Университеттің 85 жылдығына арналған Қазіргі заманғы математика
Университеттің 85 жылдығына арналған «Қазіргі заманғы математика
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TaimanovMatem
| Университеттің 85 жылдығына арналған «Қазіргі заманғы математика:
проблемалары және қолданыстары» III халықаралық Тайманов оқуларының материалдар жинағы, 25 қараша, 2022 жыл 299 but also the subject itself, and that the subject's knowledge of the surrounding world is possible only in the process of activity. In the research of psychologists, the structure of any human activity is revealed. The main components of it are recognized as motives, goals, actions and operations. Activities, actions, and operations are inextricably linked to each other, intersect with each other, and define each other. The formation of activity according to A. N. Leontiev occurs through the formation of actions, and the formation of actions-through the formation of operations. Of great importance in psychology and pedagogy is the thesis of A. N. Leontiev that thinking is not a process that takes place only in the "mind", in the form of internal mental activity. Thinking can also act in an external form, in the form of actions with external objects. Learning activity is an activity of the subject in which the acquisition of knowledge (about the world, about a person, about oneself, about mathematics, numbers, etc.), the acquisition of skills, the acquisition of methods of obtaining knowledge is the main and conscious goal of the subject. Take, for example, the following problem: The school buffet brought milk in two flasks, one of which is 40 liters, and the other 20 liters. How many students will be able to get milk for breakfast if one liter is enough for five servings? If the task describes a real situation that occurred in the buffet, and the task is solved by an employee of this buffet, then the fulfillment of the task requirement is the ultimate goal of its solution. Another thing is if the problem is included in the math lesson in the second grade. The purpose of working on it can be: a) students ' mastery of how to apply the relationship between proportional quantities to solve practical problems; b) mastering the method of obtaining new mathematical knowledge (on the basis of solving the problem in different ways, the justice of equality can be established (20 + 40) ⋅ 5 = 20 ⋅ 5 + 40 ⋅ 5, reflecting the distributive law of multiplication with respect to addition); c) mastering the general methods of solving problems — methods of action) - components of the ability to solve problems; d) mastering the method of solving problems of this type; e) obtaining a new property of arithmetic operations — the distributive law of multiplication; f) solving this problem, i.e. getting an answer to the question of the problem, etc. A task will be an element of some educational task only if the students have accepted the goals a) – d). Regardless of the training, any text task of a school mathematics course is specifically practical, since the acceptance of its requirements as the goal of the activity sets a specific practical activity. The inclusion of a text task in the curriculum occurs only if the students accept the learning goals and find ways to achieve these goals. A text task is not identical to a learning task-a component of learning activity. A text task becomes an element of a learning task when students understand and accept the learning goal of working with the task. The text task together with the educational goal, for the sake of which it is considered by the student, make up the educational task. The statement and acceptance by students of an educational task, which includes a text task, means the acceptance and understanding by students of both the requirements of the text mathematical (physical, chemical, etc.) task, and what educational goal you need to achieve in the process of working with it (what you need, would like to learn, what to master). This understanding of the educational task requires the formation of students ' learning activities to develop such a method of teaching problem solving and methods of using tasks in teaching, in the implementation of which the educational goals of including text tasks in the lesson could be understood and accepted by students, and in the initial period, the prerequisites for such understanding and acceptance would be created. In the study of M. V. Matyukhina and O. I. Tsikina, it was found that " younger schoolchildren experience great difficulties in accepting and retaining goals set by another person. The goal set by the student himself creates |