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7DETERMINATION OF THE LOGICAL SEQUENCE AS A NEW TRAINING
TECHNOLOGY
HASANOVA KHALIDA SIDGALI GYZY
Dosent of the State University of Sumgait Sumgait, Azerbaijan
BAYRAMOVA NOVRASTA SIDGALI GYZY
Dosent of the State University of Sumgait Sumgait, Azerbaijan
ALIYEVA AYNURA RUSLAN GYZY Assistant of the State University of Sumgait Sumgait, Azerbaijan
Annotation: The presented article shows that the definition of the logical sequence of pedagogical technologies, ie algorithms, visual-model learning elements and computerization can be noted. Also, the algorithmization of learning is based on the principles of conscious and active learning, strength of knowledge, cognitive development of students. The principles of systematization and consistency, consciousness and creative activity, positive emotional background, visibility of learning and development of theoretical thinking are shown to be the basis of computerization technology. It is obvious that the systematization and management of technology is related to the characteristics of the use of technical means in the learning process in universities and the possibility of changing the degree of inclusion of computerization in the learning process. It is emphasized that the reproducibility of the technology has led to a wider range of elements of computerization.
Key words: Pedagogical technologies, learning process, learning algorithms, systematicity, consistency, theoretical analysis of the work
Pedagogical technologies are commited in a different way by the various authors. According to V.P.Bespalko, he takes into consideration the pedagogical technology as the "implementation of the beforhand designed educational process as a sequence, and in systematic practice" [1, p. 5], but in accordance with V.M.Monaxov, he receives the theory of pedagogical technology as a "pedagogical activity model which all the details have been taken into consideration by the combining the "self-designing, providing of favorable conditions for both teachers and students, and organizing and holding of the training process. [5]. As for D.V.Chernilevcki's words about pedagogical technology depend upon the "implementation of the beforhand designed educational process as a sequence, and in systematic practice" ... like a system which consists of some methods and tools in order to control this process in terms of achieving the goals which have been put forward.
In accordance with our opinions, such a technology that fully meets these requirements can depend on the determination of the logical sequence, with other words, algorithmization, visualmodel training elements and computerization.
On the basis of algorithmization of training stands the consciousness and activity of training, robustness of knowledge, principles of students' cognitive development. The rationale for the use of algorithms on the one hand, is related with psychological regulations of mastering the training materials (as a theory of (Galpery - to form with a gradually transition to more compact mental activities than beforhand purposefully programmable thinking operations and massive foreign missions fulfilled in a given sequence, on the other hand, the usage of algorithmization elements is related to the special-methodical features of a learned material in a learning process of a mathematical analysis [2].
The basic of a computerization technology can be considered a systematicity and consistency,
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deliberateness and creative activity, positive emotional background, obviousness of training and principles of theorotical cognitive development. Systematic and manageable degree of this technology is tied with the features of using from technical vehicles during a training process in the high schools and is also related with opportunities to be changed the degree of inclusion of computerization for the training process. The reproducibility of the technology makes the elements of computerization more widely used. At the same time, it allows you to use the facts and methods used in the teaching of one subject in the teaching of another subject.
We encounter algorithms when working with any teaching material. Thus, the definitions of formulas, rules, laws, tables, concepts and theorems are in themselves an algorithm that does not reveal the program of action, which is given in a hidden form. The course of mathematical analysis is no exception. A comprehensive analysis of mathematical analysis textbooks, manuals, and workbooks allows us to say that the vast majority of textbooks currently in use are not algorithmic. Even in the inclusion of the concept of limit, which is the most complex concept of mathematical analysis, the authors are satisfied with the expression of the definition, the synthesis of well-solved examples, which also do not show the main stages of the solution [3]. The same situation is observed in workbooks. In some of them, well-researched examples are found [4]. However, the solution algorithm of the study is not clearly indicated. A number of workbooks provide a list of exercises without showing any examples. As a result, students face certain predictable difficulties in the process of solving such problems. This difficulty is related to determining the application of an algorithm using a definition or expression of a theorem.
One of the main difficulties in studying the course of mathematical analysis is the understanding of the algorithm and its discovery. There is a direct correlation between the algorithmic knowledge of mathematical analysis and the successful practical application of theoretical knowledge. Algorithms in themselves possess the function of direction, instruction function and a person is able to use it in order to perform a certain operation. According to LM Friedman's words, algorithms "affect the separation of its guiding basis from the process of mastering the operations of mental activity, which leads to a significant increase in the effectiveness of training" [6]. Thus, algorithms in many cases provide training in mental and practical operations.
On condition that the student is unable to make the transition from the closed form of the algorithm to the open form, or if the teacher does not try to follow the sequence steps, this material will be mastered "by face" and a number of practical operations will be performed incorrectly.
An important and initial stage of algorithmization is the theoretical analysis of the solved problem. Usually, the work with an algorithmic solution is not tied with isolation, but it is in relation to a part of the world around us, which is called the material field. Theoretical analysis of the work means, first of all, the construction of its model in the material field, in other words, the determination of the objects belonging to this concept, the properties of these objects and the relations between them. That is, the definition of keywords here to some extent affects the opening of the algorithm. This allows you to describe the processes and events that take place in the material world, to accurately determine the formulation of the work and the operations that lead to the solution of the work. Note that algorithmization is a creative process. Therefore, the working out of certain algorithms should be conducted with the help of a teacher or be given for the first time to the students in a ready way. In this case, on condition that the algorithm is worked out together with the students, it is necessary not only to express the sequence of these operations, but also to explain why these operations have necessity. This will make it help to consciously master and work out the algorithm. One of the important steps in working with an algorithm is the sample method, in which the teacher demonstrates an example of working with the algorithm.
Another feature of the algorithmization of knowledge from mathematical analysis is that sometimes it is necessary to express it in an inverted way in order to determine the algorithm given in the theorem.
Based on this, the following basic practical recommendations should be taken into account
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when using algorithms in the study of the course of mathematical analysis:
1. The teacher should gradually move from giving ready-made algorithms to students to defining their own algorithms, which often occurs in generalizing the method of solving the given group works.
2. The teacher should present the algorithm openly as a program of steps.
3. In the explicit presentation of the algorithm, it is useful to specify the key words included in the expression of the theorem or definition.
4. On condition that the algorithm is developed together with the students, it is important not only to express the sequence of operations, but also to explain why this operation is necessary.
5. It is useful to indicate the algorithm with branching steps in the form of a block diagram, so that, meantime, the algorithm makes the sense by systematizing the acquired knowledge.
6. It is useful to use comments and exercises in the initial consolidation phase. In this process, as the steps of the algorithm improve, the habit of applying of the algorithm begins to develop.
Let's look at examples of building algorithms based on the expression of definitions and theorems:
Model 1. Definition of sequence of limit: (A = lim xn oVs> 0 3ns, Vn > ns ^ \xn - A| <s)
Now let's show the transition from the obscure algorithm given in the definition to an open algorithm that can be widely used in practices. The definition states that for an arbitrary number s> 0, if a natural number ns is found depending on s that if it satisfies the inequality | xn - A | <s for all n greater than ns, then the number A is called the limit of the sequence xn. Note the key words of this definition:
1) for an arbitrary s real number;
2) if found;
3) natural number ns;
4) depending on s;
5) all n> nE;
6) If the inequality | xn - A | <s is satisfied.
There is already a correlation between the symbols included in the definition: s is an arbitrary natural number depending on nE-s and it must be sought. It is necessary to find such a number that to satisfy the given inequality ranging from the first number to the last ns numbers. Thus, we see that there are three conditions that these must also be compulsorily performed:
1) s-arbitrary,
2) | xn - A | <s inequality is satisfied,
3) nE is a natural number. Based on these conditions, it is necessary to find the natural number ns. Let's compile the algorithm step by step:
1) Let's choose an arbitrary s positive number;
2) Let's solve the inequality | xn - A | <s with respect to n;
3) Let us choose the integer part of the number taken as nE.
Now let's look at an example of the transformation of the expressive forms of a number of theorems of mathematical analysis in order to build an algorithm that is useful in practice.
Model 2. The theorem on the relationship between the continuity of a function and its differentiation. If the function y = / (x) is differentiable at point x0, then it is continuous at this point. The theorem expressed in this form is not of great importance for practice, as it is simpler than the study of its differentiability. However, if we replace the theorem with an equivalent inverse theorem, it will be more useful: on condition that the function y = / (x) intersects at point x0, then it is not differentiable at this point. A practical algorithm is derived from this sentence:
1) determine whether the function is interrupted at any point;
2) conclude that the function is not differentiable.
Let's explain what we said with an example.
x2 +1
For example. To prove that the function y=- is not differentiable at x = 1, it is not
x -1
necessary to show that the definition of differentiation is not satisfied.
Suffice it to say that the function is simply intersected at x = 1. Therefore, in order for students to master the methods of independent action in solving problems from mathematical analysis, the exercises must meet certain requirements:
The work should be presented to the student in such a way that,
- to be able to express and understand the purpose of his activity;
- to see the possibility of applying of the results obtained from the implementation of the work in order to understand the importance of the results obtained for him;
- to think about the activity he performs;
- to be able to control not only its activities, but also the result.
In addition, the system of exercises should be designed such a way that to ensure the transition from a more rigorous management of organization of student activities to a less serious one:
a) to involve the expressive form of exercises to research activities, in other words, to have a motivating function;
b) the exercises to perform different functions, in other words, to be complex in nature and, therefore, to allow the student to perform different types of activities (practical, research, constructive).
c) Forms of expression should be clear to students, exercises should be appropriate to the level of preparation of students.
In our opinions, the following exercises presented to students in the practical classes from mathematical analysis during experimental research meet the following requirements:
- complex exercises (conditional, single, several tasks);
- work on the description of the performed operations and expression of the result;
- level exercises;
- dynamic test ladder structured exercises (higher level task solution which depends on lower level previous test solution).
During the process of studying mathematical analysis, we have taken into account several methods of using algorithms, which confirms the effectiveness and necessity of using algorithms. Thus, the algorithmization of studying of mathematical analysis: is an effective tool for organizing of the learning process;
1) serves for more conscious mastering of educational material;
2) independent compilation of algorithms improves the job skills of expressing for theoretical propositions when it is necessary;
3) allows the building and systematization of practical skills and habits, as well as a theoretical knowledge on the subject.
All this affects the increasing of the quality of students' mastery of the course of mathematical analysis.
LITERATURE
1. Bespalko V.P. Components of pedagogical technology. M., 1989, p. 192.
2. Grudenov Ya.I. Psychological patterns and their use in training and education. Taganrog, 2001, p. 27.
3. Kudryavtsev L.D. Course of mathematical analysis. Volume 1, M., 1980, p. 172.
4. Kudryavtsev L.D. Collection of problems in mathematical analysis. St. Petersburg: Nauka, 1994. - 495 p.
5. Monakhov V.M. Technological foundations for designing and costing the educational process [Text]. Volgograd: Change, 1995, -152 p.
6. Fridman L.M., Kulagina I.Yu. Psychological handbook of the teacher. M., 1991.
7. Chernilevsky D.V. Didactic technologies in higher education. M., 2002, p. 50.
