An analysis of the peculiarities of elementary school pedagogy

My interest in solving text problems arose after classes in mathematics. After studying the methodological literature on the problems of learning to solve problems, getting acquainted with the articles of journals in which the authors advocate a wider and more active inclusion of children in solving problems, I decided to test the methodology in practice. In practice, most teachers pay little attention to problem solving. Pupils often do not know how to isolate the data and data needed, to establish a connection between the values included in the task; make a decision plan; check the result. Unreasonably a lot of attention and unjustified expenditure of time is spent on making a short record and solving a problem. In this case, the main focus is on the implementation of the only goal -obtaining an answer to the question of the problem. Also, in the course of mathematics in elementary school, a lot of time is devoted to calculating according to ready-made mathematical models, that is, from a familiar description of a phenomenon using mathematical symbolism. All this negatively affects the formation of common skills to solve a problem, and does not have the necessary impact on the development of students' thinking.

The most common among alternative systems is the didactic system, developed under the guidance of Academician L.V. Zankova. I would like to draw attention to the fact that the vast majority of teachers, students (even those who attended a retraining course, where the principles of training, methods and methods of work were examined and disclosed) need thorough help, which would be to concretize methodological methods and working methods, because the absence of such leads to a contradiction between the proposed principles and their implementation in practice. And I would also like to analyze some of the difficulties that a teacher and student have when solving text problems. But besides the system of L.V. Zankova there is still a system of DB Elkonina and V.V. Davydova. This system is also inherently complex and causes difficulties for teachers and students. When solving problems, many difficulties arise, sometimes it seems that it is impossible to write a short record of the problem, and there can "Мировая наука" №12(33) 2019                 science-j.com      44

be no talk of a solution. I would like to help resolve all the difficulties in solving text problems in the DB system. Elkonina –V.V. Davydova. But I would like to add that no matter what problem we solve, in all cases this is a very difficult matter.

In the primary education of mathematics, the role of text problems is great. Solving problems, students acquire new mathematical knowledge, prepare for practical activities. Tasks contribute to the development of their logical thinking. Of great importance is the solution of problems in the education of the student’s personality. Therefore, it is important that the teacher has a deep understanding of the text problem, its structure, and is able to solve such problems in various ways. There are simple and complex tasks. Tasks that are solved in one action are called simple tasks that are solved in two or more - composite. A text problem is a description of a certain situation (situations) in natural language with a requirement to give a quantitative description of a component of this situation, to establish the presence or absence of some relationship between its components, or to determine the form of this relationship. Any textual task consists of two parts: conditions and requirements (questions).The condition provides information about the objects and some quantities characterizing these objects, about the known and unknown values of these quantities, about the relationship between them. Task requirements are an indication of what you need to find. It can be expressed by a sentence in the imperative (Find the area of the rectangle) or interrogative form (What is the area of the rectangle?).Consider the problem: “On the Kirovets tractor, a collective farm field can be plowed in 10 days, and on the Kazakhstan tractor in 15 days. Both tractors are put on plowing. How many days will the field be plowed? ”The condition for this task. “On the Kirovets tractor, a collective farm field can be plowed in 10 days, and on the Bukhara tractor in 15 days. Both tractors are plowed. ” It describes the relationship between three quantities: the volume of work, labor productivity and the time it takes to complete the work, and in three different situations. First situation. A certain amount of work is performed only on the Kirovets tractor with a certain productivity. The value of one value is known, namely, the operating time is 10 days. The values of other quantities are known. The second situation. The same amount of work is performed only on the Bukhara tractor with a certain productivity. Known uptime - 15 days. The values of other quantities are unknown. The third situation. The same amount of work is performed by two tractors with the corresponding performance. The values of all three quantities are unknown. Requirement (question) of the task: “How many days will the field be plowed?” It indicates that you need to find one of the unknown values of the quantities, namely the time of collaboration. The same requirement should be formulated in the imperative form: “Find the number of days that will be required for plowing the field with two tractors when working together.”In this problem, there are five unknown values of quantities, one of which is contained in the requirement of the problem. We call this value of the quantity sought.

What distance does the dog run during this time? You can understand the contents of this task, isolate the condition and requirement of it, if you ask special questions in the text and answer them.

• 1.    What is this task about? (The problem of the movement of two boys and a dog. This movement is characterized for each of its participants by speed, time and distance traveled.)

• 2.    What needs to be found in the task? (In the problem, it is required to find the distance that the dog will run for all this time.)

• 3.    What do the words “all this time” mean? (The task says that the dog runs between the boys from “from the beginning of the movement until the second boy catches up with the first.” Therefore, the words “for all this time” mean “for all the time from the beginning of the movement before the second boy catches up with the first ”.)

• 4.    What is known in the problem about the movement of each of its participants?

In the problem it is known that:

• a)    the boys go in the same direction;

• b)    before the start of the movement, the distance between the boys was 2 km;

• c)    the speed of the first boy walking in front, 4 km / h;

• d)    the speed of the second boy walking behind, 5 km / h;

• f)    the dog’s running speed is 8 km / h;

• g)    the time of movement of all participants is the same: this is the time from the beginning of the movement, when the distance between the boys was 2 km, until the boys met, i.e. until the distance between them became 0 km.)

• 5.    What is further known? (In the problem, it is not known for how long the second boy will catch up with the first, that is, the time of movement of all its participants is not known. It is also unknown at what speed the boys approach each other. And the distance the dog has run is unknown - this must be found out in the task .)

• 6.    What is the desired one: number, value of magnitude, type of some relation? (The value sought is the value - the distance that the dog ran for the total movement time for all participants.)

Solving text problems and finding different ways to solve them in mathematics lessons contribute to the development of children's thinking, memory, attention, creative imagination, observation, sequence of reasoning and its evidence; to develop the ability to briefly, clearly and correctly state your thoughts. Solving problems in different ways, obtaining new, more complex problems from it and solving them in comparison with solving the original problem creates the prerequisites for the student to form the ability to find his own “original” way of solving the problem, fosters the desire to “independently search for a solution to a new problem”, that, which he had not met before. Tasks with multi-way solutions are also very useful for extracurricular activities, as this opens up opportunities to truly differentiate the results of each participant. Such tasks can be successfully used as additional individual knowledge for those students who easily and quickly cope with the task in the lesson, or for those who wish as additional homework.

Sources used:

• 1.    Andreev V.I. Pedagogy: Training course for creative self-development / V.I. Andreev. - Kazan, 2000 - p. 440-441.

• 2.    Pedagogy №4, 2004: Periodical / V.S. Lazarev, B.P. Martirosyan. -

• Pedagogical innovation: object, subject and basic concepts - p. 12-14.

• 3.    Pidkasisty I.I. Pedagogy: Textbook / II. Pidkasisty. - Moscow: Russian

  Pedagogical Agency, 1995 - p. 49-54.

• 4.    Podlasyy I.P. Pedagogy: New Deal / I.P. Podlasy. - Moscow, 2000. - Book 1. - p. 210-212.

• 5.    Vocational education №4 2004: Periodical / N.I. Kostyuk - New Principles for the Organization of Primary Vocational Education - C.30.

• 6.    Vocational education №1 2006: Periodical / V.G. Kazakov - New time -new technologies of professional training - C.12.

• 7.    Vocational education №4 2006: Periodical / G.А. Balykhin - Federal Targeted Program for the Development of Education: Innovative Solutions for the Future - p.14-15.