “solution of quadratic equations”, “read the text expressively”, “introduce the principle of action”. These goals do not describe learning outcomes and are difficult to verify. In the diagnostic goal, the student's actions are described in terms of: knows, understands, applies, etc.

The learning technology focuses on the guaranteed achievement of goals and the idea of ​​complete assimilation through learning procedures. After determining the diagnostically set goals for the subject, the material is divided into fragments - educational elements to be mastered. Then verification work is developed in sections (the sum of educational elements), then training is organized, verification - current control, adjustment and repeated, in other operations, training. And so on until the complete assimilation of the given educational elements. Current assessments are made according to the type of "mastered - not mastered." The results are explained to each student.

1. Communication of the necessary knowledge.

2. Formation of skills at the reproductive level.

2.1. Demonstration of activities in general and by elements (this can be combined with the announcement of titles on the principle of “demonstration + explanation”).

2.2. Organization of skill development in simplified conditions.

2.3. Organization of independent practice with continuous feedback and positive assessment of the teacher.

3. Transition to the search, productive phase.

3.1. Organization of problem situations - solving specific problems, simulation modeling.

3.2. Mandatory analysis by students of their activities with the teacher and the group.

The foregoing can serve as a support for the teacher when studying a section, topic.

An essential feature of learning technology is the reproducibility of the learning cycle, i.e., the possibility of repeating it by any teacher. The learning cycle contains the following elements: setting learning objectives; preliminary assessment of the level of training; training, a set of training procedures; adjustment according to feedback results; final evaluation of the results and setting new goals. In this case, the educational process acquires a modular character: it consists of blocks-modules, each of which represents a learning cycle on a topic.

Feedback, objective control of knowledge is an essential feature of learning technology. Measuring the level of assimilation of knowledge and their assessment are currently uncertain and subjective: in the programs, learning outcomes are described in a non-diagnostic way, it is impossible to measure and evaluate them objectively. This is the reason for the formalism in the assessment of knowledge. However, the rejection of knowledge assessment is generally unrealistic: the record of progress is one of the components of the management of the didactic process and the entire teaching system.

In connection with the development of programmed learning, the concept of algorithm , algorithmization of learning. In didactics, an algorithm is an unambiguously understood prescription for performing strictly sequential operations with educational material, leading to the solution of a problem or a class of problems. The algorithm underlies the learning program of the algorithmic type (the majority of these are now), however, the teacher can use learning by the algorithm in other types of learning, creating algorithms for students, instructions for mastering knowledge, rules, solving problems, performing exercises, practical work(for example, in mathematics - an algorithm for adding two positive numbers, finding a common denominator, etc.). On fig. 7.4 is an example of a species recognition algorithm simple sentences when learning syntax. Analyzing the sentence, the student must consistently answer the questions.

Rice. 7.4.

The use of algorithms in teaching allows the teacher to more strictly control the actions of students and, therefore, more effectively achieve results, but under certain conditions: the success of students' work with algorithms depends on the initial subject knowledge and skills, as well as on the mental skills necessary to carry out logically sequential actions, and a number of other factors.

Algorithms for students are of different levels: some are designed for the assimilation of specific material (as in the above example), others provide a solution to a class of problems, others prescribe the actions of learning, assimilation. There are also algorithms for the teacher, describing his actions to develop a specific learning process.

Block and Modular Learning

As the development of programming ideas in learning, block learning is born, then modular learning. Idea block learning consists in such an organization of educational material that would provide a balance between the clear instructions of the program and the freedom of action of the student, which makes the program flexible, therefore this species learning is sometimes called semi-programmed. Block programming provides students with a variety of intellectual operations and the rapid use of acquired knowledge in solving certain problems. The creator of block education, Polish didactics Cheslaw Kupisiewicz, distinguishes the following blocks of the training program: 1) informational; 2) test-information (checking what has been learned); 3) correctional and informational (in case of an incorrect answer - additional training); 4) problematic (solving problems based on acquired knowledge); 5) block of verification and correction.

Modular learning(as the development of a block) provides for such an organization of the learning process, in which the student works with the curriculum, which includes modules (blocks): target, information, operational, i.e. methodological guide to achieve learning goals, as well as a block of knowledge testing. This type of learning management is being developed mainly for higher education and adult education, although it can also be applied to secondary schools.

Modern communication tools make it possible to create complex electronic learning systems, telecommunication networks, which in the future have great didactic capabilities. In particular, interactive programs are being developed in which the student works in an interactive mode with complex information systems, databases, expert systems that perform didactic functions. Currently, the carrier of the training program is a computer. Teachers and scientists, methodologists, didactics specialists have the opportunity to create a variety of educational software products for computer, e-learning, such as skills training, educational and familiarization exercises, educational and cognitive games, memorization exercises, modeling - mastering concepts.

The history of programmed learning has shown that although the period of belief in its unlimited possibilities has passed, programmed learning based on developing technology has great prospects, especially in combination with other approaches: traditional, problem-based and distance learning, information technology. The concept of programs that manage learning is a fruitful didactic basis for creating modern learning systems.

Distance (distance) education. Distance learning is understood as a purposeful process of interactive interaction between teachers and students among themselves and with learning tools, invariant (indifferent) to their location in space and time, which is implemented in a specific pedagogical system. Sometimes the term "distance learning" is used to refer to forms of learning that existed long before the advent of computers. Correspondence, correspondence, home education, external study - these types of education claim the name distant, because they mean learning at a distance, distances. Considering this circumstance, concretizing the concept distance learning given above, we will try to formulate it as follows: distance learning- this is learning using telecommunications, in which subjects of learning remote from each other (pupils, students, teachers, moderators, etc.) carry out the educational process, accompanied by the creation of educational products and their internal changes (increments). Modern distance learning is carried out mainly with the help of Internet technologies and resources.

Distance learning is based on self-learning principle. Its implementation depends entirely on self-organization by students of independent cognitive activity, i.e. teaching, and for this, as rightly noted in the works of distance learning researchers (E. S. Polat, A. E. Petrova, A. V. Khutorskoy, etc.), the student must possess the skills:

• - independently acquire knowledge using various sources of information;
• - work with this information at a convenient time for him;
• - select, design the necessary and sufficient methods of cognitive activity, adequate to the goals and objectives of the study;
• – to apply the obtained and assimilated knowledge in the course of solving various real problems of social and professional significance;
• - interact with the teacher on the most significant and complex issues of the assimilated fragment of the training course;
• - constantly in the course of working on a training course to return to what has been passed, studying it each time from new positions and more deeply.

The specificity of teaching in distance learning is its focus on solving specific didactic tasks: the search for knowledge, their comprehension and consolidation; formation and development of practical skills, as well as intellectual, organizational and gnostic skills; further generalization and systematization of knowledge as the student progresses from the lowest stage of his formation as a specialist, professional to the highest. That is why, from the position of a teacher, his functions in the distance learning system, independent work appears for him and for the student as a means of organization, pedagogical guidance, management of educational and cognitive activities (teaching) of students, which they carry out in overall structure distance learning process based on interactive television(two-way TV), computer telecommunication networks (regional, global), a combination of CD and Internet technologies.

In order for such a system of organization and self-organization of educational work in the process of distance learning to function normally, the student - at first at the level of theoretical ideas - should understand:

• a) activity goals, i.e. the final results that he must achieve in the process of studying this discipline at the time given to him (the final state of the experience being gained);
• b) forms and methods of control, which allow him to assess the degree of achievement of the goal, as well as guidelines that should be relied upon when choosing a strategy and tactics of educational and cognitive activity. In addition, it is necessary to have appropriate programs that organize the conscious cognitive activity of the student to master the planned knowledge and skills, providing him with all the necessary information about the content and standards of educational activity in the optimal amount, taking into account the psychological and pedagogical characteristics of the perception of this information;
• c) motivational attitude, interest and conviction in the importance and necessity of acquiring the indicated knowledge and skills, which would encourage him to be active and ensure the functioning of channels of internal and external feedback.

The interest, independence, consciousness and activity of students in the process of distance learning largely depend on the nature and organization of their activities; from forms and methods of control, self-control, and sometimes mutual control; from those results and attitudes towards them, to which students come in the learning process. And the better the body of knowledge to be mastered is constructed and systematized, the more the objectives of the study and the importance of mastering this system of knowledge and skills are clear to the students, the better and more firmly this knowledge is assimilated, and the skills are developed. When developing distance learning programs, the teacher must assess what knowledge, for what purpose and to what extent he intends to form students as a result of studying this material. To do this, it is necessary to take into account the features of certain types of training sessions and determine the totality of various types of activities of the subjects of training, which will ensure the achievement of the goals set in the formation of the mental and mental qualities of the trainees. The most important role in this is played by the establishment of the sequence of actions of trainees, the structure of the operational composition of actions (definition of performing, evaluative and especially indicative actions), the search and finding ways to increase the motivation of trainees.

The development of distance (distance) learning is due to a number of its advantages and capabilities. First of all, these are more flexible conditions for education for children who could not or cannot carry it out in the usual way due to their remoteness from qualified educational institutions or due to physical defects, individual features and needs. Distance learning can satisfy additional personal educational needs students. A talented student of a rural school, a student of a peripheral university, etc. can, for example, simultaneously study remotely from highly qualified specialists located anywhere in the country and the world, without leaving their place of residence. With the help of electronic networks, a student from any city, town or village has access to the treasures of world culture and science, can study at prestigious universities in the world.

The dominant feature of distance learning is the personal productive activity of students, built with the corresponding personal interests and requests, the needs of the student with the help of modern means of telecommunications. This approach involves the integration of information and pedagogical technologies that ensure the interactivity of the interaction between the subjects of education and the productivity of the educational process. The exchange and forwarding of information in this case play the role of an auxiliary environment for the organization of productive educational activities of students. In parallel with the creation of educational products by students, their internal educational personal increments take place. The personal, creative and telecommunicative nature of education are the main features of distance learning.

The experience of using Internet resources in education revealed the problem of information overload and disorganization of the student, who is unprepared for productive activities. To combat these phenomena, a student entering the ocean of Internet information must be able not only to assimilate, but also to create their own educational products. The student's creative position, which prevents him from "absorbing" ecologically unfiltered information, is necessary condition personality-oriented distance education. In order to implement this focus in distance learning, the following pedagogical principles: - productive orientation of learning;

• – individualization of education;
• – openness of the content of education and the educational process;
• - priority of activity content over information content;
• – integration of pedagogical and telecommunication technologies;
• – the optimal combination of face-to-face and remote forms student activities;
• – activity evaluation criteria.

Verification should not be informational, but activity learning outcomes. In this case, the face-to-face test or distance exam for students is based on reflective questions and tasks such as: "Describe how you achieve your results." Such a control system evaluates not so much the student's materialized product, for example, an abstract that can be taken from a "collection of abstracts", but the student's personal activity, which characterizes his internal educational increments.

• When writing this section, the material of the Doctor of Pedagogical Sciences, Corresponding Member of the Russian Academy of Education A. V. Khutorsky was used.

In connection with the development of programmed learning, the concept of an algorithm has entered into theory and practice. algorithmization of learning. An algorithm in didactics is an unambiguously understood prescription for performing strictly sequential operations with educational material, leading to the solution of a problem or a class of problems. It should be clear to the teacher that the algorithm is the basis of the algorithmic type of training program (there are now most of them). It is important, however, that in other types of learning, the teacher can also use algorithmic learning, creating algorithms for students, instructions for mastering knowledge, rules, solving problems, performing exercises, and practical work. For example, an algorithm for adding two positive numbers, finding a common denominator, and many others in mathematics. Here is an example of an algorithm for recognizing types of simple sentences when learning syntax. Analyzing the sentence, the student must consistently answer the questions (see Diagram 4).

Scheme 4

The use of algorithms in teaching makes it possible to more strictly control the actions of students and, therefore, more effectively achieve results, but under certain conditions. The success of students' work with algorithms depends on the initial subject knowledge and skills, as well as on the mental skills necessary to carry out logically sequential actions, and a number of other factors.

Algorithms for students are of different levels: some are designed for the assimilation of specific material (as in the above example), others provide a solution to a class of problems, others prescribe the actions of learning, assimilation. There are also algorithms for the teacher, describing his actions to develop a specific learning process.

block learning

The ideas of programmed learning are currently being used in the concepts of block and modular learning. The idea of ​​block learning is to organize the educational material in such a way that would provide a balance between the clear instructions of the program and the student's freedom of action, which makes the program flexible and even received the name "semi-programming". Block programming provides students with a variety of intellectual operations and the operational use of acquired knowledge in solving certain problems. The Polish didactic C. Kupisiewicz, the creator of block learning, highlights such blocks of the training program. Information block; then test-information(check learned); then correctional information(in case of an incorrect answer - additional training); Further - problem block: solving problems based on the acquired knowledge; then also block checks and corrections. On the diagram it looks like this:

Scheme 5

Modular learning (as the development of block learning) is such an organization of the learning process in which the student works with a curriculum that includes modules (blocks): target, information, operational, that is, methodological guidance for achieving learning goals, knowledge testing block. This type of learning management is developed mainly for higher education and adult education.

Modern communication tools make it possible to create complex electronic learning systems, telecommunication networks, which in the future have great didactic capabilities. In particular, interactive programs are being developed in which the student works in an interactive mode with complex information systems, databases, expert systems that perform didactic functions. Currently, the carrier of the training program is a computer. Teachers and scientists, methodologists, didactics have the opportunity to create a variety of educational software products for computer and e-learning. Here are some types of products (in the first place - the most numerous, then - in descending order): skills training, educational and familiarization exercises, educational and cognitive games, memorization exercises, modeling, mastering concepts.

The history of programmed learning has shown that it has not found wide application in secondary and higher education, which at one time had great hopes. This is clear! The educational process is impossible without live human communication between students and a live teacher, who cannot be replaced by a machine. The use of the “technological” methods and methods of work described in this chapter can only be limited and is carried out in combination with other approaches: within the framework of distance learning, partly as an element of problem-based learning, as one of the ways to implement the principle of informatization of education, etc.

These are the main teaching models that have received varying degrees of distribution in modern school practice.

Introduction

Chapter 1

1.1. The essence of programmed learning

1.2. Learning algorithm

1.3. Algorithm and its main types

Conclusions on Chapter I

Literature

Introduction

The most important task pedagogical science is to improve the planning of the learning process as a whole and to increase the efficiency of managing the cognitive activity of students.

Search best ways learning management resulted in the creation of a new system of educational work, called programmed learning, one of the components of which is algorithmization.

At present, science and technology are developing so rapidly that the timely generalization of the flow of scientific information without the use of cybernetic means is a significant difficulty.

No less difficult is the communication of knowledge to students, as their volume increases from year to year, while the terms and methods of teaching remain unchanged. In this regard, an increasing number of teachers come to the conclusion about the insufficiency of traditional methods of teaching and the need to improve them based on the latest achievements of science and technology.

Computers have already appeared in schools, but this is not enough. The best option is to equip each classroom with such equipment and include elements of working on a computer in curricula in all subjects. But this requires a technical base. At present, only elements of programmed and algorithmic learning can be used in elementary grades. Therefore, the topic of this work is relevant today.

The development of programming and algorithmization in education was carried out by such scientists as P. Ya. Galperin, L. N. Landa, N. F. Talyzina. In their work and research, they proved the effectiveness of programmed learning and algorithmization.

Target term paper- theoretical substantiation of the need for algorithmization of the process of teaching younger students.

In accordance with the goal, the following tasks are defined:

Define the essence of the concept of "programmed learning" and "algorithmization";

Identify the main types of algorithms;

Determine the features of working with different types of algorithms.

Chapter 1

1.1. The essence of programmed learning

In psychological and pedagogical research, conventional or traditional education is considered to be poorly managed. According to the majority of domestic scientists and teachers, the main disadvantages of traditional education are the following:

1. The average overall pace of learning the material.

2. A single average volume of knowledge acquired by students.

3. An unreasonably large proportion of knowledge obtained by students in finished form through teachers without relying on independent work to acquire this knowledge.

4. Almost complete ignorance by the teacher of the progress of assimilation of the reported knowledge by students (no internal feedback and weak external feedback).

5. Lack of stimulation cognitive activity students, relying mainly on the teacher.

6. Predominance verbal methods presentations of knowledge that create objective preconditions for distraction of attention.

7. Difficulty in independent work of students with a textbook due to insufficient dissection of the educational material, dryness of the language, and almost complete absence of emotional impact.

The emergence of programmed learning is associated with an attempt to eliminate these and other shortcomings of conventional learning.

Programmed learning is a system of sequential actions (operations), the implementation of which leads to a pre-planned result.

A significant role in the formation of programmed learning was played by the famous psychologist B.F. Skinner, who in 1954 called on the pedagogical community to increase the effectiveness of teaching by managing the learning process, building it in full accordance with psychological knowledge about him.

The main postulate of B.F. Skinner's theory is the thesis that the result of a previous action (or rather, its psychological effect) affects subsequent behavior. Consequently, the behavior itself can be controlled by selecting certain rewards (reinforcements) for the right actions, thus stimulating further behavior in the expected direction.

The category of control acts as a central concept for constructing programmed learning. As N.F. Talyzina notes, “the real problem is that at all levels of education, education should be well managed, including elementary school and even preschool institutions” .

B.F. Skinner and his followers identified the laws by which behavior is formed, and on their basis formulated the laws of learning:

1. The law of the reinforcement effect: if the connection between the stimulus and the response is accompanied by a state of satisfaction, then the strength of the connections increases, and vice versa. Hence the conclusion: in the learning process, you need more positive emotions.

2. The law of exercises: the more often the connection between the stimulus and the response is manifested, the stronger it is (all data are obtained experimentally).

3. The Law of Readiness: Every connection between a stimulus and a response has an imprint nervous system in her individual, specific state..

B. F. Skinner put two requirements at the basis of the technology of programmed learning:

1) get away from control and move to self-control;

2) to transfer the pedagogical system to self-education of students.

The concept of programmed learning is based on general and particular didactic principles of consistency, accessibility, systematicity, and independence. These principles are implemented during the execution of the main element of programmed learning - a training program, which is an ordered sequence of tasks. For programmed learning, the presence of a "didactic machine" (or a programmed textbook) is essential. In this training, to a certain extent, an individual approach is implemented as an account of the nature of the student's mastering the program. However, the main thing remains that the process of assimilation, development of skills is controlled by the program.

Programmed learning in the late 60s - early 70s. received a new development in the works of L.N. Landa, who proposed to algorithmize this process.

An algorithm is a rule (the converse assertion is illegal) that prescribes a sequence of elementary actions (operations), which, due to their simplicity, are unambiguously understood and performed by everyone; this is a system of instructions (prescriptions) about these actions, about which of them and how to perform them One of the advantages of learning algorithms is the possibility of formalization and model representation of this process.

The advantages of management, programming in the educational process are most fully and theoretically justified in teaching based on the psychological theory of the gradual formation of mental actions by P. Ya. Galperin.

In the theory of P. Ya. Galperin, the process of forming mental actions goes through 5 stages:

1. Preliminary acquaintance with the action, with the conditions for its implementation.

2. Formation of an action in a material form with the deployment of all the operations included in it.

3. Formation of action in external speech.

4. Formation of action in inner speech.

5. Transition of action into deep convoluted thought processes.

Together with N.F. Talyzina, P.Ya. Galperin put this theory into practice in the learning process. The following provisions developed in Russian psychology by L. S. Vygotsky, S. L. Rubinshtein, A. N. Leontiev served as the initial theoretical postulates:

Every internal psychic is a transformed, internalized external; first, the mental function appears as interpsychic, then as intrapsychic;

The psyche (consciousness) and activity are a unity, not an identity: the mental is formed in activity, the activity is regulated by the mental (image, thought, plan);

mental, internal activities has the same structure as the external, subject;

Psychic development has a social nature: the development of human individuals proceeded not through the development of internal experience, hereditarily laid down by species experience, but through the assimilation of external social experience, fixed in the means of production, in language;

The active nature of the mental image allows us to consider action as its unit. It follows from this that the formation of images can be controlled only through the actions by which they are formed.

P. Ya. Galperin set fundamentally new tasks for learning: to describe any formed action by the totality of its properties to be formed; create conditions for the formation of these properties; develop a system of guidelines necessary and sufficient to control the correctness of the formation of an action and avoid errors. P.Ya.Galperin distinguished two parts of the objective action being mastered: its understanding and the ability to perform it. The first part plays the role of orientation and is called indicative, the second - executive. P.Ya.Galperin attached particular importance to the indicative part, considering it to be the “managing authority”; later he would call it "navigator's card".

As a result of the research carried out by P.Ya. Galperin and his students, it was found that:

a) along with actions, sensory images and concepts about the objects of these actions are formed. The formation of actions, images and concepts are different aspects of the same process. Moreover, schemes of actions and schemes of objects can largely replace each other in the sense that certain properties of an object begin to designate certain modes of action, and certain properties of its object are assumed behind each link of action;

b) the mental plan is only one of the ideal plans. The other is the plane of perception. It is possible that the third independent plan of activity of an individual is the plan of speech. In any case, the mental plane is formed only on the basis of the verbal form of the action;

c) the action is transferred to the ideal plan either in its entirety, or only in its tentative part. In this last case, the executive part of the action remains on the material plane and, changing along with the orienting part, eventually turns into a motor skill;

d) the transfer of an action to an ideal, in particular mental, plan is accomplished by reflecting its objective content by means of each of these plans and is expressed by multiple successive changes in the form of the action;

e) the transfer of action to the mental plane, its internalization constitute only one line of its changes. Other, inevitable and no less important lines are changes: the completeness of the links of action, the measure of their differentiation, the measure of their mastery, tempo, rhythm and strength indicators. These changes, firstly, cause a change in the methods of performance and forms of feedback, and secondly, determine the achieved quality of the action. The first of these changes leads to the transformation of an ideally performed action into something that is revealed in self-observation as a mental process; the latter allow you to control the formation of such properties of action as flexibility, reasonableness, consciousness, criticality, etc. . P.Ya. Galperin considered rationality to be the main characteristic of the actions performed.

The theory of the phased formation of mental actions was the foundation of a new direction developed by N.F. Talyzina - the programming of the educational process. Its purpose is to determine the initial level of cognitive activity of students, new formed cognitive actions; the content of learning as a system of mental actions, means, i.e. actions aimed at mastering a wide circle of knowledge on the third type of orientation (in terms of extended speech); five main stages in the formation of mental actions, each of which has its own requirements for actions; development of an algorithm (system of prescriptions) for actions; feedback and providing on its basis the regulation of the learning process.

Essential for the implementation of the direction of programming training are General characteristics actions: in form (material, external speech, speech “to oneself”, mental);

according to the degree of generalization; as it expands; in the process of mastering and whether the action is given in finished form or mastered independently.

In action, orienting, executive and control functions are distinguished. According to N.F. Talyzina, “any human action is a kind of microcontrol system, including the “Control body” (the indicative part of the action), the executive, “working body” (the executive part of the action), the tracking and comparing mechanism (the control part of the action)” .

The central link in the formation of mental actions is its indicative basis, characterized by completeness, generalization and the degree of independent mastering of actions. The third type of the orienting basis of actions (in extended speech), differing in the optimum of completeness, generalization, independence, ensures the highest efficiency in the formation of mental actions.

Correlating existing approaches to learning, N.F. Talyzina notes that, compared with the behavioral theory of programming, the theory of the gradual formation of mental actions “builds the most rational structure (system of cognitive actions)”; it is the true management of human development. At the same time, this theory serves as an example of the consistent implementation of the activity approach to learning.

In general, programmed learning is characterized by a combination of five features/principles:

1) the presence of a measurable goal of educational work and an algorithm for this goal;

2) the division of the educational part into steps associated with the appropriate doses of information that ensure the implementation of each step;

3) completion of each step by self-examination, the results of which make it possible to judge how successful he is, and the offer to the student is sufficient effective remedy for this self-examination and, if required, the appropriate corrective action;

4) use of an automatic, semi-automatic (matrix, for example) device;

5) individualization of training (within sufficient and affordable limits).

A special role belongs to the creation of appropriate programmed manuals. Programmed manuals differ from traditional ones in that in the latter only educational material is programmed, and in programmed ones - not only educational material, but also its assimilation and control over it. When teaching, it is very important to note the formation of semantic barriers in time. They arise when the teacher, operating with certain concepts, means one thing, and the students understand another.

Minimization and overcoming of semantic barriers is one of the hard-to-solve problems of teaching. In this regard, the didactic support of programmed learning necessarily includes feedback: internal (to the student) and external (to the teacher).

The material basis of programmed learning is a training program, which is a manual specially created on the basis of the five principles noted above. In this manual, as already mentioned, not only is it programmed educational material, but also its assimilation (understanding and memorization), as well as control. The training program performs a number of teacher functions:

Serves as a source of information;

Organizes the educational process;

Controls the degree of assimilation of the material;

Regulates the pace of studying the subject;

Gives necessary explanations;

Prevents errors, etc..

The student's action is usually immediately controlled by the responses. If the action is performed correctly, then the student is asked to proceed to the next step. In case of an incorrect action, the training program usually explains the characteristic mistakes made by the trainees.

Thus, the training program is an indirect material implementation of the algorithm of interaction between the student and the teacher, which has a certain structure. It begins with an introductory part in which the teacher directly addresses the student, indicating the purpose of this program. In addition, in the introductory part there should be some “enticement” to interest the student, as well as short instruction for the execution of the program.

The main part of the tutorial consists of several steps. They are introductory, introductory-training or training. Each step may include several frames if it is a computer program. On one, brief, measurable information is given and then a task or question, so that the student can give his decision, answer the question posed, i.e. perform some operation Such a frame is called information-operational. If the student answered correctly, information is displayed confirming the correctness of his answer, and an incentive is given for further work. If the student answered inaccurately or incorrectly, a frame appears with leading questions or information explaining his mistake.

The final part of the training program is of a general nature: bringing into the system the material reported in the main part, instructions for checking the generalized data (self-checking or checking by the teacher).

If the training program is machineless (now this is rarely practiced, since there is a computer), then it is recommended to draw up a methodological note for the teacher. It includes the specification of the training program and recommendations to the teacher for the correct use of the training program and the consideration of its results. The specification is the following indications:

1. Purpose of the program: university, college, semester, specialty, characteristics of the initial level of advancement of students (what they should know and be able to do in order to complete this program).

2. The purpose of the program: what and using what material the student will learn as a result of the implementation of the given program.

3. The time required to complete the program.

4. Characteristics of the program according to the degree of mass character (frontal, individual-group), according to the specifics of the course of the educational process (introductory, training, familiarization-training), goals (type of activity: orally, in writing), at the place of implementation (classroom, home, laboratory) , attitude to learning devices (machine, machineless).

5. Relation to other tutorials and non-programmed manuals (i.e. what was before it and what will be after it).

The peculiarity of this type of training is that the student works independently in a feasible mode and the result of the tasks is fixed, while an individual approach to each student is carried out.

1.2. Learning algorithm

Among psychological research aimed at improving the educational process, important place belongs to the development of methods for algorithmization of learning. thinking process consists of a series of mental operations. Most often, many of them are not realized, and sometimes they are simply not suspected. Psychologists emphasize that for effective training, these operations must be identified and specially trained for them. This is no less necessary than learning the rules themselves. Without mastering the operational side of thinking, knowledge of the rules often turns out to be useless, because the student is not able to apply them. In this case, the performance of mental actions is similar to the performance of labor actions. In fact, it is impossible to perform one or another labor task, for example, to make a detail, without performing certain labor operations. In the same way, it is impossible to solve a grammatical, mathematical, physical, or in general any intellectual problem without performing a series of intellectual operations. If this were not so, if, for example, knowledge of the rules alone was sufficient for literate writing, then there would be no poor students in the Russian language at school (6.37).

An algorithm is usually understood as an exact, generally understandable description of a certain sequence of intellectual operations, necessary and sufficient for solving any of the problems belonging to a certain class.

Psychologists explore several kinds of algorithms. The main attention was paid to the study of recognition algorithms (i.e., such algorithms that prescribe what and how to do in order to recognize which class a given object belongs to). This is quite natural, given the role of the recognition process in school practice. In fact, any transformations that the student must carry out include as a component, and often a special task, the recognition of membership in a particular class. Special training in recognition processes and elucidation of the possibilities of their algorithmization therefore become an important task of training.

How relevant this is, says, for example, the analysis of errors that occur when solving a grammatical problem.

A grammatical error is an indicator of the inability to solve a grammatical problem. Research shows that students who remember all the rules well make mistakes precisely because they do not know how to apply these rules, do not know the appropriate methods of action and reasoning. Not knowing common methods solving grammatical problems, students cannot give a complete answer to the question of what and in what sequence should be done in order to recognize a given grammatical phenomenon (for example, whether this sentence is complex or complex). Psychologists note the great heterogeneity of methods for solving the same problem by different students . It was also noted that, in analyzing a sentence, the student goes one way, while analyzing the next, similar one, in another, although in fact the method of action in both cases should be common, unified. In this regard, students often experience uncertainty in their actions and decisions. Often errors occur because students know and apply only a part of the operations necessary to recognize a particular grammatical phenomenon, or use them in the wrong order. .

Algorithms can be trained in different ways. You can, for example, give students ready-made algorithms so that they can simply memorize them, and then reinforce them during exercises. But it is possible to organize the educational process in such a way that the algorithms are “discovered” by the students themselves. This method, the most valuable didactically, requires, however, a large investment of time. At first, educational algorithms were developed mainly on the basis of the grammar of the Russian language, then other educational subjects began to be included in the "orbit" of the algorithmic approach.

Having compiled algorithms for analyzing (recognizing), say, syntactic phenomena, scientists began to teach them to students in the same way as algorithms for division or multiplication in arithmetic. At the same time, the application of the algorithm to the solution of a syntactic problem with the same necessity should have led to the determination of the correct punctuation, with which the application of the algorithm for dividing two numbers leads to obtaining the correct quotient. The learning experiment began with the so-called "logical lesson", during which, using simple examples, schoolchildren were led to an understanding of the relationships underlying the recognition of certain syntactic phenomena. Then the assimilation of these relations was fixed in the course of an algorithmic analysis of a particular syntactic phenomenon.

In order to quickly control the assimilation of the algorithm, scientists proposed to introduce specially designed notebooks for independent work. For these notebooks, special types of tasks-exercises were developed. Their specificity lies in the fact that, performing such tasks, the student must divide the decision process into separate operations, and then, with the need to perform all of them, clearly and clearly aware of each of them. The student cannot avoid doing the necessary work, since he must record the results of each operation in a notebook (all of them are strictly numbered and arranged in a certain order).

Thanks to the maintenance of such notebooks, the teacher has the opportunity to carry out a significant part of the control work right in the lesson, while the students are doing the task. The results of the experiment were quite convincing.

Without disputing the effectiveness of this method of teaching, its opponents still put forward a number of objections. There is a concern that learning algorithms can lead to the standardization of thinking, to the suppression of creative forces children. But, the supporters of algorithmization answer, it is necessary to educate not only creative thinking. A huge place in training is occupied by the development of various automated actions - skills. These skills are a necessary component of the creative process, without them it is simply impossible. Further, learning algorithms is not limited to memorizing them. It also involves independent discovery, construction and formation of algorithms, and this is a creative process. Thus, algorithmization can be an excellent means of teaching creative thinking. Finally, algorithmization does not cover the entire educational process, but only those of its components where it seems appropriate.

It is also incorrect to present the matter as if algorithmization, by automating some aspects of educational activity, to some extent diminishes the role of the teacher. The teacher, according to the supporters of this method of teaching, has been and will remain the main figure in teaching. It will continue to have the functions of organizing a team and educating students. The influence of his personality cannot be replaced by any algorithmic manual or learning machine. The opinion that algorithms are some kind of super-program material that complicates the educational process is also unfounded. Additional burden and difficulties for students are created not when a certain order and system is introduced into their mental activity, but when these order and system are absent.

1.3. Algorithm and its main types.

Algorithm is one of the most important concepts in computer science. An algorithm is an exact, unambiguously understood prescription for the execution in a specified sequence of operations (actions) that lead to the solution of any of the problems belonging to a certain class (or type). The prescribed operations (actions) must be available to the addressee. They can be both elementary (simplest) and complex, based on elementary ones. The requirements for the algorithms are:

unambiguity of prescribed actions and operations;

efficiency, assuming that when a finite number of operations are performed, the desired result will be obtained;

mass character, which means that the algorithm is applicable to solving a whole class of problems.

In the process of solving the problem according to the algorithm, there should be: the prescription itself, consisting of instructions (commands) on the performance of actions or operations on certain objects and usually fixed (in the form of diagrams, words, signs) on various material carriers; the executing system (human or machine) to which these instructions are addressed and which executes them; objects to which actions or operations are directed and which are transformed under their influence.

An example of an algorithm is the well-known method of adding two numbers in a “column”. This algorithm can be represented as a system of instructions: allocate digits of units in terms and add units, if the resulting amount is less than 10, write it in the digit of units under the lower number, if the sum is greater than or equal to 10, write only the number of units in the units digit; select the tens place in the terms and write down the tens obtained by adding the units over the tens place of the 1st (upper) term; add tens, etc. Similar instructions are given for adding units of other digits of a number. The executing system of this algorithm can be either a computer or a person.

In the theory and practice of learning, the concept of an algorithm has entered the con. 50s in connection with the development of programmed learning and the use of learning machines.

Human participation in the learning process imposes a number of restrictions on the use of algorithms. When creating an algorithm for a computer, the compiler of the algorithm knows exactly the set of operations available to her. A person's capabilities are determined by his previous acquired experience, creative data, and other individual factors that are almost impossible to fully take into account. Therefore, when developing algorithms for humans, the requirements for the constructability and effectiveness of algorithms are met with a known approximation. Algorithms intended for human use are sometimes referred to as algorithmic type prescriptions, and more commonly just prescriptions. The possibility of solving problems with the help of such prescriptions is probabilistic in nature and depends on a number of individual characteristics of the performer (his intellectual level, attention, emotional state and etc.)

An algorithm is a prescription that determines the content and sequence of operations that turn the initial data into the desired result.

According to the theory of V.P. Bespalko, the main properties of the algorithm are:

1. Certainty (simplicity and uniqueness of operations).

2. Mass character (applicability to a whole class of problems).

3. Efficiency (mandatory summarizing the answer).

4. Discreteness (division into elementary steps)".

The learning algorithm should not be confused with machine algorithms - in them logical operations should be extremely elementary;

The steps of the learning algorithm are built taking into account the actual level of development of students and their previous training;

In learning algorithms, the sequence of operations is sometimes determined not by logical-grammatical or logical-mathematical, but by purely didactic principles;

The learning algorithm allows for greater freedom in the nature of its use by students (its prescriptions can be applied in different ways).

This is the difference between learning algorithms and machine algorithms.

Thus, a learning algorithm is such a logical construction that reveals the content and structure of the student's mental activity in solving problems of this type and serves practical guide for the development of skills or the formation of concepts.

In the learning process, there are such types of algorithms:

Search algorithms that provide the correct identification of features and unmistakable, quick identification of those places in the text where one of the resolving algorithms must be applied;

Resolving algorithms that serve to distinguish between similar spellings, categories and forms.

Resolving algorithms are built on the principle of tasks with one or more alternative questions. Resolution algorithms are heterogeneous in volume: from 3-4 steps to 30-40 or more.

An algorithm with a wide coverage of rules can be called generalizing. They generalize a series of homogeneous rules. The main advantage of generalizing algorithms is that they help form correct and complete generalizations from the very beginning of studying the material, teach students how to find the answer most economically and correctly when solving educational and cognitive problems. The effectiveness of using generalizing algorithms is largely determined by their simplicity and accessibility, the level of similarity of all methods of describing models in a common chain: rule - algorithm - scheme of oral reasoning samples of oral reasoning, graphic fixation of mental actions. All these actions have an effective impact only in combination, therefore, "reliance only on patterns of substantiation of rules or only on schemes of algorithmic prescriptions significantly reduces the effectiveness of teaching rational methods of applying knowledge..

In the existing practice of teaching spelling, DICHOTOMIC ALGORITHM models are most often used - in the form of a feature tree with alternative answers: "yes" - "no". Using dichotomous algorithms, the student mentally moves from top to bottom, gradually carrying out operations of choice from two possible options: "yes" or "no", and thus comes to the correct conclusion. Less commonly used are models of polytomic algorithms that perform the functions of both recognizing and resolving prescriptions. These models are very useful in the formation of skills and abilities.

When teaching, the polytomic prescription model facilitates the work of students at the stage of applying knowledge, but does not eliminate many of the difficulties that they encounter in the process of working with dichotomous algorithms.

The experience of applying the prescription models described by E.T. Shatova showed that the polytomic algorithm is more visual and compact, better viewed and remembered.

But in our opinion, other types of algorithms are preferable in elementary grades, since younger students are not able to capture the general picture indicated in the polytomic algorithm. It is easier for them to trace the logic of working according to the rule with the help of a dichotomous prescription.

Where possible, prescriptions of dichotomous and polytomic types are replaced by models of the algorithm-formula type. An algorithm-formula is a certain system of signs (letters, numbers, short graphic symbols) reflecting the structure and content of both spelling rules and methods and patterns of their application. This model proved to be more efficient.

Let's use a concrete example to show one of the variants of the methodology for constructing and entering an algorithm - formulas in relation to the topic "Letters E and I in the case endings of nouns". First, students are offered a "clean" table, which is filled in under the guidance of a teacher in the process of a heuristic conversation and, as a result, takes the following form:

As a result of the joint work of the teacher and students, the formula of the generalized spelling rule for the letter E is first introduced (the conditional name is the rule-formula). The train of thought during the construction, and then when reading the formula of this rule, is extremely clear for students: based on the table, they move from top to bottom - from the declension (first tier) to the group (second tier) and then to cases and endings.

The form of the judgment should guide students to perform mental actions according to the principle: "First explain ("if so-and-so..."), and then write down ("I write so-and-so..."), which is very important for the formation of motivated generalizations. at the initial learning stage.

The learning task is the goal of cognitive activity; it always contains a question (the defining part of the problem), execution conditions, execution order (solution plan or algorithm) and the result of the decision - the answer. The method of solving grammar - spelling problems is applied to all checked spellings, but the types of problems and the order in which they are solved are different. Consider constituent elements problem and its solution by example.

The question, that is, the realization of the purpose of what is to be received. To check the word "scales" [v"isy], the task is to find out which letter should be written after "v" to indicate a vowel sound.

Conditions: no stress (unstressed vowel at the root of the word). It is important to emphasize the position of the unstressed vowel sound - it is at the root of the word: "weight-".

The order of execution (algorithm): selection of an unstressed vowel - determination of its place in the morpheme (in this case - in the root) - selection of a test word with a vowel being checked. In this example, the test word is "weight".

Conclusion: the test confirmed that the letter "e" should be written at the root of the word "scales": "scales".

M. R. Lvov, M. Razumovskaya indicate that: "When solving a spelling problem, the student must perform the following actions:

firstly, to see the spelling in a word, phrase, text;

secondly, to determine its type: verifiable or not; if so, to which grammar - spelling topic does it apply; remember the rule

thirdly, to determine the way to solve the problem, depending on the type of spelling, on the corresponding rule;

fourthly, to determine the "steps", steps of the solution and their sequence, that is, to compose (usually restore in memory) an algorithm for solving the problem;

fifthly, solve the problem, that is, perform sequential actions according to the algorithm, without missing a single one and without making a mistake at any of the steps; get a result - a conclusion about the correct spelling;

sixth, write a word in accordance with the solution of the problem and carry out self-examination.

This is, in general terms, the structure of the actions of a student who checks the spelling with the help of rules by the method of solving a problem. Actions are very difficult for an 8-9 year old child. As a rule, non-observance of the specified order leads to errors.

A slightly different procedure is described by N.N. Algazina:

1) the student must discover the spelling (identification stage of the analysis);

2) determine which spelling rule should be applied in this case (selective stage of analysis);

3) to resolve the issue of a specific spelling, highlighting the essential features necessary and sufficient for the application of the spelling rule (the final stage of the analysis)".

The ideas of modeling and algorithmization of the mental activity of students are increasingly penetrating into school practice. To help students, memos are created, instructions in the form of a poster-instruction, where 3-4 recommendations are given in the desired sequence.

Learning to use algorithms takes place in 3 stages.

1. Preparatory stage - preparation of the base for working with new material, updating the skills on which the application of the algorithm is based, the formation of a new skill. Students should be prepared to perform all the elementary operations of the algorithm.

The time allotted for this work depends on the level of preparedness of the students.

Without this stage, exercises on the algorithm can lead to the fixation of errors.

2.Main stage:

a) begins with the explanation of the rule. The class should actively participate in the compilation and writing of the algorithm. The teacher conducts conversations)", as a result of which a record of the algorithm appears on the board. It facilitates the understanding and assimilation of the algorithm.

c) cards with algorithms are distributed or work is carried out according to a general table.

d) detailed commenting (cards are closed)

e) children try not to use cards and comments (but use them if necessary).

Training material at this stage: textbook exercises, specially selected words and texts, recording from dictation and independently from the textbook (phrases, sentences or selective words).

Z. Stage of reduction of operations.

At this stage, the process of automating the skill takes place: some operations are performed in parallel, some - in an intuitive way, without memory strain. The process of curtailment occurs non-simultaneously and in different ways for different students.

Reduced comments and samples contribute to the timely folding of the algorithm. Comments are effective when they hide a coherent logical system, when they are interconnected by common features and have a certain sequence.

The problems of working with generalizing algorithms are about the same.

To improve the assimilation of the algorithm model, there are special techniques:

1) perform exercises at home according to the algorithm and try to remember the sequence of operations;

2) writing using an algorithm without a scheme, one of the students can be asked to ask alternative questions, and the other to answer them;

3) students' questions like: "what will we write with two answers" yes ", with four" no "?

The auxiliary algorithm does not require any special working methods. They are simple and assimilated without visual diagrams and cards. For example, in the lessons of the Russian language they are built on the basis of an analysis of the grammatical meaning and grammatical forms of the word. First, there is a distinction between words by meaning (subject: who? what?). At the same time - practical skills in determining grammatical forms: number (one-many), person (I-you-he), etc. Then the algorithm for determining parts of speech:

1) Establish a connection between words.

2) What does the word mean?

3) What does its ending (suffix) mean?

4) How does the word change?

5) What questions does it answer?

The system of work on algorithms involves, first of all, the mastery of search algorithms. There are course algorithms. Which cover all the studied spelling rules, indicate the main types of spelling and oblige students to comprehensively check the text. Each item of this algorithm is expanded into an independent search algorithm, which, in turn, sometimes also break up into search algorithms.

When using such an algorithm, the following exercises can be:

Designate with the corresponding numbers all the spellings right under the lines;

Designate orthograms selectively (for example, only with the numbers 3,4,5);

A commented letter with the simultaneous designation of the corresponding spellings by numbers;

An exercise with writing words in headings or lines corresponding to the points of this algorithm.

It is important that the whole class participate in the compilation of the algorithm, so that the children remember the constructed model for applying the rule.

“Learning to write in this way, the student analyzes each word phonetically and by composition. This teaches him to notice all types of spelling, to find out where to write, how you hear, where to check with the rule, where to visually or aurally recall spelling. Such exercises are especially useful for mediocre successful and lagging students.

Tables can successfully replace more economical graphic tools:

arrows;

Questions;

Key words;

Letter designations presented before the control words, after them and in the margins. As a result, the pace of work is accelerating. But it is impossible to switch to a line-by-line (non-table) form of fixation before students have mastered the skills of clear mental activity.

Chapter conclusions.

1. Programmed learning - a system of educational work with predominantly mediated program management of the cognitive activity of students.

2. Program learning is a qualitatively new didactic system. It arises at the intersection of cybernetics and pedagogy. Programmed learning uses cybernetic principles to guide the pedagogical process.

3. The emergence of the ideas of programmed learning led to the need for an explicit allocation of learning algorithms in the content of learning (they are often called algorithmic prescriptions). Training algorithms serve as a subject of assimilation for students, and often as a teaching tool, showing what actions and in what order students must perform in order to acquire knowledge.

4. Revealing or building algorithms in the content and process of learning and presenting them in some form of a step-by-step program by the activity of learning or teaching is called learning algorithms. In the activities of students in the process of learning and teachers in the process of teaching, two fundamentally different various ways solutions of problems arising in these processes: algorithmic. When the subject performs its activities in accordance with the algorithm known to it, which determines a clear sequence of elementary operations for this subject to solve any problem from the class; heuristic, when the main component of his activity is the search for a plan or method for solving a given problem. As a rule, these two methods of activity in training do not differ and are carried out in a joint single process.

5. The psychological significance of the algorithmization of learning lies in the fact that it helps students to clearly distinguish between the content and operational aspects of the knowledge being studied and master the general way of solving a wide class of problems, as well as to clearly distinguish its indicative basis from the process of mastering mental actions, which significantly increases the effectiveness of learning .

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In educational work in general and in the teaching activity of a teacher in particular, there are two types of learning tasks: traditional, similar to those that have already been solved many times in the same ways and always in exactly the same sequence, and tasks of another group that have to be solved not in traditional , familiar situations, and in unusual conditions. The solution to this problem is multivariate. It has no analogues in previous activities: everything must be done anew, i.e. to create, hence the name: the creative task. In the real practice of the teacher, both groups of tasks are encountered. Let us dwell on the characteristics of the first group: traditional teaching methods for solving educational problems.

What gives algorithmization

If you look closely at the solution of educational tasks by the teacher in the lesson, you can notice the exact and strict sequence of most teaching actions, operations and techniques. The teacher gives strictly consistent instructions for performing a particular operation, which are called algorithms. An algorithm is a concept of mathematics, cybernetics - a system for solving problems (mathematical and others), prescribing a strictly exact sequence of operations leading to the same result. At the same time, the initial data must also be unambiguous, i.e. avoid different interpretations. There are many examples of solving such problems according to the algorithm in the school course: any rule for arithmetic operations, solving problems in algebra, physics, chemistry is carried out according to well-known formulas that prescribe a strictly defined sequence of actions. But here we need to clarify: not every rule is an algorithm, although it can be, because it does not contain prescriptions that strictly determine the sequence of operations. Let us give an example of algorithmic prescriptions for teaching literacy: I) select a word from a sentence; 2) divide the word into syllables; 3) highlight sounds in it, etc. in exact sequence, until they reach the symbolic image of sound, i.e. letters.
You can also recall the rules for spelling words in the language, for example, prefixes pre- and pre-, company - campaign, merged or separate spelling of the “not” particle with words, etc. There is a certain sequence in the teaching actions of the teacher, for example, in the lessons of labor, physical education, foreign languages etc. This means that algorithmic actions of the teacher are also possible here.
Algorithmization means (in the first sense) “the stage of solving a problem, which consists in finding an algorithm for solving it according to the problem statement”1. With regard to teaching, this means the following: a) there are a number of similar didactic tasks; b) they have the same and unambiguously understood source data; c) it is necessary to develop exact rules for strictly consistent educational actions and operations of the student, the implementation of which is guaranteed to lead to the necessary (given) result; d) the same exact sequential actions must be developed and implemented in the teaching actions of the teacher. This is, in fact, the algorithmization of the educational process, without which neither programmed learning nor pedagogical technology is inconceivable. The difficulty here is that neither students nor teachers have strictly identical initial data. In this sense, we mean conditionally admissible similarities. Suffice it to say that even when learning to read and write, one student can easily pick out sounds from a word, while the same task is difficult for another. And the teacher resorts (forced!) to other, non-algorithmic didactic techniques. But nevertheless there is a possibility of use of algorithms.
The study of learning algorithms was carried out by L.N. Landa, N.F. Talyzin, as well as methodologists for teaching languages ​​and mathematics. In their opinion, the algorithms have some essential features; M.P. Lapchik calls them “properties”, N.F. Talyzina calls them “requirements”. These authors arrange them in a different order.

determinism

Determinism (L.N. Landa), or strict certainty (M.P. Lapchik), constructiveness (N.F. Talyzina), presupposes the unambiguity of the prescribed actions and operations, excluding randomness in the choice of actions. These are such elementary actions and operations that a person or a machine “can perform in a uniform way” (L.N. Landa). This means that in order to algorithmize the learning process, it is necessary to find the simplest operations in a complex action.
Here it is appropriate to recall the idea of ​​I.G. Pestalozzi ( early XIX c.) about elementary, or rather, about elemental education, when even an illiterate peasant woman could comprehend the simplest element of education (and education) and, using it, step by step would achieve the necessary, sufficiently high result of educational work.
The simplest operations should be arranged in a strict, unambiguously prescribed sequence. This part of the algorithmization, if the simplest operations are found, is already simple.

Efficiency

It means that the algorithm is aimed at obtaining the desired result. If the initial data are defined and unambiguous, then an exact result is obtained. But it should be noted that not every instruction on the performance of operations is an algorithm (LN Landa). For example, a language teacher after a control dictation (or a mathematician after a test) invites students to perform the following sequential operations (i.e. gives instructions): 1) read the entire dictation carefully; 2) find in it such places where the student had doubts about spelling; 3) remember once again the corresponding rule; 4) if a mistake is made, then it should be corrected. Formally, this prescription follows the sequence of the proposed operations. They are helpful for students. Meanwhile, these prescriptions cannot be called an algorithm in its exact sense, since the initial data are not unambiguous. Indeed, each student may have an error on different spelling rules or solving a mathematical problem and, therefore, the final result of the proposed operations will also be different. For this reason, the listed order of actions (operations) can be called, rather, not a strict prescription, i.e. not an algorithm, but some optional useful tips.

Mass character and discreteness

Mass character as a trait means that the algorithm is suitable for solving a whole class of tasks of the same type.
Discreteness as a property (feature) of algorithms has been added by practitioners involved in algorithmization. This is due to the fact that the described integral process must be divided into separate successive steps. It turns out an ordered set of "prescriptions, directives, commands clearly separated from each other"1. They form a discrete, discontinuous structure of the algorithm. First, it is necessary and exactly to fulfill the requirements of only the first prescription, then you can proceed to the implementation of the second, and so it is mandatory for all subsequent ones.

Clarity

The algorithm is compiled for performers with different characteristics: for teachers of unequal qualifications; various levels of education - from a first-grader to a graduate student; learning machines of different systems. Performers with different characteristics can accept for unconditional execution only those commands that they understand, are available: so that the performer can read in the language in which the instruction is written, so that he can comprehend each command, what and how to do and how to perform all those actions, which give algorithmic prescriptions.

Results

So, algorithms have the following properties (features): determinism (definiteness), uniqueness, mass character, discreteness and understandability.
Algorithmization involves, as already mentioned, the compilation of algorithmic prescriptions. In the educational process, they are addressed, firstly, to the student studying different academic subjects. He receives instructions (commands) on the exact performance of operations on the material being studied: these can be the rules for solving, for example, quadratic equations, performing arithmetic operations, for example, adding multi-valued numbers, calculating the surface area of ​​a truncated cone, etc. Secondly, the teacher himself can receive or have such precise instructions, for example, on the use of achievement tests in the educational process, on conducting demonstration experiments in physics, chemistry, etc. Thirdly, algorithms are necessary for learning machines. Generally speaking, a person and a machine in most cases can have common algorithms, but still for a machine they will be more strict. Otherwise, she simply will not “understand” and will not accept instructions on how to act. And a person who is oriented in the situation can understand less strict prescriptions, although this is completely undesirable. If we compare the algorithmic instructions to the student and the teacher, then their difference lies in the performance of actions: the teacher has the actions of learning, the student has the actions of teaching, because the goals of the action are different.
Algorithms can be presented in the form of a diagram or verbal notation. The scheme of an algorithm is its graphic visual representation. Prescriptions are of two types: arithmetic and logical. In the first case, it is prescribed to perform a series of consecutive works in one direction until the result is obtained. Logical prescriptions involve branching, allowing for an alternative solution (either a condition or an answer).