Academicia: An International Multidisciplinary Research Journal

III. METHODS AND ALGORITHMS FOR THE NUMBER OF MATHEMATICAL 
MODELS. 
 
(5), (6), (7) solving the problem D= {0 ≤ x ≤ l, 0 ≤ x ≤ T} identification of the demand for the 
field. Industry flat 
h
i
x
i


,



j
t
j
,
M
j
N
i
...,
,
1
,
0
,
...,
,
1
,
0


covered with mesh, 
h
and 

- 
training moved table movement and time. 
(5) in a system of differential equations, the system of the following confidential devoid 
equations 
is 
formed 
by 
changing 
the 
ratio 
of 
the 
limiting 
spices.




















0
/
)
(
/
)
(
0
/
)
(
/
)
(
1
1
1
1
h
q
q
W
S
S
m
h
q
q
W
S
S
m
j
si
j
si
j
si
j
si
j
ni
j
ni
j
ni
j
ni


( 18) 
Here
j
and 
i
- single room shelves, η and 
h-
respectively, t and x are variable steps. From here 
)
,
(
t
x
S
n
and 
)
,
(
t
x
S
s
functional values of pure nodes 
Over time, a step-by-step algorithm appears: 
)
(
)
/(
)
(
1
1
j
ni
j
ni
j
ni
j
ni
q
q
h
m
W
S
S









)
(
)
/(
)
(
1
1
j
si
j
si
j
si
j
si
q
q
h
m
W
S
S









( 19) 
)
,
(
t
x
S
n
and 
)
,
(
t
x
S
s
the values of the functions are based on the computational algorithms of 
(18) relations. when 
0

j
the formulas are ( 18)
)
(
)
/(
)
(
0
1
0
0
1







ni
ni
ni
ni
q
q
h
m
W
S
S

)
(
)
/(
)
(
0
1
0
0
1







si
si
si
si
q
q
h
m
W
S
S

( 20) 
comes to appear. Here, the‖ 0 " superscript represents the t layer time. The initial conditions are 
given in this layer (6). Therefore, (20) the expressions on the right side of the relation can be 
considered exact. 
j
n
S
0
, 
j
s
S
0
values 
m
j
,...,
1
,
0

(7) determined from the boundary conditions. 
Thus, 
)
,
(
t
x
S
n
и 
)
,
(
t
x
S
s
assume that the functions are calculated in the first time layer. Now in 
the formula ( 18) comes out 
1

j

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ACADEMICIA 
)
(
)
/(
)
(
1
1
1
1
2







ni
ni
ni
ni
q
q
h
m
W
S
S

)
(
)
/(
)
(
1
1
1
1
2







si
si
si
si
q
q
h
m
W
S
S

(21) 
From formulas 
)
,
(
t
x
S
n
и 
)
,
(
t
x
S
s
the functions stand in the second layer t time, etc. 
IV. SOFTWARE AND EXPERIMENTAL CALCULATIONS. 
(x, t) и 
(x, t) the calculation program in the function values is shown in Figure 1. It is also 
clear from this program that this problem consists of modules of this problem on the computer 
resolution.
)
,
(
s
n
n
S
S
f
, 
)
,
(
s
n
s
S
S
f
, 
)
,
(
s
n
g
S
S
f
, 
)
,
(
s
n
n
S
S
q
, 
)
,
(
s
n
s
S
S
q
The calculation of the 
function values of the corresponding models is performed by non-standard functions. Parameters 
of oil and gas layers in the Bouder S ++ 6 environment (M-porosity coefficient, 
k-
conductivity 
coefficient)), phase parameters (
n

,
s

,
g

-dynamic viscosity) is defined as the main 
parameters. The most optional calculations can be performed easily by changing their values. 
TABLE 1 VALUES OF THE FAT, GAS, AND WATER PHASE SATURATION 
FUNCTIONS 
x 
S
Н 
S
С
 
S
Г

0 
0.15 
0.75 
0.1 
1 
0.391 
0.480 
0.129 
2 
0.386 
0.478 
0.136 
3 
0.382 
0.477 
0.141 
4 
0.380 
0.476 
0.144 
5 
0.379 
0.474 
0.147 
6 
0.381 
0.471 
0.148 
7 
0.384 
0.466 
0.149 
8 
0.389 
0.460 
0.150 
9 
0.397 
0.453 
0.151 
10 
0.407 
0.441 
0.151 
η = 0,0001; h = 1.0; ( j1 = 10000; j2 = 20000;) j3 = 30000; t = 30000;
S
ni 
= 0,45; S
si
= 0,25; S 
ni
= 0,15; S
si
= 0,75; µ
0 
=µ
n
µ
s
=20.0;
υ
0
=µ
n
µ
g
=100,0; m = w = 0,375; t 
s 
= 3,000000 
н
S
с
S

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ACADEMICIA 
V. CONCLUSION
Computer calculations on a computer demonstrated the operation of a program developed using 
numerical methods. The results of the calculation of the experiment in the framework of a porous 
medium, the development of software for computer modeling showed more concrete results. 
The results of the calculation of oil and gas gas on computer simulations on computers 
correspond to the results of natural oil production allows us to conclude that the software can be 
used.

 REFERENCE 
1.
 
Konovalov A.N. Filtration problems for multiphase incompressible fluid. - Novosibirsk: 
Science. Siberian branch, 1988 .-- 166 p. 
2.
Somerville, Ian. Software Engineering, 6th Edition. Per. from English - M .: Publishing house 
"Williams", 2002. - 624s. silt - Parallel. tit. eng. 

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ACADEMICIA 
ACADEMICIA
 
A n I n t e r n a t i o n a l
M u l t i d i s c i p l i n a r y
R e s e a r c h J o u r n a l
(Doubl e B l i nd Ref ereed & P eer Revi ew ed Journal )
 
DOI:
10.5958/2249-7137.2021.01492.0
 
METHODS FOR THE DEVELOPMENT OF STOCHASTIC 
COMPETENCE IN MATHEMATICS LESSONS AT SCHOOL
 
Toshboyeva Saidaxon Raxmonberdiyevna*; Sodiqova Moxlaroy Shavkatjonqizi**
 
*Teacher, 
Fergana State University, 
UZBEKISTAN 
**Student
UZBEKISTAN
ABSTRACT 
Stochastic Oscillator is the full name of one of the most popular technical indicators, which is 
included in 80% of all existing trading strategies, if not more. It is a favorite tool for identifying 
trend reversal points for both beginners and seasoned pros. And all thanks to its simplicity and 
high efficiency. The following article investigates the ways to promote stochastic competence in 
a school setting.
 
KEYWORDS:
Stochastic Process, Probability, Random, Probabilistic-Statistical Material, 
Guesses. 
INTRODUCTION 
The modern education system faces the goal of developing such personality traits that are 
necessary for the individual and society to be included in socially significant activities that 
require the use of methods of logical-variable thinking based on the laws of formal logic and 
obligatory evaluating all possible outcomes of observed phenomena and events. 
In accordance with the requirements of the modernization of mathematical education, the basis 
for the formation of such thinking skills is strong logical knowledge (about general methods of 
thinking used by people of any profile to carry out their activities) and stochastic knowledge 
(about patterns associated with random phenomena). 
Stochasticity (ancient Greek ζηόχος - goal, assumption) means randomness, "stochastic" literally 
means "able to guess", i.e. random, probabilistic [6]. 

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ACADEMICIA 
In modern mathematical, methodological and didactic literature, the combination of elements of 
probability theory (Latin probabilitas - probability), combinatorics (Latin combina - to combine, 
combine), mathematical statistics (Latin status - state) and some other branches of mathematics 
(set theory, graph theory , mathematical logic, etc.) is called stochastics (Greek from 
stochazomai - to assume) - the theory of probabilities. 
It is necessary to teach children to live in a probabilistic situation. That is, you need to teach 
them to extract, analyze and process information, make informed decisions in a variety of 
situations with random outcomes. Orientation on the multivariance of the possible development 
of real situations and events, on the formation of a personality capable of living and working in a 
complex, constantly changing world, inevitably requires the development of probabilistic and 
statistical thinking in the younger generation. 
The universality of probabilistic laws 
They became the basis for describing the scientific picture of the world. Modern sciences: 
physics, chemistry, biology, demography, sociology, linguistics, philosophy and the whole 
complex of socio-economic sciences are built and developed on a probabilistic basis. A teenager 
in his life is faced with probabilistic situations on a daily basis. Play and excitement are an 
essential part of a child's life. The range of issues related to the relationship between the concepts 
of ―probability‖ and ―reliability‖, the problem of choosing the best solution among several 
options, assessing the degree of risk and chances of success, the idea of fairness and injustice in 
games and in real life conflicts - all this, undoubtedly, is in sphere of interests of the teenager.
The changes taking place in modern society require its members to effectively solve problems, 
most of which are of a stochastic nature. Today, the entire cycle of natural and socio - economic 
sciences is built and developed on the basis of probabilistic laws, and without appropriate 
preparation it is impossible to adequately perceive and correctly interpret social and political 
information. In the modern, constantly changing world, a huge number of people are faced with 
problems in life, which are mostly associated with the analysis of the influence of random factors 
and require decision-making in situations that have a probabilistic basis. The presence of 
stochastic knowledge and ideas has become a necessary condition for creative work in many 
areas of human activity. Competencies in combinatorics, probability theory and mathematical 
statistics are becoming an essential prerequisite for socialization. Probability theory has won a 
very important place in science and applied activity. Its ideas, methods and results are not only 
used, but also literally permeate all natural and technical sciences, economics, planning, 
organization of production, communications, as well as such sciences as far from mathematics as 
linguistics and archeology. Without a good idea that the phenomena and processes with which 
we are dealing are subject to the complex laws of the theory of probability, productive activity of 
people in any area of society is impossible. 
The inclusion of elements of statistics and probability theory in the school curriculum in 
mathematics is due to the role played by probabilistic and statistical knowledge in the general 
education of a modern person. The approximate program of basic general education in 
mathematics includes material that creates the basis of mathematical literacy, which is necessary 
both for those who will become scientists, engineers, inventors, economists and will solve 
fundamental problems related to mathematics, and for those for whom mathematics will not 
become a direct professional sphere. Activities. The program says that the section "Probability 

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ACADEMICIA 
and Statistics" is a mandatory component of school education, which enhances its applied and 
practical importance. This material is necessary, first of all, for the formation of functional 
literacy in students - the ability to perceive and critically analyze information presented in 
various forms, to understand the probabilistic nature of many real dependencies, and to make the 
simplest probabilistic calculations. Learning the basics of combinatorics will allow students to 
consider cases, enumerate and count the number of options, including in the simplest applied 
problems. 
When studying statistics and probability, ideas about the modern picture of the world and 
methods of its research are enriched, an understanding of the role of statistics as a source of 
socially significant information is formed, and the foundations of probabilistic thinking are laid.
Thus, the elements of stochastics are the very material without which it is impossible to form the 
correct worldview of students, since without a minimum probabilistic and statistical literacy it is 
difficult to adequately perceive social, political, economic information and make informed 
decisions based on it. 
The age framework for studying stochastic material in the school course of mathematics 
In addition to the relevance of studying the elements of probability theory and statistics, no less 
important are the questions of what exactly from stochastics, in what volume, at what age and 
how to study for schoolchildren in basic school. To answer these questions, one should, first of 
all, refer to the approximate curriculum of basic general education in mathematics and other 
methodological sources. 
Considering the issue of choosing the optimal age range for starting the study of stochastic 
material in the school course of mathematics, the researchers (Bunimovich E.A., Tkacheva M.V., 
Vasilkova E.N., Chuvaeva T.V.), on the basis of the conducted experiments on the readiness
students to study the theory of probability, note the following important points: 
- at the age of primary grades, in the students' ideas about the world, a lot is still not sufficiently 
formed, and there is not enough mathematical apparatus to explain the concepts of probability (it 
is obvious that it is too early to start studying); 
- starting the presentation of probabilistic material in high school, as the experiment showed, is 
already ineffective, it turns out that even a good knowledge and understanding of other sections 
of mathematics by schoolchildren of senior specialized grades, in itself, does not provide the 
development of probabilistic thinking (apparently, it is too late to start studying ); 
- at the age of 5th grade, children have a fairly high level of probabilistic thinking and most 
students in grades 5-6 are ready to perceive stochastic material and, it is very important then, 
during grades 6-8, to develop this level, otherwise the skills of solving probabilistic problems in 
children are significantly reduced. It is also advisable to teach children in grades 5-6 self-
directed collection of information about the phenomena of life around them.
Due to the novelty for the school of probabilistic-statistical material and the lack of 
methodological traditions of teaching it, variability in its structuring is possible. The beginning 
of the study of this material can be attributed to both the fifth and seventh grades. In addition, its 
presentation is possible both within the framework of a mathematics course or an algebra course, 
respectively, or presented as a separate module. The latter option can only be realized if the 

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ACADEMICIA 
number of hours spent on mathematics is increased in comparison with the invariant part of the 
Basic Curriculum (educational) plan. 
The stochastic competence will be further developed in the higher education and a student is 
expected to acquire certain skills after being introduced to the content:
Student with stochastic competence: 
- When problems arise in their lives, they can solve them using stochastic methods;
- Can apply stochastic knowledge under conditions of uncertainty;
- can collect case data;
- can analyze, make the right decision while sorting out the problem of the assessment situation.