=Paper=
{{Paper
|id=Vol-2732/20201233
|storemode=property
|title=The Use of Digital Technologies for Flipped Learning Implementation
|pdfUrl=https://ceur-ws.org/Vol-2732/20201233.pdf
|volume=Vol-2732
|authors=Oksana Klochko,Vasyl Fedorets,Svitlana Tkachenko,Olena Maliar
|dblpUrl=https://dblp.org/rec/conf/icteri/KlochkoFTM20
}}
==The Use of Digital Technologies for Flipped Learning Implementation==
https://ceur-ws.org/Vol-2732/20201233.pdf
The Use of Digital Technologies
for Flipped Learning Implementation
Oksana Klochko1[0000-0002-6505-9455], Vasyl Fedorets2[0000-0001-9936-3458],
Svitlana Tkachenko3[0000-0003-0530-5973], Olena Maliar4[0000-0001-5924-4120]
1,3 Vinnytsia Mykhailo Kotsiubynskyi State Pedagogical University, Vinnytsia, Ukraine
{klochkoob, tsvitjane}@gmail.com
2,4 Communal Higher Education Institute "Vinnytsia Academy of Continuous Education",
Vinnytsia, Ukraine
{bruney333@yahoo.com, malayryk@gmail.com}
Abstract. The article presents the study of the use of digital technologies for
flipped learning implementation. In this context, the use of the virtual learning
environment has been analyzed. The assessment of the efficiency of flipped
learning implementation based on this environment and the process of defining
the ways of improving the components of the scientific-methodological system
of flipped learning was carried out using the technologies of machine learning.
The innovative and personalized nature of flipped learning implemented with
the use of the virtual learning environment is a methodological condition for in-
creasing the students’ interest in learning, activating their study process, reveal-
ing their cognitive and personal potentials as well as developing digital compe-
tences, independence and individuality etc. The authors emphasize that the use
of flipped learning based on digital technologies requires thorough development
of the virtual learning environment, a detailed selection of the study content and
its adaptation to the concrete groups of students. By stating this we mean the
search for more effective and systemic ways of achieving learning objectives:
the methods of problem-based learning, flipped learning; the selection of digital
tools for presenting lecture materials, development of supplementary tasks; cor-
rection of the theoretical materials and the tasks on the basis of the study results
and achievements of the students; motivating students to work with the study
materials on their own etc. Machine learning was used to group the students by
clustering the results of their educational achievements. Based on these data, the
personalized learning vector, characteristic of a specific group of students, was
determined.
Keywords: digital technologies, flipped learning, virtual learning environment,
machine learning, cluster analysis, innovative pedagogy.
1 Introduction
Nowadays, we cannot imagine the field of education without the use of digital tech-
nologies in the education process. With the appearance of virtual learning environ-
ments, we may observe a rapid accumulation of educational data. In conditions of
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
active free use of digital educational environments, the assessment of the data of
virtual learning environments with the use of machine learning methods is becom-
ing more and more significant.
In modern conditions, a society requires educational services that follow the princi-
ples of student-centric education thus making the student a central figure of the teaching
process. In this context, innovative teaching methods include: shifting the role of a
teacher to that of a facilitator, application of interactive, project work and research
methods, particularly, the methods of problem-based learning, flipped learning, the
clicker technology. In the course of implementation of these principles, the most popu-
lar mixed learning model, namely, the flipped classroom model, requires particular
attention.
The innovative and personalized nature of flipped learning may be provided with
the help of virtual learning environment (VLE), which is a methodological condition
for raising the students’ interest in learning, activating their study process, revealing
their cognitive and personal potentials as well as developing digital competences,
independence and individuality etc. VLE contains study materials (lectures, tasks,
tests, reference materials etc.) and is a useful tool while introducing the flipped learn-
ing method in the process of studying a course.
А. Littlejohn explains the ideas of intellectual and personal students’ potentials ac-
tualization based on the use of digital technologies. This includes the development of
individual learning plans by the students, knowledge artefacts and contemplations on
the achievements [1]. Such learning model is focused on how students plan, study,
learn, create and reflect/assess, its components include: consuming knowledge, creat-
ing new knowledge, connecting with people, contributing new knowledge resources
[1].
M. Shyshkina, U. Kohut, M. Popel have conducted a comparative analysis of the
cloud learning components, which provide access to mathematical software [2].
O. Glazunova, M. Shyshkina presented the conceptual-methodological foundations
for the development of a university cloud learning and research medium [3]. On the
basis of the presented methodology, the model and the experimental study, the ways
of resources and services integration, of increasing the learning efficiency and of
providing access to the necessary educational tools are revealed [3].
The systemic nature of students’ individual work in the cloud learning medium was
studied by O. Kolgatin, L. Kolgatina, N. Ponomareva, and E. Shmeltser, who empha-
size the low cognitive interest of the students as one of the problems that may be
solved by personalization of tasks and exercises developed; proper time management;
facilitation of students’ cooperation; actualization of creative aspects of the tasks
etc. [4].
Digital technologies of open distance education were studied by V. Kukharenko,
T. Oleinik, they define the problems of open distance learning and of mixed learning
as well as suggest ways of overcoming them [5].
In the modern conditions of educational services transformation and rapid educa-
tional data accumulation, the integrated use of digital technologies, namely, the
VLE and machine learning in combination with teaching techniques of flipped
learning are becoming more and more appealing and relevant. But so far this field
has not been sufficiently studied by the researchers.
Thus, such scientists as V. Naidu, B. Singh, K. Farei, N. Suqri claim that ma-
chine learning may be the revolutionary approach to finding out the needs of the
student according to his/her skills in the course of implementation of the student-
centric approach based on the flipped classroom model. They also suggest ways of
increasing the effectiveness of flipped teaching by decreasing the number of manual
tasks of the teachers [6].
In this respect, there is an important study of flipped learning with the applica-
tion of machine learning methods (Neural Networks, Naïve Bayes, Random Forest,
kNN, and Logistic regression) conducted by J. Nouri, M. Saqr, U. Fors. The authors
forecasted the activities of students in the flipped classroom by providing and re-
ceiving feedback. Flipped learning is presented as a pedagogical condition of effec-
tive learning interaction of students, by managing the educational process, which
includes forecasting its results, and is also viewed as a systemic opportunity for
using digital technologies [7].
An empirical comparison of clustering machine learning methods with the aim of
statistical analysis of the data received in the course of a survey on the presence of
an Internet-addiction formed as a result of improper Internet use, which was con-
ducted among the students majoring in computer studies, is carried out by
O. Klochko and V. Fedorets [8].
The application of machine learning techniques for processing VLE data will allow
the educators to conduct the analysis of the students’ learning achievements and de-
termine the ways of increasing the efficiency of flipped learning application on the
basis the received results.
Unsolved aspects of the problem. Despite the experience and the result of this is-
sue’s study by the Ukrainian and foreign researchers and taking into consideration the
novelty of using machine learning for VLE data processing in the course of flipped
learning application, the issue of developing the techniques for study content selection
and its adaptation to concrete groups of pupils has not been fully solved by the re-
searchers. The problems that occur in the course of looking for effective machine
learning methods for solving the set tasks in order to improve the study results also
remain relevant. The issues outlined above need to be studied further.
The purpose of the research is to describe the aims, content and ways of broaden-
ing the flipped learning possibilities with the application of the virtual learning envi-
ronment and machine learning.
2 Methods of the Research
The study on the introduction of the flipped learning method with the application of
VLE was conducted on the example of studying the subject of Geometry, topic
“Geometrical Transformations” in the 9 th form.
Flipped learning is a form of learning, which allows change the traditional educa-
tional process in an innovative and personally-oriented way. Accordingly, the learn-
ing process is formed on the basis of the following system-organizing components:
the students’ homework is to watch the videos with the study materials of the next
lesson; the students cover the theoretical material on their own, and the study time
in class is spent on doing practical tasks [9-13] as well as for discussion and actual
application of the theoretical knowledge and defining the optimal ways of its appli-
cation to the real needs. Thus, flipped learning corresponds to the competence para-
digm, which is based on the idea of practical application of knowledge.
A flipped lesson is a nourishing medium, which directly provides the formation
of general and special competences. This includes the creation of conditions for
gaining [9-13]: experience and practice reflection, development of skills of stating
the problem and problematization; ability to set goals and defining the ways to
achieve them; actualization of the activity-based and practically oriented nature of
learning, i.e. involving the students in the implementation of the socially and vitally
significant activity – researching, designing, modelling etc. In this respect, the sig-
nificant points are: orientation of the study process towards development of the
student’s independence and responsibility for the results of his/her work, organiza-
tion of effective discursive interaction between the participants of the educational
process and of fruitful group work; an obligatory inclusion of developing and crea-
tive tasks into the content of a lesson [14]; actualization of critical thinking [4] as
well as of personal and intellectual-value potential of a personality.
In order to implement flipped learning an educational website “Geometrical
Transformations” (VLE) [15] was developed; it contains a system of various meth-
odological developments that a teacher may use to work with students while study-
ing the topic “Geometrical Transformations”: a topical plan, multi-media presenta-
tions, lesson drafts, tests etc.
The flipped learning technique presupposes a combined form of traditional and
e-learning, using the VLE tools. Figure 1 presents a structural model of the scien-
tific-methodological system of teaching students the topic “Geometrical Transfor-
mations” based on flipped learning with the use of machine learning techniques.
According to the personality oriented approach, a student, as the subject of an edu-
cational process, occupies the central place in this model. A teacher is another sub-
ject of an educational process. The following blocks were singled out as the other
interrelated elements of the scientific-methodological system: target, content, meth-
odological, organizational-activity, diagnostic-comparative (with the use of ma-
chine learning tools). This model is designed on the basis of the systemic approach,
it is an open dynamic system and it interacts with the educational space.
In order to solve the set tasks, the following research methods were used: analy-
sis of the works of the scientists in the field of application of the flipped learning
method with the use of digital technologies; synthesis – in order to generalize and
conceptualize the Ukrainian and foreign experience, as well as to particularize the
conceptual framework, improving the experience of drafting and developing of an
educational website of a teacher, formulating the received results; observation, test-
ing students in general secondary educational institutions (GSEI); observation and
conducting surveys among master students, school teachers and university profes-
sors; statistical methods and machine learning methods, particularly, cluster analy-
sis, in order to process the results of the research; modeling; drafting an educational
website of a teacher.
Fig. 1. A structural model of the scientific-methodological system of teaching students the
topic “Geometrical Transformations” using the flipped learning method based on VLE with
the use of machine learning.
While defining the organizational-pedagogical conditions, needed for successful
student training on the topic “Geometrical Transformations” using flipped learning
with the application of VLE, we took into consideration: the technical possibilities
of a GSEI; the presence of a necessary licensed software; the use of flipped learning
in order to form the necessary competences in students; the presence of the neces-
sary methodological materials for giving lessons; forming positive motivation
among the students towards studying the topic “Geometrical Transformations” us-
ing flipped learning; the use of current digital educational tools and techniques (e.g.
the educational websites).
The first stage of the research was ascertaining (April 2019). The purpose of this
stage was to study the state of the researched problem and define ways of solving it,
carrying out the diagnostics of the initial level of knowledge in Geometry among
the students (particularly, in the context of the topic “Geometrical Transfor-
mations”). The research was conducted on the basis of the 9 th forms of general sec-
ondary educational institutions (GSEI) of the Vinnytsia oblast. The number of stu-
dents involved in the research was 41. Pupils of two classes took part in the experi-
ment, the number of students – 20 and 21 in each class, which we selected as a con-
trol and experimental groups respectively.
At the ascertaining stage of the research, the questionnaire method was applied,
which allowed us to clarify the organizational conditions of studying the topic “Ge-
ometrical Transformations” using flipped learning with the application of VLE in
GSEI.
The second stage of the study was exploring (May 2019). At this stage, flipped
learning using VLE was applied for studying the topic “Geometrical Transfor-
mations”.
This stage included searching for, analyzing and testing the VLE tools and
flipped learning techniques with the application of machine learning methods. The
students passed the tests several times in order for us to determine the ways of
adapting the study content to certain groups of students according to the results of
their study achievements. To assess the efficiency of introduction of particular
components, a methodology for assessing the study achievements of pupils on the
given topic was developed.
The purpose of the forming stage of the research (May 2019) was the assessment
of the efficiency of the developed teaching methodology on the topic “Geometrical
Transformations” using flipped learning with the application of VLE.
In order to carry out the forming stage of the research, the control and experi-
mental groups of students were taught within the GSEI in accordance with the de-
fined organizational-pedagogical conditions. The control group was taught using
the traditional methods and methodology and the experimental group – using
flipped learning with the application of VLE.
To compare the results and achievements of the students of the control and ex-
perimental groups, we used a Wilcoxon-Mann-Whitney test [16, p. 87]. The theoreti-
cal (T) and empirical (Wα) value of this criterion are calculated by the formula (1-2):
T=S–n1(n1+1)/2 (1)
n1
where S = R (x ) – is the rank sum R(х ) і-th characteristic х ; n – sample size
i =1
i і і 1
(control group).
n1 n 2 n n (n 1 + n 2 + 1)
W = + x 1 2 , (2)
2 12
where n1 is the size of the control group, n 2 – the size of the experimental group,
n=n1+n2; хα – normal distribution quantile (for the significance level α=0.05
хα=1.64).
To detect typical students’ mistakes in order to adapt the components of the sci-
entific-methodological system of teaching students using the flipped learning meth-
od based on VLE, we applied such clustering machine learning methods as Canopy,
EM (Expectation Maximization) and Farthest First on the basis of the Weka plat-
form [17, 18, 19, 20]. A more detailed description of the EM (Expectation Maximi-
zation) and Farthest First algorithms are presented in the work of O. Klochko and
V. Fedorets [8, 18, 19].
The main idea of the Canopy algorithm lies in the possibility to decrease the
number of distance calculations necessary for clustering by first dividing the data
into subsets that overlap according to the greedy algorithm and then only measuring
the distances between data point pairs that belong to the subset.
The clustering process using this algorithm can be divided into two stages. At the
first stage, we use the shortest distance in order to create a certain number of over-
lapping subsets, the so-called “canopy”. Canopy is simply a subset of elements (i.e.
data points or elements), which according to some level of similarity are located
within some threshold distance from the central point. It should be mentioned that
some element may be under more than one canopy and that each element must be
under at least one canopy [17].
At the second stage, we apply any traditional clustering algorithm using an exact
distance criterion, but with a restriction that we do not calculate the distance be-
tween the two points that never appear in one “canopy”, considering the distance
between them to be infinite [17].
Within the framework of this research, we used the following general parameters
for each of the algorithms: the size of the test sample – 215; the number of clusters
– 4, determined with the help of validity indices for testing Dunn, DB, SD, СDbw
and S_Dbw [21; 22; 23] (Table 1). The test was on Geometry, on the topic “Geomet-
rical Transformations”. They consisted of 10 tasks, for the first 8 tasks you could
receive 8 marks (one mark per task) and for the other 2 – maximum 4 marks (2 marks
for each task).
Table 1. Number of clusters (calculated with the help of quality indices).
Algorithms
Index
Expectation Maximization Canopy Farthest First
Dunn 4 6 7
DB 4 5 5
SD 4 4 4
СDbw 4 4 4
S_Dbw 4 5 6
3 Results and Discussion
Having conducted the analysis of the organizational conditions that may be applied in
the course of studying the topic “Geometrical Transformations” using flipped learning
with the application of VLE, having analyzed the results of the survey conducted
among school teachers of the Vinnytsia oblast (15 people), master students majoring
in Secondary Education (Computer Studies) and Secondary Education (Mathematics)
(7 people), professors of Mykhaylo Kotsiubynskyi Vinnytsia State Pedagogical Uni-
versity (6 people), we have determined the main organizational-pedagogical condi-
tions (see Fig. 2). As can be seen from Figure 2 the following organizational-
pedagogical conditions received the highest number of points from the afore stated
respondents who took part in the survey: forming positive motivation among the stu-
dents towards studying the topic “Geometrical Transformations” using flipped
learning – 271 points; the use of flipped learning in order to form the necessary
competences in students – 261 points; the use of current digital educational tools
and techniques (e.g. the educational websites) – 256 points. The fewer number of
points was received by the following organizational-pedagogical conditions (see
Fig. 2): the technical possibilities of a GSEI – 169 points; the presence of a neces-
sary licensed software – 137 points; the presence of the necessary methodological
materials for giving lessons – 179 points.
Such a result is determined by the fact that if compared with the first three condi-
tions, other organizational-pedagogical conditions, the ones that received a smaller
number of points, are not defining, however, they are also important for the respond-
ents. The absence of those organizational-pedagogical conditions that received the
highest number of points, makes the integrated use of flipped learning and modern
digital tools of educational technologies ineffective. For instance, if students lack the
motivation to study the topic “Geometrical Transformations”, it is impossible to
achieve high results using flipped learning. As for the need to have licensed software,
we may state that nowadays software market offers free software, which can be used
in the educational process without a license, namely, Google cloud technologies.
Fig. 2. Results of the respondents’ assessment of the organizational-pedagogical conditions
necessary for effective teaching of the topic “Geometrical Transformations” using flipped
learning with the application of VLE.
Let us look at the components of the “Geometrical Transformations” website [14],
which was used in the course of the study (see Fig. 3): 1) a topical plan highlights the
sequence of subtopics, which need to be mastered in the course of studying the stated
topic; 2) the “Theoretical Reference Guide” section contains a multi-media presenta-
tion on the topic as well as some useful links; 3) the “Lesson Drafts” section contains
materials for every subtopic: motivation of the students’ study activity, preparatory
tasks for forming the conceptual framework and typical cognitive schemes, tasks for
consolidation of the knowledge received, tasks for laboratory work, tasks ensuring the
formation of key competences and cross-topic references, test tasks, project tasks;
4) the “Problem Books” contain problem books, training videos and games, which
could be used while studying the given topic.
The results of the ascertaining stage of the research have shown that the average
level of preparation of students in Geometry at the start of studying the topic “Ge-
ometrical Transformations” in the control and experimental groups was relatively
homogeneous and was 6.8 and 6.5 points respectively.
Fig. 3. Structure scheme of the “Geometrical Transformations” website (home page, topical
plan, theoretical reference guide, lesson drafts, interesting materials, problem books, education-
al videos, educational games).
The analysis of the research results showed that after studying the topic “Geometrical
Transformations” using flipped learning with the application of VLE, the experi-
mental group demonstrated positive dynamics, but the changes were insignificant
(Table 2, Fig. 4). The average point was (Table 2, Fig. 4): in the control group – 6.6,
the average level of educational achievements is “sufficient”; in the experimental
group – 8.2, the average level of students’ educational achievements is “medium”.
Table 2. Levels of educational achievements of students on the topic “Geometrical Transfor-
mations” at the forming stage of the research.
Level Forming stage
of educational Experimental group Control group
achievements of Number Number
% %
students of students of students
Low, Sufficient 5 23.81 12 60.00
Medium 11 52.38 5 25.00
High 5 23.81 3 15.00
Total: 21 100.00 20 100.00
Average point - 8.20 - 6.60
Let us prove the statistical validity of the received results. The number of students:
control group – n1 = 20; experimental group – n2 = 21.
Using the bilateral Wilcoxon-Mann-Whitney test [16, p. 87], let us check the hy-
pothesis H0: P(X ≥ Y) = 0.5, which presupposes that the marks of the students of the
control (X) group are with identical probability P = 0.5 statistically higher (or equal)
to the points of the experimental (Y) groups, i.e. the marks of the students of one
group are on average (statistically) higher (or equal) to the marks of the students of
the other group. If this hypothesis does not prove to be true, then we accept the alter-
native hypothesis: H1: P(X < Y) ≠ 0.5.
Fig. 4. Levels of educational achievements of students on the topic “Geometrical Transfor-
mations” at the forming stage of the research.
On the basis of the received data, we calculate the value of the T criterion by the for-
mula (1):
T= 424.5–20·21/2=214.5,
21
S= R (x ) =24.5 .
i =1
i
The empirical value of the Wα is calculated using formula (2):
20 21 20 21 (20 + 21 + 1)
W = + 1.64 = 272.9
2 12
Thus, T=214.5 < Wα=272.9, and according to the decision making rule when using
the bilateral criterion, the null hypothesis H0 deviates at the level α=0.05 and an alter-
native hypothesis H1 is accepted. We make a conclusion that the level of educational
achievements of students in the experimental group is statistically higher than the
level of educational achievements of the control group.
In this research, we use clustering methods of machine learning in order to adapt
the components of the scientific-methodological system of studying the topic “Geo-
metrical Transformations” using the flipped learning method based on VLE. Namely,
determining the main typical mistakes in studying the stated topic that were made in
the test taken at the end of studying the topic (students took tests several times). Re-
ceived the following results:
1. The EM (Expectation Maximization) algorithm (Fig. 5, Table 3). There are 25
objects in the first cluster, 66 in the second, 47 in the third and 77 in the fourth. Ob-
jects of the first cluster are the students, whose overall mark for the test approximates
3; objects of the second cluster are the students, whose overall mark for the test ap-
proximates 10, objects of the third cluster are the students, whose overall mark for the
test approximates 6 and objects of the fourth cluster are the students, whose overall
mark for the test approximates 7.
Objects of each of the clusters are united by the fact that most of them have made a
mistake in tasks 9 and 10.
Fig. 5. Visual presentation of the test data after clustering following the EM algorithm.
Table 3. Cluster distribution of the objects, EM algorithm.
Clusters Clustered Instances
0 25 (12%)
1 66 (31%)
2 47 (22%)
3 77 (36%)
2. The Canopy algorithm (Fig. 6, Table 3). There are 106 objects in the first cluster,
30 in the second, 25 in the third and 54 in the fourth. Objects of the first cluster are
the students, whose overall mark for the test approximates 11; objects of the second
cluster are the students, whose overall mark for the test approximates 8, objects of the
third cluster are the students, whose overall mark for the test approximates 3 and ob-
jects of the fourth cluster are the students, whose overall mark for the test approxi-
mates 6.
Objects of each of the clusters are united by the fact that most of them made a mis-
take in task 10.
3. The Farthest First Algorithm (Fig. 7, Table 5). There are 52 objects in the first
cluster, 7 in the second, 138 in the third and 18 in the fourth.
Fig. 6. Visual presentation of the test data after clustering following the Canopy algorithm.
Table 4. Cluster distribution of the objects, Canopy algorithm.
Clusters Clustered Instances
0 106 (49%)
1 30 (14%)
2 25 (12%)
3 54 (25%)
Objects of the first cluster are the students, whose overall mark for the test approxi-
mates 5; objects of the second cluster are the students, whose overall mark for the test
approximates 2, objects of the third cluster are the students, whose overall mark for
the test approximates 9 and objects of the fourth cluster are the students, whose over-
all mark for the test approximates 3.
Objects of each of the clusters are united by the fact that most of them made a mis-
take in tasks 9 and 10.
As a result of using all three clustering algorithms, we may make an overall con-
clusion that most mistakes were made in tasks 9 and 10 (this refers to both groups):
Fig. 7. Visual presentation of the test data after clustering following the Farthest First algorithm
Table 5. Cluster distribution of the objects, Farthest First algorithm.
Clusters Clustered Instances
0 52 (24%)
1 7 (3%)
2 138 (64%)
3 18 (8%)
Task 9: Find the coordinates of the image of point B (7;-6) under a translation by the
vector ⃗b(-10; -1). Possible answers: 1) (-3; -7); 2) (-3; 7); 3) (17; -5); 4) (17; 5).
Task 10: One rhombus was received from another one by means of rotation. The
diagonals of the first rhombus are 12 cm and 16 cm. Find the side of the second
rhombus. Possible answers: 1) 14 cm; 2) 5 cm; 3) 10 cm; 4) 20 cm.
Having analyzed the received results, we may conclude that the main reason for
these mistakes is the students’ incorrect application of the key notions of the topic
“Geometrical Transformations” to the geometrical problems of a more general type
(this most concerns Task 10).
4 Conclusion
1. On the basis of methodological reflection on the results of the research and analysis
of the works of the scientists, we may conclude that using digital technologies for
conducting flipped learning is advisable and that the efficiency of the teaching activi-
ty increases in conditions of integrated use of the stated learning techniques. Such
organization of the educational process is viewed as one of the forms of innovative
education as an effective way of implementing the personality-oriented and compe-
tence approaches. The advantages of the integrated use of digital technologies and
flipped learning include: actualization of the activity-based nature of learning, which
includes active participation of students in the process – researching, designing, mod-
elling, perceiving and reflecting on the results and experiences; orientation of the
study process towards the development of initiative, creativity, skills of self-control,
reflection and goal-setting as well as independence and responsibility of a pupil for
the results of his/her work; stimulating the increase of the students’ interest in learn-
ing; activating their study process; revealing their cognitive and personal potentials;
developing students’ digital competences, their independence, individuality etc. Stu-
dents’ motivation for mastering new study material increases considerably as learning
parts of the study materials takes place in the course of active creative search outside
the classroom, primarily, with the help of innovative tools, using a wide spectrum of
digital technologies. At the same time, an important intellectual capacity of teachers
and their task is to be able to use and develop their own digital learning tools. The
stated organizational-pedagogical conditions allow conducting flipped learning more
effectively, in a humanistic and personality-oriented way.
2. In the course of the research, we determined the organizational-pedagogical
conditions for implementing the flipped learning method using virtual learning envi-
ronments. Based on the analysis of the survey results conducted among school teach-
ers, master students, university professors, the following main organizational-
pedagogical conditions were defined: forming positive motivation among the students
towards studying the topic “Geometrical Transformations” using flipped learning; the
use of flipped learning in order to form the necessary competences in students; the use
of current digital educational tools and techniques (e.g. the educational websites).
3. The use of flipped learning based on virtual learning environments requires
thorough preparation. In order of prepare for such kind of educational process, an
educational website “Geometrical Transformations” was created; it is a technological
foundation for the introduction of flipped learning at lessons of Geometry while stud-
ying the topic “Geometrical Transformations” in the 9th form. The website contains a
topical plan, a short theoretical guide, lesson drafts and interesting materials that refer
to the topic “Geometrical Transformations” (problems, educational games and vide-
os).
4. The application of flipped learning based on virtual learning environments also
requires a detailed selection of the study content as well as its adaptation to concrete
groups of students. We assessed the effectiveness of flipped learning implementation
on the basis of the stated environment and determined the ways of improving the
components of the scientific-methodological system of flipped learning using ma-
chine learning techniques. The application of the Canopy, EM (Expectation Maximi-
zation) and Farthest First clustering algorithms on the basis of the Weka platform for
grouping the results of students’ educational achievements in the course of studying
the topic “Geometrical Transformations” allowed us to detect the main typical mis-
takes made by the students. In our case, the main reason for making these mistakes
was the students’ incorrect application of the key notions of the topic “Geometrical
transformations” to geometrical problems of a more general nature. The clustering
model presented in the research can also be used for selecting study tasks under the
“traditional” organization of the educational process.
5. The analysis of the results of the research using the bilateral Wilcoxon-Mann-
Whitney criterion proved the effectiveness of using the stated method at the lessons of
Geometry in the 9th form while studying the topic “Geometrical Transformations”. It
has been determined that the level of educational achievements of the students from
the experimental group is statistically higher than the level of educational achieve-
ments of the students from the control group. In addition, after studying the topic
“Geometrical Transformations” using flipped learning and virtual learning environ-
ments, the experimental group demonstrated positive dynamics of educational
achievements; and the control group also demonstrate positive changes, which are
relatively insignificant. The average point was 6.6, the average level of educational
achievements is “sufficient”; and 8.2 in the experimental group, average level of stu-
dents’ educational achievements is “medium”; there was an increase of the average
level of educational achievements from “sufficient” to “medium”.
The article determines the ways of increasing the effectiveness of flipped learning
implementation using virtual learning environments on the basis of machine learning
techniques: determining the individual learning trajectory, characteristic of a concrete
group of students on the basis of clustering their educational achievements with the
help of machine learning; selecting the study content and adapting it to concrete
groups of students; searching for more effective and systemic ways of achieving ped-
agogical goals (selecting and correcting the theoretical materials and tasks, selection
of digital tools for presenting the lecture material, development of tasks, motivating
students to individually work with the study materials, the methods of problem-based
learning, flipped learning etc.). Thus, flipped learning is effective if the teacher takes
his/her professional activity creatively and, accordingly, modifies and controls the
educational process. It is important to adapt the learning environment to the individual
needs of the students and to timely correct the imperfections.
The theoretically and practically significant generalizations, concepts, proposals
formulated in the research may be used for improving the quality of education and
broadening the possibilities of the educational landscape: in the scientific-research
field – for further scientific-practical developments in the stated field; in the course of
designing and using virtual learning environments in the educational process.
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