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Table 1  The efficiency of the model of teaching quality monitoring


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Table 1 
The efficiency of the model of teaching quality monitoring 
School, 
class 
Number of 
pupils 
Degree of progress 
High 
Medium 
Low 
Experiment 
963 
412 
487 
159 
Control 
952 
144 
513 
295 
Based on the results of the above table, the overall average performance of 
the pupils in the experimental and control groups on the results of experiment held 
to identify the level of effectiveness of the model of education quality monitoring 
in the secondary education system was analysed by means of χ

mathematical and 
statistical method of Student and Pierson. 
Defining the indicators of progress and the number of pupils in the 
experimental group as X
i
n
i
and the control group as Y
j
m
j
, statistical group variation 
rows were identified: high indicator was marked as 3 points, medium – 2 points, low 
– 1 point. 


71 
Progress indicators in the experimental group: 



159;
487;
347;
n
1;
2;
3;
X
)
1
(
i
i




3
1
993
i
i
n
n
Progress indicators in the control group: 





295;
513;
144;
m
1;
2;
3;
Y
)
2
(
j
j




3
1
952
i
j
m
m
The statistical analysis was calculated on the basis of suitable statistical 
probability formulas of the above frequency variation rows n
i
and m
j

i
i
n
n

and
j
j
m
m




0.16;
0.49;
0.35;
n
1;
2;
3;
X
)
3
(
i
i



3
1
1
i
i
P




0.31;
0.54;
0.15;
m
1;
2;
3;
Y
)
4
(
j
j



3
1
1
j
j
q
The statistical analysis of the average progress indicators of both groups 
produced the following results for the two groups of statistical analysis:
19
.
2
16
.
0
98
.
0
05
.
1
1
16
.
0
2
49
.
0
3
35
.
0
3
1














n
i
i
i
X
P
X
In percentage
%
73
%
100
3
19
.
2
%



X
84
.
1
31
.
0
08
.
1
45
.
0
1
31
.
0
2
54
.
0
3
15
.
0
3
1














n
i
j
j
Y
q
Y
In percentage
%
3
.
61
%
100
3
84
.
1
%



Y
Average progress in the experimental group increased by (73 – 61.3)
%
11.7
%
This means that it was higher than the indicator of the control group 
19
.
1
%
3
.
61
%
73

times. 
As a result of the experiment, the level of efficiency of the formation of 
basic competences in pupils was analysed (Table 2). 
 


72 
Table 2 
The efficiency of formation of basic competences in pupils 
Groups 
Number of 
pupils 
Level of progress 
Excellent 
Good 
Fair 
Poor 
Communicative competence 
Experimental 
group 
1672 
501 
754 
334 
83 
Control group 
1718 
171 
343 
859 
345 
Information competence 
Experimental 
group 
1672 
411 
812 
361 
88 
Control group 
1718 
201 
246 
1031 
240 
Competence of developing as a person 
Experimental 
group 
1672 
392 
702 
456 
122 
Control group 
1718 
159 
256 
1083 
220 
Competence of the socially active citizenship 
Experimental 
group 
1672 
378 
698 
503 
93 
Control group 
1718 
144 
307 
1122 
145 
General cultural competence 
Experimental 
group 
1672 
532 
814 
291 
35 
Control group 
1718 
254 
395 
852 
217 
Mathematical literacy 
Experimental 
group 
1672 
423 
725 
468 
56 
Control group 
1718 
211 
302 
963 
242 
Based on the results of the above tables, we did a mathematical and 
statistical analysis. From the obtained results for the final state of the experiment 
we found the average quadratic deviation, selective dispersion, variability indices, 
Student’s selection criteria, level of freedom on the basis of Student’s criteria, 
Pierson’s compliance criteria and reliable deviations. 


73 
X
Y
2
x
S
2
y
S
x
C
y
C
y
x
T
,
K
2
,m
n
X
т

к

1. 2.19 1.84 0.4739 0.4344 


11.32 
1946.88 
125.35 0.04 0.04 
2. 

2.2 
0.7 
0.76 


27.62 
3361.82 
707.5 
0.04 0.04 
3. 2.94 2.24 0.6564 0.7024 


25 
3200 
767.77 0.04 0.04 
4. 2.83 2.2 0.7611 
0.6 


22.5 
3280.5 
589.69 0.04 0.04 
5. 2.83 2.26 0.7011 0.5124 


27.1 
3240 
504.18 0.04 0.03 
6. 3.11 2.41 0.5579 0.7819 


25 
3263.2 
640.33 0.04 0.04 
7. 2.89 2.28 0.6779 0.7216 


21.03 
3444.5 
532.44 0.04 0.04 
According to the obtained results, we will calculate the quality indicators of 
the experiments. 
1. Communicative competence: 
is equal to 
Х
=3;
Y
=2.2
;
04
.
0


x
04
.
0


y
32
.
1
24
.
2
96
.
2
04
.
0
2
.
2
04
.
0
3
)
(
)
(










y
x
aet
Y
Х
C
> 1; 
8
.
0
16
.
2
96
.
2
)
04
.
0
2
,
2
(
)
04
.
0
3
(
)
(
)
(













y
x
akl
Y
Х
C
> 0; 
2. Information competence
is equal to 
Х
=2.94;
Y
=2.24
;
04
.
0


x
04
.
0


y
27
.
1
28
.
2
9
.
2
04
.
0
24
.
2
04
.
0
94
.
2
)
(
)
(










y
x
aet
Y
Х
C
> 1; 
7
.
0
2
.
2
9
.
2
)
04
.
0
24
.
2
(
)
04
.
0
94
.
2
(
)
(
)
(













y
x
akl
Y
Х
C
> 0; 
3. Competence of developing as a person: 
is equal to 
Х
=2.83;
Y
=2.2
;
04
.
0


x
04
.
0


y
25
.
1
24
.
2
79
.
2
04
.
0
2
.
2
04
.
0
83
.
2
)
(
)
(










y
x
aet
Y
Х
C
> 1; 
63
.
0
16
.
2
79
.
2
)
04
.
0
2
.
2
(
)
04
.
0
83
.
2
(
)
(
)
(













y
x
akl
Y
Х
C
> 0; 
 
4. Competence of the socially active citizenship: 
is equal to 
Х
=2.83;
Y
=2.26
;
04
.
0


x
03
.
0


y
 
22
.
1
29
.
2
79
.
2
03
.
0
26
.
2
04
.
0
83
.
2
)
(
)
(










y
x
aet
Y
Х
C
> 1; 


74 
56
.
0
23
.
2
79
.
2
)
03
.
0
26
.
2
(
)
04
.
0
83
.
2
(
)
(
)
(













y
x
akl
Y
Х
C
> 0; 
5. General cultural competence: 
is equal to 
Х
=3.11;
Y
=2.41
;
04
.
0


x
04
.
0


y
25
.
1
45
.
2
07
.
3
04
.
0
41
.
2
04
.
0
11
.
3
)
(
)
(










y
x
aet
Y
Х
C
> 1; 
7
.
0
37
.
2
07
.
3
)
04
.
0
41
.
2
(
)
04
.
0
11
.
3
(
)
(
)
(













y
x
akl
Y
Х
C
> 0; 
6. Mathematical literacy: 
is equal to 
Х
=2.89;
Y
=2.28
;
04
.
0


x
04
.
0


y
23
.
1
32
.
2
85
.
2
04
.
0
28
.
2
04
.
0
89
.
2
)
(
)
(










y
x
aet
Y
Х
C
> 1; 
61
.
0
24
.
2
85
.
2
)
04
.
0
28
.
2
(
)
04
.
0
89
.
2
(
)
(
)
(













y
x
akl
Y
Х
C
> 0; 
As a result of mathematical and statistical processing of the results of the 
experiments, the research hypothesis about the formation of basic competences in 
pupils in secondary school subjects was fully confirmed. 
CONCLUSION 
As a result of the researches conducted on the theme of the doctoral 
dissertation “Improving the model of teaching quality monitoring in the secondary 
education system”, the following conclusions were presented: 
1. The researches conducted in recent years in our country have shown that 
there is a need to improve the model of teaching quality monitoring that identifies 
the development strategy of the secondary education system and its effectiveness. 
educational research projects to identify indicators of quality of the education 
system, the practical implementation. Monitoring of the teaching quality was 
defined as a pedagogical process allowing to determine the mutual conformity of 
education objectives and obtained results, to identify the factors affecting them, as 
well as to correct the educational process and predict its future state. 
2. We established that the improvement of the model of teaching quality 
monitoring in the secondary education system consists of the relationship of 
several interconnected pedagogical, psychological and socially independent 
concepts. We compared the scientific descriptions of such concepts as teaching 
quality, monitoring and model, and substantiated the monitoring mechanism and 
technologies scientifically and methodologically. 


75 
3. Theoretical and methodological substantiation of monitoring technologies 
allowed us to assess and correct the degree of formation of general and 
interdisciplinary integrated competences relevant to basic and secondary school 
subjects corresponding to the age and psycho-physiological characteristics of 
pupils. 
4. As an independent direction of the assessment of teaching quality, the 
national system of assessment of pupils’ academic achievements has developed on 
the basis of international assessment systems, which allowed not only to analyse 
the pupils’ knowledge and skills, but also their attitude, interest and desire to learn 
subjects, and to develop the strategies of education systems. 
5. An important condition for the economic, political and spiritual 
development of the country, as well as possessing its rightful place among the 
developed countries of the world is considered the diagnostics of the state of 
teaching quality in the education system on the basis of information and 
communication technologies. Taking this into account, we developed an improved 
model of internal and external monitoring. 
6. We succeeded in increasing the efficiency of the educational process by 
creating pedagogical conditions for the identification of the performance dynamics 
of the requirements of state educational standards for secondary education model 
of teaching quality monitoring and the factors impacting on it; according to the 
results of the monitoring, definition of the measures aimed at filling the identified 
gaps in pupils’ knowledge and realizing the quality educational process; 
preparation of proposals on the introduction of amendments in the comments of the 
state educational standards and curricula on the basis of the monitoring results and 
the requirements necessary for the development of the state, society, science, 
machinery and technologies; comparison of results of the use of different teaching 
technologies; identification of gaps in the use of advanced pedagogical, 
information and communication technologies, psychological, didactic and teaching 
methods, the development of measures on the coordination of ways to fill them; 
definition of performance of the requirements for qualification and categories by 
teachers; identification of the ratings of teachers, education establishments and 
regional public education bodies on the basis of education quality indicators; 
identification of the state of the quality of education of pupils, educational 
establishments and regional public education bodies. 
7. As a result of the improvement of the model of teaching quality 
monitoring, the factors affecting the quality of education are identified and 
classified. As a result, the factors are identified related to the pupils’ family 
facilities, teachers’ level of preparedness and professional skills, school 
administration activities for the effective organization of the educational process, 
activities of teaching unions and methodological councils in schools, material and 
technical base of education establishments and the state of its efficient use, 
methodological assistance provided for teachers and the quality of their 
professional development. Indicated parameters of quality of organization of the 
process of training and education; and the parameters of the quality organization of 


76 
the education process are determined, which contributes to the intellectual, 
spiritual and moral development of pupils. 
8. The effectiveness of the educational process is guaranteed by the 
provision of the following principles in the system of education quality indicators: 
the productivity of the educational process; healthy and safe learning environment; 
cooperation of family, local community, educational institutions and publicity; 
inclusive education; gender sensitivity in education. 
9. The introduction of the model of teaching quality monitoring into practice 
allowing to diagnose the state of the teaching quality, correct and make 
management decisions on the basis of information and communication 
technologies helps to ensure the effectiveness of the educational process. 
10. The automated information management system of teaching quality 
monitoring ensures the effectiveness of teaching quality management on the basis 
of timely, regular and systematic information about the state of education quality 
in the secondary education system. 


77 

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