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UDC 371
Kuromboev Kh.N.
Allanazarov K Shokirov J.
TSTU named after Islam Karimov INDIVIDUAL ABILITIES OF STUDENTS IN TEACHING
MATHEMATICS
Abstract: This article discusses the importance of topics for the formation of general cultural competence in the field of mathematics.
Keywords: Mathematics, science, features of the student, information, individuality
At the present stage of institute development, the idea of humanizing education is acquiring great importance. The main goal of education is not to achieve a student of certain knowledge and skills, but to ensure his individual development, attention to his individuality as a unique education; not educating the performer, and the formation of a creative personality. The humanistic orientation of education implies the realization in the process of learning of subject-subject relations, a holistic approach to the student as a carrier of physical, social and spiritual principles.
In this regard, it is necessary to take into account the individual characteristics of students in their studies, in particular, to take into account cognitive styles that reflect the differences between people in the nature of perception and processing of information. One of the first steps in this direction was the strengthening of the role of differentiation in education.
Many Russian methodologists studied the problems of differentiation of mathematical education: Gleiser G.D., Gusev V.A., Smirnova I.M. etc. At the same time, it was mainly about level and profile differentiation, as individual characteristics, mainly age features and temperament, as well as general and special abilities were considered. Of course, these are important points affecting the process of education. However, apart from the individual characteristics characteristic of this group of people (age, social, etc.), each person has his own individual psycho-physiological features and his own subject experience. The development of man as a person requires an appeal to his psycho-physiological characteristics. In this connection, the application of psychological differentiation in the learning process becomes relevant.
The problem of reorientation of education, taking into account the psycho-physiological characteristics of students (in particular, cognitive styles), was considered by many psychologists, they showed the connection of some cognitive styles with academic performance in the humanities, natural-mathematical, artistic and musical cycles. In the works of the methodologist Soboleva O.J. an attempt was made to write a textbook taking into account the functional asymmetry of the brain of students. But it was intended for teaching Russian in elementary institute, while in the field of mathematics teaching methods there are practically no works
describing ways of taking into account the selected individual characteristics of students when constructing the educational process.
Focusing on the "average" student, the traditional institute does not involve focusing on the individual characteristics of institute student. While, according to psychologists, "talents grow out of the individuality of the individual, and the system of education for the "middle student"actually leads to the erasure of individual characteristics." Each person perceives, processes and interprets the information received in his own way, depending on his psycho-physiological characteristics and subject experience. As noted by the famous Russian psychologist V.A. Krutetsky, who had studied the psychology of the mathematical abilities of institute student for a long time, "there is no" absolute inability to mathematics ", a kind of" mathematical blindness ". Every normal and healthy student of institute, with the right education, is able to more or less successfully master the institute course of mathematics and acquire relevant knowledge and skills. " Often, the teacher perceives a poor perception of educational information by the teacher as a lack of learning. But this may be due to the manifestation of the personal position, the subject experience of the student, the discrepancy between the style of presentation of information and the peculiarities of the student's perception.
Without taking into account the individual characteristics of the cognitive processes of students, the modern institute focuses the educational process mainly on students with a verbal-logical perception of the world, with a dominant left hemisphere. This, in particular, due to the fact that even in the XIX century. English neurologist X. Jackson experimentally proved the dominance of the left hemisphere of the brain in controlling movement of the hand, speech, and consciousness. And the right hemisphere has long been considered secondary, subdominant. Overestimating the role of the left hemisphere and logical thinking, institute teaching methods train and develop mainly the left hemisphere.
For a long time, the main task of teaching, in particular, teaching mathematics, was the development of logical thinking, the development of analytical skills, that is, attention was focused on the development of the functions of the left hemisphere. And now many teachers forget about the figurative component of thinking, considering it not so important for mathematical creativity.
However, the optimal solution of problems is possible only with the integration of the activities of both hemispheres of the brain: the right hemisphere mainly uses intuitive-spatial figurative thinking, holistic synthetic strategies; left "prefers" analytical strategy, rational-logical thinking. Occurring not only in lessons, but also in real life situations, tasks sometimes require both a "left-hemisphere" and a "right-hemisphere" solution. The need for the development of the figurative component of thinking is shown by the results of psychological research. In addition, it is the activation of figurative components of thinking that is the basis of creative activity.
Offering not only knowledge and skills, but also ways of mastering them, the institute often strictly defines "rational" and "non-rational" methods. For example, in mathematics lessons, the attention of students is focused on an analytical solution based on logical reasoning. An intuitive, imaginative solution is considered to be insufficiently strict and unreliable. However, the student at the first encounter with a task of a certain type solves it in the way that seems most convenient to him, it is this way that is rational for him. Later, in the process of learning, he will master other methods of solution, but he will still use the most convenient for himself. Therefore, the preferential development in the process of learning of one kind of thinking is not justified either from the point of view of the process of mastering knowledge, or from the point of view of personal development in general. So, when teaching mathematics it is important to develop such an individual feature.
Cognitive styles (which include cognitive styles and information coding styles (leading modality)) are influencing the learning process. Currently, in the psychological literature one can find a description of about 20 different cognitive styles, most of which are bipolar formations. The inadequate perception of educational information by a student may be due to the discrepancy between the style of information presentation (teacher's, textbook's style) and the student's cognitive style, and the mismatch between the specific student's style and that of most students in the class. Low academic performance can be the result of organizing control without taking into account the individuality of the student. Thus, "reflexive" students do not feel very comfortable within the time limit (on control, verification work). At the same time, according to the results of psychological research, it is "reflexive" people who make significant discoveries in science.
Often, in a class, several people learn well the information obtained only with a certain method of its presentation: audial, visual or kinesthetic. But if the teacher moves to another modality, the student has to translate the information into his own. Disconnecting, temporarily, from reality, the student does not hear the teacher's explanation, as a result of which the student has gaps in knowledge, which becomes clear most often only during the test. Therefore, attentive attitude to the student's leading modality is important.
The perception of educational information by a student also depends on his subject experience, which is acquired through communication in the family, with peers, through various sources of information and through targeted training. The student translates any information into his language based on this experience. As a result, the student develops his own system of knowledge, which represents a holistic mental structure. This means that new information should be consistent with the ideas already formed in the student, everyday concepts, values, emotional codes, methods of information processing that constitute the student's subject experience. But the everyday concept does not always coincide with the scientific one, which may be the reason for the inadequate perception of the educational material by the student. Therefore, it is important to reveal the subject experience
of the student, that is, to identify the meaning he invests in the concept being studied, and to correct the subject experience of the student with the socio-historical one.
Thus, when teaching, it is important to take into account not only the psycho-physiological features of the student, but also his subjective experience, which is rightly attributed to social phenomena.
References:
1. Hadamard J. Study of the psychology of the process of invention in the field of mathematics. France. 1959
2. Akimova M.K., Kozlova V.T. Student individuality and individual approach. M .: Knowledge, 1992
3. Boltyansky V.G., Glazer G.D.. On the problem of differentiation of school mathematics education // Mathematics at school, 1988
УДК 511
Куромбоев Х.Н. Муродхужаев Р. Носирхужаев Н. ТГТУ имени Ислама Каримова ПОНЯТИЕ КОМПЛЕКСНЫХ ЧИСЕЛ Аннотация: В данной статье рассматривается решение задач с комплексными числами
Ключевые слова: Математика, наука, вычисление, сложение, корень, комплексное число, решение
Kuromboev Kh.N. Murodhudjaev R. Nosirkhudjayev N. TSTU named after Islam Karimov CONCEPT OF COMPLEX NUMBERS Annotation: This article discusses the solution of problems with complex numbers.
Key words: Mathematics, science, calculation, addition, root, complex number, solution
Хорошо известно, что при решении квадратных уравнений иногда отрицательным результатом является корень, то есть дискриминант квадратного уравнения является отрицательным числом:
D = в2 - 4ас < 0.
В этом случае невозможно извлечь действительное число из корня, при условии, что данный квадрат не имеет корней. До сих пор было исследовано, что квадратный корень был найден только для положительных вещественных чисел. Не имеет значения, являются ли корневые
