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SUBJECT OF MATHEMATICS TEACHING METHODOLOGY
Duzelova Dilnoza,
Djumabekova Zuxra,
Kalenova Muxabbat
Mathematics teachers of the Karakalpak Academic Lyceum of the Ministry of Internal Affairs of
the Republic of Uzbekistan
https://doi.org/10.5281/zenodo.14709898
Abstract. This article discusses the subject and methods of mathematics teaching
methodology.
Keywords: mathematics, method, form, formula, astronomy.
ПРЕДМЕТ МЕТОДИКИ ПРЕПОДАВАНИЯ МАТЕМАТИКИ
Аннотация. В статье рассматриваются предмет и методы методики
преподавания математики.
Ключевые слова: математика, метод, форма, формула, астрономия.
The word mathematics is derived from the ancient Greek word mathema, which means
"knowledge of science." The object of study of mathematics is the spatial forms of existing objects
in matter and the quantitative relationships between them. At present, mathematics is conditionally
divided into two: 1) elementary mathematics, 2) higher mathematics. Elementary mathematics is
also a science with an independent content, which is built on the basis of elementary data obtained
from various branches of higher mathematics, namely theoretical arithmetic, number theory,
higher algebra, mathematical analysis and the logical course of geometry. Higher mathematics
deals with the study of mathematical laws that fully and deeply reflect the spatial forms of the real
world and the quantitative relationships between them. Elementary mathematics forms the basis
of the school mathematics course. The goal of the school mathematics course is to convey to
students the system of mathematical knowledge through a certain method (methodology), taking
into account their psychological characteristics. (The word methodology is a Greek word meaning
"without".) Mathematical methodology is one of the main branches of pedagogy and didactics,
and is an independent discipline that studies the laws of teaching and learning mathematics that
correspond to the goals of education at the level of development of our society.
Mathematics methodology answers the following three questions related to the educational
process:
1. Why should we study mathematics?
2. What should we learn from mathematics?
3. How should we study mathematics?
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The concept of mathematics methodology was first described in the work of the Swiss
pedagogue-mathematician G. Pestalozzi, written in 1803, “The Demonstrative Study of Numbers”.
From the first half of the 17th century, issues related to the methodology of teaching mathematics
were addressed by Russian scientists, including academician S.E. Gurev (1760-1813), and from
the first and second half of the 16th century, by N.1. Lobachevsky (1792-1856), LN. Ulyanov
(1831-1886). L.N. Tolstoy (1828-1910) and the outstanding methodologist-mathematician S.I.
Shokhor-Trotsky (1853-1923), A.N. Ostrogradsky and others were engaged in this, and they
looked at mathematics from a scientific point of view and developed its progressive foundations.
For example, AN. Ostrogradsky wrote that “Consciousness arises after observation, consciousness
is based on the real, existing world.”
Later, N.A. Izvolsky, Y.M. Bradis, S.E. Lyapin, I.K. Andronov, N.A. Glagoleva, I.Ya.
Dempman, AN. Barsukov, S.1. Novoselov, A.Ya. Khinchin, N.F. Chetverukhin, AN.
Kolmogorov, AI. Markushevich, AI. Fetisov and others were engaged in various areas of
mathematics teaching methodology. Since 1970, the content of the school mathematics course has
been changed based on a new program, as a result of which its teaching methodology has also been
developed. The methodology of school mathematics, which is taught based on the current program,
was developed by professors Y.M. Kolyagin, R.S. Cherkasov, P.M. Erdniyev, J. Ikramov, N.
Gaybullayev, T. Tulaganov, A. Abdukodirov and other methodologists have been and are still
working on it. Mathematics teaching methodology is taught in the III-IV courses of pedagogical
universities. It is conditionally divided into three according to the nature of its structure.
1. General methodology of teaching mathematics. This section reveals the purpose,
content, form, methods and methodological system of mathematics, based on the laws of
pedagogy, psychology and didactic principles.
2. Special methodology of teaching mathematics. This section shows the ways of applying
the laws and rules of general methodology of teaching mathematics to specific subject materials.
3. Specific methodology of teaching mathematics.
This section consists of two parts:
1. Specific issues of general methodology.
2. Specific issues of special methodology.
For example, if we talk about the methodology of planning and conducting mathematics
lessons in the 6th grade, this is a specific issue of general methodology.
As is known, the science of mathematics teaching methodology is a specific section of pedagogical
science, which is engaged in the study of the rules of teaching mathematics. Mathematics teaching
methodology is closely related to the sciences of pedagogy, logic, psychology, mathematics,
linguistics and philosophy in the process of studying the laws of teaching mathematics. In other
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words, the problems of teaching mathematics at school are solved in close 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, method and
the laws of applying its tools to the lesson process. Mathematics is also closely related to the
sciences of physics, drawing, chemistry and astronomy.
The integral connection of mathematics with other disciplines is achieved in two ways:
1) adapting the programs of neighboring disciplines without violating the integrity of the
mathematical system;
2) using materials in the mathematics course related to the study of mathematical laws,
formulas, and theorems in other disciplines.
Currently, the issue of adapting the mathematics program to other subjects has been solved
quite successfully. For example, students begin to study some of the information used in physics
about functions and their graphical representation starting from the 7th grade. Much of the
knowledge about geometric constructions given in the 8th grade will be rich material for the
subject of drawing, the task of drawing is to consolidate this knowledge by performing various
drawing tasks. It is difficult to clearly indicate the issue of using other subjects in mathematics
lessons in the program, this is implemented by the teacher himself, that is, he should take it into
account when planning the educational material and preparing for the lesson. For example, during
the study of equations, equations reflecting the relationships between physical quantities, namely
the heat balance equation, the equation of linear expansion from heat, and equations similar to
sh!tn, can also be solved.
The percent of the program; It is appropriate to use chemistry and physics problems in
studying proportions and other chapters (mixtures, mixtures, and the like), for example: I) How
much work is needed to dissolve 240 g of solute in 240 g of water to form a 20% solution? 2) 400
g of a 5% solution was boiled and brought to 200 g.
Now what is the acidity of the solution? Useful work in mathematics lessons from materials related
to neighboring subjects further strengthens the interdisciplinary connection.
Comparison method
Definition. The method that determines the similarities and differences of things in the
mathematical object being studied is called the comparison method. The comparison method is
also one of the methods of scientific research.
When applying the comparison method to the materials of the subject being studied in mathematics
lessons, the following principles are followed:
1) the mathematical concepts being compared must be homogeneous;
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2) the comparison must be relative to the main properties of the things in the mathematical
object being studied.
Example 1. When comparing a triangle and a rectangle, their similar sides are determined:
vertices, angles; their different sides:
a) a triangle has three vertices and three sides;
b) it is determined that a rectangle consists of four vertices and four sides. In this example,
both principles of comparison are fulfilled, that is, the triangle and the rectangle are homogeneous
concepts, both are special cases of a polygon, and the comparison method is applied to the main
properties of both figures.
Example 2. In the 8th grade algebra course, deriving the formula for calculating the n-term
of an arithmetic progression is also carried out using the comparison method. Definition. An
arithmetic progression is a sequence of numbers formed by adding an odd number to each of the
previous terms, starting from the second term.
Generalization method
The concept of generalization is also considered one of the scientific research methods in
teaching mathematics. The importance of the generalization method is described by the
outstanding scientist A.N. Kondakov as follows. “Generalization is a logical method through
which one moves from single thoughts to general thoughts.”
In the school mathematics course, the concept of generalization is applied as follows: 1)
generalization of mathematical concepts; 2) generalization in proving theorems; 3) Generalization
in solving problems and issues. Now the applications of generalization will be considered
separately.
REFERENCES
1.
Bikboyeva N. U. va boshqalar «Boshlang'ich sinflarda matematika o'qitish metodikasi», T.,
«O'qituvchi», 1996.
2.
G'aybullayev N., Ortiqov. «Geometriya 7-sinfuchun darslik» T. «O'qituvchi», 1998.
3.
O. G'aybullayev N., Ortiqov. «Geometriya 8-sinf uchun darslik» T. «O'qituvchi», 1999.
4.
Galitskiy M.A. va boshqalar «Algebra va matematik analiz kursini chuqur o'rganish» T.,
«O'qituvchi», 1995.
5.
Antonov K. P. To'plam. «O'qituvchi», 1975.
