210 CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 

___________________ 
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License 
Attribution 4.0 International (CC BY 4.0). 

The usage of digital technologies in the university 
training of future bachelors (having been based on the 

data of mathematical subjects) 

Oksana M. Hlushak1[0000-0001-9849-1140], Svetlana O. Semenyaka1[0000-0001-5083-1433], 
Volodymyr V. Proshkin1[0000-0002-9785-0612], Stanislav V. Sapozhnykov2[0000-0001-6674-7631] 

and Oksana S. Lytvyn1[0000-0002-5118-1003] 

1 Borys Grinchenko Kyiv University, 18/2 Bulvarno-Kudriavska Str., Kyiv, 04053, Ukraine 
o.hlushak@kubg.edu.ua, s.semeniaka@kubg.edu.ua, 
v.proshkin@kubg.edu.ua, o.lytvyn@kubg.edu.ua 

2 Alfred Nobel University, 18 Sicheslavska Naberezhna Str., Dnipro, 49000, Ukraine 
sapozhnikov70@meta.ua 

Abstract. This article demonstrates that mathematics in the system of higher 
education has outgrown the status of the general education subject and should 
become an integral part of the professional training of future bachelors, including 
economists, on the basis of intersubject connection with special subjects. Such 
aspects as the importance of improving the scientific and methodological 
support of mathematical training of students by means of digital technologies 
are revealed. It is specified that in order to implement the task of qualified 
training of students learning econometrics and economic and mathematical 
modeling, it is necessary to use digital technologies in two directions: for the 
organization of electronic educational space and in the process of solving 
applied problems at the junction of the branches of economics and mathematics. 
The advantages of using e-learning courses in the educational process are 
presented (such as providing individualization of the educational process in 
accordance with the needs, characteristics and capabilities of students; 
improving the quality and efficiency of the educational process; ensuring 
systematic monitoring of the educational quality). The unified structures of 
“Econometrics”, “Economic and mathematical modeling” based on the Moodle 
platform are the following ones. The article presents the results of the pedagogical 
experiment on the attitude of students to the use of e-learning course (ELC) in 
the educational process of Borys Grinchenko Kyiv University and Alfred 
Nobel University (Dnipro city). We found that the following metrics need 
improvement: availability of time-appropriate mathematical materials; individual 
approach in training; students’ self-expression and the development of their 
creativity in the e-learning process. The following opportunities are brought to 
light the possibilities of digital technologies for the construction and research 
of econometric models (based on the problem of dependence of the level of the 
Ukrainian population employment). Various stages of building and testing of the 
econometric model are characterized: identification of variables, specification 
of the model, parameterization and verification of the statistical significance of 
the obtained results. 

mailto:o.hlushak@kubg.edu.ua
mailto:s.semeniaka@kubg.edu.ua
mailto:v.proshkin@kubg.edu


CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 211 

 

Keywords: digital technologies, e-learning course, economic and mathematical 
modelling, econometrics, university training, future bachelor. 

1 Introduction 

In the conditions of modern development of the economy of Ukraine, special attention 
is paid to solving complex theoretical and applied problems that quantitatively and 
qualitatively describe the relationship between different economic objects [10]. It 
demands the development and study of new areas of economic theory and related 
scientific disciplines. First of all, there is a need for the development and 
implementation of innovative teaching methods, the usage of which would make it 
possible to form for future bachelors new economic thinking and understanding of the 
essence of economic processes or phenomena, to obtain appropriate know-how of 
regulation and management of these processes at any level of complexity, to predict 
their development [23]. In this regard, the formation and development of competencies 
associated with the ability to optimally combine the possibilities of logical analysis with 
knowledge not only of the laws of mathematics and economics, but also the basics of 
mathematical modeling become important. 

Mathematical modeling with the maximum usage of its potential makes it possible 
to identify and solve professional problems of different nature: to define clearly the 
purpose of the research, to find quickly possible ways to achieve it, to develop 
appropriate models of economic objects or phenomena and on the basis of these models 
to create effective algorithms and programs for optimal solutions to current problems 
[19]. Obviously, mathematics in the system of higher education has outgrown the status 
of the general educational subject and should become an integral part of the 
professional training, on the basis of intersubject connections with special subjects [14]. 
In this regard, it becomes actual to resolve the contradictions between the needs of 
highly qualified specialists who effectively use mathematical tools in their professional 
activities, and the lack of scientific and methodological support for mathematical 
training of students, in particular by means of digital technologies. 

In Ukraine, the development of educational informatization takes place in 
accordance with national and European programs (“Digital agenda of Ukraine – 2020” 
[18], containing priority areas, initiatives, projects of digitalization of Ukraine until 
2020, the thesis of the updated recommendations of the European Parliament and the 
EU Council for lifelong learning [7], etc.). Various aspects of educational 
informatization in the context of mathematical training of students have become the 
subject of research for a number of scientists. Thus, Natalya V. Rashevska [11; 20] 
investigated mobile information and communicational technologies of higher 
mathematics teaching. Kateryna I. Slovak [21; 22] developed a methodology for the 
use of mobile mathematical environments in the process of higher mathematics 
teaching for students of economic specialties. Oksana I. Tyutyunnik [15] described the 
usage of computer math systems in the process of linear programming teaching. Mariia 
A. Kyslovа [12; 13] presented the development of mobile educational environment of 
higher mathematics, Mariia M. Astafieva, Dmytro M. Bodnenko and Volodymyr V. 
Proshkin [2; 1] found out the possibilities of the educational environment for the 



212 CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 

 

formation of critical thinking of students in the process of mathematics learning. 
Oksana M. Hlushak, Volodymyr V. Proshkin and Oksana S. Lytvyn [9] revealed the 
possibilities of e-learning course (ELC) on “Analytical geometry” in the process of 
professional training of students. In these works, the theoretical and methodological 
foundations of the usage of electronic educational environment in the process of 
professional training of bachelors are revealed, the tendencies of the development of 
mathematical educational informatization are indicated. The studies on the use of ICT 
in the process of economic and mathematical modeling learning are of particular 
interest. So, Dana Országhová [16] investigated the e-learning approach in 
mathematical training of future economists. Dimitros Asteriou, Stephen G. Hall [4, pp. 
29–91] and Roberto Pedace [17, pp. 59–134] reviewed the classical linear regression 
model. 

In the above mentioned works the features of formation of qualitative modern 
cloud-oriented educational environment in the context of mathematical subjects 
learning are presented. In addition, the experience of using e-learning courses 
is interesting for our research. Thus Charlotte Brooke, Pamela McKinney and Angie 
Donoghue [5] claim that students who take e-learning courses on the distance learning 
platform use their own time allocated for training more efficiently. Similar ideas are 
found in the works of other scientists (Jana Burgerova, Martina Adamkovičovа [6], 
Paul Drijvers, Carolyn Kieran, Maria-Alessandra Mariotti, Janet Ainley, Mette 
Andresen, Yip Cheung Chan, Thierry Dana-Picard, Ghislaine Gueudet, Ivy Kidron, 
Allen Leung, Michael Meagher [8] etc.). At the same time, the analysis of scientific 
researches testifies the limitation of investigation methodical questions of learning 
econometric modeling in combination with ICT. 

2 The objective of research  

The purpose of the article is to highlight the areas of the use of digital technologies in 
the university training of future bachelors (having been based on the data of 
mathematical subjects). 

3 Research methodology 

The usage of appropriate methods such as scientific literature analysis with the aim of 
establishing the state of readiness of the studying problem, the definition of categorical 
and conceptual apparatus of the research; synthesis, generalization, systematization of 
theoretical justification of the use of digital technologies in the educational process at 
the university and empirical ones: diagnostic (interview, content analysis, testing), 
statistical (Fisher and Student criteria) to test the statistical significance of mathematical 
model promoted to achieve the purpose of the research. 

The research was carried out within the framework of the project “Partnership for 
mathematics learning and teaching at the university” (PLATINUM) of the EU Erasmus 
+ KA203 – Strategic partnership for higher education, 2018-1-NO01-KA203-038887 
and the complex scientific theme of the department of computer science and 



CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 213 

 

mathematics of Borys Grinchenko Kyiv University “Theoretical and practical aspects 
of the use of mathematical methods and information technologies in education and 
science”, SR No. 0116U004625. The experimental base of the research is Borys 
Grinchenko Kyiv University and Alfred Nobel University (Dnipro city). 

4 Results and discussion 

We believe that in order to implement the task of high-quality training of students 
studying economic and mathematical modeling in “Econometrics”, “Economic and 
mathematical modeling” subjects, it is necessary to introduce digital technologies in 
two directions: for the organization of educational space and in the process of solving 
applied problems at the junction of the branches of economics and mathematics 
branches. 

The background for the organization of educational space is the availability of the 
necessary material and technical base (computers, software, communication channels) 
and informational educational environment, the effectiveness and basis of which are 
digital technologies. We believe that the informational and educational environment 
can be organized through the activities of the teacher with the use of an e-learning 
course of the subjects that are aimed at teaching economic and mathematical modeling, 
on the basis of the distance learning platform. The Moodle distance learning platform 
has been introduced into the educational process at the Borys Grinchenko Kyiv 
University. Therefore, electronic courses of “Econometrics”, “Economic and 
mathematical modeling” subjects are presented on the basis of this platform. 

Let us present the advantages of ELC using in the educational process. 
Firstly, it is providing the individualization of the educational process in 

accordance with the needs, characteristics and capabilities of students. The basis 
for the implementation of this ELC characteristic is clearly structured nature, so that 
the placement and sequence of teaching materials corresponds to the logic of the 
mathematical subject studying. For example, the ELC can be presented in the form of 
a chain: a description of the ELC indicating the educational and professional program; 
general information of the academic subject (working curriculum, syllabus, assessment 
criteria, sources, glossary, announcements, information about the author); teaching 
materials for each module: theoretical material, practical (laboratory, seminar) works, 
tasks for individual work of students, modular control, accompanied by video 
materials and hyperlinks that allow students to increase the amount of information. 
Besides, ELC provides information for the final assessment (advancement questions, 
self-assessment test, final test) and contains a list of references and addresses of Internet 
sources for the implementation of independent students’ work. 

Indeed, the structure of ELC allows students to choose a convenient time and rate of 
assimilation of mathematical material, based on their own rhythm of life, individual 
characteristics and abilities. This helps in the best way to realize an individual 
educational trajectory consistent with the following principles: education is for 
everyone and is lifelong. 



214 CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 

 

Secondly, it is improving the quality and efficiency of the educational process. 
This characteristic is directly correlated with the quality of teaching materials, allowing 
to form the mathematical competence of students [3]. The advantage of ELC is the 
following one: its content can be constantly updated in accordance with the 
development of mathematical science, the latest methods of the educational process. As 
a rule, the ELC consists of two types of electronic resources: 

─ resources designed to present the content of educational material (lecture notes, 
multimedia presentations of courses, audio and video materials, guidelines, etc.); 

─ resources that provide the consolidation of the studying material, the formation of 
skills, acquisition of competencies, self-assessment and evaluation of educational 
achievements of students (tasks, questionnaires, testing, forums, including using of 
Web 2.0). 

The ability to receive advice, recommendations and explanations through digital 
interaction, for example, in forums, also contributes to the quality of students’ 
education. 

It should also be noted that the quality of the ELC is also related to the fact that these 
resources are created and reviewed by a number of teachers whose mathematical 
competence meets the immediate requirements of the time. 

Thirdly, it is ensuring systematic monitoring of the education quality. In order 
to implement this characteristic, a clear schedule of the curriculum for implementation 
by students has been submitted on the ELC website. There are also opportunities for 
interactive communication between teachers and students, as well as students among 
themselves. ELC contains a system of monitoring and evaluation of all types of 
educational activities of students. Thus, for the self-test, the testing is submitted. 
Assessment of tasks is carried out automatically that excludes subjective assessment 
from the teacher. 

According to the above mentioned, electronic educational courses of 
“Econometrics”, “Economic and mathematical modeling” subjects have the unified 
structure (Fig. 1): general information on the subject (curriculum of the subject, plan, 
assessment criteria, printed sources and Internet resources, glossary); thematic 
modules, which include information about the main topics of the module the theoretical 
material in the form of a structured lecture material submitted by means of the lesson, 
multimedia presentations of lectures, audio, video learning materials and tests (training 
and advancement); laboratory work, which reflect the content of the work, list of 
individual tasks and methodical recommendations about performance of work; tasks 
for individual work with the guidelines of the performing task, a list of individual tasks 
and their assessment criteria; tasks for module test, which provides individual tasks and 
criteria of assessment of the work performed. 

Each of these ELC blocks contributes to the implementation of individual tasks. 
Thus, the theoretical material is built in such a way that a student who missed classes 
could easily master the training material, and a student who was in the audience at the 
lesson could systematize the material obtained at the lesson, test himself for 
understanding and perception of the topic with the help of tests, which had been built 



CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 215 

 

into the lectures. If students have questions, they have the opportunity to ask them on 
the forum discussion on the topic of each content module. 

 

Fig. 1. ELC structure of “Econometrics” 

ELC laboratory works are presented in the form of web pages with a common structure: 
theme, purpose, tasks, form of result presentation, deadlines and assessment criteria 
(Fig. 2). Educational and methodological materials recommended to read are presented 
under the laboratory work: these are guidelines for tasks, questions for laboratory work, 
preparation step-by-step algorithms for tasks, examples of construction and research of 
models. In addition, the block of laboratory works contains instructional videos for 
performing tasks according to protocol of the laboratory work. 

For self-test is planned the block of the task for individual work of students which 
provides individual tasks for each student, methodical recommendations to their 
performance and advancement questions. 

At the end of the study of each module, a modular test work is offered for students 
of economic and mathematical specialties. The form of module tests for each content 
module is different: a complex test that involves answers to 40 questions of different 
types: multivariate, alternative, with a short answer, numerical, questions to establish 
compliance, or the construction and research of economic and mathematical models for 
an individual set of input data. 

In our opinion, such a methodological approach to supply educational material with 
the use of digital technology for building electronic educational environment will 
promote student’s motivation for the subject learning, implementation of a systematic 
approach to mastering academic content and implementation of the principles of 
personality-oriented approach. Therefore, due to the use of this ELC in the educational 



216 CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 

 

process of studying “Econometrics”, “Economic and mathematical modeling” subjects, 
the teacher will be able to organize individual, group and frontal form of student work. 

 

Fig. 2. Example of the structure of laboratory work 

To find out the real attitude of students to the use of ELC in economic and mathematical 
modeling, we conducted a pedagogical experiment during 2018-2019. The basis of the 
experiment was Borys Grinchenko Kyiv University and Alfred Nobel University 
(Dnipro city). In total, 125 students of “Finance, banking and insurance”, 
“Management”, “Economics”, “Accounting and taxation” specialties took part in the 
research. Respondents were asked 10 questions about the usefulness of the ELC with 
economic and mathematical modeling with the following answers: “Yes”, “rather Yes 
than No”, “rather No than Yes”, “No”. In the research, we were interested only in “Yes” 
answer, which we considered as a clear indicator of readiness for the effective use of 
ELC in the educational process. 

As a result of the survey, the following results were obtained (see table 1). 
According to the results of the research, students generally express a positive attitude 

to the use of ELC with economic and mathematical modeling in the educational 
process. Special noticeable dynamics in the evaluation of the following indicators: is 
constant communication with the teacher (+7.2%), ability to study mathematics 
conveniently (+5.5%), favorable conditions for learning (+3.4%). The following 
indicators need to be improved: availability of educational mathematical materials that 
meet the requirements of the time; individual approach in teaching; self-expression of 
students and development of their creativity in the e-learning process. 

The second direction of the introduction of digital technologies in the process of 
economic and mathematical modeling teaching of future bachelors is the demonstration 
of ICT as a tool for the construction and research of econometric models. Let’s consider 



CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 217 

 

more detailed influence of the following factors on the example of the problem of 
dependence of the level of employment of the population of Ukraine: 

1. share of employees with higher education in % to the list number; 
2. labor productivity growth rate; 
3. growth rate of the average wage; 
4. capital investment index; 
5. export-import coverage ratio. 

Table 1. Attitude of students to the use of ELC in economic and mathematical modelling 

Questions 
Answer: “Yes” 

At the beginning 
of the experiment 

At the end of 
the experiment 

1. ELC provides opportunities to conveniently study 
mathematics (at any time, in a convenient place and pace) 

16.3 21.8 

2. The use of ELC improves the results of teaching 
mathematical subjects 

12.2 14.2 

3. ELC helps students to keep in touch with the teacher 
(on-line or off-line) 

8.0 15.2 

4. ELC is available educational mathematical materials 
that meet the requirements of the time 

12.6 12.5 

5. ELC provides an individual approach in the educational 
process 

8.2 10.5 

6. ELC of mathematical subjects effectively contributes to 
the formation of mathematical competence 

12.3 12.7 

7. ELC enriches the educational process with the most 
advanced digital technologies 

8.0 8.9 

8. ELC provides students with equal opportunities to 
study mathematical subjects 

16.1 18.9 

9. ELC does not limit self-expression of students and 
contributes to the development of their creativity 

8.3 8.7 

10. ELC creates favorable conditions for studying (ELC 
allows students to feel comfortable when checking 
knowledge; eliminates subjective attitude on the part of 
teachers) 

8.9 12.3 

 
The statistics for the task are taken from the official website of the State Statistics 
Service of Ukraine [24]. The problem will be solved with the help of general-purpose 
application software MS Excel. 

The first stage for constructing and researching of an econometric model is the 
identification of variables. According to the results of identification we get: 

Y – level of employment of the population of Ukraine; 
X1 – share of employees with higher education in Ukraine; 
X2 – growth rate of labor productivity in Ukraine; 
X3 – growth rate of average wages in Ukraine; 
X4 – index of capital investments in Ukraine; 
X5 – export-import coverage ratio in Ukraine. 



218 CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 

 

The specification of the model is the second stage of construction, it provides the 
choice of the form of f communication between the factor and the resultant variable. 
We will carry out the construction of the correlation field depending on the level of 
employment of the population from each of the factors using a scatter chart in MS Excel 
(Fig. 3). To determine the best type of relationship between the factor and the result, 
we will use the trend line. Using the trend line format dialog box, we will display the 
coefficient of determination and the equations of the model on the chart (Fig. 4). 
Comparing the determination coefficients for each type of corresponding dependencies 
R2, we can conclude that the most optimal were the dependencies for which the value 
R2 takes the maximum value of possible ones. As a result, on the basis of the above 
research, it was established the existence of a linear relationship between the relevant 
factors of the econometric model. 

Hence, the theoretical multiple regression equation will take the form 

 𝑌 = 𝑎0 + 𝑎1𝑋1 + 𝑎2𝑋2+𝑎3𝑋3 + 𝑎4𝑋4 + 𝑎5𝑋5 + 𝑢, (1) 

where u – probabilistic component that is not directly determined from the equation. 
 

 

Fig. 3. Scatter chart 

The next stage of the model construction is the parameterization stage: finding of 
parameter estimate 𝑎�̂� (𝑖 = 0,5̅̅ ̅̅ )  and constructing of the corresponding regression 
equation. This step can be implemented in MS Excel in several ways. The first method 
is purely mathematical, and consists in determination of the estimates of parameters 
using the least squares method using numerical calculations. To do this, we write down 
the vector-column of observations of the dependent (productive) variable 𝑌 and the 
matrix of observations of independent (factor) variables 𝑋𝑖 and we apply to calculate 
estimates of regression coefficients by the formula  

 �̂� = (𝑋𝑇𝑋)−1𝑋𝑇𝑌,  (2) 

y = 0.7159x - 11.67
R² = 0.0301

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

55 56 57 58 59 60 61

Distribution of employees by level of 
education and regions as of December 31



CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 219 

 

where �̂� - the vector is a column of estimates of the equation coefficients, 𝑋𝑇 – the 
transposed matrix to the matrix 𝑋.,  (𝑋𝑇𝑋)−1 – inverse matrix to the product of two 
𝑋𝑇𝑋. To implement this method, students will be able to multiply matrices, find 
transposed and inverse matrices in MS Excel using the mathematical functions 
MMULT, TRANSPOSE, MINVERSE. 

 

 

Fig. 4. The parameters of the trend line 

The second method of finding parameter estimates is implemented through “Analysis 
package” add-in and “Regression” tool. After entering a range containing a set of 
statistics of the dependent variable (employment rate of the population of Ukraine) – 
𝑌 and 𝑋𝑖 a set of observations of independent (factor) variables MS Excel displays the 
results, which reflect the estimates of the coefficients (Fig. 5). 

The third way to find parameter estimates is to use LINEST statistical function, 
which after entering the known values 𝑌,  𝑋𝑖 , constant and statistics, displays the result 
as a table of 5 rows and 6 columns by pressing the combination of Ctrl+Shift+Enter 
(table 2). 

Table 2. The result of applying of LINEST statistical function 

-0.8864 0.0157 -0.0017 0.00002 0.5061 45.7234 
1.0676 0.0231 0.0020 0.0002 0.3097 8.0111 
0.2517 1.5171 #N/A #N/A #N/A #N/A 
0.7401 11.0000 #N/A #N/A #N/A #N/A 
8.5174 25.3179 #N/A #N/A #N/A #N/A 

 



220 CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 

 

 

Fig. 5. Finding of parameter estimates using “Regression” tool of “Analysis package” add-in 

The first row of the table shows the value of parameter estimates. Thus, the resulting 
multiple regression equation will take the form: 

 �̂� = 45.723 + 0.506𝑋1 − 0.00002𝑋2 − 0.002𝑋3 − 0.016𝑋4 + 0.886𝑋5. (3) 

Note that the last two methods of finding parameter estimates, in our opinion, is 
advisable to use only after familiarizing of students with the first method, which 
demonstrates the step-by-step application of the mathematical apparatus for finding 
parameter estimates. 

The next stage is the research of the model – check for adequacy, which involves 
finding the average value of the relative errors of approximation 𝐴𝑖, which are measured 
as a percentage and determined by the formula: 

 𝐴𝑖 =    |
𝑢𝑖

𝑦𝑖
|   ⋅  100%. (4) 

Hence,  

 �̄� =
1

𝑛
⋅ ∑ 𝐴

𝑖
. (5) 

Students are offered to make these calculations in the table 3 and finding the coefficient 
of determination by formula. 

Table 3. Table for registration of calculations 

Y X1 X2 X3 X4 X5 �̂� u u2 
𝑢𝑖

𝑦𝑖

 Y2 

 
So, having carried out calculations we will receive  

 �̅� ≈ 1.7%,    𝑅2=0.888207527≈0.89. 



CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 221 

 

We can say that the model is adequate, since the average value of the relative 
approximation errors is in the range of 8-10%. The coefficient of determination tends 
to 1, and the closer R2 to 1, the more significant is the relationship between these 
variables, that is, the change in the resulting variable is largely due to the change in the 
factor variable and only a small part of the changes – other factors. 

The last stage of the research of the model is the check of statistical significance. To 
check the statistical significance of the results, we offer students two criteria: Fisher 
criterion (F-criterion) and Student criterion (t-criterion). 

Checking the statistical significance, we put forward two hypotheses – the null 
hypothesis 𝐻0: 𝑅2 = 0 and the alternative one to it 𝐻1: 𝑅2 ≠ 0. Next, we calculate the 
experimental value according to the formulas of each criteria, find the tabular values of 
each of the criteria for a certain number of degrees of freedom and compare the 
experimental values. Make appropriate conclusions: if the experimental value exceeds 
the table one, the null hypothesis is rejected. 

Students should note that the tabular values for F-criterion) and t-criterion shall be 
found using the statistical functions FINV and TINV. 

According to the described calculations we find 𝐹1 = 17.479 and 𝐹0 = 3.204. Since 
𝐹1 > 𝐹0, the null hypothesis is rejected, so the model is statistically significant. 

Similar results are obtained by the t-criterion. Thus, t1 = 9.349 and t0 = 2.593. Since 
𝑡1 > 𝑡0, the null hypothesis is rejected, so the model is statistically significant. 

5 Conclusions 

1. As a result of the analysis of scientific sources it is established that mathematical 
modelling with the maximum use of its potential makes it possible to identify and 
solve professional problems of different nature: to define clearly the purpose of the 
research, to quickly find possible ways to achieve it, to develop appropriate models 
of economic objects or phenomena and on the basis of these models to create 
effective algorithms and programs for optimal solutions to current issues. It is noted 
that in order to implement the task of obtaining high-quality training of future 
bachelors on study of build and research of economic and mathematical modelling 
within “Econometrics”, “Economic and mathematical modelling” subjects it is to 
introduce digital technologies in two directions: for the organization of educational 
space and in the process of solving applied problems at the junction of economic 
sectors and mathematics. 

2. It is established that for the organization of educational space it is advisable to use 
e-learning courses of “Econometrics”, “Economic and mathematical modelling” 
subjects, which is a complex of teaching materials created for individual and group 
learning using digital technologies for teaching mathematical modelling to students. 
Based on the indicated possibilities of application of the electronic learning course, 
as well as its didactic functions, the structure of the electronic learning course of 
“Econometrics”, “Economic and mathematical modelling” subjects on the basis of 
Moodle platform is developed and described. 



222 CTE Workshop Proceedings, 2020, Vol. 7: CTE-2019, pp. 210-224 

 

3. The results of a pedagogical experiment regarding the study of attitude of students 
to the use of electronic learning courses are presented. It is established that students 
in general positively evaluate the use of ELC in the educational process. At the same 
time, the following indicators need to be improved: availability of educational 
mathematical materials that meet the requirements of the time; individual approach 
in teaching; self-expression of students and development of their creativity in the e-
learning process. 

4. Features of application of MS Excel on an example of a problem of dependence of 
employment level of the population of Ukraine on influence of the chosen factors 
are considered. Various stages of building and study of the econometric model are 
characterized, they are following ones: identification of variables, specification of 
the model, parameterization and verification of the statistical significance of the 
obtained results. 

We see the prospect of further scientific inquiry in the research of implementing an 
interactive approach using electronic learning courses. 

Gratitude. The research, the results of which are presented in the article, was carried 
out in the framework of the project “Partnership for teaching and teaching mathematics 
at the University” (PLATINUM) of EU Erasmus + KA203 – Strategic partnership for 
higher education, 2018-1-NO01-KA203-038887. This article reflects only the views of 
the author and the European Commission cannot be responsible for any usage of the 
information contained here. 

References 

1.  Astafieva M., Bodnenko, D., Proshkin, V.: Cloud-oriented Training Technologies as a 
Means of Forming the XXI Century Skills of Future Mathematics Teachers. CEUR 
Workshop Proceedings 2387, 507–512 (2019) 

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