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ADVANTAGES AND DISADVANTAGES OF THE METHOD OF WORKING IN SMALL GROUPS IN TEACHING HIGHER
MATHEMATICS Mardanova F.Ya.1, Rasulov T.H.2
1Mardanova Feruza Yadgarovna - Assistant, DEPARTMENT OF THEORY OF PRIMARY EDUCATION;
2Rasulov Tulkin Husenovich - Candidate of Physical and Mathematical Sciences,
Head of Department, DEPARTMENT OF MATHEMATICS, BUKHARA STATE UNIVERSITY, BUKHARA, REPUBLIC OF UZBEKISTAN
Abstract: the following article deals with the feedback on the use of the "Working in small group method", that is one of the interactive methods of modern education in the teaching of Higher Mathematics in higher education institutions. The structure and application of this method are described in the example of teaching the topic "Matrices and operations on them". Also, we have considered about scientific novelty of matrix theory that can be used to justify the relevance of the topic to other disciplines. The advantages and disadvantages of using the method have been discussed as well.
Keywords: working in small group method, modern education, higher mathematics, matrix theory, advantage and disadvantage.
Deep reforms in the field of education, positive changes in the education system abroad, the desire to approach world educational standards, the creation of a new generation of textbooks and curricula, the organization of lessons in a more compact and interesting way, large-scale reforms in education, improving the content of education, government decisions, linking education to life, increasing the effectiveness of teaching, comprehensive for a rapidly evolving society requires to bring up harmoniously developed generation. Therefore, it is advisable to organize training sessions using modern pedagogical technologies.
As we know, modern pedagogical technologies serve as an important impetus to increase students' attitude to the lesson and their enthusiasm for learning. An important educational value of the use of such technologies is that, they reveal the hidden abilities and talents in the student and they will be brought up with a confident approach to their capabilities. Using of interactive methods of teaching in the practice of higher education helps the student not only to study the scientific concepts and laws studied in each subject, but also to identify the causes that lead to it. Modern pedagogical technologies [1-6] play an important role in the formation of the scientific worldview of the student, in the introduction of himself, in the ability to freely choose the right solution independently in difficult situations.
We can say that, Higher Mathematics teaches students to own the characteristics of ambition, concentration, ability and imagination, moral qualities of the person (determination, purposefulness, creativity, independence, responsibility, diligence, discipline and critical thinking); develops their point of views and beliefs and evidence-based defense skills. The object of study of the science of Higher Mathematics consists of the spatial forms of things in matter and the quantitative relations between them. In the process of determining the quantitative relationship between these forms, mathematicians use scientific methods of research as a tool. Observations show that in most cases, the teacher works alone during the lesson, while the students remain observers. This kind of education does not increase the intellectual thinking of students, does not increase their activity, and suppresses their creative activity in the educational process. The main purpose of pedagogical technologies in education is to bring the student to the center of the learning process, to develop independent and creative activity, to become an active
participant in the lesson, away from students simply memorizing and automatically repeating learning materials. In this article, we will provide some feedback on the "Small Group Work Method", that is one of the interactive teaching methods.
"Small group work method" is a creative work in a lesson aimed at studying the learning material or completing a given task by dividing students into small groups in order to activate them. When this method is used in the sessions of Higher Mathematics in higher education institutions, the student has the right to work in small groups, to actively participate in the lesson, to play a leading role, to learn from each other and appreciate different points of view.
The "Small group method" is most effective when it is used in practice. We emphasize that when using this method, the teacher is able to save more time than other interactive methods. Because the teacher is able to engage all the students in the group on the topic at the same time, increase their activity and evaluate. The structure of the "Method of working in small groups" is explained below in the example of teaching the subject "Matrices and operations on them" in Higher Mathematics:
First, the topic is covered: the concepts of matrix and its order are defined. The concepts of square matrix, unit matrix, diagonal matrix, symmetric matrix are explained. Addition, subtraction and multiplication of matrices by numbers are defined. The main properties associated with the entered actions are listed. Their content is explained in the examples. In order to determine the level of mastery of the topic by students and to fill in the gaps in them, small groups of students are formed. In this case, depending on the number of students can be divided into 3 to 5 small groups. For example, in a group of 32 students, 4 small groups of 8 students each can be formed. It is important to consider the talents of the students when selecting members of small groups. Equally powerful assignments pre-formed for each subgroup are then presented to the groups.
(2 3 5^
Task for group 1: For matrix A =
v0 1 6,
give an example for B matrix that has a
multiplicative value of A • B and find the matrix of A • B
(3 0^
Task for group 2: For matrix A =
2 1
V5 4J
give an example for B matrix that has
multiplicative value of A • B and find the matrix of A • B (1 3 5 ^
Task for group 3: A =
0 4 6 2 3 0
give an example for B matrix that has a multiplicative
value of A • B and find the matrix of A • B (4 5 3^
Task for group 4: A =
V2 1 0 J
give an example for B matrix that has a multiplicative
value of A • B and find the matrix of A • B .
Appropriate instructions will be given and directed to all groups. Time is set to complete assignments. At the end of the assignments, the group presentations are discussed, analyzed and evaluated. In order to determine the product of matrices, students must first know the conditions of their order, and secondly, be able to apply the formula for finding the calculation of matrices.
It is advisable to provide students with elements of scientific news and research results related to matrices after the process of consolidating their knowledge on the topic. For example, giving information about the types of averages for positively defined matrices, linear substitutions and relationships between matrices, the problem of generalizing the properties of positive numbers to
a
positively defined matrices, and the generalization of appropriate properties for numerical matrices leads to develop the interests of students to the subject of Mathematics [7-17].
Now let's talk about the advantages of the "small group method". First, it leads to better mastery of the teaching content. Second, it leads to the development of communication skills in students. Third, it gives the opportunity to save time by working with multiple students at the same time and evaluating them. Fourth, the active participation of a small group is observed. Finally, there will be opportunities for self-assessment and intergroup assessment.
In addition to the advantages of the method of working in small groups, there are some disadvantages as well. In small groups strong students are also more likely to receive low grades because of weak students. The ability to monitor all students when monitoring group activities is low. Negative competition between groups may arise. Mutual conflict may arise at the expense of students who are not active within the group. But these shortcomings can be partially overcome by equally distributing gifted students with leadership skills into small groups.
References
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THE METHOD OF USING PROBLEMATIC EDUCATION IN TEACHING THEORY OF MATRIX TO STUDENTS Boboeva M.N.1, Rasulov T.H.2
1Boboeva Muyassar Norboevna - Assistant, DEPARTMENT OF THEORY OF PRIMARY EDUCATION;
2Rasulov Tulkin Husenovich - PhD in Mathematics, Head of Department, DEPARTMENT OF MATHEMATICS, BUKHARA STATE UNIVERSITY, BUKHARA, REPUBLIC OF UZBEKISTAN
Abstract: the following article firstly deals with brief overview of theory of matrix. The issue of the relevance of problem-based education in the teaching of mathematics in higher education institutions was discussed as well. Examples of problem solving using elements of matrix theory are given. In the first problem, the problem of solving a matrix equation was brought to the solution of a system of linear equations. In the second problem, the problem of determining the order of the determinant corresponding to the matrix and the sign of the expression using the given expression has been analyzed.
Keywords: problematic education, matrix theory, methods of teaching, higher education, matrix equation, determinant.
In the current rapid development world, Mathematics plays an important role in training intelligent, creative thinking and independent decision-maker students. It is well known to us that the mathematical training of students must provide a theoretical basis for the study of other natural-scientific, general and specialized disciplines. For fulfilling this, it is important to teach students the elements of matrix theory using a variety of interactive methods.
It is well known that the first problem of linear algebra is the problem of linear equations. In the process of solving such equations, the concept of determinant emerges. As a result of studying the system of linear equations and their determinants, the concept of matrix was introduced. The introduction of the concept of color of the matrix by G. Frobenius allows finding the conditions for the solution of a system of linear equations. The concept of the matrix was introduced by James Joseph Sylvester in 1850 year. Initially, the matrix was developed in connection with the replacement of geometric objects and the solution of linear equations. Nowadays, matrices are one of the most important applied tools of Mathematics.
Matrices are widely used in various fields of Mathematics, Engineering and Economics. For example, they are used in Mathematics to solve systems of algebraic and differential equations, in quantum theory to predict physical quantities, and in the construction of modern aircraft in aviation. That is why, it is important to provide students with detailed information about matrix theory.
A variety of interactive methods [1-6] can be used to teach matrix theory to students. In this article, we have suggested to focus on the advantages of problem-based learning in teaching this theory.
Problem-based learning is a learning process based on solving problem situations. Problems and examples in the theoretical subject materials studied in Mathematics in Higher education institutions can be divided into problematic and non-problematic types according to their content. If the problem-solving process in the study material contains new mathematical concepts, facts, and rules for students that cannot be solved by the previous method, but requires new methods of
