Volume 02 Issue 07-2022
5
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
07
Pages:
05-09
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
ABSTRACT
This article discusses methodology and subject of teaching mathematics. The task of a mathematics teacher is to
develop students’ independent logical thinking skills and to educate them to be interested in learning the laws of
mathematics. Formation of students’ mathematical thinking and mathematical culture. During the students’ gradual
study of these laws, their logical thinking develops, and the culture of making mathematical conclusions is formed.
Mathematical culture is formed in students by teaching them to correctly express the ideas of a mathematical law in
a symbolic language and, on the contrary, to be able to express a mathematical law expressed in a symbolic language
in their native language.
KEYWORDS
Methodology, subject, teaching mathematics, independent logical thinking skills, mathematical culture, mathematical
culture, mathematical conclusions.
INTRODUCTION
The word mathematics is derived from the ancient
Greek word mathema, which means “knowledge of
science”. The subject (object) of mathematics is the
spatial forms of the existing things in matter and the
critical relations between them. In the present period,
Research Article
METHODOLOGY AND SUBJECT OF TEACHING MATHEMATICS
Submission Date:
July 12, 2022,
Accepted Date:
July 19, 2022,
Published Date:
July 26, 2022
Crossref doi:
https://doi.org/10.37547/ajast/Volume02Issue07-02
Malika M. Tokhirova
Teacher, Presidential school in Tashkent, Tashkent, Uzbekistan
Journal
Website:
https://theusajournals.
com/index.php/ajast
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Volume 02 Issue 07-2022
6
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
07
Pages:
05-09
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
the science of mathematics is conventionally divided
into two.
1)
Elementary mathematics,
2)
Higher mathematics.
Elementary mathematics is also a science with an
independent content, and it is built on the basis of
elementary knowledge obtained from various
branches of higher mathematics, that is, theoretical
arithmetic,
number
theory,
higher
algebra,
mathematical analysis, and the logical course of
geometry.
The science of higher mathematics is used to find
mathematical laws that fully reflect the spatial forms of
the real world and the quantitative relationship
between them.
THE MAIN FINDINGS AND RESULTS
Elementary mathematics forms the basis of the school
mathematics course. The purpose of the school
mathematics course is to convey the system of
ipathermic knowledge to the students in a certain way
(methodology), taking into account the psychological
characteristics
of
the
students.
(The
word
methodology is a Greek word that means “way”).
Mathematical methodology is one of the main
branches of pedagogy and didactics, and it is an
independent science that studies the laws of teaching
and learning mathematics that are compatible with the
educational goals of our society. Mathematical
methodology answers the following three questions
related to the educational process:
1. Why should you study mathematics?
2. What should be learned from mathematics?
3. How to learn mathematics?
The concept of the methodology of mathematics was
first described in the work written by the Swiss
pedagogue-mathematician Giestalotsi in 1803. Later,
N.A.Izvolsky, V.M.Bradis, S.E.Lyapin, I.K.Andronov,
N.A.Glagoleva, I.Ya.Dempman, A.N.Barsukov, S.Kh
Novoselov,
A.Ya.Khinchin,
N.F.Chetverukhin,
A.N.Kolmogorov, A.I. Markushevich, A.I. Fetisov and
others were involved.
Starting from 1970, the content of the school
mathematics curriculum was changed based on the
new program, as a result, the methodology of its
teaching was also developed. Professors V. M.
Kolyagin, J. Ikromov, R. S. Cherkasov, P. M. Erdniev, N.
Gaybullaev, T. To'laganov, A. Abdukadirov and other
method scientists are engaged in the methodology of
school mathematics taught on the basis of the current
program. Mathematics teaching methodology is
taught in the III-IV courses of pedagogical institutes. It
is conditionally divided into three according to the
nature of its structure:
1.
General
methodology
of
teaching
mathematics. In this section, the purpose,
content, form, methods and methodical
system
of
the
mathematical
science,
pedagogy, psychological laws and didactic
principles are explained.
2.
Special methodology of teaching mathematics.
This section shows how to apply the laws and
rules of the general methodology of teaching
mathematics to specific subject materials.
3.
Specific
methodology
of
teaching
mathematics.
This section consists of two parts:
1. Special issues of general methodology;
2. Special issues of special methodology.
For example, if it is said whether to plan mathematics
lessons in the VI grade and the method of conducting
it, this is considered a special issue of the general
methodology.
The purpose of teaching mathematics in secondary
schools is determined by the following three factors:
1. Universal educational goal of teaching mathematics.
2. Mathematics is the educational goal of teaching.
Volume 02 Issue 07-2022
7
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
07
Pages:
05-09
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
3. The practical purpose of teaching mathematics.
The general educational goal of teaching mathematics
sets the following tasks:
a)
Providing students with mathematical knowledge
based on a specific program. This system of
knowledge should provide sufficient information
about mathematics and prepare for studying
higher branches of mathematics. In addition, on
the basis of the program1, students should learn to
check the reliability of the work they have acquired
during their studies, that is, they should master the
main methods of proof and control.
b)
Developing oral and written mathematical
knowledge of students.
Studying mathematics should help students
master the skills of speaking correctly in their
mother tongue, expressing their thoughts clearly,
clearly and succinctly. This word means to make
students able to speak each mathematical rule
correctly in their native language and to
thoroughly form their ability to correctly write the
mathematical expression of this rule using
formulas;
c)
To teach students to know the real truth based on
mathematical principles. Here, it is intended to
provide students with knowledge that will allow
them to understand the spatial forms of all of
them, from the simplest to the most complex
phenomena that occur in the real world, and the
quantitative relationship between them.
By imparting such knowledge, students’ spatial
imagination is formed and their logical thinking
develops further.
The educational goal of teaching mathematics includes
the following:
a)
Formation of students’ scientific outlook. This idea
is based on the theory of knowledge.
b)
Education of students’ interests in the study of
mathematics.
We know that in mathematics classes, students learn
to draw conclusions independently from the first days
of study. They draw conclusions first from
observations, and then from logical thinking. These
conclusions are confirmed by mathematical laws.
The task of a mathematics teacher is to develop
students’ independent logical thinking skills and to
educate them to be interested in learning the laws of
mathematics. Formation of students’ mathematical
thinking
and
mathematical
culture.
Every
mathematical conclusion studied in mathematics
classes requires rhyme, which in turn is represented by
many mathematical concepts and laws. During the
students’ gradual study of these laws, their logical
thinking develops, and the culture of making
mathematical conclusions is formed. Mathematical
culture is formed in students by teaching them to
correctly express the ideas of a mathematical law in a
symbolic language and, on the contrary, to be able to
express a mathematical law expressed in a symbolic
language in their native language.
The practical purpose of teaching mathematics has the
following tasks:
a)
Teaching to be able to apply the theoretical
knowledge obtained in the mathematics
course to solving elementary problems
encountered in everyday life. In this, students
are taught to solve specially designed practical
problems to develop the ability to connect
theoretical knowledge to practice, to form
their skills in performing operations on various
numbers and mathematical expressions, and
to strengthen them.
b)
Formation of skills in the use of technical tools
and demonstration weapons in the teaching of
mathematics.
In
this,
the
students;
mathematics lessons include the ability to use
technical tools, mathematical instruments,
tables and calculation tools.
c)
Teaching students to acquire mathematical
knowledge independently. It mainly consists in
forming the skills of independent reading of
Volume 02 Issue 07-2022
8
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
07
Pages:
05-09
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
students from textbooks and scientific and
popular mathematical books.
In other words, the problems of teaching mathematics
at school are solved in an integral connection with the
sciences of logic, psychology, pedagogy, mathematics
and philosophy. The methodological basis of
mathematics teaching methodology is based on the
theory of knowledge.
The science of mathematics methodology studies the
purpose, content, form, style and methods of
mathematical education and the laws of its application
to the teaching process. Mathematics is physics. it has
a close relationship with the sciences of drawing,
chemistry and astronomy. The integral connection of
mathematics with other subjects is carried out in the
following two ways:
1)
Adaptation of programs of reading subjects
without violating the integrity of the mathematics
system.
2)
Use of materials related to the study of
mathematical laws, formulas and theorems in
other subjects in the mathematics course.
Currently, the issue of matching the mathematics
program with other subjects has been solved quite
successfully. For example, students begin to learn
some information about functions and their graphic
representation used in physics starting from the 7th
grade. A lot of knowledge about geometric
constructions given in the VIII grade is a rich material
for the science of drawing, the task of drawing is to
refine this knowledge by performing various drawing
works.
The issue of using other subjects in mathematics
lessons is difficult to clearly indicate in the program, it
is done by the teacher himself\herself, that is, he/she
should take into account when planning the
educational material and preparing for the lesson.
During the study of problems and equations, it is
possible to solve the equations that reflect the
connections between physical quantities, that is, the
heat balance equation, the linear expansion equation
from heat, and similar equations. When studying
percentages, proportions and other chapters of the
program, it is good to use problems of chemistry and
physics (mixtures, castings and the like), for example:
1) how much of a soluble substance should be added to
240 g of water to make a 20% solution 2) 400 g of 5%
solution was boiled and brought to 200 g. Now what is
the sharpness of the solution? The use of materials
related to neighboring subjects in mathematics lessons
further strengthens the interdisciplinary connection.
After the independence of the Republic of Uzbekistan,
a lot of attention was paid to school education. In
particular, on August 29, 1997, at the IX session of the
Supreme Assembly of Uzbekistan, the national
program of personnel training based on the law on
education was adopted. According to this adopted
law, the activity of the continuing education system
includes the following types of education based on
state educational standards.
The academic institute provides secondary special
education in accordance with the state educational
standards. Taking into account the abilities and
interests of students, their rapid intellectual
development ensures deep, specialized, career-
oriented education.
Vocational college provides secondary special,
vocational education at the level of relevant state
educational standards, in which students' aptitude for
the profession, deep development of knowledge and
skills, one or more of the chosen profession allows you
to acquire several specialties.
CONCLUSION
Mathematical methodology is related to pedagogy,
psychology
and
youth
psychology.
Primary
mathematics methodology is related to other science
methodologies of education (methodology of teaching
mother tongue, science, art, work and other subjects).
REFERENCES
Volume 02 Issue 07-2022
9
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
07
Pages:
05-09
SJIF
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MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
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