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# 24 (2018)
INFORMATION TECHNOLOGIES OF FORMATION
OF THE CONTENT OF DISCIPLINES AND OPTIMIZATION
OF THE CURRICULUM OF THE SPECIALTY
UDC 621.031
DOI: https://doi.org/10.35546/2313-0687.2018.24.45-56
STENIN Alexander
Doctor of Technical Sciences, Professor, Department of Technical Cybernetics, Igor Sikorsky Kyiv Polytechnic Institute,
pr. Pobedy, 37, Kiev, Ukraine., 03056, E-mail: alexander.stenin@yandex.ru
TKACH Mikhail
Candidate of Technical Sciences, Professor of the Department of Technical Cybernetics, Department of Technical Cybernetics
Igor Sikorsky Kyiv Polytechnic Institute, pr. Pobedy, 37, Kiev, Ukraine., 03056, E-mail: mm.tkach77@mail.com
GUBSKIY Andrey
Candidate of Technical Sciences, Department of Technical Cybernetics, Igor Sikorsky Kyiv Polytechnic Institute,
pr. Pobedy, 37, Kiev, Ukraine., 03056, E-mail: andrew.gubskiy@gmail.com
SHITIKOVA Irina
Candidate of Technical Sciences, Senior Researcher, Institute of Telecommunications and Global Information Space of the National Academy
of Sciences of Ukraine, Chokolovsky boulevard, 13, Kiev, Ukraine, 03186, E-mail: irinashitikova@gmail.com
Abstract. The main purpose of the higher education system is the professional training of highly qualified specialists in
accordance with the social order. Therefore, it is the professional activity of specialists that sets and defines the goals of
studying all academic disciplines, and hence the content, structure and forms of the corresponding educational activities of
students preparing for future professional work. In this context, of great importance is the formation of a variable part of
the curriculum specialty. The variable part provides an opportunity to expand and (or) deepen the knowledge and skills
determined by the content of the basic disciplines, allows the student to gain in-depth knowledge and skills for successful
professional activity and (or) to continue professional education in the master's degree. The disciplines of the variable part
of the curriculum of the specialty must meet a number of indicators: the importance of the discipline in the system of train-
ing of specialists in this profile; the content of the discipline material (scientific level, depth of presentation); methodical
level of presentation (logic of material placement, clarity of presentation) and others.
45
# 24 (2018)
ПРОБЛЕМИ ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ
Since Universities and experts of this profile of professional activity are scattered throughout Ukraine and it is not al-
ways possible to collect them in one place, proposed to use the Internet survey system to collect the necessary expert as-
sessments with their subsequent processing.
The article proposes an approach to the formation of the content of academic disciplines of the University using a sys-
tematic approach that reflects the main didactic indicators of the educational process. The proposed approach to the for-
mation and optimization of the variable part of the curriculum of the specialty is universal to solve such problems in various
fields of human activity. There are no restrictions on the number of experts, indicators of the quality of the studied objects.
The main problem is the multi-criteria nature. When a small number of criteria, this problem solved on the paired domi-
nance of the criteria as shown in this article. With a large number of criteria proposed to use a linear convolution. At the
same time, the use of the Internet survey system allows you to connect a wide range of experts to increase the confidence
probability of the optimality of the results.
Keywords: optimization, training plan, Internet survey, expert estimations, linear convolution, the Pareto set.
Problem statement. The education system in Ukraine
has entered a period of fundamental changes, character-
ized by a new understanding of the goals and values of
education, awareness of the need to move to the wide-
spread use of computer technology for the formation of the
material of academic disciplines of the University.
According to the national program "Education Ukraine of
XXI century" the main goal of the higher education system is
the professional training of highly qualified specialists in
accordance with the social order. Therefore, it is the profes-
sional activity of specialists that sets and defines the goals of
studying all academic disciplines, and hence the content,
structure and forms of the corresponding educational activi-
ties of students preparing for future professional work. That
is why research aimed at the study of professional activity
and the development of a "portrait" of a specialist of a par-
ticular profile are now of particular importance. The practical
result of such studies was the creation of qualification charac-
teristics of specialists with higher education. The characteris-
tics describe the main activities of the specialist, his function-
al responsibilities, the requirements for his training. Prepara-
tion of qualification characteristics is an important step in
solving the problem of formulating the goals of training and
determining the content of his professional activity
In this context, of great importance is the problem of
formation informative content of academic disciplines in
the field of selected specialties. Currently, there are many
works devoted to the study of this problem, in particular [1-
3]. However, due to the specifics of the subjects studied,
most of them are highly specialized. Nevertheless, it is
possible to approach the formation of the content of aca-
demic disciplines of the University from a single system
positions, reflecting the main didactic indicators of the
educational process. In this sense, it is necessary to create
universal targets for different subjects, forms of presenta-
tion of theoretical material and models of its assimilation, a
system of criteria for objective control and evaluation of
knowledge of the student. This paper proposes one of the
solutions to this problem.
In addition, it is important to optimize the curriculum of
the specialty. This gives the opportunity to expand and (or)
deepen the knowledge, skills and abilities determined by the
content of the basic disciplines, allows the student to gain in-
depth knowledge and skills for successful professional activi-
ty and (or) to continue professional education in the master's
degree. The disciplines of the curriculum of the specialty
must meet a number of indicators, such as: the importance of
discipline in the system of training of specialists in this pro-
file; content of the discipline material (scientific level, depth
of presentation); methodical level of presentation (logic of
material placement, clarity of presentation) and others.
The most preferable method for the formation and op-
timization of such a plan is the method of expert assess-
ments [5]. In this case, the optimal qualitative composition
of disciplines curriculum will be the result of collective work
of experts in the field of future activities of students of this
specialty, and specialists of higher education with high
competence in relation to the selected indicators of quality
of academic disciplines
Since Universities and experts of this profile of profes-
sional activity is scattered throughout Ukraine and it is not
always possible to collect them in one place, it is proposed
46
ПРОБЛЕМИ ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ
# 24 (2018)
to use the Internet survey system to collect the necessary
expert assessments with their subsequent processing by
the method proposed below.
Form of presentation and model of learning. There
are four forms of presentation of educational material corre-
sponding to different levels of abstraction in the description:
–Phenomenological (descriptive) level;
–Analytical and logical level;
–Mathematical level;
–Axiomatic level.
The form of presentation of educational material de-
pends on the specific subject area. However, for any of the
above forms, a universal model for the development of
educational material is proposed. This model of educational
material shows the sequence of the study of all topics and
the logical links between them [4].
At the initial stage of designing the training course, the
training material planned for study divided into separate
training elements.
In the model included the relationship matrix of the se-
quence and logical relationships of the educational ele-
ments, the sequence of learning topics, count logical links
of training elements.
The construction of the model carried out in four stages:
–Formation of the matrix of priority relations of
educational elements;
–Building a sequence of learning elements of edu-
cational content
–Formation of the matrix of logical connections of
educational elements;
–Construction of a graph of logical connections of
educational elements.
The size of the square matrix of relations of sequence
and logical relations of elements equals to the number of
training elements. First, empty matrices are constructed,
and their rows and columns numbered according to the
number of training elements (see Fig. 1 and Fig. 2). Then
the matrix cells filled with zeros and ones row by row.
1
2
3
4
5
6
7
8
9
10
Σ
1
1
1
1
1
1
1
1
1
1
1
10
2
0
1
0
0
1
1
1
1
1
1
7
3
0
1
1
0
1
1
1
1
1
1
8
4
0
1
1
1
1
1
1
1
1
1
9
5
0
0
0
0
1
0
1
1
1
1
5
6
0
0
0
0
1
1
1
1
1
1
6
7
0
0
0
0
0
0
1
0
0
0
1
8
0
0
0
0
0
0
1
1
0
0
2
9
0
0
0
0
0
0
1
1
1
0
3
10
0
0
0
0
0
0
0
1
1
1
3
Fig. 1. Relationship matrix of the sequence of training elements
1
2
3
4
5
6
7
8
9
10
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
4
0
1
1
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
1
1
1
1
7
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
0
0
1
0
0
0
10
0
0
0
0
0
0
1
0
0
0
Fig. 2. Matrix of logical connections of educational elements
47
# 24 (2018)
ПРОБЛЕМИ ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ
Fig. 3. Sequence of learning elements
When filling in the cells of the matrix, the sequence
relationships analyze the sequence relationship between
the two training elements. The unit put in the cell if the
training element specified in the row number studied
after the training element specified in the column num-
ber. The opposite relation of precedence denoted by zero.
All cells of the main diagonal of the matrix of sequence
relations filled with units. Matrix cells that are symmetric
about the main diagonal must have opposite values.
Therefore, the analysis of the pair sequence relations
carried out only for the lower left or for the upper right
triangle of the matrix, filling its remaining part on the
anti-symmetry property. When filling in the matrix of
logical connections we must put the unit in a cell, if the
educational topic specified in the row number logically
linked with the educational topic in column number.
Drawing up a matrix of logical relations is convenient to
conduct on the basis of the matrix of priority relations by
excluding units from those cells for which there are no
logical, reference links between the elements (Fig.1,
Fig.2). The process of filling in the matrices is advisable to
conduct, having before the eyes of the texts with educa-
tional material for all educational elements. The analysis
of the content of the educational material allows reveal
more objectively the pair relations of priority and logical
connections between educational elements.
Not only objective but also subjective factors of the ex-
perts have an impact on the form of matrices of priority
relations and logical connections, and, consequently, on the
form of presentation of educational material.
Fig. 4. Graph of logical connections
The sequence of studying the elements in the training
procedure is determined in the process of processing the
matrix of priority relations, summing up the coefficients of
each row of the matrix. The totals recorded in the column
to the right of the matrix (Fig.1). The values of the sums
indicate the sequence numbers of the corresponding train-
ing elements in the list of the sequence of study of the
training material (Fig.1, in Fig.3). Logical connections of
educational elements displayed for clarity in the form of a
directed graph (Fig. 4). A graph builds on the matrix of
logical connections of educational elements.
The edges of the graph logical connections indicate the
reference links between the educational elements. For ex-
ample, the link between of a training element 2 and training
48
ПРОБЛЕМИ ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ
# 24 (2018)
elements 5 and 6 (Fig.4), shows that in order to master the
content of the training material from the training element 2,
it is necessary to first study the material of the training ele-
ments 5 and 6. The model of development of the educational
material determines the sequence of its presentation in the
learning system, variants of the trajectories of its study,
logical connections in the construction of hypertext. The
complete graph of logical connections constructed similarly
to the complete matrix of logical connections.
Optimization of curricula of specialties. Let there
be N academic disciplines offered for inclusion in the curric-
ulum of the specialty, M - the number of experts inter-
viewed via the Internet, a specific discipline (training
course) will be designated through
i
k
(
i 1, N=
).
We must select
L
disciplines (
LN<
) that meet the
selected quality indicators
k
J
(
LN<
).
By the Internet survey system enters the experts 'as-
sessments in the table of academic disciplines' grade
grades (table. 1).
Here
k
ij
r
- rank (assessment) of the i-th discipline (i=1,
. .,N) of j-th expert (j=1,…,M) by k-th quality indicator
(k=1,...Q). The rank is a natural number in the accepted
score scale.
Table 1
Assessments of experts
Quality indicator
1
J
…
Q
J
Discipline
Expert
1
k
…
…
N
k
…
1
k
2
k
…
N
k
1
Э
1
11
r
… …
1
1N
r
…
Q
11
r
Q
12
r
…
Q
1N
r
2
Э
1
21
r
… …
1
2N
r
…
Q
21
r
Q
22
r
…
Q
2N
r
… … … … … … … … … …
M
Э
1
M1
r
… …
1
MN
r
…
Q
M1
r
Q
M2
r
… Q
MN
r
The sum of the
ranks
1
1
∑
…
…
1
N
∑
…
Q
1
∑
.
Q
2
∑
…
Q
N
∑
Average rank
1
1
r
… …
1
N
r
…
Q
1
r
Q
2
r
…
Q
N
r
The sum of ranks and the average rank are determined according to the formulas:
1
kM
k
ij
ij
r
=
=
∑∑
.
(1)
1k
k
jj
rM
=
∑
. (2)
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# 24 (2018)
ПРОБЛЕМИ ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ
Without losing the generality of the result, let us as-
sume that we have 7 academic disciplines, which as a result
of ranking the experts ' assessments on the indicators of the
content of the material (J1) and the methodological level of
presentation (J2) formed the following system of inequali-
ties relative to the average rank of the discipline:
16123754
:Jk k k k k k k>>>>>>
.(3)
26217354
:Jk k k k k k k>>> >>>
.(4)
The meaning of inequalities (3) and (4) lies in the pair
preferences of one discipline in relation to another within
the chosen quality indicator.
It known that the correctness of the expert estimates
obtained during the processing depends on the consistency
of the expert group. To assess the consistency of the ex-
perts, we calculate the variance coefficient of concordance
for the selected quality indicators [6]:
23
1
12
()
k
k
Mk
j
j
S
WMN N M T
=
=−−
∑
.
(5)
where
0
11
()
NM
k kk
ij
ij
S rr
= =
= −
∑∑
. (6)
0
k
r
- the average rank score on the k-th indicator
0
1
k
ki
rr
N
=
∑
. (7)
k
j
T
– the index of related ranks in the ranking of the j-th expert, which is defined as:
3
1
()
j
H
k
j pp
p
T hh
=
= −
∑
.
(8)
where:
j
H
- number of groups of equal ranks of the j-
th expert;
p
h
- the number of equal ranks in the p-th group
of related ranks when ranked by the j-th expert.
If
k
W 0.7≥
the expert group considered to be work-
ing in a coordinated manner. Otherwise, the group of ex-
perts must restructure.
In addition, it is useful to distinguish between experts
by the degree of competence and the importance of their
views, i.e. it is necessary to rank the experts themselves.
When ranking, each of them is assigned a rank of signifi-
cance from 1 (the most influential expert) to M (the least
influential expert). The opinion of each expert is taken in
the calculations with a coefficient proportional to1/
j
m
,
where
j
m
- the rank of the j-th expert (
1,jM=
).
To assess the relationship of ranked disciplines of train-
ing courses, we calculate the Spearman rank correlation
coefficient [7]:
50
ПРОБЛЕМИ ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ
# 24 (2018)
3
6
1S
NN
ρ
= − −
.(9)
If the value is close to one, it characterizes the linear av-
erage relationship between the rankings on the indicators
under consideration.
For the two indicators considered in our case, this suggests
that the disciplines that have received a high assessment of the
content, are highly rated on the methodological level.
Then we perform the ordering of subjects on two
quality indicators, the highlighting from the inequali-
ties (3) and (4) consistently dominating subset of (Pa-
reto set). For clarity, we give a graphical interpretation
of this approach. For ratios (3) and (4) in Fig. 5 aca-
demic disciplines are presented according to table. 1.
with a central point, the coordinates of which are de-
termined by the place of the discipline among the
disciplines under consideration, according to its aver-
age rank.
Fig. 5. Graphic interpretation of rank correlation of academic disciplines
Assume that the quality indicators
1
J
and
2
J
are equal, i.e. the total quality indicator is defined as:
12
JJJ= +
.(10)
In this case, the vector of change
J
in the quality index passes at an angle
0
45
(Fig. 5). Then, as can be seen from fig.
5, the Pareto set for the whole set of disciplines includes only one discipline
6
k
. Excluding discipline from consideration,
we again highlight the set of Pareto, which includes two discipline each of these is more effective than any other in both
respects, but they are incomparable, because for
1
J
12
kk>
, but for
2
J
21
kk>
.
Continuing this procedure, we get the following chain of preferences of academic disciplines:
6 12 37 5 4
( )( )k kk kk k k> > >>
.(11)
51
# 24 (2018)
ПРОБЛЕМИ ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ
Hence, if, for example, we need to choose 5 out of 7 ac-
ademic disciplines, the disciplines
5
k
and
4
k
excluded
from consideration. If you need to select 4 courses, in addi-
tion
5
k
and
4
k
, we must exclude one of the
3
k
or
7
k
that can be done by the introduction of an additional indi-
cator. It should note that with this approach, with a large
number of indicators and disciplines, the task of forming
the optimal variable part of the curriculum of the specialty
is significantly complicated, which is associated with the
analysis of the hyperspace of quality criteria.
In the case of a multi-purpose problem, it is neces-
sary to find a solution that belongs to the intersection
of sets of optimal solutions to all one-objective prob-
lems. However, this intersection is usually an empty
set, so we should consider the so-called negotiating set
of effective solutions (Pareto optimality). The optimali-
ty criterion of the Italian economist V. Pareto used in
solving such problems, when optimization means im-
provement of some indicators, that others do not get
worse.
We can distinguish the following main methods for
solving multi-criteria optimization problems:
1) Optimization by one criterion, which recognized as
the most important, while other criteria play the role of
additional restrictions;
2) Convolution of many criteria to one by introducing
expert weights for each criterion in such a way that the
more important criterion gains higher weight;
3) Ordering of a given set of criteria and sequential op-
timization for each of them (this approach is the basis of
the method of successive concessions) [8].
The most common of these methods is the second
method, which uses a linear convolution of criteria at each
level of the hierarchy. In our case, we can distinguish two
levels of hierarchy. At the lower level is formed on the basis
of table 1 criterion of assessment by experts of the i-th
discipline on the k-th criterion. Let's denote it as Eik. Table 1
shows, what Eik=
k
i
r
. Then the criterion of the upper level
for the evaluation of the i-th discipline on the set of criteria
of the lower level will have the form:
1
Q
i ik ik
k
JE
λ
=
=∑
. (12)
where λik –weight coefficients of importance of the k-th
criterion in the evaluation of the i-th discipline, which from
table 1 are defined as
1
11
()
()
Qk
i
k
ik Q
Nk
i
ik
r
r
λ
=
= =
=
∑
∑∑
.
(13)
with
1
1, 0
Q
ik ik
k
λλ
=
= ≥
∑
. (14)
Taking into account the integer ranking of criteria,
which leads to a large range of estimates spread, it is
proposed to use a convolution of the relative values of
the criteria of i-th disciplines relative to their maxi-
mum and minimum values for a more accurate assess-
ment [7,9]. The convolution method consists in solving
the problem of minimization of a linear combination
with non-negative weighting coefficients denoting the
importance of the k-th criterion and satisfying the
condition (13):
52
ПРОБЛЕМИ ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ
# 24 (2018)
max
1max min
()
()
Qik ik
i ik
kik ik
EE
jEE
λ
=
−
=−
∑
. (15)
Further, according to the obtained (12) values of the
upper level criteria, we rank the list of disciplines in de-
scending order and select the specified number of disci-
plines in the variable part of the curriculum of the specialty.
Conclusion. This article propose to approach the
formation of the content of academic disciplines of the
University with a single system positions, reflecting the
main didactic indicators of the educational process. In
this sense, it is necessary to create universal targets for
different subjects, forms of presentation of theoretical
material and models of its assimilation, a system of
criteria for objective control and evaluation of
knowledge of the student. The paper propose a univer-
sal approach to optimizing the curriculum of the special-
ty, based on the methods of expert assessments, and
which can be used to solve such problems in various
fields of human activity. At the same time, there are no
restrictions on the number of experts, quality indicators
and studied objects. The main problem is the multi-
criteria nature of the problem solved. With a small num-
ber of criteria solved on the pair dominance criteria as
shown in this article. With a large number of criteria
proposed to use a linear convolution. At the same time,
the use of the Internet survey system allows you to
connect a wide range of experts to increase the confi-
dence probability of the optimality of the results.
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Kharkov humane University» - Kharkiv, 2000. – Vol. 6, 59-64.
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4. Solovov A.V. Proektirovanie kompyuternyh sistem uchebnogo nazn acheniya: uchebnoe posobie. - Samara: SGAU, 1995
5. Nejlor K. Kak postroit ekspertnuyu sistemu. – M.: Energoatomizdat, 1991. – 286 s.
6. Dobrov G.M. i dr. Ekspertnye ocenki v nauchno-tehnicheskom prognozirovanii. Naukova Dumka, 1974. – 160 s.
7. Beshelev S.L., Gurvich F. G. Matematicheskie met ody ekspertnyh ocenok. – Statistika, 1980. – 263 s.
8. Podinovskij V.V., Gavrilov V. M. Optimizaciya po posledovatelno primenyaemym kriteriyam. M., “Sov. radio”, 1975, 192 s.
9. A.I.Orlov Expert assessments. MGTU name's N. Bauman. - 2009. Part 2011,
53
# 24 (2018)
ПРОБЛЕМИ ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ
СТЕНІН Олександр Африканович
Доктор технічних наук, професор, Кафедра технічної кібернетики. Національний технічний університет України
«Київський політехнічний інститут імені Ігоря Сікорського» пр. Перемоги, 37, м.Київ, Україна., 03056,
E-mail: alexander.stenin@yandex.ru
ТКАЧ Михайло Мартинович
Кандидат технічних наук, професор кафедри технічної кібернетики, Кафедра технічної кібернетики
Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського»
пр. Перемоги, 37, м.Київ, Україна., 03056, E-mail: mm.tkach77@mail.com
ГУБСЬКИЙ Андрій Миколайович
кандидат технічних наук, Кафедра технічної кібернетики, Національний технічний університет України
«Київський політехнічний інститут імені Ігоря Сікорського» пр. Перемоги, 37, м.Київ, Україна., 03056,
E-mail: andrew.gubskiy@gmail.com
ШИТІКОВА Ірина Геннадіївна
кандидат технічних наук старший науковий співробітник
Інститут телекомунікацій і глобального інформаційного простору НАН України,
Чоколівський бульвар, 13, г. Киев Україна, 03186, E-mail: irinashitikova@gmail.com
ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ ФОРМУВАННЯ КОНТЕНТУ НАВЧАЛЬНИХ
ДИСЦИПЛИН І ОПТИМІЗАЦІЇ НАВЧАЛЬНОГО ПЛАНУ СПЕЦІАЛЬНОСТІ
Анотація. Основною метою системи вищої освіти є професійна підготовка фахівців вищої кваліфікації в відпо-
відності з соціальним замовленням. Тому, саме професійна діяльність фахівців задає і визначає цілі вивчення всіх
навчальних дисциплін, а значить і зміст, структуру і форми відповідної навчальної діяльності студентів, які готу-
ються до майбутньої професійної роботи. У цьому контексті велике значення набуває формування варіативної
частини навчального плану спеціальності. Варіативна частина дає можливість розширення та (або) поглиблення
знань, умінь і навичок, визначених змістом базових дисциплін, дозволяє студенту отримати поглиблені знання і
навички для успішної професійної діяльності та(або) для продовження професійної освіти в магістратурі. Дисциплі-
ни варіативної частини навчального плану спеціальності повинні відповідати цілому ряду показників, таких як:
важливість дисципліни в системі підготовки фахівців даного профілю; змістовність матеріалу дисципліни (науковий
рівень, глибина викладу); методичний рівень викладу (логіка розміщення матеріалу, ясність викладу) та інші.
Оскільки Вузи, де є дана спеціальність, і фахівці-експерти даного профілю професійної діяльності розкидані по
всій Україні і не завжди є можливість зібрати їх в одному місці, пропонується використовувати систему Інтернет-
опитування для збору необхідних експертних оцінок з наступною їх обробкою.
У статті пропонується підхід до формування контенту навчальних дисциплін вузу з єдиних системних позицій,
що відображають основні дидактичні показники навчального процесу. Запропонований підхід до формування та
оптимізації варіативної частини навчального плану спеціальності носить універсальний характер і може бути вико-
ристаний для вирішення подібних завдань в різних сферах діяльності людини. При цьому немає обмежень на кіль-
кість експертів, показників якості та досліджуваних об'єктів. Головна проблема полягає в багатокритеріальності
розв'язуваної задачі. При невеликому числі критеріїв вона вирішується на основі парної домінантності критеріїв
так, як це показано в даній статті. При великому числі критеріїв пропонується використовувати лінійну згортку. При
цьому використання системи Інтернет-опитування дозволяє підключити широке коло фахівців-експертів для під-
вищення довірчої ймовірності оптимальності отриманих результатів.
Ключові слова: оптимізація, навчальний план, Інтернет-опитування, експертні оцінки, лінійна згортка,
множина Парето.
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СТЕНИН Александр Африканович
Доктор технических наук, профессор, Кафедра технической кибернетики, Национальный технический университет Украины
«Киевский политехнический институт имени Игоря Сикорского» пр. Победы, 37, г. Киев, Украина, 03056,
E-mail: alexander.stenin@yandex.ru
ТКАЧ Михаил Мартынович
Кандидат технических наук, профессор кафедры технической кибернетики, Кафедра технической кибернетики,
Национальный технический университет Украины «Киевский политехнический институт имени Игоря Сикорского»
пр. Победы, 37, г. Киев, Украина, 03056, e-mail: mm.tkach77@mail.com
ГУБСКИЙ Андрей Николаевич
Кандидат технических наук, Кафедра технической кибернетики, Национальный технический университет Украины
«Киевский политехнический институт имени Игоря Сикорского» пр. Победы, 37, г. Киев, Украина, 03056, E-mail: andrew.gubskiy@gmail.com
ШИТИКОВА Ирина Геннадиевна
Кандидат технических наук, старший научный сотрудник,
Институт телекоммуникаций и глобального информационного пространства НАН Украины,
Чоколовский бульвар, 13, г. Киев Украина, 03186, E-mail: irinashitikova@gmail.com
ИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ ФОРМИРОВАНИЯ КОНТЕНТА УЧЕБНЫХ
ДИСЦИПЛИН И ОПТИМИЗАЦИИ УЧЕБНОГО ПЛАНА СПЕЦИАЛЬНОСТИ
Аннотация. Основной целью системы высшего образования является профессиональная подготовка специа-
листов высшей квалификации в соответствии с социальным заказом. Поэтому, именно профессиональная деятель-
ность специалистов задает и определяет цели изучения всех учебных дисциплин, а значит и содержание, и структу-
ру, и формы соответствующей учебной деятельности студентов, готовящихся к будущей профессиональной работе.
В этом контексте большое значение приобретает формирование вариативной части учебного плана специальности.
Вариативная часть дает возможность расширения и (или) углубления знаний, умений и навыков, определяемых
содержанием базовых дисциплин, позволяет обучающемуся получить углубленные знания и навыки для успешной
профессиональной деятельности и(или) для продолжения профессионального образования в магистратуре. Дисци-
плины вариативной части учебного плана специальности должны отвечать целому ряду показателей, таких как:
важность дисциплины в системе подготовки специалистов данного профиля; содержательность материала дисци-
плины (научный уровень, глубина изложения); методический уровень изложения (логика размещения материала,
ясность изложения) и другие.
Поскольку ВУЗы, где есть данная специальность, и специалисты-эксперты данного профиля профессиональной
деятельности разбросаны по всей Украине и не всегда есть возможность собрать их в одном месте, предлагается
использовать систему Интернет-опроса для сбора необходимых экспертных оценок с последующей их обработкой.
В статье предлагается подход к формированию контента учебных дисциплин ВУЗа с единых системных позиций,
отражающих основные дидактические показатели учебного процесса. Предложенный подход к формированию и
оптимизации вариативной части учебного плана специальности носит универсальный характер и может быть исполь-
зован для решения подобных задач в различных сферах деятельности человека. При этом нет ограничений на коли-
чество экспертов, показателей качества и исследуемых объектов. Главная проблема состоит в многокритериальности
решаемой задачи. При небольшом числе критериев она решается на основе парной доминантности критериев так,
как это показано в данной статье. При большом числе критериев предлагается использовать линейную свертку. При
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этом использование системы Интернет-опроса позволяет подключить широкий круг специалистов-экспертов для
повышения доверительной вероятности оптимальности полученных результатов.
Ключевые слова: оптимизация, учебный план, Интернет-опрос, экспертные оценки, линейная свертка, мно-
жество Парето
ЛІТЕРАТУРА:
1. Н.В. Шаронова Информатизация высшего образования и информационное обеспечение системы управления качеством образования
. Ученые записки Харьков. гуманит. ин-та "Нар. укр. акад." – Х.,2000. – Т. 6. –С. 59-64.
2. А.Ф. Манако, Е.М. Синица Информационные техноло гии в образовании Управляющие системы и машины. – 2017. – № 2. – С. 46-57
3. Сергеева Т. Новые информационные технологии и содержание обучения / Т. Сергеева // Информатика и образование. – М., 1991. –
№ 1. – С. 3-10.
4. Соловов А.В. Проектирование компьютерных систем учебного назначения: учебное пособие. - Самара: СГАУ, 1995
5. Нейлор К. Как построить экспертную систему. – Энергоатомиздат, 1991. – 286 с.
6. Добров Г.М. и др. Экспертные оценки в научно-техническом прогнозировании. – К.: Наукова Думка, 1974. – 160 с.
7. Бешелев С.Л., Гурвич Ф. Г. Математические методы экспертных оцено к. – М.: Статистика, 1980. – 263 с.
8. Подиновский В.В. , Гаврилов В. М. Оптимизация по последовательно применяемым критериям. М., “Сов. радио”, 1975, 192 с.
9. А.И.Орлов Экспертные оценки. – М.: Изд-во МГТУ им. Н.Э. Баумана. – 2009. Ч. 2 : – 2011. – 486 с.
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